AN13 and CT13 Abstracts

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Annual Meeting (AN13) Abstracts...... 3

Control & Its Applications (CT13)...... 127

SIAM Presents Since 2008, SIAM has recorded many Invited Lectures, Prize Lectures, and selected Minisymposia from various conferences. These are available by visiting SIAM Presents (http://www.siam.org/meetings/presents.php). 2013 SIAM Annual Meeting • SIAM Conference on Control & Its Applications 3

AN13 Abstracts 4 AN13 Abstracts

IC1 system including cars, buses, pedestrians, ants and molecu- Social Networks as Information Filters lar motors, which are considered as ”self-driven particles”. We recently call this interdisciplinary research on jamming Social networks, especially online social networks, are of self-driven particles as ”jamology”. This is based on driven by information sharing. But just how much informa- mathematical physics, and and includes engineering appli- tion sharing is influenced by social networks? A large-scale cations as well. In the talk, starting from the backgroud experiment measured the effect of the social network on the of this research, simple mathematical models, such as the quantity and diversity of information being shared within asymmetric simple exclusion process and the Burgers equa- Facebook. While strong ties were found to be individu- tion, are introduced as basis of all kinds of traffic flow. ally more influential, collectively it is the weak ties that Then it is extended in order to account various traffic phe- wield more influence and provide more diverse information nomena, and the comparison between theory and experi- exposure. This sharing behavior not only generates large ment is given to show that the models are able to capture cascades, but can also cause information to evolve. Joint fundamental features of observations. speaker with the SIAM Workshop on Network Science. Katsuhiro Nishinari Lada Adamic School of Engineering, The University of Tokyo University of Michigan, Ann Arbor PRESTO, Japan Science and Technology Corporation School of Information, Center for the Study of Complex [email protected] Syste [email protected] IC5 Stochastic Multiscale Modeling IC2 Cost-Minimizing Regulations for a Wholesale Elec- We consider systems that are governed by stochastic tricity Market ordinary and partial differential equations (SODEs and SPDEs), and we will present some effective methods for ob- We consider a wholesale electricity market model with gen- taining stochastic solutions. These can be coarse-grained erators interacting strategically and general networks in- molecular systems exhibiting multi-rate dynamics and gov- cluding externalities such as transmission losses. Previous erned by a very large number of SODEs or continuum mul- work shows how mechanisms such as the case when prices tiscale systems governed by SPDEs. We will present meth- correspond to the Lagrange multipliers of a centralized cost ods derived from the Mori-Zwanzig framework combined minimization program allow the producers to charge signif- with PDF evolution equations as well as recent extensions icantly more than marginal price. This situation originates of generalized polynomial chaos in high dimensions. We a important regulatory problem. In this presentation we will also discuss various applications in biophysics and in consider an incomplete information setting where the cost mesoscopic materials. structure of a producer is unknown to both its competitor and the regulator. We derive an optimal regulation mech- George E. Karniadakis anism and compare its performance to the ”price equal to Brown University Lagrange multiplier”. Division of Applied Mathematics george [email protected] Alejandro Jofré Universidad de Chile, Santiago, Chile [email protected] IC6 The Mathematics of Conservation Decision Making

IC3 Species are currently becoming extinct at least 100 times Keeping Ford Green with Mathematics the background rate. The resources available to save biodiversity are inadequate. Consequently we need to optimise Scientific societies, universities, research institutes, and the return on investment from conservation decisions. In foundations all over the world have banded together to ded- this talk I will show how we have been using optimisation icate 2013 as a special year for the Mathematics of Planet tools to solve conservation problems such as reserve system Earth. In line with this theme, I will describe how Ford’s design and allocating funds to threatened species manage- strategic sustainability efforts, as outlined in the Blueprint ment. for Sustainability, are supported by mathematical models. I will present examples of these modeling efforts, such as Hugh P. Possingham constructing global energy models, defining CO2 targets Department of Mathematics and School of Life Sciences over time, helping fleet customers reduce CO2 emissions, The University of Queensland and developing a future product and technology portfolio [email protected] that reduces emissions. Ford is committed to employing sustainable business processes and developing sustainable products: it’s not easy being green, but mathematics sure IC7 helps! Nonlinear Waves and Patterns: Two Examples

Erica Klampfl Nonlinear waves and patterns are ubiquitous in nature. Ford Motor Company Surface waves on rivers, lakes and oceans, cloud patterns eklampfl@ford.com in the air, crystal structures in materials and animal skin patterns are just a few examples encountered in our everyday lives. The underlying mathematical problems lead IC4 to nonlinear systems involving ordinary differential equa- Traffic Jams of Self-driven Particles tions or partial differential equations. This talk focuses on the analysis of two kinds of nonlinear waves and patterns. Jamming phenomena are seen in various transportation Relying upon techniques from the areas of dynamical sys- AN13 Abstracts 5

tems and bifurcation theory, we shall discuss, on the one physical significance. hand the dynamics of nonlinear water waves, and on the other hand, the existence of defects, such as dislocations Walter Craig and grain boundaries, in pattern forming systems. Department of Mathematics and Statistics McMaster University Mariana Haragus [email protected] Laboratoire de Mathematiques de Besancon Universite de Franche-Comte, France [email protected] IP1 Likelihood-based Climate Model Evaluation IC8 Climate models can be evaluated by comparing their out- Orthogonal Polynomials and Cubature Rules put to observations. Remote sensing data provide new possibilities for such comparisons because they are spa- Gaussian quadrature rules are important tools for numer- tially and temporally dense enough to go beyond simple ical integration. Their nodes are necessarily zeros of or- moments and estimate distributions. We evaluate climate thogonal polynomials. Does this relation extend to cuba- model fidelity to observations by the likelihood that a sum- ture (synonym for quadrature in higher dimension) rules mary statistic computed from an observational time series and orthogonal polynomials in several variables? The ex- arises from a sampling distribution of that same statistic tension works in some extend, but the relation becomes far calculated from a given climate model’s time series. We more complicated in higher dimension. For starter, it is demonstrate using models from the CMIP5 archive and necessary to consider common zeros of a family of poly- observations from NASA’s Atmospheric Infrared Sounder nomials, or, variety of a polynomial idea, in the language mission. of algebraic geometry. This talk explains what is known about zeros of orthogonal polynomials and cubature rules, Amy Braverman mostly restricted to two variables, and it includes several Jet Propulsion Laboratory recent examples that provide efficient numerical integration California Institute of Technology rules. [email protected] Yuan Xu University of Oregon IP2 [email protected] Correlation and Causality

While everyone knows Berkeleys 1710 dictum correlation IC9 does not imply causation few realize that the converse cau- Photoacoustic Tomography: Ultrasonically Break- sation does not imply correlation is also true. This conun- ing through Optical Diffusion and Diffraction Lim- drum runs counter to deeply ingrained heuristic thinking its that is at the basis of modern science. Ecosystems are particularly perverse on this issue by exhibiting mirage correla- Photoacoustic tomography (PAT), combining optical and tions that can continually cause us to rethink relationships ultrasonic waves via the photoacoustic effect, provides we thought we understood. Identifying causal networks is in vivo multiscale non-ionizing functional and molecular important for effective policy and management recommen- imaging. PAT is the only modality capable of imaging dations on climate, epidemiology, financial regulation, and across the length scales of organelles, cells, tissues, and or- much else. Here we introduce a method based on Takens gans with consistent contrast. PAT has the potential to theorem that can distinguish causality from correlation in empower multiscale systems biology and accelerate trans- dynamical systems. It is a radically different empirical ap- lation from microscopic laboratory discoveries to macro- proach for leveraging time series information from complex scopic clinical practice. PAT may also hold the key to the systems of interacting parts. earliest detection of cancer by in vivo label-free quantification of hypermetabolism, the quintessential hallmark of George Sugihara cancer. The basic principle of PAT and the recent progress UCSD will be covered. Scripps Institution of Oceanography [email protected] Lihong Wang Washington University in St. Louis [email protected] IP3 AMS Invited Presentation: On the Geometry and Complexity of Solving Systems of Polynomial IC10 Equations Dynamics of Near Parallel Vortex Filaments Theoretical computer science has a well developed notion of Techniques have been developed for the phase space anal- complexity. Numerical analysis doesn’t have a comparably ysis of the dynamics of many model nonlinear Hamiltonian developed theory. In this context Steve Smale included in PDEs. In this talk I will describe some extensions of these his list of problems for the next century: Problem 17: Solv- ideas to a problem in fluid dynamics concerning the inter- ing Polynomial Equations. Can a zero of n-complex poly- action of two near-parallel vortex filaments in three dimen- nomial equations in n-unknowns be found approximately, sions. In addition, as well as generalizations of this prob- on the average, in polynomial time with a uniform algo- lem, I will describe a number of promising further applica- rithm? I will describe progress on this problem including tions of the techniques of Hamiltonian PDEs and nonlinear the eigenvalue problem (the answer looks like yes), and the evolution problems to other systems in fluid dynamics of mathematics employed.

Michael Shub 6 AN13 Abstracts

IMAS, CONICET, Argentina and Graduate School of SP2 CUNY The John von Neumann Lecture: What Sparsity [email protected] and l1 Optimization Can Do For You Sparsity and compressive sensing have had a tremendous IP4 impact in science, technology, medicine, imaging, machine Short-Term Renewable Energy Forecasting: Cur- learning and now, in solving multiscale problems in applied rent Status, Challenges and Opportunities partial diﬀerential equations. l1 and related optimization solvers are a key tool in this area. The special nature of The cost of integrating power from variable renewable en- this functional allows for very fast solvers: l1 actually for- ergy sources such as wind and solar into electric systems is gives and forgets errors in Bregman iterative methods. I strongly linked to the accuracy of short-term (0-48 hours) will describe simple, fast algorithms and new applications predictions. Although forecasts from current approaches ranging from sparse dynamics for PDE, new regularization are providing considerable value, they often fail to antic- paths for logistic regression and support vector machine to ipate critical events in which the energy resource experi- optimal data collection and hyperspectral image process- ences large and rapid changes. The presentation will pro- ing. vide an overview of the current status of renewable energy forecasting tools and performance, the key challenges that Stanley J. Osher must be addressed to increase the value of forecasts and the University of California near-term opportunities associated with new atmospheric Department of Mathematics sensor and modeling technology. [email protected]

John Zack MESO, Inc. SP3 [email protected] Past President’s Address: Chebfun

Chebfun is a Matlab-based open-source software project IP5 for “numerical computing with functions” based on algo- The Search for a Human Fingerprint in the Chang- rithms related to Chebyshev polynomials. In recent years ing Thermal Structure of the Atmosphere developing Chebfun has been my main research activity, together with the closely linked project of writing the book Satellite temperature measurements reveal multi-decadal Approximation Theory and Approximation Practice (SIAM tropospheric warming and stratospheric cooling, punctu- 2013). This talk will present some highlights of the Cheb- ated by short-term volcanic signals of reverse sign. Sim- fun endeavor and will be followed by a two-part Chebfun ilar long- and short-term temperature signals occur in minisymposium. model simulations driven by human-caused changes in atmospheric composition and natural variations in volcanic Nick Trefethen aerosols. Previous research attempted to discriminate Oxford University a human-caused latitude/altitude pattern of atmospheric [email protected] temperature change (”fingerprint”) from the background noise of internal variability. We present the first evidence that a human fingerprint can also be identified relative to SP4 the larger ”total” noise arising from internal variability, W. T. and Idalia Reid Prize in Mathematics Lec- solar irradiance changes, and volcanic forcing. ture: Solvability for Stochastic Control Problems

Benjamin Santer Some stochastic control problems for continuous time sys- Lawrence Livermore National Laboratory tems are described where optimal controls and optimal [email protected] costs can be explicitly determined by a direct method. The applicability of this method is demonstrated by examples including the linear quadratic control problem with the sys- SP1 tem driven by an arbitrary noise process with continuous AWM-SIAM Sonia Kovalevsky Lecture: Introduc- sample paths, a controlled Brownian motion in a symmet- tion to Radar Imaging ric space and the linear exponential quadratic Gaussian control problem. The problems for linear systems can be Radar imaging is a technology that has been developed, modified to allow for equations in an infinite dimensional very successfully, within the engineering community dur- Hilbert space that describe stochastic partial differential ing the last 50 years. Radar systems on satellites now make equations. beautiful images of regions of our earth and of other plan- ets such as Venus. One of the key components of this im- Tyrone E. Duncan pressive technology is mathematics, and many of the open University of Kansas problems are mathematical ones. This lecture will explain, Department of Mathematics from first principles, some of the basics of radar and the [email protected] mathematics involved in producing high-resolution radar images. SP5 Margaret Cheney I. E. Block Community Lecture: From Razor Colorado State University Clams to Robots: The Mathematics Behind Bio- and Naval Postgraduate School logically Inspired Design [email protected] Many natural systems have evolved to perform certain tasks – climbing, sensing, swimming – as perfectly as possible within the limits set by the laws of physics. This AN13 Abstracts 7

observation can be used both to guide engineering design, other is based directly on the Nyquist hodograph. and to gain insights into the form and function of biological systems. In this talk we will consider both of these themes Dmitry A. Altshuller in the context of crawling snails, digging clams and swim- Crane Aerospace and Electronics ming microorganisms. We will discover how an analysis of [email protected] the physical principles exploited by snails and clams leads to the development of novel robotic diggers and crawlers, and explore the role of mathematics in the design, control, CP1 and assessment of unconventional robotic systems. Global Dynamics of SEIR Model with Holling Type II Incidence Function Anette Hosoi Massachusetts Institute of Technology The paper presents a model for the transmission dynam- 77 Massachusetts Avenue, Room 3-173, Cambridge MA ics of an arbitrary disease. The model, consisting of four 02139 mutually-exclusive compartments representing the human [email protected] dynamics, has a globally-asymptotically stable disease- free equilibrium (DFE) whenever a certain epidemiological threshold, known as the basic reproduction number (R) SP6 is less than unity, in such a case the endemic equilibrium James H. Wilkinson Prize Lecture: Interpolative does not exist. On the other hand, when the reproduction Decomposition and Novel Operator Factorizations number is greater than unity, it is shown, using Nonlin- ear Lyapunov function theory and LaSalle Invariance Prin- I will discuss some recent results on developing new factor- ciple, that the unique endemic equilibrium of the model izations for matrices obtained from discretizing differential is globally-asymptotically stable under certain conditions. and integral operators. A common ingredient of these new Furthermore, the disease is shown to be persistent when- factorizations is the interpolative decomposition for numer- ever R > ∞. ically low-rank matrices. As we shall see, these factorizations offer efficient algorithms for applying and inverting Salisu M. Garba these operators. This is a joint work with Kenneth Ho. Department of Mathematics University of Pretoria Lexing Ying [email protected] University of Texas Department of Mathematics [email protected] CP1 A Robust Numerical Method for Solving Hiv- Malaria Co-Infection Model with a Distributed De- JP1 lay Applied and Computational Mathematics for En- ergy Efficient Systems We construct a nonstandard finite difference method for the numerical solution of an HIV-malaria co-infection Recent advances in the development of sustainable energy model with a distributed delay. Firstly, we analyze the sources have led to an emphasis on energy-supply technolo- continuous sub-models. Based on the qualitative proper- gies and the corresponding mathematical sciences needed ties of these models, we construct an efficient numerical for these technologies. However, energy efficient end-use technique. These qualitative properties are further used in technologies may also be viewed as an energy resource. measuring the competitiveness of our numerical method. Since buildings are responsible for 32% of energy consump- Proposed method preserves some essential properties of the tion and for 26% of end-use C02 emissions, optimizing the solution which are biologically relevant for the model. efficiency of a whole building system is a ”grand challenge control” problem with huge payoffs in the global energy sec- Kailash C. Patidar tor. We discuss mathematical challenges and opportunities University of the Western Cape that occur in designing practical controllers for energy ef- [email protected] ficient buildings. Examples are presented to illustrate the ideas. CP1 John A. Burns A New Class of Split Exponential Propagation It- Virginia Tech erative Methods of Runge-Kutta Type (sEPIRK) Interdisciplinary Center for Applied Mathematics for Semilinear Systems of ODEs [email protected] We propose a new class of exponential propagation iterative methods of Runge-Kutta (EPIRK) type specifically CP1 targeted for problems y(t)=Ly(t)+N(y(t)) where the lin- On the Robust Stability of the Hill Equation with ear operator L is responsible for the stiffness of the system a Delay Term: A Frequency-Domain Approach and N(y(t)) is the nonlinear remainder. Upon constructing specific schemes with desirable qualities, we then turn The paper considers the problem of robust stability of the to numerical experiments. Through various test problems Hill equation with a damping and a time-delay term. An- we will present comparative performance between these alytical results are presented in terms of the coefficients of new EPIRK type methods and previously proposed EPIRK the equation. The derivation is based on the frequency- methods designed for the fully nonlinear right-hand-side domain approach, specifically, the geometric interpreta- function, y(t)=f(y(t)). tion of the Yakubovich stability criterion for linear time- periodic. There are two approaches to this interpretation: Greg Rainwater One involves analysis of the so-called Lipatov plots and the University of California, Merced [email protected] 8 AN13 Abstracts

Mayya Tokman on feature extraction and linear classification has been de- University of California, Merced veloped and implemented in two stages. In stage one the School of Natural Sciences classifier is trained and validated by different sets of pat- [email protected] terns from reference materials. In stage two the trained classifier is applied to patterns from bacterial spores and environmental sampling: pattern recognition occurs by in- CP1 formation fusion. A large data set (> 5, 000 patterns) has Exponential Splitting for Cocycles over Multival- been analysed. Bacillus subtilis patterns are discriminated ued Non-Autonomous Dynamical Systems in Ba- from those of other materials. Progress will be reported nach Spaces in the classification of patterns from outdoor sampling and from confounder materials. As the state space of many dynamical systems that describe processes from engineering and physics is of infinite Giovanni F. Crosta, Caterina Casati dimension, the approach is appropriate by means of as- Department of Earth- & Environmental Sciences sociated operator families. Therefore, we introduce sev- University of Milan Bicocca eral notions of exponential splitting induced on Banach Giovanni [email protected], [email protected] spaces by skew-evolution cocycles over multivalued non– autonomous dynamical systems, as well as various concepts Yong-Le Pan, Gorden Videen of dichotomy. Characterizations for these notions and con- U.S. Army Research Laboratory nections between them, underlined by examples and coun- ADELPHI, MD terexamples, are also provided. [email protected], [email protected] Codruta S. Stoica Department of Mathematics and Computer Science Kevin Aptowicz Aurel Vlaicu University of Arad, Romania West Chester University [email protected] WEST CHESTER, PA [email protected]

CP1 Richard Chang Numerical Simulation of A Singularly Perturbed Yale University Harmonic Oscillator NEW HAVEN, CT [email protected] A mass-spring system with a small mass forms a singularly perturbed damped harmonic oscillator. In a short time period, the spring oscillates rapidly and displays a boundary CP2 layer because of the small mass. Then the oscillation be- Determining Number of Motifs in Wind Genera- comes smooth and it can be approximated in the absence of tion Time Series Data the small mass. An adaptive piece-wise uniform numerical simulation scheme is proposed. The accuracy is achieved It is a challenge to schedule wind energy on the power grid at a high level with a constant mesh points for a family of especially when forecasts are inaccurate. Using techniques singularly perturbed harmonic oscillators. from time series analysis, we show how motifs, or frequently occurring diurnal patterns, in wind generation data can be Weiqun Zhang used to guide scheduling decisions. We discuss how quality Wright State University analysis can be applied to determine the number of motifs [email protected] that exist in data from wind farms in Tehachapi Pass and mid-Columbia Basin. CP2 Ya Ju Fan, Chandrika Kamath Randomized Dimensionality Reduction in Machine Lawrence Livermore National Laboratory Learning [email protected], [email protected] We show how certain random sampling and random projections methods can be used to design efficient dimensional- CP2 ity reduction techniques for three popular machine learning Convergence and Stability of the Split-Step θ- problems: (i) K-means Clustering, (ii) Canonical Correla- Milstein Method for Stochastic Delay Differential tion Analysis, (iii) Support Vector Machine Classification. Equations In all cases, we argue that randomized dimensionality reduction is provably efficient. A new splitting method designed for the numerical solutions of a kind of stochastic delay differential equations Christos Boutsidis is introduced and analysed. Under Lipschitz and lin- Computer Science Department ear growth conditions, this split-step θ-Milstein method is Rennselaer Polytechnic Institute proved to have a strong convergence of order 1 in mean- [email protected] square sense, which is higher than that of existing split- step θ-method. Further, mean-square stability of the proposed method is investigated. Numerical experiments and CP2 comparisons with existing methods illustrate the computa- Classification and Recognition of Light Scattering tional efficiency of our method. Patterns from Airborne Particles Qian Guo,WenwenXie TAOS is an experimental technique which collects the in- Shanghai Normal University tensity pattern of LASER light scattered by a single, air- [email protected], [email protected] borne material particle, ≈ 1μm in size. An algorithm based AN13 Abstracts 9

Taketomo Mitsui [email protected] Doshisha University [email protected] Christophe Besse Laboratoire Paul Painlevé CNRS et Universite des Sciences et Technologies de Lille CP2 christophe besse ¡[email protected] An Integrated ANN Approach to Identify the Types of Disturbances for An SPC/EPC System Anais Crestetto Autocorrelation often results in an increased rate of false Institut de Mathématiques de Toulouse alarms for typical statistical process control (SPC) charts. CNRS et Université Paul Sabatier To overcome this difficulty, the engineering process control [email protected] (EPC) is employed to compensate for the effects of autocorrelation. However, because of the over-control problem of Pierre Degond EPC, it becomes much more difficult to identify the types CNRS & Institut de Mathematiques de Toulouse, France of underlying process disturbances. We propose an artifi- [email protected] cial neural network (ANN) approach to effectively identify the types of disturbances for a SPC/EPC system. Alexei Lozinski Laboratoire de Mathématiques de Besanon Yuehjen E. Shao CNRS et UniversitédeFranche-Comté Fu Jen Catholic University [email protected] [email protected] Jacek Narski, Claudia Negulescu CP2 Institut de Mathématiques de Toulouse 1 CNRS et Université Paul Sabatier A Deeper Look at the -Graph [email protected], We aim to improve current methods of graph construction [email protected] for use in dimensionality reduction, clustering, and label propagation. In particular, we study Cheng, et al.’s “1- Chang Yang graph.’ This method simultaneously computes the graph University Claude Bernard, Lyon structure and edge weights by decomposing each data point [email protected] as a linear combination of the remaining samples so that the 1-norm of the coefficients is minimized. We seek further theoretical justification for the 1-graph’s experimen- CP3 tal success, as well as improvements to this method through Phase Change at the Nanoscale the framework of block sparsity. Additionally, we aim to utilize the structure of the dual polytope associated with Nanoparticles have generated tremendous interest in the the overcomplete data dictionary to reduce the construc- scientific community in the last few decades: they exhibit tion complexity via “warm-starting’ several of the numer- unique optical, electrical, and magnetic properties not seen ous 1-minimization problems that must be solved. Time at the bulk scale. These properties and their size make permitting, we will also discuss the structure of the pro- them attractive for industrial and biomedical applications. duced graph. One form of application, based on the melting process of nanoparticles, is used in drug delivery or microelectronics. Chelsea Weaver In this talk, we present a mathematical model describing University of California, Davis the melting of nanoparticles that takes into account the [email protected] Gibbs-Thomson effect and the thermal expansion of the nanoparticles, which turn out to be no-negligible at that Naoki Saito scale. The melting times obtained from our results are in Department of Mathematics good agreement with experimental observations. University of California, Davis Francesc Font Martinez,TimothyMyers [email protected] Centre de Recerca Matemàtica ff[email protected], [email protected] CP3 Efficient Asymptotic Preserving Schemes for Higly CP3 Anisotropic Ellitpic Problems, Application to the Virtual Nuclear Reactor Modeling Using Lime Simulation of the Ionospheric Plasma Disturbances The Lightweight Integrating Multiphysics Environment li- An Asymptotic-Preserving scheme is introduced for the brary (LIME) is built as an extension to the Trilinos approximation of singularly perturbed anisotropic elliptic solver framework to enable generalized multiphysics code equations. This numerical method is designed to offer an coupling. LIME’s coupling algorithms span fixed-point efficiency, with respect to both the precision and the nu- coupling, placing no restrictions on models or methods, merical cost, independent of the anisotropy strength. A through Newton-based coupling, requiring residuals from class of anisotropic elliptic problems occurring in the sim- participating codes. This talk will present enhancements to ulation of magnetized plasma and more specifically iono- fixed-point based coupling applied to nuclear reactor per- spheric plasma disturbances, is addressed to illustrate the formance modeling. These enhancements represent various capabilities of the AP-scheme. types of acceleration or mixing methods applied within a Fabrice Deluzet hierarchical multiphysics problem. Institut de Mathematiques Russell W. Hooper 10 AN13 Abstracts

Sandia National Laboratories CP4 [email protected] N Masses on a String One-dimensional time-harmonic waves interact with N CP3 identical scatterers. We solve this classical problem using Upscaling of Microscale Reactive Transport to the transfer matrices. For a row of N equally spaced scat- Darcy Scale terers, the reflection and transmission coefficients can be calculated explicitly, using Chebyshev polynomials. Here, We have developed a subsurface simulation capability to the emphasis is placed on problems where the scatterers resolve pore scale processes at the microscopic scale (¡ 10 are perturbed from their equispaced positions. Explicit re- microns) on a continuum scale domain (1 meter). The sults are obtained. They are useful in understanding the pore scale data can be upscaled to the continuum scale to construction of effective media for one-dimensional random obtain heterogeneous values of permeability and reaction media. rates. For example, we use a combination of flux weighted averaging for the velocity and the divergence theorem for Paul A. Martin gradient of pressure to obtain a permeability value from Department of Applied Mathematics and Statistics a local pore scale patch that is equivalent to a represen- Colorado School of Mines tative elemental volume for the Darcy equations. We also [email protected] discuss an adaptive modeling technique for fully coupling the microscopic and macroscopic equations with an AMR framework where the continuum model is refined to a pore CP4 scale model only in local areas of interest in the domain. On a Representation of Functions of Several Vari- ables As Superposition of Functions of One Vari- David Trebotich, Sergi Molins able and Addition by Using An Algebraic Identity Lawrence Berkeley National Laboratory [email protected], [email protected] A theorem is given for representing functions of many variables as superposition of differentiable functions of one variable and addition through the use of an algebraic iden- CP4 tity that rewrites a product of n variables as additions of Radial Basis Function (RBF) Approximation Is In- nth power functions. The relations between this theorem distinguishable From Hermite Function Interpola- and Kolmogorov’s superposition theorem are discussed. tion on a Finite Interval: RBFs Without Matrix Besides, an application of this theorem to piecewise lin- Inversion ear function approximation for a non linear function having more than two variables-multiplication terms, is intro- On a uniform grid, very accurate approximations to Gaus- duced. sian RBF cardinal functions can be constructed by multi- plying polynomial cardinal functions by a Gaussian. Using Hideaki Okazaki the Gaussian-times-polynomial basis gives approximations Dept. of Applied Computer Sciences to a smooth function f(x) which are as accurate as those Shonan Institute of Technology of radial basis functions. The new basis is equivalent to [email protected] approximation on a finite interval by Hermite functions. Matrix inversion and the contour Pade and RBF-QR algo- Hideo Nakano rithms are unnecessary. Shonan Institute of Technology [email protected] John P. Boyd University of Michigan Ann Arbor, MI 48109-2143 USA CP5 [email protected] Solving Composite Minimization and Its Applica- tion to Image Deblurring

CP4 We study the following composite minimization problem Perturbation of *-Derivations on Fuzzy Banach *- \ Algebras min{f(A§), §∈R }, (1) Let A be a Banach ∗-algebra. A linear mapping δ : A → A where A is a matrix and the function f is proper, lower is said to be a ∗-derivation on A if δ(ab)=δ(a)b+aδ(b)for semi-continuous, convex but not necessarily differentiable. all a, b ∈ A and δ(a∗)=δ(a)∗ for all a ∈ A. Every bounded This problem covers a large range of problems in image ∗-derivation δ on a C∗-algebra arises as an infinitesimal processing, i.e., denoising, deblurring, inpainting. An it- generator of a dynamical system for R.Forseveralrea- erative algorithm is proposed to solve the composite mini- sons the theory of bounded derivations of C∗-algebras is mization problem. Further if the function is separable, an important in the quantumn mechanics. We establish the accelerated variant algorithm is proposed. Each step in functional equations of ∗-derivation induced by the Cauchy the iterate has closed form and therefore can be efficiently equation and the Jensen equation, respectively. And we implemented . Also, convergence of the algorithms can also prove the stability of derivations on fuzzy Banach ∗- be guaranteed understand certain conditions. Finally, we algebras and also prove the superstability of derivations. apply the proposed algorithms to solve the L2-TV and L1- TV deblurring problems. Numerical results show that the proposed iterative procedures can outperform some state- Sun Jang of-art algorithm in terms of CPU time and PSNR. Department of Mathematics, University of Ulsan [email protected] Feishe Chen Syracuse University [email protected] AN13 Abstracts 11

CP5 nificant attention in the medical imaging area for their im- From Proteins to Cells; Progress in Large Field proved image quality while reducing the radiation dose in Electron Microscope Tomography CT X-ray imaging, at the cost of significantly increased computational complexity. We propose to use the SLIM In combination with other techniques electron tomography algorithm, for the medical image reconstruction. SLIM is can provide three dimensional reconstructions of protein a sparse signal recovery algorithm that has excellent inter- assemblies, correlate 3D structures with functional inves- ference/noise suppression and high resolution properties. tigations at the light microscope level and provide struc- The most attracting property of SLIM is that it can be im- tural information which extends the findings of genomics plemented very efficiently by using the conjugate gradient and molecular biology. Because of rapid advances in instru- (CG) and the fast Fourier transform (FFT). The computa- mentation and computer-based reconstruction, the routine tional complexity will be evaluated by comparing with the imaging of molecular structure in context appears to be benchmarks of the available IR algorithms. likely within the next few years. We will discuss the inversion of the generalized Radon transform which appears in Ming Xue the context of EM tomography. University of Maryland Medical Center [email protected] Albert F. Lawrence, Xiaohua Wan, Sebastien Phan, Mark Ellisman University of California, San Diego CP5 lawrence @sdsc.edu, [email protected], Synchrosqueezed Wave Packet Transform for 2D [email protected], [email protected] Mode Decomposition

This paper introduces the synchrosqueezed wave packet CP5 transform as a method for analyzing 2D images. This Repulsive Random Walk in Automatic Number transform is a combination of wave packet transforms of Plate Recognition a certain geometric scaling, a reallocation technique for sharpening phase space representation, and clustering al- The Repulsive Random Walk is an exploration algoritm gorithms for mode decomposition. For a function that based on particle swarm models and random walks. The is a superposition of several wave-like components satis- interaction between the particles and the space formed by fying certain separation conditions, we prove that the syn- an image are used to detect license plates as part ANPR chrosqueezed wave packet transform identifies these com- system, through which a sample may be obtained proper- ponents and estimates their instantaneous wavevectors. A ties of the image elements. The results indicate that it is discrete version of this transform is discussed in detail and a viable method for scanning images. numerical results are given to demonstrate properties of the proposed transform. Yosefat Nava Alemán Universidad Autónoma de Nuevo León Haizhao Yang Facultad de Ciencias Fsico-Matemáticas Stanford University yosefat [email protected] [email protected]

Lexing Ying CP5 University of Texas Estimating the Optimal Truncated SVD Filter for Department of Mathematics Image Restoration [email protected] Image restoration is a challenging inverse problem for which solutions involving filters have been proposed. In CP6 this work we use statistical analysis and observed proper- Ritz-Galerkin Isogeometrics and Transformation ties of the noise to estimate the optimal parameter for the Optics to Describe Metasolenoid Electromagnetic truncated SVD filter. The resulting restorations for several Singularities test images compare favorably to those using parameters estimated through generalized cross-validation (GCV) and This is a continuation of the invisibility-cloaking research the discrepancy principle and are not much different from presented at the Society for Industrial and Applied Math- restorations using the true (generally unknown) optimal ematics (SIAM) Conference on Partial Differential Equa- parameter. tions November 14, 2011. Principles of finite element analysis, isogeometrics and transformation optics will be used Viktoria Taroudaki to develop a model of a perfectly lensing metasolenoid. The Applied Mathematics and Scientific Computing Program conjecture is that fields at microwave frequencies are dis- University of Maryland torted and electromagnetic black hole singularities will be [email protected] formed at the boundaries (Ikonen et. al 2005). The Ritz- Galerkin Method and iosgeoemtric analysis will be used Dianne P. O’Leary to evaluate PDEs for the Helmholtz electromagnetic equa- University of Maryland, College Park tions, as well as General Relativity applied to optics and Department of Computer Science electromagnetism. Implications include no loss wireless an- [email protected] tenna metasolenoids, cloaking and electromagnetic black hole research, and possible applications in string theory to describe quantum effects in EM black holes. CP5 Medical Imaging Via Slim Scott M. Little SunWize Technologies Iterative reconstruction (IR) algorithms have attracted sig- Northcentral University 12 AN13 Abstracts

[email protected] [email protected]

Dan Cervo, Doug Bebb Valia Guerra-Ones MAD Fellows LLC Delft University of Technology [email protected], [email protected] Institute of Applied Mathematics [email protected]

CP6 Electromagnetic XFEM with Weak Discontinuities CP7 New Results on the Kogbetliantz Method In electromagnetic multimaterial problems, surface effects are critical, as current tends to concentrate on material The Kogbetliantz method is an important tool for comput- surfaces, Lagrangian meshes are often untenable due to ing the singular value decomposition (SVD) of triangular large deformations, leaving Eulerian meshes with a mixture matrices. It preserves almost diagonality and triangular- model as the only option. We present an alternative edge ity of the starting matrix and is nicely suited for subspace element extended finite element method based on a tied tracking problem. It can serve as the core algorithm of Heaviside approach. We prove its equivalence to a body-fit block Jacobi methods for the SVD problem of dense ma- finite element problem and demonstrate that it retains the trices using CPU and GPU computations. All known prop- expected order of convergence. erties and the new relative accuracy results of the method will be presented. Christopher Siefert Sandia National Laboratories Vjeran Hari,JosipMatejaˇs [email protected] University of Zagreb [email protected], [email protected] Thomas Voth Sandia National Laboratory [email protected] CP7 A Paradigm of Complex Symmetric Matrices in Pavel Bochev Matrix Analysis Sandia National Laboratories A huge expansion of matrix analysis is achieved for non- Computational Math and Algorithms defective nonsingular complex symmetric matrices as a [email protected] new paradigm especially for physically realizable systems. Those matrices describe systems with periodic excitations CP6 not included in prior matrix analysis. They are also complex definite and diagonalizable by either complex orthog- Optimum Experimental Design for Egdm Modeled onal similarity or unitary consimilarity. Another paradigm Organic Semiconductor Devices includes well-known Hermitian matrices existing in physi- We apply optimum experimental design (OED) to organic cal systems with random excitations. Symmetry is a criti- semiconductors modeled by the extended Gaussian disor- cal factor to understand interwoven theories including con- der model (EGDM), see [Pasveer et al., 2005]. We present similarity. an algorithm based on Gummel’s method coupled with Gordon E. Martin Newton’s method. Automatic differentiation is used to get retired derivatives with the required accuracy for OED. We show [email protected] that the linearized confidence regions of the mobility parameters can be reduced significantly by OED, resulting in new experiments with a different setup. CP8 Christoph Weiler Partial Differential Equations Practicum IWR Heidelberg In this Partial Differential Equations (PDEs) practicum, [email protected] we show practical and quick tools for solving linear and nonlinear PDEs. More specifically, we help you CP7 find analytic solutions to linear PDEs; first order linear and nonlinear PDEs; and higher order nonlinear Randomized Matrix Algorithms for Spectral Clus- PDEs. Navier-Stokes, Black-Scholes, Vlasov-Maxwell, tering Schrodinger, Poisson, Wave are just some of the PDEs Spectral clustering is a class of methods to solve problems you can solve. Steve Anglin, Sc.M., Ph.D. (h.c.) of in the fields of machine learning, pattern recognition and http://facebook.com/Diffequations is a mathematical en- image and mesh processing. They are related or based on gineer and former Case lecturer. eigenvalues, eigenvectors or eigenspace projections derived Steve Anglin from very large and dense affinity matrices. Eigenproblems DiffEquations.com associated with the Normalized k-Cut will here exemplify Case Western Reserve University that randomized matrix techniques are particularly suit- [email protected] able for such computations. Additionally we show how useful information can be extracted directly from the affinity matrix. CP8 Angelika Bunse-Gerstner Image-Driven Inverse Problem for Estimating Ini- Universitaet Bremen tial Distribution of Brain Tumor Modeled by Zentrum fuer Technomathematik, Fachbereich 3 AN13 Abstracts 13

Advection-Diﬀusion-Reaction Equation [email protected]

We present results for solving an image-driven inverse problem of brain tumor growth. Our objective is to reconstruct CP9 initial distribution of the tumor in the patient’s brain. Tu- Nonlinear Gerschgorin Regions and Applications mor growth is modeled as an advection-diffusion-reaction equation which is coupled to an elasticity equation model- We consider an extension of Gerschgorin’s theorem to non- ing parenchyma deformation. Our inversion algorithm is an linear eigenvalue problems T (z)v =0,whereT (z)= adjoint-based Newton scheme that requires efficient evalu- A − zI + E(z) is a matrix-valued function that is analytic ation and inversion of Hessian operator. We will present over some simply connected domain in the complex plane. problem formulation, our novel numerical scheme, and re- As with the conventional Gerschgorin circle theorem for sults on a clinical dataset. the linear eigenvalue problem, this nonlinear Gerschgorin theorem is a useful tool for deriving other eigenvalue local- Amir Gholaminejad ization problems, such as a nonlinear variant of the Bauer- PhD Student, Institute for Computational Engineering Fike theorem. and Sciences, University of Texas at Austin [email protected] David Bindel Cornell University George Biros [email protected] University of Texas at Austin [email protected] CP9 A Non-Gap-Revealing Method for Determining CP8 Numerical Rank Wave of Chaos and Pattern Formation in Spatially Extended Three Species Model Systems The rank revealing problem arises widely in scientific computing and engineering applications, such as signal process- The complex dynamics of two types of tri-trophic food ing, information retrieval, numerical polynomial algebra, chain model systems, modeling two real situations of ma- and so on. Some of those applications give rise to a large rine ecosystem, are investigated in this study. The study matrix whose rank or nullity is known to be small apriori. has been carried out with the objective to explore and com- Several methods have been proposed for this purpose. In pare the competitive effects of fish and molluscs species be- general, they compute a gap-revealing factorization for es- ing the top predator, when phytoplankton and zooplankton timating the singular values. In this talk, we will present species are undergoing spatial movements in the subsurface a rank-revealing method to deal with large matrices with water. Wave of Chaos mechanism is found to be the re- low ranks/low nullities by constructing an orthonormal ba- sponsible factor for the pattern formation in one dimension sis for the subspace of the matrix directly. seen in the food chain ending with top generalist predator. In the present work, WOC phenomenon is reported for the Tsung-Lin Lee first time in literature, in a three species spatially extended National Sun Yat-set University food chain model system. An ecosystem having top preda- [email protected] tor as specialist leads to the stability of the system. Nitu Kumari CP9 Indian Institute of Technology Mandi, Himachal Pradesh Similarity Reduction to Upper Hessenberg Form India, 175001 [email protected], [email protected] Input your abstract, including TeX commands, here. Al- ternatives previously devised for stable similarity reduction of real nonsymmetric matrices to low bandwidth Hessen- CP8 berg form rely on bounded gaussian transformations ap- Mathematical Modeling and Simulation of Biofilm plied to successive matrix rows and columns. Interaction Dispersal of large multipliers limit magnitudes allowed for stabli- tiy. The new QG algorithm relies primarily on orthogonal Biofilm is the community of microorganism which are en- (Householder) transformations with at most one nonzero cased in an extracellular polymeric matrix. The bacte- element in each row eliminated with a bounded gaussian rial cells engage in a cell-cell communication called quorum transformation. This doubles the flops but leads to less sensing with which they coordinate their behaviour. Bac- interaction, thus allowing larger multipliers which yield terial cells can disperse from the biofilm into the aqueous smaller bandwidths. phase. We study the mathematical model of biofilm dispersal with the underlaying mechanisms of quorum sensing Eugene L. Wachspress leading to a system of partial differential equation. We in- Columbia University vestigate the magnitude and timing of the cell dispersal. [email protected]

Blessing Uzor CP9 Department of Mathematics and Statistics A Linear Complexity Structured Selected Inversion University of Guelph for Large Sparse Matrices [email protected] We propose a structured method for extracting the diagonal of a sparse matrix, using the multifrontal method and Hermann J. Eberl rank structured matrices. The method has nearly O(n) Dept. Mathematics and Statistics complexity for some 2D and 3D problems, after the struc- University of Guelph 4 3 tured factorization of about O(n)andO(n / )ﬂops,re- 14 AN13 Abstracts

spectively, where n is the size of the matrix. The memory ting is used for space discretisation, employing the FEM requirement is also about O(n). In comparison, existing for parabolic PDE components and FVM for hyperbolic inversion methods cost O(n1.5)in2DandO(n2)in3D, ones. with O(n log n)andO(n4/3) memory, respectively. Also, our method can quickly extract an arbitrary entry of the Julian E. Mindel, Roman Manasipov, Stephan Matthaei inverse in about O(1) to O(log2n) flops, due to the data Montan University of Leoben, Austria sparsity. [email protected], [email protected], Yuanzhe Xi [email protected] Purdue University [email protected] CP10 Jianlin Xia Fourth-Order Mimetic Finite Difference Modeling Department of Mathematics of Free Surfaces on Elastic Media Purdue University In this work, we apply fourth-order mimetic finite differ- [email protected] ences to computationally simulate the wave pattern excited by a point source located along a flat free surface of a lin- Stephen Cauley early elastic and isotropic half plane. The physical free Athinoula A. Martinos Center for Biomedical Imaging surface boundary condition represents homogeneous linear Department of Radiology, Massachusetts General Hospital equations satisfied by the traction vector components. This [email protected] coupled system of differential equations, elastodynamics in the interior and Newmann-type boundary conditions, is Venkataramanan Balakrishnan discretized on a staggered grid using mimetic finite differ- School of Electrical and Computer engineering ences that provide both, central and lateral stencils, avoid- Purdue University ing the location of grid points beyond the physical bound- [email protected] aries, and making our numerical implementations memory- saving. Xiao Liu Department of Mathematics Otilio Rojas Purdue University Universidad Central De Venezueal [email protected] [email protected]

CP10 CP10 Optimal Error Analysis of Linearized Backward Gradient-Augmented Schemes for Reinitialization Euler Galerkin Fems for Time-Dependent Nonlin- and Other Hamilton-Jacobi Equations ear Joule Heating Equations We demonstrate how the semi-Lagrangian “jet scheme’ We study two linearized backward Euler schemes with framework can be applied to solve certain Hamilton-Jacobi Galerkin finite element approximations for the time- equations, such as the reinitialization equation that is pop- dependent nonlinear Joule heating equations. By introduc- ular in the context of level set methods. The resulting ing a time-discrete system as proposed in [LI & Sun, Error numerical approaches are high order accurate, with an op- analysis of linearized semi-implicit Galerkin finite element timally local update rule. Information is propagated cor- methods for nonlinear parabolic equations, Int. J. Numer. rectly along characteristics, even in the presence of shocks. Anal. & Modeling, 10 (2013), 622-633.], we present uncon- Benjamin Seibold ditionally optimal error estimates of r-th order Galerkin ≤ ≤ Temple University FEMs (1 r 3). [email protected] Huadong Gao Department of Mathematics, CityU of HK CP10 Kowloon, Hong Kong [email protected] Chebyshev Collocation Methods for Hyperbolic Balance Laws with Non-Stationary Singular Source Terms CP10 This work proposes the use of a class of piecewise poly- Combined Finite-Element, Finite-Volume, and Dis- nomials compactly supported to approximate the Dirac crete Event Simulation of Structurally Complex delta distribution with the desired order of accuracy and Hydrocarbon Reservoirs smoothness, in the numerical solution of hyperbolic bal- Multiphase flow processes accompanying the production ance laws with this singular source term, using spectral of structurally complex hydrocarbon reservoirs occur on methods. For spatial discretization is used the spectral vastly different time- and length scales. This impacts reser- Chebyshev collocation method with Gauss-Lobatto nodes voir simulation to date because global time-stepping strate- and the third order total variation diminishing (TVD) gies are still used. Creation of a direct or indirect depen- Runge-Kutta scheme for time integration. The accuracy dence on the CFL condition is unavoidable and particu- of the numerical scheme is analyzed for various choices of larly restrictive when spatially adaptive gridding / flow- the support length, using an approximation to the Dirac based upscaling is used so that small cells discretize zones delta with three vanishing moments (third order accurate) of fast flow. To overcome such limitations, we apply an and two continuous derivatives. Numerical results supports asynchronous time-stepping methodology called Discrete the effectiveness of the proposed methodology, showing a Event Simulation to model reservoir flow. Operator split- convergence order according to the asymptotic behavior of AN13 Abstracts 15

2 ∞ the spectral interpolation error in the Lw and L norms. PML, the interface conditions are tranformed to include the auxiliary variables. Numerical experiments are pre- Jean P. Suarez sented demonstrating the stability and high order accuracy 4783 35Th St Apt 8 of the layer. [email protected] Kenneth Duru Gustaaf Jacobs Department of Geophysics, Stanford University, Stanford Department of Aerospace Engineering CA San Diego State University Stanford University [email protected] [email protected]

CP10 CP11 On the Numerical Integration of Initial-Boundary Modeling Surface Currents in The Eastern Levan- Value Problem to One Nonlinear Parabolic Equa- tine Mediterranean tion We consider the problem of reconstructing meso-scale fea- In the presented work the general initial-boundary value tures of the currents in the Levantine Mediterranean re- problem to the following nonlinear parabolic equation gion by combining in-situ (floaters) and altimetry data. Lagrangian trajectories of the floaters are used to improve ∂U ∂2U ∂U 2 the coarse Eulerian field obtained by altimetry. The in- = a (x, t, U) + b (x, t, U) + f (x, t) ∂t ∂x2 ∂x verse problem is solved using a variational assimilation technique, whereby the velocity correction is obtained by is considered. For the considered problem the equivalent minimizing the distance between a model solution and ob- initial-boundary value problem is obtained to which the servations of the floaters position. This approach shall be difference scheme is constructed. For mentioned difference validated with real data from the region. scheme the theorem of existence of its solution and the theorem of convergence of its solution to the solution of Leila Issa the source problem are proved under some restrictions on Lebanese American University coefficients a (x, t, U)andb (x, t, U).Therateofconver- [email protected] gence is established and it is equal to O τ + h2 .Thecor- responding numerical experiments were conducted which Julien Brajard confirmed the validity of the theorems. LOCEAN, UPMC Paris VI university Mikheil Tutberidze [email protected] Ilia State University Associated Professor [email protected] CP11 3D Underwater Acoustical Imaging with Contrast Source Inversion Technique CP11 Numerical Evidence of Extreme Diffusive Stabiliza- A non-linear inversion approach is presented for the acous- tion in Immiscible Models of Chemical Enhanced tical imaging of 3D objects located in a water reservoir Oil Recovery such as lake, ocean, etc. The space which is composed of air-water-soil layers is modelled as a three layered medium The effect of diffusion of species in the Hele-Shaw model having rough surfaces at the air-water and water-soil inter- of chemical enhanced oil recovery on the hydrodynamic faces. Through the Green’s function of the background the instability is numerically studied. We provide numerical problem is reduced to the solutions of two coupled system evidence of remarkable stabilization of fluid flow instabil- of non linear integral equations which are solved iteratively ities when interfaces between fluid phases are treated as by the application contrast source inversion method. The impermeable to species diffusion and concentrations of the Greens function of the layered media is calculated by the species are in dilute regimes. This is consistent with a spec- buried object approach. It is also accelerated through the ulation made earlier by the author. Several new features method of discrete images. The method yields quite accu- of the numerical solutions are noted rate results even with the incomplete data. Prabir Daripa Ibrahim Akduman Texas A&M University Istanbul Technical University Department of Mathematics Electrical and Electronics Eng. Faculty [email protected] [email protected]

CP11 Hulya Sahinturk Yildiz Technical University On the Stability of Perfectly Matched Layer for [email protected] the Wave Equation in Heterogeneous and Layered Media CP12 We will discuss the efficiency of the perfectly matched layer for the wave equation in heterogeneous and layered media. A Mathematical Model for Eradication of the We prove the stability of the layer for discontinuous me- Screwworm Fly by Sterile Insect Release Method dia with piecewise constant coefficients and derive energy The Sterile Insect Release Method is used to control inva- estimates for discontinuous media with piecewise smooth sive insect species by introducing large quantities of steril- coefficients. In order to ensure the stability of the discrete 16 AN13 Abstracts

ized male insects into a wild population of invading insects. [email protected] When fertile insects mate with sterile insects their offspring are not viable and wild insects may be eradicated. Moti- vated by a spatially symmetric sterile insect barrier that CP12 is characteristic of the screwworm fly eradication program, AStochasticModelforEscherichia Coli O157:H7 In- we consider a reaction-diffusion model of SIRM and ana- fection in Cattle lyze two spatially inhomogeneous steady-state solutions of this model. These steady states may result from an inef- Escherichia coli O157:H7 is an important foodborne fective barrier (fertile flies are extant on both sides) or an pathogen with a natural reservoir in the cattle population. effective barrier (fertile flies are extant on one side but ex- To understand the spread and persistence of the infection tinct on the other). We determine the minimum effective in cattle, we developed a stochastic model to study E. coli barrier size. O157:H7 transmission in cattle. In this presentation, I will talk about the extinction and outbreak of infection by solv- John G. Alford ing the Kolmogorov equations associated with statistics of Sam Houston State University the time to extinction and outbreak. The results provided [email protected] insight into E. coli O157:H7 transmission and apparent extinction, and suggested ways for controlling the spread of infection in a cattle herd. Specifically, this study high- CP12 lighted the importance of ambient temperature and sani- Mussel/Oyster Population Dynamics and Control tation, especially during summer.

The Asian Green Mussel was found to be in competition Xueying Wang with the resident Eastern Oyster shortly after its discovery Texas A&M University as an invasive species in the Tampa Bay area. We model [email protected] the population dynamics as a Lotka-Volterra type system of diﬀerential equations, with additional terms taking into Linda J. S. Allen account environmental conditions. Relative parameter val- Texas Tech University ues were estimated based on observations. A correspond- [email protected] ing optimal control problem looks at using salt dumps to manage the mussel population. Renata Ivanek, Raju Gautam, Pablo Pinedo Daniel L. Kern, Matthew Neubek Texas A&M University Florida Gulf Coast University [email protected], [email protected], Dept of Chemistry and Mathematics [email protected] [email protected], [email protected] CP13 CP12 Noise Induced Oscillations and Coherent Stochas- Periodicity of An Arizona Tiger Salamander Pop- tic Resonance in a Generic Model of the Non- ulation isothermal Minimal Chemical Oscillator

Arizona Tiger Salamanders exhibit facultative paedomor- Oscillating chemical reactions are common in biological phosis in which salamander larvae either metamorphose systems and they also occur in artificial non-biological into terrestrial adults or become sexually mature while still chemical systems. Generally, these systems are subject in their larval form. Although many salamanders exhibit to random fluctuations in environmental conditions which cannibalism of larvae, the Arizona Tiger Salamander also translate into fluctuations in the values of some physical exhibits cannibalism of young by the aquatic adults. We variables, for example, temperature. We formulate a math- formulate an ODE model of this system, construct periodic ematical model for a nonisothermal minimal chemical os- solutions and compare them with existing data. cillator containing just a single negative feedback loop and study numerically the effects of stochastic thermal fluctu- Maeve L. McCarthy ations in the absence of any deterministic limit cycle or Murray State University periodic forcing. We show that thermal noise can induce [email protected] sustained limit cycle oscillations with a relatively narrow frequency distribution and some characteristic frequency. These properties differ significantly depending on the na- CP12 ture of the noise correlation. Here, we have explored white Ant-Isocial Dynamics: Studying Ant Social Net- and colored (correlated) noise. A plot of the characteristic work Accumulation frequency of the induced oscillations as a function of the correlation exponent shows a sharp maximum, therefore in- Social network analysis is used to study animal interac- dicating the existence of coherent (autonomous) stochastic tions. Animal social networks analysis generally uses time- resonance. aggregated networks. Our approach differs because we analyze how interactions accumulate over time. Ant species David S. Simakov, Juan Perez-Mercader Formica subsericea lives in large colonies and relies on Department of Earth & Planetary Sciences interaction to share information. We compare how the Harvard University interactions of different-sized groups of these ants accu- [email protected], mulate over time using network statistics including, path [email protected] length, average interactions per ant, clustering coefficient, and largest connected component size. CP13 Amanda L. Traud Surface Traction and the Dynamics of Elastics North Carolina State University AN13 Abstracts 17

Rods at Low Reynolds Number literature.

The past forty years have witnessed an ever-increasing in- Leela Rakesh terest in applications of slender-body dynamics (such as Central Michigan University Kirchhoff rod theory), in particular with regard to the Applied Mathematics Group shape, movement, or material parameters of biomolecules [email protected] or materials. In most applications, hydrodynamic interactions (i.e. surface traction often approximated by resis- Mohammad Zannon, Mohamad Qatu tive force theory) have been of utmost importance since CMU the biologically relevant scales usually result in very small [email protected], [email protected] Reynolds number. However, the formulation of classical Kirchhoff slender-body assumes no surface traction in the development of the constitutive relation. We will discuss an CP14 asymptotic approach to reconciling this apparent inconsis- A Minimum Sobolev Norm Technique for the Nu- tency and provide velocity bounds for which the compati- merical Solution of PDEs bility of Kirchhoff rod and resistive force theory hold. We present a method for the numerical solution of PDEs Eva M. Strawbridge based on finding solutions that minimize a certain Sobolev University of Chicago norm. Fairly standard compactness arguments establish Department of Mathematics convergence. The method prefers that the PDE is pre- [email protected] sented in first order form. A single short Octave code is used to solve problems that range from first-order Charles Wolgemuth Maxwell’s equations to fourth-order bi-harmonic problems. University of Arizona The method is high-order convergent even on complex Department of Physics curved geometries. [email protected] Shivkumar Chandrasekaran University of California, Santa Barbara CP13 Department of Electrical and Computer Engieering A Model for Transient Evolution of a Material with [email protected] Complex Microstructure from Elastic Deformation to Flow CP14 We consider a subclass of non-Newtonian materials which Application of Fft-Recursive-Relation Based Hy- behave as solids at equilibrium, and flow only under suffi- brid Fast Algorithms to Computing Interfacial ciently high stresses. At intermediate applied stresses, the Flows material waits for a long time before flowing; for example, ketchup. The slow and fast time scales are interpreted in This talk will be based on current work in progress on com- the light of a large relaxation time limit of a viscoelastic puting interfacial flows that makes use of fast algorithms constitutive model for the microstructure, together with a developed by one of the authors (PD) in combination with solvent. Homogeneous unidirectional extension, given an front tracking and level set methods. Performance of these instantaneous tensile stress, is addressed. methods on such problems arising the context of chemical enhanced oil recovery will be presented. Holly Timme VIrginia Tech JoungDong Kim [email protected] Texas A&M University [email protected] Yuriko Renardy Virginia Tech Prabir Daripa Department of Mathematics Department of Mathematics [email protected] Texas A&M University [email protected]

CP13 Mathematical Modeling of Transverse Shear Defor- CP14 mation Thick Shell Theory Hp Finite Element Method for Linear Dispersive Waves IIn this paper, the three dimensional elasticity theories in curvilinear coordinates of thick shells are discussed. The Maxwells equations are a system of partial differential relationship between forces, moments and stresses are given equations which model electromagnetism. Coupled with and the equations of motion are derived using Newtons constitutive laws, they are of interest in simulating electro- 2nd law of motion and Hamiltons principle. The necessary magnetic waves in various media. In this paper we focus theoretical assumptions are discussed to reduce the three primarily on Debye model which is a linear first order or- dimensional (3-D) elasticity to two-dimensional (2-D) shell dinary differential equation in time which models a simple theory of third order to a first order equation. Equilibrium relaxing dielectric. This model, called Maxwell-Debye is equations are formulated using the equations of stress re- singularly perturbed and results in complex dispersive and sultants to arrive at a system of differential equations and diffusive wave behavior. This behavior is frequency de- solved by Fourier expansion. The results are compared pendent and stiff. Solving this problem numerically has with the three- dimensional elasticity theory from existing applications to biomedical imaging and seabed mapping. Adapting the the work of Ainsworth, we proceed to produce bounds on the dispersion error of hp finite element 18 AN13 Abstracts

methods for for the one dimensional Maxwell-Debye. This CP15 analysis suggests that neither h nor p adaptive finite ele- Symmetry-Breaking Hopf Bifurcations to 1-, 2- ments will be sufficient to adequately reduce the dispersion , and 3-Tori in Small-Aspect-Ratio Counter- error. A number of numerical simulations are presented as Rotating Taylor-Couette Flow well. Nonlinear dynamics in differentially counter-rotating cylin- Duncan A. Mcgregor ders is investigated by solving the full three-dimensional Oregon State University Navier-Stokes equations. Dynamics are dominated by the Department of Mathematics jet of angular momentum emerging from the inner cylin- [email protected] der boundary layer at about the mid-plane. The sequence of bifurcations consists of an axisymmetric Hopf bifurca- Vrushali A. Bokil, Nathan L. Gibson tion breaking the reflection symmetry of the basic state Oregon State University leading to an axisymmetric limit cycle with a half-period- [email protected], flip spatio-temporal symmetry. This undergoes a Hopf bi- [email protected] furcation breaking axisymmetry, leading to quasi-periodic solutions evolving on a 2-torus that is only half-period-flip Pavel Solin symmetric due to precesion. A further Hopf bifurcation in- Department of Mathematics and Statistics troducing a third incommensurate frequency leading to a 3- University of Nevada, Reno torus on that a saddle-node-on-an-invariant-circle (SNIC) [email protected] bifurcation takes place, destroying the 3-torus and leaving a pair of symmetrically-related 2-tori states on which all symmetries of the system have been broken. CP14 A Balancing Domain Decomposition Method by Sebastian A. Altmeyer Constraints for Raviart-Thomas Vector Fields Department of Mathematics Kyungpook National University A BDDC preconditioner for vector field problems dis- sebastian [email protected] cretized with Raviart-Thomas elements is introduced. Our method is based on a new type of weighted average devel- Younghae Do oped to deal with more than one variable coefficient. A Kyungpook National University bound on the condition number is provided which is inde- [email protected] pendent of the values and jumps of the coefficients and has a polylogarithmic bound in terms of the number of degrees Juan Lopez of freedom of the individual subdomains. Arizona State University, Tempe, Arizona 85287 Duk-Soon Oh [email protected] Louisiana State University [email protected] Fernando Marques Universitat Politecnica de Catalanya, Olof B. Widlund 08034 Barcelona, Spain Courant Institute [email protected] [email protected]

Clark R. Dohrmann CP15 Sandia National Laboratories Simulating Three-Dimensional Fluid Flow in [email protected] Porous Media Numerically modeling fluid flow through explicit porous CP14 media is computationally demanding. However, fluid flow Semilinear Elliptic PDE on Manifolds through samples of explicit pore spaces can be simulated efficiently, while reproducing key physics of percolating In this paper we begin by introducing the Closest Point flows, by combining non-oscillatory (viz. high-resolution) Method (CPM) and the Gradient Newton Galerkin Algo- Navier-Stokes integrators with semi-implicit representation rithm (GNGA). We use GNGA to solve PDEs on manifolds of elementary (i.e., first-order) immersed-boundary forcing. by first finding eigenfunctions of the Laplacian restricted Here, fluid flow is allowed to reach steady state in a given to the manifold using the CPM. Finally we use a Galerkin porous medium, and the resulting velocity and pressure expansion in eigenfunctions of the Laplacian, to find the fields are analyzed. We compute attributes of particle tra- desired solutions. In this paper we extend the theoretical jectories including tortuosity, trajectory length, and first underpinnings of GNGA to solving the desire PDE on man- passage percolation time. The fluid velocity fields become ifolds. This extended method combined with utilizing the more homogeneous with increasing porosity indicated by CPM to generate the needed eigenfunctions allows us to a decrease in the variance of tortuosity, trajectory length, compute on manifolds with relative ease. In this paper we and travel time distributions. present several examples on basic manifolds which do not require the CPM calculation, followed by more interesting Jeffrey D. Hyman examples where CPM is necessary. University of Arizona Program in Applied Mathematics DarylJ.Springer [email protected] Department of Mathematics Arizona State University Piotr Smolarkiewicz [email protected] 2European Centre for Medium-Range Weather Forecasts AN13 Abstracts 19

Reading, United Kingdom CP15 [email protected] Onset of Buoyancy-driven Convection in Cartesian and Cylindrical Geometries Larrabee Winter University of Arizona We perform a linear stability analysis to examine the on- Department of Hydrology and Water Resources set of buoyancy-driven convection relevant to subsurface [email protected] carbon dioxide injection in confined, porous Cartesian and cylindrical domains. The lateral boundaries impede the onset. The patterns of the most unstable perturbation mode CP15 in Cartesian and cylindrical domains are highly different, Uncoupling Groundwater-Surface Water Flow Us- and we hypothesize that this may eventually lead to differ- ing Partitioned and Multi-Rate Methods ent behavior in the two geometries. Our results may guide future numerical studies that can investigate this hypoth- Partitioned methods for the evolutionary Stokes-Darcy esis. equations uncouple the system so that at each time step we solve separate ground- and surface water problems using Philip C. Myint codes optimized for the physics in each sub-domain. Chal- Yale University lenges include maintaining stability and accuracy along the Department of Chemical and Environmental Engineering interface and when given small parameters. We adapt par- [email protected] titioned methods to obtain multi-rate splitting methods. This is advantageous since flow in aquifers with low con- Abbas Firoozabadi ductivity moves slowly, requiring accurate calculations over Yale University long time periods. abbas.fi[email protected] Michaela J. Kubacki University of Pittsburgh CP16 [email protected] The Effects of Numerical Model Error on 4D- Variational Data Assimilation Marina Moraiti University of Pittsburgh, USA 4D-Variational data assimilation is typically used for fore- [email protected] casting physical systems. It finds an initial condition for a numerical model, by combining observations with pre- Xin Xiong dictions. The numerical model is then used to produce a Department of Mathematics forecast. Numerical model error affects the accuracy of the University of Pittsburgh initial condition and its forecast. We find an upper bound [email protected] for the numerical model error introduced by finite difference schemes used to solve the linear advection equation and analyse its order of convergence. CP15 Sin E. Jenkins, Chris Budd, Melina Freitag, Nathan Turbulent Fluid Mixing of Multiphase Flow Smith We develop an interface tracking simulation for predicting University of Bath interaction of droplets in rotating flows relevant to opti- [email protected], [email protected], mized design of centrifugal contactor devices used in sol- [email protected], [email protected] vent extraction processing and other separation operations. We study the turbulent Taylor-Couette flow mixing of a CP16 two-phase (organic and aqueous) mixture in a centrifugal contactor. We find extensive fluid mixing and an enhanced Structure Oriented Attributes Using Cuda Kernels interfacial area for chemical reactions to occur at the infor Oil Exploration terface between the two phases. In this talk we present a class of structure oriented filters Hyunkyung Lim which are based on 3D gradient structure tensor approach. SUNY at Stony Brook These kind of filters can be used to compute many orienta- Dept of Applied Mathematics tion attributes encased in seismic data and its can help to [email protected] the seismic interpretation. These filters allow to determinate local orientation, possible reflection terminations and smoothing of the data in the directions of the local ori- James Glimm entation. The computation is done on a multi-GPU ma- State University of New York, Stony Brook chine using CUDA. Computation and visualization on-the- [email protected] fly (Real Time) can be done. In this case, we have used a 3D synthetic data to show results. Yijie Zhou SUNY at Stony Brook German A. Larrazabal [email protected] University of Carabobo Valencia-Venezuela Xiangmin Jiao [email protected] Stony Brook University [email protected] 20 AN13 Abstracts

CP16 Problems with Discontinuous Coefficients and Sin- Mpi Geometrical Partitioner gular Sources Data partitioning has a key importance in parallel com- The aim of this talk is to solve elliptic interface problem putations. We present a new MPI geometrical partitioner with discontinuous coefficient and singular source term by which includes Recursive Coordinate Bisection, Recursive spectral collocation method. First, we develop an algo- Internal Bisection and Hilbert Space Filling Curve algorithm for the elliptic interface problem defined in the sim- rithms based on fast parallel randomized selection algo- ple domain with simple interface and then generalize it to rithm. We compare our partitioner with state-of-the-art curved interface. For complicated domain with curved in- partitioner Zoltan on a data set arisen in real reservoir terface we use spectral element collocation method. We simulations and show that our algorithms generates par- give some numerical experiments to show efficiency of our titioning of the same quality, but are considerable faster. algorithm and its spectral convergence. Peyman Hessari Vladislav Pravilnikov, Vladimir Rerikh Institute of Mechanical Engineering Technology Neurok Software LLC Kyungpook national university, Daegu, 702-701, South [email protected], Korea [email protected] [email protected]

Serguei Y. Maliassov Byeong Chun Shin ExxonMobil URC Department of mathematics, Chonnam National [email protected] university Gwangju 500-757, Korea [email protected] CP16 Hypergraph Partitioner for Reservoir Simulations CP17 Data partitioning is one of the most important procedures Delta Functions and the Euler-Maclaurin Formula in parallel computations. We present a new hypergraph partitioning algorithm based on multilevel approach and One aspect of the Chebfun software project is numerical intended for application in modern reservoir simulations. computation involving delta functions. This relates to so- It includes new hypergraph coarsening schemes based on lutions of differential equations involving Green’s functions mixed vertex-hyperedge coarsening and can utilize geo- and to the Euler-Maclaurin formula and related results metrical information from underlying grids. Being com- quantifying the accuracy of the trapezoid rule applied to pared with state-of-the-art partitioner Zoltan, our algo- analytic functions — also to the theory of hyperfunctions. rithm shows comparable quality, while considerable better We present recent results in this area. performance as shown by examples arisen in real reservoir simulations. Mohsin Javed University of Oxford, UK Vladimir Rerikh, Vladislav Pravilnikov [email protected] Neurok Software LLC [email protected], [email protected] CP17 Anti-Differential Operators: An Application of the Serguei Y. Maliassov Pseudo-Inverse ExxonMobil URC This talk presents approaches to approximate diagonal- [email protected] ization of variable-coefficient differential operators using similarity transformations of operators rather than matri- CP17 ces. The similarity transformations are constructed using canonical transformations of symbols and anti-differential A High Order Accurate Solution Technique for operators, which use the pseudo-inverse of the differentia- Free Space Scattering Problems in Variable Media tion operator, for making lower-order corrections. Numer- This talk describes a new technique for solving free space ical results indicate that the symbols of transformed oper- scattering problems where there is localized variation from ators can be made to closely resemble those of constant- constant coefficient. In the region of variable media, an coefficient operators, and that approximate eigenfunctions approximate Dirichlet-to-Neumann operator is constructed can readily be obtained. by a composite spectral method. This operator is then James V. Lambers coupled to the rest of space via an integral equation that is University of Southern Mississippi amenable to fast solvers, has second kind behavior and is Department of Mathematics high order accurate. Numerical results illustrate the per- [email protected] formance of the method.

Adrianna Gillman CP17 Dartmouth College Department of Mathematics Numerical Methods for the Poisson-Fermi Equa- [email protected] tion in Electrolytes The Poisson-Fermi equation is applied to and numerically CP17 studied for electrolytes and biological ion channels in three dimensional space. This is a fourth-order nonlinear PDE Pseudo-Spectral Method for Elliptic Interface that deals with both steric and correlation eﬀects of all ions AN13 Abstracts 21

and solvent molecules involved in a model system. Vari- multi-state system. The main implication of our results ous numerical methods are developed to tackle a range of is that in determining the optimal scheduled PM, choosing numerical problems concerning geometric singularities, the the right repair type will significantly improve the efficiency fourth-order term, nonlinearity, stability, efficiency, and ef- of the system maintenance. fectiveness. The steric and correlation effects are demonstrated by showing good agreement with Monte Carlo sim- Shey-Huei Sheu ulation data for a charged wall model and an L type cal- Providence University cium channel model. [email protected]

Jinn-Liang Liu Yen-Luan Chen National Hsinchu University of Education, Taiwan Takming University of Science and Technology [email protected] [email protected]

CP17 Chin-Chih Chang Providence University A Overlapping Surface Decomposition Based [email protected] Kernel-Free Boundary Integral Method for Vari- able Coefficient Elliptic Pde CP18 An overlapping surface decomposition based kernel-free boundary integral method for variable coefficient elliptic Developing Approximation Algorithms for Risk- partial differential equations will be presented in this talk. Averse Stochastic Selection Problems The method avoids direct computation of boundary inte- We consider a supplier facing a single period of uncertain grals involving the Green’s function and approximates the demands and revenues in a collection of markets. The sup- boundary integral with a structured grid based solution, plier chooses markets z and other decisions y to minimize which solves an equivalent interface problem on a larger ariskmeasureρ of a cost function Γ(y,z). This func- regular box. The method works with complex domains de- tion includes lost revenues in deselected markets as well fined implicitly through a level set function. The method as logistics and newsvendor-type costs for the collection of does not need the generation of unstructured grids for both selected markets. We develop high-probability constant- the problem domain and its boundary. factor approximation algorithms to minimize ρ(Γ(y,z)) us- Wenjun Ying ing rounding and sample average approximation. Department of Mathematical Sciences Zohar Strinka Michigan Technological University University of Michigan [email protected] [email protected]

CP18 Edwin Romeijn Logconcavity of Compound Distributions with Ap- University of Michigan plications in Stochastic Optimization Industrial and Operations Engineering [email protected] Compound distributions come up in many applications telecommunication, hydrology, insurance, etc.), where some of the typical problems are of optimization type. Log- CP18 concavity property is paramount in these respects to ensure Geometric Asian Options under Heston Model: convexity. We prove the logconcavity of some compound Pricing and Hedging Poisson and other compound distributions by the use of Turan-type inequalities on some orthogonal polynomials. In this talk, we derive semi-analytic closed-form solution for price geometric Asian options when the underlying as- Anh Ninh, Andras Prekopa set prices follow Heston’s stochastic volatility model. Our RUTCOR method involves the generalized Fourier transform tech- Rutgers University niques. In addition, we derive the discrete-time variance [email protected], [email protected],edu optimal hedging strategy and the corresponding expected hedging error explicitly. Numerical results for prices and hedging strategies are presented with comparison of com- CP18 putational stability, efficiency and accuracy. Optimal Preventive Maintenance and Repair Poli- cies for Multi-State Systems In-Suk Wee Dept. of Mathematics, Korea University This paper studies the optimal preventive maintenance [email protected] (PM) policies for multi-state systems. The scheduled PMs can be either imperfect or perfect type. The improved ef- Jerim Kim fective age is utilized to model the effect of an imperfect Dept. of Mathematics, Korea University PM. The system is considered as in a failure state once [email protected] its performance level falls below a given customer demand level. If the system fails before a scheduled PM, it is re- paired and becomes operational again. We consider three CP18 types of major, minimal, and imperfect repair actions, re- Problem of Non-Monotone Quadratic Estimating spectively. The deterioration of the system is assumed to Equations in Saddlepoint Approximating the Mov- follow a non-homogeneous continuous time Markov process ing Average Model of Order One with finite state space. A recursive approach is proposed to efficiently compute the time-dependent distribution of the Here our aim is to approximate the distribution of maxi- 22 AN13 Abstracts

mum likelihood estimator (MLE) of moving average model sumption and erosion due to the surrounding fluid. We of order one [MA(1)] using the approach introduced by have coupled biofilm growth and deformation in a novel Daniels (1980) . Under this method, the MLE of the MA continuum model using Morphoelasticity Theory. The (1) parameter is expressed as a quadratic estimating equa- model tracks the evolving biofilm surface using the Level tion (QEE). Monotone QEE whose unique root is the esti- Set Method combined with the eXtended Finite Element mator of interest, the profiling out of nuisance parameters, Method (XFEM). and the accurate saddlepoint approximations to the cumu- lative distribution function of the MLE are some of the key Jared A. Hicks steps of the method. When the QEE is not monotone with Engineering Sciences and Applied Mathematics respect to the parameter, above approach cannot be fol- Northwestern University lowed. Therefore for the case of non-monotone QEE of the [email protected] MLE, we try to apply a method that combines the results of both Skovgaards (1990) and Butlers (2007). According David L. Chopp to the obtained results, it is clear that the above approach Northwestern University gives pretty good approximations though there are some Dept. of Engineering Science and Applied Mathematics slight disagreements when the value of the true parameter [email protected] is close to one. Indika P. Wickramasinghe CP19 Department of Mathematical Sciences Stable Explicit Interface Advancing Scheme for Eastern New Mexico University Fluid-Solid Interaction with Applications to Fish [email protected] Swimming Simulation

Alex Trindade We propose a numerical scheme for fluid-structure inter- Department of Mathematics and Statistics action when there are both elastic and rigid bodies inside Texas Tech University the fluid. There can also be rigid bodies lying inside the [email protected] elastic bodies. To develop a numerical scheme, we have to deal with the famous quadratic nonlinearities in the governing equations of the fluid and the rigid body. We use CP19 a natural semi-implicit discretization with explicit fluid- Low-Reynolds-Number Swimming in Two-Phase structure interface advancing. Consequently, the scheme Fluids does not require Newton type iterations. The scheme is characteristics-free even though we are working on a time The fluid media surrounding many microorganisms are of- varying domain for the fluid. All those features make the ten mixtures of multiple materials with very different phys- numerical scheme very efficient. We prove the uncondi- ical properties. The composition and rheology of the mix- tional stability of the fully discrete scheme. As an applica- ture may strongly affect the related locomotive behaviors. tion, we perform the fish swimming simulation and numer- We study the classical Taylors swimming sheet problem ically confirm some observations made by Purcell in 1976 within a two-fluid model, which consists of two intermixed concerning how microorganisms swim in a very viscous liq- fluids with different properties. Our results indicate that uid. the swimming behavior may change substantially relative to those for a single-phase fluid. Jie Liu National University of Singapore Jian Du Department of Mathematics Department of Mathematics [email protected] Florida Institute of Technology jdu@fit.edu CP19 James P. Keener Eulerian/Lagrangian Sharp Interface Schemes for University of Utah Compressible Multimaterials [email protected] We present multi-material simulations using both Eule- rian and Lagrangian schemes. The methods employed are Robert D. Guy based on classical Godunov-like methods that are adapted Mathematics Department to treat the case of interfaces separating different materials. University of California Davis In the models considered the gas, liquids or elastic materi- [email protected] als are described by specific constitutive laws, but the governing equations are the same. Examples of gas-gas and Aaron L. Fogelson gas-elastic material interactions in two space dimensions University of Utah are presented. [email protected] Thomas Milcent I2M Bordeaux CP19 [email protected] A Continuum Model for the Simultaneous Growth and Deformation of Biofilms CP19 Microbial Fuel Cells are water treatment systems that use A Supercavitating Flexible Hydrofoil in a Stream bacteria to break down wastewater nitrates while simulta- of Ideal Fluid neously generating electricity. A key factor in their efficiency is balancing the biofilms growth from nutrient con- We consider a cavitation problem for a flexible hydrofoil in AN13 Abstracts 23

a stream of ideal fluid with a Tulin single-spiral-vortex cav- Silas Alben ity closure condition. Several geometries of the hydrofoil University of Michigan, USA are studied including a straight hydrofoil, a wedge, and a [email protected] polygonal hydrofoil. The last case is used as an approximation to study a cavitating circular hydrofoil. The physical problem in all cases is reduced to a Riemann-Hilbert prob- CP20 lem and then further reduced to a system of algebraic and Global Synchronization For Coupled Map Lattices transcendental equations. The later is solved numerically. in Ecology The numerical results for certain geometries are presented. We shall investigate non-smooth coupled map lattices in ecology. Such model is to describe how masting of a mature Anna Zemlyanova forest happens and synchronizes. The sufficient and nec- Department of Mathematics essary conditions for global synchronization of the model Texas A&M University with lattice size 2 are to be presented. [email protected] Jonq Juang Department of Applied Math, National Chiao Tung CP20 University Extreme Events and Travel Time Reliability in [email protected] Coupled Spatial Networks Chun-Ming Huang Transport process on spatial networks can represent a lot Department of Applied Math of real world systems, which are often interdependent. This National Chiao Tung University paper studies the extreme events (EE) on coupled spatial [email protected] networks. The occurrence probability of EE on the coupling nodes depends strongly on the routing strategy and the density of commuters. As a result, the travel time CP20 reliability of the networks is also affected. To optimize Stabilizing Gene Regulatory Networks Through the system, one needs to enhance the capacity of coupling Feed Forward Loops nodes. The global dynamics of gene regulatory networks are Mao-Bin Hu known to show robustness to perturbations of different University of Science and Technology of China, P.R. kinds: intrinsic and extrinsic noise, as well as mutations China of individual genes. One molecular mechanism underlying [email protected] this robustness has been identified as the action of so-called microRNAs that operate via different types of feedforward Qing-Song Wu loops. We will present results of a computational study, School of Engineering Science, using the modeling framework of generalized Boolean net- University of Science and Technology of China works, that explores the role that such network motifs play [email protected] in stabilizing global dynamics.

Rui Jiang Claus Kadelka School of Engineering Science Virginia Bioinformatics Institute, Virginia Tech University of Science and Technology of China [email protected] [email protected] David Murrugarra School of Mathematics, Georgia Tech CP20 [email protected] Optimization of Two and Three-Link Snake-Like Locomotion Reinhard Laubenbacher Virginia Bioinformatics We analyze two- and three-link planar snake-like locomo- Institute tion and optimize the motion for efficiency. The locomoting [email protected] system consists of two or three identical inextensible links connected via hinge joints, and the angles between the links are actuated as prescribed periodic functions of time. Effi- CP20 ciency is defined as the ratio between distance traveled and Crosstalk Dynamics of Nls Solitons in Many-Body the energy expended within one period, i.e. the inverse of Interaction the cost of locomotion. The optimal set of coefficients of friction to maximize efficiency consists of a large backward We derive a general reduced model that describes the coefficient of friction and a small transverse coefficient of contribution of n-pulse interaction to the amplitude shift friction, compared to the forward coefficient of friction. For in fast collisions of N solitons of the NLS equation in the two-link case with a symmetrical motion, efficiency is the presence of generic weak nonlinear loss of the form mc maximized when the internal angle amplitude is approxi- | |2m mately π/2, for transverse coefficient sufficiently large. For 2m+1 ψ ψ,whereψ is the physical field. Our ana- m=0 the three-link case, the efficiency-maximizing paths are tri- lytic calculations and numerical simulations show that n- angles in the parameter space of internal angles. pulse interaction with high n values plays a key role in fast soliton collisions in the presence of generic nonlinear loss. Fangxu Jing The scalings of n-pulse interaction effects with n and m University of Southern California and the strong dependence on initial soliton positions lead [email protected] 24 AN13 Abstracts

to complex collision dynamics, which is very different from CP21 the one observed in fast soliton collisions in the presence of Fractional Order Model of Rabies cubic loss [A. Peleg et al. Phys. Rev. A 82 053830 (2010)]. Rabies is a preventable but still endemic disease in warm-blooded animals. We give a general one species- Quan M. Nguyen mathematical model to explain the transmission of rabies. International University, Vietnam National This model consists of fractional order differential equa- University-HCMC tions and it can be used to understand the dynamics of the Vietnam disease in many different species. [email protected] Elif Demirci Avner Peleg, Paul Glenn Ankara University State University of New York at Buffalo [email protected] apeleg@buffalo.edu, paulglen@buffalo.edu CP21 CP20 Analysis of Si Model for a Chronic Disease with A Unified Approach for Controlling Crosstalk in Multiple Interacting Populations Using Subpopu- Broadband Optical Waveguide Systems lations with Forcing Terms We present a unified approach for analyzing and controlling As a system of differential equations describing an epidemi- the dynamics of soliton amplitudes in broadband optical ological system becomes large with multiple connections waveguide systems, induced by energy exchange (crosstalk) between subpopulations, the expressions for reproductive in pulse collisions. The approach, which is based on single- numbers and endemic equilibria become algebraically com- collision analysis along with collision rate calculations, plicated which makes drawing conclusions based on biolog- shows that for a variety of waveguide systems, crosstalk- ical parameters difficult. We present a new method which induced amplitude dynamics of N soliton sequences is de- deconstructs the larger system into smaller subsystems, scribed by N-dimensional Lotka-Volterra models. Stability captures the bridges between the smaller systems as exter- analysis of the equilibrium states of the models uncovers nal forces, and bounds the reproductive numbers of the full ways for achieving stable transmission with equal nonzero system in terms of reproductive numbers of the smaller sys- amplitudes for all soliton sequences. tems, which are algebraically tractable. This method also allows us to analyze the size and stability of the endemic Avner Peleg equilibria. We demonstrate the model on the example of State University of New York at Buffalo a sexually transmitted chronic disease with bisexual and apeleg@buffalo.edu heterosexual populations.

Quan M. Nguyen Katharine Gurski International University, Vietnam National Department of Mathematics University-HCMC Howard University Vietnam [email protected] [email protected] Evelyn Thomas Yeojin Chung Bennett College Southern Methodist University [email protected] [email protected] Kathleen A. Hoﬀman University of Maryland, Balt. Co. CP20 Deapartment of Math. and Stat. Spiking Properties of Fractional Order Leaky khoﬀ[email protected] Integrate-and-Fire Model

We develop the fractional order leaky integrate-and-fire CP21 model to study the fundamental properties of voltage dy- Mathematical Modeling of the Spread of Antibiotic namics on spiking activity. This dynamics depends on the Resistant Bacteria in a Hospital voltage-memory trace that we define it as the integrated value of all past values of the voltage. The fractional or- The increase in antibiotic resistance continues to pose a der model displays slow spike frequency adaptation, spike major public health risk leading to a more intense focus latency and high interspike interval variability. Its spiking on ways to limit and even reduce this threat. In order for activity deviates from the Markov chain model, and reflects mathematical models to be useful in evaluating the poten- the temporal accumulated intrinsic membrane dynamics. tial effects of different treatment protocols or stewardship practices, the models must be refined to more accurately Wondimu W. Teka represent a typical hospital. In this talk, we focus on these Department of Mathematics refinements using both deterministic and stochastic mod- Florida State University eling. [email protected] Michele Joyner,EdSnyder,AdamWhite Toma Marinov, Fidel Santamaria East Tennessee State University University of Texas at San Antonio [email protected], [email protected]], Neurosciences Institute [email protected]] [email protected], fi[email protected] AN13 Abstracts 25

CP21 Necibe Tuncer Optimal Control of Influenza Model University of Tulsa [email protected] This study considers an optimal intervention strategy for influenza outbreaks. Variations in the SEIAR model are considered to include seasonal forcing and age structure, CP21 and control strategies include vaccination, antiviral treat- Utilizing Female-Killing Strategies in the Optimal ment, and social distancing such as school closures. We Control of the Dengue Vector, Aedes Aegypti formulate an optimal control problem by minimizing the incidence of influenza outbreaks while considering inter- Dengue fever is spread primarily by Aedes aegypti vention costs. We examine the effects of delays in vaccine mosquitoes. Although traditional control measures have production, seasonal forcing, and age-dependent transmis- been implemented for many years, dengue remains endemic sion rates on the optimal control and suggest some optimal in many parts of the world. Recently, control strategies in- strategies through numerical simulations. volving the release of genetically modified mosquitoes have been proposed. Among those for Ae. aegypti that have Jungeun Kim seen the most progress are Female-Killing (FK) strategies. Yonsei University Cage experiments showed that repeated introductions of [email protected] individuals from one FK strain of Ae. aegypti led to either reduction or extinction of caged wild-type populations. Jeehyun Lee Any future open releases should be conducted according Mathematics to plans that consider temporal and financial constraints. Yonsei University, Korea We develop an optimal control model to assess the role [email protected] that such constraints will play in conducting FK releases. Through numerical simulation, we obtain optimal release Hee-Dae Kwon strategies for a variety of scenarios and assess the feasibil- Inha University ity of integrating FK releases with other forms of vector [email protected] control. Michael A. Robert, Fred Gould, Alun Lloyd CP21 North Carolina State University [email protected], fred [email protected], Hybrid On-Off Control for An HIV Model Based alun [email protected] on a Linear Control Problem

We consider a model of HIV infection with various com- CP22 partments, including target cells, infected cells, viral loads and immune effector cells, to describe HIV type 1 infec- A Perfect Match Condition for Point-Set Match- tion. We show that the proposed model has one unin- ing Problems Using the Optimal Mass Transport fected steady state and several infected steady states and Approach investigate their local stability by using a Jacobian matrix We study the performance of optimal mass transport-based method. We obtain equations for adjoint variables and methods applied to point-set matching problems. The characterize an optimal control by applying Pontryagins present study, which is based on the L2 mass transport Maximum Principle in a linear control problem. In ad- cost, states that perfect matches always occur when the dition, we apply techniques and ideas from linear optimal product of the point-set cardinality and the norm of the control theory in conjunction with a direct search approach curl of the non-rigid deformation field does not exceed to derive optimal on-off HIV therapy strategies. The re- some constant. This analytic result is justified by a numer- sults of numerical simulations indicate that hybrid on-off ical study of matching two sets of pulmonary vascular tree therapy protocols can move the model system to a healthy branch points whose displacement is caused by the lung steady state in which the immune response is dominant in volume changes in the same human subject. The nearly controlling HIV after the discontinuation of the therapy. perfect match performance verifies the effectiveness of this Hee-Dae Kwon mass transport-based approach. Inha University Pengwen Chen [email protected] National Taiwan University [email protected] CP21 Spread of Avian Influenza Pandemic to Usa Via Ching-Long Lin Air Travel University of Iowa [email protected] We introduce a two-patch mathematical model to forecast the global spread of pandemic avian influenza. We suppose I-Liang Chern that the pandemic starts in Asia and spreads to USA by air Department of Mathematics travel. We consider total of 12 major airports in Asia and National Taiwan University USA. We derive the reproduction number of the two-patch [email protected] model and compute the sensitivity of the parameters such as transmission and death rate of pandemic avian influenza. CP22 Trang Le Dynamic Congestion and Tolls with Mobile Source Ms. Emission [email protected] This paper proposes a dynamic congestion pricing model 26 AN13 Abstracts

that takes into account mobile source emissions. We con- method and the Taylor series are provided. sider a tollable vehicular network where the users self- ishly minimize their own travel costs including travel time, Victor A. Miroshnikov early/late arrival penalties and tolls. On top of that, we College of Mount Saint Vincent assume that part of the network can be tolled by a central [email protected] authority whose objective is to minimize both total travel costs of users and total emission on a network-wide level. The model is formulated as a mathematical programming CP23 with equilibrium constraints (MPEC) problem and then A Massively Parallel Finite Element Solver for reformulated as mathematical programming with comple- High Definition Chromatography Simulations mentarity constraints (MPCC). The MPCC is solved using a quadratic penalty-based gradient projection algorithm. Packed bed chromatography is a very important unit operation, applied by biotechnology industry for purifying Ke Han, Terry Friesz, Hongcheng Liu, Tao Yao target molecules from contaminants. Aiming at high The Pennsylvania State University definition chromatography simulations, we present a fi- [email protected], [email protected], [email protected], nite element approach which accurately captures all rel- [email protected] evant transport and binding phenomena in miniaturized chromatography devices. We apply a stabilized space- time FEM to solve both low Reynolds number fluid flow CP23 and convection-dominated transport and binding of solute Stokes Flow Past a Porous Body of Arbitrary molecules. Our code runs efficiently on several thousand Shape compute cores.

Flow past a permeable body of an arbitrary shape in an Andreas Puettmann incompressible fluid at low Reynolds number is discussed. German Research School for Simulation Sciences The Brinkman equations are assumed in the permeable [email protected] body and an approximate, analytic solution is obtained for an arbitrary flow. The results are compared with the exact Eric Von Lieres solution when the body is spherical. The effect of perme- Research Center Jülich ability on the physical parameters of the flow is discussed. [email protected] T. Amaranath University of Hyderabad CP23 India Two-Way Coupling of Lagrangian and Eulerian [email protected] Governing Equations for Particles in Incompress- ible Fluids CP23 Spectral methods formulations of Navier-Stokes equations Slip Flow Past Bodies of Arbitrary Shape in a Vis- for an incompressible fluid and the small particle equation cous, Incompressible Flow of motion are coupled together in a numerical scheme for investigating interactions between the fluid and the dis- Stokes flow past a body of arbitrary shape satisfying slip- persed particles in the fluid. In this two-way coupling nu- stick boundary conditions is discussed and an analytic but merical scheme, the fluid velocity field affects the motion of approximate solution is obtained in the entire domain. The the particles while the surface forces generated by the par- method is illustrated in the case of a singularity driven flow ticles affecting the fluid. The solver utilizes FFT to handle due to a Stokeslet outside an ellipsoid. The effect of the Fourier expansions in two directions and Chebychev poly- slip-parameter on physical quantities like drag as well as nomial expansion in the third. In order to handle insta- the convergence of the method for different values of the bilities of the fluid motion, as a semi-implicit time step- slip-parameter are discussed. ping scheme, Modified Adams-Bashforth/Crank-Nicolson is used. The method is demonstrated on two problems: (i) Sri Padmavati Bhavaraju rise of bubbles in water columns; (ii) motion of particles in Department of Mathematics & Statistics, Benard cells. University of Hyderabad, Hyderabad - 500046, India [email protected] Ilker Tari METU [email protected] CP23 Computing Nonlinear Waves of the Korteweg-De Sibel Tari Vries and Korteweg-De Vries-Burgers Equations in Middle East Technical University Invariant Structures [email protected] Periodic and aperiodic travelling waves of the Korteweg- de Vries and Korteweg-de Vries-Burgers equations are re- CP23 duced to canonical dynamic equations for pulsations and oscillations of conservative and dissipative systems in a cu- Effectiveness of Stiffly-Stable Projection Schemes bic potential well. By integrated computing, the canon- for Smooth Particle Hydrodynamics Simulations of ical dynamic equations for the conservative and dissipa- Transient Viscous Flows tive systems are resolved in invariant trigonometric and Smoothed particle hydrodynamics is a meshless colloca- exponential-trigonometric structures, respectively. Com- tion method that provides a natural platform for solving parisons of symbolic-numeric solutions with those com- the Navier-Stokes equations in a Lagrangian framework. puted by the Fehlberg fourth-fifth order Runge-Kutta While the method remains an attractive choice for simu- AN13 Abstracts 27

lating viscous flows, the standard numerical scheme incurs [email protected] a severe timestep restriction due to the use of an artificial compressibility assumption and explicit timestepping. In this work we implement a stiffly-stable projection scheme CP24 and demonstrate its ability to efficiently achieve more ac- Modeling Sustainability of Biological Systems curate results for transient flows at low Reynolds number. The possibility of interacting with biological systems en- Nathaniel Trask, Martin Maxey ables us to design adequate strategies for their use and Brown University preservation ranging from ecosystems to synthetic biologi- Department of applied mathematics cal constructions. In this talk we first provide an overview nathaniel [email protected], martin [email protected] of the possible applications of control theory to the design of sustainable policies at several space-time scales and then we focus on specific aspects of the corresponding mathe- CP24 matical modeling. We present a more technical example A Discrete Model of Denitrification in Pseu- related to synthetic biology. domonas Aeruginosa Luis J. Martinez, Pablo Padilla Pseudomonas aeruginosa is a metabolically flexible mem- IIMAS ber of the Gammaproteobacteria. Under anaerobic condi- UNIVERSIDAD NACIONAL AUTONOMA DE tions and the presence of nitrate, Pseudomonas aeruginosa MEXICO can perform (complete) denitrification, a respiratory pro- [email protected], [email protected] cess of dissimilatory nitrate reduction to nitrogen gas via nitrite, nitric oxide and nitrous oxide. To our knowledge, our model is the first mathematical model of denitrifica- CP24 tion for this bacterium. This study aims to capture the Modeling the Cell Biology of the Heat Shock Re- effect of phosphate on a denitrification network of Pseu- sponse of Barley Aleurone Cells domonas aeruginosa in order to shed light on the reason of greenhouse gas nitrous oxide accumulation during oxygen When heat shocked, plant cells distribute their energy to depletion in Lake Erie. make a very different set of proteins than when at normal temperatures. When barley is heat shocked, the cells’ pro- Seda Arat duction of α-amylase and other secretory proteins is largely Virginia Tech reduced and a set of heat shock proteins that repair dam- [email protected] aged proteins is produced. The purpose of this project is to create and test a mathematical model to analyze what Michael Schalis, George Bullerjahn elements have influenced α-amylase production. Our cur- Bowling Green State University rent model and simulations are able to capture the impact [email protected], [email protected] of different temperature regimes and levels of fluidity on α-amylase synthesis and are in good qualitative agreement Reinhard Laubenbacher with the experimental data. Virginia Bioinformatics Hoa Nguyen Institute Trinity University [email protected] [email protected]

CP24 CP25 Models for Comparing Chikungunya and Dengue Numerical Validation of Data Assimilation Codes Chikungunya is a re-emerging mosquito-borne infectious Generated by the Yao Software disease that is spreading rapidly across Africa and Asia. The YAO software is a general framework used to gener- Two common mosquito species, Aedes aegypti and Aedes ate codes that implement a numerical model. Furthermore albopictus, are competent vectors for chikungunya virus. YAO provides a toolbox to conduct assimilation data ex- We design and analyze an ordinary differential equation periments. The CADNA library estimates numerical accu- model with mosquito dynamics for the spread of both racy of a computation. It was integrated to YAO in order chikungunya and dengue. The model is parameterized us- to provide automatically a numerical validation of coming current literature, data, and lab experiments. We show plete assimilation processes. Several applications regarding that dengue and chikungunya exhibit different disease dy- oceanic and hydrographic modeling were generated using namics, resulting in different risk profiles and providing YAO-CADNA and were numerically validated. areas of focus for greatest effect in controlling the spread of chikungunya. Julien Brajard LOCEAN, UPMC Carrie A. Manore,SenXu,KyleS.Hickmann Paris VI university Tulane University [email protected] [email protected], [email protected], [email protected] Pei Li, Fabienne jezequel LIP6. UPMC, Paris VI university Helen Wearing [email protected], [email protected] University of New Mexico [email protected] Hector-Simon benavides, Sylvie thiria LOCEAN, UPMC, Paris VI university Mac Hyman [email protected], [email protected] Tulane University 28 AN13 Abstracts

built to leverage high-performance parallel computing, and has been used in calculations of materials failure under hy- pervelocity impact, elasto-plastic failure in structures un- CP25 der seismic ground acceleration, and risk in financial port- Uncertainty Quantification Based on Joint folios. Response-Excitation Pdf Equations Michael McKerns We study the evolution equation of joint excitation- California Institute of Technology response PDF (REPDF) which generalizes the existing [email protected] PDF equations and enables us to compute the PDF for any stochastic dynamical system and first order PDEs Houman Owhadi driven by colored noise. An efficient numerical method Applied Mathematics is developed for the evolution equation by using the adap- Caltech tive discontinuous Galerkin (DG) method for the response [email protected] space and probabilistic collocation method (PCM) combined with sparse grid for the excitation space. The effec- Tim Sullivan tiveness of the proposed new algorithm is demonstrated in University of Warwick two prototype applications dealing with randomly forced [email protected] nonlinear oscillators and the results are compared with kernel density estimation based on Monte Carlo simulation and the solution to the effective Fokker-Planck equa- Alta Fang tion. Also, stochastic inviscid Burgers equation is studied Princeton University to investigate the PDF when discontinuity occurs in the [email protected] physical domain. Michael Aivazis Heyrim Cho California Institute of Technology Brown University [email protected] Providence, RI heyrim [email protected] CP25 Daniele Venturi Multi-Scale Modeling with Generalized Dynamic Division of Applied Mathematics Discrepancy Brown University daniele [email protected] Bayesian calibration can be an effective tool for multi-scale modeling, since it enables a quantification of uncertainty created through scale-bridging through the application of George E. Karniadakis either experimental or high-fidelity simulator data. In or- Brown University der to realize this promise in dynamic systems, small-scale Division of Applied Mathematics models – such as those governing transient chemical ki- george [email protected] netics – require dynamic approaches to model discrepancy. But a traditional approach to discrepancy must incorporate CP25 dependence on a functional input space in order to capture the dynamic character of a model, which is often imprac- Separating Intrinsic and Parametric Uncertainty in tical. A new approach to dynamic discrepancy is intro- Stochastic Simulations

We present a method of UQ for stochastic simulations. For duced. Strictly speaking, the approach is intrusive, but is these types of simulations random events cause quantities broadly applicable to a number of dynamic problems. The of interest (QOI) to vary over a wide range of values for dynamic discrepancy approach reduces the dependency of fixed input parameters. Further uncertainty is introduced the discrepancy function to a concurrent scalar value of from imprecisely known parameters. We discuss a novel time-dependent inputs. Stochastic differential equations statistical surrogate model that combines multiple emula- engendered by the approach are solved through the use of tion strategies to represent intrinsic and parametric vari- the Bayesian Smoothing Spline Analysis of Variance (BSS- ation separately. QOI samples from the simulation and ANOVA) formalism. This approach to discrepancy leads from the statistical surrogate model are combined to de- to portability, and to an attendant iterative approach to scribe the uncertainty in the model’s prediction. scale-bridging. The methods are demonstrated in the context of problems in chemical process modeling. Kyle S. Hickmann Tulane University David S. Mebane [email protected] Department of Mechanical and Aerospace Engineering West Virginia University [email protected] CP25 mystic: a Framework for Uncertainty Quantification Sham Bhat and Predictive Science Statistical Sciences Group Los Alamos National Laboratory We have built a robust software framework (mystic)that [email protected] lowers the barrier to solving high-dimensional and highly- constrained global optimization problems. mystic provides Curtis Storlie tools for rigorously constraining design space, including Los Alamos National Laboratory suites of standard and statistical constraints, discrete and [email protected] symbolic math, and uncertainty quantification. mystic is AN13 Abstracts 29

MS1 Department of Mathematics Title Not Available at Time of Publication [email protected] Abstract not available at time of publication. MS2 Ming Gu Coursework and Programs in Applied and Compu- University of California, Berkeley tational Mathematics at the University Level Mathematics Department [email protected] Abstract not available at time of publication. Jeff Humpherys MS1 Department of Mathematics Fast Direct Solvers for Integral Equations Brigham Young University jeff[email protected] The last several years have seen great progress in the development of linear complexity direct solvers for the large sparse linear systems arising upon finite element and fi- MS2 nite difference discretizations of elliptic PDEs such as the Examples of Good Practice in Mathematical Mod- Laplace and Helmholtz equations. This talk will describe eling Education recent work on direct solvers for the dense linear systems associated with integral equation formulations. Recently, Abstract not available at time of publication. linear complexity algorithms with high practical efficiency have been developed for variable coefficient problems in the Rachel Levy plane. We will describe these techniques, and will show Harvey Mudd College tentative results for how they can be extended to handle [email protected] boundary integral equations in 3D. Gunnar Martinsson MS2 Univ. of Colorado at Boulder Coursework in Applied and Computational Math- [email protected] ematics at the High School Level Last Fall, the working group discussions on possible ‘Intro MS1 to STEM’ coursework at the high school level were wide- Randomized Sparse Direct Solvers with Applica- ranging, thoughtful, and provocative. This portion of the tions mini-symposium will provide an overview of our critical questions, discuss data likely needed to address the ques- We present some fast randomized structured direct solvers tions, make recommendations for next tasks (including re- for large sparse linear systems, including the matrix-free search topics), and explore links with both college readi- variations. The work involves new flexible randomized ness and undergraduate curriculum issues. Even within methods for exploiting structures in large matrix compu- our small working group, many different viewpoints were tations, so as to provide both higher efficiency and bet- expressed about the presence, success, and appropriate role ter applicability than some existing structured methods. of applied and computational mathematical sciences within New efficient ways are proposed to conveniently perform the K-12 educational framework. Please join us to explore various complex operations which are difficult in standard these ideas further in a constructive conversation. rank-structured solvers. Nearly O(n) complexity for various situations will be shown. Extension of the techniques Katherine Socha to least squares, eigenvalue problems, and sparse selected Math for America inversion will also be given. We also study the following is- [email protected] sues: 1. Develop matrix-free structured solvers and update a structured factorization when few matrix entries change. MS2 2. Relaxed rank requirements in structured solvers, especially for 3D problems. 3. Develop structured precondi- SIAM-NSF Workshop on Modeling Across the tioners for problems without significant rank structures, Curriculum: Introduction and analyze the effectiveness. In this talk, an introduction to the SIAM-NSF Workshop Jianlin Xia on Modeling across the Curriculum (August, 2012) will be Department of Mathematics presented. The meeting proposal pre-dated but responded Purdue University to teh PCAST ”Engage to Excel” report and its call for one [email protected] million new college STEM graduates in the next decade. This talk will provide an overview of the workshop and some of the more recent developments. Yuanzhe Xi Purdue University Peter R. Turner [email protected] Clarkson University School of Arts & Sciences [email protected] MS1 Title Not Available at Time of Publication MS3 Abstract not available at time of publication. An Efficient Algorithm for Simulating the Evolu- Lexing Ying University of Texas 30 AN13 Abstracts

tion of Multiple Elastically Stressed Precipitates Angelique Stephanou Laboratoire TIMC-IMAG In this talk, we present a space-time rescaling scheme for [email protected] computing the long time evolution of multiple precipitates in an elastically stressed medium. The scheme is motived by a recent paper (Li, Lowengrub and Leo, J. Comput. MS3 Phys., 335 (2007), 554) for a single particle case. The algo- Modelling Cell Motility with the Evolving Surface rithm is second order accurate in time, spectrally accurate Finite Element Method in space and enables one to simulate the long time evolution of precipitates. The method relies on a space-time We propose a framework for the modelling and simulation rescaling scheme to expedite the numerical simulation, and of cell motility. The membrane dynamics is governed by also employs a parallel adaptive treecode to speed up the a geometric evolution law. For cell polarisation we pos- GMRES solver. We will present numerical results. tulate a reaction-diffusion system for species on the membrane. Protrusion is achieved by back-coupling these sur- Amlan Barua face quantities to the geometric equation. The numerical Illinois Institute of Technology method is based on surface finite elements for both the [email protected] geometric and the surface equations. We include simulations of pseudopod-driven chemotaxis and the motion of Shuwang Li keratocytes. Department of Applied Mathematics Illinois Institute of Technology Chandrashekar Venkataraman [email protected] University of Warwick [email protected] Hualong Feng, Xiaofan Li Illinois Institute of Technology Charles Elliott [email protected], [email protected] Mathematics Institute University of Warwick John Lowengrub [email protected] University of California, Irvine [email protected] Bjorn Stinner University of Warwick [email protected] MS3 Mathematical Modelling and Numerical Simula- tions of Actin Dynamics in the Eukaryotic Cell MS4 Adaptive Least-Squares Methods for Viscoelastic The aim of this talk is to present recent results on the study Flows of cell deformation and cell movement by considering both the mechanical and biochemical properties of the cortical This talk concerns solutions of viscoelastic flow problems network of actin filaments and its concentration. Actin is a by adaptive least-squares finite element methods. Model polymer that can exist either in filamentous form (F-actin) problems considered are the flow past a planar channel and or in monometric form (G-actin) and the filamentous form a 4- to-1 contraction problems. In this talk, algorithms is arranged in a paired helix of two protofilaments. By will be proposed to construct optimal adaptive mesh re- assuming that cell deformations are a result of the corti- distribution to resolve the high gradient region, the corner cal actin dynamics in the cell cytoskeleton, we consider a singularities and formation of vortices in the model prob- continuum mathematical model that couples the mechan- lems. Numerical results of both Newtonian (Stokes) and ics of the network of actin filaments with its bio-chemical Oldroyd-B model equations are presented. dynamics. Numerical treatment of the model is carried out using the moving grid finite element method. Further- Tsu-Fen Chen more, by assuming slow deformations of the cell, we use Department of Mathematics linear stability theory to validate the numerical simulation National Chung Cheng University results close to bifurcation points. Far from bifurcation [email protected] points, we show that the mathematical model is able to describe the complex cell deformations typically observed MS4 in experimental results. Our numerical results illustrate cell expansion, cell contraction, cell translation and cell re- Can a Defect Correction Method Be Viewed As a location as well as cell protrusions. In all these results, Turbulence Model? the contractile tonicity formed by the association of actin A method for resolving turbulent flows is sought, which filaments to the myosin II motor proteins is identified as a is faster than the existing approaches, and competitive in key bifurcation parameter. terms of stability and accuracy. We introduce a Defect Cor- Anotida Madzvamuse rection Method (DCM) for approximating the averaged so- University of Sussex lution of (turbulent) Navier-Stokes equations, and we com- Dept of Mathematics pare it against the Approximate Deconvolution Model of [email protected] turbulence. We prove stability of the method, verify its accuracy numerically, and demonstrate the superiority of DCM in terms of CPU time. Uduak George University of Wisconsin Alexander Labovsky [email protected] Department of Mathematical Sciences Michigan Technological University AN13 Abstracts 31

[email protected] Yangfeng Su Fudan University, China [email protected] MS4 Least Squares Approach for Optimization Based Ding Lu Domain Decomposition Fudan University, China and University of California, Davis We consider solution algorithms for multi-physics prob- [email protected] lems, where a coupled system is formulated as an optimal control problem for domain decomposition. A Neumann type control is introduced to enforce a boundary condition MS5 on the interface of subdomains, and the control problem Nonsymmetric Multigrid Preconditioning for Con- is reformulated as a least squares problem for which the jugate Gradient Methods Gauss-Newton algorithm is considered. Two examples will be presented for the approach; the Stokes-Darcy problem We numerically analyze the possibility of turning off post- and a fluid structure interaction problem. Numerical re- smoothing (relaxation) in geometric multigrid when used sults are presented to validate convergence and accuracy as a preconditioner in conjugate gradient linear and eigen- of the method. value solvers for the 3D Laplacian. The geometric Semi- coarsening Multigrid (SMG) method is provided by the Hyesuk Lee hypre parallel software package. We solve linear sys- Clemson University tems using two variants (standard and flexible) of the pre- Dep. of Mathematical Sciences conditioned conjugate gradient (PCG) and preconditioned [email protected] steepest descent (PSD) methods. The eigenvalue problems are solved using the locally optimal block preconditioned MS4 conjugate gradient (LOBPCG) method available in hypre through BLOPEX software. We observe that turning off On Robust Discretizations for Coupled Flow Prob- the post-smoothing in SMG dramatically slows down the lems standard PCG-SMG. For the flexible PCG and LOBPCG, Robust discretization of coupled flow problems like our numerical results show that post-smoothing can be Rayleigh-Benard convection or the Nernst-Planck-Poisson- avoided, resulting in overall acceleration, due to the high Stokes system in micro fluidics remains to be a challenging costs of smoothing and relatively insignificant decrease in problem. Due to the multi-physics character of such flow convergence speed. We numerically demonstrate for linear processes, discretizations for the full nonlinearly coupled systems that PSD-SMG converges nearly identical to flexi- system have to respect many different qualitative prop- ble PCG-SMG if SMG post-smoothing is off. A theoretical erties of the underlying physical processes at the same justification is provided. [http://arxiv.org/abs/1212.6680] time, e.g., discrete maximum principles for temperature or species concentrations and discrete mass conservation. Henricus M. Bouwmeester This talk will focus on the problem of poor mass conser- Department of Mathematics vation in coupled flow problems. Poor mass conservation University of Colorado at Denver arises due to the impact of large irrotational forcings (in [email protected] the sense of Helmholtz-Hodge decomposition) in the momentum equations, and reflects a lack of L2-orthogonality of (only) discretely divergence-free and irrotational vector Andrew Dougherty fields. UC Denver [email protected] Alexander Linke Weierstrass Institute for Applied Analysis and Stochastics Andrew Knyazev Germany Mitsubishi Electric Research Laboratories [email protected] CU-Denver [email protected] MS5 Recent Development of the Nonlinear QR Algo- MS5 rithm for Genuine Nonlinear Eigenvalue Problems Structured Backward Relative Error Bounds for Eigenvalues of Tridiagonal Matrices In this talk, we first present the algorithmic improvements of the nonlinear QR algorithm of Kublanovskaya for solv- The variability of the sensitivity of eigenvalues of tridiag- ing genuine nonlinear eigenvalue problems. We show how onals is illustrated in pictures. A few relative condition to avoid the full rank-revealing QR decomposition to re- numbers that respect the sparsity structure are developed duce computation and communication costs in the inner and put to use. Finally a way is shown to compute, in QR loop, and how to accelerate the rate of the conver- O(n) operations, a tight bound on the smallest maximal gence in the presence of multiple eigenvalues. In addition, relative change to any parameter that makes a computed we will discuss a number of numerical treatments in the eigentriple exact. This is the most desirable accuracy mea- implementation of the nonlinear QR algorithm towards a sure that is warranted by the problem and complements blackbox solver for small to medium size genuine nonlinear the appropriate condition number. eigenvalue problems. Beresford N. Parlett Zhaojun Bai University of California Departments of Computer Science and Mathematics Department of Mathematics University of California, Davis [email protected] [email protected] 32 AN13 Abstracts

Froilan Dopico compressible Fluids Subject to Implicitly Consti- Department of Mathematics tuted Boundary Conditions Universidad Carlos III de Madrid, Spain [email protected] We study flows of incompressible fluids in which the devi- atoric part of the Cauchy stress and the symmetric part of Carla Ferreira the velocity gradient are related through an implicit equa- Department of Computer Science tion. Although we restrict ourselves to responses charac- Universidade Nova de Lisboa, Portugal terized by a maximal monotone graph, the structure is rich [email protected] enough to include power-law type fluids, stress power-law fluids, Bingham and Herschel-Bulkley fluids, etc. We are interested in the development of (large-data) existence the- MS5 ory for internal flows of such fluids subject to various type Bounds for the Rayleigh Quotient and the Spec- of boundary conditions. We show, in particular, that the trum of Self-Adjoint Operators implicit relations on the boundary can have a significant impact on the development of the mathematical theory If x is an eigenvector of a self-adjoint bounded operator even for the Navier-Stokes equations and its generalization. A in a Hilbert space, then the Rayleigh quotient (RQ) of the vector x, denoted by ρ(x), is an exact eigenvalue of A. There are three traditional kinds of bounds for eigenvalue Josef Malek errors: a priori bounds via the angle between vectors; a Charles University, Prague posteriori bounds via the norm of the vetor residual; mixed Mathematical Institute type bounds using both the angle and the norm of the [email protected]ff.cuni.cz residual. We propose a unifying approach to prove known bounds of the spectrum, analyze their sharpness, and de- MS6 rive new sharper bounds. The proof approach is based on novel RQ vector perturbation identities. On Spatial Distribution of the Discretization and Algebraic Error in Numerical Solution of Partial Peizhen Zhu Differential Equations University of Colorado, Denver [email protected] In the adaptive numerical solution of partial differential equations, local mesh refinement is used together with a posteriori error analysis in order to equllibrate the dis- Merico Argentati cretization error disctribution over the domain. Since the University of Colorado Denver discretized algebraic problems are not solve exactly,anat- [email protected] ural question is whether the disctribution of the algebraic error is analogous to the distribution of the discretization Andrew Knyazev error. We demonstrate that this may not hold. On the Mitsubishi Electric Research Laboratories contrary, the algebraic error can significantly dominate the CU-Denver total error in some part of the domain. [email protected] Jan Papez Charles University in Prague MS6 Dept Numerical Mathematics Finite Element Approximation of Steady Flows of [email protected] Incompressible Fluids with Implicit Power-Law- Like Rheology Zdenek Strakos Institute of Computer Science We present the analysis of finite element approximations Academy of Sciences of the Czech Republic of implicit power-law-like models for viscous incompress- [email protected]ff.cuni.cz or [email protected] ible fluids. In contrast to the recent existence proof in [1], a practical convergent finite element method needs to perform the different limits simultaneously. This introduces MS6 several serious difficulties: Fluids and Solids Described by Implicit Constitu- • For common stable finite element pairs the velocity tive Theories approximations are typically not exactly divergence free. In this talk I will discuss implicit constitutive theories to • We require a finite element counterpart of the Acerbi- describe the response of fluids and solids. Such models Fusco Lipschitz truncation of Sobolev functions. seem most appropriate for describing fluids whose material moduli depend on the pressure and shear rate. Im- [1]M.Bul´ıˇcek, P. Gwiazda, J. Málek, and A. Swierczewska-´ plicit theories for elastic solids include as special subclasses Gwiazda, On steady flows of incompressible fluids with im- Cauchy and Green elastic solids and thus provide a much plicit power-law-like rheology, Adv. Calc. Var. 2 (2009), larger class of models within which one can describe the no. 2, 109–136. elastic response of solids. Moreover, the linearization of such models leads to models that are well suited to de- Christian Kreuzer scribe the fracturing of elastic solids. Ruhr University of Bochum Faculty of Mathematics K. R. Rajagopal [email protected] Texas A&M University [email protected] MS6 On Unsteady Flows of Implicitly Constituted In- AN13 Abstracts 33

MS9 deal with the ill-conditioning that is often associated with Some Lessons I Learned radial basis function methods. Since then, the method has been adapted to more general settings by several other au- Abstract not available at time of publication. thors. In particular, in [Fasshauer & McCourt, Stable evaluation of Gaussian RBF interpolants, SIAM J. Sci. Com- Anne Gelb put. 34 (2012), A737–A762] the method was formulated Mathematics Department within the context of eigenfunction expansions of the (pos- Arizona State University itive definite) kernels of associated Hilbert-Schmidt opera- [email protected] tors. In this talk we will introduce a matrix factorization of the from K = ΨΛΦT of the RBF interpolation matrix K in terms of matrices generated by the orthogonal eigen- MS9 functions. This Hilbert-Schmidt SVD is not a traditional Adventures at Convergence of the Mathematical singular value decomposition of K, but shares a number and Biological Sciences of properties with the SVD. Most importantly, the matrix factors are obtained without ever having to form the ill- Onwards and upwards. In this talk, I will discuss my mean- conditioned matrix K. We will use the Hilbert-Schmidt dering career path. This will include a discussion of finding SVD to present a particularly simple implementation of the right graduate program on the second try and finding the RBF-QR method, and also to obtain MLE and GCV an academic with the right balance in a tough job market. estimates of the “optimal” RBF shape parameter within Throughout the journey, experiences and challenges will be the RBF-QR framework. This is joint work with Mike Mc- highlighted. Court. Sarah D. Olson Gregory Fasshauer Worcester Polytechnic Institute Illinois Institute of Technology [email protected] [email protected]

MS9 MS10 ExperiencesAsaProgramOfficer High-order Vector Decomposition with Radial Ba- Abstract not available at time of publication. sis Functions Karen I. Pao The Helmholtz-Hodge decomposition guarantees the nat- Office of Science ural decomposition of any smooth vector field into cer- US Department of Energy tain divergence-free, curl-free and harmonic components. [email protected] This decomposition is fundamental to the analysis of vector fields, especially those arising in electromagnetic or computational fluid dynamics. We describe a meshless kernel MS10 method, based on radial basis functions, that leads to a On a New Stable Basis for Rbf Interpolation high-order approximation of the decomposition on a large class of bounded domains. Error estimates will be pre- It is well-known that RBF interpolants suffer of bad con- sented, and some numerical examples will be given. ditioning if the basis of translates is used. The new basis arises from a weighted singular value decomposition of the Edward Fuselier kernel matrix. The basis is related to a discretization of High Point University Department of Mathematics and Computer Science the compact operator TΦ :→, [email protected]

TΦ[f](x)= Φ(x, y)f(y)dy ∀x ∈ Ω Ω MS10 A Comparison Between the RBF-Finite Difference and provides a connection with the continuous basis aris- and the RBF-Partition of Unity Methods for Shal- ing from an eigen-decomposition of TΦ. Using the eigenval- low Water Flows on the Sphere ues of TΦ, we provide convergence estimates and stability bounds for interpolation and discrete least-squares approx- The shallow water wave equations are an idealized test-bed imation. for the horizontal dynamics (known as the dynamical core) of all 3D climate model developments. We present two Stefano De Marchi meshfree, high-order, computationally efficient methods for University of Padova (Italy) these equations that are both based on radial basis func- [email protected] tions (RBFs). The first is the relatively new RBF-finite difference method and the second is the new RBF-partition Gabriele Santin of unity method. We compare both methods in terms of University of Padova accuracy, efficiency, and scalability for several well-known [email protected] test cases.

Grady B. Wright MS10 Department of Mathematics The Hilbert-Schmidt SVD: An Alternative Inter- Boise State University, Boise ID pretation for the RBF-QR Method [email protected] The RBF-QR method was introduced in [Fornberg & Piret, A stable algorithm for ﬂat radial basis functions on a sphere, SIAM J. Sci. Comp. 30 (2007), 60–80] as a way to 34 AN13 Abstracts

MS11 to estimate the parameters in the stochastic model. This Mimetic Curvilinear Environmental Model: Har- parameterization includes three stochastic components: a nessing the Power of Gpu’s stochastic trigger that turns the precipitation state on and off (a Markov jump process), and stochastic closures which Castillo-Grone Mimetic (CGM) difference operators have represent variability in precipitation and moisture conver- shown to perform superior in many fields that deals with gence/divergence. numerical solution of partial differential equations (PDEs). Majority of the problems in environmental sciences, includ- Kimberly Leung ing large scale fluid flow in the oceans and Atmosphere, San Diego State University canbeexpressedbyPDEsusingdivergenceandgradient [email protected] operator. In this talk a new numerical model, capable of simulating geophysical fluid, based on CGM difference op- Aneesh Subramanian erators is introduced. Furthermore, this model harnesses University of California, San Diego, USA the power of the many cores available on the Graphics Pro- [email protected] cessing Units (GPUs). Hence, the model implementation on the GPUs is discussed and some performance analysis Guang Zhang is provided. Scripps Institution of Oceanography [email protected] Mohammad Abouali, Jose Castillo Computational Science Research Center San Diego State University Samuel S. Shen [email protected], [email protected] San Diego State University [email protected]

MS11 MS11 Data Assimilation for Hydrodynamical Modeling of San Quintin Bay, Ensenada, B.C., Mexico Application of a Shallow Water Hydrodynamics Model to Study Circulation Patterns in Lake Va- San Quintin Bay (SQB), B.C. forms an interesting ecosys- lencia, Venezuela tem in which aquaculture has been developed for more than 30 years. The most important biological process for culti- A numerical model for simulation of shallow water flows in vating organisms is the reproductive cycle which is princi- any water body is presented. It uses a MacCormack-TVD pally regulated by the amount and quality of the food as numerical scheme to solve simultaneously the continuity well as by temperature and salinity. Furthermore, the hy- and momentum equations in the Saint Venants system of drodynamic state has to be known with high accuracy for equations. The model allows calculation of tides and cur- efficient ecological monitoring of the bay. A regional nu- rents generated by wind and it was applied to Lake Valen- merical model using Delft3d is presented to provide infor- cia, Venezuela. A set of wind-driven circulations patterns mation on the water velocities and water elevation around were generated from field data. Although the use of shallow SQB. In this study data assimilation aims to incorporate water models is fairly standard in the study of lakes circula- measured observation into a dynamical system model in tion, its application to the Lake Valencia is new. Therefore, order to produce accurate estimates of all the current state the steady circulation patterns developed in this numerical variables of the system. To pursue this goal, the open- study represent an original contribution. source software environment OpenDA for sensitivity anal- Juan Guevara ysis and simultaneous parameter optimization is used. The Universidad Central de Venezuela purpose of this study is to give short-term operational pre- [email protected] dictions of the hydrodynamical state of the SQB. A limited set of coastal measurement observed data can be used to explore how filtering methods can be used to combine Maira Valera-López,JoséLeón model output with observed data. Facultad de Ciencias, Universidad Central de Venezuela [email protected], [email protected] Mariangel Garcia INTEVEP Reinaldo Garc´ıa, Ivan Saavedra Venezueal Facultad de Ingeniera, Universidad Central de Venezuela [email protected] rgarcia@fiu.edu, [email protected]

MS11 MS12 Stochastic Diﬀerential Equation Modeling of Pre- Numerical Optimization of Laplacian Eigenvalues cipitation in Convection of 4D Domains Recent studies have used statistical measures inferred In this talk we consider the numerical solution of shape from observational data to characterize the transition to optimization problems involving Laplacian eigenvalues of deep convection at a critical value of column water vapor 4D domains. The eigenvalue problems are solved by the (CWV), around which there is a sharp transition in mean Method of Fundamental Solutions with a particular choice precipitation and a peak in precipitation variance. How- for the location of the source points. ever, the parameters used in these variable functions are derived from a combination of empirical and theoretical es- Pedro R. Antunes timates. In this study, the functional relationships between GFM - University of Lisbon the precipitation, column water vapor and the transition Lusophone University of Humanities and Technologies probability to strong convection are estimated, and simu- [email protected] lation statistics are analyzed with respect to observations AN13 Abstracts 35

MS12 MS13 Minimal Convex Combinations of Sequential On Integral Kernels with Applications to Shape Laplace-Dirichlet Eigenvalues Problems In this talk, the shape optimization problem where the ob- A shape representation is proposed based on the integral jective function is a convex combination of three sequential kernels and a variational framework is presented for the Laplace-Dirichlet eigenvalues is presented. Our computa- construction of diffeomorphisms that establish meaning- tions based on the level set approach and the gradient de- ful correspondences between images, in that they preserve cent method not only reproduce previous results on signal the local geometry of singularities such as region bound- eigenvalue optimization but also extend these results to aries. At the same time, the shape representation allows sequential eigenvalue problems. Several properties of min- enforcing shape information locally in determining such re- imizers are studied computationally, including uniqueness, gion boundaries. Our representation is based on a kernel connectivity, symmetry, and eigenvalue multiplicity. descriptor that characterises local shape. This shape descriptor is robust to noise and forms a scale-space in which Chiu-Yen Kao an appropriate scale can be chosen depending on the size Claremont McKenna College of features of interest in the scene. In order to preserve [email protected] local shape during the matching procedure, we introduce a novel constraint to traditional approaches to estimate dif- Braxton Osting feomorphic deformations, and enforce it in a variational University of California, Los Angeles framework. [email protected] Byung-Woo Hong Chung-Ang University, Korea MS12 [email protected] Spectral Shape Analysis with Applications in Med- ical Imaging Stefano Soatto UCLA Complex geometric objects have gained much importance [email protected] in many applied fields. Methods to compare and analyze shape are essential to process the vast amounts of available geometric data. This talk will give an overview on spectral MS13 methods in shape analysis. Eigenvalues and eigenfunctions Schrdinger Distance Transforms, Gradient Density of the Laplace-Beltrami operator yield powerful tools to de- Estimation and Application to Vision Problems scribe and analyze shape. Due to their isometry invariance they are optimally suited to deal with non-rigid shapes Methods based on Hamilton-Jacobi and classical mechanics often encountered in nature, such as a body in different formulations have proliferated over the past thirty years. postures. The normed beginning sequence of the spectrum In contrast, methods based on Schrdinger and quantum (’ShapeDNA’) can be used as a global signature for shape mechanics formulations are hard to find. We redress this matching, while the eigenfunctions and their topological imbalance by developing a Schrdinger distance transform analysis can be applied for shape registration, segmenta- (SDT) based on solutions to a linear differential equation. tion and local shape analysis. Examples of applications Next, we show that the squared magnitude of the Fourier such as database retrieval of near isometric shapes, statis- transform of the SDT, when appropriately normalized, is tical shape analysis of subcortical structures of the human an approximation to the distance transform gradient den- brain and hierarchical segmentation of articulated shapes sity function. will be presented. Anand Rangarajan Martin Reuter University of Florida MIT-CSAIL Departments of Computer Information Science and [email protected] Engineering [email protected]fl.edu

MS12 A Natural Extension of Laplacian Eigenfunctions MS13 from Interior to Exterior and its Application The Implicit Closest Point Method for the Numer- ical Solution of Partial Differential Equations on In 2008, we proposed a method to compute eigenfunctions Surfaces of Laplacian defined on a domain of general shape (satisfying some nonlocal boundary condition) by diagonalizing Many applications in the natural and applied sciences re- an integral operator commuting with the Laplacian. These quire the solutions of partial differential equations (PDEs) eigenfunctions can be harmonically extended to the exte- on surfaces or more general manifolds. The Closest Point rior of the original domain by the Nyström extension. In Method is a simple and accurate embedding method for this talk, we discuss their properties, the relationship with numerically approximating PDEs on rather general smooth the so-called Krein–von Neumann self-adjoint extension of surfaces. In this talk, we describe the implicit Closest Point unbounded symmetric operators, and certain applications Method for surface PDEs. Key features of the method are including image extrapolation. that it maintains the order of accuracy of the discretization of the underlying embedding PDE, it works on sharply de- Naoki Saito fined bands without degrading the accuracy of the method, Department of Mathematics and it applies to general smooth surfaces. We demonstrate University of California, Davis the method on a variety of problems including the Laplace- [email protected] Beltrami eigenvalue eigenvector problem, and problems involving up to fourth order derivatives. This talk describes 36 AN13 Abstracts

joint work with Colin Macdonald and Jeremy Brandman. issues.

Steven Ruuth Richard Carter Mathematics GL-Group Simon Fraser University [email protected] [email protected]

Colin McDonald MS14 University of Oxford Computational Sciences for Oil and Gas Explo- [email protected] ration and Production Research Hydrocarbon exploration and production faces significant Jeremy Brandman computational challenges. Although information about Courant Institute of Mathematical Sciences the subsurface can be gleaned from seismic imaging, well New York Univeristy logging, and fluid production history, ultimately we need [email protected] modeling to evaluate and optimize the economic returns on oil and gas investments. Successful commercializa- MS13 tion of these modeling technologies requires integration of high-end computational sciences with software develop- Fluctuating Distance Fields with Connections to ment technologies. I illustrate with examples of ExxonMo- Modica-Mortola, Eigenspaces of Positive Definite bil proprietary modeling products. Operators and Discrete Algorithms Thomas C. Halsey Adding a non-local term, namely squared expectation, ExxonMobil Upstream Research Company to the Modica-Mortola length functional gives rise to a [email protected] surprising result: A diffuse field which is distance, curvature and part aware arises. In the discrete setting, this field is the projection of a shape indicator func- MS14 tion to the eigen-space of a rank one modification to Comfort Estimation and Incentive Design for En- the Laplace operator. Among its several properties, the ergy Efficiency field suggests an interesting skeleton model in the form: gross structure + deformable parts + residual. In this set The comfort of the occupants of a building depends on up, distinction between shape skeleton and the shape seg- many factors including metabolic rates, clothing, air tem- mentation fades away. The talk focuses on discrete prob- perature, mean radiant temperature, air velocity, humid- lems. ity, lighting and noise. Here, we describe a methodology to provide incentives to the occupants of a building in or- Sibel Tari der to be more energy efficient. We develop a method to Middle East Technical University estimate the comfort inter-relations among occupants by [email protected] combining various methodologies developed in social network analysis, statistics and economics. This technique MS14 is then used to design the incentives to encourage energy efficient behavior. Models and Products, Processes, and Measure- ments Alberto Speranzon United Technologies Research Center Inventions often involve the application of an idea from one [email protected] area to solve a problem in another. Applied math fits this paradigm in a number of ways. We will review some concrete examples from history and current experience show- Tuhin Sahai ing successful implementation. One limitation in the past United Technologies was the limit of practical computation; some mathematical [email protected] models or algorithms which once were impractical are now validated, vindicated, and a part of everyday life. Andrzej Banaszuk United Technologies Research Center John Abbott [email protected] Corning Inc. [email protected] MS14 Mathematics in the Development of Biomarkers MS14 and Therapeutics The Messy Art of Balancing the Elegant and the Practical in Industrial Software We describe examples of the application of mathematics to the development of therapeutics and biomarkers. A We review common issues in transitioning mathematical biomarker is defined as an indicator of a biological state. software from research grade projects into products that It is a characteristic that is objectively measured and eval- are used and useful, as gleaned from our work in the uated as an indicator of normal pharmacologic responses pipeline industry. Mathematical elegance can equate with to a therapeutic intervention. practicality, but only if it is unveiled at the right time under the right conditions. Mixed integer NLP algorithms Jeffrey Saltzman for compressor unit selection, nonserial dynamic program- AstraZeneca ming for network optimization, and algorithms for tran- Predictive Computational Sciences - RDI sient pipeline optimization can be used to illustrate these Jeff[email protected] AN13 Abstracts 37

MS15 faster computation of matchings on multicore machines. Investigating Graph Operations on Gpu Architec- tures Alex Pothen Purdue University GPUs have become an integral component in many areas Department of Computer Science of scientific computing , however, it is challenging to effi- [email protected] ciently map operations on graphs, representable as sparse matrices, to GPUs. The data-driven, highly irregular, low Arif Khan computational intensity and poor locality of many graph Purdue University operations requires algorithmic reformulation and imple- [email protected] mentation which mitigates the negative impact of these operations on the memory subsystem and utilize efficient par- Mahantesh Halappanavar allel primitives which are amenable to the SIMD machine Pacific Northwest National Laboratory model. Using breadth-first search (BFS) as the archetype [email protected] of graph operations on GPUs we will discuss maximal independent sets and graph partitioning. MS15 Luke Olson Computing Strongly Connected Components in UIUC Modern Architectures [email protected] Finding the strongly connected components of a directed Steven Dalton graph is a fundamental graph problem. For example, it University of Illinois at Urbana-Champaign is part of computing the block triangular form of a sparse [email protected] matrix. Tarjan’s algorithm is an efficient serial algorithm, but relies on depth-first search which is hard to parallelize. The parallel algorithm by Fleischer et al. uses divide-and- MS15 conquer, but has only been evaluated on distributed mem- Matrix Transversals on GPUs ory systems. We develop multithreaded versions and compare several variations of this algorithm. We design, implement, and evaluate algorithms for finding maximum cardinality matchinge in bipartite graphs on Sivasankaran Rajamanickam GPUs. To the best of our knowledge, ours is the first study Sandia National Laboratories that provides a GPU implementation and a through eval- [email protected] uation. Our motivating application lies in the solutions of sparse linear systems. We compare our algorithms with ex- Erik G. Boman isting sequential and multicore implementations on many Sandia National Labs, NM real-life matrices where in majority of the cases the GPU- Scalable Algorithms Dept. accelerated algorithm is much faster. [email protected] Mehmet Deveci THe Ohio State University MS16 [email protected] An Incremental SVD for Feature Extraction from Fluid Flow Kamer Kaya The Ohio State University The dynamic mode decomposition approximates the evo- Department of Biomedical Informatics lution operator of a physical system via a few dominant [email protected] modes. These modes are computed from experimental snapshots, without relying on the mathematical descrip- Bora Ucar tion of the system. However, these snapshots are expen- LIP, ENS-Lyon, France. sive to acquire and store, and the modes are expensive to [email protected] compute. We present a new algorithm, based on the Low- Rank Incremental SVD. This algorithm approximates the Umit V. Catalyurek dynamic modes in an online manner, with significant com- The Ohio State University putational savings. Department of Biomedical Informatics Christopher G. Baker [email protected] Oak Ridge National Laboratory [email protected] MS15 Parallel Algorithms for Matching Graphs on Mul- Lionel Mathelin ticore Computers LIMSI - CNRS [email protected] We discuss recent work on developing parallel algorithms for computing edge-weighted matchings in graphs on mul- Kyle Gallivan ticore computers. An algorithm that includes locally Florida State University heavy edges in the matching is known to provide a half- [email protected] approximation to the weighted matching problem. We evaluate this algorithm on multicore machines using a shared memory programming paradigm. We show that MS16 exploiting the structure of a bipartite graph can lead to RandomizedSVDMethodsinHyperspectralImag- 38 AN13 Abstracts

ing data via a symmetry preserving singular value decomposition (SPSVD). We present a randomized singular value decomposition (rSVD) method for the purposes of lossless compression, Mili Shah reconstruction, classiﬁcation, and target detection with hy- Loyola University Maryland perspectral (HSI) data. Recent work in low-rank matrix [email protected] approximations obtained from random projections suggests that these approximations are well suited for randomized Danny C. Sorensen dimensionality reduction. Numerical results on HSI will be Rice University presented. [email protected] Jennifer Erway Wake Forest University MS17 [email protected] Hierarchical Structure and Predictability of the Madden Julian Oscillation from Infrared Bright- Jiani Zhang ness Temperature Data Tufts University [email protected] The convection-coupled tropical atmospheric motions are highly nonlinear and multiscaled, and play a major role in Xiaofei Hu weather and climate predictability in both the tropics and Wake Forest University mid-latitudes. In this work, nonlinear Laplacian spectral [email protected] analysis (NLSA), a manifold generalization of PCA, is applied to extract spatiotemporal modes of variability in trop- Qiang Zhang ical dynamics from infrared brightness temperature satel- Wake Forest School of Medicine lite data. The method reveals a wealth of spatiotemporal [email protected] patterns, including the Madden-Julian oscillation and its interaction with diurnal convective processes.

Robert Plemmons Dimitris Giannakis Wake Forest University New York University [email protected] [email protected]

MS16 MS17 Truncated Tensor-SVD Methods for Facial Recog- Uncertainty Quantification in Ocean State Estima- nition tion Recent work on tensor-tensor decomposition by Kilmer A Hessian-based method is developed for Uncertainty and Martin has lead to tensor factorizations reminiscent Quantification in global ocean state estimation and ap- of rank-revealing matrix factorizations. In this work, we plied to Drake Passage transport. Large error covariance discuss the application of the truncated tensor SVD to the matrices are evaluated by inverting the Hessian of a model- facial recognition problem. Comparisons with traditional observation misfit functional. First and second derivative matrix-PCA and TensorFaces show our method has the codes of the MIT general circulation model are generated potential for superior compression for a fixed recognition by algorithmic differentiation and used to propagate the rate, among other advantages. uncertainties between observation, control and target variable domains. The dimensionality of the calculations is Ning Hao reduced by eliminating the observation null-space. Tufts University Department of Mathematics Alex Kalmikov [email protected] Massachusetts Institute of Technology Cambridge (MA), USA Misha E. Kilmer [email protected] Tufts University [email protected] Patrick Heimbach Massachusetts Institute of Technology Karen S. Braman, Randy Hoover [email protected] South Dakota School of Mines [email protected], [email protected] MS17 Uncertainty Predictions, Non-Gaussian Data As- MS16 similation and Bayesian Inference of Dynamical Applications of a Symmetry Preserving SVD Model Equations Knowing information about structural symmetry is advan- Abstract not available at time of publication. tageous in many SVD applications. For example, in protein dynamics, determining symmetry allows one to pro- Pierre Lermusiaux vide SVD major modes of motion that best describe the Massachusetts Institute of Technology symmetric movements of the protein. In facial recognition, [email protected] symmetry in the SVD allows for more efficient compression algorithms. This talk will concentrate on constructing such an SVD which preserves symmetry inherent in the AN13 Abstracts 39

MS17 [email protected] Bayesian Hierarchical Model Applications in Ocean Forecasting Sebastian Aland, Axel Voigt TU Dresden Ensemble surface winds and ensemble surface stresses are [email protected], [email protected] obtained from Bayesian Hierarchical Models, given data stage inputs from satellites and weather-center analyses. Process model distributions are based on leading order MS18 terms from a Rayleigh Friction Equation balance and from Diffusion Driven Instabilities on Evolving Surfaces formulae for bulk transfers. The forcing ensembles exploit precise observations and precise specifications of error to Reaction diffusion systems defined on evolving surfaces has infer error in ocean forecasts based on two different kinds of many application in mathematical biology. Examples of data assimilation (DA) systems; i.e., a sequential DA sys- such applications include tumor growth, pattern formation tem in the Mediterranean Sea and a variational DA system on seashells, butterfly wing pigmentation patterns and an- in the California Current System. imal coat markings. We develop and analyze a finite element method to approximate solutions of nonlinear reac- Ralph F. Milliff tion diffusion systems defined on evolving surfaces. The Cooperative Institute for Research in Environmental method we propose is based on radially projected finite Science elements. University of Colorado milliff@colorado.edu Necibe Tuncer University of Tulsa Christopher Wikle [email protected] Department of Statistics University of Missouri [email protected] MS18 A Phenomenological Model for Cell Migration and Polly Smith Deformation: Application to the Immunity Re- Ocean Sciences Department sponse University of California, Santa Cruz We simulate the immune response system incorporating [email protected] cell deformation. We model leukocyte transport through small blood vessels (SBV), as a result of acidity result- Andrew M. Moore ing from infecting bacteria. The leukocytes leave the SBV Univ. of California at Santa Cruz by vessel wall-penetration and enter the surrounding tis- [email protected] sue where they neutralize bacteria. The model combines stochastic processes, SDEs, PDEs and temporal displace- Nadia Pinardi ment of surfaces. Gruppo Nazionale di Oceanografia Operativa Istituto Nazionale di Geofisica e Vulcanologia Fred J. Vermolen [email protected] Delft University of Technology [email protected] Christopher Edwards Ocean Sciences Department MS19 University of California, Santa Cruz [email protected] Parametric Model Reduction for Bousinesq Equa- tions

MS18 A number of applications, such as uncertainty quantification, require multiple numerical simulations of a PDE Particles at Fluid-Fluid Interfaces: A New Navier- within a narrow parameter range. Brute force simulation Stokes-Cahn-Hilliard Surface Phase-Field Crystal is not suitable for complex simulations and model reduc- Model tion methods are an attractive option. We discuss several Colloid particles that are partially wetted by two immisci- strategies for improving model reduction of the Boussi- ble fluids can become confined to fluid-fluid interfaces. At nesq equations by combining sensitivity analysis, sampling sufficiently high volume fractions, the colloids may jam and strategies, and selecting appropriate time windows for com- the interface may crystallize. The fluids together with the puting POD bases. The stability of these resulting models interfacial colloids form an emulsion with interesting ma- will also be discussed. terial properties and offer an important route to new soft Jeff Borggaard materials. We develop an improved Navier-Stokes-Cahn- Virginia Tech Hilliard-Surface-Phase-Field-Crystal model based on the Department of Mathematics principles of mass conservation and thermodynamic con- [email protected] sistency. To validate our approach, we derive a sharp interface model and show agreement with the diffuse interface model. We demonstrate jamming and the solid-like MS19 behaviour of the crystallized interface by simulating the Consistent Vorticity Boundary Conditions for a fall of a solid ball through a colloid-laden multiphase fluid. Velocity-Vorticity Splitting Method John Lowengrub We derive boundary conditions for vorticity, if we are Department of Mathematics given that velocity is no-slip, in the context of a velocity- University of California at Irvine vorticity splitting algorithm for approximating solutions to 40 AN13 Abstracts

the Navier-Stokes equations. We show numerically this al- the solution has been accomplished using various approxi- lows for optimal convergence, and test of several bench- mate methods and heuristic accelerations to prior methods, mark problems. but all are missing a rigorous error quantiﬁcation. I will present new rigorous error bounds for speciﬁc approximate Leo Rebholz methods. This is joint work with Zachary Clawson and Clemson University Alex Vladimirsky. Department of Mathematical Sciences [email protected] Adam Dante Chacon Cornell University Center for Applied Mathematics Maxim A. Olshanskii [email protected] Department of Mathematics University of Houston Zachary D. Clawson [email protected] Cornell University [email protected]

MS20 Alexander Vladimirsky Humans Make Suboptimal Decisions in Face of Dept. of Mathematics Structured Input Cornell University [email protected] It is unclear whether the principle of Bayesian optimality can describe perception of visually structured inputs. To address this question, we examined whether humans take MS20 into account spatial correlations when detecting a target Modeling and Computations for Multi-scale Eddy among a group of distractors. Varying correlation strength Current Problems between distractors changed the amount of structure. We found that subjects were suboptimal - humans were not In this paper, we study the nonlinear Maxwell equations able to infer the correct correlation structure, but appear with laminated conductors. Direct simulation of three- to see structure even when there is none. dimensional (3D) eddy currents in grain-oriented (GO) silicon steel laminations is very challenging since the system Manisha Bhardwaj has multiple sizes and the magnetic reluctivity is nonlinear University of Houston and anisotropic. We proposed a new eddy current model [email protected] which omits micro scales and thus reduces the scale ratio. The new model is validated by ﬁnite element computations Ronald van den Berg of an engineering benchmark problem—Team Workshop University of Cambridge, UK Problem 21c-M1. [email protected] Xue Jiang, Weiying Zheng WeiJiMa Academy of Mathematics and Systems Science Baylor College of Medicine Chinese Academy of Sciences [email protected] [email protected], [email protected]

Kresimir Josic MS20 University of Houston Department of Mathematics A Study of the Cochlea Using the Immersed [email protected] Boundary Method This talk studies the cochlea (inner ear) using the immersed MS20 boundary (IB) method where the basilar membrane is represented by the immersed boundary. To model the sound Parallel and Approximate Methods for Solving ampliﬁcation ability of the cochlea, we include a paramet- Eikonal Equations ric forcing via the elastic stiﬀness of the membrane. A The Eikonal PDE Floquet analysis of the linearized equations is presented that suggests the existence of parametric resonance. Nu- n |∇u(x)|F(x)=1, on Ω ⊂ R ; merical simulations of the full IB equations are performed to verify the Floquet analysis.

u(x)=q(x), on ∂Ω. Will Ko,JohnStockie Simon Fraser University can be interpreted as an equation for the time-of-arrival [email protected], [email protected] function u(x)fromapointx to the boundary of the domain Ω by following the (a priori unkown) optimal path MS20 under a given speed function F (x). This is a type of Hamilton-Jacobi equation and thus solutions are generally Finite Element Methods for the Evolution Problem non-smooth. A system of coupled nonlinear equations re- in General Relativity sults from approximating the value function u by first-order Einstein’s equations of General Relativity, the equations upwind finite differences. Nowadays there are several effi- that describe how space and time bend in the presence of cient algorithms for solving the Eikonal equation. I will masses, cannot be solved analytically except under special spend the first half of the talk reviewing and comparing circumstances. Thus numerical calculations are essential in various state-of-the-art methods. In the second half of the predicting what these changes might look like. But com- talk, I focus on the problem of solving the Eikonal equation puter simulations have themselves proven very challenging. at one point instead over all of Ω. Efficiently computing AN13 Abstracts 41

I have expanded the application of the finite element meth- efforts to reduce communication in AMG, including the ods to General Relativity, by adapting the recently devel- use of agglomeration, redundancy as well as additive ap- oped Finite Element Exterior Calculus framework. The proaches. resulting numerical method is the first computer implementation of the Electric-Magnetic formulation, producing Ulrike Meier Yang simulations for General Relativity from a new perspective. CASC Lawrence Livermore National Laboratory [email protected] Vincent Quenneville-Belai University of Minnesota [email protected] MS21 On Parallelization of an Energy Minimizing Multi- grid MS20 Survival Analysis on Patients with Chronic Hep- The linear systems arising from multi-physics simula- atitis B: Modeling the Onset of Liver Cancer tions may challenge traditional algebraic multigrid (AMG) solvers. AMG methods based on energy minimization Using survival analysis, we model the onset of liver can- prove to be an effective approach. They contain two com- cer in Taiwanese patients with chronic hepatitis B. We ponents: an a priori chosen nonzero pattern of a prolon- construct time-independent and time-dependent propor- gator, and interpolation of low energy modes; both act as tional hazards models and compare using residual analyses constraints in an optimization problem. In this talk, we and information criteria scores. We demonstrate that our discuss a parallel implementation, challenges of solving the model treating liver cirrhosis as a time-dependent covariate constrained problem, and the performance of energy mini- performs better than time-independent models. We con- mization AMG. clude that monitoring and early diagnosis of liver cirrhosis in hepatitis B patients can be crucial in preventing the on- Andrey Prokopenko, Jeremie Gaidamour set of liver cancer. Advisor Dr. Ke Wu, California State Sandia National Laboratories University, Fresno. Conducted as part of the 2012 REU in [email protected], [email protected] Mathematics at California State University, Fresno. Jonathan J. Hu James Stinecipher Sandia National Laboratories California State University, Fresno Livermore, CA 94551 [email protected] [email protected]

Lin Han Raymond S. Tuminaro Stony Brook University, New York Sandia National Laboratories [email protected] [email protected]

MS21 MS21 AMG Preconditioning for Embedded Uncertainty AMG Shifted Laplacian Preconditioners Viewed Quantification Through Chebyshev Polynomials In this talk we consider algebraic multigrid (AMG) pre- In this talk, we will provide some motivation for us- conditioning for systems arising from stochastic Galerkin ing the Shifted Laplacian preconditioner in indefinite methods for uncertainy quantification. In particular, we Helmholtz problems with analysis of Chebyshev polyno- will consider various AMG approaches for solving block mial smoothers. We will attempt to give some reasoning structured systems whose degrees of freedom are ordered to the choice of the complex shift parameter in the pre- such that each individual block’s sparsity corresponds to conditioner. In conclusion, we will show some numerical the stochastic discretization and the outer sparsity is that results of using smoothed-aggregation algebraic multigrid of the deterministic PDE. We provide numerical studies for the Shifted Laplacian, applied to examples in structural and give an overview of the software underpinning this ef- dynamics. fort. Paul Tsuji Jonathan J. Hu Sandia National Laboratories Sandia National Laboratories [email protected] [email protected]

MS22 MS21 Your Career Trajectory Reducing Communication in Algebraic Multigrid What are the types of influences on your career path - Algebraic Multigrid (AMG) solvers are an essential compo- andwhatcanyoudotostayonyourchosentrajectory? nent of many large-scale scientific simulation codes. Their Online advice includes: “be proactive, not reactive”. More continued numerical scalability and efficient implementa- realistic is: “be both proactive and reactive” depending tion is critical for preparing these codes for emerging com- on the situation. Advancing, improving, developing - and puter architectures. Previous investigations have shown altering: all likely have their place at some time as we that the increasing communication complexity on coarser blend, or separate, our work and personal lives. grids combined with the effects of increasing numbers of cores lead to severe performance bottlenecks for AMG on Bettye Anne Case various multicore architectures. We will discuss several Florida State University 42 AN13 Abstracts

[email protected] variety of organizations, including The Aerospace Corpora- tion. The CTBS currently captures standard computer system performance information along with on-demand fea- MS22 tures new to the cloud. This talk will present the CTBS My Life as a Mathematician and its use to guide appropriate server selection in virtual- ized on-demand computing systems. Abstract not available at time of publication. Douglas Enright, Andrew Brethorst, Jacob Everist Sarah Ann Fleming Computing Systems Research Dept Belmont University The Aerospace Corporation sarahann.ﬂ[email protected] [email protected], [email protected], [email protected] MS22 Ronald Scrofano Sometimes Good Things Happen Computing Systems Research Departme Abstract not available at time of publication. The Aerospace Corporation [email protected] Sigal Gottlieb Department of Mathematics Larry Wang University of Massachusetts Dartmouth Technical Computing Services [email protected] The Aerospace Corporation [email protected]

MS22 More Than Survive-We Want to Thrive! MS23 Design of the Advanced EHF-1 Orbit Transfer Say you have landed a postdoc or tenure-track position, now what? What do you need to do in order to suc- Two days after launch, in August 2010, the feed system ceed? How should you choose your research directions? for the Advanced EHF-1 satellites liquid apogee engine What about networking? How can you be a successful (LAE) malfunctioned, stranding the spacecraft in its ini- teacher without spending all your time preparing for lec- tial transfer orbit. Building on optimal control theory used tures? How much time should you devote to administrative for the pre-anomaly transfer design, mission analysts at duties? And how and when should you say no? How do The Aerospace Corporation developed a low-thrust trans- you balance work and family? fer concept that was more fuel-efficient than the original, time-optimal design. This presentation reviews the princi- Anita T. Layton pal tools, theory, and mission trades involved in redesigning Duke University the orbit transfer. Department of Mathematics [email protected] David Garza Flight Mechanics Department The Aerospace Corporation MS23 [email protected] Application of a Comprehensive Second-Order Near-Field Interferometric Sar (insar) Model to the Terrain Retrieval Problem at W-Band (with MS23 Lidar Validation) Lunar Imaging with Synthetic Aperture Radar We describe a near-field extension of the canonical far field We describe the use of the Goldstone Solar System Radar spotlight SAR image model and the corresponding InSAR (GSSR) to make Earth-based interferometric maps of the terrain retrieval model. The model extends the far field southern lunar surface. Using Interferometric Synthetic model to regions of significant wavefront curvature and ac- Aperture Radar (InSAR) to form image pairs from 90 counts for interaction between wavefront curvature effects minute apertures, we produce topographic maps with hor- and SAR aperture non-planarity. The extended InSAR izontal resolution of 40 m and vertical height accuracy of model has been successfully applied to W-band SAR data 4 m. Long apertures and orbital mechanics dictate that in collected by Aerospaces 95GHz rail SAR. Results are vali- addition to the usual problems of image registration and so- dated by comparison with ground based LIDAR. lution of the interferometric equations, novel space-variant autofocus techniques were developed. Ronald Bloom, Lawrence Weintraub Radar & Signal Systems Dept Lawrence Weintraub, Ronald Bloom The Aerospace Corporation Radar & Signal Systems Dept [email protected], [email protected] The Aerospace Corporation [email protected], [email protected] MS23 Cloud Benchmarking: The Ongoing Evolution of MS24 Computer System Evaluation Numerical Study of Hybrid Block Pseudospectral and Radial Basis Function Method for PDE The Cloud Tester Benchmark Suite (CTBS) is a set of tools for the standardized benchmarking of computer sys- We numerically investigate a hybrid technique based on tem performance within Cloud Infrastructure-as-a-Service BPS and RBF to address partial differential equations environments which are quickly becoming the standard at a whose solutions are smooth, but exhibit localized features. AN13 Abstracts 43

The implementation of the algorithm is similar to over- functions. lapping grid method, where BPS grids are used as background grid and RBF nodes are concentrated in high activ- Rosemary A. Renaut ity regions. The two methods are coupled through penalty- Arizona State University type coupling. Numerical experiments in solving time- School of Mathematical and Statistical Sciences dependent collocation problems will be shown. [email protected]

Alfa Heryudono Shengxin Zhu University of Massachusetts Dartmouth Oxford Center for Collaborative and Applied Department of Mathematics Mathematics [email protected] Oxford University [email protected] MS24 An Adaptive RBF-WENO Reconstruction Method MS25 Nesting ROMS and UCOAM: A Case Study in We present an adaptive RBF-WENO method using the Monterey Bay multi-quadric RBFs for the local reconstruction. The method is that the shape parameters are adaptively deter- The Regional Ocean Modeling System (ROMS) is a hydro- mined based on the regularity of the local reconstruction static free-surface ocean model ideally suited to simulate in each stencil. By this flexibility, the reconstruction can medium to large-scale coastal ocean processes. The Uni- enhance accuracy and convergence although using polyno- fied Curvilinear Ocean Atmosphere Model (UCOAM) is a mials in each stencil allows only a fixed convergence rate. non-hydrostatic LES model designed specifically for high- We construct the ENO and then WENO reconstructions resolution simulations, and is capable of accurately repro- and show how the accuracy is enhanced with numerical ducing the interaction of currents with steep bathymetric examples. features. In this study, non-hydrostatic UCOAM is nested within ROMS, and the nested model is used to study real- Jae-Hun Jung istic currents in Monterey Bay. SUNY at Buffalo jaehun@buffalo.edu Paul Choboter Dept of Math Cal Poly San Luis Obispo MS24 [email protected] A Radial Basis Functions Method for Solving Frac- tional Diffusion Equations MS25 Diffusion processes in complex systems are often observed Distributed Coupling Toolkit to deviate from standard laws and are poorly represented by second-order diffusion models. Such deviations are ob- The Distributed Coupling Toolkit (DCT) is a library to served in as diverse contexts as stock market volatility or couple multi-physics and multi-resolution models in a truly random displacements of living species in their search for distributed manner. The DCT has a user-friendly interface food. An ongoing issue with fractional diffusion models is to formulate the coupling of variables and fields within the design of anefficienthigh-order numerical discretization. pairs of model components. DCT distributed approach We will show that RBFs are exceptionally suited for this guarantees scalability both at the model complexity and problem. parallel processing levels. The DCT is used to weakly couple different components of The General Environmental Cecile M. Piret Coastal Ocean Modeling (GECOM). We present some new Université catholique de Louvain capabilities implemented in DCT and we show some per- [email protected] formance results of using DCT. Emmanuel Hanert Dany De Cecchis UCLouvain Universidad de Carabobo Earth and Life Institute - Environmental Sciences Venezueal [email protected] [email protected]

MS24 MS25 Application of Fredholm Integral Equations Inverse A Cyberinfrastructure-Based Computational Envi- Theory to the Radial Basis Function Approxima- ronment for General Environment Coastal Ocean tion Problem (GECOM) Models

The relationship between the solution and stability of Fred- GECOM models require lengthy simulations, sub-km scale holm integral equations and radial basis function approx- meshes (1010 cells), and TBytes of data. To facilitate run- imation or interpolation is discussed. Underlying system ning simulations, we have developed a computational envi- matrices have a smoothing property dependent on the ker- ronment (CE) that includes a parallel, MPI framework that nel. Techniques from inverse theory are useful for interpret- runs on distributed, heterogeneous resources, and compu- ing and mitigating instability. Numerical results demon- tational services based on the Cyberinfrastructure Web strate that interpolation weights may be regarded as sam- Application Framework (CyberWeb). CyberWeb capabili- plings of a weighted solution of an integral equation which ties include: user accounts; authentication; task execution, is relevant for mapping between the centers of radial basis management, and history; data management; and visualization. In this talk we discuss our experiences in develop- 44 AN13 Abstracts

ing the GECOM CE and community portal. used in a second step to optimize the plasmon resonances with respect to the shape, and the inter-distance between Mary Thomas the particles. San Diego State University [email protected] Faouzi Triki Universite Joseph Fourier, Grenoble Laboratoire Jean Kuntzmann MS26 [email protected] Sharp Estimates on the Magnetic and Pauli Spec- tra of Plane Domains Eric Bonnetier Universit´e Joseph Fourier, Grenoble We investigate sharp upper bounds on spectral functionals Laboratoire Jean Kuntzmann of the magnetic Laplacian (for a particle without spin) and [email protected] the Pauli operator (a particle with spin), on convex and starlike plane domains. Our results cover the ﬁrst eigenvalue, spectral zeta function, partition function, and more. MS26 The geometric normalization involves moment of inertia, Waves in Honeycomb Structures area, and a natural log-L2 measure of the roughness of the boundary. Abstract not available at time of publication.

Richard S. Laugesen Michael I. Weinstein University of Illinois, Urbana-Champaign Columbia University [email protected] Dept of Applied Physics & Applied Math [email protected] Bartlomiej Siudeja Department of Mathematics University of Oregon MS27 [email protected] A Cluster-Cluster Treecode Algorithm We present a new Cartesian treecode algorithm that uses MS26 both far-field and near-field multipole expansions unlike Adjoint-Based Photonic Design: Optimization for the standard treecode algorithms which use only one kind Applications from Super-Scattering to Enhanced of expansion. The algorithm eliminates the need for re- Light Extraction peated computation of Taylor series coefficients in iterative simulations and it’s shown to be more efficient for medium Adjoint-based optimization techniques are fast and efficient accuracy requirements in test problems in computational methods for exploration of large design spaces. We em- chemistry. ploy them towards photonic design problems; in particular, we present applications in super-scattering from metallic Henry A. Boateng nano-particles, as well as enhanced light extraction from Department of Mathematics two-dimensional thin films. For the scattering problem, University of Michigan we exploit contour integration to transform the frequency- [email protected] averaged scattering to a single, complex-frequency computation. This yields significant performance benefits and Robert Krasny enables faster and more efficient optimal design. University of Michigan Department of Mathematics Owen D. Miller [email protected] EECS Department University of California, Berkeley [email protected] MS27 A Parallel Adaptive Treecode for Evolution of Mi- Steven Johnson crostructure in Elastic Media MIT [email protected] We describe an O(N logN ) adaptive treecode for elastostat- ics computation. The code is tested both with randomly generated data and in a spectrally accurate method for MS26 materials science problems. We also present a parallelized Optimization of Plasmon Resonances of Nanopar- version of the treecode. The new version is relatively eas- ticles ier to implement, because it entails less communication between processors. We show that the parallel version scales This talk is concerned with plasmon resonances of metallic linearly for a moderate number of processors for both uni- nanoparticles. We show that these values are the complex form and non-uniform data. eigenvalues of Maxwell’s equations that only occur when the dielectric permittivity of the nanoparticles is negative, Hualong Feng, Amlan Barua, Shuwang Li, Xiaofan Li and the ratio δ between the size of the nanoparticles and Illinois Institute of Technology the incident wavelength is small enough. Afterward, we [email protected], [email protected], [email protected], prove that the resonances satisfy a nonlinear spectral prob- [email protected] lem on the boundary of the nanoparticles. Using Fredholm theory and the generalized Rouché Theorem we derive the complete asymptotic of the plasmon resonances as the pa- MS27 rameter δ tends to zero. The asymptotic expansion is then Gpu and Treecode Accelerated Electrostatics Com- AN13 Abstracts 45

putation for Implicitly Solved Biomolecules resolution spectral sensors onboard that can be exploited for shallow water bathymetry (i.e., measuring the water We present a treecode-accelerated boundary integral depth in shallow waters) and identifying benthic habitats. (TABI) solver for electrostatics of solvated biomolecules. We have enhanced WorldView-2s water depth retrieval by The method employs a well-conditioned boundary integral improving the speed and accuracy of bathymetric calcu- formulation. The surface is triangulated and the integral lations on high resolution imagery. This presentation will equations are discretized by centroid collocation. The lin- introduce the shallow water bathymetry application and ear system is solved by GMRES iteration and the matrix- discuss some recent algorithmic advances for solving this vector product is carried out by a Cartesian treecode which large inverse problem. reduces the cost from O(N 2)toO(N log N)forN boundary elements. We also present parallel TABI simulations Brett W. Bader on GPUs. Sandia National Laboratories Computer Science and Informatics Department Weihua Geng [email protected] University of Alabama [email protected] Grzegorz Miecznik DigitalGlobe, Inc. Robert Krasny [email protected] University of Michigan Department of Mathematics [email protected] MS28 Stochastic Optimization for Model Mis-specification Mitiga- MS27 tion A Treecode for Fast Summation of Matern Covari- ance Kernels Numerical simulation is instrumental for description, prediction, control and design of complex systems. Fidelity of Evaluating sums of multivariate Matern kernels is a com- the simulation process plays a central role in attainment mon computational task in statistical and machine learn- of meaningful predictive capabilities. Frequently, the sim- ing community. The quadratic computational complexity ulation model is mis-specified to a certain extent. Such of the summation is a significant barrier to practical appli- misspecification may originate from incomplete or approx- cations. We develop a Cartesian treecode algorithm to ef- imated physical description of the problem (i.e. govern- ficiently estimate sums of the Matern Kernel. The method ing equations, geometry, boundary conditions, input model uses a far-field Taylor expansion in Cartesian coordinates parameters, etc.), the use of approximated numerics (i.e. to compute particle-cluster interactions. The Taylor coef- floating point round-off error, truncated expansions, dis- ficients are obtained by recurrence relations which allows cretization error, numerical approximation, etc.), lineariza- efficient computation of high order approximations. In the tion of non-linear processes, or any other unknown sources serial code, for a given order of accuracy, the treecode CPU of modeling error. In this study, we supplement a mis- time scales as O(N log N) and the memory usage scales as specified observation model by a low rank addition. For O(N), where N is the number of particles. Parallel code that purpose a nuclear norm stochastic optimization tech- also gives promising scale. nique was developed. We demonstrate the utility of the approach for ill-posed imaging problems. Lei Wang,JieChen Argonne National Laboratory Lior Horesh [email protected], [email protected] Business Analytics and Mathematical Sciences IBM TJ Watson Research Center [email protected] MS28 An Industrial Perspective on Global Optimization Ning Hao Global optimization is the goal of almost every user in Tufts University aerospace design but among the most difficult goals to re- Department of Mathematics alize. We discuss some of our experience with global opti- [email protected] mization algorithms on industrial problems. In particular, for problems with more than a handful of variables, we Misha E. Kilmer have found the most success by applying a version of the Tufts University algorithm of Rinnooy Kan and Timmer, modified to han- [email protected] dle nonlinear constraints. We discuss some of our successes and failures and propose some open areas of research that we are interested in. MS28 Improved Estimation of the T2 Distribution from Mark Abramson Nmr Measurements Boeing Research & Technology Applied Mathematics Group The inversion of the relaxation distribution from NMR [email protected] data is a non-unique and ill-conditioned problem. It is often solved in the literature by finding the smoothest solution that fits the measured data by use of regularization. MS28 In this paper, we modify this algorithm by further con- High-Resolution Bathymetry Using 8-Band Multi- straining it with linear functionals of the solution that can spectral Imagery from WorldView-2 be directly estimated from the measured data. We find that the new algorithm provides better estimates of the DigitalGlobes WorldView-2 satellite has eight high- 46 AN13 Abstracts

solution. MS29 Cellular Automata and Pedestrian Dynamics Lalitha Venkataramanan, Fred Gruber, Tarek Habashy, Philip Singer, Denise Freed Many collective phenomena in pedestrian dynamics have Schlumberger been modeled, simulated, and theoretically analyzed by [email protected], lvenkatara- applying cellular automata so far. In this talk three ex- [email protected], [email protected], lvenkatara- amples are presented. Firstly, it is shown that an obstacle [email protected], [email protected] which is appropriately set near an exit may decrease the total evacuation time. Secondly, a new designing method for large queuing system is introduced. Thirdly, a method MS29 for improving pedestrian flow by imposing a rhythm is pro- A Multi-class Dynamic Assignment Approach to posed. Traffic and Event Management Daichi Yanagisawa To aid decision making in planning for everyday and spe- College of Science cial events, the City of Vancouver developed the Down- Ibaraki University town Vancouver Emergency and Transportation Manage- [email protected] ment System (DVTEMS). DVTEMS is a multi-modal dynamic traffic assignment model with a specific focus on pedestrian behavior and route choice. DVTEMS explicitly MS30 models changing demand and network conditions and can Strategies for Calibration of Large-Scale Climate represent traffic flow in a far more accurate manner com- Models pared to the conventional regional planning model using static traffic assignment. Computer model calibration is the process of determining input parameter settings to a computational model Karen Giese that are consistent with physical observations. This is of- PTV Group ten quite challenging due to the computational demands [email protected] of running the model. This talk will show how the En- semble Kalman filter (EnKF, Evensen 2009) can be used for computer model calibration. It is motivated by the MS29 mean and covariance relationship between the model in- Empirical and Experimental Studies on Uninter- puts and outputs, efficiently producing posterior ensemble rupted Traffic Flow of the calibration parameters. While this approach may not fully capture effects due to nonlinearities in the com- The systematic investigation of traffic flow behavior has puter model response, its computational efficiency makes it quite a long history. Many interesting traffic phenomena a viable choice for exploratory analyses, design problems, have been observed. For example, capacity drop, phantom or problems with large numbers of model runs, inputs and jam, the wide scattering of data in the flow-density plane in outputs. An example in which parameters from the Com- congested flow. However, there is still many controversies munity Atmosphere Model. in this field, mainly due to lack of traffic flow data. In this presentation, I will present some results of our empirical Dave Higdon observations and car-following experiment. Los Alamos National Laboratory Statistical Sciences Rui Jiang [email protected] School of Engineering Science University of Science and Technology of China [email protected] MS30 Application of Polynomial Chaos Methods to Mao-Bin Hu Ocean Modeling University of Science and Technology of China, P.R. China Abstract not available at time of publication. [email protected] Mohamed Iskandarani Rosenstiel School of Marine and Atmospheric Sciences MS29 University of Miami Starting Wave in a Queue of Pedestrians and an [email protected] Analogy with Compressible Fluid Flow

”Slow-in Fast-out” is the keyword to resolve the queue. MS30 Starting wave, which is a wave of people’s successive reac- Distilling Regional Climate Model Data from Nar- tions in the relaxation process in a queue, has an essential ccap for Use in Impacts Analysis role for pedestrians and vehicles to achieve the fast-out strategy. Moreover, starting wave is assumed as a sonic The North American Regional Climate Change Assess- wave in the fluid dynamics. In this talk, the analogy be- ment Program (NARCCAP) is an international, multi- tween the starting wave in a queue and the sonic wave in institution collaboration to simulate climate change over the fluid will be presented. North America using high-resolution regional models. The data archive for NARCCAP is more than forty terabytes Akiyasu Tomoeda in size and includes more than fifty variables. As data Meiji Univeristy providers, to make these results usable by impacts users [email protected] and other non-specialists, we need to do more than just publish the raw model output; we need to encapsulate our knowledge and understanding of the models by providing AN13 Abstracts 47

derived data products that are well-matched to end-user MS31 needs. In this talk, I will discuss some of the complicating Geometry of SAR Imagery factors that make bias-correction, regridding and interpolation, and climatology creation more diﬃcult than may be Abstract not available at time of publication. expected, and the statistical methods that we use in generating derived data products. I will aso cover some lessons Emre Ertin learned about the practicalities of archiving large datasets, The Ohio State University and the implications of these issues for data analytics and [email protected] publishing as we move into the era of big data. Seth McGinnis MS31 NCAR, Boulder Challenges in Advanced Moving-Target Processing [email protected] in Wide-Band Radar In this talk we will describe real-world challenges for de- MS30 tecting and tracking moving targets in wideband synthetic Model Error Analysis: Uncertainty Inherent in aperture radar (SAR) data containing strong background Model Physics Parameterizations clutter returns.

Uncertainty in model parameterizations is a primary source Douglas Page, Howard Nichols of forecast error in weather and climate prediction. In this BAE Systems presentation, a Markov chain Monte Carlo algorithm is [email protected], used to examine the relationship between model parameter [email protected] uncertainty and the convective scale dynamics and environment. We find that constraint of microphysical parameters with observations uniquely determines many aspects of the MS32 deep convective structure. Where this is not the case, the Deconvolution-Based Indicator Functions in Non- results indicate which additional observations may be re- linear Filters for Regularization Models quired. We study a trapezoidal-in-time, finite-element-in-space dis- Derek Posselt cretization of a new Leray regularization model that locally Univ. of Michgan, Ann Arbor chooses the filtering radius using a deconvolution based in- [email protected] dicator function to identify regions where regularization is needed. Because this indicator function is mathematically based, it allows us to establish a rigorous analysis of the MS31 resulting numerical algorithm. We prove well-posedness, Waveform-Diverse Moving-Target unconditional stability, and convergence of the proposed Synthetic-Aperture Radar algorithm, and test the model on several benchmark problems. Abstract not available at time of publication. Abigail Bowers Margaret Cheney Department of Mathematical Sciences Colorado State University Clemson University and Naval Postgraduate School [email protected] [email protected] Leo Rebholz Clemson University MS31 Department of Mathematical Sciences Interferometric Waveform Inversion [email protected] In synthetic aperture radar imaging, fitting cross- correlations of wavefields rather than the wavefields them- MS32 selves can result in improved robustness vis-a-vis model Efficient Augmented Lagrangian-type Precondi- uncertainties. This approach however raises two chal- tioning using Grad-Div Stabilization lenges: (i) new spurious local minima may complicate the inversion, and (ii) one must find a good subset of cross- Grad-Div stabilization can be exploited in a preconditioner correlations to make the problem well-posed. I will explain for the Oseen Problem. It turns out that it behaves sim- how to address these two problems with lifting, semidef- ilar to the classical augmented Lagrangian approach, but inite relaxation, and expander graphs. This mix of ideas with the advantage of being able to easily construct the has recently proved to be the right approach in other con- system matrix efficiently. This simplifies the construction texts as well, such as angular synchronization (Singer et of inner preconditioners. I will discuss the difficulty of the al.) and phase retrieval (Candes et al.). Joint work with trade-off between solution accuracy from stabilization and Vincent Jugnon. solver efficiency. Finally, I will present numerical results to demonstrate the robustness preconditioner. Laurent Demanet Professor of Mathematics, MIT Timo Heister [email protected] Texas A&M University Department of Mathematics [email protected] 48 AN13 Abstracts

MS32 new computational framework will also be presented. or Validation of An Open Source Framework for the Simulation of Blood Flow in Rigid and Deformable other high-level commands. Do not include references or Vessels citations separately at the end of the abstract. Instead, all citations must be in text in the general form [Authorname, We discuss the validation of an open source framework for Title, etc] the solution of problems arising in hemodynamics. The Zhu Wang framework is assessed through experimental data for steady University of Minnesota flow in an idealized medical device with rigid boundaries [email protected] and a numerical benchmark for flow in compliant vessels. The core of the framework is an open source parallel finite element library that features several algorithms for MS33 fluid and fluid-structure interaction problems. A detailed account of the methods is provided. A Hamilton-Jacobi Equation for the Continuum Limit of Non-dominated Sorting Tiziano Passerini Department of Math & CS Non-dominated sorting is a fundamental problem in multi- Emory University objective optimization, and is equivalent to several impor- [email protected] tant combinatorial problems. It is used, for instance, to combine results from multiple search engines, or retrieve Annalisa Quaini images from a database that are similar to multiple queries. University of Houston We prove that non-dominated sorting of random points in [email protected] Euclidean space has a continuum limit that corresponds to solving a Hamilton-Jacobi equation. I will describe this Umberto E. Villa result and give some theoretical and practical applications. Dept. of Mathematics and Computer Science Emory University Jeff Calder [email protected] Department of Mathematics University of Michigan Alessandro Veneziani [email protected] MathCS, Emory University, Atlanta, GA [email protected] Selim Esedoglu University of Michigan Suncica Canic Department of Mathematics [email protected] University of Houston [email protected] Alfred O. Hero The University of Michigan Dept of Elect Eng/Comp Science MS32 [email protected] Nonlinear Reduced Order Modeling of Complex Flows MS33 The reduced-order models (ROMs) are frequently used in Modeling Immunotherapy of the Tumor - Immune the simulation of complex flows to overcome the high com- Interaction putational cost of direct numerical simulations, especially for three-dimensional nonlinear problems. The proper or- Cancer is still a leading cause of death, and years ago a thogonal decomposition (POD), as one of the most com- model was proposed by Kirshcner and Panetta to analyze a monly used tools to generate ROMs, has been utilized in particular type of treatment of cancer. Starting with some many engineering and scientific applications. Its original fundamental biological concepts, we explore their proposed promise of computationally efficient, yet accurate approx- system used to explain the immunotherapy of the tumor imation of coherent structures in high Reynolds number by reviewing their system of ordinary differential equations, turbulent flows, however, still remains to be fulfilled. To and contemplating their results. balance the low computational cost required by ROMs and the complexity of the targeted flows, appropriate closure Joseph Ferrara, Mahbubur Rahman modeling strategies need to be employed. In this talk, University of North Florida we put forth several closure models for the POD-ROMs [email protected], [email protected] of structurally dominated turbulent flows. These models, which are considered state-of-the-art in large eddy simu- MS33 lation, are carefully derived and numerically investigated. We also discuss several approaches for an efficient and ac- Wavelet Frame Based CT Image Reconstructions curate numerical discretization of general nonlinear POD X-ray computed tomography (CT) has been widely used closure models. We numerically illustrate these develop- in diagnosis of cancer and radiotherapy. However it is im- ments in several computational settings, including a three- portant to reduce the radiation dose as low as reasonably dimensional turbulent flow past a cylinder at Reynolds achievable because the x-ray radiation is harmful to the number Re = 1000. A rigorous numerical analysis of the patients. Moreover, the interior tomography which illumi- nate a region-of-interest (ROI) can save the radiation dose. AN13 Abstracts 49

Two robust wavelet tight frame based CT reconstruction in A). We describe higher order Fr´echet derivatives and methods will be introduced for both global reconstruction some applications: the conditioning of Lf (A, E)andthe and interior tomography to reduce the error caused by me- level-2 condition number of a matrix function. The latter chanical inaccurate execution of the huge sparse projection shows some very interesting behaviour that is not yet fully matrix. Numerical simulation results show that our pro- understood. posed analysis based approach can apparently outperform all the popular methods in terms of both the visual quali- Samuel Relton, Nicholas Higham ties and mean structural similarity. Additionally, our pro- University of Manchester, UK posed synthesis based approach can preserve most useful [email protected], [email protected] tiny features and suppress the noise and artifacts.

Jia Li MS33 National University of Singapore A Globally Convergent Numerical Method for Op- [email protected] tical Tomography Inverse Problem In our terminology “globally convergent numerical Bin Dong method” means a numerical method whose convergence to The University of Arizona a good approximation of the correct solution is indepen- [email protected] dent of the initial approximation in inverse problems. A numerical imaging algorithm has been proposed to solve Zuowei Shen a coeﬃcient inverse problem for an elliptic equation and National University of Singapore then the algorithm is validated with the data generated by [email protected] computer simulation.

Ge Wang Pengcheng Xiao Biomedical Imaging Division University of Texas at Arlington Virginia Tech and Wake Forest University [email protected] [email protected] Jianzhong Su Hengyong Yu University of Texas at Arlington Department of Radiology Department of Mathematics Wake Forest University Health Sciences [email protected] [email protected] Natee Pantong Chuang Miao University of North Carolina at Charlotte Wake Forest University Health Science [email protected] [email protected]

MS34 MS33 A Spectral Analysis for Linear-Transform based The Flag of Best Fit as a Representative for a Col- Regularizations lection of Linear Subspaces of Rn Regularization is a widely used technique to incorporate Simple object recognition often requires the computation prior information into mathematical models to favor de- of averages or exemplars for sets of labeled samples. When sired solutions. Whencomputingpiecewise polynomial solu- the sets of labeled samples are point clouds on a Grassmann tions whose derivative of a certain order are sparse, acom- manifold, the most common average used is the Karcher monregularizer is the L1 norm of the derivative. This study mean. We present a new average for data that can be is motivated by the observation that approximations to the represented by points on a Grassmannian, called the flag desired solution are often far more accurate, sometimes up mean, and compare it to other averages in the literature. to orders of magnitude, than approximations to the sparse derivatives. We explain such a phenomenon by a spectral Tim Marrinan, Bruce Draper, Michael Kirby, Chris analysis of discrete derivative operators. Based on the un- Peterson derstanding gained, we propose alternative regularizers to Colorado State University enhance finite difference regularizers. [email protected], [email protected], [email protected], [email protected] Jorge Castanon Rice University Department of Computational and Applied Mathematics MS33 [email protected] Higher Order Fréchet Derivatives of a Matrix Func- tion and Applications MS34 The natural derivative for matrix functions is the Fréchet Data Assimilation for Parameter Estimation in derivative Lf (A, E). The Fréchet derivative is useful in Coastal Ocean Hydrodynamics Modeling optimization and image registration, also being used to define the condition number (sensitivity of f to perturbation Coastal ocean models are used for a variety of applica- 50 AN13 Abstracts

tions, including modeling tides and hurricane storm surge. systems will be addressed and numerical examples will be These models numerically solve the shallow water equa- presented. Potential direction for future research and con- tions, which are derived by depth integrating the Navier- nections with experimental results will be discussed. Stokes equations. One significant source of uncertainty in these models is poorly known bottom friction. In this work Anna Zemlyanova we will estimate bottom friction using statistical data as- Department of Mathematics similation methods. Texas A&M University [email protected] Talea Mayo University of Texas at Austin [email protected] MS35 Thermodynamic Modeling and Numerical Simula- tion of the Flow of Wormlike Micellar Solutions MS34 Optimizing Treatment Regimes to Hinder Antimi- In this talk, we present a new model for wormlike microbial Resistance in Pandemic Influenza Across cellar solutions, a class of viscoelastic fluids. The dy- Time Scales namic aggregation/de-aggregation processes of the surfactant molecules were described using a nonequilibrium ex- The large-scale use of antimicrobials during influenza pan- tension to the mass-action treatment of chemical reac- demics posses a significant selection pressure for drug- tion kinetics. The model has few parameters and satisfies resistant pathogens to emerge and spread in the popula- the principles of nonequilibrium thermodynamics. Time- tion. This requires treatment strategies to minimize to- dependent simulations were performed on an inhomoge- tal infections as well as the emergence of resistance. Here neous shear flow using a semi-implicit Chebyshev method. we propose a mathematical model in which individuals infected with a wild-type strain, if treated, can develop de novo resistance and further spread the resistant pathogen. Natalie Germann,L.PamelaCook Our main purpose is to explore the impact of two important University of Delaware factors influencing the effectiveness of treatment strategies: [email protected], [email protected] i) the relative transmissibility of the drug-resistant strain, and ii) the likelihood of de novo resistance occurrence. For Antony N. Beris the long-term scenario, we find a condition between these Department of Chemical and Biomolecular Engineering two parameters that indicates whether treatment regimes University of Delaware will be most beneficial at intermediate or more extreme val- [email protected] ues. Moreover, we present analytical expressions for effective treatment regimes and provide evidence of its applica- MS35 bility across time scales.Therefore, our results provide long- and short-term insights for the control of drug-resistance Boundary Feedback Control Designs for the in influenza pandemics. Boussinesq Equations with Application to Control of Energy Efficient Building Systems Oscar Patterson Lomba Arizona State University Theoretical and numerical results for feedback stabiliza- Mathematical and Theoretical Biology Institute tion of the Boussinesq Equations with fnite dimensional [email protected] boundary controllers are discussed. The problem is motivated by design and control of energy effiefficient building systems. In particular, new low energy concepts such as MS34 chilled beams and radiant heating lead to problems with Curvature-dependent Surface Tension in Modelling Dirichlet, Neumann and Robin type boundary conditions. of Fracture It is natural to consider control formulations that account for minimizing energy consumption and providing reason- A new model of fracture mechanics which takes into ac- able performance. We discuss a LQR type control problem count interfacial effects due to a curvature-dependent sur- for this system with Robin/Neumann boundary control in- face tension will be considered. This model is based on a puts and apply the results to a 2D problem to illustrate physically valid assumption that the behavior of molecules the ideas and demonstrate the computational algorithms. near a surface of a material is significantly different from those in the bulk and depends on the local curvature Weiwei Hu of the material surface. The theory will be presented University of Southern California through three examples: a curvilinear non-interface crack, [email protected] a straight interface crack and contact problems for a rigid stamp indentation into an elastic half-plane. It will be MS35 shown that the incorporation of surface effects on the crack boundary will eliminate the power and oscillating singular- Formulation and Simulation of the Force-Based ities at the crack tips which are predicted by linear elastic Blended Quasicontinuum Method fracture mechanics. The mechanical problems will be re- The development of consistent and stable atomistic-to- duced to the systems of singular integro-differential equa- continuum coupling models for multi-dimensional crys- tions. The regularization and numerical solution of these talline solids remains a challenge. For example, proving AN13 Abstracts 51

stability of the force-based quasicontinuum (QCF) model Peak Loads remains an open problem. In 1D and 2D, we show that by blending atomistic and Cauchy– Born continuum forces, Analyses of the available methodologies for weather nor- one obtains positive-definite blended forcebased quasicon- malizing temperature sensitive loads within a geographi- tinuum (B-QCF) models. We establish sharp conditions cally and customer diverse service territory has been con- on the required blending width, which is much narrower ducted. Multiple explanatory variables have been analyzed than the macroscopic regions. in conjunction with various extreme heat / thermal comfort models in order to create adaptive temperature sensitive Xingjie Li correlation techniques for normalized distribution substa- Brown University tion peak loads. A field study of extreme value analysis the- xingjie [email protected] ories was also conducted to determine the best probabilistic approach for determining one-in-ten year temperatures for distribution substations using an ensemble of weather MS35 stations with limited historical information. Results from Finite-Temperature Dynamics of Matter-Wave each study are provided to demonstrate the robustness of Dark Solitons in Linear and Periodic Potentials the proposed models, as well as limiting the volatility of weather normalized substation peak loads to increase long We study matter-wave dark solitons in atomic Bose- term forecast accuracy. Einstein condensates at finite temperatures, under the effect of linear and periodic potentials. Our model, namely Frank Gonzales a dissipative Gross-Pitaevskii equation, is treated analyti- Southern California Edison cally by means of dark soliton perturbation theory, which [email protected] results in a Newtonian equation of motion for the dark soliton center. For sufficiently small wavenumbers of the periodic potential and weak linear potentials, the results MS36 are found to be in good agreement with pertinent ones A Mathematician’s Apology obtained via a Bogoliubov-de Gennes analysis and direct numerical simulations. A reflection of thiry four years working in industry, by a mathematician with no initial inclination or notion to work Yannan Shen outside academia. The presentation will discuss: common University of Minnesota mathematical themes, the role of a theoretical mathema- [email protected] tion as an engineering project team member, preparation for industry, keeping it interesting, challenging, rewarding, and fun. MS36 Polynomial Systems in Receptor Pharmacology Karl Rudnick SAIC Pharmacology studies interactions between biological pro- [email protected] cesses and therapeutic agents. It is usually viewed as consisting of two subdisciplines: pharmacokinetics (what the body does to the drug) and pharmacodynamics (what the MS36 drug does to the body). Receptor pharmacology is a com- Systems Pharmacology: Current Applications of mon foundation, which, at the beginning of the research Mathematics in Pharmaceutical R&D pipeline, is concerned with ”pharmacostatics”, the in vitro equilibrium states of key biochemical interactions involv- The cost of new marketed drugs continues to climb due to ing receptors. At the core of the applicable mathemat- the time it takes to bring a drug candidate from discov- ical models are certain systems of polynomial equations. ery to approval and the rising costs of developing the drug. Established practices are to solve these systems in closed Recent data suggest the average cost for a drug approval is form at all cost (or give up). Sometimes the assumptions now between $400 million to $1 billion. One main reason intended to justify such simplifications are dubious. Some- for these soaring costs is the high attrition rate of drugs in times the simple, closed-form formulas are incapable of re- Phase 2 clinical trials. The root cause of these failures is vealing experimentally observed features. As a result, can- typically the drug’s mechanism of action. Efforts have been didate molecules can be assessed overoptimistically or dis- underway in the industry to better understand drug mech- carded prematurely. This presentation will discuss efforts anisms long before they reach Phase 2 trials. In fact, the to develop methods to solve these polynomial systems sys- area now known as systems pharmacology was created in tematically with a priori assurance of convergence, and a large part to better understand drug mechanisms early in related success case of simulating and explaining an un- the discovery phase through clinical development. Systems foreseen experimental observation. pharmacology is the integration of numerous disciplines, including mathematics, engineering, physics, biology and Gilles Gnacadja chemistry, with the goal of building dynamical systems to Amgen, Inc. model drug mechanisms via computer simulation and the- [email protected] oretical analysis. Methods that are commonplace in engineering and physics are now being implemented in drug discovery programs, such as mass-balance principles, dy- MS36 namical systems analysis, optimization and inverse prob- Weather Normalization of Temperature Sensitive lems, and model-parameter sensitivity analysis. This pre- 52 AN13 Abstracts

sentation will showcase examples of these methods in a PDEs on S2. drug discovery setting within pharmaceutical R&D. Francis J. Narcowich, Stephen Rowe, Joseph D. Ward Michael Zager Department of Mathematics Pﬁzer Global Research and Development Texas A&M University Michael.Zager@pﬁzer.com [email protected], [email protected], [email protected]

MS37 Advances in Smoothed Particle Hydrodynamics MS37 An RBF-FD Method for the Simula- In this paper, we systematically explore the accuracy and tion of Reaction-Diffusion Equations on Stationary stability of different methods for satisfying boundary condi- Platelets Within the Augmented Forcing Method tions and capturing viscous diffusion in smoothed particle hydrodynamics (SPH). Smoothed particle hydrodynamics The Augmented Forcing Method (AFM) is a recently- (SPH) is a Lagrangian method for compressible and incom- developed numerical methodology for the simulation of pressible flows. The state of fluid system is represented by PDEs on irregular domains. Our specific motivation is a set of moving basis functions which interpolate the mate- the modeling of the chemistry of platelet aggregation. rial properties. The mesh-free formulation of the method This involves solving chemical diffusion equations in the and its inherent stability make it popular for problems that blood around platelets with boundary conditions obtained have complex geometry or large deformations. Our re- from the solution of reaction-diffusion equations on the search focuses mathematically on an accurate and efficient platelet surfaces. In this talk, we present a methodol- treatment for physical boundary conditions. Also, we ana- ogy for using Radial Basis Function (RBF)-Finite Differ- lyze several smoothing kernels and diffusion schemes. We ences to solve reaction-diffusion equations on platelet sur- compare different techniques for non-slip, non-penetration faces, RBF-based modifications to the AFM to eliminate conditions such as fixed fluid particles, ghost particles and some of its limitations, and results for coupled problems boundary particle forces. We verify our results by com- involving stationary platelets on irregular domains in two- paring computations to exact solutions for 2D planar and dimensions. circular, steady and unsteady Couette flows. Varun Shankar Louis F. Rossi, Zhenyu He School of Computing University of Delaware University of Utah [email protected], [email protected] [email protected]

Grady B. Wright MS37 Department of Mathematics A Numerical Study of the Accuracy of Divergence- Boise State University, Boise ID Free Kernel Approximations [email protected] We present a numerical study of the accuracy of divergence-free radial basis function discretizations. When Aaron L. Fogelson compared to standard interpolants, our results indicate University of Utah that using a divergence-free basis improves accuracy of [email protected] derivatives present in the divergence operator. Derivatives in other directions are often less accurate. In this talk we Robert M. Kirby explore strategies for improving approximations in these School of Computing, University of Utah directions and compare accuracy of methods based on ra- [email protected] dial kernels and multivariate polynomials.

Arthur Mitrano MS38 Arizona State University Near-Optimal Column-Based Matrix Reconstruc- [email protected] tion We study the problem of constructing low-rank approxi- MS37 mations to a matrix by using only a small subset of its Kernel Quadrature and Meshless Galerkin Meth- columns. We present (deterministic and randomized) ap- ods on S2 proximation algorithms with respect to both the spectral and the Frobenius norm. In terms of approximation Recently, Fuslier, Hangelbroek, N., Ward and Wright have bounds, our algorithms are optimal, up to small constant obtained accurate, stable quadrature formulas for S2 that factors. The main tools we introduce to obtain our results use their newly developed robust bases for certain spaces of are: (i) the use of fast approximate SVD-like decomposi- kernels. Such bases consist of Lagrange-like functions that tions, and (ii) two deterministic algorithms for selecting are rapidly decaying spatially and have “small footprint’ rows from matrices with orthonormal columns, building in the set of kernels. In this talk we discuss applying these upon the sparse representation theorem for decompositions quadrature formulas to study Galerkin methods for solving AN13 Abstracts 53

of the identity that appeared in [BSS09]. tive algorithm for robust PCA taking inspiration from recent developments in randomized numerical linear algebra. Christos Boutsidis We illustrate the performance of our method on synthetic Computer Science Department data as well as astronomical spectra from the Sloan Digital Rennselaer Polytechnic Institute Sky Survey. [email protected] David Lawlor Department of Mathematics MS38 Duke University Sketching Algorithms and the Skylark Project [email protected] Sketching methods could be summarized as follows: a sketch of a matrix A is its product SA with a sketching MS39 matrix S, where S is chosen so that SA behaves likes A, in Zeros of Entire Fourier Transforms, Lee-Yang Mea- || || the sense that for all vectors x, SAx is about the same as sures and the Riemann Hypothesis Via Orthogonal || || Ax . From this *subspace embedding* property follows Polynomials a number of applications where SA can be used in place of A, and yield provably good appropriate solutions. When The following fundamental problem arose independently in S has a small number of rows, so does the sketch SA, and two seemingly completely distinct areas as number theory using SA in place of A results in fast approximation algo- and statistical mechanics. The principal question was for- rithms. I will briefly describe a few sketching matrices, a mulated first by George Pólya in 1926 who was motivated few applications, and an ongoing project, called “Skylark”, by his efforts to settle the Riemann hypothesis. It states: to implement numerical linear algebra algorithms based on under what additional conditions on the sufficiently smooth sketching, for large-scale data analysis. and rapidly decreasing kernel K(t) its Fourier transform is an entire function which possesses only real zeros? Essen- Ken Clarkson tially the same question arose in Statistical Mechanics. A IBM Almaden Research Center measure is said to have the Lee-Yang property if all ze- [email protected] ros of its Fourier transform are real and the problem is to characterize those measure. It has been motivated by MS38 the celebrated Lee–Yang theorem, established in 1952, for which Lee and Yang were awarded the 1957 Nobel Prize in Accuracy of a Randomized Algorithm for Comput- physics. The theorem states that if the partition functions ing Leverage Scores of models with ferromagnetic interactions are considered The leverage scores of an m × n matrix A (m>n)are as functions of an external field, then all zeros are purely the squared row norms of any matrix containing an or- imaginary. The original version of the result concerns the thonormal basis for the column space of A. Leverage scores so-called Ising model. Further extensions and generaliza- give information about the importance of rows in regres- tions are due to R. Griffiths and B. Simon (1973), C. New- sion problems and have also been used in the construc- man (1974) and Lieb and Sokal (1981). We report a result tion of sampling probabilities for low-rank matrix approx- which provides a characterization of the Lee–Yang mea- imation. Drineas et al. (2011) have developed a random- sures and a solution of Pólya’s problem too, in terms of ized algorithm for approximating leverage scores that uses the polynomials, orthogonal with respect to the measure. random projections. We present new bounds on the er- Dimitar K. Dimitrov ror produced by the algorithm that improve upon previous State University of So Paulo UNESP analysis and do not rely on the random projections being [email protected] Johnson-Lindenstrauss transforms.

John Holodnak MS39 Department of Mathematics Asymptotics of Carleman Polynomials for Level North Carolina State University Curves of the Inverse of a Shifted Zhukovsky Trans- [email protected] formation

Ilse Ipsen In this talk we study the asymptotic behavior of polyno- North Carolina State University mials orthogonal over the interior of the analytic Jordan Department of Mathematics curve L = {z = w − 1+(w − 1)−1, |w| = R},forsome [email protected] R>2. Surprisingly, this variation of the classical example of the ellipse turns out to be quite sophisticated. After properly normalizing the corresponding orthonormal MS38 polynomials pn, n =0, 1,..., and on certain critical sub- Robust PCA for Massive Data region of the orthogonality domain, a subsequence {pnk } The problem of low-dimensional approximation in the pres- converges if and only if logμ4 (nk) converges modulo 1 (μ ence of outliers is well studied in the statistics and ap- being an important quantity associated to L). plied mathematics communities. Unfortunately, all exist- Peter Dragnev ing methods are either intractable or computationally in- Indiana UniversityPurdue University Fort Wayne tensive for modern “massive’ data. We propose an innova- [email protected] 54 AN13 Abstracts

Erwin Miña-D´ıaz the total mass of the measure. University of Mississippi [email protected] Andrei Martinez-Finkelshtein University of Almeria Michel Northington V [email protected] Vanderbilt University [email protected] Evgenii Rakhmanov University of South Florida [email protected] MS39 Generalized Hurwitz Matrices, Multiple Interlac- Ramon Orive ing, and Forbidden Sectors of the Complex Plane University La Laguna, Tenerife [email protected] We examine polynomials whose generalized Hurwitz matrices are totally positive and establish that their zeros always avoid specific sectors of the complex plane. We also point MS40 out some intriguing connections with (branching) contin- ATaleofTwoTheorems ued fractions and with zero interlacing. I will explain and draw connections between the follow- Olga Holtz ing two classical theorems: (1) Classification of varieties University of California, Berkeley of minimal degree by Del Pezzo and Bertini, (2) Hilbert’s Technische Universitat Berlin theorem on nonnegative polynomials and sums of squares. [email protected] This will lead to a sharp generalization of Hilbert’s result. (Joint work with Greg Smith and Mauricio Velasco). Sergey Khrushchev Kazakh-British Technical University Greg Blekherman svk [email protected] Georgia Institute of Technology [email protected] Olga Kushel Technische Universitaet Berlin MS40 [email protected] Truncated Moment Problems, Extensions, and Positivity Mikhail Tyaglov Shanghai Jiaotong University At present, several interrelated solutions to the multivari- [email protected] able truncated moment problem are known, based on flat extensions of positive moment matrices and positive extensions of Riesz functionals. In general, these are ab- MS39 stract solutions. We discuss several cases in which con- Equilibrium Measure and Phase Transitions in the crete solutions can be obtained, and some cases in which Random Matrix Models approximate representing measures can be produced based on limits of positive flat moment matrices. The large-scale behavior of many models in mathematics and physics, such as a unitary random matrix ensemble, Lawrence A. Fialkow the non-intersecting Brownian paths, or the asymptotics of SUNY New Paltz orthogonal polynomials with respect to a varying weight, fi[email protected] are described in terms of a measure solving an extremal problem from the logarithmic potential theory. This measure (the equilibrium measure in an external field) provides MS40 a crucial information: the associated functionals give us the Inequalities on Polynomials in Matrix Variables leading terms of the asymptotics, and its support is typically the place where oscillations occur. In particular, the Matrix inequalities which occur in much of linear system phase transitions in the random matrix models are asso- theory often require that several polynomials in matrices ciated to the change of the topology and connectivity of are positive semidefinite. Our goal is to describe some the support of the equilibrium measure under variations theory under development for noncommutative polynomial of the external field. In a rather broad class of problems inequalities. It parallels classical real algebraic geometry. the potential (or the external field) on the real line is given The work described is joint with Igor Klep, Scott Mccul- by a polynomial. Much has been written about the phase lough and Chris Nelson. transitions for the polynomial potentials. In this talk we J. William Helton show that the main known (and a few unknown) facts can Math. Dept be derived in a unified fashion from two basic properties UC San Diego of the equilibrium measures. As an illustration, we dis- [email protected] cuss in more detail the case of the quartic external field, focusing on the possible transitions between different configurations of the limiting spectrum under the variation of AN13 Abstracts 55

MS41 as a confounding factor, artificially improving the results. Mutliresolution Spectral Image Segmentation Therefore, a data set with ground truth and uniform acquisition conditions is provided to determine the extent of this Spectral image segmentation requires numerical solution of factor’s influence. While many previously successful meth- an eigenvalue problem for the corresponding graph Lapla- ods turn out to be ineffective, supervised machine learning cian matrices of very large sizes. We demonstrate that our on features extracted from Hidden-Markov-Tree modeling LOBPCG [2001 AV Knyazev Toward the optimal precon- of the paintings’ wavelet coefficients demonstrates its po- ditioned eigensolver: Locally optimal block preconditioned tential to distinguish copies from originals in this data set. conjugate gradient method. SIAM Journal Scientific Com- In order to further study and improve this approach, a puting 23 (2), 517-541.] eigenvalue solver in the BLOEX- larger data set is created under similar conditions. In addi- hypre software library [2007] AV Knyazev, ME Argentati, tion, more careful analysis and experiments are conducted I Lashuk, EE Ovtchinnikov, Block locally optimal pre- to provide new insights. conditioned eigenvalue xolvers (BLOPEX) in HYPRE and PETSc, SIAM Journal Scientific Computing 29 (5), 2224- Yi Grace Wang 2239.] can be used for efficient and high quality spectral SAMSI image segmentation. We numerically analyze two alterna- [email protected] tive mutliresolution approaches. Gungor Polatkan Andrew Knyazev Princeton University Mitsubishi Electric Research Laboratories [email protected] CU-Denver [email protected] Sina Jafarpour Yahoo! Research MS41 [email protected] Fast and Robust PCA Ingrid Daubechies Consider a dataset of vector-valued observations that con- Duke sists of a modest number of noisy inliers, which are ex- Department of Mathematics plained well by a low-dimensional subspace, along with a [email protected] large number of outliers. We first review a convex optimization problem and its efficient implementation that can MS42 reliably fit a low-dimensional model to this type of data. We then modify this framework to obtain a procedure for Applications of Painlevé Functions to Nonlinear robust truncated SVD. We demonstrate its partial theo- Wave Equations retical support and experimental successes. This talk is It has recently been discovered that solutions of nonlinear based on four different joint works: 1) with Teng Zhang, wave equations in certain transition regions can be univer- 2) with Michael McCoy, Joel Tropp and Teng Zhang, 3) sally described for wide classes of initial conditions in terms with Matthew Coudron, and 4) with Tyler Maunu of Painlevé functions. These functions play a role for non- Gilad Lerman linear equations analagous to the role played by the classi- University of Minnesota, Minneapolis cal special functions for linear equations. We will present School of Mathematics our recent result with P. Miller establishing Painlevé-type [email protected] asymptotics in solutions of the semiclassical sine-Gordon equation.

MS41 Robert J. Buckingham Dept. of Mathematical Sciences On the Optimal Design of Cascaded Classiﬁers for The University of Cincinnati Object Detection [email protected] Abstract not available at time of publication.

Nuno Vasconcelos MS42 Electrical and Computer Engineering Semi-Classical Orthogonal Polynomials and the UC San Diego Jacobs School of Engineering PainlevéEquations [email protected] In this talk concerns the relationship between the Painlevé equations and orthogonal polynomials with respect to MS41 semi-classical weights. Orthogonal polynomials satisfy a Forgery Detection in Paintings three-term recurrence relation and for some semi-classical weights, the recurrence coefficients can be expressed in This work studies how machine learning and image analysis terms of Wronskians of special functions which arise in the tools can be used to assist art experts in the authentication description of classical solutions of Painlevéequations.Or- of unknown or doubtful origin. Previous work has shown thogonal polynomials with respect to a semi-classical La- that variation in image clarity in the experimental data guerre weight and semi-classical generalizations of Charlier sets was correlated with authenticity, and may have acted 56 AN13 Abstracts

and Meixner polynomials will be discussed. multi-scale dynamical systems with moderate scale gap, = O(10−1), to the case of no scale gap with = O(1), Peter Clarkson in the presence of model errors through reduced dynam- University of Kent ics from rigorous stochastic subgrid-scale parametrizations. Kent UK We will demonstrate that for linear problems, an effective [email protected] covariance inflation is achieved by a systematically derived additive noise in the forecast model, producing superior MS42 filtering skill. For nonlinear problems, we will study an analytically solvable stochastic test model, mimicking tur- Asymptotic Behavior of Rational Solutions to the bulent signal in regimes ranging from a turbulent energy Inhomogeneous Painlevé-II Equation transfer range to a dissipative range to a laminar regime. The inhomogeneous Painlevé-II equation with constant pa- In this context, we will show that multiplicative noise nat- rameter α has a unique rational solution exactly when α urally arises in addition to additive noise in a reduced is an integer. This talk concerns the asymptotic behavior stochastic forecast model. Subsequently, we will show that of this rational solution in the limit of large |α|.Using a “statistical” inflation factor that involves mean correction Riemann-Hilbert techniques, we prove the existence of a in addition to covariance inflation is necessary to achieve curvilinear triangle asymptotically confining the poles and accurate filtering in the presence of intermittent instabil- zeros. In the interior of the triangle the rational solution ity in both the turbulent energy transfer range and the is asymptotically described by elliptic functions. Near the dissipative range. three corners, however, the Hamiltonian of the tritronquée John Harlim solution of the Painlevé-I equation describes the asymp- North Carolina State University totic behavior. This is joint work with R. Buckingham. [email protected] Peter D. Miller University of Michigan, Ann Arbor MS43 [email protected] A Spectral Based Approach to Conditional Simu- lation of Climate MS42 A rising body of evidence suggests that a changing cli- Numerical Nonlinear Steepest Descent and mate may not simply involve increasing temperatures, but Painlevé Transcendents changing variability across multiple spatial and temporal Abstract not available at time of publication. scales as well. We propose a method of quantifying changing dependence structure that involves estimating the ratio Sheehan Olver of two spectral densities of climate model output under var- The University of Sydney ious GHG emissions scenarios. This estimated change in [email protected] the dependence structure is used to produce conditional simulations of climate variables under different GHG emissions scenarios. MS43 Bayesian Approaches to the Analysis of Computer William Leeds Model Output Univ. of Chicago [email protected] I discuss frameworks for incorporating large-scale computer model output into hierarchical Bayesian models. The framework allows analysts to treat uncertainties in model MS44 output by structuring them in the likelihood function or Moving Target ISAR Imaging in the prior formulation or both. A hybrid approach is also discussed and illustrated. Examples presented involve Abstract not available at time of publication. geophysical problems. Duy Nguyen Mark Berliner SAIC The Ohio State University [email protected] [email protected] MS44 MS43 Mathematical Problems Associated with Imaging The Role of Additive and Multiplicative Noises in Moving Objects Filtering Complex Dynamical Systems An understanding of Fourier transform theory provides Covariance inflation is an ad-hoc treatment that is widely much of the mathematical background needed to under- used in practical real-time data assimilation algorithms stand some commonly used SAR processing methods. But to mitigate covariance underestimation due to model er- some inadequately solved problems in SAR signal process- rors, nonlinearity, or/and, in the context of ensemble fil- ing motivate the study of other mathematical ideas. For ters, insufficient ensemble size. In this paper, we system- example, unknown target motions lead to geometric inverse atically derive an effective statistical inflation for filtering problems. Also, problems in SAR signal analysis have mo- AN13 Abstracts 57

tivated us to want better understanding of methods for approaches and Kalman filters, with a computational cost solving variational problems, and numerical issues related that scales linearly with the problem size. We illustrate to repeated interpolations. with examples from CO2 monitoring and crosswell seismic tomography. Mark Stuff Michigan Tech Research Institute Eric F. Darve mastuff@mtu.edu Stanford University Mechanical Engineering Department [email protected] MS44 On SAR Imaging through the Earth’s Ionosphere Sivaram Ambikasaran Institute for Computational and Mathematical Ionospheric distortions of spaceborne SAR images are due Engineering to mismatches between the actual radar signals subject to Stanford University temporal dispersion and Faraday rotation, and their un- [email protected] garbled form assumed by the signal processing algorithm. We propose to probe the terrain and the ionosphere on two carrier frequencies. Then, we analyze the two images and Judith Yue Li retrieve the plasma parameters responsible for mismatches. Stanford University This allows us to correct the matched filter and reduce im- [email protected] age distortions. Work supported by AFOSR. Peter K. Kitanidis Mikhail Gilman, Erick Smith, Semyon Tsynkov Dept. of Civil and Environmental Engineering North Carolina State University Stanford University [email protected], [email protected], [email protected] [email protected]

MS45 MS44 A Dynamically Bi-Orthogonal Method for Time- Feature Extraction and Classification of Ground Dependent Stochastic Partial Differential Equation Moving Targets from ISAR Image Sequences We develop a dynamically bi-orthogonal method to study This paper presents algorithms for target model learning time dependent stochastic partial differential equations. and discrimination using ISAR image sequences collected The main advantage of our approach is to construct the during vehicle turns. We begin by detecting range-cross Karhunen-Loeve expansion of the stochastic solution on- range bins associated with target scattering centers in each the-fly without the need to form the covariance matrix. image frame and associate them across frames to estimate We propose an adaptive strategy to dynamically remove features. We present an assumed-model feature model- or add modes, and perform a detailed complexity analy- ing method and a distribution-free method. The algo- sis. Several numerical experiments including stochastically rithms are tested using airborne radar data. The results forced Navier-Stokes equations will be provided to demon- show promising discrimination capability, in particular the strate the effectiveness of the method. distribution-free method using Henze-Penrose statistic. Tom Hou Ravi Prasanth, Mikael Yamaguchi Clatech Systems & Technology Research [email protected] [email protected], [email protected] Mulin Cheng Exxon-Mobile Duy Nguyen, John Bennett [email protected] SAIC [email protected], [email protected] Zhiwen Zhang Caltech Mark McClure [email protected] Systems & Technology Research [email protected] MS45 Data Free Inference in Computational Models MS45 Fast Numerical Algorithms for Kalman Filters and Model calibration is frequently done in a context where raw Data Assimilation data is not available, relying instead on data summaries or other information. We present a computational procedure A common feature amongst inverse problems is that the pa- for Bayesian inference in this context, relying on maximum rameters we are interested in estimating are hard to mea- entropy arguments. The method provides a pooled param- sure directly, and a crucial component of inverse model- eter posterior based on many proposed data sets that are ing is using sparse data to evaluate many model param- consistent with the given information. We illustrate the eters. We will present fast algorithms for geostatistical structure and performance of the method using a model 58 AN13 Abstracts

chemical system. the quality of the network. We also provide computational results to validate eﬃcacy of the algorithm. Habib N. Najm Sandia National Laboratories John Arellano Livermore, CA, USA Rice University [email protected] [email protected]

Robert Berry MS47 Climate Corporation San Francisco, CA Euclidean Hub-and-spoke Networks [email protected] The hub-and-spoke distribution paradigm has been a fundamental principle in geographic network design for more Cosmin Safta, Khachik Sargsyan than 40 years. One of the primary advantages that Sandia National Laboratories such networks possess is their ability to exploit economies [email protected], [email protected] of scale in transportation by aggregating network flows through common sources. In this paper, we consider the Bert J. Debusschere problem of designing an optimal hub-and-spoke network Energy Transportation Center in continuous euclidean space: the spokes of the network Sandia National Laboratories, Livermore CA are distributed uniformly over a service region, and our ob- [email protected] jective is to determine the optimal number of hub nodes and their locations. We consider five different backbone Kenny Chowdhary network topologies for connecting the hub nodes, namely Sandia National Laboratories the Steiner and minimum spanning trees, a travelling sales- [email protected] man tour, a star network, and a complete graph. We describe the asymptotically optimal (or near-optimal) configurations that minimize the total network costs as the MS45 demand in the region becomes large and give an approxi- Effective Approximation of Stochastic Navier- mation algorithm that solves our problem on a convex pla- Stokes Equation nar region for any values of the relevant input parameters. A new class of high-order stochastic approximations based on Wick-Malliavin series expansions for Gaussian and Uni- John Gunnar Carlsson form distributions will be discussed. Applications of these University of Minnesota -Twin Cities approximations to solutions of randomly forced Navier- tba Stokes and Burgers equations will be considered.

Boris Rozovsky MS47 Brown University On the 4/3 Conjecture for the Symmetric TSP Boris [email protected] The Traveling Salesman Problem (TSP) arises in ﬁelds George E. Karniadakis ranging from route planning, to manufacturing, to genet- Brown University ics. Better solutions to this problem will reduce operating Division of Applied Mathematics costs across a diverse spectrum of industries. This talk george [email protected] examines an approach to proving a tight bound on the in- tegrality gap of the Held-Karp relaxation of the integer Remigijus Mikulevicius program model of the TSP. The approach is constructive, University of Southern California and can be used to motivate an improved approximation [email protected] heuristic for the TSP.

Daniele Venturi Caleb Fast Division of Applied Mathematics Computational and Applied Mathematics Brown University Rice University daniele [email protected] [email protected]

MS47 MS47 Branch Decomposition Techniques for Matroid Finding all Minimal k-Cores in Graphs for Model- Circuit Problems ing k-Assemblies

We present a new algorithm to address the linear matroid We present a recursive algorithm to find all minimal k- cogirth problem which utilizes the branch decomposition. cores of a given undirected graph, which belongs to the Addressing this problem can lead to significantly enhanc- class of NP-complete problems. The proposed method is a ing the design process of sensor networks. The solution to modification of the Bron and Kerbosch algorithm for find- this problem provides the degree of redundancy of the cor- ing all cliques of an undirected graph. The minimal k-core responding sensor network, and allows for the evaluation of problem has applications in the area of neuroscience. For AN13 Abstracts 59

example, in the study of associative memory, a cell as- MS48 sembly is a group of neurons that are strongly connected Dynamic Model of DNA Structure and Function and represent a “concept” of our knowledge. This group is wired in a specific manner such that only a fraction of Our research has focused on developing a dynamic sta- its neurons will excite the entire assembly. Recent studies tistical mechanical model for predicting the mechanical have linked the concept of a particular type of cell assem- behavior of DNA in an evolving biological environment. bly called k-assembly to the closure of a minimal k-core. We model events like transcription and protein binding. Therefore, the proposed method puts us a step closer to Among the measures calculated are the time-series proba- test its mathematical definition. bility distribution, time-dependent energy of opening and probability of opening for each base pair of the DNA chain. Cynthia Wood Our dynamic model thus enables a better understanding of Computational and Applied Mathematics mechanisms in the cell and function of DNA in vivo. [email protected] Cheryl Sershen University of Houston MS48 [email protected] Application of Population Dynamics on Het- erotypic Cell Aggregation in Tumor Metastasis MS48 This work studied the process of polymorphonuclear neu- Transmission Dynamics of Escherichia Coli trophils tethering to the vascular endothelial cells, and O157:H7 in a Cattle Population subsequential tumor cell emboliformation in a shear flow, an important process of tumor cell extravasation during Escherichia coli O157:H7 is an important foodborne metastasis. The focus lies in modeling of the process and pathogen with a natural reservoir in the cattle popula- application of Bayesian framework to the related param- tion. To understand the spread and persistence of E. coli eter identification problems. Quantitative agreement was O157:H7 infection in cattle so that better infection control found between numerical predictions and in vitro experi- strategies can be designed, I proposed a stochastic model ments. The effects of factors, including: intrinsic binding for E. coli O157:H7 transmission in cattle. In this work, molecule properties, near-wall heterotypic cell concentra- the Kolmogorov equations that determine the probability tions, and cell deformations on the coagulation process, distribution and the expectation of the first passage time were discussed. Sensitivity analysis has been done, and were rigorously derived in a general setting. As an applica- we concluded that the reaction coefficient along with the tion of the theoretical results to E. coli O157:H7 infection, I critical bond number on the aggregation process should be will talk about the extinction and outbreak of infection by recommended as the most critical variables. solving the Kolmogorov equations associated with statistics of the time to extinction and outbreak. The results Yanping Ma provided insight into E. coli O157:H7 transmission and ap- Loyola Marymount University parent extinction, and suggested ways for controlling the [email protected] spread of infection in a cattle herd. Specifically, this study highlighted the importance of ambient temperature and sanitation, especially during summer. MS48 Uncertainty Quantifi- Xueying Wang cation for Large-Scale Bayesian Inverse Problems Texas A&M University with Application to Ice Sheet Models [email protected] We address the problem of quantifying uncertainty in the solution of inverse problems governed by Stokes models MS50 of ice sheet flows within the framework of Bayesian infer- Reduced Complexity Models for Stochastic Sys- ence. The posterior probability density is explored using tems a stochastic Newton MCMC sampling method that employs local Gaussian approximations based on gradients We consider nonlinear advection-reaction and Hessians (of the log posterior) as proposal densities. equations (AREs) with uncertain (random) velocity and The method is applied to quantify uncertainties in the in- reaction parameters. For a class of reactions we derive a ference of basal boundary conditions for ice sheet models. deterministic equation that governs the evolution of cu- mulative distribution function (CDF) of a solution of the underlying ARE. This differential equation is subject to Noemi Petra uniquely defined boundary and initial conditions, and can Institute for Computational Engineering and Sciences be solved with classical techniques once a closure is intro- (ICES) duced. Here we analyze the accuracy and robustness of the The University of Texas at Austin large-eddy-diffusivity closure. [email protected] Daniel M. Tartakovsky University of California, San Diego [email protected]

Francesca Boso 60 AN13 Abstracts

University of California Oak Ridge National Laboratory [email protected] [email protected]

Sreekanth Pannala MS50 Computer Science and Mathematics Division Coarse-Grid Sampling Interpolatory Methods for Oak Ridge National Laboratory Approximating Correlated Random Fields [email protected] Random fields, corresponding to the parameters of a PDE, can be approximated using grid-based discretizations of Miroslav Stoyanov their covariance functions followed by factorization of the Oak Ridge National Laboratory resulting covariance matrix. In this paper, we consider ef- [email protected] ficiency gains obtained by using low-rank approximations based on constructing a coarse grid covariance matrix, fol- MS51 lowed by factorization and interpolation from the coarse Randomized Preconditioning onto the fine grid. The result is coarser sampling and smaller decomposition problems than that for full-rank ap- Abstract not available at time of publication. proximations. Haim Avron Marta D’Elia Business Analytics & Mathematical Sciences Department of Scientific Computing IBM T.J. Watson Research Center Florida State University, Tallahassee, FL [email protected] [email protected]

Max Gunzburger MS51 Florida State University Randomized Solvers for Regession Problems [email protected] We will review recent development of randomized subspace embedding algorithms and emphasize their applica- MS50 tions to large-scale strongly over-determined p regression A Multilevel Stochastic Collocation Algorithm for and quantile regression problems. For 2, we show that a Optimization of PDEs with Uncertain Coefficients (1 + )-approximate solution to the 2 regression problem specified by a matrix A ∈ Rn×d (n d)andavector Gradient-based algorithms for optimization of PDEs b ∈ Rn can be computed in O(nnz(A) + d3 log(d/ )/ 2) with uncertain coefficients are often computationally in- time; for p, via a subspace-preserving sampling procedure, tractable. We investigate an adaptive multilevel stochastic we show that a (1 + )-approximate solution to the p re- − collocation framework for the solution of such optimization gression problem minx∈Rd Ax b p can be computed in problems. Our framework is based on the trust-region al- O(nnz(A) · log n + poly(d) log(1/ )/ 2) time; and similar gorithm for which we prove global convergence under weak results apply to quantile regression problems. assumptions on gradient inexactness. In the stochastic collocation framework, the state and adjoint equations are XIangrui Meng solved concurrently. Numerical results for the adaptive so- LinkedIn Corporation lution of these optimization problems are presented. [email protected]

Drew P. Kouri Jiyan Yang Mathematics and Computer Science Division ICME Argonne National Laboratory Stanford University [email protected] [email protected]

MS50 Michael Mahoney Stanford University High Dimensional Interpolation for Multiphysics Applied and Computational Mathematics Models [email protected] Cycle-to-cycle variations in power output of combustion engines is a major obstacle to increasing fuel eﬃciency, MS51 however, the causes of such variations are not fully under- Subsampling, Regularization and Leverage Scores stood. We take a multiphysics computationally expensive engine model that combines turbulence, thermodynamics Abstract not available at time of publication. and chemistry. Using high dimensional interpolation techniques, we create a cheap model approximation that is used Garvesh Raskutti to study the correlation between the various parameters of Department of Statistics and Operations Research engine operations and the cycle-to-cycle power variations. University of North Carolina [email protected]

Clayton G. Webster AN13 Abstracts 61

MS51 ics and medical image analysis. This talk will discuss our Sensitivity of Leverage Score Estimation recent work about variation of LB spectrum via conformal deformation and its applications in shape analysis. Leverage scores were introduced in 1978 by Hoaglin and Welsch for outlier detection in statistical regression anal- Rongjie Lai ysis. Starting about ten years ago, Mahoney et al. pio- Mathematics, University of Southern California neered the use of leverage scores for importance sampling [email protected] in randomized algorithms for matrix computations. We present perturbation bounds for leverage scores in terms MS52 of principal angles between subspaces. We also consider the context of machine learning applications, where per- Extremal Eigenvalues of the Laplace-Beltrami Op- turbations are small only when compared to regularization erator terms, and present perturbation bounds for large leverage Let (M,g) be a 2-dimensional, compact, connected Rie- scores. This is joint work with Ilse Ipsen. mannian manifold and denote by λk(g)thek-th eigen- Thomas Wentworth value of the Laplace-Beltrami operator, Δg.Inthistalk, Department of Mathematics we ﬁx M and consider the dependence of the mapping → North Carolina State University g λk(g). In particular, we propose a computational [email protected] method for solving the eigenvalue optimization problem of maximizing λk(g)overaconformalclass[g]ofﬁxedvol- ume, vol(M, g) = 1. Ilse Ipsen North Carolina State University Braxton Osting Department of Mathematics University of California, Los Angeles [email protected] [email protected]

MS52 Chiu-Yen Kao Claremont McKenna College Isoperimetric Inequalities for a Wedge-like Mem- [email protected] brane

: For a wedge-like membrane, Payne and Weinberger Rongjie Lai proved in 1960 an isoperimetric inequality for the funda- Mathematics, University of Southern California mental eigenvalue which in some cases improves the classi- [email protected] cal isoperimetric inequality of Faber-Krahn. In this work, we introduce “relative torsional rigidity’ for this type of MS53 membrane and prove new isoperimetric inequalities in the spirit of Saint-Venant, Pólya-Szeg˝o, Payne, Payne-Rayner, On Stable Discretizations for Non-Newtonian Flow Chiti, and Talenti, which link the eigenvalue problem with Model by DG and Nonconforming FEMs the boundary value problem in a fundamental way. (Joint We present a class of stable discretization schemes for solv- work with A. Hasnaoui, University of Tunis, El Manar) ing the 3-dimensional non-Newtonian flow model by Dis- Lotfi Hermi continuous Galerkin and nonconforming FEMs. In this University of Arizona formulation, unlike the case the conforming finite elements Department of Mathematics are used, the velocity fields approximated by low order [email protected] piecewise polynomials can be shown to satisfy the strong divergence-free condition, still achieving the stability in terms of the energy norms. Numerical Experiments will be MS52 presented to demonstrate the robustness of the algorithm. Principal Eigenvalue Minimization for An Elliptic This is the joint work with Q. Hong and J. Xu Problem with Indefinite Weight and Robin Bound- ary Conditions Young Ju Lee Department of Mathematics Abstract not available at time of publication. Rutgers University [email protected] Michael Hintermüller Humboldt-University of Berlin [email protected] MS53 Regularity and Multigrid Analysis for Laplace- Type Axisymmetric Equations MS52 Applications of Laplace-Beltrami Spectrum Via We discuss new high-order full regularity estimates in Conformal Deformation weighted Sobolev spaces for a class of 2D equations reduced from 3D Poisson’s equation on axisymmetric do- The spectrum of Laplace-Beltrami (LB) operator plays an mains. Based on these estimates, we develop high-order important role in surface analysis and has been made suc- finite element methods that approximate singular solutions cessful applications in many fileds such as computer graph- of these equations in the optimal rate. Then, we show our 62 AN13 Abstracts

analysis on the condition number of the system from the Motion ﬁnite element discretization. This, together with our results on the approximation properties of the ﬁnite element Abstract not available at time of publication. solution and the smoothing properties of the smoother in I. G. Kevrekidis the multigrid V-cycle algorithm, will lead to the uniform Princeton University convergence of the multigrid method for the axisymmetric [email protected] equations.

Hengguang Li MS54 Wayne State University Spin Models for Suspensions of Swimming Mi- [email protected] croorganisms

MS53 One of the striking results from numerical simulations of force-dipole swimmer suspension models is the proclivity Uncertainty Quantification for Elliptic Problems on of swimmers with a positive force dipole to create struc- Polyhedral Domains tured patterns and those with negative force dipole to pre- Let D ⊂ Rd, d =2, 3, be a bounded domain with piece- fer isotropy. We investigate some simple spin models which wise smooth boundary ∂D and let U be an open subset abstract some features of these swimmer models, where of a Banach space Y . We consider a parametric family we can develop, through a system of associated stochastic PDE’s, much more precise, and we hope instructive, results Py of uniformly strongly elliptic, second order partial dif- concerning correlation structure and pattern formation. ferential operators Py on D in divergence form, where the parameter y ranges in the parameter domain U so that, Peter R. Kramer for a given set of data f ,thesolutionu and the coeffi- y Rensselaer Polytechnic Institute cients of the parametric boundary value problem P u = f y y Department of Mathematical Sciences are functions of (x, y) ∈ D × U. Under suitable regular- [email protected] ity assumptions on these coefficients and on the source term f, we establish a regularity result for the solution Oleg Zaboronski u : D × U → R of the parametric, elliptic boundary value University of Warwick problem P u(x, y)=f (x)=f(x, y), x ∈ D, y ∈ U,with y y Mathematics Institute mixed Dirichlet-Neumann boundary conditions. This will [email protected] help in developing optimal finite element methods for these equations. This is joint work with Christoph Schwab, ETH Zurich. MS54 Victor Nistor An Optimal Transport Approach to Statistical In- Pennsylvania State University ference Across Multiple Scales [email protected] In many statistical inference applications, ranging from “sloppy’ models in systems biology to flow in porous media, MS53 data ultimately depend on a low-dimensional set of coarse- scale quantities. In this context, we can exploit conditional Convergence of Goal-Oriented Adaptive Finite El- independence of scales, identified through multiscale mod- ement Methods for Nonlinear Problems els, to efficiently sample the Bayesian posterior. We de- In goal-oriented methods we are concerned with approxi- scribe a new inference methodology, based on inversion of mating a given quantity of interest, a function of the weak a triangular optimal transport map, to condition the fine solution to the PDE. The adaptive algorithm is driven by scale on coarse observables. The map is constructed as estimating the error in both the primal and a dual problem the continuous limit of a discrete transport map, allowing at each iteration. We will discuss the formation of appro- flexible application to a wide range of physical phenomena. priate dual problems for nonlinear PDE and how they may Matthew Parno, Tarek El Moselhy, Youssef M. Marzouk be used to attain convergence and in some cases contrac- Massachusetts Institute of Technology tion results for the adaptive method. We will compare [email protected], [email protected], [email protected] estimates for bounding the error in the goal function and how these estimates may be used in a convergence framework. Finally, we will look at some numerical experiments. MS54 This is joint work with Michael Holst and Yunrong Zhu. Simulating Multiscale Particle-Based Models of Sara Pollock Bacterial Chemotaxis with Asymptotic Variance Department of Mathematics Reduction University of California, San Diego We discuss variance reduced simulations for an individual- [email protected] based model of chemotaxis of bacteria with internal dynamics. The variance reduction is achieved via a coupling MS54 of this model with a simpler process in which the internal dynamics has been replaced by a direct gradient sensing Coarse-Graining Agent-Based Models of Collective of the chemoattractants concentrations. We first compute AN13 Abstracts 63

a deterministic solution of the kinetic density description University of Riverside of the direct gradient sensing model; the deviations due to [email protected] the presence of internal dynamics are then evaluated via the coupled individual-based simulations. We show that the resulting variance reduction is asymptotic, in the sense MS55 that, in the diffusive asymptotics, the difference between Spatial Features of Density Dependence and the two processes has a variance which vanishes according Weather Extremes in Population Models to the small parameter. The spatial scale and spatial coherence of processes rele- Giovanni Samaey vant for population dynamics, population persistence, and Department of Computer Science, K. U. Leuven life histories has yet to be elucidated for many mobile or- [email protected] ganisms. Using fish populations as a model system, I show how the definition of the correct spatial scale for density- dependent processes and of spatial coherence of weather MS55 extremes increases the predictive power of models of evo- Spatial Models of Biodiversity lution of life histories and population viability.

Most biodiversity models are spatially implicit, for reasons Simone Vincenzi of mathematical and computational tractability. Spatially University of California Santa Cruz explicit models, however, are required to provide more real- [email protected] istic descriptions of biodiversity patterns and to interface with spatially explicit data, which are becoming increasingly available. I will present two research projects on MS56 this topic: The first looks at spatially explicit models of Coarse-graining of Time and Space for Materials species abundance distributions and the second looks at with Defects how species-area curves are affected by different landscape Crack propagation, defect nucleation and movement, and fragmentation patterns. plastic deformation are usually characterized by rare events Ryan Chisholm where the system oscillates in an energy well and only National University of Singapore rarely moves to a new state. The defects interact with [email protected] boundaries and each other through long range elastic effects. Direct molecular dynamics cannot thus reach the time and space scales necessary for meaningful scientific MS55 and technological information. Thus, coarse-graining of the Optimal Control of Spatial Models of Populations time dynamics to focus only on the state-to-state dynamics is needed concurrently with coarse-graining in space. The tool of optimal control is used to investigate issues of resource allocation and movement along a resource gra- Mitchell Luskin dient for population models. The models are formulated School of Mathematics as diffusive partial differential equations with nonlinear University of Minnesota growth terms. Some models include advection terms for [email protected] directed movement. Gideon Simpson S.M. Lenhart University of Minnesota University of Tennessee, Knoxville [email protected] [email protected] Alexander V. Shapeev MS55 School of Mathematics Integrative Evaluation of Diverse Conservation University of Minnesota Strategies for a Rare Shrub Species under Global [email protected] Change David Aristoff We link urban growth, species distribution, fire risk and University of Minnesota population simulation models to investigate the impact of [email protected] urban development, climate change and altered fire regime on the spatial distribution and persistence of a rare fire- sensitive shrub endemic to southern California, Ceanothus MS56 verrucosus. The modeling framework is used to rank TowardsRareEventsStatisticsinMolecularDy- spatially-explicit management actions: land conservation namics and a range of translocation scenarios. Results show that Rare event simulation and estimation for systems in equi- spatial conservation actions are only beneficial with appro- librium are among the most challenging topics in molecular priate temporal management of fire. dynamics. As was shown by Jarzynski and others, nonequi- Helen M. Regan librium forcing can theoretically be used to obtain equilib- Biology Dept rium free energy differences. The advantage seems to be that the external force can speed up the sampling of the 64 AN13 Abstracts

rare events by biasing the equilibrium distribution towards more accurate, model. We demonstrate the effectiveness of a distribution under which the rare events is no longer rare. this approach on several test problems. Yet algorithmic methods based on Jarzynski’s and related results often fail to be efficient because they are based on Jonathan Weare samplinginpathspace.Wepresentanewmethodthat University of Chicago replaces the path sampling problem by an optimal control. Department of Mathematics We show how to solve the related optimization problem in [email protected] an efficient way by using an iterative strategy. This approach results in a zero variance estimator for committor Bo Qi, Seyit Kale functions, transition rates, or the statistics of first passage University of Chicago times. [email protected], [email protected]

Christof Schuette Aaron Dinner University of Berlin James Franck Institute Germany University of Chicago [email protected] [email protected]

MS56 MS56 Importance Sampling in the Neighborhood of a Metastability and Interacting Particle Systems Stable Equilibrium Point Metastablitiy of interacting particle systems can be stud- We discuss importance sampling schemes for the estima- ied based on large deviations for the sample path of the tion of finite time exit probabilities of small noise diffusion dynamics, in the spirit of Fredlin-Wentzell theory. We es- processes that involve escape from an asymptotically sta- tablish a large deviation principle for a general class of ble equilibrium. We build importance sampling schemes finite state mean field interacting particle systems. One with provably good performance both pre-asymptotically, highlight of our proof is it applies to the models that al- i.e., for fixed size of the noise, and asymptotically, i.e., as lows simultaneous jumps of particles, which is novel in the the size of the noise goes to zero, and that do not degrade literature of LDPs for weakly interacting processes. With as the time horizon gets large. Simulation studies demon- addition of some mild conditions, we also obtain a locally strate the theoretical results. uniform LDP. Based on joint work with Paul Dupuis and Kavita Ramanan. Konstantinos Spiliopoulos Boston University Paul Dupuis Department of Mathematics and Statistics Division of Applied Mathematics [email protected] Brown University [email protected] Paul Dupuis Division of Applied Mathematics Kavita Ramanan, Wei Wu Brown University Brown University [email protected] kavita [email protected], wei [email protected]

MS56 MS57 Using Coarse Grained Models to Speed Conver- SAR Imaging Considerations for Multi-Baseline In- gence to the Minimum Energy Pathway terferometry and Tomography

The minimum energy pathway (MEP) is the most likely Synthetic aperture radar (SAR) interferometry and tomog- transition pathway between reactant and product states raphy use the complex phase information as well as the in a chemical reaction at low temperature and provides a magnitude information from multiples vantages to extract convenient, one dimensional, description of the event. For vertical information. In order to obtain valid information large complex systems interrogation of the reaction mecha- of maximal quality necessitates some specialized process- nism by straightforward simulation is often impossible due ing schemes to preserve phase and maximize correlation. to the presence of a vast range of time scales. For this rea- Moreover, adaptations are needed to support low frequency son, eﬃcient techniques that focus on discovery of the MEP radars. This talk will cover some of the SAR signal pro- are important. Unfortunately in large complex systems dis- cessing considerations for these applications. covery of the MEP can itself be prohibitively expensive. In this work we develop a technique for discovery of the MEP Scott Hensley, Thierry Michel, Ron Muellerschoen, Brian (and other pathwise descriptions of a reaction) that uses Hawkins cheap, coarse grained models to accelerate convergence. In Jet Propulsion Laboratory most practical settings the reaction pathway corresponding [email protected], [email protected],gov, to the coarse grained model does not accurately describe [email protected], [email protected] the reaction of interest. Nevertheless, by carefully arranging the calculation, the coarse grained system can be used MS57 to accelerate convergence to the MEP of a more expensive, Considerations in the Development of Passive Mul- AN13 Abstracts 65

timode Radar Massachusetts Institute of Technology [email protected], [email protected] Passive multimode radar attempts to identify noncoopera- tive transmissions and exploit them in a multistatic configuration to enhance target detection, location, and identifi- MS58 cation. This talk discusses passive multimode radar system Predicting Energy Savings Due to Building implementation issues, modeling and simulation, and sig- Retrofit nal processing. Building energy performance is significantly affected by Bill Melvin uncertainties in its parameters (e.g. equipment efficien- Georgia Tech Research Institute cies) and by a number of uncertain processes (e.g. oc- [email protected] cupancy patterns). Building retrofits often fail to deliver expected energy savings because uncertainties are typically neglected during the design. We present methodology for MS57 uncertainty analysis for buildings that helps designers mit- Motion Estimation in Synthetic Aperture Radar igate uncertainty and estimate correct energy performance bounds. The approach utilizes a number of different un- Abstract not available at time of publication. certainty analysis techniques. George C. Papanicolaou Slaven Peles, Sunil Ahuja Stanford University United Technologies Research Center Department of Mathematics [email protected], [email protected] [email protected]

MS58 MS57 A Traveling Salesman Learns Bayesian Networks Interrupted SAR Persistent Surveillance Via Joint Sparse Reconstruction of Multi-Pass Data Structure learning of Bayesian networks is an important problem that arises in numerous machine learning and We apply sparse signal recovery techniques for synthetic uncertainty quantification applications. In this work, we aperture radar (SAR) image formation from interrupted present a novel approach for learning the structure of phase history data, with application to persistent surveil- Bayesian networks using the solution of an appropriately lance SAR imaging. We extrapolate the missing samples constructed traveling salesman problem. In our approach, by jointly processing multipass data using a sparse recov- one computes an optimal ordering (partially ordered set) of ery technique with a group support constraint. We eval- random variables using methods for the traveling salesman uate change detection performance using images from the problem. This ordering significantly reduces the search Gotcha SAR and we find that joint processing results in space for the subsequent greedy optimization that com- coherent change detection gains regardless of interrupt pat- putes the final structure of the Bayesian network. We tern. demonstrate our approach of learning Bayesian networks Les Novak, Ivana Stojanovic on real world census and weather datasets. In both cases, Science Systems Company, Inc. we demonstrate that the approach very accurately captures [email protected], [email protected] dependencies between random variables. We check the accuracy of the predictions based on independent studies in Clem Karl both application domains. Boston University Tuhin Sahai [email protected] United Technologies [email protected] MS58 Designing Uncertainty: Sensitivity Analysis for Stefan Klus Systems with Spatially Distributed Variability United Technologies Research Center [email protected] Engineers typically strive to minimize the amount of uncertainty in the systems they design. However, reducing Michael Dellnitz uncertainty is typically associated with some cost. For ex- University of Paderborn ample, tightening manufacturing tolerances incurs higher [email protected] manufacturing costs. The cost associated with reducing uncertainty often competes with the benefits of improving performance, implying that there may be some optimal bal- MS58 ance between the level of uncertainty and the performance An Adaptive Wavelet Stochastic Collocation of the system. We present an approach for computing the Method for Irregular Solutions of PDEs with Ran- sensitivity of the statistics of performance to the level of dom Inout Data uncertainty, and apply this approach to analyze and optimize problems with spatially distributed uncertainties. Accurate predictive simulations of complex real world applications require numerical approximations to first, op- Eric Dow,QiqiWang pose the curse of dimensionality and second, converge 66 AN13 Abstracts

quickly in the presence of steep gradients, sharp transitions, Communities with Niche and Neutral Dynamics bifurcations or finite discontinuities in high-dimensional parameter spaces. In this talk we present a novel multi- Whether and how dynamic processes underlying popu- dimensional multi-resolution adaptive (MdMrA) sparse lation growth influence species abundance distributions grid stochastic collocation method, that utilizes hierarchi- (SADs) is not yet well understood. We investigate the dif- cal multi-scale piecewise Riesz basis functions constructed ferences between SADs resulting from a stochastic competi- from interpolating wavelets. The basis for our non- tion model with neutral dynamics (based only on stochas- intrusive method forms a stable multiscale splitting and tic demographics), and with competition based on trait thus, optimal adaptation is achieved. Error estimates and differences that gives rise to niches. We consider how the numerical examples will used to compare the efficiency of differences in SADs vary with factors such as number of the method with several other techniques. niches, and how detectable we expect these differences to be in abundance data. Max Gunzburger Florida State University Rosalyn Rael [email protected] Department of Ecology and Evolutionary Biology University of Michigan Clayton G. Webster, Guannan Zhang [email protected] Oak Ridge National Laboratory [email protected], [email protected] MS60 Top-Down Bottom-Up Effects In The Chesapeake MS60 Bay Fisheries Ecosystem Model Using Fast-slow Dynamical Systems Theory to Un- In this talk, I will discuss both prey control (bottom-up derstand how Coevolution Shapes the Population control) and predator control (top-down control) mecha- Dynamics of Predator-prey Systems nisms in a Chesapeake Bay ecosystem model. Through an- Coevolution between predators and prey can potentially alyzing different scenarios of harvest and predation rates of alter the population dynamics of predator-prey systems. the Atlantic menhaden, I will discuss evidence of bottom- Here, I use fast-slow dynamical systems theory to explore up and top-down effects, with a particular interest in those effects. One prediction is that coevolution can ef- striped bass and phytoplankton biomass. The impacts of fectively reverse the cycle orientation of predator-prey sys- phytoplankton and zooplankton abundance on the dynam- tems, yielding clockwise cycles in the phase plane. I com- ics of species in higher trophic levels will also be discussed. pare this prediction to three experimental data sets and Shari Wiley discuss new questions in dynamical systems that arise from Department of Mathematics fast-slow eco-coevolutionary models. Hampton University Michael H. Cortez [email protected] Cornell University [email protected] MS61 Numerical Construction of Green’s Functions for MS60 High Dimensional Elliptic Problems with Variable Bifurcations, Infectious Disease Ecology and The Coefficients Art of Approximation: Linking Biological Mecha- We describe an algorithm for approximating the Green’s nisms with Dynamics function for elliptic problems with variable coefficients in I’ll discuss the dynamics of a consumer-resource (predator– arbitrary dimension d. The basis for our approach is the prey) model, with infectious disease among consumers, in separated representation, which appears as a way of ap- two parts: First I’ll describe how resource-dependent epi- proximating functions of many variables by sum of prod- demiological processes observed in natural systems can im- ucts of univariate functions. As a corollary to this work, pact these three-species dynamics. Second, I’ll discuss an we describe a randomized algorithm for maintaining low approximation method that exploits the presence of mul- separation rank of the functions used in the construction tiple time scales in this system to describe how certain of the Green’s function. biological assumptions yield a Bautin (Generalized Hopf) David Biagioni bifurcation. This approximation provides useful biological University of Colorado, Boulder - Applied Math Dept insight, and raises new mathematical questions. National Renewable Energy Laboratory Paul J. Hurtado [email protected] Cornell University [email protected] MS61 A Partition of Unity Method with Penalty for MS60 Fourth Order Problems Species Abundance Distributions in Ecological The partition of unity method provides an easy way to construct smooth approximation spaces. One can use these AN13 Abstracts 67

approximation spaces in a Galerkin method, but special MS62 treatment is needed to enforce the Dirichlet boundary con- Ramanujan and Symbolic Computation ditions. In this talk, we discuss a way to use the partition of unity method for fourth order problems with Dirichlet This talk will be devoted to efforts using symbolic compu- boundary conditions using Nitche’s method. Details on the tation (MACSYMA) to place Ramanujan’s fifth and sev- method, error estimates, and numerical examples will be enth order mock theta functions in a coherent context. presented. Among other things, this project has produced several new and unexpected identities related to derivatives of false Christopher B. Davis theta functions. Louisiana State Univesity Department of Mathematics George E. Andrews [email protected] Penn State University Department of Mathematics [email protected] MS61 A Direct Solver for Variable Coefficient Elliptic PDEs MS62 Creative Telescoping for Rational Functions using The talk describes a highly accurate technique for solving the Griffiths-Dwork Method elliptic PDEs with variable coefficients and smooth solutions. The domain is tessellated into squares, and the dif- Creative telescoping algorithms compute linear differential ferential operator is discretized via high order (p=10 or equations with polynomial coefficients satisfied by multi- 20) spectral differentiation on each square. A hierarchical ple integrals depending on a parameter. We describe an direct solver is used to solve the resulting discrete system. algorithmic version of the GriffithsDwork method for the The method is very efficient; e.g., a Helmholtz problem on creative telescoping of rational functions. This leads to a domain of size 200x200 wavelengths is solved to ten digits bounds on the order and on the coefficients degree of the of accuracy in ten minutes on a standard laptop (using 6M differential equation, and to the first complexity result degrees of freedom). which is simply exponential in the number of variables. One of the important features of the algorithm is that it Gunnar Martinsson does not need to compute certificates. Univ. of Colorado at Boulder [email protected] Alin Bostan INRIA Saclay Ile-de-France [email protected] MS61 A Fast Algorithm for Spherical Grid Rotations and its Application to Singular Quadrature MS62 Recent Results for the Lambert W Function and We present a fast and accurate algorithm for evaluating its Relatives singular integral operators on smooth surfaces that are globally parametrized by spherical coordinates. Problems We show that many functions containing the Lambert W of this type arise, for example, in simulating Stokes flows function are Stieltjes functions. We discuss some of the with particulate suspensions and in multi-particle scatter- consequences of this result, including some interesting def- ing calculations. For smooth surfaces, spherical harmonic inite integrals, series, and rational approximations. I think expansions are commonly used for geometry representation just add a sentence. We also discuss the convergence in the and the evaluation of the singular integrals is carried out complex plane of series expansions for W. with a spectrally accurate quadrature rule on a set of rotated spherical grids. We propose a new algorithm that David Jeffrey interpolates function values on the rotated spherical grids Department of Applied Mathematics via hybrid nonuniform FFTs. The algorithm is nearly op- University of Western Ontario timal in computational complexity and reduces the cost of djeff[email protected] applying the quadrature rule from O(√)toO(√ log √) Rob Corless for a spherical harmonic expansion of degree p. University of Western Ontario in London [email protected] Zydrunas Gimbutas Courant Institute New York University MS63 [email protected] Performance Breakdown of Stochastic Simulation Algorithms Shravan Veerapaneni Department of Mathematics We study the performance of stochastic simulation algo- University of Michigan rithms for the propagation of epistemic uncertainty in non- [email protected] linear parabolic and elliptic models. For the estimation of first and second order moments, the loss of regularity of state variables in probability space with increasing vari- 68 AN13 Abstracts

ance, together with dimensionality limitations, aﬀect neg- University of Minnesota atively the performance of methods based in generalized [email protected] Polynomial Chaos decompositions. Monte Carlo methods and their variants are shown to perform more robustly in application scenarios. MS63 A Hyper-Spherical Sparse Grid Approach for High- David A. Barajas-Solano Dimensional Discontinuity Detection Dept. of Mechanical and Aerospace Engineering University of California, San Diego High-dimensional discontinuity detection is important in [email protected] UQ area, but conventional adaptive sparse-grid interpolation leads to dense reﬁnement around discontinuities. We Daniel M. Tartakovsky propose a novel method for identifying jump discontinu- University of California, San Diego ities in by incorporating a hyper-spherical coordinate sys- [email protected] tem (HSCS) into the sparse-grid approximation framework. The basic idea is to transform the Cartesian coordinate system to an N-dimensional HSCS. Then a sparse-grid ap- MS63 proximation is constructed in the N-1 dimensional subspace Exploiting the Interpolating Property of Sparse where the discontinuity locations are estimated using New- Grids ton method.

It is common for a quantity of interest Q to be deﬁned Clayton G. Webster, Guannan Zhang as an integral, expressed in terms of some state variable u Oak Ridge National Laboratory depending on parameters λ. Estimating Q by a sparse grid [email protected], [email protected] requires evaluating the integrand at numerous settings for λ, and solving a nonlinear system for u(λ). We investigate MS64 cases in which intermediate information produced by the sparse grid evaluation can be exploited to construct good A Multiscale Model of Fibrinolysis: from Single starting values for the nonlinear state iteration. Molecules to Full 3-D Clots

Max Gunzburg Fibrinolysis, the enzymatic degradation of the fibrin mesh School of Computational Science that stabilizes blood clots, is initiated through a reac- Florida State University tion involving tissue-type plasminogen activator (tPA). [email protected] tPA is used clinically to degrade blood clots, but bleed- ing complications often arise post-treatment. We develop Clayton G. Webster a 3-dimensional stochastic multiscale model of fibrinolysis Oak Ridge National Laboratory to investigate other possible treatments. The microscale [email protected] model contains detailed biochemistry and represents a single fiber cross section. Data from the microscale model are used in a macroscale model of the full fibrin clot, where we John Burkardt explore various treatment options. Department of Computational Science Florida State University Brittany Bannish [email protected] Department of Mathematics University of Central Oklahoma MS63 [email protected] Numerical Methods for Stochastic James P. Keener, Aaron L. Fogelson Quasi-Geostrophic Equations University of Utah With the continuous increase in computational power, [email protected], [email protected] complex mathematical models are becoming more and more popular in the numerical simulation of oceanic and MS64 atmospheric flows. For some geophysical flows in which computational efficiency is of paramount importance, how- A Model of Particle Transport Through a Periodic ever, simplified mathematical models are central. For ex- Array of Beating Cilia ample, in climate modeling the Quasi-Geostrophic Equa- In this talk, I will introduce a regularization method that tions (QGE), are commonly used in the numerical simula- gives a smooth formulation for the fundamental solution tion of large scale wind-driven ocean circulations. Due to to Stokes flow driven by an infinite, triply-periodic array the requisite of long time integration in climate modeling, of point forces. With this formulation, the velocity at even for the simplified model, fast and accurate numeri- any spatial location may be calculated, including at and cal algorithms are still desired. In this talk, we will pursue very near the point forces; these locations typically lead this direction and discuss efficient numerical approaches for to numerical difficulties due to the singularity within the QGE when uncertainty effects such as the random wind Stokeslet when using other methods. For computational forcing are considered. efficiency, the current method is built upon previous meth- Zhu Wang ods in which the periodic Stokeslet is split into two rapidly decaying sums, one in physical space and one in recipro- AN13 Abstracts 69

cal, or Fourier, space. I will show a few validation stud- with protons and water). To determine the equilibrium in- ies and then discuss a recent extension of the method to terface, a variational approach is employed. We analyze: i) doubly-periodic flow. Finally, using the extended method, the existence and uniqueness of the electrical potential, ii) simulations of doubly-periodic arrays of beating cilia will the shape derivatives of state variables and iii) the shape be presented. differentiability of the corresponding energy and the corresponding Euler-Lagrange equation. The latter leads to Karin Leiderman a modified Young-Laplace equation on the interface. This Applied Mathematics modified equation is compared with the classical Young- UC Merced Laplace equation by computing several equilibrium shapes, [email protected] involving a fixed point algorithm.

Arian Novruzi MS64 University of Ottawa Sperm Interactions: Biochemistry and Hydrody- [email protected] namic Signals Peter Berg Sperm have been observed to form sperm trains and self Department of Physics organize into vortices. What is the relative role of biochem- NTNU, Norway istry and hydrodynamics in these interactions? In this talk, [email protected] we will present recent computational results on attraction, synchronization, and the formation of sperm trains using the method of regularized Stokeslets. The coupling of bio- Sven-Joachim Kimmerle chemistry will be through the flagellar waveform and the Universitat der Bundeswehr Munchen, Germany role of these interactions in chemotaxis towards the egg will [email protected] be discussed. MS65 Sarah D. Olson Worcester Polytechnic Institute On Embedded Eigenvalues of Non-Homogeneous [email protected] Operators In oscillatory systems extended in one dimension and con- MS64 taining a localized defect, embedded eigenvalues are made Multiphase Models and Simulations for Bacterial possible by symmetry, which allows a decoupling of propa- Biofilm Accounting for Cell Motility gating and evanescent motions. The corresponding eigenfunctions (bound states) have infinite support and decay Biofilms are complex biological organisms ubiquitous al- exponentially. In systems without obvious symmetry or most everywhere in our daily life. Modeling and un- that are extended in multiple directions, such bound states derstanding the intricate biological, fluid mechanical, are rare, and the obstructions are of algebraic nature. We chemical-mechanical transduction of chemical signal and examine special systems that do admit exponentially de- mechanical forces is a daunting task across multiple disci- caying bound states at embedded eigenvalues and discuss plines. In this presentation, we will present a systematic how asymmetry affects the resonant excitation of a bound approach tooted in kinetic theory for complex fluids and state by radiation under small perturbations. expanded to include various biological and chemical mech- anistic models to investigate how the biofilm flows in vari- Stephen P. Shipman ous geometry and boundary conditions. Hopefully, this will Department of Mathematics shed light on how to treat biofilm infections in medical set- Louisiana State University tings or take advantage of the biofilm’s barrier properties [email protected] in their beneficial applications. Models and 3-D numerical simulations will be discussed in a few selected applications. MS66 Qi Wang,JiaZhao Variable-Degree HDG Method for Convection- University of South Carolina Diffusion Equations on Meshes with Hanging [email protected], [email protected] Nodes The discontinuous Galerkin (DG) method is known to han- MS65 dle nonconforming meshes easily. But the presence of hang- Modeling, Shape Analysis and Computation of the ing nodes degrades its order of accuracy. This also holds Equilibrium Pore Shape near a PEM-PEM Inter- for the hybridizable DG methods, more accurate than all section classic DGM. We provide the first, rigorous a priori error analysis that shows the superconvergence properties of the In this work we investigate the equilibrium shape of an HDG methods remain unaffected by the presence of hang- interface that represents the boundary of a pore channel ing nodes for certain family of unstructured meshes. We embedded in an elastomer. The model consists of a system also discuss the variable-degree case. of PDEs, comprising a linear elasticity equation for displacements within the elastomer and a nonlinear Poisson Yanlai Chen equation for the electric potential within the channel (filled Department of Mathematics University of Massachusetts Dartmouth 70 AN13 Abstracts

[email protected] MS67 A Useful Factorization in PDE-constrained Dis- Bernardo Cockburn tributed Optimal Control Problems School of Mathematics University of Minnesota A distributed optimal control problem with a constraint of [email protected] Poisson’sequationisconsideredinordertodevelopanef- ficient numerical method and lead to further development for more complicated problems. A saddle point system MS66 that arises in the PDE-constrained optimization problem is Multigrid Methods for Degenerate and Singular El- solved using a useful factorization of a Schur complement. liptic Equations Two factors in the factorization, then, solved by the parallel linear solver, FETI-DPH. Scalability and regularization We present fast multilevel methods for the approximate so- dependency study of FETI-DPH shows that the method is lution of discrete problems that arise from the discretiza- robust and versatile. tion of a class of general degenerate elliptic equations such as the fractional Laplacian—a nonlocal operator. To local- Youngsoo Choi ize it, we solve a Dirichlet-to-Neumann-type problem via Farhat Research Group, Stanford University an extension operator, which requires incorporating one [email protected] more dimension to the problem. Using a framework of Xu and Zikatanov, we prove nearly uniform convergence of a multilevel method that employs a line smoother. MS67 Optimal Fishery Harvesting on a Nonlinear Long Chen Parabolic Pde in a Heterogeneous Spatial Domain University of California at Irvine [email protected] The overexploitation of fisheries has called for an improved understanding of spatiotemporal dynamics of resource stocks as well as their harvesters. There is pressure MS66 to find methods for optimally solving these management A Hierarchical Error Estimate for a Schrodinger- problems.Weusethetoolofoptimalcontroltoinvesti- Type Operator gate harvesting strategies for maximizing yield of a fish population in a heterogeneous, finite domain. We deter- We provide a hierarchical error estimate for a Schrödinger mine whether these solutions include no-take marine re- operator with inverse square potential, and argue that serves as part of the optimal solution. The fishery stock it is efficient and reliable on a family of geometrically is modeled using a nonlinear, parabolic partial differential graded meshes. The potential term not only introduces equation with logistic growth, movement by diffusion and new sources of singularities, but is also of the same order advection, and with Robin boundary conditions. The ob- as the Laplacian, which makes the analysis more challeng- jective for the problem is to find the harvest rate that max- ing. Numerical experiments demonstrate the efficacy of imizes the discounted yield. Optimal harvesting strategies this approach. A direct comparison with adaptively re- are found numerically. fined meshes is also provided. Michael Kelly Jeffrey S. Ovall University of Tennessee - Knoxville University of Kentucky, Mathematics [email protected] [email protected]

Hengguang Li MS67 Wayne State University Optimal Control Applied in Coupled Within-host [email protected] and Between-host Models

An immuno-epidemiological model is formulated and an- MS66 alyzed for a “within-host” system of ODEs coupled with A Posteriori Estimates and Adaptivity for Nonlin- a “between-host” system of PDEs and ODEs. Using the ear Problems method of characteristics and a ﬁxed point argument, we prove the existence and uniqueness of solution to our sys- In this talk, we will present an a posteriori error estimate tem. An optimal control problem for the coupled model is for problems in 3D based on a hierarchical basis approach. considered, and existence, characterization and uniqueness This error estimator is developed for general linear ellip- results established. A forward backward sweep numerical tic problems and we will show its eﬀectivity for nonlinear method is used to solve the optimality system. problems with singularities in the solution. I will also discuss extensions of the approach to geometric PDE. Eric Numfor University of Tennessee Ryan Szypowski [email protected] Department of Mathematics University of California, San Diego [email protected] MS67 Multigrid Solution of Distributed Optimal Control AN13 Abstracts 71

Problems Constrained by Semilinear Elliptic Pdes a unique LPAI dominance equilibrium exists. Similarly, if H R > ∞ a unique HPAI dominance equilibrium exists. We study a multigrid solution strategy for distributed op- The equilibria are locally stable if Rˆ Hw < 1(Rˆ Lw < 1cor- timal control problems constrained by semilinear elliptic respondingly). A unique coexistence equilibrium is present PDEs. Working in the discretize-then-optimize framework, if both invasion numbers are larger than one. Simulations we solve the reduced optimal control problem using New- show that this coexistence equilibrium can lose stability tons method. Further, adjoint methods are used to com- and coexistence in the form of sustained oscillations is pos- pute matrix-vector multiplications for the reduced Hessian. sible. Cross-immunity and duration of protection increase In this work we introduce and analyze a matrix-free multi- the probability of coexistence. Simulations also show that grid preconditioner for the reduced Hessian which proves increasing LPAI transmission increases LPAI prevalence to be of optimal order with respect the discretization. and decreases HPAI prevalence. This observation in part Jyoti Saraswat may explain why wild birds which have much higher trans- Department of Mathematics & Statistics mission of LPAI compared to domestic birds also have University of Maryland Baltimore County much lower prevalence of HPAI. [email protected] Necibe Tuncer University of Tulsa Andrei Draganescu [email protected] Department of Mathematics and Statistics University of Maryland, Baltimore County Juan Torres [email protected] Department of Mathematics University of Florida MS68 [email protected]fl.edu Lymphatic Filariasis: Transmission Dynamics and Diagnostics During MDA Maia Martcheva University of Florida Lymphatic filariasis (LF) is a significant public health maia@ufl.edu problem in many countries, especially Papua New Ginea (PNG) where the level of transmission by the mosquito MS68 vector, human infection rates and clinical morbidity are among the highest in the world. WHO launched its Global A Mathematical Approach to Skeletal Muscle and Program to Eliminate Lymphatic Filariasis (GPELF) in Insulin Sensitivity in Type 2 Diabetes this region by 2020. Various reasons have been attributed Studies on the role of exercise in regulating skeletal mus- to the failure of many countries to make progress, without cle metabolism and insulin action suggest that exercise in- substantive evidence. This study attempts to develop and creases insulin sensitivity and is associated with elevated analyze a mathematical model that captures the dynamics expression of genes linked to metabolism. However, mech- of Lymphatic Filariasis in PNG on which impact of the di- anisms underlying exercise and insulin sensitivity on gene agnostics methods and treatment programs can be studied. expression are not well understood. A transcriptional net- The population in the model is stratified based on the hosts work derived from experimental work and corresponding microfilarial and antibody levels. The survival of the in- mathematical model of gene expression is proposed. We fected mosquitoes (vector) depends on the size of the load investigate dynamics of potential biological pathways and of microfilaria engorged. Data from Papua New Guinea the role of key transcription factors. are used to estimate the parameters, and understand the LF transmission dynamics. We compare the effect of the Anarina Murillo mosquitos mortality rate caused by the high microfilaria AMLSS-Mathematical, Computation & Modeling load on the reproduction number. Moreover, we identify Sciences Center conditions when vector control and mass treatment can be Arizona State University jointly or individually beneficial over time. [email protected] Ridouan Bani Northeastern Illinois University MS68 [email protected] An Agent-Based Approach to Model Host Switch- ing of Two Trypanosoma Cruzi Infected Triatomine MS68 Vector Species on Two Preferred Sylvatic Hosts Modeling Low and High Pathogenic Avian In- The parasite Trypanosoma cruzi, spread by triatomine vec- fluenza tors, affects over 100 mammalian species throughout the Americas, including humans, in whom it causes Chagas’ This talk introduces and age-since recovery model of LPAI L H disease. In the U.S., only a few cases have been docu- R R and HPAI in birds. Reproduction numbers ( , ) mented of human infection by vectors, but prevalence is Rˆ Rˆ and invasion reproduction numbers ( Hw , Lw )ofLPAI high in sylvatic hosts. Sylvatic transmission of T. cruzi is and HPAI are computed. It is shown that the system has spread by Triatominae vector species biting hosts, creating a unique disease-free equilibrium that is locally and glob- L H L multiple interacting vector-hosts cycles. We aim to quan- ally stable if R < ∞ and R < ∞.IfR > ∞ 72 AN13 Abstracts

tify contacts between diﬀerent host and vector species. MS69 Theory of Transition Path Process Kamuela E. Yong University of Iowa Understanding rare events like transitions of chemical sys- [email protected] tem from reactant to product states is a challenging problem due to the time scale separation. In this talk, we Anuj Mubayi will discuss some recent progress in mathematical theory of Northeastern Illinois University transition paths. In particular, we identify and character- [email protected] ize the stochastic process corresponds to transition paths. The study of transition path process helps to understand Christopher Kribs-Zaleta the transition mechanism and provides a framework to an- University of Texas Arlington alyze numerical approaches for rare event sampling and [email protected] simulation.

Jianfeng Lu MS69 Mathematics Department Estimating Reactive Fluxes using an Analogy with Duke University Electric Circuits [email protected]

The transition process between two metastable sets of James Nolen stochastic system driven by a deterministic potential force Duke University and a small white noise can be quantified be a vector field Mathematics Department called the reactive current. The reactive current coincides [email protected] with the electric current for a properly defined electric flow. I propose a method for estimation of the percentages of the reactive current via a network of reactive channels exploit- MS69 ing this analogy. Geometry and Approximation of Intrinsically Low- Dimensional Dynamical Systems in High Dimen- Maria K. Cameron sions University of Maryland [email protected] We introduce a novel technique for approximating stochastic systems in high-dimensions that have low-dimensional effective state spaces, by simpler stochastic systems that MS69 may be simulated very efficiently, and are learned only Free Energy Landscape and Kinetics of Particles from configurations observed in short runs of the under- with Short-Ranged Interactions lying system. We apply this construction to toy models and to molecular dynamics data. The construction does We propose a new way to look at particles interacting with not require a priori knowledge of reaction coordinates. short-ranged potentials (such as colloids), based on taking the limit as the range of the interaction goes to zero. In this Miles Crosskey, Mauro Maggioni limit, the landscape is entirely defined by geometrical man- Department of Mathematics ifolds plus a single control parameter, while the dynamics Duke University on top of the manifolds are given by a hierarchy Fokker- [email protected], [email protected] Planck equations coupled by ”sticky” boundary conditions. We illustrate this theory with several applications, such as computing the low-dimensional manifolds, free energies, MS70 and transition rates for n¡=8 identical particles, comparing 3D SAR Point Clouds these to experiments with colloids, and enumerating rigid packings of hard spheres. We present a new technique for the processing of SAR data for the accurate measurement of scattering center locations Miranda Holmes-Cerfon in three dimensions. Through the use of coherent SAR col- Harvard University lections that form a sparse aperture, the approach produces [email protected] a 3D point cloud, not dissimilar from lidar point clouds. In this talk we will present the background and technical de- Michael Brenner velopment of the technique and present several examples Harvard Univ. of high-density point clouds derived from SAR data collec- Cambridge, MA tions. [email protected] Richard E. Carande Steven Gortler Neva Ridge Technologies, Inc. Harvard University [email protected] [email protected] MS70 Operator-theoretic Formulation of Radar Detec- AN13 Abstracts 73

tion and Waveform Design Problems represent multi-dimensional random variables from data. Conventional methods such as kernel density estimation Delay–Doppler processing of radar signals is naturally de- 2 cannot handle high dimensions. Here we present a method scribed in the language of Hilbert–Schmidt operators on L based on normal copula model and polynomial chaos ex- spaces of signals. This perspective is developed, and some pansion, which allows one to represent high dimensional standard types of problems in detection and waveform de- dependent non-Gaussian random variables. sign are shown to manifest in terms of questions about the spectra of such operators. Jinglai Li Shanghai Jiaotong University Douglas Cochran [email protected] School of Electrical, Computer and Energy Engineering Arizona State University Youssef M. Marzouk [email protected] Massachusetts Institute of Technology [email protected] MS70 Detection Theory for Multi-static Active and Pas- MS71 sive Radar Model Reduction for Systems of Differential Equa- This talk describes the detection problem for multi-static tions with Initial Condition and Parametric Uncer- active and passive radar and proposes some new Bayesian tainty detectors based on marginalisation over Grassmanian man- In many time-dependent problems of practical interest the ifolds. initial conditions or parameters entering the equations de- Stephen Howard scribing the evolution of the various quantities exhibit un- Defence Science and Technology Organization certainty. One way to address the problem of how this [email protected] uncertainty impacts the solution is to expand the solution using polynomial chaos expansions and obtain a system of differential equations for the evolution of the expansion co- MS70 efficients. We present an application of the Mori-Zwanzig Uncertainty Propagation in Radar, A System-Level formalism to the problem of constructing reduced models Perspective of such systems.

Abstract not available at time of publication. Panagiotis Stinis University of Minnesota, Twin Cities Eric Keydel [email protected] Science Applications International Corporation [email protected] MS71 Reservoir Model Reduction Techniques for Uncer- MS71 tainty Quantification Probabilistic Conditioning Without Bayes Model reduction plays an important role in the practical as- In this work we propose a method for constructing best sessment of uncertainty in reservoir production forecast. In approximations of spatially conditioned random vectors on this talk, we discuss the rationale for constructing coarser finite order Wiener chaos spaces. Conditioning is achieved and simpler reservoir models and recently developed tech- by an iterative algorithm, projecting alternatively on the niques, including new ideas on geologic modeling and more constraints domain of interest and on the finite order chaos traditional model coarsening and upscaling techniques. In space. In many applications physical constraints require particular, the Dirichlet-Neumann representation (DNR) that uncertain parameters/fields are confined in a specific method for upscaling and multiscale simulation will be dis- domain. Even though the Wiener chaos expansions of cussed in some detail. such random parameters maintain this property, truncated chaos expansions in principle do not, leading to instabili- Xiao-Hui Wu, Yahan Yang ties of numerical methods. We circumvent this obstacle by ExxonMobil Upstream Research Company solving a modified problem using appropriately best ap- [email protected], proximations of the conditioned random parameters. [email protected]

Roger G. Ghanem, Evangelia Kalligiannaki University of Southern California MS73 [email protected], [email protected] Numerical Approximation Methods for Non- Uniform Fourier Data

MS71 In this talk I discuss the reconstruction of compactly sup- Representing High-Dimensional Random Variables ported piecewise smooth functions from non-uniform sam- from Data ples of their Fourier transform. This problem is relevant in applications such as magnetic resonance imaging (MRI) In predictive modeling and simulations, one often needs to and synthetic aperture radar (SAR). Two standard re- 74 AN13 Abstracts

construction techniques, convolutional gridding (the nonuniform FFT) and uniform resampling, are summarized, and some of the difficulties are discussed. It is then demon- Lixin Shen strated how spectral reprojection can be used to mollify Mathematics Department, Syracuse University both the Gibbs phenomenon and the error due to the non- [email protected] uniform sampling. It is further shown that incorporating prior information, such as the internal edges of the un- MS73 derlying function, can greatly improve the reconstruction Constructing Approximation Kernels for Non- quality. Finally, an alternative approach to the problem Harmonic Fourier Data that uses Fourier frames is proposed. Imaging modalities such as magnetic resonance imaging Anne Gelb (MRI) and applications such as radio astronomy often Arizona State University require the reconstruction of signals from non-harmonic [email protected] Fourier measurements. The Dirichlet kernel, which characterizes the approximation properties of harmonic Fourier MS73 reconstructions, is no longer applicable. This talk discusses A Framework for Moving Least Squares Method the design of approximation kernels for non-harmonic with Total Variation Minimizing Regularization Fourier reconstruction, incorporating features of the underlying signal such as compact support and piecewise In this study, we propose a computational framework to smoothness. Numerical results and applications to convo- incorporate regularization terms used in regularity based lutional gridding reconstructions as well as jump and edge variational methods into least squares based methods. By detection in one and two dimensions will be presented. putting schemes from both approaches into a single framework, the resulted scheme benefits from the advantageous Aditya Viswanathan properties and overcomes the drawbacks of both parties. California Institute of Technology As an example, in this study, we propose a new denois- [email protected] ing scheme where the total variation minimizing term is adopted by the moving least squares method and show nu- MS74 merical comparison. Mimetic Finite Difference PDE Based Models in Yeon Ju Lee Image Processing Institute of Mathematical Sciences, Ewha W. University We introduce the use of mimetic methods to the imaging [email protected] community, for the solution of the initial-value problem ubiquitous in the machine vision and image processing and Sukho Lee analysis elds. PDE-based image processing and analysis Dept. Software Engineering, Dongseo Univ., techniques comprise a host of applications such as noise Busan, S. Korea removal and restoration, deblurring and enhance- ment, [email protected] segmentation, edge detection, inpainting, registration, motion analysis, etc. In these applications, the digital images Jungho Yoon are given on discrete (regular) grids. This lends itself for Dept. Mathematics, Ewha W. Univ., discretizing the PDEs to obtain numerical schemes that Seoul, S.Korea can be solved on a computer. Because of their favorable [email protected] stability and eciency properties, semi-implicit - nite dier- enceandniteelementschemeshavebeenthemethodsof MS73 choice (in that order of preference). We propose a new approach for the numerical solution of these problems based Blind One-Bit Compressive Sampling on mimetic methods. In this talk, we introduce an optimization model for re- Carlos Bazan construction of sparse signals from 1-bit measurements. Computational Science Research Center The model targets a solution that has the least l0-norm San Diego Satate Univrsity among all signals satisfying consistency constraints stem- [email protected] ming from the 1-bit measurements. An algorithm for solving the model is developed. Convergence analysis of the algorithm is presented. Our approach is to obtain a se- MS74 quence of optimization problems by successively approx- Mimetic Discretization Methods imating the l0-norm and to solve resulting problems by exploiting the proximity operator. We examine the perfor- Mimetic Operators satisfy a discrete analog of the diver- mance of our proposed algorithm and compare it with the gence theorem and they are used to create/design conserva- binary iterative hard thresholding (BIHT) for 1-bit com- tive/reliable numerical representations to continuous mod- pressive sampling reconstruction. Unlike the BIHT, our els. We will present a methodology to construct mimetic model and algorithm does not require a prior knowledge versions of the divergence and gradient operators which on the sparsity of the signal. This makes our proposed exhibit high order of accuracy at the grid interior as well work a promising practical approach for signal acquisition. as at the boundaries. As a case of study, we will show the AN13 Abstracts 75

construction of fourth order operators in a one-dimensional We present example problems, and the advantages and de- staggered grid. Mimetic conditions on discrete operators sign of the MTK. are stated using matrix analysis and the overall high order of accuracy determines the bandwidth parameter. This Eduardo J. Sanchez contributes to a marked clarity with respect to earlier ap- San Diego State University proaches of construction. We present theoretical aspects [email protected] of a mimetic method based on the extended Gauss Diver- gence Theorem as well as examples using this methods to MS75 solve partial differential equations. Efficient Implementation of the Hardy-Ramanujan- José E. Castillo Rademacher Formula San Diego State University It is well known that the Hardy-Ramanujan-Rademacher Department of Mathematics (HRR) formula allows efficiently evaluating the integer par- [email protected] tition function p(n) for large n. We investigate theoretical and practical aspects of implementing the HRR for- MS74 mula, and show that quasi-optimal complexity for com- GPU Acceleration of a Fourth-order Mimetic Fi- puting p(n) can be achieved. With a new implementa- nite Difference Method for Elastic Wave Propaga- tion, which runs more than 500 times faster than previ- tion ously published software, we have computed several billion Ramanujan-type congruences, greatly extending tables In this work, we use GPU (Graphics Processing Unit) to previously computed by Weaver. accelerate a previously tested serial fourth-order mimetic finite-difference method to computationally simulate 2-D Fredrik Johansson elastic motion subject to a free surface boundary condi- RISC, JKU Linz tion. The mimetic discretization of the underlying math- [email protected] ematical model, linear elastodynamics in the interior and a Newmann-type boundary condition at the free surface MS75 (zero traction), is performed on a staggered grid and em- Symbolic Computation and Modular Forms ploys central stencils (at interior) and lateral stencils (at the free surface). It avoids the location of grid points The talk reports on recent developments arising from joint beyond the physical boundary that makes the original work with Silviu Radu (RISC). This, for instance, includes method memory-saving and very precise. Here, we describe a new unified computational framework for proving Ra- the new CUDA implementation of this method on NVIDIA manujan’s celebrated partition congruences modulo powers Tesla C2050 graphics card and detail the optimized use of of 5, 7, and 11. registers and fast shared memory to accelerate the computational performance. Our preliminary results show an Peter Paule improvement factor above 15% with respect to the perfor- RISC, JKU Linz mance of the serial version when using very dense (data [email protected] size up to memory card capacity 3 GB) and fine (10 grid points sampling minimum S wavelength ?Smin along propagating distances of 300?Smin ) grids. These encouraging MS75 results motivate us to generalize this method’s GPU im- A Solution of Sun’s $520 Challenge Concerning plementation to 3-D rectangular meshes making it more 520/pi suitable for realistic seismic propagation problems. Series for 1/π and their relation to modular forms have a Jaime A. Parada long history going back to Ramanujan. We will review this Universidad Central connection and give a brief account of the history. We then Venezuela indicate how to prove a Ramanujan-type formula for 520/π [email protected] that was conjectured by Zhi-Wei Sun. A key ingredient is a hypergeometric representation of the relevant double series, which relies on a recent generating function for Legendre MS74 polynomials by Wan and Zudilin. This is joint work with Advances in the Development of the Mimetic Mathew Rogers. Methods Toolkit (MTK): An Object-Oriented API for Mimetic Discretization Methods Armin Straub Tulane University The Mimetic Methods Toolkit (MTK) is an Application [email protected] Programming Interface that allows for an intuitive implementation of Mimetic Discretization Methods (MDMs) for the solution of Partial Differential Equations. The MDMs MS75 yield numerical solutions that guarantee an uniform order Differential Equations, Belyi Maps, and Modular of accuracy, while ensuring the satisfaction of conservative Curves laws. The MTK is developed in C++, thus exploiting the Let L be a homogeneous linear differential equation with advantages of the Object Oriented programming paradigm. polynomial coefficients. L is called a CIS equation if it has 76 AN13 Abstracts

a non-zero Convergent Integer power Series among its so- Feng Bao, Xiaoying Han lutions. All known CIS equations of order 2 are solvable Auburn University in terms of hypergeometric functions; they have solutions fzb@[email protected], [email protected] of the form r0 h + r1 h’ where h = 2F1(a,b;c | f), and r0, r1, f are algebraic functions. A key step to find such a solution is to construct the function f, which is often MS76 a Belyi map. If f is a rational function then we can use The Mixed Finite Element Method for Parameter recent algorithms by T. Fang and V. Kunwar and the clas- Identification in Porous Media sification in arXiv:1212.3803. An example where f is not We analyze a stochastic inverse problem in porous media, a rational function is the generating function of the Apery using the mixed finite element method. We estimate statis- numbers, listed at oeis.org/A005259. A non-rational f has tical moments (mean value, variance) of input data, given at least one conjugate g not equal to f. Then f,g satisfy the PDF of quantities of physical interest, by using sev- an algebraic relation P(f,g)=0. Our strategy to classify all eral identification objectives. We prove the existence of non-rational f’s is to classify these relations P. It turns out an optimal solution, establish the validity of the Lagrange that equations for the modular curve X0(N) provide such multiplier rule, obtain a stochastic optimality system of P. equations, provide error estimates and illustrate the theo- Mark van Hoeij retical results with numerical examples. Florida State University, Mathematics Catalin S. Trenchea [email protected] Department of Mathematics University of Pittsburgh MS76 [email protected] Scaling of High Dimensional Function Approxima- tion MS76 High dimensional function approximation can arise in a Sensitivity and Uncertainty diverse number of circumstances and we specifically fo- While intelligent sampling methods such as sparse grid col- cus on the applications of uncertainty quantification and location has expanded the class of random systems that can data analysis to demonstrate fast scalable methods that be simulated to aid uncertainty quantification, the statis- can capture piecewise smooth functions in high dimensions tical characterization of the model parameters are rarely with high order accuracy and low computational burden. known. We use the Fréchet derivative to determine the Within the field of uncertainty quantification, the devel- most significant parametric variations and generate a low oped methods can be used for both approximation and order family of linearizations of the input-output mapping, error estimation of stochastic collocation methods where which is used in the parameter identification problem. We computational sampling can either be guided or come from illustrate our methods with a numerical example. a legacy database. High dimensional function approximation can also be used in hierarchical data analysis of large, V´ıtor Nunes possibly distributed data, to represent statistics of data in Virginia Polytechnic Institute and State University acompactform. [email protected] Rick Archibald Computational Mathematics Group Hans-Werner Van Wyk Oak Ridge National Labratory Department of Scientific Computing [email protected] The Florida State University [email protected]

MS76 Jeff Borggaard Numerical Solutions for Stochastic Stokes Equa- Virginia Tech tions with White Noise Loading Terms Department of Mathematics [email protected] The nonlinear filter problem can be classified as an inverse problem of identifying the state of a system with noise perturbation given an observation of the system, MS77 also perturbed by noises. Traditional numerical simula- A Spatially Adaptive Iterative Solution of Nonlin- tion methods include unscented Kalman filter and particle ear Operator Eigenproblems filter. In this talk, we attempt to construct efficient numerical methods using forward backward stochastic differential We present a new algorithm for the iterative solution of equations and implicit function theory. Numerical exper- nonlinear operator eigenvalue problems arising from partial iments demonstrate that our methods are more accurate differential equations. This algorithm combines Chebfun- than Kalman filter and more stable than the particle filter. style automatic spatial resolution of linear operators in coefficient space with the infinite Arnoldi method for nonlin- Yanzhao Cao ear matrix eigenproblems. Department of Mathematics & Statistics Auburn University Stefan Guettel [email protected] The University of Manchester AN13 Abstracts 77

[email protected] interpolation of solutions of the forward transport equation, as well as the structures of the specific inverse prob- Elias Jarlebring lems. KTH Stockholm [email protected] Kui Ren University of Texas at Austin [email protected] MS77 Chebfun and Quadrature MS78 Chebfun is an open-source Matlab-based software sys- Marriage and Mathematics of Computed Tomog- tem that extends familiar methods of numerical com- raphy and Magnetic Resonance Imaging putation involving numbers to continuous analogues for functions. This talk discusses Chebfun’s fast capabilities Omni-tomography is enabled by interior tomography that for Clenshaw–Curtis, Gauss–Legendre, –Jacobi, –Hermite, has been developed over the past five years. By omni- and –Laguerre quadrature, based on algorithms of Wald- tomography, we envision that the next stage of biomedi- vogel, Hale and Townsend, and Glaser, Liu, and Rokhlin. cal imaging will be the grand fusion of many tomographic We show how such methods can be applied to quadra- modalities into a single gantry (all in one) for simultaneous ture problems, including: integrals over rectangles, frac- data acquisition of numerous complementary features (all tional derivatives, functions on unbounded intervals, and at once). This integration has great synergistic potential fast computation of barycentric weights. for development of systems biology, personalized and preventive medicine, because many physiological processes are Nick Hale dynamic and complicated, and must be observed promptly University of Oxford and comprehensively. In this perspective, we first present [email protected] the background for and power of omni-tomography, and then discuss a top-level design for the first CT-MRI scanner as a simplified omni-tomographic machine. An impor- MS77 tant application of the CT-MRI scanner is for vulnerable Chebfun2: Extending Chebfun to Two Dimensions plaque characterization known as a holy grail of cardiology, which might bring us exciting collaborative opportunities. An object-oriented MATLAB system is described that extends the capabilities of Chebfun to smooth functions of Ge Wang two variables defined on rectangles. Bivariate functions Biomedical Imaging Division are approximated to essentially machine precision by using Virginia Tech and Wake Forest University iterative Gaussian elimination with complete pivoting to [email protected] form chebfun2 objects representing low rank approximations. Fundamental operations such as integration, eval- Hao Gao uation, and global optimization are described along with Emory University numerical examples. [email protected] Alex Townsend Oxford University MS78 [email protected] Towards the Clinical Implementation of Iterative Cone-beam CT Reconstruction for Radiation Ther- MS77 apy using a Multi-GPU System Chebfun and Approximation Theory An iterative cone beam CT (CBCT) reconstruction system is developed on a quad-GPU workstation. The least Chebfun is all about connecting ideas and theorems of ap- square step is accelerated by distributing the forward and proximation theory with practical numerical computations. backward projection operations among GPUs according to We present some of the highlights in this area. projection angle. The regularization step is accelerated by Nick Trefethen having each GPU processing a sub-volume. A parallel- Oxford University reduction algorithm is employed to accumulate data at [email protected] GPUs. High quality CBCT images for various real clinical applications can be obtained. Efficiency gain is also analyzed. MS78 Fast Algorithms for Some Inverse Problems in Xiaoyu Wang, Hao Yan Medical Imaging Department of Radiation Oncology UCSD We review here some fast numerical techniques for recon- [email protected], [email protected] structions in medical imaging modalities (mainly diffuse optical tomography, optical molecular imaging and quanti- Laura Cervino tative photoacoustic tomography) that are based on the ra- Center for Advanced Radiotherapy Technologies diative transport equation. The methods presented rely on University of California, San Diego the combination of preconditioning, precomputation and [email protected] 78 AN13 Abstracts

Steve Jiang Chiu-Yen Kao UCSD Claremont McKenna College [email protected] [email protected]

Xun Jia Ali Nadim Nadim University of California, San Diego Claremont Graduate University [email protected] [email protected]

Remy Friends Ndangali MS78 Amherst College Variable Step Lengths and Line Search for Nons- [email protected] mooth Image Reconstruction

Despite a burst of advances in optimization algorithms re- Ami Radunskaya Radunskaya cently for nonsmooth image reconstructions, e.g. using to- Pomona College tal variation as regularization, the algorithms either does [email protected] not work, or works with extremely low efficiency, for most real-world image reconstruction problems such as those Scott Shell from medical imaging. The low efficiency is usually due EHDD to the very restrictive constraint on step lengths when [email protected] some subproblems are approximately solved in each iteration. We introduce a new algorithm with nonmonotone line MS79 search strategy that can automatically tune step lengths to Attributing Tropospheric Ozone Formation to Pre- significantly boost the overall convergence with low search cursor Sources Considering Nonlinear Chemistry cost. The improvements are demonstrated on various medical image reconstruction problems. Abstract not available at time of publication.

Xiaojing Ye Antonio Palacios School of Mathematics San Diego State University Georgia Tech Department of Mathematics [email protected] [email protected]

MS79 MS79 Using In Vitro Data to Predict Pathway-Based Ef- Developing Algorithms to Distinguish and Classify fects of Environmental Chemicals Locations Based on Their Weather Sensitivity

Abstract not available at time of publication. Abstract not available at time of publication.

Cymra Haskell Robert Tucker Department of Mathematics Southern California Edison University of Southern California [email protected] [email protected]

MS80 MS79 Stability and Phase Transition in the Kuramoto Next Generation Thermal Management of Build- Model of Coupled Oscillators ings We consider the Kuramoto system of coupled oscillators, This project explores next-generation, environmentally- a model for synchronization and related phenomenon. We friendly cooling and heating of buildings. We explore the prove an index theorem which counts the dimension of the thermal properties of an idealized house, focusing on pas- unstable manifold to a stationary solution, and use this to sive heat losses, solar gain and passive cooling. We discuss prove the existence of a phase transition in the limit of a heat exchange through phase change materials (PCM). We large number of oscillators. Interestingly this phase tran- further discuss model reﬁnements which would be useful in sition does not occur in the scaling primarily considered in building design, selection of materials and in optimizing the previous literature, but in a slightly diﬀerent scaling. building management. Jared Bronski Eun Heui Kim University of Illinois Urbana-Champain California State University at Long Beach Department of Mathematics [email protected] [email protected]

Jan M. Baetens Lee DeVille Ghent University University of Illinois, Department of Math [email protected] [email protected] AN13 Abstracts 79

MS80 range of coexisting structures, including bilayers, pore net- Instability Indices for Matrix Pencils works, pearled pores, and micellular structures. We model the amphiphilic systems through the Functionalized Cahn- There is a well-established instability index theory for lin- Hilliard free energy, and show that competition between ear and quadratic matrix pencils for which the coefficient structures is mediated through the far-field chemical po- matrices are Hermitian and skew-Hermitian. This theory tential. We analyze this competition, showing it can lead relates the number of negative directions for the Hermitian to instabilities and deriving the coupled geometric evolu- matrix coefficients to the total number of unstable eigen- tion of mixed states. values for the pencil. We extend the theory for alternating pencils of any finite degree, and derive quite general re- Keith Promislow, Shibin Dai sults. We also consider Hermitian pencils, and derive some Michigan State University results for cases in which the coefficient matrices satisfy [email protected], [email protected] certain definiteness properties. Arjen Doelman Todd Kapitula Mathematisch Instituut Department of Mathematics [email protected] Calvin College [email protected] Noa Kraitzman Michigan State University Elizabeth Hibma, Hwa-Pyeong Kim [email protected] Calvin College [email protected], [email protected] MS81 Jonathan Timkovich Polynomials with No Zeros on a Face of the Bidisk University of Michigan [email protected] Abstract not available at time of publication. Greg Knese MS80 University of Alabama [email protected] Colliding Convectons

Convectons are strongly nonlinear, spatially localized MS81 states found in thermally driven fluid flows. In a horizontal layer with up-down symmetry odd parity convectons Christoffel Functions and Universality Limits for are stationary. When this symmetry is broken these states Multivariate Orthogonal Polynomials drift. Direct numerical simulations are used to study head- Abstract not available at time of publication. on and follow-on collisions between drifting convectons in binary fluid convection (Mercader et al., J. Fluid Mech. Doron S. Lubinsky 722 (2013) 240), and the results compared with the corre- Georgia Institute of Technology sponding dynamics in a Swift-Hohenberg model. [email protected]

Edgar Knobloch University of California at Berkeley MS81 Dept of Physics On Koornwinder Bivariate Orthogonal Polynomi- [email protected] als

Isabel Mercader, Oriol Batiste Abstract not available at time of publication. UPC, Barcelona, Spain Miguel Pinar [email protected], [email protected] University of Granada [email protected] Arantxa Alonso Fisica Aplicada UPC, Barcelona MS81 [email protected] The C-Function Expansion of the Multivariable Ba- sic Hypergeometric Function

MS80 Abstract not available at time of publication. Competitive Instability and Geometric Evolution in Amphiphilic Systems Jasper Stokman University of Amsterdam Amphiphilic systems possess a surfactant phase which low- [email protected] ers overall free energy by wetting interfacial structures. Unlike classical phase separating systems, such as modeled by the Cahn-Hilliard free energy, which are dominated by MS82 single-layer interfaces, amphiphilic systems support a wide A Two-Phase Augmented Lagrangian Filter 80 AN13 Abstracts

Method tem. It can be shown that in the convex case, the solution of the bound-constrained subproblem is also a solution of We develop a new active-set method whose main computa- a QP subproblem for a stabilized sequential quadratic pro- tional effort can be built on scalable parallel solvers. Our gramming (SQP) method. Numerical results are presented two-phase method consists of a first phase in which we ap- for the method. proximately minimize the augmented Lagrangian to estimate the optimal active set. In the second phase, we solve Elizabeth Wong, Philip E. Gill an equality-constrained QP. An augmented Lagrangian fil- University of California, San Diego ter determines the accuracy of the augmented Lagrangian Department of Mathematics minimization and ensures global convergence. We present [email protected], [email protected] a convergence analysis and preliminary numerical results.

Sven Leyﬀer MS83 Argonne National Laboratory Sensor Geometry leyﬀ[email protected] From the perspective of estimation performance, rather than data collection, after C.R. Rao, Amari, and others, MS82 a sensor may be characterized as a Riemannian manifold Continuous Method Models for Quadratic Pro- where the metric is the Fisher Information. Here we con- gramming with Bound Constraints sider the issue of changing sensors and how to analyse the resulting collection of Riemannian manifolds. It transpires In this talk, some continuous method models for quadratic that, subject to some reasonable hypotheses, such collec- programming problems with bound constraints are intro- tions of sensors can themselves be naturally parametrized duced. The main components for these models are some by a Riemannian manifold. We discuss the calculation of simple dynamical systems which only involve matrix vector geodesics on this manifold for some simple cases. multiplications. Therefore these new models are suitable for large-scale problems. Based on these models, various William Moran theoretical properties including the strong convergence of University of Melbourne these dynamical systems will be explored and addressed. [email protected] Some preliminary numerical results are presented to illustrate the attractiveness of these new models. MS83 Li-Zhi Liao Radar Imaging Work at MIT Lincoln Laboratory Hong Kong Baptist University [email protected] Abstract not available at time of publication. Heather Palmeri MS82 Rensselaer Polytechnic Institute On Solving L-BFGS Trust-Region Subproblems [email protected]

We present a new method called the Moré-Sorensen Se- quential (MSS) method for computing the minimizer of MS83 a quadratic function defined by a limited-memory BFGS Radar Waveform Design matrix subject to a two-norm trust-region constraint. This Abstract not available at time of publication. solver is an adaptation of the Moré-Sorensen direct method into a L-BFGS setting for large-scale optimization. The Ali Pezeshki MSS method uses a recently proposed fast direct method Colorado State University for solving large shifted BFGS systems of equations. [email protected] Jennifer Erway Wake Forest University MS83 [email protected] Statistical and Analytical Techniques in Synthetic Aperture Radar Imaging RoummelF.Marcia University of California, Merced We present a synthetic-aperture radar inversion scheme [email protected] (correlation SAR imaging) that performs data pre- processing in which we correlate pairs of received data with different slow-time values and frequencies. It is found that MS82 the point-spread function (PSF) of the image-fidelity oper- Primal-Dual Regularized Methods for Nonlinear ator has a narrower main lobe and also reduced sidelobes Programming when compared to the standard SAR PSF. It is shown that when data pairs are chosen carefully the effect of volume We present a regularized method for solving general scattering clutter is mitigated. quadratic programs (QP). The method solves a sequence of bound-constrained subproblems in the primal-dual vari- Kaitlyn Voccola ables, which involve the solution of a regularized KKT sys- Colorado State University AN13 Abstracts 81

[email protected] MS84 CDF Solutions of Nonlinear Hyperbolic Equation with Uncertain Parameters MS84 Fast Linear Algebra for Stochastic Inversion in Uncertainty is everywhere, from the nuclear reactors, mate- Large-Scale High-Dimensional Complex Systems rial discovery to reactive transport in heterogeneous porous media. Quantifying the uncertainty associated with the pa- Large scale inverse problems, which frequently arise in en- rameters in complex systems is critical, which can help us gineering applications, involve estimating unknowns from to verify our modern simulation codes and assess confidence sparse data. The goal is to evaluate the best estimate, levels. Our aim is to use accurate computational simula- quantify the uncertainty in the solution, and obtain con- tions to predict the behavior of complex systems. The im- ditional realizations. Traditional Bayesian approaches to portance of uncertainty quantification has been recognized obtain the above, suffer from the fact that the method by the computational science and engineering communi- becomes computationally expensive, when the number of ties. Many stochastic algorithms and techniques have been unknowns is large; typically scaling as the square or cube developed. The explosion in computational effort associ- of the number of unknowns, and thereby making it compu- ated with the large number of random dimensions is often tationally intractable. In this talk, I will present fast lin- prohibitive, even for modern supercomputers. As such, ear algebra techniques based on fast multipole method and advanced stochastic approximation techniques are neces- hierarchical matrices that reduce the computational com- sary to minimize the complexity of mathematical mod- plexity to almost linear complexity. This new technique is els and make numerical solutions feasible. This mini- applied to a realistic large scale stochastic inverse problem symposium will explore recent advances in numerical al- arising from a cross-well seismic tomography application. gorithms and applications for uncertainty quantification, Sivaram Ambikasaran model reduction, and stochastic inversion in large-scale Institute for Computational and Mathematical high-dimensional complex systems. Engineering Peng Wang, Alexandre M. Tartakovsky, Kenneth D. Stanford University Jarman [email protected] Pacific Northwest National Laboratory [email protected], [email protected], Eric F. Darve [email protected] Stanford University Mechanical Engineering Department Daniel M. Tartakovsky [email protected] University of California, San Diego [email protected] MS84 Bayesian Treed Multivariate Gaussian Process for MS84 Uncertainty Quantification Improved Diffusion Monte Carlo for Quantum Computer experiments (numerical simulations) are widely Monte Carlo, Rare Event Simulation, Data Assim- used in scientific research to study and predict the behavior ilation, and More of complex systems, which usually have responses consist- Diffusion Monte Carlo (DMC) is a workhorse of stochastic ing of a set of distinct outputs. The computational cost computing. It was invented forty years ago as the central of the simulations at high resolution are often expensive component in a Monte Carlo technique for estimating var- and become impractical for parametric studies at different ious characteristics of quantum mechanical systems. Since input values. To overcome these difficulties we develop a then it has been used in applied in a huge number of fields, Bayesian treed multivariate Gaussian process (BTMGP) often as a central component in sequential Monte Carlo as an extension of the Bayesian treed Gaussian process techniques (e.g. the particle filter). DMC computes aver- (BTGP) in order to model and evaluate a multivariate pro- ages of some underlying stochastic dynamics weighted by cess. A suitable choice of covariance function and the prior a functional of the path of the process. The weight func- distributions facilitates the different Markov chain Monte tional could represent the potential term in a Feynman- Carlo (MCMC) movements. We utilize this model to se- Kac representation of a partial differential equation (as in quentially sample the input space for the most informative quantum Monte Carlo) or it could represent the likelihood values, taking into account model uncertainty and exper- of a sequence of noisy observations of the underlying sys- tise gained. A simulation study demonstrates the use of tem (as in particle filtering). DMC alternates between an the proposed method and compares it with alternative ap- evolution step in which a collection of samples of the un- proaches. derlying system are evolved for some short time interval, Guang Lin, Bledar Konomi and a branching step in which, according to the weight Pacific Northwest National Laboratory functional, some samples are copied and some samples are [email protected], [email protected] eliminated. Unfortunately for certain choices of the weight functional DMC fails to have a meaningful limit as one decreases the evolution time interval between branching Georgios Karagiannis steps. We propose a modification of the standard DMC pacific Northwest National Laboratory algorithm. The new algorithm has a lower variance per [email protected] workload, regardless of the regime considered. In partic- 82 AN13 Abstracts

ular, it makes it feasible to use DMC in situations where fects. the “naive’ generalization of the standard algorithm would be impractical, due to an exponential explosion of its vari- Valerio Lucarini ance. We numerically demonstrate the effectiveness of the Universität Hamburg, Hamburg, Germany new algorithm on a standard rare event simulation problem [email protected] (probability of an unlikely transition in a Lennard-Jones cluster), as well as a high-frequency data assimilation prob- MS85 lem. We then provide a detailed heuristic explanation of Estimating Uncertainties in Statistics Computed why, in the case of rare event simulation, the new algo- from Simulations of Chaotic Systems rithm is expected to converge to a limiting process as the underlying stepsize goes to 0. We propose an extension of Richardson extrapolation that can be applied to simulation outputs that are affected by Jonathan Weare sampling error, such as statistical outputs from simulations University of Chicago of chaotic systems. The method involves a direct estimate Department of Mathematics of the sampling error that is used to formulate a Bayesian [email protected] inverse problem to infer parameters of a discretization error model. The process is demonstrated on the Lorenz Martin Hairer equationsaswellasDNSofaRe = 180 channel flow. The University of Warwick τ [email protected] Todd Oliver,RobertD.Moser University of Texas at Austin [email protected], [email protected] MS85 Towards Least Squares Sensitivity Analysis of Chaotic Fluid Flows MS85 Challenges in Sensitivity Analysis and Uncertainty We present the least squares sensitivity analysis method Quantification of Chaotic Systems of computing sensitivity derivatives of long time averaged quantities in chaotic dynamical systems. This method is Many dynamical systems of scientific and engineering im- based on linearizing the least squares problem of the gov- portance are chaotic. These chaotic systems can be found erning equation, instead of the ill-conditioned initial value in unsteady fluid flows, our climate system and molecular problem. We demonstrate least squares-based sensitivity dynamics. In these systems, it is interesting to compute computation on a variety of chaotic systems, and its appli- the derivative of output quantities of interest to input pa- cation in optimization and error estimation. rameters. These sensitivity derivatives are useful in many aspects of computational engineering, including optimiza- Patrick Blonigan tion, uncertainty quantification, statistical inference, error MIT estimation and mesh adaptation. However, we show that [email protected] existing methods for sensitivity analysis, including the tangent linear method and the adjoint method, often fail in Qiqi Wang chaotic systems. The inability to exchange a limit and a Massachusetts Institute of Technology derivative is the mathematical reason of this failure. We [email protected] present analysis of the challenge and potential methods for overcoming it. MS85 Qiqi Wang Multi-Level Dynamical Systems: Connecting the Massachusetts Institute of Technology Ruelle Response Theory and the Mori-Zwanzig Ap- [email protected] proach

We consider the problem of deriving approximate au- MS86 tonomous dynamics for a number of variables of a dynami- Immunity Consequences of Crispr-Induced Host- cal system, which are weakly coupled to the remaining vari- Viral Co-Evolution ables. We show that by using the Ruelle response theory on such a weakly coupled system it is possible to construct A new form of adaptive immune defense has recently been a surrogate dynamics, such that the expectation value of discovered in bacteria and archaea (known as CRISPR) any observable agrees, up to second order in the coupling where hosts acquire resistance from genetic material of in- strength, to its expectation evaluated on the full dynam- fecting viruses. We show using an eco-evolutionary model ics. We then show that such surrogate dynamics agree up how CRISPR-induced resistance facilitates the emergence to second order to an expansion of the Mori-Zwanzig pro- and ﬂuctuation of distributed immunity (DI) - the extent jected dynamics. This implies that the parametrizations of to which immunity is due to a diversity of alleles. Our ﬁnd- unresolved processes suited for prediction and for the rep- ings suggest novel ways host-viral interactions are linked to resentation of long term statistical properties are closely complex population structure. related, if one takes into account, in addition to the widely adopted stochastic forcing, the often neglected memory ef- Lauren Childs Harvard University AN13 Abstracts 83

Department of Epidemiology Processes [email protected] In this work, we conduct finite difference simulations of mode II dynamic ruptures along a straight interface (fault) MS86 within a 2-D elastic medium where the constitutive friction Computational and Statistical Models for Detect- law accounts for a strong weakening behavior of the friction ing Natural Selection in Humans coefficient at high velocities and the thermal pressurization of pore fluid. Thus, the mathematical model is given by New sequencing technologies have revolutionized the field linear elastodynamics at off-fault points combined to non- of population genetics since sequencing whole genomes is linear boundary conditions at the sliding interface. In our now faster and cheaper. However, in order to get max- numerical implementation, we use as a starting point the imal benefit from the data one needs to combine better fourth-order Mimetic Operators with Split-Nodes (MOSN) statistical estimators of mutation frequencies with detailed method for rupture simulations on velocity-and-state fric- mathematical models that enables the inference of demo- tional interfaces that applies an implicit Euler integration graphic and natural selection parameters. I will discuss of the semi-discrete elastic-fault system which is highly stiff these approaches in an application to find the genetic basis at early stages of rupture propagation. Here, we add a for adaptation to high altitude in Tibetans. semi-analytical integration of the coupled diffusion equations for temperature and pore pressure evolution. Emilia Huerta-Sanchez University of California Berkeley Sergio Rivas [email protected] Dept of Computer Science UCV Venezuela [email protected] MS86 A Multi-Scale Mathematical Model of Aspergillus Adelis Nieves Fumigatus in the Airway Dept of Computer Sience The innate immune response to exposure to the ubiqui- Universidad Central de Vzla tous fungus Aspergillus fumigatus, the causative agent of [email protected] invasive aspergillosis, is complex, and involves mechanisms at several spatial scales, from molecular networks inside Otilio Rojas different types of cells to tissue-level and organism-level Dept of Computer Science phenomena. This talk will describe a multi-scale mathe- Universidad Central de Vzla matical model of the immune response that incorporates [email protected] both important aspects of the host response as well as the fungus. Steven Day Dept Of Geological Science Reinhard Laubenbacher San Diego State University Virginia Bioinformatics [email protected] Institute [email protected] MS87 Low Dispersive Mimetic Modeling of Rayleigh MS86 Waves on Partly Staggered Grids Dynamics of an mRNA-Protein Model with Delay In elastic media, current finite difference (FD) implemen- In this talk I will describe a dynamical systems approach tations of free surface boundary conditions on partly stag- for the study of a mRNA-protein model that incorporates gered grids (PSG) use the highly dispersive and low accu- negative feedback, nonlinear interactions, and delays. I will rate vacuum formulation. So called because the physical show how the DDE system undergoes an important transi- boundary is replaced by a thin vacuum grid layer where tion from equilibrium to oscillations via a Hopf bifurcation. material parameters are practically zeroed at grid points The final outcome results in closed form expressions for the (null Lame constants at stress nodes and density 0.001 kg limit cycle amplitude and frequency of oscillation, which m-3 at displacement nodes) and surface displacements are are then used to prove that delays can drive oscillations in computed by the discretized interior elastodynamics. In gene activity. this work, we enhance a 2-D PSG by the inclusion of Com- pound nodes (stress-displacement grid points) along a flat Anael Verdugo free surface boundary and use lateral mimetic second-order Virginia Tech FD discretization of the exact zero-traction conditions to Virginia Bioinformatics Institute calculate surface displacements. At interior grid points, [email protected] spatial discretization replicates existent PSG schemes and applies mimetic fourth-order staggered FD along cell di- MS87 agonals, while nodal second-order FD allows progressing Finite Difference Modeling of Rupture Propagation wavefields in time. under Velocity-dependent and Thermal Weakening Otilio Rojas Universidad Central De Venezueal 84 AN13 Abstracts

[email protected] Dept Math U. Tennessee Beatriz Otero [email protected] Department d’Arquitectura de Computadors, Universitat Politè Cheng Wang Spain University of Massachusetts [email protected] Dartmouth, MA [email protected] Jose Castillo Computational Science Research Center John Lowengrub San Diego State University Department of Mathematics [email protected] University of California at Irvine [email protected] MS87 High-Order Mimetic Modelling of 3D Surface MS88 Waves A High-Performance Solution to the Functionalized Cahn-Hilliard Equation We present a mimetic approach to the modelling of 3D elastic seismic waves in the presence of topography. The The Functionalized Cahn-Hilliard (FCH) equation in three 2 2 2 finite-difference computational grid is smoothly deformed dimensions, ut =Δ( Δ − W (u)+ η)( Δu − W (u)), in order to honor the topography. By using high-order describes pore network formation in a functionalized poly- Castillo-Grone operators, the free-surface condition can be mer/solvent system. The physical process is defined by accurately fulfilled. Consequently, the number of points multiple time-scales, requiring very long, accurate simula- required to model a desired wavelength remains low. This tions to correctly describe the physics. We use a Fourier is of crucial importance when performing large-scale simu- spectral method in space with an exponential time integra- lations of seismic waves in rough hilly terrains. tor to obtain a fast, numerically stable, and time-accurate method for solving the FCH equation. Numerical results Josep de La Puente on a GPU show a 10x speedup over a fully-parallelized Barcelona Supercomputing Center eight-core CPU. Spain [email protected] Jaylan S. Jones, Andrew Christlieb, Keith Promislow Michigan State University José E. Castillo [email protected], [email protected], San Diego State University [email protected] Department of Mathematics [email protected] MS88 Miguel Ferrer, Jose Maria Cela A Thermodynamically Consistent Algorithm for Barcelona Supercomputing Center Liquid-Vapour Phase Transition [email protected], [email protected] In this work, novel numerical technologies are developed for multiphase flow problems with particular focus on the MS88 isothermal Navier-Stokes-Korteweg equations. First, in the presence of a non-local surface energy term, entropy vari- Second-order Convex Splitting Schemes for the ables are generalized to a functional definition. It will be Periodic Nonlocal Cahn-Hilliard and Allen-Cahn shown that the weighted residual formulation in terms of Equations the functional entropy variables leads to an unconditionally We devise second-order accurate, unconditionally uniquely energy stable semi-discrete formulation. Second, a fam- solvable and unconditionally energy stable schemes for the ily of new quadrature rules is developed with the aim of nonlocal Cahn-Hilliard (nCH) and nonlocal Allen-Cahn generating new temporal discretizations. This time inte- (nAC) equations for a large class of interaction kernels. We gration methodology enjoys several appealing features: (1) prove the unconditionally solvability and energy stability. the nonlinear stability of the semi-discrete scheme is in- We also present numerical evidence that both schemes are herited at the fully discrete level; (2) the time accuracy is convergent, and in the case of the nAC equation, a proof second-order; (3) there is no convexity requirement for the of convergence can be carried out. Finally we demonstrate entropy function. A comprehensive set of numerical ex- the performance of our algorithms by simulating nucleation amples is studied to examine the aforementioned theories. and crystal growth for several choices of interaction kernels. Ju Liu Zhen Guan Institute for Computational Engineering and Sciences UC Irvine The University of Texas at Austin [email protected] [email protected]

Steven Wise Hector Gomez AN13 Abstracts 85

University of A Coru˜na MS89 [email protected] Maintaining An Online Publication List

John Evans, Thomas Hughes Abstract not available at time of publication. Institute for Computational Engineering and Sciences Tamara G. Kolda The University of Texas at Austin Sandia National Laboratories [email protected], [email protected] [email protected] Chad Landis Aerospace Engineering and Engineering Mechanics MS89 The University of Texas at Austin SIAM’s New Online Community Platform [email protected] Abstract not available at time of publication.

MS88 Karthika Muthukumaraswamy A Gradient Stable Numerical Method For The SIAM Functionalized Cahn-Hilliard Equation [email protected]

I will discuss a nonlinear semi-implicit numerical scheme for a high order nonlinear diffusive phase field model equa- MS90 tion describing phase transformation and porous network Investigation of Iterative Image Reconstruction for formation in a functionalized polymers and solvent system. X-Ray Phase-Contrast Imaging The modeling equation is highly nonlinear and stiff, therefore very restrictive on time step size for explicit numerical X-ray phase-contrast (XPC) computed imaging methods simulation. The physical process has two different scales: are rapidly emerging and hold great potential for biomed- early phase separation, which requires accuracy in both ical imaging. A compelling advantage of XPC imaging time and space discretization; late porous network combi- over conventional radiographic methods is that it does not nation and slow evolution to steady state, which demands rely solely on X-ray attenuation contrast and is sensitive the simulation to be run for a long range of time. The to the refractive and small-angle scattering properties of scheme we shall discuss is unconditionally gradient stable, tissues. In this work, we describe iterative algorithms for therefore allowing adaptive time step strategy for the accu- reconstructing volumetric images of tissue properties from rate and fast simulation of the physical process while pre- knowledge of noisy and/or incomplete measurement data. serving the discrete energy law. The scheme is designed by Mark Anastasio, Qiaofeng Xu, Huifeng Guan, Trey splitting the chemical potential in an explicit-implicit fash- Garson ion based on contraction and expansion of gradient com- Washington University in St. Louis ponents. [email protected], [email protected], Zhengfu Xu [email protected], [email protected] Michigan Technological University Dept. of Mathematical Sciences MS90 [email protected] Adaptive Algorithms for Accelerated Dynamic MRI MS89 We introduce adaptive parametric image representations Tools for Social Media to represent dynamic MRI signal. The parameters and Abstract not available at time of publication. the representation are simultaneously estimated from the under-sampled measurements. Since the number of de- David F. Gleich grees of freedom of this model is much smaller than Purdue University that of current low-rank and compressed sensing methods, [email protected] this scheme provides improved reconstructions for datasets with considerable inter-frame motion. The utility of different dictionary constraints and penalties on the coefficients MS89 are explored to further improve the reconstructions. Nu- More Tools for Social Media merical comparisons of the proposed scheme with classical methods demonstrate the significant improvement in per- I will discuss how and why social media can be useful for a formance in the presence of motion. researcher, both as a consumer and a contributor, drawing on my own experiences of using Twitter and blogging with Mathews Jacob Wordpress. I will also discuss how SIAM is using social Electrical and Computer Engineering media. University of Iowa [email protected] Nicholas J. Higham University of Manchester Sajan Goud Lingala School of Mathematics University of Iowa [email protected] 86 AN13 Abstracts

[email protected] pled scheme, called the kinematically coupled beta-scheme, will be introduced. Stability and convergence will be discussed, and numerical examples will be presented. MS90 Dose Shaping and Carving - Utilizing Sparsity and Suncica Canic Learning Department of Mathematics University of Houston Treatment planning in radiotherapy is a multi-objective op- [email protected] timization problem, with various objectives and unknown balancing. The dose map and the control fluence variables Martina Bukac relate via a linear system, analogous to CT reconstruction. University of Pittsburgh Our work addresses these issues from two perspectives: (1) Department of Mathematics various sparsity objectives are introduced to enable dose [email protected] shaping and carving, based on desired dose properties; and (2) a learning approach with approximate consistency to B. Muha automate balancing the various objectives in the compos- University of Zagreb ite optimization. Department of Mathematics Dan Ruan, George Sayre, Patrick Kupelian, Daniel Low [email protected] UCLA [email protected], [email protected], pku- MS91 [email protected], [email protected] Algorithms Composition Approach Based on Dif- ference Potentials Method MS90 In this talk we will discuss an efficient and flexible Al- Source Recovery in RTE-based Bioluminescent To- gorithms Composition Framework for the elliptic and mography parabolic problems in composite and complex domains. As one of the new emerging optical molecular imaging The elliptic and parabolic equations which will be stud- modalities, bioluminescence tomography is to reconstruct ied in this work serve both as the simplified models, and the light distribution inside a small animal body from the as the first step towards future development of the pro- measured photon data on its surface. Such light distri- posed framework for more realistic systems of materials, bution can either be generated by external light sources fluids, or chemicals with different properties in the different (DOT), or by internal bioluminescent source (BLT), both domains. The developed Algorithms Composition Frame- of which can be described by the radiative transfer equation work can handle the complex geometries of the domains (RTE). In this paper, we consider the BLT source recovery without the use of unstructured meshes, and can be em- problem of RTE. The model is constructed to minimize the ployed with fast Poisson solvers. Our method combines difference between a predicted distribution and the light the simplicity of the finite difference methods on Carte- distribution generated by a predicted source within the sian meshes with the flexibility of the Difference Potentials body, together with the difference between the predicted method. The proposed framework is very well suited for distribution and the data measured on boundary. The to- parallel computations as well, since most of the computa- tal variation of the light source is taken as one of the regu- tions in each domain are performed independently of the larization term so that the minimization of surface area of others. Some numerical results to illustrate the accuracy a light source is achieved. We apply the alternating direc- and the efficiency of the developed method will be pre- tion multiplier method to decouple the system governing sented as well. the light distribution and source data. A Projected Uzawa Yekaterina Epshteyn method and Alternating Lagrangian Multiplier Method are Department of mathematics apply to minimize the total variation regularization term. University of Utah Tianyi Zhang, Jianfeng Cai, Weimin Han [email protected] Department of Mathematics University of Iowa MS91 [email protected], [email protected], weimin- Solving PDEs in Dynamic, Complex Geometries: [email protected] The Diffuse Domain Method

Abstract not available at time of publication. MS91 A Loosely Coupled Scheme for Fluid Structure- John Lowengrub Structure Interaction with Application to Blood University of California, Irvine Flow Department of Mathematics [email protected] The speaker will talk about modeling and simulation of FSI between an incomprensible, viscous ﬂuid and a structure composed of several layers: a thin layer modeled by the MS92 membrane or shell equations, and a thick layer modeled by Relaminarization of Turbulent Channel Flow by the equations of 2D or 3D elasticity. A stable loosely cou- AN13 Abstracts 87

Pre-determined Control optimization-based methods. Numerical examples are included. Abstract not available at time of publication. Hans-Werner Van Wyk Koji Fukagata Department of Scientiﬁc Computing Keio University, Japan The Florida State University [email protected] [email protected]

MS92 Kevin Pond Airforce Institute of Technology Well-Posedness of Supersonic and Transonic kevin.pond@afit.edu Characteristic Discontinuities in Two-Dimensional Steady Compressible Euler Flows Jeff Borggaard We present several important physical problems involv- Virginia Tech ing strong vortex sheets/entropy waves and discuss global Department of Mathematics well-posedness (existence in Bounded Variation space and [email protected] L1-stability) of these characteristic discontinuities for two- dimensional steady supersonic and transonic Euler flows MS93 using the wave front tracking method. Our results indicate that steady vortex sheets/entropy waves in these flows, as Streaming Singular Value Computations on GPU time-asymptotics, are stable in structure globally, in con- Platforms trast with the prediction of the instability of these waves at Graphics processing units provide a significant computa- high Mach numbers as time evolves. Some related control tional advantage over traditional CPUs, but they present problems will be discussed. This is joint work in part with challenges due to their relatively limited memory and the Gui–Qiang G. Chen (University of Oxford) and Hairong latency involved in device/host communication. We de- Yuan (East China Normal University). scribe an implementation of the Low-Rank Incremental Vaibhav Kukreja SVD which exploits the streaming characteristic of the al- Naval Postgraduate School gorithm to overcome these challenges. We demonstrate [email protected] the performance of the method, compare it against traditional approaches, and discuss possible application on other memory-constrained platforms. MS92 Optimally Controlling Unsteady Shock Waves Christopher G. Baker Oak Ridge National Laboratory This talk will demonstrate formulation of unsteady shock [email protected] wave attenuation as an optimal control problem. An adjoint-based shooting algorithm is used to satisfy all first- MS93 order necessary optimality conditions. Distributed control solutions with certain physical constraints are calcu- Multifrontal Sparse QR Factorization on a GPU lated for attenuating blast waves similar to those generated Sparse direct methods exhibit a mix of regular and ir- by Ignition Over Pressure (IOP) from the Shuttle’s Solid regular computations. Nodes in a multifrontal assembly Rocket Booster during launch. Results are presented for tree represent the factorization of a dense submatrix, and attenuating shocks traveling at Mach 1.5 and 3.5 down to edges represent the assembly of data from child to par- 85%, 80% and 75% of the uncontrolled wave’s driving present. We demonstrate a sparse QR multifrontal method in sure. which multiple frontal matrices are simultaneously factor- Nathan D. Moshman ized and assembled on the GPU with a high occupancy rate Naval Postgraduate School and streamlined asynchronous data movements to/from [email protected] the CPU. Timothy A. Davis MS92 University of Florida Identifying Random Parameters Through Parallel Computer and Information Science and Engineering Inversion [email protected]

The incorporation of parametric uncertainty in the sim- Sanjay Ranka ulation of complex physical phenomena has become com- CISE, University of Florida, USA mon practice. Yet, exact stochastic descriptions of these [email protected]fl.edu model parameters are often unknown and must be estimated from measurements of related model outputs. We Sencer Nuri Yeralan, Helia Zandi present a sampling-based method for the identification of Computer and Information Science and Engineering distributed stochastic parameters that lends itself more University of Florida readily to parallel implementation than it’s Bayesian coun- [email protected]fl.edu, [email protected]fl.edu terpart, while allowing for more adaptivity than related 88 AN13 Abstracts

Sharanyan Chetlur MS94 NVIDIA Efficient Exponential Time Differencing Methods [email protected]fl.edu for the Valuation of American Options with Multi- State Regime Switching

MS93 We propose new exponential time differencing schemes to KokkosArray : Multidimensional Arrays for Many- solve the PDE systems for pricing two assets American op- core Performance-Portability tion with regime switching. Multistate regime switching for two assets adds significant complexity in the PDE sys- Performance on manycore devices is dependent data ac- tems due to regime coupling. Different interest rates and cess patterns where different devices (NVIDIA, Intel- volatilities make the problem more challenging. Numeri- Phi, NUMA) require different data access patterns. A cal examples demonstrate the efficiency and reliability of performance-portable programming model does not force the methods for pricing American options as well Greeks a false-choice between arrays-of-structures or structures- in several regimes. of-arrays, instead it defines abstractions to transparently adapt data structures to meet device requirements. The Muhammad Yousuf KokkosArray library implements this strategy through sim- King Fahd University of Petroleum and Minerals ple and intuitive multidimensional array abstractions. Us- Dhahran, Saudi Arabia ability and performance-portability is demonstrated with [email protected] proxy-applications for finite element and molecular dynamics codes. Ruihua Liu University of Dayton H. Carter Edwards Department of Mathematics Sandia National Laboratories [email protected] [email protected] Abdul M. Khaliq MS93 Middle Tennessee State University Exploiting Trends in Emerging Manycore Proces- Department of Mathematical Sciences sors [email protected]

Although there is still a lot of uncertainty in the design of future manycore systems, some trends are emerging and are MS94 worth targeting for new algorithms and software. In this Improved Convergence Order of Binomial Tree presentation we talk about strategies that we can use today Methods for Pricing American Options for designing algorithms and software that will be useful Traditional binomial tree for pricing American options has now and in the future. We discuss in particular motivation √ only an accuracy of O(1/ n) where n is the number of and strategies for introducing vectorization, threading and time-steps. In this talk I will present a control variate latency tolerance techniques. technique using capped options to reduce the early exer- Michael A. Heroux cise errors and to improve the convergence order of the Sandia National Laboratories binomial tree. Rigorous proofs of the convergence order Albuquerque, New Mexico, USA are provided and numerical examples are carried out to [email protected] support the theoretical ﬁndings. Jingtang Ma MS94 Southwestern University of Finance and Economics Utility Optimization and Turnpike Properties for [email protected] Long Term Investments

Turnpike properties show that if utility at large wealth lev- MS94 els are similar to power utility, then the investment strategy Implicit-Explicit Time Discretizations for Option converges to the power utility strategy. We study utility Pricing under Jump-Diffusion Models optimization problem and turnpike property. We give a Partial-integro differential (PIDE) formulations are often new and direct proof by use of PDE approach and the used to price options under jump-diffusion models. Their duality method. Our results generalize and improve the discretizations lead to dense matrices or matrix blocks. previous results. We discuss also the turnpike property for With implicit-explicit (IMEX) time discretizations, solu- consumption problem. This talk is based on a joint work tions with these dense matrices can be avoided. Such dis- with H. Zheng. cretizations lead to an efficient and accurate way to price Baojun Bian options. Tongji University Santtu Salmi [email protected] University of Jyvaskyla santtu.salmi@jyu.fi

Jari Toivanen AN13 Abstracts 89

Stanford University Bin Liu [email protected] Brown University School of Engineering bin [email protected] MS95 Fluctuating Hydrodynamics Thermostats for Dy- Thomas R. Powers namic Studies of Soft Materials Using Implicit- Brown University Solvent Coarse-Grained Models Division of Engineering Thomas [email protected] Abstract not available at time of publication.

Paul J. Atzberger MS95 University of California-Santa Barbara [email protected] Stochastic Eulerian Lagrangian Methods for Fluid- Structure in Conﬁned Geometry

MS95 We study the fluid-structure interactions subject to thermal fluctuations in confined geometries. A stochastic Eule- Kinetic Density Functional Theory of Freezing rian Lagrangian method with stochastic force field genera- A theory of freezing of a dense hard sphere gas is presented. tion is presented. To validate the methodology, we perform Starting with a particle description the revised Enskog the- both the pinned particle and particle constrained by the ory is chosen as the equation of motion. Using the Chap- harmonic spring subjected to thermal forces tests. To fur- mann Enskog method, non-local hydrodynamics is derived ther demonstrate the applicability of the methodology, we for the kinetic theory. The over damped limit and the study the mobility and diffusivity of ellipsoids in confined hydrodynamics are analyzed to understand the model as geometry. a time dependent density functional theory. The ability Yaohong Wang of the so derived density functional theory to capture the Department of Mathematics solid liquid phase transition, the existence of a metastable UCSB branch of the liquid phase and the jamming transition is [email protected] demonstrated. Some numerical results to demonstrate the ability of the hydrodynamic model to capture the solid liquid phase transition are also presented. Paul J. Atzberger University of California-Santa Barbara Arvind Baskaran [email protected] Department of Mathematics University of California, Irvine MS96 [email protected] Vortex Swarms

Aparna Baskaran We investigate the dynamics of N point vortices in the Brandeis University plane, in the limit of large N. We consider relative equi- Department of Physics libria, which are rigidly rotating lattice-like configurations [email protected] of vortices. These configurations were observed in several recent experiments [Durkin and Fajans, Phys. Flu- John Lowengrub ids (2000) 12, 289293; Grzybowski et.al PRE (2001)64, Department of Mathematics 011603]. We show that these solutions and their stabil- University of California at Irvine ity are fully characterized via a related aggregation model [email protected] which was recently investigated in the context of biological swarms [Fetecau et.al., Nonlinearity (2011) 2681; Bertozzi MS95 et.al., M3AS (2011)]. By utilizing this connection, we give explicit analytic formulae for many of the configu- Locomotion of Helical Bodies in Viscoelastic Fluids rations that have been observed experimentally. These Many microorganisms swim by rotating helical flagella, of- include configurations of vortices of equal strength; the ten propelling themselves through fluids that exhibit both N+1configurations of N vortices of equal strength and one viscous and elastic responses to deformations. We have vortex of much higher strength; and more generally, N+K studied numerically the force-free swimming of a rotat- configurations. We also give examples of configurations ing helix in a viscoelastic (Oldroyd-B) fluid. The intro- that have not been studied experimentally, including N+2 duction of viscoelasticity can either enhance or retard the configurations where N vortices aggregate inside an ellipse. swimming speed depending on the body geometry and the fluid properties. The numerical results show how the small- Theodore Kolokolnikov amplitude theoretical calculations connect smoothly to the Dalhousie University large-amplitude experimental measurements. [email protected] Saverio E. Spagnolie University of Wisconsin [email protected] 90 AN13 Abstracts

MS96 Michigan State University Spectral Stability Properties of Periodic Traveling fi[email protected] Waves in the Sine-Gordon Equation Xia Wang We study the spectral stability properties of periodic trav- Department of Mathematical Sciences eling waves in the sine-Gordon equation, including waves University of Cincinnati of both subluminal and superluminal propagation veloc- [email protected] ities as well as waves of both librational and rotational types. We prove that only subluminal rotational waves are spectrally stable and establish exponential instability MS97 in the other three cases. Our proof corrects a frequently Uncertainty Quantification for Regional Climate cited one given by Scott. This is joint work with Chris Change Projection Jones, Robert Marangell, and Ramón Plaza. Regional climate model (RCM) output can be very-large- Peter D. Miller to-massive. Several RCMs run for the same period only add University of Michigan, Ann Arbor to the data size. By modeling the RCM output spatially [email protected] and statistically, uncertainties can be quantified, however dimension reduction is a practical imperative. We take a fully Bayesian approach involving dimension reduction. MS96 That reduces the computation time to on the order of Wavenumber Selection in the Wake of Fronts hours. Outputs from the North American Regional Cli- mate Change Assessment Program (NARCCAP) will be We’ll discuss patterns that emerge in the wake of fronts. analyzed. Examples include spinodal decomposition, chemotaxis, and oscillations in chemistry and biology. We focus on the ques- Emily L. Kang tion of wavenumbers selected in the wake. Main results Department of Mathematical Sciences show existence of fronts and predict wavenumbers in terms University of Cincinnati of absolute spectra. [email protected] Arnd Scheel Noel Cressie University of Minnesota National Institute for Applied Statistics Research School of Mathematics Australia [email protected] University of Wollongong [email protected] MS97 Projecting Future Climate Based on Model- MS97 Observation Consistency in the Past Inferential Uncertainty Introduced by Biased Or Forecasting future regional climate is an important societal Missing Observations issue, but challenging. A Bayesian space-time methodology Large volume of climate data have been collected by satel- is proposed, which is based on blending different members lite remote sensing instruments and ground observations of an ensemble of regional climate model (RCM) simula- for climate study. However, many such data sets may tions while accounting for the discrepancies between these carry significant intrinsic bias for statistical inference, due simulations, under present day conditions, and observa- to satellite orbit configuration, ground station locations, or tional records for the recent past. Results are shown for missing observations. In this talk, we discuss the effects of blended forecasts of 21st century climate based on simula- such bias in statistical inference and some potential meth- tions from the North American Regional Climate Change ods to address such issues. This is joint work with Tian Assessment Program (NARCCAP). Chen and Prof. Elizabeth Stasny Dorit Hammerling Tao Shi Statistial and Applied Mathematical Sciences Institute The Ohio State University [email protected] [email protected] Esther Salazar Department of Electrical and Computer Engineering MS97 Duke University Influence of Climate Change on Extreme Weather [email protected] Events

Bruno Sanso The increasing frequency of extreme weather events raises Department of Applied Mathematics and Statistics the question of to what extent such events can be at- University of California Santa Cruz tributed to human causes. This talk will discuss an ap- [email protected] proach to these issues based on extreme value theory, incorporated into a Bayesian hierarchical model for combining Andrew Finley climate models runs and the observational record. We il- Departments of Forestry and Geography lustrate the method with examples related to the European AN13 Abstracts 91

heatwave of 2003, the Russian heatwave of 2010, and the This is joint work with Dennis Ameluxen. Texas/Oklahoma heatwave and drought of 2011. This is joint work with Michael Wehner (Lawrence Berkeley Lab). Martin Lotz School of Mathematics The University of Manchester Richard Smith [email protected] University of North Carolina [email protected] MS98 How Much does it Cost to Find Eigenvalues of Ma- MS98 trices? Phase Transitions in Convex Geometry and Opti- mization: Geometric Foundations The question of the cost of finding eigenvalues of matrices with respect to different algorithms and a probability This is part 2 of the joint work with Martin Lotz. distribution on the space of matrices is an open problem. I will discuss homotopy methods studied in the work of Dennis Ameluxen Diego Armentano and the Francis shift for the QR algo- School of Operations Research and Information rithm. Engineering Cornell University Michael Shub [email protected] IMAS, CONICET, Argentina and Graduate School of CUNY [email protected] MS98 Numerical Homotopy Tracking for Determinantal Representations of Hyperbolic Curves MS99 Radar Imaging through Dispersive Media A smooth curve in the real projective plane is hyperbolic if its ovals are maximally nested. By the Helton-Vinnikov In this work we employ microlocal analysis to solve an in- Theorem, any such curve admits a definite symmetric de- verse scattering problem in radar imaging. Our goal is to terminantal representation. We compute such representa- sense objects of interest embedded in a material that is tions numerically by tracking a specially designed homo- temporally dispersive and address the problem to improve topy in a space of regular real polynomial systems. Giving imaging resolution. We provide with numerical simulations theoretical complexity bounds for the resulting algorithm is of the inverse algorithm. a wide open question. (Joint work with Daniel Plaumann) Jose Hector Morales Barcenas Metropolitan Autonomous University Anton Leykin Mexico City School of Mathematics [email protected] Georgia Institute of Technology [email protected] MS99 A Multiscale Approach to Synthetic Aperture MS98 Radar in Dispersive Random Media Phase Transitions in Convex Geometry and Opti- mization: the Statistical Dimension and Applica- Abstract not available at time of publication. tions Knut Solna Convex optimization provides a powerful approach to solv- University of California at Irvine ing a wide range of problems under structural assumptions [email protected] on the solutions. Examples include solving linear inverse problems or separating signals with mutually incoherent MS99 structures. A curious phenomenon arises when studying Is a Curved Flight Path in SAR better than a such problems; as the underlying parameters in the opti- Straight One? mization program shift, the convex relaxation can change quickly from success to failure. We reduce the analysis of In the plane, we study the transform Rf of integrating a these phase transitions to a summary parameter, the sta- unknown function f over circles centered at a given curve tistical dimension, associated to the problem. We prove γ. This is a simplified model of SAR, when the radar is a new concentration of measure phenomenon for some in- not directed but has other applications, like thermoacoustic tegral geometric invariants, and deduce from this the ex- tomography, for example. We study the problem of recov- istence of phase transitions for a wide range of problems; ering the wave front set WF(f). If the visible singularities the phase transition being located at the statistical dimen- offhitγ once, we show that WF(f) cannot be recovered in, sion. We furthermore calculate the statistical dimension i.e., the artifacts cannot be resolved. If γ is the boundary of in concrete problems of interest, and use it to relate pre- a strictly convex domain Ω, we show that this is still true. viously existing—but seemingly unrelated—approaches to On the other hand, in the latter case, if f is known a priori compressed sensing by Donoho and Rudelson & Vershynin. to have singularities in a compact set, then we show that 92 AN13 Abstracts

one can recover WF(f), and moreover, this can be done in MS100 a simple explicit way, using backpropagation for the wave An Explicit Cross-Entropy Scheme for Mixtures equation. The key issue in importance sampling is the choice of the al- Plamen Stefanov ternative sampling distribution, which is often chosen from Purdue University the exponential tilt family of the underlying distribution. [email protected] However, when the problem exhibits certain kind of non- convexity, it is very likely that a single exponential change of measure will never attain asymptotic optimality and can MS100 lead to erroneous estimates. In this paper we introduce a Metastability and Coarse-Graining of Stochastic simple iterative scheme with combines the cross-entropy System method and the EM algorithm to find an efficient alter- The study of rare events in physical, chemical and biologi- native sampling distributions in the form of mixtures. We cal systems are important and challenging due to the huge also study the applications of this scheme to the estimation span of time scales. Coarse-graining techniques, Markov of rainbow option prices. state models for example, are employed to reduce the de- Hui Wang gree of freedom of the system, and hence enables simulation Division of Applied Mathematics and understanding of the system on a long time scale. In Brown University this talk, we will introduce a novel construction of Markov hui [email protected] state model based on milestoning. We will focus on the analysis of quality of approximation when the original sys- Xiang Zhou tem is metastable. The analysis identifies quantitative cri- Department of Math teria which enable automatic identification of metastable Cityu Univeristy of Hong Kong sets. [email protected] Jianfeng Lu Mathematics Department MS100 Duke University Uncertainty Quantification in Molecular and Meso- [email protected] scopic System

Eric Vanden-Eijnden We propose a method to quantify the uncertainties in a Courant Institute mesoscopic system based on dissipative particle dynamics New York University (DPD). This method employs l1 minimization to recover [email protected] the coefficients in generalized polynomial chaos (gPC) expansion given prior knowledge that the coefficients are “sparse”. We implement this method to study hydrody- MS100 namic properties (viscosity, diffusivity) of DPD fluid. As Sparse Surrogate Model Construction Via Com- DPD simulation is costly, this method exploits information pressive Sensing for High-Dimensional Complex from the limited data, hence it is efficient. Models Xiu Yang,HuanLei For complex models with a large number of input pa- Brown University rameters, surrogate model construction is challenged by xiu [email protected], Huan [email protected] insufficient model simulation data as well as by a prohibitively large number of parameters controlling the surro- George E. Karniadakis gate. Bayesian sparse learning approaches are implemented Brown University in order to detect sparse-basis expansions that best capture Division of Applied Mathematics the model outputs. We enhanced the Bayesian compres- george [email protected] sive sensing approach with adaptive basis growth and with a data-driven, piecewise surrogate construction. MS101 Khachik Sargsyan, Cosmin Safta Hybrid (adjoint/ensemble) Uncertainty Quantifi- Sandia National Laboratories cation Methods for Data Assimilation and Adap- [email protected], [email protected] tive Observation of Environmental Plumes

Bert J. Debusschere Abstract not available at time of publication. Energy Transportation Center Sandia National Laboratories, Livermore CA Thomas Bewley [email protected] Dept of Mechanical and Aerospace Engineering University of California, San Diego Habib N. Najm [email protected] Sandia National Laboratories Livermore, CA, USA [email protected] AN13 Abstracts 93

MS101 a technique for model reduction of nonlinear dynamical How Well Does Polynomial Chaos Model Chaos? systems. I will describe a methodology for automatically applying the method given only code for evaluating the full We explore the effectiveness of polynomial approximations model. Although DEIM has been effective on some very for modeling time averaged statistics from a chaotic dy- difficult problems, it can under certain conditions intro- namical system as a function of the system parameters duce instabilities in the reduced model. I will present a in an attempt to answer, how well does polynomial chaos problem that has proved helpful in developing a method model chaos? for stabilizing DEIM reduced models.

Paul Constantine Russell Carden Stanford University Computational and Applied Mathematics [email protected] Rice University [email protected] MS101 Optimal Maps for Data Assimilation in Nonlinear MS102 Chaotic Systems An Exact Solution Formula for the Kadomtsev- Petviashvili Equation We present a new optimal-map approach to sequential data assimilation, i.e. nonlinear filtering and smoothing. The In general, nonlinear partial differential equations main idea is to push forward a fixed reference measure (NPDEs) do not yield exact solutions and are solved us- to each assimilated state distribution. Our algorithm in- ing numerical methods. Our goal is to use a systematic herently avoids issues of sample impoverishment, since it method to obtain a formula for certain exact solutions to explicitly represents the posterior as the pushforward of a the Kadomtsev-Petviashvili equation, a NPDE in two spa- reference measure. We demonstrate the efficiency and ac- tial and one temporal variable. The formula is expressed curacy of the map approach via data assimilation in several in terms of a constant matrix quadruplet and matrix ex- canonical dynamical models, e.g., Lorenz-63 and Lorenz-96 ponentials. systems. Alicia Machuca Tarek Moselhy Department of Mathematics MIT The University of Texas-Arlington [email protected] [email protected]

Youssef M. Marzouk Massachusetts Institute of Technology MS102 [email protected] Resonant Instability and Nonlinear Wave Interac- tions in Electrically Forced Jets

MS101 We investigate the problem of linear temporal instability of Continuum Heat Transfer Constitutive Laws with the modes that satisfy the dyad resonance conditions and Quantified Uncertainty Extracted from Atomistic the associated nonlinear wave interactions in jets driven Simulations Using Bayesian Inference by either a constant or a variable external electric field. A mathematical model, which is developed and used for the Unclosed partial differential equations (PDE) arise owing temporally growing modes with resonance and their nonlin- to their derivation from coarse-grained small-scale pro- ear wave interactions in electrically driven jet flows, leads cesses. Their closure is a ubiquitous problem in compu- to equations for the unknown amplitudes of such waves tational science. We propose a solution to this problem that are slowly modulated. using Bayesian inference to estimate constitutive relationships based on samples of the underlying small-scale pro- Saulo Orizaga cesses. Uncertainty quantification is required to propagate Department of Mathematics the uncertain closure models through the continuum solu- Iowa State University tion. Both parametric and non-parametric results are pre- [email protected] sented for continuum heat conduction informed by atomistic data. MS102 Jeremy Templeton A Model of Photoreceptor Degeneration in Ze- Sandia National Laboratories brafish Via a Cone Mutation [email protected] Photoreceptors are responsible for vision, and their degeneration, often caused by mutations of the rods or cones, is MS102 one of the leading causes of blindness. Zebrafish, with their Automating and Stabilizing the Discrete Empirical cones more numerous in comparison to the rods than in hu- Interpolation Method for Nonlinear Model Reduc- mans, are important to study for cone mutations that may tion lead to blindness in humans. We propose a mathematical model of photoreceptor interactions of the Zebrafish with The Discrete Empirical Interpolation Method (DEIM) is a cone mutation, analyze the long term dynamics of the 94 AN13 Abstracts

system, and compare results with recent biological investi- Centrum Wiskunde & Informatica gations and findings. The Netherlands [email protected] Stephen Wirkus Arizona State University Amparo Gil Division of Mathematical and Natural Sciences Depto. de Matematicas, Est. y Comput. [email protected] Universidad de Cantabria [email protected] MS103 Special Function Integrals by the Method of Brack- Javier Segura ets Departamento de Matematicas, Estadistica y Computacion Originally developed by Gonzalez and Moll in the study of Universidad de Cantabria, Spain Feynmann diagrams, the ”method of brackets” is a heuris- [email protected] tic method for symbolic definite integration. A Sage implementation and testing against a table of integrals has MS103 shown that this method can be very effective for definite integration problems involving many special functions. Ex- Stieltjes-Wigert Polynomials and the q-Airy Func- perimentation with integrals involving such special function tions as Bessel functions and orthogonal polynomials has Asymptotic formulas are derived for the Stieltjes-Wigert led to improvements of the method. polynomials Sn(z; q) in the complex plane, with the q−Airy Karen Kohl function Aq(z) being used as the approximant. One for- University of Southern Mississippi - Gulf Coast mula holds in any disc centered at the origin, and the other [email protected] holds outside any smaller disc centered at the origin; the two regions together cover the whole plane. For x>1/4, a limiting relation is also established between the q−Airy MS103 function Aq(x) and the ordinary Airy function Ai(x)as Toward an On-Demand Data Service for Special q → 1. Functions Roderick Wong Tables of function values, formerly essential for scientific City University of Hong Kong computing, have been replaced with software. Generally [email protected] available software covers vastly greater argument ranges but accuracy is not uniform. Old tables were painstakingly MS104 checked to avoid this defect. Using interval techniques, NIST and the University of Antwerp are developing an Nonlinear Response of Bio-Polymers Subject to online tables-on-demand capability. It returns uniformly Stretching Flow with Thermal Noise accurate numerical values for specified arguments and pre- The dynamics of elastic filaments subject to hydrodynamic cision, and optionally a digit-by-digit comparison to values forces exhibits complex nonlinear dynamics in the neigh- entered from another source. borhood of stagnation points in the flow. Here, the mo- Daniel Lozier tion of a single inextensible bio-polymer with anisotropic National Institute of Standards and Technology friction tensor subjected to a stretching flow is modeled [email protected] with stochastic differential equations as well as dissipative particle dynamics simulations. Our results show that the Annie Cuyt negative tension induces a stretch-coil transition beyond a University of Antwerp critical value, where the noise is amplificated due to the Dept of Mathematics and Computer Science interaction of thermal noise and nonlinear effects. [email protected] Mingge Deng Division of Applied Math, Brown University MS103 mingge [email protected] Numerical Methods for Special Functions Bruce Caswell For the numerical evaluation of special functions we men- School of Engineering, Brown University tion the basic tools: series expansions, recursions, and [email protected] quadrature. We give examples on how to use tools in recently developed software in our project, in particular how George E. Karniadakis to handle highly oscillating integrals in the complex plain. Brown University We explain how to select suitable quadrature rules, and Division of Applied Mathematics why the simple trapezoidal rule may be very efficient for a george [email protected] certain class of integrals that represent special functions.

Nico M. Temme AN13 Abstracts 95

MS104 the hydrophobic hydration, dry-wet fluctuation, and many Increased Accuracy of Immersed Boundary Meth- other important solvation properties. This talk begins with ods Using Fourier Approximations of Delta Func- a review of the level-set VISM and continues to present tions new developments around the VISM. These include: (1) the coupling of solute molecular mechanical interactions In immersed boundary methods, the fluid and structure in the VISM; (2) the effective dielectric boundary forces; communicate through smoothed approximate delta func- and (3) the solvent fluid fluctuations. Mathematical theory tions with small spatial support. We take a different ap- and numerical methods are discussed, and applications are proach and construct highly accurate approximations to presented. This is joint work with J. Andrew McCammon, the delta function directly in Fourier space. This method Li-Tien Cheng, Joachim Dzubiella, Jianwei Che, Zhong- leads to high-order accuracy away from the boundary and ming Wang, Shenggao Zhou, and many others. significantly smaller errors near the boundary. We present accuracy tests and simulation results from an application Bo Li in cell biology in which large errors in the traditional IB Department of Mathematics, UC San Diego method produce unphysical results. [email protected]

Robert Guy Deptartment of Mathematics, U.C. Davis MS106 [email protected] A Difference of Convex Method to Select Point Correspondences for Image Registration David Hartenstine This talk will present an algorithm for image registration Department of Mathematics that is based on minimizing a difference of convex model. Western Washington University The method selects point correspondences between images [email protected] by identifying pairs of points that have similar local features and are also consistent with a given deformation Wanda Strychalski model. We consider both affine transformations and more Department of Mathematics general smooth displacement fields. The unknown defor- University of California, Davis mation is reconstructed from estimated displacements at [email protected] relatively few points.

Ernie Esser MS104 University of California Irvine The Moment of Fluid Interface Reconstruction UC Irvine Math Department with Filaments: Increasing Sub-Gridcell Resolu- [email protected] tion

The Moment of Fluid (MOF) method is a highly accurate MS106 technique for reconstructing material interface(s) that ex- Compressive Video Using Single Pixel Cameras actly captures material volume and minimizes error in the centroid(s). The method has been extended to perform re- ”Single-pixel cameras” are a new modality for image ac- construction for an arbitrary number of materials in a cell. quisition using compressive measurements. In contrast to In the two material case, the introduction of a fictitious conventional imaging, which relies on arrays of many pho- third material can allow for the resolution of thin, unre- todetectors, single picture cameras obtain high resolution solved structures (filaments) or regions of high curvature, images using only a single detector. This is accomplished detected via error in the centroid(s). using a ”coded aperture,” which compresses global image information into each measurement rather than observing Matthew B. Jemison, Mark Sussman one pixel at a time. In this talk, we discuss the challenges Florida State University of applying these new compressive imaging tools to video [email protected], [email protected] acquisition. Compressive video poses many challenges that imaging does not. We are no longer imaging a static scene, MS104 but rather we must explicitly model the motion of objects Variational Implicit Solvation of Biomolecules and exploit correlations between adjacent frames. Further- more, real-time reconstruction of video from compressive Recent years have seen the initial success of variational measurements requires the use of sophisticated numerical implicit-solvent models (VISM), implemented by the level- algorithms and parallel hardware implementations. set method, for biomolecular interactions. Central in VISM is an effective free-energy functional of all possible solute- Tom Goldstein solvent interfaces, coupling together the solute surface en- Rice University ergy, solute-solvent van der Waals interactions, and elec- Electrical and Computer Engineering trostatic contributions. The level-set relaxation of such [email protected] a functional determines numerically biomolecular equilibrium conformations and minimum free energies. Com- MS106 parisons with experiments and molecular dynamics sim- Fast Algorithms for Adaptive Temporal Compres- ulations demonstrate that the level-set VISM can capture 96 AN13 Abstracts

sion in Video Data Louisiana State University [email protected] Video data is redundant both spatially and temporally, where the temporal redundancy is closely related to the motion changes between successive frames. Recent video MS107 compression often relies on a fixed and relatively low tem- Diffuse Optical Cortical Mapping Using the poral sampling rate. In this talk, we investigate adaptive Bem++ Boundary Element Library video compression by combining the idea of patch based polynomial interpolation with learning. A new technique Diffuse Optical Cortical Mapping (DOCM) is a method of is proposed to detect real-time motion changes based on a mapping the functional activation in the brain by detect- small amount of previously compressed frames. Numerical ing its effect on optical absorption in the near-infrared. It experiment on real data shows this information can help is commonly achieved using a dense array of sources and predict the compression rate adaptively. detectors and a volume model of optical photon propoga- tion. This is a highly underdetermined inverse problem so Yi Yang is usually postprocessed to project the reconstruction onto University of California, Los Angeles the cortical surface. In our method we use a BEM sur- Mathematics Department face formulation. We discuss the implementation of this [email protected] using the public-domain BEM++ library developed by the authors. Hayden Schaeffer University of California, Los Angeles Simon Arridge,TimoBetcke [email protected] University College London [email protected], [email protected] Stanley J. Osher University of California Wojciech Smigaj Department of Mathematics Department of Mathematics [email protected] University College London [email protected]

MS106 Martin Schweiger Alternating Direction Approximate Newton Department of Computer Science Method for Partially Parallel Imaging University College London [email protected] It has been shown that the Bregman operator splitting algorithm with variable stepsize (BOSVS) is globally convergent and asymptotically eﬃcient for magnetic resonance MS107 image reconstruction. However, the convergence of the al- Accelerated Statistical Im- gorithm relies on the choice of a number of parameters. age Reconstruction Methods in X-Ray Computed This paper propose a new algorithm, alternating direction Tomography (ct): Advances in Algorithm Devel- approximate newton (ADAN) method for solving convex opments and Clinical Practices and possibly nonsmooth optimization problem. The global convergence of this algorithm will be established. Experi- Abstract not available at time of publication. mental results and computational analysis are given using Guang-Hong Chen partially parallel magnetic resonance image reconstruction. Department of Medical Physics We show that ADAN yields comparable performance to University of Wisconsin, Madison BOSVS, but it is simpler to implement and employs fewer [email protected] parameters.

Maryam Yashtini MS107 University of Florida Mathematics Department Tensor Framelet based Novel Reconstruction myashtini@ufl.edu Methods for Better and Faster CT Imaging This talk will attempt to address the following two ques- William Hager tions: (Q1) ”Better” Imaging: provided with the same Department of Mathematics CT sinogram, can we develop new reconstruction method University of Florida to further improve the state-of-art image quality? (Q2) hager@ufl.edu ”Faster” Imaging: under the similar image quality standard, can we fully explore the new method for faster CT Cuong Ngo imaging, in terms of (1) faster undersampled 3D/4D data University of Florida acquisition, and (2) faster image reconstruction speed that Department of Mathematics is clinically usable? A key is (A1) the use of L1-type itera- ngocuong@ufl.edu tive reconstruction method based on tensor framelet (TF). Another critical component for developing fast clinically- Hongchao Zhang usable reconstruction is (A2) the rapid parallel algorithm Department of Mathematics and CCT for computing X-ray transform and its adjoint (O(1) per AN13 Abstracts 97

parallel thread). Then we will move on to (A3) the super- rich water injection into sedimentary basins. Thermophys- resolution technique for spiral CT to enhance axial im- ical properties of charged aqueous solutes are computed age resolution and reduce axial partial volume artifacts, using the Helgeson-Kirkham-Flowers model, coupled with (A4) fused Analytical and Iterative Reconstruction (AIR) an advection-diffusion heat transport model, to determine method as a general framework to fuse analytical recon- spatial and temporal temperature profiles during injection. struction method and iterative method, and (A5) adaptive Results show an increase in temperature, caused by the ar- TF Technique for 4D imaging. rival of the CO2-rich injectant, which is in agreement with well data. Hao Gao Emory University Christopher Paolini [email protected] San Diego State University [email protected] MS108 Chris Binter An Overview of Web-Based CO2 Subsurface Flow Exxon Modeling Houston, USA [email protected] Accumulation of greenhouse gases from the combustion of fossil fuels has led to an increase in solar radiation trapped between the earth and atmosphere, which may lead to MS108 catastrophic changes in global weather conditions. With A Study of High-Performance Computing Tools in CO2 being the most abundant greenhouse gas, efforts are Simulating Carbon Dioxide Geologic Sequestration underway to reduce the level of CO2 entering the atmo- Scenarios sphere through sequestration into deep rock formations. Through numerical simulation, one can predict if CO2 can In Carbon Sequestration, codes that simulate water-rock remain permanently sequestered in such formations. interaction and reactive transport sequentially solve mass balance equations for each control volume representing a Christopher Paolini lithology containing charged aqueous solutes. This is not San Diego State University well suited for execution on many-core computers. We [email protected] present the theory and implementation of a numerical scheme whereby solute concentrations in all control vol- Johnny Corbino umes are solved simultaneously by constructing a large Computational Science Research Center block-banded matrix. These matrices are factored with Su- SDSU perLU DIST (Berkeley Laboratory). Performance metrics [email protected] are evaluated.

Eduardo J. Sanchez MS108 San Diego State University Numerical Poroelastic Pressure Diﬀusion Simula- [email protected] tion in CO2 Sequestration

CO2 sequestration in underground aquifers shows signifi- MS109 cant potential in reducing greenhouse gas emissions. How- Best Location of Actuators for the Stabilization of ever, rock fractures, formed during injection, may release the Navier-Stokes Equations toxic species into the water table and release CO2 back into the atmosphere. A pore pressure diffusion module has been We study the boundary feedback stabilization, about an implemented into a reactive transport modeling application unstable stationary solution, of a two dimensional fluid to simulate effects of fluid gain stresses on rocks caused flow described by the Navier-Stokes equations, around a by CO2-rich water injection. Results are compared with disk in a channel. The control is a Dirichlet boundary bottom-hole pressure data from an Oligocene Frio Forma- control localized on the boundary of the disk in two slots tion observation well. of a fixed aperture. A feedback control law is determined by stabilizing the linearized Navier-Stokes equations about Jonathan Mathews the unstable stationary solution. We determine the best CSRC control zone, that is the one minimizing the control norm SDSU of the closed loop linear system, in the case of the worst ¡[email protected]¿ perturbation in the inflow boundary condition. This approach allows us to improve the efficiency of the feedback MS108 control laws when they are applied to the nonlinear system. It will be confirmed by several numerical simulations. This Using the Helgeson-Kirkham-Flowers Model to is a joint work with J.-M. Buchot and M. Fourniéfrom Study Reservoir Temperature Evolution During the Toulouse Mathematical Institute, and C. Airiau and J. CO2 Injection Weller from the Institute of Fluid Mechanics in Toulouse. A one-dimensional numerical heat transfer module has Jean-Pierre Raymond been implemented into a reactive transport modeling ap- Universite Paul Sabatier plication to study temperature effects resulting from CO2- Institut de Mathématiques 98 AN13 Abstracts

[email protected] ditional complexity and detail.

Katherine J. Evans, Richard Archibald MS109 Oak Ridge National Laboratory Balanced POD: Approximation Capability and Po- [email protected], [email protected] tential for Nonlinear Model Reduction

The excellent data approximation capability of proper or- MS110 thogonal decomposition (POD) is well known and is a ma- Reproducibility and Repeatability: A Roadmap for jor reason why POD is widely used for nonlinear model the Computational Scientist reduction. Balanced POD is a recent data-based model reduction algorithm for linear systems of ordinary and par- The ubiquitous presence of parallelism at all levels of com- tial differential equations. We present new results showing puting is forcing difficult choices between reproducible, that balanced POD can produce excellent approximations repeatable computing and performance. This concern is of two separate data sets, and we discuss the potential of emerging within the broader concerns of verification and balanced POD for nonlinear model reduction. validation, creating both new issues and, perhaps, new opportunities. In this presentation, we give a broad overview John Singler of the issues that are of particular interest to computational Missouri S & T scientists. Mathematics and Statistics [email protected] Michael A. Heroux Sandia National Laboratories Albuquerque, New Mexico, USA MS109 [email protected] An Adjoint-Based Approach for the Understanding of Flapping Wings MS110 Adjoint-based methods show great potential in flow control Efficient Reproducible Floating Point Reduction and optimization of complex problems. When unsteady Operations on Large Scale Systems flapping motion and deformation is considered, however, the traditional adjoint-based approach used commonly in On large-scale systems, with highly dynamic scheduling to airfoil design falls short of the definition of sensitivity at improve load balance, users should no longer expect to ob- the unsteady moving/morphing boundary. Using the idea tain identical results from run-to-run for floating point op- from non-cylindrical shape analysis, we are able to derive erations like summation. We propose a technique to obtain an adjoint-based analysis in a rigorous and simple manner reproducibility for the global sum with no extra commu- for the optimization of moving/morphing objects such as nication. Input numbers are decomposed into vectors of flapping wings. floating-point numbers using pre-determined boundaries. All processors can perform their local computations inde- Mingjun Wei,MinXu pendently. The final result is produced by using a special Mechanical and Aerospace Engineering reduction operator: the maximum of boundaries followed New Mexico State University by the sum of corresponding components. This technique [email protected], [email protected] performs well at very large scale where communication time dominates computing time, so that the running time of the reproducible sum is almost equal to the running time of the MS109 standard sum. This technique can be applied to other oper- Malliavin Calculus for Stochastic Point Vortex and ations for example the dot product and the matrix-matrix Lagrangian Models multiplication, as well as to other higher level driver rou- tines such as trsv, trsm. Abstract not available at time of publication. Hong Diep Nguyen Meng Xu University of California-Berkeley Rockefellor University [email protected] [email protected] James Demmel MS110 UC Berkeley Strategies and Challenges of Reproducibility in [email protected] Global Climate Modeling

The standards for reproducibility for climate simulation MS111 are necessarily strict, given the level of attention from the H-to-P Efficiently: A Progress Report on High- broad scientific community, economic and political stake- Order Fem on Manifolds with Applications in Elec- holders, and the general public. A brief summary of several trophysiology recent global Earth system simulation efforts are presented, In this talk, we describe the numerical discretisation of an with a focus on the challenges and strategies to attain re- embedded two-dimensional manifold using high-order spec- producibility as these models are extended to include ad- tral/hp elements. Such methods provide an exponential AN13 Abstracts 99

reduction of the error with increasing polynomial order, systems. while retaining geometric flexibility of the domain. Em- bedded manifolds are considered a valid approximation for Matthew Reyna many scientific problems ranging from the shallow water Rensselaer Polytechnic Institute equations to geophysics. We describe and validate our dis- Department of Mathematical Sciences cretisation technique and provide a motivation of its appli- [email protected] cation to modeling electrical propagation on the surface of the human left atrium. Fengyan Li Rensselaer Polytechnic Institute Chris Cantwell [email protected] Imperial College London [email protected] MS111 Sergey B. Yakovlev, Robert Kirby H-to-P Efficiently: A Progress Report on Hdg in University of Utah 3D School of Computing In this talk, we assess the performance of the Hybridized [email protected], [email protected] Discontinuous Galerkin (HDG) method applied to three dimensional elliptic operators by comparing it to the stati- Nicholas Peters cally condensed continuous Galerkin (CG) method. Perfor- National Heart and Lung Institute mance comparison will include such items as set-up costs, Imperial College London rank, bandwidth and solve times of the global trace system [email protected] and the parallelization efficiency for the two methods.

Spencer Sherwin Sergey B. Yakovlev Imperial College London University of Utah [email protected] School of Computing [email protected] MS111 David Moxey High Order Asymptotic Preserving Methods for Department of Aeronautics Discrete-velocity Kinetic Equations Imperial College London A family of high order asymptotic preserving schemes are [email protected] proposed for several kinetic models with discrete velocity. The methods are based on the micro-macro decomposition Robert Kirby of the equations, and they combine discontinuous Galerkin University of Utah spatial discretizations and IMEX temporal discretizations. [email protected] Both theoretical and numerical studies are carried out to demonstrate the performance of the methods. Spencer Sherwin Imperial College London Juhi Jang [email protected] University of California, Riverside, USA [email protected] MS111 Fengyan Li Error Estimates of RKDG Methods for the Vlasov- Rensselaer Polytechnic Institute Maxwell System [email protected] In this talk, error analysis is established for Runge-Kutta discontinuous Galerkin (RKDG) methods to solve the Jingmei Qiu, Tao Xiong Vlasov-Maxwell system. This nonlinear hyperbolic system University of Houston describes the time evolution of collisionless plasma particles [email protected], [email protected] of a single species under the self-consistent electromagnetic field, and it models many phenomena in both laboratory MS111 and astrophysical plasmas. The methods involve a third or- On the Bound of DG and Central DG Operators der TVD Runge-Kutta discretization in time and upwind for Linear Hyperbolic Problems discontinuous Galerkin discretizations of arbitrary order in phase domain. With the assumption that the exact solu- 2 It is observed that central discontinuous Galerkin (DG) tion has sufficient regularity, the L errors of the particle methods often admit larger time steps than DG methods. number density function as well as electric and magnetic To understand this, we show that for the linear advection fields at any given time T are obtained under certain CFL equation, the norm of the derivative operator from the up- condition. The analysis can be extended to RKDG meth- wind DG method grows quadratically with the order of the ods with other numerical fluxes and to RKDG methods method, while that of the central DG methods grow lin- solving relativistic Vlasov-Maxwell equations. early. Our estimates are validated numerically, and they can be extended to higher dimensions and linear hyperbolic He Yang 100 AN13 Abstracts

Rensselaer Polytechnic Institute (SCTDE) of dumped discretization matrix possessing this Department of Mathematical Sciences conservation property. However, convergence of the Krylov [email protected] subspace approximation of the SCTDE matrix function de- celerates due to appearance of the square root singularity. Fengyan Li We improve convergence by employing extended Krylov Rensselaer Polytechnic Institute subspace. [email protected] Vladimir L. Druskin Schlumberger-Doll Research MS112 [email protected] The Matrix Unwinding Function Rob Remis We introduce a new primary matrix function, called the TU Delft matrix unwinding function, that is instrumental in deriv- rob remis [email protected] ing correct identities involving logarithms. We show that it facilitates the understanding of other complex multivalued Mikhal Zaslavsky matrix functions including inverse trigonometric functions. Schlumberger We also use it to study the matrix sign function. Finally, [email protected] we give a numerical scheme for computing the matrix unwinding function and show how it can be used to compute the matrix exponential using the idea of argument reduc- MS112 tion. Transient Electromagnetic Simulation in Geophys- ical Exploration Mary Aprahamian School of Mathematics In recent work we explored how the initial value problem The University of Manchester for the quasi-static Maxwell’s equations arising in transient [email protected] electromagnetic modeling (TEM) can be solved eﬃciently in the frequency domain by solving a small projected model Nicholas Higham for each relevant frequency using simple shift-and-invert University of Manchester type Krylov subspace projection much in the style of clas- [email protected] sical model order reduction for linear time-invariant control problems. In this work we present more advanced rational Krylov subspace methods employing more elaborate pole MS112 selection techniques. We also compare this frequency do- Block Krylov Subspace Methods and a Precondi- main approach with solving the problem in the time do- tioning Approach for the Matrix Exponential Ac- main using the same rational Krylov subspace methods to tion approximate the action of the matrix exponential.

In the first part of the talk a brief introduction to the Oliver G. Ernst minisession topics will be given. In the second part of TU Bergakademie Freiberg the talk a preconditioned iterative scheme for comput- Fakultaet Mathematik und Informatik ing actions of the matrix exponential will be presented. [email protected] The scheme is based on an acceleration of the exponential Richardson iteration, recently considered in [M.A.Botchev, Stefan Güttel V.Grimm, M.Hochbruck, Residual, restarting and Richard- University of Manchester son iteration for the matrix exponential, SISC, 2013]. This School of Mathematics talk is partly based on a joint work with I. Oseledets [email protected] and E. Tyrtyshnikov, Institute of Numerical Mathematics, RAS, Moscow. Ralph-Uwe Börner Mike A. Botchev Institute of Geophysics University of Twente TU Bergakademie Freiberg [email protected] [email protected]

MS112 MS113 Matrix Functions and Their Krylov Approxima- Stochastic Nucleation in Biology tions for Wave Propagation in Unbounded Do- Stochastic Nucleation in Biology The binding of individ- mains ual components to form composite structures is a ubiqui- Solution of wave problems in unbounded domains requires tous phenomenon within the sciences. Within heteroge- computation of the exponential of the spatial PDE op- neous nucleation, clusters form around exogenous struc- erator with continuous spectrum. To avoid spurious res- tures such as impurities or boundaries, while in homo- onances, the reduced order model should preserve spec- geneous nucleation identical particles cluster upon direct tral continuity of the original problem. The authors intro- contact. Particle nucleation and growth have been exten- duce so-called stability-corrected time-domain exponential sively studied, often assuming inﬁnitely large numbers of AN13 Abstracts 101

monomers and unbounded cluster sizes. These assump- and ribosome size on density profiles and particle currents. tions led to mass-action, mean field descriptions such as The latter translate directly into synthesis rates for the cor- the well known Becker Doering equations. In cellular biol- responding protein. Some intriguing results for real genes ogy, however, nucleation events often take place in confined will be presented. high-level commands. spaces, with a finite number of components, so that discrete and stochastic effects must be included. In this talk we ex- Beate Schmittmann amine finite sized homogeneous nucleation by considering Department of Physics a fully stochastic master equation, solved via Monte-Carlo Virginia Tech simulations and via analytical insight. We find striking [email protected] differences between the mean cluster sizes obtained from our discrete, stochastic treatment and those predicted by Jiajia Dong mean field treatments. We also consider heterogeneous nu- Bucknell University cleation stochastic treatments, first passage time results [email protected] and possible applications to prion unfolding and clustering dynamics. Royce Zia Department of Physics Maria D’Orsogna Virginia Tech CSUN [email protected] [email protected]

MS113 MS113 A Discontinuous Method for Analyzing and Mod- Introducing Stochasticity into a Continuum Model eling Delay Due to Pauses During Transcription for Transcription A Discontinuous Galerkin Finite Element Method is used Experimental data indicates that polymerase motion on for the simulation of a nonlinear conservation law model- DNA exhibits abrupt, frequent pausing. Assuming a ing traffic flow with several traffic lights. This is used to certain density-velocity relationship incorporating a non- model the motion of polymerases on ribosomal RNA dur- uniform distribution of pauses, a nonlinear conservation ing the process of transrciption. Physically relevant pauses law model with discontinuous velocity is proposed and along the rrn operon are incorporated into the model. Us- shown to be the limit of a mean occupancy ODE system ing the DG solution, the average delay experienced by a model. Discontinuous Galerkin simulations and conver- polymerase due to the pauses is estimated. gence results are given. We attempt to quantify the affects that both pause location and mean duration time have on Jennifer Thorenson,LisaG.Davis the overall production of mRNA. Montana State University [email protected], [email protected] Lisa G. Davis Montana State University Tomas Gedeon [email protected] Montana State University Dept of Mathematical Sciences Tomas Gedeon [email protected] Montana State University Dept of Mathematical Sciences [email protected] MS114 Property Testing in the Real Number Model Jennifer Thorenson Montana State University Property testing asks for checking with a randomized algo- [email protected] rithm whether a given piece of data represents with high probability a certain kind of object. In the talk we consider real function value tables as data and want to check in how MS113 far they represent certain low degree polynomials over the From Asymmetric Exclusion Processes to Protein real numbers. Our computational model is the real num- Synthesis ber Turing machine introduced by Blum, Shub, and Smale. Such questions are central in relation to obtaining so-called Asymmetric exclusion processes, with periodic or open probabilistically checkable proofs for complexity classes like boundaries, have been studied extensively in the math- NP over the reals. This is ongoing joint work with Martijn ematics and statistical physics communities, as paradig- Baartse. matic models for stochastic particle transport far from equilibrium. Though significant progress was made only re- Klaus Meer cently, the original model was actually introduced decades Technical University Cottbus ago to model protein synthesis. In this talk, I will describe [email protected] recent efforts to develop a comprehensive theory for protein synthesis, building on asymmetric exclusion processes MS114 with extended objects, modeling ribosomes covering multiple codons. We discuss the effects of local hopping rates Faster Real-Solving for Random Sparse Polynomial 102 AN13 Abstracts

Systems MS115 Recent Advancement in Photoacoustic Tomogra- Any set, A,ofn + k points in Rn determines a family phy Iterative Image Reconstruction of polynomials FA with exponent vectors corresponding to the points of A. We describe an efficient polyhedral method Photoacoustic computed tomography (PACT) is an emerg- to compute the topology of the real zero set of most f in ing soft-tissue imaging modality that has great potential FA. The regions defining “most” depend on a refinement for a wide range of preclinical and clinical imaging applica- of the tropical discriminant. This theory also extends to tions. In this talk, we review our recent advancements in polynomial systems, but the data structures become more practical image reconstruction approaches for PACT. Such subtle. advancements include physics-based models of the measurement process and associated inversion methods for re- J. Maurice Rojas constructing images from limited data sets in acoustically Texas A&M University heterogeneous media. [email protected] Mark Anastasio, Kun Wang, Chao Huang, Bob Schoonover MS114 Washington University in St. Louis A Concrete Approach to Hermitian Determinantal [email protected], [email protected], Representations [email protected], [email protected] If a Hermitian matrix of linear forms is positive definite at some point, then its determinant is a hyperbolic hypersur- MS115 face. In 2007, Helton and Vinnikov proved a converse in Quantitative Photoacoustics Using Transport and three variables, namely that every hyperbolic plane curve Diffusion Models has a definite Hermitian determinantal representation. In this talk I will discuss a concrete proof of this statement Abstract not available at time of publication. and a method for computing these determinantal representations in practice. This involves relating the definiteness Simon Arridge of a matrix to the real topology of its minors and extend- University College London ing a classical construction of Dixon from 1902. This is [email protected] joint work with Daniel Plaumann, Rainer Sinn, and David Speyer. MS115 Cynthia Vinzant Gradient-based Bound-constrained Split Bregman University of Michigan Method (GBSB) for Large-scale Quantitative Pho- Dept. of Mathematics toacoustic Tomography [email protected] We aim at solving large-scale 3D Quantitative Photoa- coustic Tomography (QPAT), e.g., to recover both absorp- MS114 tion map and scattering map in the setting of multi-source Computing Regularity from Singularity QPAT. QPAT is formulated as a bound-constrained nonlinear minimization problem with the solution regularized In this talk we show how to compute a regular system from by TV norm, and then the development of the solution al- a singular polynomial system. For that we defined two op- gorithm is based on the Split Bregman method, namely, erations of defation and of kerneling. Deflation replaces a GBSB, gradient-based bound-constrained split Bregman function by the components of its gradient and kerneling method. The proposed GBSB algorithm can be easily ex- adds the components of a certain Schur complenent when tended for multi-wavelength QPAT and RTE based QPAT. some criteria are satisfied. We explain how performed exact computation from certified numerical tests. This work Hao Gao is done in collaboration with Marc Giusti. Emory University tba Jean-Claude Yakoubsohn Université Paul Sabatier [email protected] MS116 Interannual Variability and Memory Reemergence of North Pacific Sea Ice in Comprehensive Climate MS115 Models Ultrasound Modulated Optical Tomography We apply nonlinear Laplacian spectral analysis (a mani- Abstract not available at time of publication. fold generalization of PCA) to extract joint spatiotemporal patterns of variability of sea ice, oceanic, and atmo- Habib Ammari spheric variables from comprehensive climate models. We Ecole Normale Superieure use the recovered modes to study intraseasonal to inter- [email protected] annual variability, including year-to-year memory reemergence, of Arctic sea ice, which is a key component of the global climate. The question of constructing empirical dis- AN13 Abstracts 103

tance metrics for high-dimensional multivariate data is ad- the Mikulevicius-Rozovskii formula. The main idea is that dressed. the multiplication between the log-normal coeﬃcient and the gradient can be regarded as a Taylor-like expansion in Dimitris Giannakis,MitchellBushuk terms of the Wick product. We focus on the diﬀerence be- New York University tween the classical model and the Wick-type model with [email protected], [email protected] respect to the standard deviation of the underlying Gaus- sian random process. Andrew Majda Courant Institute NYU Xiaoliang Wan [email protected] Louisiana State University Department of Mathematics David Holland [email protected] Courant Institute of Mathematical Sciences New York University Boris Rozovskii [email protected] Brown University boris [email protected]

MS116 Zwanzig-Type PDF Equations and Exponential In- MS116 tegrators for Functionals of the Solution to Non- PDF Method for Power Generation Systems linear SPDEs with High-Dimensional Parametric Uncertainty Understanding the mesoscopic behavior of dynamical systems described by Langevin equations with colored noise The determination of the statistical properties of the solu- is a fundamental challenge in variety of fields. We propose tion to a system of stochastic differential equations (SDEs) a new approach to derive closed-form equations for joint is a problem of major interest in many areas of science. and marginal probability density functions (PDFs) of state Even with recent theoretical and computational advance- variables. This approach is based on a so-called Large- ments, no broadly applicable technique has yet been de- Eddy-Diffusivity (LED) closure and can be used for mod- veloped for dealing with the challenging problems of high eling a wide class of non-Markovian processes described by dimensionality, possible discontinuities in parametric space the noise with arbitrary correlation function. and random frequencies. Among different uncertainty quantification approaches, methods that model the prob- Peng Wang ability density function (PDF) of the state variables via Pacific Northwest National Laboratory deterministic equations have proved to be effective in pre- [email protected] dicting the statistical properties of random dynamical systems. In this talk we present recent developments on PDF alexandre tartakovsky, Zhengyu Huang methods, at both theoretical and numerical levels, address- PNNL ing the question of dimensionality of the solution to SDEs. [email protected], [email protected] In particular, we introduce a new projection operator technique of Mori-Zwanzig type and a new effective exponen- MS117 tial integrator method based on Kubo’s generalized cumu- Stability Issues in the Theory of Complete Fluid lants that allow us to determine closed (exact) evolution Systems equations for the PDF of goal-oriented functionals of the solution to SDEs with high-dimensional parametric uncer- We discuss multi-scale singular limits for compressible vis- tainty. Numerical applications are presented for nonlinear cous and rotating fluids in the regime of low Mach and oscillators driven by random noise, stochastic advection- Rossby numbers and high Reynolds number. We work in reaction and Burgers equations. the framework of weak solutions for the primitive system and classical solutions for the target system - here identi- Daniele Venturi fied as 2D-incompressible Euler flow. The results are based Division of Applied Mathematics on careful estimates independent of the scaling parameters Brown University and analysis of the associated oscillatory integrals arising daniele [email protected] in the study of the Poincare waves.

George E. Karniadakis Eduard Feireisl Brown University Mathematical Institute ASCR, Zitna 25, 115 67 Praha 1 Division of Applied Mathematics Czech Republic george [email protected] [email protected]

MS116 MS117 The Wick Approximation of Elliptic Problems with Incompressible Limits of Fluids Excited by Moving Lognormal Random Coeﬃcients Boundaries

We discuss the approximation of elliptic problems with log- We consider the motion of a viscous compressible fluid con- normal random coefficients using the Wick product and fined to a physical space with a time dependent kinematic 104 AN13 Abstracts

boundary. We suppose that the characteristic speed of the ied with a integral equation method. First, a numerical fluid is dominated by the speed of sound and perform the method for calculating the layered media Green’s func- low Mach number limit in the framework of weak solution will be derived using transfer/scattering matrix and tions. The standard incompressible Navier-Stokes system Sommerfeld-type integral. Then, a parallel fast algorithm is identified as the target problem. for the layered media integral operator will be presented with the semi fast multipole method for the Bessel func- Sarka Necasova tion based on the local-expansion. Mathematical Institute of Academy of Sciences Czech Republic Min Hyung Cho [email protected] Department of Mathematics Dartmouth College Eduard Feireisl [email protected] Mathematical Institute ASCR, Zitna 25, 115 67 Praha 1 Czech Republic MS118 [email protected] High-order Nystrom Discretization of Boundary Jiri Neustupa, Ondrej Kreml, Jan Stebel Integral Equations in the Plane Mathematical Institute ASCR, Zitna 25, 115 67 Praha 1 Boundary integral equations and Nystrom discretization [email protected], [email protected], provide a powerful tool for the solution of Laplace and [email protected] Helmholtz boundary value problems. The talk describes and compares four different high order techniques for MS117 producing very accurate Nystrom discretizations (due to Kapur-Rokhlin, Alpert, Kress, and Kolm-Rokhlin). We Regularity Problems Related to Brenner-Navier- compare the numerical performance and discuss practi- Stokes Equations cal issues (flexibility, ease of implementation, compatibility Regularity problems related to Brenner’s model of Navier- with fast summation techniques, etc). Applications to solv- Stokes equations are investigated. In two dimensional case ing 3D scattering problems involving axisymmetric scatter- we give the existence of global regular solution to the ers will be shown. initial-boundary value problem. In general case we give Sijia Hao a blowup criterion for the regular soltion in terms of upper University of Colorado at Boulder bound of the density. [email protected] Yongzhong Sun Department of Mathematics, Nanjing University MS118 Nanjing, Jiangsu, 210093, China [email protected] Spectral Deferred Correction Methods for Two- Dimensional Vesicle Suspensions

MS117 A boundary integral equation method for simulating inextensible vesicles in 2D viscous fluid is presented. By us- Relative Entropy Applied to the Study of Stability ing spectral deferred correction methods, we introduce an of Shocks for Conservation Laws, and Application adaptive time stepping strategy. This strategy allows us to to Asymptotic Analysis better control numerical errors. The relative entropy method is a powerful tool for the Bryan D. Quaife study of conservation laws. It provides, for example, the Institute for Computational Engineering and Sciences weak/strong uniqueness principle, and has been used in University of Texas at Austin different context for the study of asymptotic limits. Up to [email protected] now, the method was restricted to the comparison to Lips- chitz solutions. This is because the method is based on the 2 strong stability in L of such solutions. Shocks are known MS118 to not be strongly L2 stable. We have showed, however 2 Isogoemetric Boundary Element Methods on that their profiles are strongly L stableuptoadrift.We Smooth Domains will discuss our recent development of the theory together with applications to the study of asymptotic limits. Isogeometric analysis has emerged as a framework for integrating computational geometry and finite element Alexis F. Vasseur methods by adopting interpolation functions widely used University of Texas at Austin in computational geometry as finite element basis func- [email protected] tions. In this work, we show that isogeometric analysis is extremely beneficial for boundary element meth- MS118 ods: Singularities of certain boundary integral operators are weaker, collocation techniques can be used for hyper- Fast Integral Equation Method for Maxwell’s singular boundary integral equations, and formulations Equations in Layered Media leading to system matrices with mesh-independent condi- In this talk, Maxwell’s equations in layered media is stud- AN13 Abstracts 105

tion numbers can be introduced. Pamplona, Spain [email protected] Matthias Taus University of Texas Ester P´erez Sinus´ıa [email protected] Universidad de Zaragoza, Spain [email protected] Gregory Rodin Aerospace Engineering and Engineering Mechanics University of Texas at Austin MS119 [email protected] The Wright Function and Fractional Diﬀusion Problems

MS119 The Wright function and a number of other related func- Saddle Points, Special Functions and Electromag- tions play a role in various applications of fractional calcu- netic Pulse Propagation lus. In the recent years, intensive research has addressed analysis, modeling, and numerical treatment of fractional The angular spectrum representation is a mathematical partial differential equations, e.g., fractional diffusion equa- technique used to describe electromagnetic pulse propa- tions. These may better describe anomalous diffusion prob- gation in homogeneous material. It represents the propa- lems, providing an explanation to many phenomena. On gated field as a superposition of homogeneous or inhomo- the one hand, the fractional differential operators, being geneous plane waves. As such, saddle point methods have nonlocal in nature, can take into account delay in time proven useful in the analysis of these wave fields. This talk and nonlocality in space. On the other hand, they call will review how saddle point methods have been applied to for new numerical methods. In this talk, we will present linearly-polarized plane-wave pulses through causal mate- some new schemes, such as higher-odrder ADI methods, rial, and end with consideration of extending these meth- and show the usefulness of Wright’s functions. ods to electromagnetic beam propagation. Renato Spigler, Moreano Concezzi Natalie Cartwright Dipartimento di Matematica, Universita Roma tre. State University of New York at New Paltz Rome (Italy) [email protected] [email protected], [email protected]

MS119 MS120 Existence and Uniqueness of Tronquee Solutions of Eulerian Methods for Schrodinger Equations in the the Third and Fourth Painleve Equations Semi-Classical Regime

It is well-known that the first and second Painleve equa- We discuss Eulerian approaches to compute semi-classical tions admit solutions characterized by divergent asymp- solutions of the Schrödinger equations including the Eu- totic expansions near infinity in specified sectors of the lerian Gaussian beam method and a recently developed complex plane. Such solutions are pole-free in these sectors method which incorporating short-time WKBJ propaga- and called tronquee solutions by Boutroux. In this talk, we tors into Huygen’s principle. These Eulerian are shown to show that similar solutions exist for the third and fourth be computationally very efficient and can yield accurate equationsaswell. semi-classical solutions even at caustics.

Dan Dai Shingyu Leung City University, Hong Kong Hong Kong University of Science and Technology [email protected] [email protected]

MS119 MS120 Some New Techniques in the Approximation of A Uniformly Second Order Fast Sweeping Method Special Functions for Eiknoal Equations

We present some new methods to approximate special func- This talk is to introduce a simple and effective second or- tions, one for integrals and one for solutions of differential der method for eikonal equations. The method is based equations. For integrals we study convergent expansions of on a combination of a “superconvergence” phenomenon of integrals derived from expansions of the integrands at non- monotone upwind schemes for eiknoal equations combined standard points, including multi-point Taylor expansions. and a local linear DG formulation. By freezing the infor- Among the methods for differential equations we investi- mation of gradient which is precomputed by monotone up- gate modifications of Olver’s asymptotic method. We give wind schemes, a simple local updating formula for the cell several examples of which some have been included in the average can be obtained. This local solver is incorporated recently published NIST Handbook of Mathematical Func- into an iterative method to get a uniformly second order tions. method for the eikonal equations. Numerical examples are presented to demonstrate its efficiency. JoséLópez Universidad Pblica de Navarra, Songting Luo 106 AN13 Abstracts

Department of Mathematics, vided. Iowa State University [email protected] Asgeir Birkisson University of Oxford, Mathematical Institute [email protected] MS120 High-Order Factorization Based High-Order Hy- Tobin A Driscoll brid Fast Sweeping Methods University of Delaware Department of Mathematical Sciences The solution for the eikonal equation with a point-source [email protected] condition has an upwind singularity at the source point as the eikonal solution behaves like a distance function at and near the source. As such, the eikonal function is not MS121 diﬀerentiable at the source so that all formally high-order Chebfun and Equispaced Data numerical schemes for the eikonal equation yield ﬁrst-order convergence and relatively large errors. Therefore, it is a Chebfun is mainly designed to work with data at Cheby- long standing challenge in computational geometrical op- shev points. Some linear rational interpolants show good tics how to compute a uniformly high-order accurate solu- approximation properties with equispaced points and avoid tion for the point-source eikonal equation in a global do- the usual drawbacks of polynomial interpolation with such main. In this paper, we propose high-order factorization points. We review a few interpolation schemes as well as based high-order hybrid fast sweeping methods for point- their applications and demonstrate how they can be incor- source eikonal equations to compute just such solutions. porated into Chebfun to make this toolbox also work with equispaced points.

Jianliang Qian Georges Klein Department of Mathematics University of Fribourg, Switzerland Michigan State University [email protected] [email protected] MS121 MS120 Stability of Certain Singular and Singularly Per- Energy Conserving Local Discontinuous Galerkin turbed Diﬀerential Equations Methods for the Wave Propagation Problems We investigate an unexpected phenomenon where prob- Wave propagation problems arise in a wide range of ap- lems which are mathematically ill-posed (such as singu- plications. The energy conserving property is one of the lar ODEs) or ill-conditioned (such as singularly perturbed guiding principles for numerical algorithms, in order to ODEs) can be reliably solved using spectral methods in co- minimize the phase or shape errors after long time inte- eﬃcient space. This phenomenon is explained by showing gration. In this presentation, we develop and analyze a lo- that the perturbations present in numerics are in a very cal discontinuous Galerkin (LDG) method for solving the restricted class, therefore standard condition numbers do wave equation. We prove optimal error estimates and the not give a reliable indicator of numerical stability. This energy conserving property for the semi-discrete formula- approach is applied to reliably solve (to machine preci- tion. The analysis is extended to the fully discrete LDG sion accuracy) a famous ill-conditioned ODE from Lee and scheme, with the energy conserving high order time dis- Greengard 1997. cretization. Numerical experiments have been provided to Sheehan Olver demonstrate the optimal rates of convergence. The University of Sydney Yulong Xing [email protected] Department of Mathematics Univeristy of Tennessee / Oak Ridge National Lab Alex Townsend [email protected] Oxford University [email protected]

MS121 Computing Multiple Solutions of Nonlinear ODEs MS121 with Chebfun Computing on Surfaces with Chebfun2

An important capability of Chebfun is automatic New- Chebfun2 can be used to represent several parametric sur- ton iteration for solving nonlinear boundary-value prob- faces. In this talk we show how to use the system to com- lems (BVPs) of ordinary differential equations (ODEs). In pute with functions and vector fields defined on these sur- this talk, we describe how path-following techniques for faces. Of particular interest are operators such as gradient, obtaining multiple solutions of nonlinear equations can be Laplace-Beltrami and divergence. extended into function space. Combined with the automatic Newton iteration of Chebfun, it enables Chebfun to Rodrigo B. Platte find multiple solutions of nonlinear BVPs. Computational Arizona State University examples of the multiple solutions capability will be pro- [email protected] AN13 Abstracts 107

MS122 spaces using the concept of subdifferential. From the suffi- An Optimization Method Based on Piecewise Dif- cient condition we derive that any subdifferential operator ferentiation is monotone absorbing, hence maximal monotone when the function is convex. We present an optimization method based on algorithmic or automatic differentiation (AD) for piecewise differen- Marc Lassonde tiable objective functions. First, we approximate the tar- Universite des Antilles, Guadeloupe get function locally by a piecewise-linear model, having at [email protected] most a finite number of kinks between open polyhedral facets decomposing the function domain. On each facet MS123 we repeatedly solve quadratic subproblems. To switch between the different facets we exploit the structure of the Uncertainty Quantification in Hemodynamics, a function with the result of disjunctive quadratic subprob- Bayesian Approach to Data Assimilation lems. Computational hemodynamics is experiencing the progres- Sabrina Fiege sive improvement of measurement tools and numerical Institut für Mathematik methods. We adopt a Bayesian approach to the inclusion of Universität Paderborn noisy data in the incompressible Navier-Stokes equations. sfi[email protected] The purpose is the quantification of uncertainty affecting velocity and flow related variables of interest, all treated as random variables. We derive classical point estimators and Andreas Griewank we obtain confidence regions for the velocity and the wall HU Berlin, MATHEON Research Center, Germany shear stress, a flow related variable of medical relevance. [email protected] Marta D’Elia Andrea Walther Department of Scientific Computing Universität Paderborn Florida State University, Tallahassee, FL [email protected] [email protected]

MS122 MS123 Generalized Derivatives Via Piecewise Lineariza- Nonlinear Stochastic Estimation of Turbulence tion Subject to Levy Noise

Abstract not available at time of publication. In this work we study the existence and uniqueness of the strong pathwise solution of stochastic Navier-Stokes equa- Andreas Griewank tion with Ito-Levy noise. Nonlinear filtering problem is HU Berlin, MATHEON Research Center, Germany formulated for the recursive estimation of conditional ex- [email protected] pectation of the flow field given back measurements of sensor output data. The corresponding Fujisaki-Kallianpur- MS122 Kunita and Zakai equations describing the time evolution Evaluating a Clarke Generalized Jacobian of a of the nonlinear filter are derived. Existence and unique- Piecewise Differentiable Function ness of measure-valued solutions are proven for these filtering equations. Elements of the (Clarke) generalized Jacobian of a locally Lipschitz continuous function are useful in methods for B.P.W Fernando equation-solving and optimization, but can be difficult to Naval Postgraduate School compute. This presentation describes a variant of the for- [email protected] ward mode of automatic differentiation, in which a generalized Jacobian element is computed for a composition MS123 of known elemental nonsmooth functions. This method Multigrid Methods for Optimal Control Problems is computationally tractable, and offers significant compu- in Fluid Flow tational advantages over existing methods for generalized Jacobian element evaluation. Abstract not available at time of publication.

Kamil Khan,PaulI.Barton Ana Maria Soane Massachusetts Institute of Technology University Of Maryland, Baltimore County Department of Chemical Engineering Department of Mathematics and Statistics [email protected], [email protected] [email protected]

MS122 MS123 Subdifferential Test for Optimality Two-Dimensional Stochastic Navier-Stokes Equa- tions with Fractional Brownian Noise We provide a first-order necessary and sufficient condition for optimality of lower semicontinuous functions on Banach Perturbation of the two-dimensional stochastic Navier- 108 AN13 Abstracts

Stokes equation by a Hilbert-space-valued fractional Brow- Team nian noise is studied. With the noise being additive, simple [email protected] Wiener-type integrals are sufficient for properly defining the problem. Existence and uniqueness of mild solutions terrence liao are established under suitable conditions on the noise in- TOTAL tensities for all Hurst parameter values. Almost surely, the [email protected] solution’s paths are shown to be quartically integrable in time and space. An extension to a multifractal model is Asma Farjallah given. University of Versailles Saint-Quentin-En-Yveline [email protected] P. Sundar Lousiana State University Issam Said [email protected] PMC Univ Paris 06 and CNRS UMR 7606, LIP6 [email protected] MS124 Gmres Cache Aware Auto-Tuning Strategies for Sayan Gosh Parallel Architectures University of Houston [email protected] Krylov linear solvers such as GMRES are heavily used with success in various domains and industries despite their Alan Richardson complexity. Their convergence and speed greatly depends Department of Earth, Atmospheric and Planetary on the hardware used and on the choice of the Krylov sub- Sciences space size which is difficult to determine efficiently in ad- Massachusetts Institute of Technology vance. We present a study of a cache aware auto-tuning alan [email protected] algorithm of the GMRES subspace size on different architectures in parallel which helps the parametrization process while assuring efficient convergence. MS124 Krylov Basis Orthogonalization Algorithms on Pierre-Yves Aquilanti Many Core Architectures A*STAR Computational Resource Centre [email protected] Efficient and portable iterative linear algebra algorithms on many-core architectures have to be proposed for fu- Takahiro Katagiri ture supercomputers including large number of accelerators The University of Tokyo like GPU or MIC. However, using them efficiently requires [email protected] modifying deeply the conception and the implementation of the algorithms, especially to minimize communications. Serge G. Petiton We present our approach based on the design of generic al- CNRS/LIFL and INRIA gorithms using TRILINOS and specialized implementation serge.petiton@lifl.fr of BLAS kernels. We apply this approach to Krylov basis generation algorithm on GPU and MIC and we present Satoshi Ohshima first results on sparse systems. The University of Tokyo Christophe Calvin Information Technology Center CEA-Saclay/DEN/DANS/DM2S [email protected] [email protected]

MS124 Serge G. Petiton Petaflop supercomputers, What Programming Univ Lille 1 Model for Seismic Application Maison de la Simulation serge.petiton@lifl.fr Developing efficient Seismic Depth imaging applications on petaflop supercomputer requires to manage hundreds of Fan Ye thousands of parallel tasks. Researchers have to describe CEA/DEN/DANS/DM2S and expose the different levels of parallelism: at the in- Maison de la Simulation terconnect level by describing the explicit data and task [email protected] distribution, at the compute node level by taking advantage of either homogeneous or heterogeneous technology. In this talk we will discuss how to choose the appropriate MS124 programming model in order to preserve scalability and Programming Model for Sustainable Numerical Li- legacy in large-scale implementations braries for Extreme Scale Computing

Henri Calandra Here, we present a modular and multi-level parallelism ap- Total proach that has a strict separation between computational CSTJF, Geophysical Operations & Technology, R&D operations, data management and communication. We illustrate how under this model we are able to design more AN13 Abstracts 109

scalable algorithmic implementations that better exploit MS125 their functionalities, scalability and code reusability. The Seismic Tomography with Sparsity Constraints, at latter is important in the formulation of hybrid numerical the Global and the Exploration Scale schemes. We use the multiple explicitly restarted Arnoldi method as our test case and our implementations require Seismic tomography leads to gigantic systems of linear full reuse of serial/parallel kernels in their implementation. equations. As data volumes increase, every eﬀort has to be Our experiments include comparisons with state-of-the-art made to reduce the inversion problem to manageable size. numerical libraries on high-end computing systems. While achieving a reduction of computational complexity, new sparsity-seeking methods should be able to give addi- Leroy A. Drummond tional insight into the nature of the problem itself, and the Lawrence Berkeley National Laboratory character of the solution. Practically speaking, this means [email protected] that if we are solving systems that relate data (functionals of seismograms) to model parameters (the physical prop- Makarem Dandouna erties of the Earth) through the use of sensitivity kernels Universite de Versailles (partial derivatives of the measurements with respect to the dandouna makarem ¡[email protected]¿ unknown Earth parameters), we have opportunities for dimensional reduction on the data, the model, and the kernel Nahid Emad side. In this presentation I discusss strategies to make in- Universite de Versailles roads on all three sides of the seismic tomographic inverse Maison de la Simulation problem, using one-, two- and three-dimensional wavelets, [email protected] and 2-1 combination misﬁt norms.

Frederik J. Simons,YanhuaYuan MS125 Princeton University Geophysics Meets Spectral Graph Theory: Inter- [email protected], [email protected] ferometric Waveform Inversion Jean Charlety Abstract not available at time of publication. Geosciences Azur, France [email protected] Laurent Demanet Professor of Mathematics, MIT [email protected] Ignace Loris FNRS Chercheur Qualifié (ULB, Brussels) Mathematics MS125 [email protected] Variational Data Assimilation with Sparse Regu- larization Sergey Voronin Universite de Nice This paper studies the role of sparse regularization in the [email protected] variational data assimilation (VDA) problems. Conceptu- ally, this study is focused on data assimilation of noisy and Guust Nolet down-sampled observations when the geophysical state of Universite de Nice Sophia-Antipolis interest exhibits a sparse representation in a properly cho- CNRS, Obs. de la Cote d’Azur, Geoazur sen basis. We show that as long as the sparsity holds, 1 [email protected] -norm regularization in the selected basis produces more accurate and stable solutions than the classic data assim- Ingrid Daubechies ilation methods. To motivate further developments of the Duke proposed methodology, examples are provided via assimi- Department of Mathematics lating observations into the linear advection-diffusion equa- [email protected] tion in the wavelet and discrete cosine domains.

Eﬁ Foufoula-Georgiou, Mohammad Ebtehaj MS126 University of Minnesota A Robust Central-Upwind Scheme for 2D Shallow eﬁ@umn.edu, [email protected] Water Equations

A good numerical scheme for the 2D Saint-Venant sys- MS125 tem of shallow water equations should satisfy two impor- Sparse Solution of Nonlinear Subsurface Flow In- tant features: the scheme should be well-balanced –it ex- verse Problems actly preserves “lake at rest’ steady states, and the scheme Abstract not available at time of publication. should be positivity preserving –the water depth h remains nonnegative. We present a novel conservative, well- Benham Jafarpour balanced, and positivity preserving central-upwind scheme ViterbiSchoolofEngineering for Saint-Venant equations. Using several benchmark prob- University of Southern California lems we test the accuracy and robustness of this scheme. [email protected] 110 AN13 Abstracts

Patricia Medina, Ralph Showalter Department of Mathematics Jason Albright Oregon State University University of Utah [email protected], MATH DEPARTMENT [email protected] [email protected]

Yekaterina Epshteyn MS126 Department of mathematics Numerical Solution of Miscible Displacement un- University of Utah der Low Regularity [email protected] Miscible displacement flow is one important part of en- Alexander Kurganov hanced oil recovery. A polymeric solvent is injected in Tulane University the reservoir and it mixes with the trapped oil. Accu- Department of Mathematics rate simulation of the displacement of the fluid mixture in [email protected] heterogeneous media is needed to optimize oil production. The miscible displacement is mathematically modeled by a pressure equation (elliptic) and a concentration equation MS126 (parabolic) that are coupled in a nonlinear fashion. One A Hamilton-Jacobi Equation for the Continuum challenge in the convergence analysis of numerical meth- Limit of Non-dominated Sorting ods applied to the miscible displacement arises from the fact that the diffusion-dispersion coefficient in the concen- Non-dominated sorting is a fundamental problem in multi- tration equation is unbounded. In this work, we formu- objective optimization, and is equivalent to several impor- late and analyze discontinuous in time methods coupled tant combinatorial problems, including a random model with several finite element methods (including mixed fi- for crystal growth. The sorting can be viewed as arranging nite elements and discontinuous Galerkin) for the miscible points in Euclidean space into fronts by repeated removal displacement. The diffusion-dispersion coefficient is not as- of the set of minimal elements with respect to the com- sumed to be bounded. Other coefficients in the problem ponentwise partial order. We prove that in the (random) are not assumed to be smooth. Convergence of the nu- large sample size limit, the fronts converge almost surely merical solution is obtained using a generalization of the to the level sets of a continuous function that satisfies a Aubin-Lions compactness theorem. The Aubin-Lions the- Hamilton-Jacobi equation in the viscosity sense. We then orem is not applicable since the numerical approximations give an efficient numerical scheme for approximating the are discontinuous in time. Numerical examples with vary- viscosity solution of this PDE and show how it can be used ing order in space and time are also given. to approximately solve the non-dominated sorting problem efficiently. Beatrice Riviere Rice University Jeff Calder Houston, Texas, USA Department of Mathematics [email protected] University of Michigan [email protected] MS127 The Challenges of Wind Prediction from a Forecast MS126 Sensitivity Perspective Numerical Modeling Methane Hydrate Evolution Successful wind prediction with a numerical model relies, Modeling evolution of methane hydrates and in particular in part, on accurate initial conditions. The chaotic na- of their formation and dissociation is important for en- ture of the atmospheric attractor results in large spatial ergy and climate studies. A numerical model for the cor- variability in the sensitivity of wind forecasts to the initial responding nonlinear degenerate PDE has to account for state, resulting in different initialization techniques provid- multiple phases and solubility constraints. With an appro- ing large forecast differences. Ensemble mean forecasts can priate formulation using monotone operator techniques and also diverge from the model attractor in the presence of sig- complementarity constraints we obtain convergence results nificant nonlinear perturbation growth. These challenges comparable to those for Stefan problem or porous medium for wind prediction will be discussed in this presentation. equation but with a superior solver performance Brian Ancell Malgorzata Peszynska Texas Tech University Department of Mathematics [email protected] Oregon State University [email protected] MS127 Nathan L. Gibson Statistical Applications of Offsite Meteorological Oregon State University Measurements for Short-Horizon Wind Power Pre- [email protected] diction Many meteorologically-driven wind generation ”ramps” re- AN13 Abstracts 111

sult from passage of mid-latitude weather systems across MS128 wind farms. Measurements upstream of these features can Tipping Points: Overview and Challenges be provided to statistical and time series models for forecasting in the sub-hourly to 6 hour horizons. We demon- Abstract not available at time of publication. strate the application of advanced time-lagged and other time series modeling for improved wind power forecasting, Mary Silber wherein such models make best use of oﬀsite telemetry to Northwestern University improve prediction, relative to standard numerical weather Dept. of Engineering Sciences and Applied Mathematics models and persistence. [email protected]

Craig Collier MS129 GL Garrad Hassan [email protected] Self-Convexity (Joint work with Carlos Beltrán, Jean-Pierre Dedieu and MS127 Mike Shub). Let (M, ·, ·§)beasmooth Riemannian M→R Stochastic Learning Methods for Solar Forecasting manifold and α : > be a Lipschitz function. We can endow the manifold M with a new metric, namely We discuss a number of different techniques for extracting relevant information from cloud temporal patterns and ·, · = α(x)·, ·x their effect on the quality of solar irradiance forecasts at the x ground level. The methods used here are validated against high-quality, ground-truth solar data for several locations which is conformally equivalent to the previous one. This in the Pacific Rim. The performance of the methods is new norm will be called the α-metric and sometimes the determined in comparison to a diurnally corrected, history condition metric. It defines a Riemann–Lipschitz length optimized persistence model. structure on M.

Hugo Pedro, Carlos Coimbra Deﬁnition: We say that α is self-convex if and only University of California, San Diego if, for any geodesic γ in the α-structure, t → log α(γ(t)) [email protected], [email protected] is a convex function.

Self-convexity came out from the complexity analysis of MS128 certain homotopy algorithms for solving polynomial sys- A Mathematical Framework for Critical Transi- tems. tions: Normal Forms, Variance and Applications

Abstract not available at time of publication. I will try to survey the main results and open questions. For instance: John Guckenheimer Cornell University Theorem: The square of the condition number for linear [email protected] equation solving is self-convex. Gregorio Malajovich MS128 Departamento de Matem´atica Aplicada Asymptotics of Stochastically and Periodically Universidade Federal do Rio de Janeiro Forced Tipping: Advance Or Delay [email protected]

We compare the effects of different types of variability on transitions near a tipping point. Through an asymptotic MS129 analysis based on multiple scales and WKB-type approxi- Hamiltonian Approach to Geodesics Computation mations, we consider the relative effects of noise, periodic in Condition Metric variability, and slowly varying control parameter. The approach is applied in canonical models and in a global en- Abstract not available at time of publication. ergy balance model for average ocean temperature where Dimitri Nowicki asymmetry also plays a role. Results are reported in the University of Massachusets context of indicators for tipping point proximity and en- [email protected] ergy balance models for sea ice.

Rachel Kuske MS129 University of British Columbia Title Not Available at Time of Publication [email protected] Abstract not available at time of publication. Jielin Zhu UBC Mathematics Luis Miguel Pardo [email protected] Departamento de Matematica, Estadistica y Computacion Universidad de Cantabria [email protected] 112 AN13 Abstracts

MS130 diﬀuse optical tomography. Inverse Problems with Internal Information Hongkai Zhao Abstract not available at time of publication. University of California, Irvine Department of Mathematics Peter Kuchment [email protected] Department of Mathematics, Texas A&M University USA [email protected] MS131 Stochastic Models of Cancer Evolution

MS130 We study the accumulation of mutations in a spatial Moran Inverse Source Problem for the Wave Equation model on a torus in which each cell gives birth at a rate with an Uncertain Wave Speed equal to its fitness and replaces a neighbor at random with its offspring. We consider the inverse source problem for the wave equation that arises as a part of the photoacoustic tomography Jasmine Y. Foo problem. This problem can be solved in a stable way if the University of Minnesota wave speed is known and non-trapping. However, in prac- [email protected] tice the wave speed is know only up to some uncertainty and we consider how a modelling error in the wave speed MS131 affects on the reconstruction of the source. Numerical Techniques for Optimal Sequential Ex- Lauri Oksanen perimental Design via Dynamic Programming Washington University [email protected] How do we select the sequence of experiments that max- imizes the value of costly experimental data? We formulate this optimal sequential experimental design problem MS130 using dynamic programming, taking into account the ex- Inverse Problems in Quantitative Fluorescence pected uncertain future effects. We solve it numerically Photoacoustic Tomography using approximate dynamic programming (ADP) methods. Two major numerical issues are addressed: the represen- Quantitative fluorescence photoacoustic tomography (Qf- tation of posterior distributions in a sequential Bayesian PAT) combines quantitative photoacoustic tomography inference context, and the choice of features in value func- with fluorescence tomography to achieve high-resolution tion approximation ADP technique. Preliminary results imaging of spatial concentration of fluorescent biochemi- are demonstrated on a proof-of-concept model problem. cal markers in target tissues. Mathematically, quantitative fluorescence photoacoustic tomography can be regarded as Xun Huan,YoussefM.Marzouk an inverse coefficient problem for a weakly coupled system Massachusetts Institute of Technology of diffusion equations with interior absorbed energy data. [email protected], [email protected] We present in this talk some uniqueness and stability results as well as reconstruction strategies for such an inverse MS131 problem. A Multi-stage Sparse Grid Collocation Method for Kui Ren Stochastic Differential Equations with White Noise University of Texas at Austin [email protected] We propose a new method for long-time integration of linear stochastic partial differential equations by combining sparse grid collocation (SGC) with a multi-stage recursive Hongkai Zhao procedure. We show theoretically and numerically that University of California, Irvine SGC yields satisfactory accuracy only for small magnitude Department of Mathematics of noise and small integration time. Combining SGC with [email protected] a multi-stage approach we present a numerical example to show the effectiveness in long-time integration of the com- MS130 bined method for a stochastic advection-diffusion equation. Quantitative Photoacoustic Tomography

I will present two recent works for quantitative photoacous- Zhongqiang Zhang tic imaging. We present a Neuman series based iterative Brown University algorithm that can recover the initial wave field efficiently zhongqiang [email protected] and accurately in the first step. The second step is to reconstruct optical properties of the medium using internal Michael Tretyakov measurements from the reconstructed acoustic source dis- University of Nottingham tribution from the first step. We propose a hybrid recon- [email protected] struction procedure that uses both interior measurement and boundary current data, which is usually available in Boris Rozovsky AN13 Abstracts 113

Brown University shall also discuss the main steps of the approximation pro- Boris [email protected] cedure, under additional assumption on the cold component of the pressure in the regions of small density [E. Za- George E. Karniadakis torska: On the ﬂow of chemically reacting gaseous mixture. Brown University JDE, 2012]. Division of Applied Mathematics george [email protected] Ewelina Zatorska Institute of Applied Mathematics and Mechanics Warsaw University, Poland MS132 [email protected] BV Estimate for Isentropic Gas Dynamics

Abstract not available at time of publication. MS133 Results and Applications from a Generalized Soft- Geng Chen ware Framework for Treecode/FMM Mathematics Department, Penn State University University Partk, State College, PA Research in building treecode/FMM software has largely [email protected] been focused in three areas: mathematical analysis and control of kernel expansions, parallel tree representation and construction, and parallel tree traversals. In this talk, MS132 we present a generalized software framework in which these Asymptotic Preserving Schemes for Low Mach research areas are mostly independent. That is, we have in- Number Flow corporated new kernels and expansions without modifying the tree construction or traversal and included recent par- We present new asymptotic preserving large time step allel computing strategies without modification of the ker- methods for low Mach number flows. They belong to the nels. We will show benchmarks, profiles, and applications class of genuinely multidimensional schemes and are de- to a simple N-body example as well as a preconditioned veloped for both finite volume and discontinuous Galerkin BEM for molecular modeling. framework. Nonlinear fluxes along cell interfaces are evaluated by means of the genuinely multidimensional evolution Cris R. Cecka Galerkin operators. The key property of the method is that Harvard University they are asymptotic preserving with respect to small Mach [email protected] number. In order to take into account multiscale phenomena nonlinear fluxes are splitted into a linear part governing the acoustic and gravitational waves and to the rest MS133 nonlinear part that models advection. Time integration Parallel Higher-order Boundary Integral Electro- is realized by the IMEX type approximation. We present statics Computation on Molecular Surfaces with results for some standard meteorological test cases with Curved Triangulation small Mach numbers or for the shallow water flows with small Froude numbers. This research is done in collabora- We present a parallel higher-order boundary integral tion with S. Noelle (Aachen), K.R. Arun (Trivandrum), L. method to solve the linear Poisson-Boltzmann (PB) equa- Yelash (Mainz), G. Bispen (Mainz), F.X. Giraldo (Mon- tion. The molecular surfaces are first discretized with flat terey) and A. Mueller (Monterey). Thanks to the German triangles and then converted to curved triangles with the Science Foundation DFG LU 1470/2-2. assistance of normal information at vertices. To maintain the desired accuracy, four-point Gauss-Radau quadra- Maria Lukacova tures are used on regular triangles and sixteen-point Gauss- University of Mainz Legendre quadratures together with regularization trans- Institute of Mathematics formations are applied on singular triangles. In addition, [email protected] the schemes are parallelized with MPI implementation.

Weihua Geng MS132 University of Alabama Existence Results for a Model of the Compressible [email protected] Mixtures Flow

We consider the Cauchy problem for the system of equa- MS133 tions governing flow of reactive mixture of compress- A Petascale Fast Multipole Method for Volume Po- ible gases [V. Giovangigli: Multicomponent flow modeling. tentials Birkhäuser Boston Inc., 1999]. We will present the proof of sequential stability of weak solutions when the state equa- We present a highly scalable solver for volume potentials tion essentially depends on the species concentration and using piecewise polynomials and adaptive octree to repre- the viscosity coefficients satisfy the relation proposed in sent the source distribution and the output potential. Our [D. Bresch and B. Desjardins: On the existence of global method uses the kernel independent FMM to allow for the weak solutions to the Navier–Stokes equations for viscous use of a wide range of kernels, such as: Laplace, Stokes, compressible and heat conducting fluids.J.Math.Pures Helmholtz etc. We present convergence results for these Appl., 2007], in particular, they vanish on vacuum. We kernels with freespace and periodic boundary conditions. 114 AN13 Abstracts

We discuss algorithmic details for distributed memory par- asymptotically sharp Nikolskii inequality. allelism using MPI and shared memory parallelism on multicore CPUs and manycore accelerators on the Stampede Eli Levin and Titan supercomputers. BLAS, FFTW and SSE opti- The Open University of Israel mizations are used to achieve high FLOP rates. [email protected]

Dhairya Malhotra Institute of Computational Engineering and Sciences MS134 The University of Texas at Austin Universality Limits for Random Matrices and Or- [email protected] thogonal Polynomials Universality limits for random matrices describe phenom- MS133 ena such as spacing and distribution of eigenvalues. Or- An Approximate Deﬂation Preconditioning thogonal polynomials play a key role in the analysis, when Method Based on Multiple Grids for Wave Scat- the class of matrices are Hermitian. We survey some recent tering Problems progress in this topic.

In this talk I consider the Lippmann-Schwinger (LS) in- Doron S. Lubinsky tegral equation for inhomogeneous acoustic scattering. I Georgia Institute of Technology demonstrate that spectral properties of the LS equations [email protected] suggest that deflation based preconditioning might be effective in accelerating the convergence of a restarted GMRES MS134 method. I will present an analytical framework for con- Spectral Transforms and Orthogonal Polynomials vergence theory of general approximate deflation that is widely applicable. Furthermore, numerical illustrations of Let G be an analytic region and let m be a measure on the spectral properties also reveal that a significant portion that region. It is known that for certain regions G and of the spectrum is approximated well on coarse grids. To measures m, the corresponding orthogonal polynomials ad- exploit this, I develop a novel restarted GMRES method mit Szego asymptotics on the exterior of the closure of G. with adaptive preconditioning based on spectral approxi- Under stronger hypotheses, one can deduce that the or- mations on multiple grids. thogonal polynomials admit Szego asymptotics on an even larger region that includes the entire boundary of G. In this Josef Sifuentes talk, we will discuss some ways to modify measures that do New York University not destroy this phenomenon of the orthogonal polynomi- Courant Institute als admitting Szego asymptotic inside the region G. This [email protected] is joint work with Erwin Mina-Diaz.

MS134 Brian Simanek Vanderbilt University On Order Derivatives of Bessel Functions [email protected] New representations are derived for the derivatives with respect to order for Bessel functions of the first and sec- MS135 ond kinds. These involve integrals of the products pairs of Mathematical Problems in the Diagnosis and Bessel functions and the reciprocal function. New expan- Treatment of Disease sions are derived for two of these integrals, complementary to a known expansion for the third. The uniform asymp- It will be explained how the following problems in the di- totic behavior of the derivative with respect to order for agnosis and treatment of breast cancer have led to math- the J and Y Bessel functions is also investigated. ematical problems: 1. How can one improve the diagnosis of breast cancer? 2. How can one determine the growth Mark Dunster rate of a cancer once it has been detected? 3. In which San Diego State University order should drugs be given in order to improve relapse [email protected] and survival times? The first problem led to the design , construction, and testing of an electrical impedance spec- MS134 troscopy system combined with an x- ray mammography The Generalized Christoffel Functions and Ex- system. The second problem led to a quantitative model to tremal Problems predict the growth rate of some cancers as a function of the number of Her2 and EGF receptors on the cells involved. The bounds and asymptotics of the classical L2-Christoffel The third problem led to quantitative models capable of functions are very important in the theory of orthogonal predicting the outcome of specific chemotherapy regimens polynomials and in their applications. The more general used by Bonadonna involving the use of CMF and A (Dox- Lp-Christoffel functions are less understood. While the orubicin) for the adjuvant treatment of breast cancer. bounds for these are well known, asymptotics have never be established for . We show how such asymptotics can David Isaacson be described in terms of an extremal problem in a special RPI space of entire functions. As a consequence, we deduce an [email protected] AN13 Abstracts 115

MS135 Method for 2-D Electrical Impedance Tomography Comparison of Bipolar Injection Patterns in Terms A D-bar method for computing 2-D reconstructions of con- of Noise Propagation, Image Quality and Observ- ductivity and permittivity from EIT data is described. Re- ability constructions from numerically simulated data and in vivo Bipolar current sources in electrical impedance tomogra- human subject data are presented illustrating the method’s phy simpliﬁes the hardware and it is a common hardware potential for clinical lung applications. architecture nowadays. However, it is not clear which is Jennifer L. Mueller the best current pattern and measurement pattern for lung Colorado State University monitoring. The present numerical simulations compares Dept of Mathematics skip-n bipolar patterns in terms of noise propagation and [email protected] image quality.

Olavo L. Silva, Fernando S. Moura, Erick D. L. B. Sarah Hamilton Camargo,MarceloB.P.Amato University of Helsinki University of Sao Paulo sarah.hamilton@helsinki.fi [email protected], [email protected], [email protected], [email protected] Natalia Herrera, Miguel Montoya Colorado State University Raul G. Lima [email protected], [email protected] University of So Paulo [email protected] MS136 Optimal Methods for a Class of Composite Varia- MS135 tional Problems Benefits of using Anatomical and Physiological Pri- ors in Electrical Impedance Tomography: Experi- Abstract not available at time of publication. mental Results Guanghui Lan Anatomical and physiological information from pigs tho- Department of Industrial and Systems races were used to build statistical priors for electrical University of Florida impedance tomography. The benefits of using this prior [email protected]fl.edu and the approximation error method in Gauss-Newton and Kalman Filter algorithms is demonstrated using in vivo MS136 data from pigs and human volunteers. Polynomial Optimization with Real Varieties Erick Camargo We study the optimization problem University of Sao Paulo [email protected] min f(x) s.t. h(x)=0,g(x) ≥ 0

Fernando S. Moura with f a polynomial and h, g two tuples of polynomials University of Sao Paulo in x ∈ Rn. Lasserre’s hierarchy is a sequence of sum of Polytechnic School - Mechanical Engineering Department squares relaxations for finding the global minimum fmin. [email protected] Let K be the feasible set. We prove the following results: i) If the real variety VR(h) is finite, then Lasserre’s hierar- Thais H. S. Sousa, Olavo L. Silva, Caio Biasi, Alessandro chy has finite convergence, no matter the complex variety R. C Martins, Denise T. Fantoni VC (h) is finite or not. This solves an open question in Lau- University of Sao Paulo rent’s survey. ii) If K and VR(h) have the same vanishing [email protected], [email protected], ideal, then the finite convergence of Lasserre’s hierarchy is [email protected], [email protected], independent of the choice of defining polynomials for the [email protected] real variety VR(h). iii) When K is finite, a refined version of Lasserre’s hierarchy (using the preordering of g)hasfi- Jari Kaipio nite convergence. Department of Mathematics University of Auckland Jiawang Nie [email protected] University of California, San Diego [email protected] Raul G. Lima University of Sao Paulo MS136 [email protected] Inexact BOSVS Algorithm for Ill-Posed Inversion with Application to PPI MS135 This paper proposes an Inexact Bregman operator split- Reconstructions of Lung Pathologies by a D-Bar ting algorithm with variable stepsize (Inexact BOSVS) for 2 solving problems of the form minu φ(Bu)+1/2 Au − f 2, 116 AN13 Abstracts

where φ may be nonsmooth. The original BOSVS algo- MS137 rithm uses a line search to achieve efficiency, while a prox- Threshold Dynamics for Networks with Arbitrary imal parameter is adjusted to ensure global convergence Surface Tensions whenever a monotonicity condition is violated. The new Inexact BOSVS uses a simpler line search than that used Abstract not available at time of publication. by BOSVS, and the monotonicity test can be skipped. Nu- merical experiments based on partially parallel image re- Selim Esedoglu construction compare the performance of BOSVS, inexact University of Michigan BOSVS, and BosNewton, a Newton-Based Bregman Op- [email protected] erator Splitting scheme. MS137 Maryam Yashtini University of Florida Further Study of the Back and Forth Error Com- Mathematics Department pensation and Correction Method for Advection myashtini@ufl.edu Equations and Hamilton Jacobi Equations We further study the properties of the back and forth error William Hager compensation and correction (BFECC) method for advec- Department of Mathematics tion equations such as those related to the level set method University of Florida and for solving Hamilton-Jacobi equations on unstructured hager@ufl.edu meshes. In particular, we develop a new limiting strategy. This new technique is very simple to implement even for Hongchao Zhang unstructured meshes and is able to eliminate artifacts in- Department of Mathematics and CCT duced by jump discontinuities in derivatives of the solu- Louisiana State University tion as well as by jump discontinuities in the solution itself [email protected] (even if the solution has large gradients in the vicinities of a jump). Typically, a formal second order method method MS136 for solving a time dependent Hamilton-Jacobi equation requires quadratic interpolation in space. A BFECC method The Limited Memory Conjugate Gradient Method on the other hand only requires linear interpolation in each In theory, the successive gradients generated by the conju- step, thus is local and easy to implement even for unstruc- gate gradient method applied to a quadratic should be or- tured meshes. Collaborators: Lili Hu and Yao Li. thogonal. However, for some ill-conditioned problems, or- Yingjie Liu thogonality is quickly lost due to rounding errors, and con- School of Mathematics, Georgia Inst of Tech vergence is much slower than expected. A limited memory [email protected] version of the conjugate gradient method will be presented. The memory is used to both detect the loss of orthogonality and to restore orthogonality. Numerical comparisons to MS137 the limited memory BFGS method (L-BFGS) will be also Parametrized Maximum Principle Flux Limiters discussed. for High Order Schemes Solving Hyperbolic Con- servation Law Hongchao Zhang Department of Mathematics and CCT Maximum principle preserving is an important property of Louisiana State University the entropy solution, the physically relevant solution, to [email protected] the scalar hyperbolic conservation laws. One would like to imitate the property on the numerical level. On the other MS137 hand, preserving the maximum principle also provides a stability to the numerical schemes for solving the conser- High-Order Positivity Preserving Methods for Hy- vation law problem. The challenge exists when solving the perbolic Equations conservation law problems with high order schemes in a The construction and use of high-order positivity preserv- consistent and conservative framework. In this talk, we ing methods for hyperbolic equations is described. The will discuss how this problem is addressed by introducing methods derived are constructed using data-bounded poly- a series of maximum principle constraint. By decoupling nomials with bounded derivatives, used within the frame- those constraints, a parametrized flux limiting technique work of ENO or WENO methods. Examples of results ob- is developed to make sure the numerical solution preserves tained with these approaches will be given together with a maximum principle in the conservative and consistent man- comparison against other high-order positivity preserving ner while the scheme is still high order. Generalization of approaches. the technique to convection-diffusion problem will also be discussed. Potential application of this method will be ex- Martin Berzins plored in the future work. Scientific Computing and Imaging Institute University of Utah Zhengfu Xu [email protected] Michigan Technological University Dept. of Mathematical Sciences [email protected] AN13 Abstracts 117

MS138 two curves in the plane (or two images, or other geo- Unimodulariy and Conservation of Volumes in metric objects), how (dis)similar are these curves? We Nonholonomic Mechanics address this question using curves of deformations in a (finite-dimensional) Lie group. In this talk, I will focus In this talk I will show how the geometric structure that on the group of Euclidean isometries, showing that the underlies the equations of motion of a nonholonomic me- equations for morphing arise as constrained Euler-Poincare chanical system with symmetry can be exploited to obtain equations. At the end, some illustrative examples will be necessary and sufficient conditions for the existence of an presented. invariant volume. Using our method we have shown existence and non-existence of an invariant measure for several Joris Vankerschaver concrete mechanical problems that will be discussed in de- Imperial College London tail. Department of Mathematics [email protected] Luis Garcia Naranjo UNAM, Universidad Nacional Autónoma de México Lyle Noakes [email protected] Department of Mathematics and Statistics The University of Western Australia [email protected] MS138 The Geometry of Phase Space Lifts: From Darryl Holm Maxwells Equations to Radiative Transfer Theory Department of Mathematics We study the geometry of the phase space lift of Maxwell’s Imperial College London equations that in the short wavelength limit leads to ra- [email protected] diative transfer theory. We introduce a geometric density operator for the electromagnetic field, which, as we show, MS139 is equivalent to known optical coherence ”matrices”. With H Infinity Feedback Boundary Stabilization for In- this operator, Maxwell’s equations can be written in com- compressible Fluid Flow mutator form which allows us to lift electromagnetic theory to the cotangent bundle where time evolution is governed We study the robust or H∞ exponential stabilization of the by a matrix-valued Moyal-bracket. linearized Navier Stokes equations around an unstable stationary solution in a two-dimensional domain Ω. The dis- Christian Lessig turbance is an unknown perturbation in the boundary con- Computing + Mathematical Scienes dition of the fluid flow. We determine a feedback bound- California Institute of Technology ary control law, robust with respect to boundary perturba- [email protected] tions, by solving a max-min linear quadratic control problem. We show that this feedback law locally stabilizes the MS138 Navier Stokes system. Similar problems have been studied Symplectic Semiclassical Wave Packet Dynamics in the literature in the case of distributed controls and disturbances. The case of boundary controls and boundary I will talk about the geometry and dynamics of semiclassi- disturbances has been addressed in the current work. cal wave packets, which provide a description of the transition regime from quantum to classical mechanics by plac- Sheetal Dharmatti ing “quantum mechanical wave flesh on classical bones.” I IISER-TVM will formulate semiclassical mechanics from the symplectic- India geometric point of view by exploiting the geometry of quan- [email protected] tum mechanics. This approach effectively “strips away” quantum effects from quantum mechanics and incorporates Jean Pierre Raymond them into the classical description of mechanics. Institut de mathematique, UPS Toulouse, France Tomoki Ohsawa [email protected] University of Michigan-Dearborn Department of Mathematics and Statistics [email protected] MS139 Investigation of Steady NS Flows past a Cylinder Melvin Leok using a Spectral Method, which basis Functions University of California, San Diego Spans the Infinite Domain Department of Mathematics The main difficulty in calculating steady flow past a cylin- [email protected] der in 2D is due to the slow rate in which the velocity approaches its asymptotic value. We have developed a spec- MS138 tral technique for finding solutions in the exterior domain. An Euler-Poincare Description of Curve Matching The talk will also introduce the ”bootstrap” method. In the ”bootstrap” method, the solution to steady NS is cal- In image analysis, the following question often arises: given culated as a perturbation to solution of the Oseen system. 118 AN13 Abstracts

The results are compared with Fornberg (1985). [email protected]

Jonathan Gustafsson Vladislav Bukshtynov Naval Postgraduate School Stanford University USA Department of Energy Resources Engineering [email protected] [email protected]

Bartosz Protas Dept of Mathematics and Statistics MS139 McMaster University Mathematical Approaches to Stochastic Signaling [email protected] and Pattern Formation

In biological systems with many genes and proteins pre- MS139 senting in small numbers, the inherent fluctuations can be Dynamics of Inertial Particles in Viscous Flows large and a continuous description of changes of concen- Driven By Oscillating Cilia trations is often not sufficient. In this talk, we will present our analysis and computations of discrete stochastic mod- Aquatic microorganisms like Vorticella use oscillating cilia els governed by master equations for the changes of num- to establish streaming flows that capture nearby food par- bers of molecules, to understand what strategies are used ticles. Artificial cilia can be used to achieve similar particle to control noise propagation and refine gene expression re- capture and transport in engineered systems. This talk will gions. Our results imply a lot of interesting consistency describe the analytical, computational, and experimental between discrete stochastic systems and the corresponding investigation of inertial particle dynamics in planar viscous continuous ones. flows driven by systems of circular cylinders executing rec- tilinear vibrations. Likun Zheng Department of Mathematics Scott D. Kelly University of California at Irvine Mechanical Engineering and Engineering Science [email protected] University of North Carolina at Charlotte scott@kellyfish.net PP1 Kwitae Chong Adomian Polynomial Approximation to Reaction Mechanical and Aerospace Engineering diffusion Equation Using Fractional Derivatives UCLA [email protected] The fractional derivative concepts are used to understand the pattern formation of cells in biological system by re- Jeff D. Eldredge action diffusion equation. The goal of this research is University of California, Los Angeles to improve the solution and models a more realistic rep- Mechanical & Aerospace Engineering resentation using the sensitivity of fractional differential [email protected] equations, which is approximated by Adomian polynomials. The solution methodology and the diffusion processes are demonstrated with computer simulation and the algo- Stuart Smith rithms are developed using the environment of MATLAB Mechanical Engineering and Engineering Science and COMSOL. The results are compared with the existing University of North Carolina at Charlotte literature. Also, the sensitivity of parameters which con- [email protected] trols the pattern formation and various other techniques will also be discussed. MS139 Leela Rakesh Optimal Reconstruction of Constitutive Relations Central Michigan University in Complex Multiphysics Phenomena Applied Mathematics Group We consider optimal estimation of state-dependent consti- [email protected] tutive relations in complex multiphysics systems governed by PDEs. We will demonstrate that such problems can Azza Abushams be formulated in terms of PDE-constrained optimization CMU where solutions can be obtained using suitable gradient- Mt. Pleasant based techniques. Since the control variable is defined as [email protected] a function of the state, the cost functional gradients have a rather unusual structure and their computation leads to PP1 a number of interesting questions at the level of numerical analysis. Roots of Quadratic Interval Polynomials

Bartosz Protas In this paper, we study the zeros of interval polynomials. Dept of Mathematics and Statistics We develop a method to compute all zeros of such polyno- McMaster University mial with interval coeﬃcients and give the characterization AN13 Abstracts 119

of the roots. MAD Fellows LLC [email protected] Ibraheem Alolyan King Saud University [email protected] PP1 Optimal Bayesian Inference in Social Networks

PP1 Understanding how information propagates in a social net- AWM Workshop A Mathematical Model of Deni- work has been an active area of research over the last few trification in Pseudomonas Aeruginosa decades. It is frequently assumed that discussion improves the decisions of individuals. However, such exchanges can Lake Erie has witnessed recurrent low-oxygen dead zones negatively impact a collective decision. Then how should and related microbial production of greenhouse gas, nitrous observers integrate information to reach best decisions? oxide, which is an intermediate in complete denitrification, We establish a general result on how the individuals can a microbial process of reduction of nitrate to nitrogen gas. achieve optimal inference in presence of redundancies in a We present a discrete model of denitrification metabolic graphical Bayesian model of interacting observers. network in Pseudomonas aeruginosa, one of the taxa performing denitrification in Lake Erie. This work suggests Manisha Bhardwaj that phosphate highly affects the dynamics of the network University of Houston by inhibiting the major regulator of the system. [email protected]

Seda Arat WeiJiMa Virginia Tech Baylor College of Medicine [email protected] [email protected]

PP1 Kresimir Josic Parameter Estimation with Censored Data Via University of Houston Kalman Filtering Department of Mathematics [email protected] It has been shown that the Kalman Filter does not perform well when output measurements are censored. This PP1 work considers a modified Kalman filter that properly utilizes the information provided by censored measurements. Long-Time Asymptotics for Perturbations of the We apply this methodology to parameter estimation in a Toda Lattice nonlinear ODE model for hepatitis C viral dynamics and We consider one dimensional doubly-infinite Fermi-Pasta- compare the results to those obtained with maximum like- Ulam (FPU) lattices obtained via perturbations of the lihood estimation. completely integrable Toda interaction potential. We in- Joseph Arthur vestigate, via numerical methods, the long time asymp- North Carolina State University totics of these nearly integrable systems. In particular, we [email protected] aim to relate the asymptotic resolution into solitary waves in the perturbed systems to the soliton resolution in the Hien T. Tran integrable lattice, namely the Toda lattice. Department of Mathematics Deniz Bilman North Carolina State University University of Illinois at Chicago [email protected] [email protected]

PP1 PP1 Improved Power Forecasting Using Pid Control AWM Workshop Derivation of SPDEs for Corre- Theory and Principal Component Analysis lated Random Walk Models

This research is a novel method to accurately define the Organisms do not move in purely random directions. Of- behavior of individuals controlling climate surrounding and ten, the current direction is correlated with the prior move- represented by a discrete proportional integral derivative ment. This type of random walk is called a correlated (PID) controller. This research uses principal component random walk. In this study, correlated random walk mod- analysis and PID to make a power consumption forecasting els are studied, specifically, the telegraph equation in one- model based on historical and predicted temperature data. dimension and the linear transport equation in two dimensions. Dynamical system is constructed to determine the Douglas S. Bebb, Scott Little different independent changes. Finally stochastic telegraph MAD Fellows and linear transport equations are derived from basic prin- [email protected], [email protected] ciples. Ummugul Bulut Dan Cervo Texas Tech University 120 AN13 Abstracts

Department of Mathematics and Statistics cancer research. We propose a model using differential [email protected] equations and dynamical systems to study cell development and tumor growth (or any similar dynamical progression). The model is solved numerically and compared with exper- PP1 imental data to provide additional insight. Domain Decomposition with Interface Phenomena and Application to Modeling Solar Cells Patrick T. Davis Central Michigan University We consider domain decomposition techniques for the drift- [email protected] diffusion system in a semiconductor with a material interface. The difficulties are in accounting for nonhomogeneous Leela Rakesh jumps in the primary variables which are caused by the po- Central Michigan University tential offset at the heterojunction, as well as accounting Center for Applied Mathematics and Polymer Fluid for the thermionic emission model at the heterojunction in Dynamics the transport equations. We show that adapted forms of [email protected] the Neumann-Neumann algorithm work very well for this problem. PP1 Timothy Costa Finding Singular Solutions to Polynomial Systems Oregon State University with Perturbed Regeneration [email protected] Homotopy continuation theory is used to find solutions to Malgorzata Peszynska systems of polynomial equations. Additionally, numerical Department of Mathematics algebraic geometry, a relatively young and quickly grow- Oregon State University ing field, utilizes continuation methods to find and classify [email protected] positive-dimensional solutions. An overview of the field will be given for beginners. For active researchers in the David Foster field, perturbed regeneration will be given to efficiently ap- Oregon State University proximate singular isolated solutions for which standard re- [email protected] generation only does with possibly many costly deflations to regularize them.” Guenter Schneider Brent R. Davis Department of Physics Colorado State University Oregon State University [email protected] [email protected] Daniel J. Bates PP1 Colorado State University Successive Constraint Methods in the Collocation Department of Mathematics Reduced Basis Framework [email protected]

Successive Constraint Methods are used to efficiently eval- David Eklund, Chris Peterson uate an accurate lower bound for the ’inf-sup’ constant Colorado State University needed to numerically solve parametric Partial Differen- [email protected], [email protected] tial Equations using the Reduced Basis Method(RBM). The RBM, originally developed in the Galerkin framework, Eric Hanson has recently been extended for the collocation methods. Department of Mathematics We present adapted and new formulations and numerical Colorado State University implementations of the Successive Constrain Method to [email protected] cope with the unique challenges inherent to the Colloca- tion Framework. PP1 Andrew C. Davey Heterogeneous Multiscale Method for Steady State University of Massachusetts Dartmouth Poroelasticity University of Massachusetts Dartmouth [email protected] In this work, we apply the heterogeneous multiscale method coupling discrete and continuum scale models governing flow and deformation processes in porous media. We PP1 derive a multidimensional model for the steady state case An Exploration of Dynamical Systems with An Ap- and propose a numerical scheme to solve the dynamic mul- plication in Cancer Growth tiscale pde as a sequence of steady state multiscale poroelasticity equations. As we encounter natural systems, there is a need to design simple but accurate mathematical modeling and simula- Paul M. Delgado tions in order to prevent serious errors. Nowhere is such UTEP work needed more than in medicine and in particular with AN13 Abstracts 121

[email protected] PP1 Study of Weakly Discontinuous Solutions for Hy- Vinod Kumar perbolic Diﬀerential Equations Based on Wavelet university of texas at el apso Transform Methods [email protected] A new way to prove the one-dimensional Cauchy problems weakly discontinuous solutions for hyperbolic PDEs are on PP1 the characteristics is discussed in this paper. To do so, I AWM Workshop Applications and Recent De- use wavelet singularity detection methods based on two- velopments of Multilevel Optimization Framework dimensional wavelet and combine it with the Lipschits in- (MG/OPT) dex to strengthen the detection.

This talk will present recent progress related to the theory Shijie Gu and applications of the multilevel optimization approach University of Nevada, Reno MG/OPT. The intent of MG/OPT is to use calculations on [email protected] coarser levels to accelerate the progress of the optimization on the finest level. Significant speedup by using MG/OPT comparing to other existing techniques has shown for a PP1 particular type of tessellation problems called centroidal AWM Workshop Gene Expression: Diffusion Voronoi tessellations(CVTs) and a variety of other con- Equations Model and Numerical Simulations strained optimization problems. A mathematical model was created using coupled PDEs Zichao Di to illustrate the interactions between one miRNA segment George Mason University and several mRNA segments within tissue. The coupled [email protected] PDE system can be studied as three separate well-posed systems of equations: a unique, nonlinear diffusion equation, coupled diffusion equations at steady state, and cou- PP1 pled diffusion equations with time dependence. Stable nu- Detecting Changes in Weather Data Streams for merical simulations show sharpening in concentration pro- Wind Energy Prediction files of mRNA in tissue when miRNA has mobility.

Wind generation is highly correlated to weather conditions. Maryann Hohn We are investigating if we can predict ramp events, which University of California, San Diego are large changes in generation over short periods, by mon- [email protected] itoring the weather data near the wind farms. Using velocity density estimation, we determine the trends in the evolution of these data streams considering both temporal PP1 and spatial properties. We discuss how the density proﬁles Can Cfa Franc Promote the Trade Between the can detect changes in weather and relate them to wind Waemu (West African Economic and Monetary generation. Union) and Its Trading Partners?

Ya Ju Fan, Chandrika Kamath This paper discuss briefly the implications of the peg ex- Lawrence Livermore National Laboratory change rate CFA-Euro on the trade in the West African [email protected], [email protected] Economic and Monetary Union (WAEMU) based on the framework of SHANE-ROE-SOMWAPU, optimal control and the real business cycle theories. Hence, the study PP1 aims to show by econometrical estimation under the in- AWM Workshop Parallel in Time Using Multigrid ternational market clearance condition, the effect of the exchange rate on the trade in WAEMU. It analyzes deeply One of the main challenges facing computational science the dynamic propagation mechanism of the rate of change with future architectures is that faster compute speeds of the exchange rate on the exportation volume, consump- will be achieved through increased concurrency, since clock tion, and foreign interest rate. Definitely, the exchange rate speeds are no longer increasing. As a consequence, tradi- seems to be an important macroeconomic variable affect- tional time marching will eventually become a huge sequen- ing the trade between WAEMU and its trading partners tial bottleneck, and parallel in time integration methods such the European Union, USA, China, etc. We find that are necessary. This poster discusses optimality and par- the depreciation of the exchange rate will be effective if allelization properties of one approach for parallelization the real value of the exportation and the consumption is in time, namely a multigrid-in-time method that is fairly greater than one percent increase of the foreign interest unintrusive on existing codes. rate.

Stephanie Friedhoﬀ Kodjo M. Houssou Tufts University University of Minnesota Stephanie.Friedhoﬀ@tufts.edu [email protected] 122 AN13 Abstracts

PP1 KTH - Royal Institute of Technology Wavelets and Wavelet Packets on Point Clouds [email protected]

This research generalizes wavelet packets to data on networks, with the aim of using these wavelet packets for com- PP1 pression and as a feature extractor for classification. We AWM Workshop Optimizing Intermittent Water develop two wavelet packet transforms, the foundations of Supply which are (1) the average-interpolation wavelets of Rusta- mov and (2) the lifting scheme of Jansen, Nason, and Sil- Water distribution systems throughout the world operate verman. A basis must then be selected from among these under intermittent supply. Efficient solvers for transient wavelet packets. For compression, this is done via the best- flow problems in water pipes are a prerequisite for opti- basis algorithm of Coifman and Wickerhauser. For classi- mization methods to develop effective management tech- fication, we use the local discriminant basis algorithm of niques for such systems. This work investigates inexact Saito and Coifman. Future work will use investigate the Riemann solvers to inform a model for coupled pipes in effectiveness of these wavelet packets for compression and a water distribution network, in order to implement op- classification. timization over operational scenarios to achieve more equitable distribution of water and reduce wear on system Jeffrey Irion components. UC Davis [email protected] Anna Lieb University of California Berkeley [email protected] Naoki Saito Department of Mathematics University of California, Davis PP1 [email protected] Comparative Analysis of Multiphase Flow Simu- lation in Fractured Rock Using Asynchronous and PP1 Synchronous Time Stepping Schemes on Hybrid Fi- nite Element-Finite Volume Meshes AWM Workshop Finite-Sized Reproductive Num- bers In adaptively refined discrete fracture and matrix (DFM) models, flow velocity varies over many orders of magni- A diseases basic reproductive number, R0, is the average tude and the smallest cells of the unstructured grid often number of infections caused by an infectious individual in a feature the highest flow velocities. Thus, global CFL is pro- susceptible population. This key epidemiological quantity hibitively small, but overstepping it in implicit calculations is used to inform models of diseases spread and persistence. is a challenge because of the nonlinear saturation functions The classic formulation of R0 assumes an infinite popula- and the risk of ill-conditioned matrices due to large scale tion, and is problematic when effective population size is difference in velocities and mesh resolution. We illustrate small. We discuss the theory of finite-population repro- this with field-data based DFM models, comparing perfor- ductive numbers, and calculate some for simple models of mance and accuracy of implicit methods with our original directly transmitted and vector-borne diseases. discrete event simulation (DES) based one that facilitates Lindsay T. Keegan asynchronous time stepping. McMaster University Roman Manasipov, Julian E. Mindel, Stephan Matthaei [email protected] Montan University of Leoben, Austria [email protected], PP1 [email protected], Optimization of Pool and Tournament Play in the [email protected] Top Swedish Handball League

We present research arising from the schedule-design prob- PP1 lem for the top Swedish Handball League, Elitserien, whose Estimating the Violation of the Kkt Conditions schedule includes both geographic group play and a dou- Given x, not necessarily a local minimizer of an optimiza- ble round-robin tournament. While both round-robin and tion problem, we propose a quantitative way of estimating pool play have been addressed by researchers, little atten- how close x is to a solution of the KKT conditions. This tion has been paid to issues arising from their combina- estimate of the distance to a KKT point is the solution of tion. We construct desirable home-away pattern sets to a non-convex optimization problem. We show how to solve yield greatly improved schedules for leagues such as Elitse- this problem using an Active Set Algorithm (ASA) . rien (which will use our results in their 2013-2014 season). Delphine Mico-Umutesi University of Florida Jeffrey M. Larson delmico@ufl.edu University of Colorado Denver jeff[email protected] William Hager Department of Mathematics Mikael Johansson AN13 Abstracts 123

University of Florida Montana State University hager@uﬂ.edu [email protected]

Isaac Klapper PP1 Temple University Robust Parameter Estimation: a Bayesian Infer- tba ence Approach

When policy makers are called to act on the control of epi- David Ward demic they often face the problem of how to efficiently allo- Montana State University cate limited resources in order to minimize disease impact. tba To help aid policy makers in their decision-making, we focus on improving the current methodology for estimating PP1 transmission parameters by fusing a Bayesian statistical Micellar Formulations of Drug Modified Copoly- framework with a stochastic model of disease transmis- mers with Single Walled Carbon Nanotube for sion and making this formulation applicable to any disease. Drug Delivery This method allows us to account for measurement error in disease census data thus providing more robust parame- Computer simulations are being carried out to understand ter estimates. Increasing estimation accuracy through the the maximum therapeutic efficacy of drugs by controlling adoption of our framework will equip policy makers with the bio-distribution profile. Micelle formation by the addi- better tools for mitigating the effects of an epidemic. tion of surfactant / polymeric hydrophobic- hydrophilic- copolymers (PHBC) in mixtures with the hydrophobic Romarie Morales drugs have been studied as drug delivery systems. PBHC Arizona State University can form either lamellar or rod-like , cylindrical, spherical, [email protected] and hexagonal aggregates morphology, with different sol- ubilization capacity under certain conditions. These have PP1 different sizes and stability criteria and be used to solubi- Predicting Fetal Distress lize water insoluble drugs for the treatment of infectious disease. In order to understand these limitations we have During labor, continuous fetal heart rate (FHR) monitor- made an attempt to study the effect of functionalized drugs ing is not a reliable predictor for severe academia. This by dissipative particle dynamics (DPD). Further, we sim- condition is commonly caused by umbilical cord occlusions ulated the system in the presence of single walled carbon and can cause fetal distress and permanent brain injuries to nanotube (SWNT) as a site- specific drug carrier. the fetus. More reliable monitoring modalities and methods of signal analysis are needed. To address this, I present Leela Rakesh a mathematical model which explores the monitoring of Central Michigan University two signals, FHR and electroencephalogram (EEG), as a Applied Mathematics Group way to predict fetal distress. [email protected]

Aisha Najera Chesler PP1 Claremont Graduate University [email protected] Variance Reduction for Multilevel Monte Carlo Simulation of SDEs

Ami Radunskaya A prototypical problem in stochastic differential equations Pomona College (SDEs) is to compute the expectation of some functional Mathematics Department - called the payoff - of the SDE’s solution. The multi- [email protected] level Monte Carlo (MLMC) method, introduced in [M.B. Giles, Operations Research, 56(3):607617, 2008], dramati- PP1 cally improves upon naive Monte Carlo methods for such problems. We present two improvements to MLMC meth- Fundamental Niche Character in a Temporally ods, applicable when the payoff is twice differentiable. The Varying Environment first eliminates the variance at the lowest level by making The magnitude and extent of variation that an organism’s use of Ito’s lemma, while the second improves the scaling niche inherits from its environment is investigated through of the variance of the level differences in order to achieve a temporally varying chemostat model. Constrained opti- the theoretically optimal computational complexity. Nu- mization is used to predict how an organism should opti- merical examples are presented that confirm the results. mally respond to environmental variation occurring over Lee Ricketson several different time scales. Light data collected near UCLA Mushroom Spring, Yellowstone National Park, are then [email protected] incorporated into the model and the output is compared to the observed light niche of a phototrophic Mushroom Spring inhabitant. PP1 Shane Nowack AWM Workshop Feedback-Mediated Dynamics in 124 AN13 Abstracts

the Kidney: Mathematical Modeling and Analysis University of Houston [email protected] We developed a mathematical model of the tubuloglomeru- lar feedback (TGF) system in the kidney to study TGF- mediated oscillations in fluid dynamics variables. Model PP1 equations consist of nonlinear time-delayed differential AWM Workshop Lagrangian Data Assimilation equations. Using bifurcation analysis and numerical simu- and Its Application to Geophysical Fluid Flows lations, we investigated the impacts of parameter variabili- ties on model behaviors. Model results revealed a complex The goal of data assimilation is to combine knowledge of parameter region, where qualitatively different solutions the underlying dynamical system and observations in or- are possible. The multistability of model solutions may der to estimate the current state of the system. Lagrangian explain the emergence of irregular oscillations in sponta- data assimilation attempts to estimate the velocity field of neously hypertensive rats. a flow, given discrete observations of positions of passive drifters. In this poster I will present an overview of La- Hwayeon Ryu grangian data assimilation in the context of fluid flows, Duke University including both traditional methods and a new hybrid” ap- [email protected] proach.

Laura Slivinski, Bjorn Sandstede PP1 Brown University AWM Workshop Light Propagation In laura [email protected], bjorn [email protected] Semiconductor-Based Luminescent Solar Concen- trators PP1 Luminescent solar concentrators (LSCs) convert sunlight Uniaxial Elongational Flow of a Thixotropic Yield to electricity. We study light propagation in LSCs that Stress Fluid contain semiconductor nanoparticles and use this to predict their performance and optimal design parameters. In The uniaxial elongational flow of a thixotropic yield stress particular, a luminescent radiative transport theory is pro- fluid is studied with a viscoelastic constitutive model (Par- posed that can take the reabsorption effects into account tially Extending strand Convection model, Larson, 1984) accurately. The computational results based on the deter- combined with a Newtonian solvent with no assump- ministic theory are studied in detail and compared with tions about the existence of a yield stress or thixotropy. Monte Carlo simulations for photon transport. The results The PEC model is based on molecular theory for highly of this study will aid the development of highly-efficient branched polymers with side branches that get in the way LSCs. of fully extending. A class of initial value problems with prescribed tensile stress is addressed. If the relaxation time Derya Sahin is large, then there are two time scales which naturally UC Merced emerge: a fast time scale for elastic deformation and flow, [email protected] and a long time scale for small changes in the microstructure. The steady state curve for tensile stress vs elongation Derya Sahin rate is non-monotone for a certain parameter range. The University of California, Merced time-dependent solutions display an interplay of slow and Applied mathematics, School of Natural Sciences fast dynamics. [email protected] Holly Timme Boaz Ilan VIrginia Tech School of Natural Sciences [email protected] University of California, Merced [email protected] Yuriko Renardy Virginia Tech Department of Mathematics PP1 [email protected] AWM Workshop—Global Existence for Sur- face/Interior Reaction Diffusion Systems PP1 We consider coupled reaction-diffusion models, where some Pancreatic Beta Cells: Modeling the Interdepen- components react and diffuse on the boundary of a region, dence of Intracellular Calcium and Insulin Release while other components diffuse in the interior and react with those on the boundary through mass transport. Clas- Pancreatic beta cells secrete insulin, allowing the body to sical potential theory and estimates for linear initial bound- take up glucose for energy or storage. In diabetes, glu- ary value problems are used to prove local well-posedness cose is chronically elevated, contributing to cardiovascular and global existence. This type of system arises in mathe- disease. We study the interdependence of cell membrane matical models for cell processes. This is a joint work with potential and calcium oscillations used by beta cells to reg- Jeff Morgan at the University of Houston. ulate insulin secretion. A theoretical model is developed, and regulatory candidates are tested in simulation to iden- Vandana Sharma tify parameter values for data within the public domain. AN13 Abstracts 125

ation process compared with mono-exponential decay. The slow relaxation behavior is due to the distribution of en- Diana W. Verzi ergetic interactions between the entangled worms or other San Diego State University-Imperial Valley Campus network components at the ”mesoscale”. In order to un- [email protected] derstand the dynamics of these ﬂuids, and to avoid inaccurate closure relationships when constructing continuum- Jocelyn Alcala, Elizabeth Fletes, Dulce Hernandez, Eddie scale models, we model and simulate the evolution in the Palomares, Perla Vega transient network deformation at the mesoscale. San Diego State University Student Yun Zeng [email protected], ﬂ[email protected], can- Department of Mathematical Sciences, University of [email protected], [email protected], Delaware [email protected] Newark, DE 19716, USA [email protected]

PP1 Inhibition of Mis-Regulated Nf-KB by Decoy Oligonucleotides: A Mathematical Implication

Nuclear factor-kB (NF-kB) is a transcription factor regulating the genes that control the cell proliferation and survival. Mis-regulated NF-kB proteins could lead to many types of human tumors. The inhibition of transcriptional activity of NF-kB by Decoy Oligonucleotides is an excellent approach to cure cancer. We model the related biochemical reactions in the single cell by Stochastic Master Equations. Our numerical results are consistent with the results of single-cell experimental studies of NF-kB gene regulatory networks and clinical studies.

Zhipeng Wang Rice University [email protected]

PP1 Eulerian Ergodic Partition Using the Backward Phase Flow Method

We develop an efficient Eulerian method to compute the ergodic partition for visualizing invariant sets in a continuous dynamical system. In particular, we apply the level set method and the phase flow method to determine the long time flow map. To determine the integral of an auxiliary function along particle trajectories, we propose to iteratively interpolate our flow maps. This method incorporates well with our Eulerian approach. We will also show some preliminary results to demonstrate the efficiency of the method.

Guoqiao You The Hong Kong University of Science and Technology [email protected]

Shingyu Leung Hong Kong University of Science and Technology [email protected]

PP1 AWM Workshop Mesoscale Stochastic Modeling and Simulation of the Dynamics of Soft Gels: Tran- sient Networks

Many polydisperse entangled materials such as concentrated wormlike micellar dispersions exhibit ”slow” relax- 126 2013 SIAM Annual Meeting • SIAM Conference on Control & Its Applications 2013 SIAM Annual Meeting • SIAM Conference on Control & Its Applications 127

CT13 Abstracts 128 CT13 Abstracts

IC1 Innovation An Aerospace Perspective Simplicial Nonlinear Principal Component Analy- sis For technologically mature industries or those with high barriers to change, innovation is a challenge. One low risk, We present a new manifold learning algorithm that takes a low cost innovation path is to radically improve perfor- set of data points lying on or near a lower dimensional man- mance while minimizing change to existing infrastructure. ifold as input, possibly with noise, and outputs a simplicial In this presentation, a historical perspective on spacecraft complex that is the data and the manifold. We have im- optimal control is used to show how scientific computation plemented the algorithm in the case where the input data can act as the enabler for next generation innovation. Real is on a two dimensional manifold in R3 and can be trian- world examples will be presented where radical leaps in gulated. We provide triangulations of data sets that fall performance without altering spacecraft hardware or soft- on the surface of a torus, sphere, swiss roll, and creased ware has been achieved. sheet. We also discuss the theoretical justication of our algorithm. Nazareth Bedrossian Halliburton Thomas Hunt [email protected] Naval Postgraduate School [email protected] SP1 Arthur J. Krener AWM-SIAM Sonia Kovalevsky Lecture: Introduc- Naval Postgraduate School tion to Radar Imaging Department of Applied Mathematics Radar imaging is a technology that has been developed, [email protected] very successfully, within the engineering community during the last 50 years. Radar systems on satellites now make IC2 beautiful images of regions of our earth and of other plan- ets such as Venus. One of the key components of this im- Fast Distributed Optimization Methods over Net- pressive technology is mathematics, and many of the open works problems are mathematical ones. This lecture will explain, The standard approach for designing distributed algo- from first principles, some of the basics of radar and the rithms for optimization problems over networks rely on mathematics involved in producing high-resolution radar (sub)-gradient methods, but suffers from slow rate of con- images. vergence. In this talk, we present new distributed optimiza- Margaret Cheney tion algorithms with much faster rate of convergence. We Colorado State University first provide a completely asynchronous, distributed, and and Naval Postgraduate School fast algorithm based on Alternating Direction Method of [email protected] Multipliers for solving coupled convex optimization problems over networks. We then focus on a structured version of this problem where the local objective functions SP2 take an additive form with a differentiable and a nondif- 2011 SICON Paper Prize Lecture #1: Feedback ferentiable component and develop a distributed proximal Stabilization of a Fluid-Structure Model gradient method. We study a system coupling the incompressible Navier- Asu Ozdaglar Stokes equations in a 2D rectangular domain with a MIT damped Euler-Bernoulli beam equation, occupying the up- [email protected] per boundary of the fluid domain. Due to the deformation of the beam, the fluid domain depends on time. We IC3 prove that this system is exponentially stabilizable, locally about the null solution, with any prescribed decay rate, Control of Some Partial Differential Equations and by a feedback control corresponding to a force term in the Nonlinearity beam equation.

In this talk, we survey some methods to study the con- Jean-Pierre Raymond trollability of some nonlinear partial differential equations Universite Paul Sabatier when the nonlinearity plays an important role. This is Institut de Mathématiques for example the case when the linearized control system [email protected] around the the equilibrium of interest is not controllable or if the nonlinearity is large at infinity and one looks for global results. Applications will be presented to various SP3 equations modeling fluid flows, as the Euler and the Navier- 2013 SICON Paper Prize Lecture #1: Gossip Cov- Stokes of incompressible fluids, the shallow water equations erage Control for Robotic Networks: Dynamical and the Korteweg-de Vries equations. Systems on the Space of Partitions

Jean-Michel Coron Future applications in environmental monitoring, delivery Universit´e Pierre et Marie Curie, France of services and transportation of goods motivate the study [email protected] of deployment and partitioning tasks for groups of autonomous mobile agents. These tasks may be achieved by IC4 recent coverage algorithms, based upon the classic methods by Lloyd. These algorithms however rely upon critical re- Role Of Scientiﬁc Computation In Next Generation quirements on the communication network: information is exchanged synchronously among all agents and long-range CT13 Abstracts 129

communication is sometimes required. This work proposes SP6 novel coverage algorithms that require only gossip commu- The John von Neumann Lecture: What Sparsity nication, i.e., asynchronous, pairwise, and possibly unreli- and l1 Optimization Can Do For You able communication. Which robot pair communicates at any given time may be selected deterministically or ran- Sparsity and compressive sensing have had a tremendous domly. A key innovative idea is describing coverage algo- impact in science, technology, medicine, imaging, machine rithms for robot deployment and environment partitioning learning and now, in solving multiscale problems in applied as dynamical systems on a space of partitions. In other partial diﬀerential equations. l1 and related optimization words, we study the evolution of the regions assigned to solvers are a key tool in this area. The special nature of each agent rather than the evolution of the agents posi- this functional allows for very fast solvers: l1 actually for- tions. The proposed gossip algorithms are shown to con- gives and forgets errors in Bregman iterative methods. I verge to centroidal Voronoi partitions under mild technical will describe simple, fast algorithms and new applications conditions. ranging from sparse dynamics for PDE, new regularization paths for logistic regression and support vector machine to Ruggero Carli optimal data collection and hyperspectral image process- University of California Santa Barbara ing. [email protected] Stanley J. Osher Francesco Bullo University of California Mechanical & Environmental Engineering Department of Mathematics University of California at Santa Barbara [email protected] [email protected] SP7 Paolo Frasca Politecnico di Torino, Italy SIAG/CST Prize Lecture - Feedback Control of [email protected] Hybrid Dynamical Systems: from Cells to Power Networks

SP4 Hybrid systems have become prevalent when describing complex systems that mix continuous and impulsive dy- 2011 SICON Paper Prize Lecture #2: Optimal namics. Continuous dynamics usually govern the evolution Stopping Problem for Stochastic Differential Equa- of the physical variables in a system, while impulsive (or tions with Random Coefficients discrete) behavior is typically due to discrete events and An optimal stopping problem for stochastic differential abrupt changes in the dynamics. Motivated by the lack equations with random coefficients is considered. Dy- of tools to rigorously study these systems, a mathemati- namic programming principle leads to a Hamiltion-Jacobi- cal framework and its associated tools for the analysis and Bellman equation which, for the current case, is a back- synthesis of robust hybrid feedback control systems will be ward stochastic partial differential variational inequality presented. The focus will be on asymptotic stability and (BSPDVI, for short) for the value function. Well-posedness invariance of sets. The tools will be exercised in appli- of such a BSPDVI is established and a verification theorem cations, ranging from genetic networks to power systems. is proved.

Mou-Hsiung Chang Ricardo G. Sanfelice U. S. Army Research Oﬃce University of Arizona Mathematics Division [email protected] [email protected] SP8 Tao Pang Past President’s Address: Chebfun North Carolina State University, USA [email protected] Chebfun is a Matlab-based open-source software project for “numerical computing with functions” based on algo- Jiongmin Yong rithms related to Chebyshev polynomials. In recent years University of Central Florida developing Chebfun has been my main research activity, to- [email protected] gether with the closely linked project of writing the book Approximation Theory and Approximation Practice (SIAM 2013). This talk will present some highlights of the Cheb- SP5 fun endeavor and will be followed by a two-part Chebfun 2013 SICON Paper Prize Lecture #2: The Total minisymposium. s-Energy of a Multiagent System Nick Trefethen We introduce the s-energy of a sequence of undirected Oxford University graphs embedded in d-space. This generating function pro- [email protected] vides a new analytical lens on bidirectional agreement dynamics, which we use to bound the convergence rates of dynamical systems for synchronization, ﬂocking, opinion SP9 dynamics, and social epistemology. W. T. and Idalia Reid Prize in Mathematics Lec- ture: Solvability for Stochastic Control Problems Bernard Chazelle Princeton University Some stochastic control problems for continuous time sys- [email protected] tems are described where optimal controls and optimal costs can be explicitly determined by a direct method. The 130 CT13 Abstracts

applicability of this method is demonstrated by examples communication link for a decentralized system. In spite of including the linear quadratic control problem with the sys- their pervasive presence, very little is known about the sta- tem driven by an arbitrary noise process with continuous bility properties of these spaces, i.e. whether a given vector sample paths, a controlled Brownian motion in a symmet- space of sparse matrices contains stable (Hurwitz) matri- ric space and the linear exponential quadratic Gaussian ces. We provide in this talk a set of necessary and a set of control problem. The problems for linear systems can be sufficient conditions for the existence of stable matrices in modified to allow for equations in an infinite dimensional a vector space of sparse matrices. We further prove global Hilbert space that describe stochastic partial differential properties of the set of sparse matrix spaces that contain equations. Hurwitz matrices. The conditions we exhibit are mostly graph theoretic and show the importance of Hamiltonian Tyrone E. Duncan cycles in the study of stability from a graph theoretic per- University of Kansas spective. Finally, we present polynomial time algorithms Department of Mathematics to generate sparse vector spaces that contains stable ma- [email protected] trices. Mohamed Ali Belabbas SP10 Harvard University I. E. Block Community Lecture: From Razor [email protected] Clams to Robots: The Mathematics Behind Bio- logically Inspired Design CP1 Many natural systems have evolved to perform certain The Wasserstein Metric for Factor Analysis tasks – climbing, sensing, swimming – as perfectly as possible within the limits set by the laws of physics. This We consider the problem of approximating a (nonnegative observation can be used both to guide engineering design, definite) covariance matrix by the sum of two structured and to gain insights into the form and function of biological covariances –one which is diagonal and one which has low- systems. In this talk we will consider both of these themes rank. Such an additive decomposition follows the dictum in the context of crawling snails, digging clams and swim- of factor analysis where linear relations are sought between ming microorganisms. We will discover how an analysis of variables corrupted by independent measurement noise. the physical principles exploited by snails and clams leads We use as distance the Wasserstein metric between their to the development of novel robotic diggers and crawlers, respective distributions (assumed Gaussian) which induces and explore the role of mathematics in the design, control, a metric between nonnegative definite matrices, in general. and assessment of unconventional robotic systems. The rank-constraint renders the optimization non-convex. We propose alternating between optimization with respect Anette Hosoi to each of the two summands. Properties of these opti- Massachusetts Institute of Technology mization problems and the performance of the approach 77 Massachusetts Avenue, Room 3-173, Cambridge MA are being analyzed. 02139 [email protected] Lipeng Ning, Tryphon Georgiou University of Minnesota [email protected], [email protected] JP1 Applied and Computational Mathematics for En- ergy Efficient Systems CP1 State of the Art Hifoo: H-Infinity Controller Opti- Recent advances in the development of sustainable energy mization for Large and Sparse Systems sources have led to an emphasis on energy-supply technologies and the corresponding mathematical sciences needed We present a new state of the art version of HIFOO, a for these technologies. However, energy efficient end-use matlab package for optimizing H∞ and H2 controllers for technologies may also be viewed as an energy resource. linear dynamical systems, supporting simultaneous multi- Since buildings are responsible for 32% of energy consump- ple plant stabilization. Previous versions of HIFOO have tion and for 26% of end-use C02 emissions, optimizing the generally been limited to smaller scale problems, due to the efficiency of a whole building system is a ”grand challenge high asymptotic cost of computing the H∞ norm of the control” problem with huge payoffs in the global energy sec- transfer matrix. However, new sparse methods for com- tor. We discuss mathematical challenges and opportunities puting the H∞ norm allow HIFOO to extend efficiently to that occur in designing practical controllers for energy ef- large and sparse systems. ficient buildings. Examples are presented to illustrate the ideas. Tim Mitchell Courant Institute of Mathematical Sciences John A. Burns New York University Virginia Tech [email protected] Interdisciplinary Center for Applied Mathematics [email protected] Michael L. Overton New York University Courant Instit. of Math. Sci. CP1 [email protected] Sparse Matrices and Decentralized Control: The- ory and Algorithm CP1 Vector spaces of sparse matrices appear naturally in the An All-at-Once Multigrid Method Applied to a design of decentralized systems. In this context, one can think of the non-zero entries of the matrix as representing a CT13 Abstracts 131

Stokes Control Problem optimizing energy bids for an independent Wind Power Producer (WPP) taking part into a competitive electricity We are interested in an iterative solver for the Stokes con- market. It is assumed that the WPP is subject to financial trol problem. The discretized optimality system is a large- penalties for generation shortfall and surplus. An opti- scale and indefinite linear system. It depends on certain mization procedure is devised to minimize this risk and parameters: the discretization parameter (grid size) and maximize the expected profit of the seller. Specifically, problem parameters (like the regularization parameter). each energy bid is computed by exploiting the forecast en- We are interested in fast iterative solvers which are ro- ergy price for the day ahead market, the historical wind bust in these parameters. In the talk we will propose an statistics at the plant site and the day-ahead wind forecasts all-at-once multigrid method. We will sketch the ideas of provided by a meteorological service. We also examine and aconvergenceproof. quantify the strategic role of an energy storage device in increasing reliability of bids and mitigating the financial Stefan Takacs risks of the WPP. Visiting postdoc at Mathematical Institute University of Oxford Antonio Vicino [email protected] UniversitàdiSiena [email protected] CP2 Antonio Giannitrapani, Simone Paoletti, Donato Zarrilli Optimal Control of Crop Irrigation Based on the UniversitàdiSiena Hamilton-Jacobi-Bellman Equation Dip. Ingegneria dell’Informazione e Scienze Matematiche This paper proposes a methodology to solve the optimal [email protected], [email protected], control of crop irrigation based on a dynamic model of plant [email protected] growth in interaction with soil water reserve. We introduce the utility function corresponding to farming profit and de- CP3 rive the Hamilton-Jacobi-Bellman equation for the value function. It is solved with a backward finite-difference Development and Improvement of Active Vehicle scheme proved to converge under proper CFL conditions. Safety Systems by Means of Smart Tire Technology A few numerical test cases illustrate the resolution. In this multidisciplinary project, an integrated vehicle con- Paul-Henry Cournède trol algorithm is developed which utilizes the novel smart Laboratory of Mathematics Applied to Systems tire concept to obtain information on system states. The Ecole Centrale Paris control algorithm follows a two stage (main/servo) ap- [email protected] proach where an upper level controller decides on the stabilizing inputs and a lower level controller implements the inputs through actuator dynamics. The algorithms are val- Yuting Chen idated through numerical analysis and provide substantial Laboratory Mathematics Applied to Systems improvements in vehicle safety and performance. Ecole Centrale Paris [email protected] Mustafa A. Arat Center for Tire Research Jacques Ramanathan Virginia Tech Ecole Centrale Paris [email protected] [email protected]

CP3 CP2 Adaptive Nonlinear Control for Electromagnetic A Chaotic Model for Bird Flocking Actuators

Pidgeons may be observed to flock in models that approx- We study here the problem of robust ‘soft-landing’ control imate the Lorenz Attractor. We would like to propose a for electromagnetic actuators. The soft landing requires ac- model that is exactly observable and exactly controllable, curate control of the actuators moving element between two given certain parameters, for a flock of birds. Applications desired positions. We present here two nonlinear adaptive of this model would be divided into those that are discrete, controllers to solve the problem of robust trajectory track- and those that are continuous. Discrete applications occur ing for the moving element. The first controller is based on in graph theory and network theory. classical nonlinear adaptive technique. We show that this controller ensures bounded tracking errors of the reference Jorge Diaz-Castro trajectories and bounded estimation error of the uncertain University of P.R. School of Law parameters. Second, we present a controller based on the University of P.R. at Rio Piedras so-called Input-to-State Stability (ISS), merged with gra- [email protected] dient descent estimation filters to estimate the uncertain parameters. We show that it ensures bounded tracking errors for bounded estimation errors, furthermore, due to CP2 the ISS results we conclude that the tracking errors bounds Optimal Bidding Strategies for Wind Power Pro- decrease as function of the estimation errors. We demon- ducers with Meteorological Forecasts strate the effectiveness of these controllers on a simulation example. The inherent variability in wind power generation and the related difficulty in predicting future generation profiles, Mouhacine Benosman raise major challenges to wind power integration into the MERL electricity grid. In this work we study the problem of m [email protected] 132 CT13 Abstracts

Gokhan Atinc inaccurate when depicting the system dynamics at non- University of Illinois at Urbana-Champaign sampled regions of the state space leading to observers [email protected] that require finely tuned observer gains. We propose a method to compute the PDE operator eigenfunctions based on empirical eigenfunctions obtained from adaptive POD. CP3 The controller/observer structure is then synthesized by A Passivity-Based Trajectory Tracking Controller combining a robust state controller with a recursively up- for Robot Manipulators With Velocity Constraints dated reduced order dynamic observer. The proposed method is illustrated on the integral form of the Kuramoto- A stable control structure for trajectory tracking of robot Sivashinsky equation. manipulators subject to joint velocity constraints is proposed. The structure consists of a negative feedback con- Davood Babaei Pourkargar nection, which includes the system dynamics, a tracking Department of Chemical Engineering controller, and a non-linear passive controller. By using The Pennsylvania State University, University Park passivity and Lyapunov theory, asymptotic tracking with [email protected] bounded velocities is proved for the closed-loop system. Simulation results are provided to show the effectiveness Antonios Armaou of the proposal. Department of Chemical Engineering The Pennsylvania State University Ollin Peñaloza-Mejia [email protected] CICESE Department of Electronics and Telecommunications [email protected] CP4 Moderate Deviations Analysis for System Identifi- Luis Alejandro Marquez-Martinez, Joaquin cation under Regular and Binary Observations Alvarez-Gallegos CICESE In this talk, we will investigate identification errors in a [email protected], [email protected] moderate deviations framework. This study provides a new perspective to understand the fundamental relationship between probabilistic errors and resources that represent data CP3 sizes in computational algorithms, sample sizes in statisti- Reduced Order Observer Design for Structure and cal analysis, channel bandwidths in communications, etc. Motion Estimation This relationship is derived by establishing the moderate deviations principle for regular and binary identification. The problem of Structure and Motion Estimation in ma- Under some mild conditions, we obtain moderate devia- chine vision can be addressed by designing observers for dy- tions upper and lower bounds for regular and binary ob- namic systems. We propose and observer for feature point servations respectively. Numerical examples are provided depth and camera linear velocity. The camera’s angular to illustrate the theoretical results. velocity is assumed known. As well, we require two feature points with known displacement. Relative to previous Qi He work, we do not require linear acceleration measurements. University of California, Irvine The local exponential stability of the observer is proven us- [email protected] ing a converse Lyapunov theorem. We assume the camera motion satisfies a persistency of excitation condition and George Yin the linear acceleration is bounded and has finite energy. Wayne State University Department of Mathematics Hui Xie [email protected] Dept of Electrical and Computer Engineering University of Alberta [email protected] Leyi Wang Wayne State University [email protected] Romeo Fomena, Alan Lynch Dept of Electrical and Computer Engineering University of Al CP4 [email protected], [email protected] Optimal Control of Particle Accelerators The talk deals with the optimal control of particle accel- CP4 erators by means of exterior magnetic fields. The forward Design of Recursively Updated Reduced Order Dy- problem is modeled by a nonlinearly coupled system con- namic Observers for Distributed Parameter Sys- sisting of the instationary Maxwell’s equations, an ODE for tems the relativistic particle dynamics, and an additional elliptic equation for the scalar magnetic potential. The control A well-established approach to design controller and ob- enters the problem via the Dirichlet data in the elliptic server for distributed parameter systems is via model re- equation. First-order necessary optimality conditions and duction, computing a reduced order model (ROM) us- preliminary numerical results are presented. ing a combination of proper orthogonal decomposition (POD) variants with Galerkin method. The eigenvalues- Oliver Thoma eigenfunctions computation in this approach is based on TU Dortmund the covariance matrix of a snapshots ensemble which usu- Faculty of Mathematics ally are different from the eigenvalues and eigenfunctions [email protected] of the PDE spatial operator. Thus, the ROM might be CT13 Abstracts 133

Christian Meyer ity solution of the generalized HJB equation system. Technical University Dortmund [email protected] Ran Tao,ZhenWu Shandong University, China Sascha Schnepp [email protected], [email protected] ETH Zurich IFH CP6 [email protected] Iterative Convolution Particle Filtering for Nonlin- ear Parameter Estimation and Data Assimilation CP5 with Application to Crop Yield Prediction A Monte Carlo Method for Optimal Portfolio Ex- The complexity of plant growth models and the generally ecution scarce experimental data make the application of conven- We consider the problem of mean-variance optimal exe- tional data assimilation techniques difficult. In this paper, cution in markets with limited liquidity, as introduced in we use the convolution particle filter and an iterative adap- Almgren (2012). While most of the existing literature is tation for parameter estimation. Both methods provide concerned with deterministic strategies for the one-asset prior distributions for data assimilation sequentially per- case, our paper deals with dynamic strategies for multi- formed by CPF in order to improve model prediction and asset portfolio executions. We propose a rolling horizon to assess predictive uncertainty. The approach is evaluated Monte Carlo scheme that allows real-time execution and for the LNAS model of sugar beet growth with real data. any number of assets and stochastic drivers. We provide Yuting Chen, Samis Trevezas ample numerical experiments, which also shed new light on Laboratory of Mathematics Applied to Systems cases when deterministic strategies are optimal. Ecole Centrale Paris Nico Achtsis [email protected], [email protected] K.U.Leuven [email protected] Paul-Henry Cournède Laboratory of Mathematics Applied to Systems Dirk Nuyens Ecole Centrale Paris Dept. of Computer Science [email protected] K.U.Leuven [email protected] CP6 Parameter Estimation and Sensitivity Analysis in CP5 Ground Water Flow Equations Optimal Replication of Random Claims by Ordi- In previous works, we have proposed various methods for nary Integrals with Applications in Finance identification of the most significant parametric variations, By the classical Martingale Representation Theorem, repli- and an optimization-based framework for estimation of dis- cation of random vectors can be achieved via stochastic in- tributed parameters. Combining both approaches, we use tegrals or solutions of stochastic differential equations. We the Frchet derivative to determine the most significant (de- introduce a new approach to replication of random vec- terministic) parametric variations; this is used to generate tors via adapted differentiable processes generated by a a low order Karhunen-Loeve expansion of the unknown pa- controlled ordinary differential equation. We found that rameters specific storage and hydraulic conductivity. The the solution of this replication problem exists and is not expansion is used in the parameter identification problem, unique. This leads to a new optimal control problem: find which is formulated as an infinite dimensional constrained a replicating process that is minimal in an integral norm. optimization problem. The low order expansion allows us We found an explicit solution of this problem. Possible to estimate the infinite dimensional problem by a smooth, applications to portfolio selection problems and to bond albeit high dimensional, deterministic optimization prob- pricing models are suggested. lem, the so-called finite noise problem, in the space of functions with bounded mixed derivatives. A power method Nikolai Dokuchaev and sensitivity equations are used to evaluate the most sig- Curtin University nificant directions, and compute reduced representations of [email protected] the operator. V´ıtor Nunes CP5 Virginia Polytechnic Institute and State Universit Recursive Optimal Control Problems for Regime- [email protected] Switching Model

In this paper, we consider recursive optimal control prob- CP6 lems for regime-switching model. The system is described An Optimal Control Approach for An Hiv-Tb Co- by diffusion processes modulated by Markov chains while Infection Model the recursive utility is represented by a kind of backward stochastic differential equations. First, we obtain We consider an HIV-TB co-infection model. To possibly re- the stochastic maximum principle for the optimal control. duce the latent and infectious sub-populations, we assume Then, we derive the recursive dynamic programming prin- that detection rates of active TB individuals can be im- ciple and prove that the value funcion is the unique viscos- proved by applying more effective policies. We incorporate controls representing the fractions of active TB individuals among HIV− and HIV+ that are detected (as a result 134 CT13 Abstracts

of applying the suggested policy) and will be put under Chemical Processes treatment. The optimal system is solved using eﬃcient numerical techniques. In this paper the discrete active disturbance rejection control (DADRC) is proposed for typical process control prob- Kailash C. Patidar lems. In the DADRC framework, the external disturbances University of the Western Cape and internal dynamics associated with chemical processes [email protected] are treated as the generalized disturbance to be estimated and compensated for in real time. By employing a discrete extended state observer for estimating the generalized dis- CP7 turbance, the DADRC provides a current estimate of states Stability Analysis of a Controller/Observer for and therefore improves the performance of the closed-loop Input-Constrained DC-DC Boost Power Convert- system. ers Qing Zheng,AhmadGhaweta In this paper, a new stability analysis of a known con- Department of Electrical and Computer Engineering, troller/observer for DC-DC boost converters is presented. Gannon University The new analysis considers the overall closed–loop system, [email protected], [email protected] which includes the dynamics of the observation error as well as the dynamics of current and voltage error. This analysis Yong Zheng relies in the stability theory of cascaded time-varying sys- The Second Academy of China Aerospace tems. In addition, two real–time experiments are shown, Science & Industry Corp. illustrating the robustness of the controller/observer. [email protected] Jorge Guzman-Guemez, Javier Moreno-Valenzuela Instituto Polit´ecnico Nacional-CITEDI CP8 [email protected], [email protected] Mechanism Analysis of Robust Quantum Control

Robust Quantum Control is a novel field of research which CP7 studies how a quantum dynamical system can be coher- Homology of Lie Algebras and Evapotranspiration ently controlled to a target superposition of states in set- in Control of a Greenhouse tings where noise is prevalent. In this work, we investigate how different types of disturbances on the control field’s The following results are consequences of investigations spectrum affect its robustness. Specifically, different-order considereing the interactions between the dynamics of a state-to-state pathways associated with optimal fields’ con- production greenhouse and the dynamics of the market trol mechanism are analyzed for their sensitivity to varia- for the greenhouse. It is had a three state variable dy- tions in the fields spectral bandwidth, phase and ampli- namical system with three control variables, modelling a tude. greenhouse. In this system is identified a Lie subalgebra containing a Heinsenberg subalgebra. With the structure Andy Koswara constants of the Lie subalgebra is posible compute the asso- Purdue University ciated evapotraspiration function of the greenhouse. Ad- School of Chemical Engineering ditionally is calculated the homology of the subalgebras. [email protected] And in all the cases the Euler characteristic is null. JoséRamón Guzmán Raj Chakrabarti Economa Aplicada. Instituto de Investigaciones Carnegie Mellon University Económicas Department of Chemical Engineering Universidad Nacional Autónoma de México [email protected] [email protected] CP8 CP7 Noether’s Theorem for Control Problems on Time Probabilistic Sensitivities for Fatigue Using Ad- Scales joint Methods We obtain a generalization of Noether’s theorem for the We present a new approach to develop methods and de- optimal control problems defined on time scales. This in- sign tools to determine the sensitivity of the probability cludes the discrete-time, the quantum, and the continu- of failure of mechanically and thermally loaded hot gas ous/clasical optimal control as particular cases. The gen- components under the variation of design parameters and eralization involves a one-parameter family of smooth maps production-related deviations. This approach applied the which depend also on the control and a Lagrangian which adjoint methods to reduce the computational cost by com- is invariant up to an addition of an exact delta differen- puting these sensitivities. tial. We apply our results to some concrete optimal control problems on an arbitrary time scale. Mohamed Saadi Universität Wuppertal Agnieszka B. Malinowska [email protected] Faculty of Computer Science Bialystok University of Technology [email protected] CP7 Discrete Active Disturbance Rejection Control for CP8 Environment-Assisted One-Photon Coherent CT13 Abstracts 135

Phase Control CP9 Periodic Control System Stabilization on Time A well established result, in the coherent-control-of-states Scales community, is that control over relative product cross sec- tions using one-photon excitation is not possible in the The stabilization of periodic control systems using time weak field regime. This result was stated under the as- scales is studied. Time scale is a model of time. The lan- sumption of unitary time evolution. Here we show that guage of time scales seems to be an ideal tool to unify when the environment and its initial correlations with the the continuous-time and the discrete-time theories. In this system are taken into account, then one-photon phase con- work we suggest an alternative way to solve stabilization trol is possible. We also discuss how this environment- problems. This method is based on a combination of the assisted process can be enhanced in the non-Markovian low Lyapunov functions method with local controllability con- temperature regime, specially for sub-Ohmic spectral den- ditions. In many situations this method admits a rigorous sities. mathematical justification and leads to effective numerical methods. Applications to mechanical problems are pro- Leonardo A. Pachon vided here. Department of Chemistry, University of Toronto, Canada Institute of Physics, University of Antioquia, Colombia Francisco Miranda [email protected] School of Technology and Management Polytechnic Institute of Viana do Castelo Paul Brumer [email protected] Department of Chemistry, University of Toronto, Canada [email protected] CP9 Necessary Conditions for Feedback Passivation of CP8 Nonaffine-in-Control Systems Quantum Noises Arising During the Quantum Im- plementation of an LTI System It is well understood that an open-loop Lyapunov stable nonaffine-in-control nonlinear system can be asymptoti- Not all synthesized controllers correspond to physically cally stabilized through feedback. But stabilizing an open- meaningful quantum systems; additional quantum noises loop unstable nonaffine system remains an open research can be necessary for physical realizability. Given a state question. Toward this end, necessary conditions required space system we give a result detailing the number of addi- to render a general open-loop unstable nonlinear system tional quantum noises required to implement it as a quan- passive through static feedback are derived in this paper tum system. We then give conditions including a numerical and it is shown that this is possible only if the system procedure for determining when it is possible to implement under consideration has relative degree one and is weakly a transfer function as a quantum system with only the min- minimum phase through an appropriate output definition. imal number of additional quantum noises. Unlike feedback passivation for affine-in-control nonlinear systems this result is not sufficient. The developments and Shanon L. Vuglar,IanPetersen the essential ideas of the paper are verified for a continu- University of New South Wales, ously stirred tank reactor. Australian Defence Force Academy [email protected], [email protected] Anshu Narang-Siddarth, John Valasek Department of Aerospace Engineering Texas A&M University CP9 [email protected], [email protected] Analyze of Synchronization Bifurcation Thank to Incremental Norm for a Class of Piecewise Smooth Systems CP9 On Almost Lyapunov Functions The synchronization phenomena occur in many domains: Life sciences, engineering sciences, In this talk, it is pro- We study asymptotic stability properties of nonlinear sys- posed to study the influence of small parameter variations tems in the presence of ”almost” Lyapunov functions which on the trajectories synchronization for a class of piecewise decrease along solutions in a given region not globally but smooth systems. First, the relied stability analysis is done rather on the complement of a set of small volume. Nothing with a well-known tools of incremental norm (see also con- specific about the structure of this set is assumed besides traction theory) and after the influence of infinitesimal per- an upper bound on its volume. We show that all solu- turbations on the initial conditions between to close trajec- tions starting in the region approach a ball whose volume tories is studied. For this, an abstract problem formulation depends on the volume of the set where the Lyapunov func- is done in order to apply Lyapunov-Schmidt method and tion does not decrease, as well as on other system parame- point out the bifurcation analysis. ters. The result is established by a perturbation argument which compares a given system trajectory with nearby tra- Jean-Pierre Barbot jectories that lie entirely in the set where the Lyapunov ECS-Lab, EA 3649 function is known to decrease. ENSEA [email protected] Charles Ying Department of Electrical and Computer Engineering Djamila Benmerzouk University of Illinois University of Tlemcen, Algeria [email protected] d [email protected] Daniel Liberzon University of Illinois at Urbana Champaign 136 CT13 Abstracts

Department of Electrical and Computer Engineering CP10 [email protected] Stochastic Model and Simulation Results of Inter- actions Between Human Subjects and Air Traffic Vadim Zharnitsky Control Simulator University of Illinois at Urbana Champaign Department of Mathematics Air Traffic Control Management requires constant atten- [email protected] tion and multi-tasking from human operators, which could invite human errors. In this setting, one wonders how such errors arise as operators interact with the machine to ex- CP10 ecute decisions. In this talk, a simple stochastic model A Noise Canceling Feedback Controller for the Na- including human reaction delays is discussed, and some tional Synchrotron Light Source II experimental results collected from a game simulator in which subjects interact with a touch screen monitor are The National Synchrotron Light Source II requires that presented. disturbances to the beam at frequencies up to 500 Hz be cancelled. A feedback controller with 240 inputs (sensors) Keivan Sadeghzadeh and 180 outputs (actuators) will do this. The controller Northeastern University uses singular value decomposition with Tikhonov regular- 360 Huntington Ave, Boston, MA 02115 ization to convert the complete system into 90 single-input [email protected] single-output systems with paired (fast but weak and slow but strong) actuators. A novel control scheme apportions Rifat Sipahi the feedback between the two actuators. Department of Mechanical and Industrial Engineering Northeastern University William S. Levine [email protected] University of Maryland, College Park [email protected] CP11 Kevin Davis A Parallel Implementation of Multiagent Coordi- Carnegie-Mellon University nation Optimization Algorithm [email protected] In this paper, a parallel Multiagent Coordination Opti- Yuke Tian, Li-Hua Yu mization (MCO) algorithm is presented by introducing Brookhaven National Laboratories some MATLAB built-in function into MCO. This new [email protected], [email protected] MCO algorithm embeds cooperative swarm behavior of multiple agents into the update formula by sharing velocity and position information between neighbors to improve CP10 its performance. Numerical evaluation of the parallel MCO Application of The Fuzzy Gain Scheduling IMC- algorithm is provided in the paper by running the proposed PID to The Power Plant algorithm on supercomputers, the optimal value and consuming time are compared with serial MCO and Particle AbstractIn this paper, the use of a Fuzzy Gain Schedul- Swarm Optimization (PSO) by solving several benchmark ing IMC-PID (FGS+IMC-PID) scheme has been presented functions in the literature, respectively. Based on the sim- based on fuzzy performance degree coefficient ? self- ulation results, the performance of the parallel MCO is not adjusting controller for the improvement of IMC-PID con- only superb compared with PSO for solving many nonlin- trol. It is shown that the IMC-PID controller with the ear, noncovex optimization problems, but also is of high Fuzzy PID parameters Gain Scheduler provides satisfac- efficiency by saving the computational time. tory closed-loop responses with less overshoot and shorter rising times in case of both set point disturbance and the Qing Hui, Haopeng Zhang plant/model mismatch. Simulations are given, in which the Department of Mechanical Engineering proposed method is compared to other PID tuning meth- Texas Tech University ods (IMC, SPMG). The proposed scheme is suitable to [email protected], [email protected] implement in the complex process control system in power generation, since it does not demand significant computing CP11 resources. It has already been implemented through Func- tion Code in many typical DCS (EDPU, XDPS, Ovation Numerical Algorithms for Nonlinear Optimum Ex- etc). Field application shows that the proposed is accu- perimental Design Problems rate enough. The industrial applications show that the We are interested in nonlinear optimum experimental de- scheme achieves better performance in specific load vari- sign problems for dynamical systems. They result from ation range. Keywords-IMC control, fuzzy self-adjusting, statistical analysis of the solution of parameter estimation fuzzy gain scheduling, boiler-turbine coordinated control problems and can be regarded as non-standard optimal XiaoFeng Li control problems in the sense that the objective depends on Electric Power Research Institute of first-order derivatives of the states and exhibits a nonlinear Guangdong Power Group Co. coupling in time. We present reformulations of the prob- [email protected] lem and algorithms for efficient numerical treatment with the direct method of optimal control as well as numerical examples. Weidong Zhang Shanghai Jiaotong University Dennis Janka [email protected] Heidelberg University [email protected] CT13 Abstracts 137

Stefan Koerkel University of Maryland, College Park IWR, University of Heidelberg, Germany [email protected] [email protected] John Baras Hans Georg Bock Univ. Maryland IWR, University of Heidelberg College Park [email protected] [email protected]

CP11 CP12 ADI Iteration Parameters for CARE Application Saturation-tolerant Average Consensus with Con- trollable Rates of Convergence Continuous low order Riccati equations (CARE) have been solved with Newton iteration involving ADI iterative solu- The paper presents a distributed average consensus al- tion of Lyapunov equations. The MATLAB EIGS program gorithm for multi-agent systems that enables individual enables efficient evaluation of selected eigenvalues needed agents to set their own rate of convergence. The algorithm for determining good ADI iteration parameters. Eigenval- has a two-time scale structure and is constructed using a ues clustered near the imaginary axis require special con- singular perturbation approach. We provide a complete sideration. A new method for computing effective ADI analysis of the proposed algorithm which includes rate of iteration parameters will be described. convergence of individual agents, effects of communication delays, robustness to changes in the network topology, im- Eugene L. Wachspress plementation in discrete time, and robustness to satura- Columbia University tion. [email protected] Solmaz S. Kia Postdoctoral Fellow at University of California San Diego CP11 [email protected] Cheap Optimization of Experimental Designs Jorge Cortes Our models of interest are algebraic and dynamical sys- Department of Mechanical and Aerospace Engineering tems (DAEs, PDEs) that contain nature-given parameters University of California, San Diego p of unknown value and control functions/variables u/q. [email protected] From measurements one infers the values of p. Due to errors in the measurements p is of uncertain nature. We discuss efficient techniques to minimize the uncertainty in Sonia Martinez p by optimizing over u/q and discuss algorithmic and con- University of California, San Diego ceptual challenges using the direct approach and automatic Department of Mechanical and Aerospace Engineering differentiation. [email protected] Sebastian F. Walter Heidelberg University CP12 Interdisciplinary Center for Scientific Computing Robustness and Performance Analysis of Cyclic In- [email protected] terconnected Dynamical Networks The class of cyclic interconnected dynamical networks CP12 plays a crucial role in modeling of certain biochemical reac- Fixed Point Theory Approach to Exponential Con- tion networks. In this paper, we consider cyclic dynamical vergence in LTV Continuous Time Consensus Dy- networks with loop topology and quantify bounds on var- namics with Delays ious performance measures. First, we consider robustness of autonomous cyclic dynamical networks with respect to Distributed computation and multi-agent dynamics has external stochastic disturbances. The H∈-norm of the sys- been over the past years one of the most active research tem is used as a robustness index to measure the expected areas in the control community. In this work, we revisit steady-state dispersion of the state of the entire network. the linear time varying consensus model in the presence In particular, we explicitly quantify how the robustness in- of bounded communication delays. We prove exponential dex depends on the properties of the underlying digraph convergence of the autonomous agents to a common value of a cyclic network. Next, we consider a class of cyclic under conditions related to the topology of the communi- dynamical networks with control inputs. Examples of such cation graph, the nature of the time-varying weights, and cyclic networks include a class of interconnected dynamical the dynamics of the undelayed system. We develop a Fixed networks with some specific autocatalytic structure, e.g., Point Argument on an especially designed functional met- glycolysis pathway. We characterize fundamental limits on ric space. We consider the initial value problem. the ideal performance of such cyclic networks by obtaining lower bounds on the minimum L2-gain disturbance atten- x˙ i(t)= aij (t)(xj(t − τ) − xi(t)),t≥ t0 (1) uation. We show that how emergence of such fundamental j limits result in essential tradeoffs between robustness and efficiency in cyclic networks. where xi(t)=φi(t)fort ∈ [t0 − τ,t0] is the given initial data and τ is the positive and bounded delay constant. We Milad Siami,NaderMotee also discuss the extensions to more asymmetrical versions Lehigh University with multiple delays. [email protected], [email protected] Christoforos Somarakis The Institute For Systems Research 138 CT13 Abstracts

CP12 ometrical considerations we obtain sufficient conditions of Pseudo-Rigid Formation Design for a Group of Un- the optimal control to have a bang-singular-bang form and manned Vehicles verify that they are in accordance with the results above. We also demonstrate results of numerical experiments for The concept of pseudo-rigid formation (PRF) along with different forms of the frictions function. proposed design methodology is presented to deal with the path-planning problem for a group of unmanned vehicles. Ivan Samylovskiy Comparing to the rigid formation, the PRF is allowed to Lomonosov Moscow State University, rotate, stretch, or shear globally, specified by a homoge- Faculty of Computational Mathematics and Cybernetics nous deformation tensor, and the configuration space is [email protected] then R3 × SO(3). The overall design is composed of two parts. Firstly, the Rapidly-exploring Random Tree method Andrei V. Dmitruk equipped with some path-smoothing algorithms is applied Central Economics & Mathematics Institute, to generate a proper path for the system center. The op- Russian Academy of Sciences timal deformation tensor is then found based on properly [email protected] selected virtual potentials. The idea of Lennard-Jones potential in molecular dynamics is adopted to obtain the potentials for intra-collision between vehicles. According to CP13 the results of design examples, the proposed approach can A Variational Method Via Optimal Control be effectively used in a variety of environments to generate goal-attaining and collision-free paths for all vehicles. While optimal control theory is largely recognized as an extension of the classical calculus of variations, in this talk Li-Sheng Wang we argue that it also provides new variational approaches Institute of Applied Mechanics to boundary value problems. This is called the control vari- National Taiwan University ational method and it is based mainly on the Pontryagin [email protected] maximum principle. In this presentation, we review the results established in the literature on the control variational Fang-Chieh Chen method and its applications, in the last decade (including Institute of Appliced Mechanics, recent developments). National Taiwan University [email protected] Dan I. Tiba Institute of Mathematics, Romanian Academy Bucharest, Romania CP13 [email protected] Necessary Conditions for Impulsive Optimal Con- trol Problems CP13 We study optimal control problems for systems that are On the Goh Second Order Conditions for Boundary governed by ordinary differential equations whose vector Controls fields depend nonlinearly on the control and state variables, but linearly on the time derivatives of some components of We present second order necessary optimality conditions for the Mayer optimal control problem when the control set the control. For a problem in the Mayer form and with m final state constraints, we prove a maximum principle and is a closed subset of R . In the absence of endpoint con- higher-order necessary conditions in terms of the adjoint straints, if an optimal control is singular, then, for almost state and some Lie brackets of the involved vector fields. every t, both the Goh and a generalized Legendre-Clebsch conditions hold true, eventually reducing to a subspace. In Soledad Aronna the presence of a smooth endpoint constraint, these con- University of Padova ditions are satisfied whenever the Mayer problem is calm. [email protected] Daniela Tonon, Helene Frankowska Franco Rampazzo IMJ UPMC Paris 6 Universita di Padova [email protected], [email protected] Dept di Math Pura e Applicata [email protected] CP14 CP13 Pulsed Feedback Defers Cellular Differentiation On a Singular Subarcs in Optimal Control Problem Many cells use internal timers to autonomously defer dif- for a Simple Trolley-Type Model with Nonlinear ferentiation for multiple cell cycles following a stimulus. Friction and Bounded Fuel Expenditure How can cells build robust timers using genetic circuits? Bacillus subtilis cells respond to sudden stress with multi- We consider a problem on maximization of the distance ple rounds of replication before differentiating into spores. traveled by a material point in the presence of a nonlin- We show experimentally that a core pulsed positive ge- ear friction and bounded thrust and fuel expenditure. Us- netic feedback loop controls this deferral. We further show ing the maximum principle we obtain the form of optimal mathematically that pulsed ’polyphasic’ positive feedback control and establish conditions under which it includes a may be especially robust, allowing cells to reliably set long singular interval. We obtain these conditions by two ways. deferral times. First, using the constructions of the maximum principle we obtain necessary and sufficient conditions of the optimal Joe Levine control to be of bang-bang form. Second, using the infor- California Institute of Technology mation about the form of optimal control and applying ge- [email protected] CT13 Abstracts 139

Michael Elowitz (Day et al., 2010 Math. Biosci. Eng. 7(4):739-763) Caltech [email protected] Gregory L. Zitelli University of Tennessee, Knoxville Department of Mathematics CP14 [email protected] Are High Dimensional Spinal Neural Circuits Con- ﬁgured to Facilitate Rapid Learning? Judy Day University of Tennessee We have modeled the major interneuronal circuits of the [email protected] spinal cord, via which the brain controls limb movements. Despite the large number of controllable dimensions (about 400), simple coordinate descent models of motor learning CP15 tend to converge on good-enough solutions rather than get- Numerical Solution of Stochastic Regulator Prob- ting stuck in poor local minima. It would appear that the lem with Nonlinear State Dynamics and Un- density of such good-enough solutions rises as this dimen- bounded Terminal Condition sionality increases. Does this useful property generalize to a particular class of hyperspaces? We consider nonlinear state dynamics and a quadratic terminal condition for a stochastic regulator problem. After Yao Li providing theoretical results for the existence/uniqueness USC of the corresponding HJB equation, we solve the problem [email protected] using a probabilistic approach through Markovian backward stochastic diﬀerential equations. We study the prop- Gerald E. Loeb erties of the solutions, in particular, discuss the perturbed Univ. of Southern California linear-quadratic regulator problems and provide some nu- [email protected] merical examples.

John Sunwoo, Tomaz Cerne Coskun Cetin Dept. of Biomedical Engineering California State University, Sacramento University of Sothern California [email protected] [email protected], [email protected] Jasmina Djordjevic University of Nis CP14 Serbia Real-Time Optimal Control of the Euglycemic [email protected] ClampinMice

The ”gold standard’ test for quantifying insulin resistance CP15 in diabetes research is known as the euglycemic hyperinsu- Stabilization of Galerkin Reduced Order Models linemic clamp. The protocol administers a variable glucose (roms) for Lti Systems Using Controllers infusion in order to maintain a target plasma glucose concentration, given uncertain models of glucose metabolism; Due to the computational cost of high-ﬁdelity models it is therefore a problem of real-time optimal control under (HFM), there is a growing interest in reduced order mod- uncertainty. We present a Bayesian framework that com- els (ROMs). Unfortunately, a ROM constructed using the bines sequential Monte Carlo methods for parameter infer- POD/Galerkin approach is not guaranteed to preserve the ence with model predictive control and sample-average ap- stability of the HFM. This talk will describe an approach proximation of the underlying optimization problem, and for stabilizing Galerkin ROMs for LTI systems using con- evaluate its performance with real data. trollers. The stabilizing controller is computed using the theory of pole placement. The proposed ROM stabilization Faidra Stavropoulou approach will be evaluated on several benchmark problems. Helmholtz Zentrum Muenchen [email protected] Irina Kalashnikova, Bart G. Van Bloemen Waanders, Srinivasan Arunajatesan Youssef M. Marzouk Sandia National Laboratories Massachusetts Institute of Technology [email protected], [email protected], [email protected] [email protected]

CP14 CP15 Controlling Systemic Inflammation Using Nonlin- High-Order Numerical Methods for Wave Equa- ear Model Predictive Control with State Estima- tions with Van Der Pol Type Boundary Conditions tion We develop high-order numerical methods for solving wave We investigate the capability of a particle filter to enhance equations with van der Pol type nonlinear boundary condi- the success of a nonlinear model predictive control (NMPC) tions. Based on the wave reflection on the boundaries, we algorithm to find appropriate therapeutic strategies for im- first solve the corresponding Riemann invariants by con- proving outcomes in a highly nonlinear ordinary differential structing two iterative mappings, and then, regarding the equations model of systemic inflammation. We compare regularity of boundary conditions, propose two different with the results of previous work where the implementa- high-order numerical approaches to the system. When the tion of NMPC involved finding optimized dosing regimens degree of regularity is high, we establish a sixth-order fi- for simulated patients, but with no robust state estimation. nite difference scheme. While for a low degree of regular- 140 CT13 Abstracts

ity, we provide another method by utilizing the high-order equations. This paper examines the use of observers for Gauss-Kronrod quadrature rule. Numerical experiments fault detection in systems modeled by diﬀerential algebraic are performed to illustrate the proposed approaches. equations.

Jun Liu Jason Scott Southern Illinois University North Carolina State University [email protected] Department of Mathematics [email protected] Yu Huang Zhongshan (Sun Yat-Sen) University Stephen L. Campbell [email protected] North Carolina State Univ Department of Mathematics Haiwei Sun [email protected] University of Macau [email protected] CP16 Mingqing Xiao Observer-Based Feedback Control of a Mathemat- Southern Illinois University at Carbondale ical Model of Intimal Hyperplasia [email protected] A theoretical model of a potential treatment for intimal hyperplasia due to hemodialysis is proposed. This model CP15 consists of two parts. The first part is modeling the development of intimal hyperplasia as a diffusion process of Solving the P-Laplacian Equation by Using Fi- muscle cells from the media to the lumen, for which the nite Elements Methods Leading to a Optimization governing equation is a partial differential equation. The Problem second part is designing an observer-based feedback con- A solution for the p-Laplacian equation using finite ele- troller to stabilize the equilibrium point of the system, cor- ments methods was introduced. It leads to an optimization responding to no intimal hyperplasia. Simulation results problem that can be solved by simplex method. Besides, show that the intimal hyperplasia can be reduced to near it was briefly discussed the solution of the non-Newtonian zero in approximately 57 days of treatment. filtration equation. Jiacheng Wu, Kevin W. Cassel Abdullah Topcu Illinois Institute of Technology Mathematics, Department of Fundemantal Courses, [email protected], [email protected] Noncommisioned Officer School, Cayirhisar, [email protected] CP17 Tropical Optimization Problems: Solution Meth- CP16 ods and Application Examples Functional Observers for Nonlinear Systems Multidimensional optimization problems in the tropical The construction of a functional observer is well-motivated mathematics setting are considered. The problems are to in many monitoring and control applications where full minimize (maximize) linear and nonlinear functionals de- state information is not needed, but instead it is a given fined on finite-dimensional semimodules over idempotent fuction of the states that needs to be estimated. The semifields, subject to constraints in the form of linear equa- present paper will develop a theoretical formulation of the tions and inequalities. We outline known problems and problem of designing functional observers for general non- discuss their solution methods. New unconstrained and linear systems, in a way that directly extends linear Lu- constrained optimization problems are then examined and enberger theory of functional observers. Notions of func- related exact solutions are given in a compact vector form. tional observer linearization will also be formulated, the As an application, we present solutions of real-world prob- objective being to achieve exactly linear error dynamics in lems in project scheduling and location analysis. transformed coordinates, and with prescribed rate of de- Nikolai Krivulin cay of the error. Necessary and sufficient conditions for St Petersburg State Univ the existence of a lower-order functional observer with lin- Dept of Math & Mechanics ear dynamics and linear output map will be derived. [email protected] Costas Kravaris University of Patras CP17 [email protected] On the Integer Max-Linear Programming Problem ⊕ ⊗ ∈ CP16 Let a b =max(a, b)anda b = a + b for a, b R = R ∪{−∞} and extend these operations to matrices and Observer Based Fault Detection in Differential Al- vectors as in conventional algebra. The integer max-linear gebraic Equations programming problem seeks to minimise or maximise f T ⊗ ⊗ ⊕ ⊗ ⊕ Fault detection is an important part of most modern indus- x subject to the two sided system A x c = B x d trial systems and processes. One approach to fault detec- for integer x. Pseudopolynomial methods for solving this tion is based on the use of observers. Many physical pro- problem are known. We give a generic case where we can cesses are most naturally modeled by differential algebraic describe all feasible integer solutions, the optimal objective equations. Recently there has been significant progress in value and an optimal solution in strongly polynomial time. the design of observers for complex differential algebraic CT13 Abstracts 141

Fran¸cois Dufour INRIA Bordeaux Sud Ouest, Bordeaux, France Marie Maccaig [email protected] University of Birmingham [email protected] CP18 Multiresolution Stochastic Optimal Control CP17 Equivalence Between Control Problems for Jump- We propose an algorithm for the solution of continuous- Diffusions and Their Linear Programming Formu- time Markov decision processes with multiple time scales. lation Using singular perturbation methods we identify a sequence of models that are both smaller and are better con- We prove that a class of control problems for jump-diffusion ditioned. The proposed multiresolution algorithm uses the processes have the same optimal value as a linear program- coarse model at each level of the hierarchy to compute a ming problem for occupation measures as well as its dual good initial approximation in the next level. We describe formulation. The dual problem is strongly connected to the the convergence and complexity of the new algorithm and notion of subsolution of the HJB equation associated with give numerical results. the original control problem by means of a maximum principle for semicontinuous functions applicable to integro- Chin Pang Ho partial differential equations. Imperial College London [email protected] Rafael Serrano PhD Student, University of York, UK [email protected] CP18 Optimal Control of Weakly Connected Markov Random Fields CP18 A Sufficient Condition for Stochastic Stability We consider a spatially distributed finite state Markov decision process evolving over time with a Gibbs random field The emergent behavior in natural/manmade systems can as its spatial structure. We suppose that the graph state often be characterized by analyzing the limiting distribu- space is partitioned into areas with internally strong but tion of the governing Markov chain. While resistance trees externally weak interactions. Modeling the weak interac- have gained popularity as a computationally efficient way tions with a small scalar parameter , we obtain a singu- to characterize the stochastically stable states (i.e., sup- larly perturbed model of the Markov decision process. We port of the limiting distribution), this technique requires a discuss the asymptotic properties of the perturbed model graph theoretic analysis over a large state space. In this as → 0. work, we derive sufficient conditions for stochastic stability which entails an analysis on a reduced state space. Sei Howe Imperial College London Holly P. Borowski, Jason Marden [email protected] University of Colorado, Boulder [email protected], [email protected] CP19 David Leslie Risk-Averse Control with Time-Delay Compensa- University of Bristol tion for Networked Stochastic Systems Subject to [email protected] Communication Channel Constraints

Eric Frew This talk concerns with the formulation of a class of net- University of Colorado, Boulder worked stochastic systems when the control loop is closed [email protected] around a communication network. Speciﬁcally, all the signals exchanged from the linear dynamical controllers and the linear stochastic time-variant plants are therefore sub- CP18 jected to unknown yet constant time delays and additive Conditions for the Existence of Constrained Opti- white-noise communication channels. The novel approach mal Policies for Discounted Markov Decision Pro- to the risk-averse control problem is obtained to select opti- cesses mal controllers for ordering uncertain prospects which are characterized by network induced time delays, communi- We consider a discrete-time Markov decision process with cation channel constraints, and chi-square random perfor- Borel state and action spaces. The criterion to be mini- mance measures. mized is a total expected discounted cost subject to constraints on some discounted costs. By analyzing compact- Khanh D. Pham ness issues on the space of strategic probability measures of The Air Force Research Laboratory the policies of the Markov decision process, we are able to Space Vehicles Directorate establish the existence of a constrained optimal stationary [email protected] policy, and we also prove the solvability of the corresponding linear programming problem. We prove such results CP19 under mild hypotheses on the control model. The Origin of Control of Complex Networks Tomas Prieto-Rumeau Statistics Dept, UNED The controllability of networks provides a new perspective [email protected] to analyze large-scale, interconnected dynamical systems. We develop a theoretical framework based on the structure 142 CT13 Abstracts

of the connective topology to determine the control profile Three Nonholonomic Robot System of the network. Our analysis permits us to highlight the differences in control configurations between different types We focus on the consensus control of a three mobile- of networks. The composition of the control profile reveals robot experimental system under communication delay, the functional origin of control, which characterizes the and demonstrate stable operation of consensus using a con- flow of information, or state, through the network. troller that is based on our recent results on network/graph structures, and Responsible Eigenvalue concept. Both the- Justin Ruths ory behind control design, and experimental results in good Singapore University of Technology & Design agreement with theoretical predictions are presented. [email protected] Wei Qiao Derek Ruths Northeastern University McGill University [email protected] [email protected] Rifat Sipahi Department of Mechanical and Industrial Engineering CP19 Northeastern University Toward a Theory of Multi-Resolution Games [email protected] Multi-resolution decision-making is an important feature to achieve scalable and efficient control and computations CP20 in complex systems. In this paper, we establish a multi- Applications of Reachable Sets to Driver Assis- resolution game-theoretic framework to model such deci- tance Systems sion processes in complex systems. The framework inter- connects games of different resolutions through transition Collision avoidance for driver assistance systems is an im- triggers and graphical models. The transition triggers are portant and active field of research in car industry. A nat- transition rules between games that are dependent on the ural approach to define safety areas is to provide three outcome of the current game, while the graphical model reachable sets related to several situations: a separation captures the underlying structure of resolutions in the sys- assurance situation, a collision avoidance situation and a tem. Based on Isaacs’ tenet of transitions, we develop a collision situation. Within this definitions reachable sets games-in-games principle and use it to introduce new equi- are computed for two scenarios with multiple initial states librium solution concepts for this novel class of games. We and several secure target constraints. Sensitivity analy- apply the new analytical tools to study adaptive defense in sis for the computed sets, with respect to perturbation of network security through proactive mechanisms of diver- initial data, is given. sity and randomization. Ilaria Xausa Quanyan Zhu,TamerBasar Volkswagen A.G. University of Illinois at Urbana-Champaign [email protected] [email protected], [email protected] Robert Baier Mathematical Institute, University of Bayreuth CP20 [email protected] Delay-Independent Stable Control Design for Lin- ear Time Invariant (LTI) Systems with Multiple Olivier Bokanowski Uncertain Delays; Theory and Experiments Université Paris-Diderot [email protected] In many systems, delays are inevitable and can also be uncertain. When controlling such systems, it may therefore be beneficial to design a controller that renders the closed- Matthias Gerdts loop system “delay independent stable’. In this talk, based Universitaet der Bundeswehr Muenchen on algebraic tools, we present a non-conservative frame- [email protected] workforthecontroldesignonLTIsystemswithmulti- ple uncertain delays, and application of this framework on CP21 a speed-regulation experiment in which uncertain delays arise in multiple communication/sensing channels. Fast Optimal Control of Asymmetric Flow Field Flow Fractionation Processes Payam M. Nia Northeastern University We present optimization problem for Asymmetric Flow [email protected] Field Flow Fractionation, which is a widely used technique for segregation of two or more particles of submi- cron scale, according to their hydrodynamic radius. More Rifat Sipahi specifically, we consider an optimal control problem for the Department of Mechanical and Industrial Engineering focusing-injection stage of an Asymmetric Flow Field Flow Northeastern University Fractionation process, in which the distribution of particles [email protected] suspended in a liquid needs to be controlled. We propose an objective functional for the concentration, based on the CP20 needs of our industrial partners. The state system is given by a convection-diffusion equation for the concentration, Multi-Agent Consensus Control with Communica- where the convective flow velocity is given by the solution tion Delay: Control Design and Application to a of the quasi-stationary Stokes system, controlled on the boundary. For an optimization problem we use the sensitivities due to the special structure of the objective func- CT13 Abstracts 143

tional for this specific application and memory constraints. standard techniques to derive optimality conditions cannot be employed. It can however be shown that the control-to- state operator associated to elastoplasticity is Bouligand Tigran Nagapetyan differentiable. Based on this result, we establish second- Fraunhofer ITWM order sufficient optimality conditions. [email protected] Thomas Betz,ChristianMeyer Rene Pinnau TU Dortmund Technische Universität Kaiserslautern Faculty of Mathematics Fachbereich Mathematik [email protected], [email protected] [email protected]

Nadir Bayramov CP22 RICAM [email protected] Groebner Basis Computation of Feedback Control for Time Optimal State Transfer

CP21 The synthesis of time-optimal feedback control of a single input, continuous time, linear time invariant system with Existence and Approximate Controllability of bounded inputs is considered. The target final state is not Stochastic Semilinear Reaction Diffusion Systems necessarily the origin of the state space. The switching surfaces corresponding to the bang-bang time-optimal control In this paper, we investigate the approximate controlla- − bility of an abstract model of stochastic semilinear reac- are first parameterized as functions of the (n 1) switching tion diffusion equation in Hilbert spaces. First, we prove instants. Then a Groebner basis based elimination algo- the existence and uniqueness of mild solutions by using rithm is used to semi-algebraically represent the switching contraction mapping principle and formulated conditions surfaces implicitly in terms of the state variables. These which guarantee the approximate controllability of the representations are used along with a nested switching logic main problem. Finally, the results are applied to semilin- to synthesize a time-optimal feedback control. As a natu- ear damped stochastic wave equation and stochastic partial ral extension, we also provide a semi-algebraic character- differential equations in modelling the structural damped ization of the set of all points reachable with constrained vibrations of a string or beam. inputs. Muthukumar Palanisamy Deepak Patil, Ameer Mulla, Debraj Chakraborty Gandhigram Rural Institute - Deemed University Department of Electrical Enginnering Dindigul, Tamilnadu, India & UTARI, UTA, TX, USA Indian Institute of Technology Bombay [email protected] [email protected], [email protected], [email protected] Rajivganthi C Gandhigram Rural Institute - Deemed University CP22 Dindigul, Tamilnadu, India. Lossless Convexification for a Class of Optimal [email protected] Control Problems with Linear State Constraints

This paper presents lossless convexification for a class of CP21 finite horizon optimal control problems with non-convex Exponential Stability for a One-Dimensional Ther- control constraints and linear state constraints. Many moviscoelastic System with Dirichlet Boundaries practical problems take this form. The control set is relaxed to a convex set. Verifiable sufficient conditions are In this paper, we study the stability of a one-dimensional stated under which optimal solutions of the relaxed prob- linear thermoviscoelastic equation with memory type for lem are also optimal solutions of the original problem, Dirichlet-Dirichlet boundary conditions. After a detail hence the term lossless convexification. A numerical ex- spectral analysis, we can show that there is a sequence ample is presented to illustrate the approach. of generalized eigenfunctions that forms a Riesz basis in the energy state space. Hence, the spectrum-determined Matthew W. Harris, Behcet Acikmese growth condition holds and the exponential stability of the The University of Texas at Austin system can then be determined. This is a joint work with m [email protected], [email protected] Jing Wang and Jun-Min Wang.

Siu Pang Yung CP22 Math. Dept., University of Hong Kong Subdifferential Analysis of Differential Inclusions [email protected] Via Discretization In differential inclusions, necessary optimality conditions CP22 identify potentially optimal paths, but do not show how to Second-Order Sufficient Conditions for Optimal perturb paths to optimality. We estimate the subdifferen- Control of Elastoplasticity tial dependence of the optimal value in terms of the endpoints of the feasible paths by estimating the coderivative An optimal control problem governed by an elliptic vari- of the discretized reachable map. The discretized (nons- ational inequality (VI) is considered. This VI models the mooth) Euler-Lagrange and transversality conditions fol- static problem of infinitesimal elastoplasticity with harden- low. Results for differential inclusions are inferred by pass- ing. It is well known that the control-to-state map associated to VIs is in general not Gateaux-differentiable. Thus 144 CT13 Abstracts

ing to the limit. ent hypothesis on the measure space, that of saturation, we demonstrate not only that these fundamental results C.H. Jeffrey Pang are valid in separable Banach spaces, but also that they Mathematics, National University of Singapore are equivalent to each other and their validity implies that [email protected] the underlying probability space must necessarily be saturated. We apply our main result to variational problems with integral constraints. A novelty here is to incorpo- CP23 rate infinite-dimensional constraints into the problem in a On Lie-Algebraic Reliable Stability Conditions for general manner. To this end, the standard relaxation tech- Multi-Channel Systems nique is employed. First, we prove that the existence of optimal solutions to the relaxed variational problem with- Recently, Agrachev et al (in the paper Agrachev, A.A., Baryshnikov, Y. & Liberzon, D. out any assumption on probability spaces. Next, we purify (2012), “On robust the optimal relaxed controls by applying the purification Lie-algebraic stability conditions for switched linear sys- principle in saturated probability spaces to derive the op- tems,” Syst. Contr. Lett., 61 (2), 347–353) have presented timal control functions for the original variational prob- a new sufficient condition for exponential stability of a lem. Finally, we present a result on relaxed controls with switched system under an arbitrary switching using the infinite-dimensional constraints that improves the density Lie-brackets from a family of systems that generates the result of the finite-dimensional setting. switched system. In this talk, we show that this condition may be formulated to characterize reliable stability con- Nobusumi Sagara ditions for a finite-dimensional generalized multi-channel Faculty of Economics, Hosei University system when some of the controllers (or subsystems) fail [email protected] to operate in the way that they were originally intended to function. In particular, we make use of the Levi-Malcev M. Ali Khan decomposition theorem of Lie-algebra and provide a reli- Department of Economics able stability condition for the multi-channel system when, Johns Hopkins University at an arbitrary time instant, one of the controllers ceases [email protected] to function due to a failure.

Getachew K. Befekadu, Vijay Gupta CP23 University of Notre Dame [email protected], [email protected] Stabilization of the Korteweg De Vries Equation The Korteweg de Vries (KdV) Equation is one of the most Panos Antsaklis important partial differential equations in applied mathe- Department of Electrical Engineering matics and, starting with shallow water waves in the 1800’s, University of Notre Dame is still finding applications in many areas of physics and [email protected] mathematics. Our recent work on long waves for swirling flow through a pipe has shed light on previously unknown properties of the solutions of initial–boundary value prob- CP23 lems for the KdV equation. This talk will report on some Uniform Almost Sure Asymptotic Stabilization of these results. Problems by Adding Multi-Dimensional Wiener Processes Steve Taylor University of Auckland, New Zealand This paper derives necessary conditions for the origin of [email protected] randomized systems to be uniformly asymptotically stable with probability one under randomization by multidimensional Wiener processes. First, we revisit random- CP24 ization problems of deterministic systems by adding multi- Accessing the Role of Communication Link and dimensional Wiener processes. Next, we summarize Bardi Node Robustness in Interconnected Systems Via and Cesaroni’s stochastic Lyapunov functions are almost Eigenvalue Sensitivity the same as Lyapunov functions for deterministic systems. Then, we derive the necessary conditions with remarkable Communication networks provide a larger flexibility for the discussions. control design of interconnected systems by allowing the information exchange between the local controllers and may Yuki Nishimura improve the performance of the overall system. However, Kagoshima University it is still not well understood how significant the role of a [email protected] communication link is for improving the performance and how the network structure influences the robustness of the system. We first show via numerical example that cer- CP23 tain communication links play important role in improving The Purification and Bang-Bang Principles in In- the systems performance. Next, using eigenvalue sensitiv- finite Dimensions: Additional Characterizations of ity analysis, we characterize those links for interconnected the Saturation Property systems consisting of scalar identical subsystems with ring and uniform extended star physical topologies. We fur- We present a synthetic treatment of several results of con- ther study the relation between network robustness and sequence in mathematical economics and the theory of op- the physical topology when one of the nodes is perturbed timal control and of statistical decision-making: the Lya- and observe that there exists a trade-off between design- punov theorem, the DWW theorem, the convexity of the ing an interconnected system with high robustness and low integral and distribution of a multifunction, the bang-bang principle and the purification principle. Under a coher- CT13 Abstracts 145

communication cost. UCSD [email protected] Azwirman Gusrialdi,ZhihuaQu University of Central Florida Miroslav Krstic [email protected], [email protected] University of California, San Diego Dept of Mechanical & Aerospace Engineering CP24 [email protected] The Method of Moments for Optimal Switching Topology Networks MS1 In this work, it is presented a semidefinite relaxation to Stabilizability of Piezoelectric Beams with Mag- solve the optimal control problem of switching topology netic Effects networks based on the method of moments. This method is A PDE model for a controlled piezoelectric beam that in- the transformation of a non-convex optimal control prob- cludes magnetic effects is studied, with current and also lem into an equivalence problem with linear and convex voltage control. Both models are shown to be well-posed. structure. An equivalence convex formulation more appro- Next, we investigate stabilizability. A current controlled priated to be solved by high-performance numerical com- beam, is shown to be strongly stabilizable by a single elec- puting tools. Finally, a numerical example is presented to trical feedback controller. In the case of voltage controlled illustrate the effectiveness of the proposed approach. beam we obtain exponential stabilizability with a single Eduardo Mojica-Nava, Jimmy Salgado, Duvan Tellez electrical feedback controller, provided that the parame- Universidad Católica de Colombia ters satisfy certain conditions. This is different from the [email protected], [email protected], usual model that neglects magnetic effects. [email protected] Ahmet Ozkan Ozer Iowa State University, Department of Mathematics CP24 Ames, Iowa, 50011 [email protected] On Multi-Input Controllable Linear Systems Un- der Unknown Periodic DoS Jamming Attacks Kirsten Morris In this paper, we study remotely controlled and observed Dept. of Applied Mathematics multi-input controllable continuous linear systems, subject University of Waterloo to periodic Denial-of-Service (DoS) jamming attacks. We [email protected] first design a control and triggering strategy provenly capable of beating any partially known jammer via properly placing the closed-loop poles. Building on it, we then MS1 present an algorithm that is able to guarantee the system A Control Theoretic Approach to Low Reynolds stability under unknown jamming attacks of this class. The Number Swimming functionality of this algorithm is also theoretically proven. We consider a couplked ODE’s–PDE’s system modeling a class of low Reynolds number swimmers (which can be seen Hamed Shisheh Foroush as simplified models of cilliated microorganisms). Within MAE this model, the form of the swimmer does not change, UCSD the propelling mechanism consisting in tangential displace- [email protected] ments of the material points of swimmer’s boundary. The main theoretical results assert the exact controllability of Sonia Martinez the swimmer for prolate spheroidal shapes. In the same University of California, San Diego case, we provide theoretical bounds of the efficiency and Department of Mechanical and Aerospace Engineering we perform numerical simulations. [email protected] Marius Tucsnak University of Lorraine MS1 [email protected] Stabilization of Wave PDE/nonlinear ODE Cas- cades Jorge San Martin University of Chile The problem of compensation of input delays in nonlinear [email protected] systems was recently solved using predictor feedback. Yet, the problem of compensation of more complex input dy- Takeo Takahshi namics in nonlinear systems has remained, heretofore, un- INRIA Nancy Grand Est tackled. In this paper we consider nonlinear systems with [email protected] a wave partial differential equation (PDE) in the actuation path, and we design an explicit feedback law that compen- sates the wave actuator dynamics. We study stability of MS1 the closed-loop system with the aid of a Lyapunov func- Finite Dimensional Attractors in Flow-Structure tional that we construct by introducing two novel infinite- Interactions dimensional backstepping transformations of the actuator state. We also present a numerical example that illustrates We consider a von Karman plate with a delayed feed- the effectiveness of the proposed control design. back force. Due to physical considerations we study the model without inertial terms, producing a loss of compact- Nikolaos Bekiaris-Liberis ness - critical for studying attractors. We show asymptotic 146 CT13 Abstracts

smoothness and quasi-stability the associated dynamical such unbounded discontinuous differential inclusions. This system; this approach is novel in this context. We apply is done by developing the method of discrete approxima- our result to a flow-plate interaction and demonstrate the tions and employing appropriate tools of second-order vari- existence of a finite-dimensional, compact attractor for the ational analysis and generalized differentiation. plate dynamics. This is done by utilizing hidden dissipation from the flow. Boris Mordukhovich Department of Mathematics, Irena M. Lasiecka Wayne State University University of Virginia [email protected] [email protected]

Justin Webster MS2 Department of Mathematics, Oregon State University Properties of Control Systems with Mixed Con- [email protected] straints We report on relevant properties of some control systems MS2 with mixed constraints. The main question we address is Convergence Analysis for Discretized Control- whether state trajectories for control systems paired with State Constrained Optimal Control Problems with mixed constraints (in the form of equalities and inequalities Controls of Bounded Variation and even more general) are precisely the feasible solutions of a differential inclusions. This is of relevance since it We study convergence properties of discretized optimal allows the application of well known results for differen- control problems with ordinary differential equations and tial inclusion like compactness of trajectories, relaxation, mixed control-state constraints. Under suitable consis- generalized Filippov selections and existence of solution. tency and stability assumptions a convergence rate of order Although some if not all of our results seem to be known 1/p of the discretized control to the continuous control is we present and prove them here in a concise and clear way established in the Lp-norm. Throughout it is assumed that that may be helpful in different set-ups. the optimal control is of bounded variation. The convergence proof exploits the reformulation of first order neces- Maria do Rosari de Pinho sary optimality conditions as nonsmooth equations. Departamento de Engenharia Eletrotecnica de Computadores Matthias Gerdts Universidade do Porto Universitaet der Bundeswehr Muenchen [email protected] [email protected] MS3 Martin Kunkel Elektrobit Automotive GmbH Approximating Non-Stationary Hamiltonians for Am Wolfsmantel 46, 91058 Erlangen, Germany Minimum-Time Problems in Dynamic Environ- [email protected] ments An algorithm for solving a class of non-stationary MS2 Hamilton-Jacobi (HJ) equations is described, which can be broken into piecewise-stationary Hamiltonians. Tak- A-priori Monotonicity Properties of Minimizers ing advantage of the inherent causality of the problem, and Applications to existence Results for Non- an improved version of the algorithm using is shown to coercive Variational Problems dramatically reduce the computation time. Examples of In this talk an a-priori monotonicity property of minimizers time-optimal path planning problems with dynamic envi- of one-dimensional variational problems is discussed. Such ronments are shown. a property allows to obtain a refined version of the classi- Jason Durrie, Eric Frew cal DuBois-Reymond necessary conditions, with a limita- University of Colorado, Boulder tion on the constant appearing in the condition, besides to [email protected], [email protected] some existence and non-existence results of the minimum for non-convex, non-coercive variational problems. MS3 Cristina Marcelli Università Politecnica delle Marche Can Single-Pass Methods Solve Every Hamilton- [email protected] Jacobi Equation? The use of single-pass methods (like, e.g., the Fast March- MS2 ing method) has become popular in the solution of some nonlinear hyperbolic PDEs. The prototype of these equa- Optimal Control of the Sweeping Process Gener- tions is the eikonal equation, where the methods can be ated by Moving Convex Polyhedra applied saving CPU time and possibly memory allocation. This talk is based on the joint work in progress with Rene Naturally one would like to extend this approach to other Henrion (Weierstrass Institute at Berlin, Germany) and Hamilton-Jacobi equations. Is it possible? If not, where Nguyen Dinh Hoang (Tan Tao University, Vietnam). We the limit should be set? In this talk we try to answer those study a new class of optimal control problems of the sweep- questions analyzing several test cases. ing (Moreau) process governed by differential inclusions de- Simone Cacace scribed by the normal cone mapping to moving polyhedral Dipartimento di Matematica convex sets in finite-dimensional spaces. The main atten- UniversitàdiRoma tion is paid to deriving necessary optimality conditions for [email protected] CT13 Abstracts 147

Emiliano Cristiani MS4 Istituto per le Applicazioni del Calcolo ”M. Picone” Control of Discrete-Time Nonlinear Systems with Consiglio Nazionale delle Ricerche Long Non-Increasing Time-Varying Delays on the [email protected] Input

Maurizio Falcone We consider general discrete-time nonlinear systems with Università di Roma “La Sapienza’, Italy long non-increasing time-varying input delays, and design [email protected] a nonlinear predictor feedback controller to compensate the input delays. The input delay is modeled by a first- order partial difference equation (PdE) and a discrete-time MS3 backstepping transformation is employed to construct a Causality as a Source of Efficiency Lyapunov function. Based on the Lyapunov function, the global asymptotic stability is achieved even for the high- In this talk we will discuss the connections between growth nonlinear systems. This approach is also applied label-setting/correcting methods on graphs and a variety to linear time-invariant (LTI) systems and the global ex- of non-iterative numerical methods for static Hamilton- ponential stability is achieved in the presence of long non- Jacobi-Bellman PDEs arising in optimal control prob- increasing time-varying input delays,. Our design approach lems. We will discuss the accuracy/efficiency implica- is illustrated by a numerical example for a nonlinear plant tions of anisotropy as well as the challenges associated with high-growth nonlinearity. with the lack of small-time-controllability. We will also compare the types of causal structure present in finite- Miroslav Krstic horizon, infinite-horizon, exit-time, optimal-stopping, and University of California, San Diego stochastic-switching problems. Dept of Mechanical & Aerospace Engineering [email protected] Alexander Vladimirsky Dept. of Mathematics Joon-Young Choi Cornell University Pusan University [email protected] [email protected]

MS3 MS4 Eﬃcient Methods for Finite-Horizon Optimal Con- Asymptotic Stabilization for Feedforward Systems trol with Delayed Feedbacks

Time-dependent Hamilton-Jacobi PDEs naturally arise in We solve a state feedback stabilization problem for a large many applications including fixed-horizon optimal control class of time-varying feedforward systems with a pointwise problems. Numerical methods for these equations are typ- input delay. We use a time-varying change of coordinates ically based on using an explicit time discretization, re- and Lyapunov-Krasovskii functionals. The result applies sulting in fairly restrictive CFL stability condition on the for any constant delay, and provides controllers of arbi- allowable time-steps. The conventional wisdom states that trarily small amplitude and input-to-state stability under time-implicit methods for non-linear evolutive PDEs are actuator errors. We illustrate our work in a tracking prob- not a viable alternative for two reasons: (a) their lower lem for a model for high level formation flight of unmanned accuracy and (b) their higher computational cost. In this air vehicles. talk we will use linear advection equations and non-linear time-dependent Eikonal PDEs to investigate whether the Michael Malisoff above arguments are universally valid. Louisiana State University Department of Mathematics Changxi Zheng malisoff@lsu.edu Columbia University [email protected] Frederic Mazenc INRIA MS4 [email protected] On Participation Factors for Nonlinear Systems MS4 In this talk, we combine between recent definitions given by Prof. Abed for participation factors of linear systems Control of Fluid Flows in Channels and Poincare normal forms to propose new definitions for We investigate the finite-time boundary stabilization of a participation factors for nonlinear systems. 1-D first order quasilinear hyperbolic system of diagonal Eyad Abed form on [0,1]. The dynamics of both boundary controls Dept. of Electrical and Computer Engineering are governed by a finite-time stable ODE. The solutions University of Maryland, College Park of the closed-loop system issuing from small initial data in [email protected] Lip([0,1]) are shown to exist for all times and to reach the null equilibrium state in finite time. A finite-time stabilization is also shown to occur when using only one boundary Boumediene Hamzi control. The above strategy is then applied to the Saint- Imperial College Venant system for the regulation of water flows in a canal Department of Mathematics with one or two boundary controls. [email protected] Lionel Rosier Universite de Lorraine 148 CT13 Abstracts

[email protected] Zhaodan Kong Intelligent Mechatronics Lab Vincent Perrollaz Boston University Universite de Tours, France [email protected] [email protected] MS5 MS5 Controlled Lagrangians and Stabilization of Dis- Optimal Control of Discrete Systems crete Spacecraft with Rotor

In this talk we discuss a geometric approach to the analysis The method of controlled Lagrangians for discrete mechan- of discrete optimal control problems. We show how various ical systems is extended to the problem of stabilization mechanical problems can be formulated naturally in this of the rotations of a spacecraft with a symmetric rotor setting and we show how the approach leads to integrators about its intermediate inertia axis. The Moser–Veselov dis- for optimal control problems and mechanical systems in cretization is used to obtain the discrete dynamics of the Lie groups and homogeneous spaces. system. Stabilization conditions for the continuous model and its discretization are compared. It is shown that sta- Anthony M. Bloch bility of the discrete system is sufficient for stability of its University of Michigan continuous counterpart. Department of Mathematics [email protected] Dmitry Zenkov North Carolina State University Peter Crouch, Nikolaj Nordkvist Department of Mathematics University of Hawaii [email protected] [email protected], [email protected] Yuanyuan Peng Department of Mathematics MS5 Claflin University Distributed Line Search Algorithms for Multi- ypeng@claflin.edu Agent Systems Syrena Huynh This paper considers multi-agent systems seeking to op- North Carolina State University timize an aggregate objective function. We assume the Department of Mechanical Engineering gradient of this function is distributed, meaning that each [email protected] agent can compute its corresponding partial derivative with state information about its neighbors and itself. In such Anthony M. Bloch scenarios, the discrete-time implementation of gradient de- University of Michigan scent poses the fundamental challenge of determining ap- Department of Mathematics propriate agent stepsizes that guarantee the monotonic [email protected] evolution of the objective function. We provide distributed anytime algorithmic solutions for this problem. MS6 Jorge Cortes Department of Mechanical and Aerospace Engineering Efficiency and Risk Tradeoffs in the Smart Grid University of California, San Diego Real-time demand response has been postulated as the so- [email protected] lution to the intermittency problem created by renewable generation. The proposed market architecture is simple, Sonia Martinez namely, consumers react directly to spot market prices in University of California, San Diego order to fulfill their demands. This mechanism creates a Department of Mechanical and Aerospace Engineering closed loop system between price and demand that has im- [email protected] plications on efficiency, demand and price volatility, and risk of demand spikes. In this talk, we first present an analysis of this closed loop system for homogeneous con- MS5 sumers and highlight the tradeoffs between market effi- The Standard Parts Problem and Quantization in ciency and demand and price volatility. We demonstrate Optimal Control Problems that this analysis is consistent with the volatility of current spot market prices, suggesting the presence of inter- Mobile robotic vehicles are increasingly well endowed with nal trading and hedging in the market. Then, we present high performance sensing capabilities. This motivates re- an abstracted framework to analyze the tradeoffs between search into whether high performance biomimetic motion efficiency and risk for heterogeneous consumers when de- control can be achieved. Using a large archive of flight mands are shiftable. In this context, we expand the market data from field observations of bats, research has been con- mechanism to study the impact of coordination on such a ducted to design motion control feedback laws that use a tradeoff. For decisions based on real-time prices, we com- variety of sensing modalities to approximately interpolate pare the statistics of the aggregate electricity demand pro- stored animal trajectories. cess induced by non-cooperative and cooperative load shift- John B. Baillieul ing schemes. We show that although the non-cooperative Boston University load-shifting scheme leads to an efficiency loss (otherwise Dept of Aero/Mech Engineering known as the price of anarchy), the scheme has a smaller [email protected] tail probability of the aggregate unshiftable demand distribution. This tail distribution is important as it corresponds CT13 Abstracts 149

to rare and undesirable demand spikes. In contrast, the Simone Paoletti cooperative scheme achieves higher efficiency at the cost Università di Siena, Via Roma 56 of a higher probability of demand spikes. Such instances 53100 Siena (Italy) highlight the role of the market mechanisms in striking a [email protected] balance between efficiency and risk in real-time markets.

Munther Dahleh MS7 MIT Zero-Sum Game Between a Controller and a Dis- [email protected] cretionary Stopper We consider a stochastic differential equation that is con- MS6 trolled by means of an additive finite-variation process. Opportunities and Challenges in Smart Grid Con- A singular stochastic controller, who is a minimiser, de- trols termines this finite-variation process while a discretionary stopper, who is a maximiser, chooses a stopping time at Smart electric grid is a vision of the future where the elec- which the game terminates. We consider two closely re- tric power network is integrated with a communications, lated games that are differentiated by whether the con- computation, and control system to achieve certain objec- troller or the stopper has a first-move advantage. The tives: customer participation, integration of all generation games’ performance indices involve a running payoff as well and storage options, new markets and operations, power as a terminal payoff and penalize control effort expendi- quality, asset optimization and efficiency, self healing, and ture. We derive a set of variational inequalities that can resiliency. In this talk, we will present a few key challenges fully characterize the games’ value functions as well as yield from a controls perspective whose solution will contribute Markovian optimal strategies. In particular, we derive the to the achievement of this vision. explicit solutions to two special cases and we show that, in general, the games’ value functions fail to be C1. The non- Pramod Khargonekar uniqueness of the optimal strategy is an interesting feature ECE Dept. of the game in which the controller has the first-move ad- Univ. of Florida vantage. This is a joint work with Robert S. Simon and [email protected]fl.edu Mihail Zervos.

Daniel Hernandez-Hernandez MS6 Centro de Investigacion en Matematicas, Guanajuato, Challenges in Electricity Smart Grids of the Future Mexico [email protected] Risk-limiting dispatch is formulated as the optimal solution to a multi-stage, stochastic decision problem. The operator purchases forward energy and reserve capacity over MS7 a block of time, based on the available information, in- Optimal Ergodic Control with Minimum Variance cluding demand and renewable power. The accumulated energy blocks must at each t match the net demand. The This work concerns controlled Markov processes with either expected cost is the sum of the costs of the energy and continuous or discrete time parameter. We give conditions reserve capacity and the risk from mismatch between net for the existence of control policies that maximize the long- demand and supply. run average reward and which, in addition, minimize the limiting average variance. To this end, a key intermediate Pravin Varaiya step is to show that this variance is a constant indepen- Electrical Engineering & Computer Science Dept. dent of the initial state. Our results have applications in University of California, Berkeley, CA 94720 ergodic control problems,and also in adaptive control prob- [email protected] lems which depend on unknown parameters. Onesimo Hernandez-Lerma, Hector Jasso-Fuentes MS6 CINVESTAV-IPN Integration of Active Demand in Electricity Distri- [email protected], [email protected] bution Grids

The key idea behind the concept of Active Demand is that MS7 end users play an active role in the electricity grid, adjust- Pathwise Convergence Rates for Numerical Solu- ing their consumption patterns to mitigate the effects of tions of Markovian Switching Stochastic Differen- the introduction of renewables and energy dynamic pric- tial Equations ing policies. Participation in AD schemes generally takes place through aggregation of consumers represented by a We develop numerical approximation algorithms for solu- new subject, the aggregator, whose main objective is to tions of SDEs with Markovian switching. The existing nu- value the load profile flexibility of individuals. The objec- merical algorithms all use a discrete-time Markov chain for tive of this talk is to outline the main problems related to the approximation of the continuous-time Markov chain. this scenario, where new players operate in the energy mar- In contrast, we generate the continuous-time Markov chain ket and in the grid, consumers show a dynamic behavior, directly, and then use its skeleton process in the approxima- the transmission and distribution operators face new hard tion algorithm. Focusing on weak approximation, we take tasks with new opportunities to ensure safe operation of a re-embedding approach, and define the approximation the grid. and the solution to the switching SDE on the same space. In our approximation, we use a sequence of i.i.d. random Antonio Vicino variables in lieu of Brownian increments. By virtue of the UniversitàdiSiena strong invariance principle, we ascertain rates of conver- [email protected] 150 CT13 Abstracts

gence in the pathwise sense for the weak approximation INRA scheme. [email protected]

Son L. Nguyen University of Puerto Rico - Rio Piedras MS8 [email protected] Stabilization of the Chemostat with Delayed Sam- pled Measurements George Yin Wayne State University The classical model of the chemostat with one substrate, Department of Mathematics one species and a Haldane type growth rate function is [email protected] considered. The input substrate concentration is supposed to be constant and the dilution rate is considered as the control. The problem of globally asymptotically stabi- MS7 lizing a positive equilibrium point of this system in the Some New Perspectives About Certain Singular case where the measured concentrations are delayed and Control Problems piecewise constant with a piecewise constant control is addressed. The result relies on the introduction of a dynamic This work investigates a singular stochastic control prob- extension of a new type. lem for a multi-dimensional regime-switching diffusion process confined in an unbounded domain. The objective is Jerome Harmand to maximize the total expected discounted rewards from INRA exerting the singular control. Such a formulation stems [email protected] from application areas such as optimal harvesting multiple species and optimal dividends payments schemes in ran- Frederic Mazenc dom environments. With the aid of weak dynamic pro- INRIA gramming principle, we characterize the value function to [email protected] be the unique constrained viscosity solution of a certain system of coupled nonlinear quasi-variational inequalities. Several examples are analyzed in details to demonstrate MS8 the main results. Interval Observers with Delays for Biological Re- actors Qingshuo Song City University of Hong Kong We propose constructions of interval observers for families [email protected] of systems with a point-wise delay. First, we develop a new type of interval observer for a general class of systems Chao Zhu which present distributed delay terms. Second, we take University of Wisconsin-Milwaukee advantage of this design to design an exponentially stable [email protected] interval observer for a nonlinear biotechnological model. Frederic Mazenc MS8 INRIA Introduction to Biological Reactor Models with a [email protected] View on Differential Flatness Properties Silviu-Iulian Niculescu Various simple models of biological reactors are reviewed, Laboratoire des signaux et systèmes (L2S), UMR CNRS with biomass, substrate and product concentrations, with 8506 an emphasis on their differential flatness properties. We in Supélec 3 rue Joliot-Curie 91192 Gif-sur-Yvette cedex particular establish that quotients of biomasses over sub- FRANCE strate appear to be flat outputs for the investigated mod- [email protected] els, independently of the growth rate function model. This property yields a differential parametrization of the system in terms of the flat output. MS8 Chemostat Stabilisation Through Delayed Buffer- Denis Dochain ing CESAME, Universite Catholique de Louvain, Belgium [email protected] Global stabilization of the chemostat model under non- monotonic growth rate has received great attention from Béatrice Laroche the control community that have provided different feed- L2S, Paris-Sud-11 university back strategies. Recently, it has been shown that a struc- France ture of buffered chemostat can exhibit a global stability [email protected] without control. Analogously, we investigate the benefit of a delay in the input flow rate for enlarging the attraction Hugues Mounier basin of the stable positive equilibrium. Laboratoire des signaux et systèmes (L2S), UMR CNRS Alain Rapaport 8506 INRA Supélec 3 rue Joliot-Curie 91192 Gif-sur-Yvette cedex [email protected] FRANCE [email protected] MS9 Alain Rapaport Reduced-Order Modeling and Control of Aquatic CT13 Abstracts 151

Vehicles Exploiting Biomimetic Vortex Shedding lays for Three-Dimensional Curve Tracking

Marine animals often exploit high-dimensional hydrody- We analyze the robustness of a class of controllers that en- namics associated with vortex shedding and wake-body able three-dimensional curve tracking of free moving parti- interactions for self-propulsion and maneuvering. Biologi- cles. Using Lyapunov-Krasovskii functionals and robustly cally inspired aquatic vehicles are often intended to harness forwardly invariant sets, we prove input-to-state stability similar phenomena using relatively low-dimensional actua- under predictable tolerance and safety bounds that guar- tion. This talk will address the realization of reduced-order antee robustness under control uncertainty, input delays, models for localized vortex shedding and wake dynamics and polygonal state constraints, and adaptive tracking and and the nonlinear control of underactuated aquatic vehicles identification of unknown control gains. This can provide that vary their surface geometries or inertial properties for certified performance when the results are applied to ma- locomotion. rine robotic controllers. Scott D. Kelly Fumin Zhang Mechanical Engineering and Engineering Science School of Electrical and Computer Engineering University of North Carolina at Charlotte Georgia Institute of Technology scott@kellyfish.net [email protected]

Michael Malisoff MS9 Louisiana State University Distributed Estimation of Ocean Internal Waves Department of Mathematics Via Relative Sensing malisoff@lsu.edu We present strategies for estimating the time varying flow field generated by an ocean internal wave, by determin- MS10 ing the physical wave parameters which define the flow’s Control of Pde Systems with Delayed Actuators dynamics. The algorithm runs on a group of Lagrangian drifters which receive local, relative inter-drogue distance In this paper we discuss a boundary control problem for measurements. Our technical analysis establishes correct- parabolic partial differential equations where the control ness guarantees under noiseless measurements, character- input is the output to a dynamic actuator modeled by a izes the parameter robustness with respect to noisy mea- delay differential equation. The combined system leads to surements, and identifies a strategy for fusing parameter an infinite dimensional retarded delay differential equation. estimates. We discuss well-posedness issues and develop approximations for addressing the LQR control problem. Applica- Michael Ouimet tions to control of energy efficient systems are presented Mechanical and Aerospace Engineering and examples are given to illustrate the method. [email protected] John A. Burns Jorge Cortes Virginia Tech Department of Mechanical and Aerospace Engineering Interdisciplinary Center for Applied Mathematics University of California, San Diego [email protected] [email protected] Terry L. Herdman, Lizette Zietsman Interdisciplinary Center for Applied Mathematics MS9 Virginia Tech Gliding Robotic Fish: A Highly Maneuverable and [email protected], lzietsma@vt. edu Energy-Efficient Platform for Aquatic Sensing

We present a novel type of underwater robots, gliding MS10 robotic fish, which represent a hybrid of robotic fish and Synchronizing Controllers for Second Order Dis- underwater gliders. A gliding robotic fish is capable of tributed Parameter Systems fin-actuated swimming and buoyancy-driven gliding, and is thus highly maneuverable and energy-efficient, showing We consider the synchronization control of second order great promise in long-duration monitoring of aquatic envi- infinite dimensional systems. The objective is to design ronments. Its maneuvering in 3D space presents intriguing controllers that guarantee agreement between the position and challenging questions in dynamic modeling and con- and velocity states of N identical second order systems. To trol, which are discussed in this talk. enforce synchronization, the controller structure involves coupling terms consisting of the pairwise difference of both Feitian Zhang position and velocity states. Possible improvements of the Smart Microsystems Laboratory agreement amongst the states of each of the systems are Michigan State University considered and compared to the case of noninteracting con- [email protected] trollers. Extensions to synchronizing controllers for the case of partial connectivity are discussed. Extensive nu- Xiaobo Tan merical studies are included to provide a further insight on Michigan State University the effects of synchronizing control of second order infinite [email protected] dimensional systems. Fariba Fahroo MS9 Air Force Office of Scientific Research Robustness of Adaptive Control under Time De- [email protected] 152 CT13 Abstracts

Michael A. Demetriou techniques allow to overcome the deep regularity issues in- Worcester Polytechnic Institute herent to these systems. [email protected] Thomas Chambrion Institut de Mathématiques Elie Cartan MS10 Nancy Université Balanced POD Model Reduction Algorithms for [email protected] Parabolic PDE Systems with Unbounded Input and Output Operators MS11 Balanced POD is a data-based model reduction algorithm Stabilization of Nonlinear Systems Modeled by that has been widely used for linearized fluid flows and Partial Differential Equations: Some Tools and other linear parabolic PDE systems with inputs and out- Some Open Problems puts. We consider balanced POD algorithms for such systems when the input and output operators are unbounded, In this talk we survey some tools to stabilize nonlinear sys- as can occur when control actuators and sensors are lo- tems modeled by partial differential equations. Various ex- cated on the boundary of the physical domain. We discuss amples will be presented. They include Euler equations of computational challenges, modified algorithms, and con- incompressible fluids, Korteweg de Vries equations, shallow vergence theory. water equations, beam equations, porous media equations. However, as we will show, there are many open problems, John Singler especially for rapid stabilization. Missouri S & T Mathematics and Statistics Jean-Michel Coron [email protected] Université Pierre et Marie Curie, France [email protected] Weiwei Hu University of Southern California MS11 [email protected] Sparse Control of Social Dynamics for Large Groups MS10 Social dynamics of large group of autonomous agents An Optimal Design Problem Involving Helmholtz is of interest to various applications, such as animal Equation in Multi-Layered Materials groups, crowd dynamics, markets etc. An important The photovoltaic devices based on layers of thin-film of self-organization phenomenon is convergence to consensus, organic semiconducting materials offer a potentially low- which can emerge naturally or achieved by controls. We cost and versatile alternative to the conventional silicon present results using controls which are sparse in the num- solar panels. Efforts are made in the optimized device de- ber of controlled agents and switchings in time. sign based on mathematical models of the propagation of Benedetto Piccoli incident solar radiation and the resulting generation and Rutgers University diffusion of exciton through the heterojunction cell. Basic [email protected] questions of potential performance gain achievable by optimizing the thickness of the semiconducting organic layers and optical lens capping the device are investigated. The MS11 computation based global optimization convincingly indi- Control of Multi-scale Models for Crowd Interac- cates that the highest achievable device performance can- tion not be modified solely by the lens design. Validation of mathematical models and the computational optimization We first present the multi-scale version for the Cucker- experiments are also presented. Smale model, that describes the interaction of crowds and large groups. We discuss the interest and difficulties of con- Chunming Wang trol of this system, focusing in particular to the problem Department of Mathematics of driving the crowd to consensus. We then present results University of Southern California of controllability to consensus: we show that techniques of [email protected] sparse controllability for a finite number of agents can be adapted to the multi-scale model. Rongjie Lai University of Southern California Francesco Rossi [email protected] LSIS, Aix-Marseille Université [email protected]

MS11 Regularity Issues for the Control of the Bilinear MS12 Schrödinger Equation Equivalent Convexification in Optimal Control The dynamics of a closed quantum system submitted to An approach to convexifying non-convex optimal control an external field can be modelled, in a first approximation, problems with integral objective functionals is discussed. A by a bilinear Schrödinger equation. Many difficulties arise basis is a probabilistic relaxation of the system we extend from this modelling that involves both unbounded opera- the systems states to probability measures. The originally tors on the state and a non-linearity in the control. The given system equation is then transformed into a linear aim of this talk is to provide a survey of recent results on integral equation involving mathematical expectations of this topic, with a special focus on how geometric control the systems states and velocities, and the resulting relaxed CT13 Abstracts 153

optimal control problem turns into a problem of convex MS12 optimization under linear equality type constraints. Gen- Rauch and Bonnet-Myers Type Comparison Theo- erally, the optimal value in the relaxed problem is smaller rems for Optimal Control Problems than that in the original one (in which the objective functional is minimized). We provide conditions sufficient for We will give estimates for the number of conjugate points the equivalency of the relaxed problem to the original one along extremals of quite general optimal control problems and describe a convergent successive solution approxima- in terms of certain state-feedback invariants of the corre- tion method. sponding control systems. These estimates generalize the classical Rauch and Bonnet-Myers comparison theorems in Arkady Kryazhimskiy Riemannian Geometry. The application of these results in International Institute for Applied Systems Analysis sub-Riemannian Geometry will be discussed. Laxenburg, Austria [email protected] Igor Zelenko Department of Mathematics Texas A&M Univerisity College MS12 [email protected] Harmonic Analysis and Optimal Control: Ana- lytic Representation of Solutions of Riccati Matrix Equations MS13 Controllability and Conditionally Stationary Mea- Classical methods of feedback stabilization of linear control sures systems via optimal control are based on algebraic matrix Riccati equations. In this talk we use methods of harmonic It is well known that controllability properties of nonlin- analysis and optimal control to obtain formulas for analyt- ear control systems may give information on the supports ical representation of solutions of algebraic matrix Riccati of stationary measures for associated random dynamical equations. These analytical formulas are stated in terms systems, where the control is replaced by an appropriate of matrix transfer functions of the original linear control random input or noise. More precisely, under ergodicity system. Since matrix transfer functions can be measured assumptions for the noise, the supports of the stationary and evaluated in many applications these analytical for- measures are determined by the invariant control sets. This mulas can be used for design of stabilizing feedback with- is valid for systems in continuous time and in discrete time. out a need in an identification of linear system model in For the latter class of systems, this presentation transfers space-time domain. We also use this approach to obtain this correspondence to conditionally stationary measures analytical representation formulas for solutions of differen- and an associated notion of relatively invariant control sets. tial matrix Riccati equations. These results demonstrate Relatively invariant control sets are subsets of complete ap- how linear harmonic analysis can be exploited to find for- proximate controllability which are maximal with respect mulas for solutions of some nontrivial nonlinear differential to a given open subset W of the state space. It turns out equations. that the system can leave such a set only, if it also leaves W . We think of W as the world in which the system lives or the Yuri S. Ledyaev safe region which must not be left. Necessary and sufficient Department of Mathematics conditions for the existence of relatively invariant control Western Michigan University sets are given, and it is shown that support of every condi- [email protected] tionally stationary measure is a relatively invariant control set. Using a perturbation approach, sufficient conditions for the existence of conditionally stationary measures are MS12 given. Optimal Control Strategies for Reducing the Num- ber of Active Infected Individuals with Tuberculo- Fritz Colonius sis University of Augsburg [email protected] We consider an optimal control model for tuberculosis (TB) with reinfection and postexposure interventions. The control functions alter the fraction of early and persistent la- MS13 tent TB individuals under treatment with anti-TB drugs. On Control and Random Dynamical Systems in Re- Our aim is to study how these control measures can max- producing Kernel Hilbert Spaces imize the reduction in the number of active infected individuals while minimizing the cost associated with their We introduce a data-based approach to estimating key implementation. This objective is attained through theo- quantities which arise in the study of nonlinear control retical computations and numerical simulations. systems and random nonlinear dynamical systems. Our approach hinges on the observation that much of the ex- Cristiana J. Silva isting linear theory may be readily extended to nonlinear University of Aveiro systems - with a reasonable expectation of success - once [email protected] the nonlinear system has been mapped into a high or infinite dimensional Reproducing Kernel Hilbert Space. In Paula Rodrigues particular, we develop computable, non-parametric estima- Universidade Nova de Lisboa tors approximating controllability and observability energy [email protected] functions for nonlinear systems, and study the ellipsoids they induce. It is then shown that the controllability en- Delfim F. M. Torres ergy estimator provides a key means for approximating the University of Aveiro invariant measure of an ergodic, stochastically forced non- delfi[email protected] linear system. We also apply this approach to the problem of model reduction of nonlinear control systems. In all 154 CT13 Abstracts

cases the relevant quantities are estimated from simulated of candidate affine functions of a PA function by explor- or observed data. These results collectively argue that ing polyhedral subdivision geometry. Its implications in there is a reasonable passage from linear dynamical sys- dynamical Lipschitz piecewise affine systems will be dis- tems theory to a data-based nonlinear dynamical systems cussed. theory through reproducing kernel Hilbert spaces. This is joint work with J. Bouvrie (MIT). Jinglai Shen University of Maryland Baltimore County Boumediene Hamzi [email protected] Imperial College Department of Mathematics Teresa Lebair [email protected] University of Maryland Baltimore County, USA [email protected] Jake Bouvrie MIT [email protected] MS14 Dynamics and Control of a Chain Pendulum on a Cart MS13 Junction Conditions for Hamilton-Jacobi-Bellman The global Euler-Lagrange equations are derived for a System on Multi-Domains chain pendulum, a serial connection of n rigid links connected by spherical joints, that is attached to a rigid cart. A system of Hamilton-Jacobi-Bellman (HJB) equations on The configuration of the system is in (S2)n ×R2.Weexam- a partition of Rd with interfaces is considered. While the ine the rich structure of the uncontrolled system dynamics, notion of viscosity is by now well known, the question of and provide the corresponding controllability criterion. We uniqueness of solution, when the Hamiltonian is discon- also show that any equilibrium can be asymptotically stabi- tinuous, remains an important issue. We investigate the lized by using a PD type controller, and provide numerical junction conditions on the interfaces, the region of discon- examples. tinuity of the Hamiltonian, to provide an existence and uniqueness result for a general class of HJB equations. Taeyoung Lee Mechanical and Aerospace Engineering Zhiping Rao George Washington University ENSTA ParisTech [email protected] [email protected] Melvin Leok Antonio Siconolfi University of California, San Diego Universita La Sapienza di Roma Department of Mathematics siconolfi@mat.uniroma1.it [email protected]

Hasnaa Zidani N. Harris McClamroch ENSTA ParisTech, INRIA Saclay Aerospace Engineering [email protected] University of Michigan [email protected]

MS14 On the Coexistence of Synchronization and Chaos MS14 Contact Geometry of Optimal Control Problems In this talk we report on numerical experiments showing empirical evidence for synchronization between two cou- I will show that contact geometry, particularly a projec- pled systems even though small parameter averaging the- tivized cotangent bundle and the standard contact struc- ory shows that there is no periodic solution having a pe- ture on it, provides a natural geometric setting for optimal riod near the apparent period suggested by the numerical control problems. Specifically, the necessary condition for simulations. We relate this to simple feedback mechanisms optimality of the Pontryagin maximum principle is formu- associated with phase and amplitude control in engineering lated as a contact Hamiltonian system on the projectivized and biological models. cotangent bundle. I will also talk about a simple application of contact transformations to optimal control problems Roger Brockett and its relation to the transversality conditions. Division of Engineering and Applied Sciences Harvard University Tomoki Ohsawa [email protected] University of Michigan-Dearborn Department of Mathematics and Statistics [email protected] MS14 Polyhedral Subdivisions of Piecewise Affine Func- tions and Applications MS15 Optimal Low Thrust Orbit Transfer with Eclipsing This talk discusses the geometry of a Lipschitz piecewise affine (PA) function and its applications. It is known in It is well known that computing the trajectory of a space- the theory of piecewise differentiable functions that such craft moving from one orbit to another, can be formulated a function admits a polyhedral subdivision of a Euclidean as an optimal control problem. New spacecraft that uti- space. Motivated by robust and sensitivity analysis, we es- lize solar electric propulsion systems introduce challeng- tablish an important relation between matrix-vector pairs ing computational hurdles for numerical optimization tech- CT13 Abstracts 155

niques. First, because the thrust is very low, the resulting Applied Mathematical Analysis, LLC trajectories are very long. Second, the solar electric propul- [email protected] sion systems provide no thrust when the spacecraft passes through a shadow, and the number and location of these Karmethia C. Thompson regions cannot be determined a priori. Third, nonlinear North Carolina State University gravitational perturbations caused by oblate earth and n- Department of Mathematics body eﬀects exacerbate the sensitivity of the solution. This [email protected] talk will discuss the issues encountered when solving such real world applications. MS15 John T. Betts Numerical Solution of State-Inequality Con- Applied Mathematical Analysis, LLC strained Optimal Control Problems Using Colloca- [email protected] tion at Legendre-Gauss and Legende-Gauss-Radau Points

MS15 It is known that state inequality path constraints in op- NLP Sensitivity with Direct Transcription: A timal control problems may produce discontinuities in the Strategy to Incorporate Moving Finite Elements costate that are difficult to approximate numerically. One Within DAE Optimization approach to overcoming this computational issue is to reformulate the first-order optimality conditions of the A direct transcription strategy with moving finite elements continuous-time problem to produce continuous costates. is proposed with features that include direct location of In this presentation we will discuss a method for costate control breakpoints, and termination criteria based on a estimation of state-inequality constrained optimal control constant Hamiltonian and DAE approximation error con- problems using orthogonal collocation at Legendre-Gauss- straints. The resulting problem formulation is decomposed Radau (LGR) and Legendre-Gauss (LG) points. In the into an inner NLP problem, a fixed element direct tran- case of LGR points, the differentiation matrix associated scription, and an outer NLP, which adjusts finite elements with the costate estimate is singular, whereas the differenti- based on above termination criteria. The two layer ap- ation matrix associated with the state inequality constraint proach is implemented with the IPOPT NLP and sIPOPT multipliers is invertible. Furthermore, it is shown that the sensitivity codes. inverse of this differentiation matrix is an integration ma- Weifeng Chen trix. In the case of LG points, it is shown that the formu- Zhejiang University of Techology lation of the optimal control problem must be modified to [email protected] so that the path constraint is enforced at the boundaries of the domain where the dynamics are not collocated.

Zhijiang Shao Camila Francolin Zhejiang University University of Florida [email protected] francoli@uﬂ.edu

Larry Biegler Hongyan Hou, William Hager Carnegie Mellon University Department of Mathematics [email protected] University of Florida hhongyan@ufl.edu, hager@ufl.edu MS15 Anil Rao Direct Transcription Solution of Optimal Control Mechanical and Aerospace Engineering Problems with State and Control Delays University of Florida Direct transcription is a popular approach used to numer- anilvrao@ufl.edu ically solve many optimal control problems in industry. This talk will discuss progress on the development of an MS15 industrial grade direct transcription optimal control software package that works with processes modeled by differ- Convergence of Hp Pseudospectral Method for Un- ential algebraic equations and for which there are state and constrained Optimal Control control delays. The inclusion of DAE formulations greatly A convergence theory is established for approximations of increases the types of delayed problems that can be solved. unconstrained optimal control problems based on a Radau It also raises difficulties in determining a priori if a problem collocation scheme where both the polynomial degree on is formulated correctly for its numerical solution. The anal- each mesh interval and the number of mesh intervals can ysis of problems with control delays is also complicated by be freely chosen. Under assumptions of coercivity and the fact that even with constant delays sometimes the the- smoothness, we show that this hp-scheme has a local min- ory for uniform grids is not applicable to nonuniform grids imizer and corresponding transformed adjoint multiplier and nonuniform grids are essential in the consideration of that converge in the sup-norm to a local minimizer and large, complex problems. Theory, numerical algorithms, costate of the optimal control problem. The accuracy is and computational examples will be presented. improved either by increasing the degree of the polynomial Stephen L. Campbell within mesh intervals or by refining the mesh. North Carolina State Univ Hongyan Hou, William Hager Department of Mathematics Department of Mathematics [email protected] University of Florida hhongyan@ufl.edu, hager@ufl.edu John T. Betts 156 CT13 Abstracts

Anil Rao [email protected] Mechanical and Aerospace Engineering University of Florida anilvrao@uﬂ.edu MS16 Optimal Mass Transport as a Shape Metric for Vi- sual Tracking MS16 Optimal Control for Deformable Image Registra- We will describe an observer framework for visual tracking tion that explicitly uses shape information on the space of planar curves. Each planar shape is modeled as a pdf via the Image registration is an important component for many uniform distribution on its boundary. This allows us to use medical image analysis methods. It is a means to estab- optimal mass transport to compare the shapes employing lish spatial correspondences within or across subjects and a a Luenberger type observer. Here distance is measured via fundamental building block for example for atlas-building. the associated Wasserstein 2-metric. Optimal mass trans- This talk will discuss the optimal control viewpoint of de- port will be used in conjunction with previously developed formable image registration with a particular emphasis on geometric observer approach. adjoint solution methods and numerical solutions. Allen Tannenbaum Marc Niethammer ECE & BME University of North Carolina at Chapel Hill Boston University [email protected] [email protected] or [email protected]

Marc Niethammer MS16 University of North Carolina at Chapel Hill Dynamical Systems Framework for Anomaly De- [email protected] tection in Videos Behavior analysis in crowded scenarios is a challenging Patricio Vela computer vision problem due to vast diversity and com- Georgia Institute of Technology plexity. Recently, new insights have been obtained by School of Electrical and Computer Engineering treating crowd motion as a fluid flow driven by optical flow [email protected] in images. In this talk we present geometric and statistical concepts (Lagrangian Coherent Structures and Almost MS17 Invariant Sets) from dynamical systems theory to analyze such time dependent flow fields, and demonstrate their ap- Iterative Dual Approach for Stochastic Control plications in crowd segmentation and anomalous behavior with Information Relaxation detection. We use the information relaxation technique to develop Amit Surana value- and policy- iterative methods to solve discrete time System Dynamics and Optimization stochastic control problems. In each iteration, we can ob- United Tecnologies Research Center (UTRC) tain both upper and lower bounds for the true values-to-go. [email protected] Both methods ensure a convergence to the optimal solution within finite iterations. Some financial applications are discussed in this talk to show numerical efficiency. MS16 Nan Chen,WeiYu Convex Relaxations of Semi-Algebraic Optimiza- The Chinese University of Hong Kong tion Problems Arising in Systems Identification [email protected], [email protected] and Machine Learning

This talks discusses convex relaxations of semi-algebraic MS17 optimization problems arising in three closely related fields: identification and model (in)validation of switched sys- Stochastic Maximum Principle for Controlled Sys- tems, manifold embedding of dynamic data and semi- tems Driven by Fractional Brownian Motions supervised learning. As we will show in this talk, all of We obtain a maximum principle for stochastic control these problems are equivalent to minimizing the rank of problem of general controlled stochastic differential sys- a matrix that depends polynomially on the data. While tems driven by fractional Brownian motions. To arrive in principle this is a hard non-convex problem, the use at the necessary conditon for the optimal control, a type of moments based ideas allows for reducing it to a struc- of backward stochastic differential equation driven by both tured principal component decomposition: decomposing a fractional Brownian motion and the corresponding under- matrix as a sum of structured low-rank and sparse compo- lying standard Brownian motion is introduced. In addition nents. In turn, this problem can be very efficiently solved to this backward equation, the maximum principle also in- performing only a sequence of singular value decomposition volves the Malliavin derivatives. This is joint work with and thresholding operations. professor Yaozhong Hu and Dr. Jian Song. Mario Sznaier Yuecai Han Northeastern University Jilin University [email protected] [email protected]

Octavia Camps Yaozhong Hu Electrical and Computer Engineering The University of Kansas Northeastern University, Boston, MA, 02115 [email protected] CT13 Abstracts 157

Jian Song eter Systems The University of Hong Kong [email protected] We formulate an optimal design problem for the selection of best states to observe and optimal sampling times and locations for parameter estimation or inverse problems in- MS17 volving complex nonlinear nonlinear ordinary or partial dif- Stochastic Differential Games for Fully Coupled ferential systems. An iterative algorithm for implementa- FBSDEs with Jumps tion of the resulting methodology is proposed. Its use and efficacy is illustrated on three applied problems of practical This paper is concerned with stochastic differential games interest: (i) dynamic models of HIV progression, (ii) mod- (SDGs) defined through fully coupled forward-backward eling of the Calvin cycle in plant metabolism and growth, stochastic differential equations (FBSDEs) which are gov- and (iii) optimal design of source detection and location in erned by Brownian motion and Poisson random measure. 3D problems. First we give some basic estimates for fully coupled FBS- DEs with jumps under the monotonic condition. We also H. Thomas Banks prove the well-posedness and regularity results for fully North Carolina State Univ coupled FBSDEs with jumps on the small time interval Dept of Math & Ctr for Rsch in under a Lipschitz condition (where the Lipschitz constants [email protected] of σ, h with respect to z, k are small enough) and a linear growth condition. For SDGs, the upper and the lower value functions are defined by the controlled fully coupled FB- MS18 SDEs with jumps. Using a new transformation, we prove Randomize-then-Optimize: A that the upper and the lower value functions are determin- Monte Carlo Method for Estimation and Uncer- istic. Then, after establishing the dynamic programming tainty Quantification in Inverse Problems principle for the upper and the lower value functions of this SDGs, we prove that the upper and the lower value Many classical methods for solving inverse problems re- functions are the viscosity solutions to the associated up- quire the solution of an optimization problem, e.g., maxi- per and the lower Hamilton-Jacobi-Bellman-Isaacs (HJBI) mum likelihood (ML) and maximum a posterior (MAP) es- equations, respectively. Furthermore, for a special case timation. Uncertainty quantification (UQ) in these settings (when σ, h do not depend on y, z, k), under the Isaacs’ is typically performed using either classical Gaussian the- condition, we get the existence of the value of the game. ory or simulation techniques such as Markov chain Monte It’sbasedonacommonworkwithQingmengWei(School Carlo. In this talk, we present a Monte Carlo method for of Mathematics, Shandong University, Jinan 250100, P. R. estimation and UQ that we call randomize-then-optimize China). (RTO). Rather than creating a Markov chain, RTO makes use of the optimization algorithm used in the ML or MAP Juan Li estimation to sample from the probability density of inter- Shandong University at Weihai est. [email protected] Johnathan M. Bardsley University of Montana Qingmeng Wei [email protected] Shandong University [email protected] MS18 MS17 Parameter Subset Selction for Complex Models Viscosity Solution to Path-Dependent Bellman Increasing demands on accuracy of models require compre- Equations hensive models involving large numbers of parameters. In particular because of limited data available for parameter In this paper we study the optimal stochastic control prob- estimation in general it is impossible to identify all parame- lem for a path-dependent stochastic system. The associ- ters of a complex model. Consequently we need systematic ated Bellman equation from dynamic programming princi- methods in order to select those parameters which can be ple is a path-dependent fully nonlinear partial differential identified with sufficient accuracy. The different variants equation of second order. A novel notion of viscosity solu- of parameter subset selection provide such methods. In the tions is introduced. Using functional Itô calculus initiated talk we discuss several concepts of parameter subset. by Dupire, the value functional of the stochastic optimal control problem is characterized as the unique viscosity so- Franz Kappel lution to the associated path-dependent HJB equation. Department of Mathematics and Scientific Computing University of Graz Fu Zhang [email protected] Fudan University [email protected] MS18 Shanjian Tang Bayesian Techniques for Model Calibration and Fudan University, Shanghai, China; Quantification of Model Errors Ajou University, Suwon, Korea [email protected] Measurement and model errors produce uncertainty in model parameters estimated through least squares fits to data. In many cases, model errors are neglected during MS18 model calibration. However, this can yield nonphysical Optimal Design Techniques for Distributed Param- parameter values for applications in which the effects of unmodeled dynamics are significant. In this presentation, 158 CT13 Abstracts

we will discuss the use of autoregressive (AR) processes MS19 to quantify model errors. Densities for the model and AR Optimally Swimming Stokesian Robots process parameters are constructed using delayed rejection adaptive Metropolis (DRAM) algorithms. We illustrate as- We study self propelled stokesian robots composed of aspects of the framework in the context of distributed struc- semblies of balls, in dimensions 2 and 3, and prove that tural models with highly nonlinear parameter dependen- they are able to control their position and orientation. This cies. is a result of controllability, and its proof relies on applying Chow’s theorem in an analytic framework, similarly Nathan Burch to what has been done in [F.Alouges, A.DeSimone,and North Carolina State University A.Lefebvre,J. Nonlinear Sci., 18(3), 2008] for an axisym- [email protected] metric system swimming along the axis of symmetry. How- ever, we simplify drastically the analyticity result and ap- Ralph C. Smith ply it to a situation where more complex swimmers move North Carolina State Univ either in a plane or in three-dimensional space, hence ex- Dept of Mathematics, CRSC periencing also rotations. We then focus our attention on [email protected] energetically optimal strokes, which we are able to compute numerically. Some examples of computed optimal strokes Zhengzheng Hu are discussed in detail. Department of Mathematics North carolina State University Benot Merlet [email protected] LAGA, Universit´e Paris Nord - Institut Galil´ee [email protected]

MS19 MS19 Heat and Schroedinger Equations on Degenerate Riemannian Manifolds Common Features of Diffusions in the Sub- Riemannian and Riemannian Contexts On a two dimensional manifold, we consider the optimal T 2 2 → Despite being a “degenerate” geometry, some aspects of control problemx ˙ = u1F1 + u2F2, 0 (u1 + u2 )dt min, sub-Riemannian geometry mirror more familiar situations. α where F1 =(1, 0) and F2 =(0,x ) and initial and fi- We give two examples. First, we explain how to extend nal points are fixed. The solutions of this problem are a technique, introduced by Molchanov, for studying the the minimizing geodesics for the generalized Riemannian small-time asymptotics of the heat kernel at the cut locus 2 −2α 2 metric g = dx1 + x1 dx2. The corresponding Laplace- from the Riemannian to the sub-Riemannian context. Sec- Beltrami operator present some diverging first order terms: ond (time permitting), we discuss a class of diffusions aris- 2 2α 2 α | 1| − Δ=∂x1 + x ∂x2 x1 ∂x1 .Inthistalkwediscussthe ing from submanifolds (of Riemannian manifolds) and sub- self-adjointness and the stochastic completeness of this op- Riemannian structures that provides a common stochastic erator. framework for both geometric situations. Ugo Boscain Robert Neel CMAP, Ecole Polytechnique Department of Mathematics [email protected] Lehigh University [email protected] MS19 Perturbation Methods and Heat Kernel Asymp- MS20 totics Serial and Parallel Hybrid Two-Scale Methods for Eikonal Equations Hypoelliptic heat kernels on sub-Riemannian manifolds have been shown to encode geometric information, just as The Eikonal equation has recently found its way into a their elliptic counterparts on Riemannian manifolds. Some number of applications, which has prompted the develop- of this geometric information (e.g., the sub-Riemannian ment of many efficient numerical algorithms. In this talk distance function) can be recovered from the short-time I will survey some of the state-of-the-art methods for the behaviour of the hypoelliptic heat kernel. In principle, one Eikonal equation, and then proceed to a hybrid two-scale could try to ”read off” the sub-Riemannian geometry from method called the Heap-Cell Method (HCM). I will then the short-time behaviour of the heat kernel. In reality how- present a parallelization of the HCM and explore its com- ever, the computation of closed-form expressions for heat patibility with second-order methods. kernels for general sub-riemannian geometries is a major challenge, and, in general, no such closed-form expressions Adam Chacon can be expected. In this talk, we will show how pertur- Center for Applied Mathematics, Cornell University bation theory ideas can help in recovering the short-time [email protected] behaviour of the heat kernel, even when no closed-form expression for it is known. MS20 Abdol-Reza Mansouri Fast Replanning and Any-Angle Planning Department of Mathematics and Statistics Queen’s University In this talk, we give an overview of our research on any- [email protected] angle path planning methods and on incremental path replanning methods. In robotics or video games, one often discretizes continuous terrain into grids with blocked and unblocked cells and replans when the terrain or one’s knowledge of the terrain changes. Any-angle path plan- CT13 Abstracts 159

ning methods propagate information along grid edges (to discrete-time optimal control problems when the admissi- achieve small runtimes) but without constraining the paths ble processes ought to satisfy several kinds of constraints. to grid edges (to ﬁnd short paths). Incremental path replanning methods solve sequences of similar path planning problems faster than individual searches from scratch by Jo¨el Blot reusing information from previous searches to speed up the University Paris 1 current search. [email protected]

Sven Koenig,AlexNash University of Southern California MS21 [email protected], [email protected] Multiobjective Optimal Control over Infinite Hori- zon MS20 Multiobjective optimal control problems in the discrete- The Monotone Acceptance Ordered Upwind time case and infinite horizon framework are studied for Method: A Causal Algorithm for Minimum Time systems governed by difference equations or difference in- / Cost Optimal Control. equations with or without constraints. Pontryagin Maxi- mum Principles are established in the weak form and in The Monotone Acceptance Ordered Upwind Method the strong form. Alternative theorems and results due to (MAOUM)solvesthesameclassofproblemsastheOr- Philippe Michel are among the tools used to prove our the- dered Upwind Method of Sethian & Vladimirsky [SINUM orems. We also give sufficient conditions of optimality. 2003], but does so with a precomputed stencil that can adapt to local grid spacing. Consequently, MAOUM is able Naila Hayek to guarantee that nodes are accepted in order of their value Laboratoire ERMES, University Pantheon Assas Paris 2. and performs considerably better than the older algorithm 12 place du Panthéon. 75005 Paris when significant grid refinement is used to improve approx- [email protected] imation quality for problems with nonsmooth solutions. Ken Alton MS21 University of British Columbia Spectral Methods for the Solution of Infinite- [email protected] Horizon Optimal Control Problems

Ian M. Mitchell We consider a class of inﬁnite horizon optimal control prob- University of British Columbia lems in Lagrange form involving the Lebesgue integral in Department of Computer Science theobjective.Thisspecialclassofproblemsarisesinthe [email protected] theory of economic growth and in processes where the time T is an exponentially distributed random variable.

MS20 The problem is formulated as optimization problem in A Fast Marching Dynamic Replanning Method for Hilbert Spaces. It reads as follows: Minimize the func- Mobile Robots tional ∞ Weighted-Region Planning can formalize the problem of finding optimal paths for a robot subject to various ob- J(x, u)= r(t, x(t),u(t))ν(t)dt jectives and constraints. Roboticists commonly use graph 0 search methods in such settings, but this produces dis- n + r + cretization artefacts in the plans. Smoothing and inter- subject to all pairs (x, u) ∈ W2 ( ,ν) × L2( ,ν), satisfying polation methods have thus been proposed, but most of state equations them fail to address the root cause. However, Fast March- ing can be leveraged to properly address this issue. The x˙(t)=f(t, x(t),u(t)) , E* planner builds on fast marching, and extends it with the efficient replanning mechanism of D*. It can thus ef- control restrictions ficiently cope with scenarios for interweaved planning and control, where the underlying cost distribution frequently u(t) ∈ U, U ∈ Comp(Rr) \{∅}, changes. This talk will present the E* planner and discuss some open questions: whether focusing heuristics can and initial conditions be added, how to develop rigorous proofs for the fully dynamic case, and how to extend it to non-holonomic and x(0) = x0. anisotropic cases. TheremarkableonthisstatementisthechoiceofWeighted Roland Philippsen Sobolev- and Weighted Lebesgue spaces as state and con- Halmstad University trol spaces respectively. The function ν is a density func- [email protected] tion. These considerations give us the possibility to extend the admissible set and simultaneously to be sure that the adjoint variable belongs to a Hilbert space. For the class MS21 of problems proposed, we can proof an existence result as Pontryagin Principles for Infinite-Horizon Con- well as Pontryagins Maximum Principle. Considering strained Problems ∞ We present several results on the necessary conditions and T sufficient conditions of optimality for infinite-horizon and x, y := x(t) y(t)ν(t)dt 0 160 CT13 Abstracts

as scalar product in the weighted Lebesgue - space a spec- utilized. However, its accuracy and efficiency in a highly tral method is developed to construct a numerical scheme nonlinear system are severely limited due to the intrinsic for the solution of the problem. features of the POD method. In this talk, we propose a systematic, goal-oriented model reduction methodology for Sabine Pickenhain general complex systems. Its mathematical theory and nu- Brandenburg University of Technology Cottbus, Germany merical behavior will also be discussed. [email protected] Zhu Wang University of Minnesota MS22 [email protected] Structure-Preserving Model Reduction for Nonlin- ear Port-Hamiltonian Systems MS22 This work proposes a structure and stability preserving Reduced Order Controllers for Boussinesq Equa- model reduction approach for large-scale input-output non- tions with a Nonlinear Observer linear Port-Hamiltonian systems with an a-priori error bound. Two techniques for constructing reduced-order Reduced-order models are essential in the design of feed- bases are considered: Proper orthogonal decomposition back control laws for complex distributed parameter sys- (POD) and a quasi-optimal H2 model reduction. The non- tems. It is well known that reduced models must cap- linear term is reduced efficiently using an extension of the ture the input-output behavior of the underlying system. discrete empirical interpolation method (DEIM). Numeri- This is also true when nonlinear observers are incorporated. cal tests are shown using a nonlinear ladder network and a However, we add additional constraints that the reduced Toda lattice model with exponential interactions. models provide accurate representations of the distributed nature of the controller. This approach is demonstrated Christopher A. Beattie on a control problem arising in the development of energy Virginia Polytechnic Institute and State University efficient buildings. [email protected] Jeff Borggaard Serkan Gugercin Virginia Tech Virginia Tech. Department of Mathematics Department of Mathematics [email protected] [email protected] Lizette Zietsman Saifon Chaturantabut Virginia Tech Virginia Tech Interdisciplinary Center for Applied Mathematics [email protected] [email protected]

MS22 MS23 Volterra Series Interpolation Framework for Model Strategies for Distributed Information Acquisition Reduction of Bilinear Systems and Propagation in Networks The interpolatory model reduction methods for bilinear The talk will define the concept of an “interaction den- systems so far have focused on interpolating the homoge- sity” that describes the way information at each node is nous subsystems individually. In this talk, we introduce relatedtotheinformationheldateachothernodeofa a new framework where multi-point interpolation is per- network. This density is useful in defining information the- formed on the underlying full Volterra series. This, in turn, oretic quantities such as conditional entropy, mutual infor- has a direct connection to optimal-H2 model reduction of mation,anddirected information may be studied. I shall bilinear systems and allows us to produce optimal-H2 ap- describe the role of the concepts in understanding connec- proximants by solving only regular Sylvester equations. tion patterns that optimize information transfer in various networks. Garret Flagg Western Geco, Houston, TX John B. Baillieul gfl[email protected] Boston University Dept of Aero/Mech Engineering Serkan Gugercin [email protected] Virginia Tech. Department of Mathematics MS23 [email protected] Stochastic Surveillance Strategies for Spatial Quickest Detection MS22 We design robotic surveillance strategies for the quickest Systematic Goal-Oriented Reduced-Order Models detection of anomalies taking place in an environment of for Complex Systems interest. From a set of predefined regions in the environ- Many grand challenge problems at the frontier of computa- ment, a team of autonomous vehicles collects noisy ob- tional science, such as flow control and optimization prob- servations, which a control center processes. The overall lems, require repeated numerical simulations of large-scale objective is to minimize detection delay while maintaining dynamical systems. To alleviate the tremendous compu- the false alarm rate below a desired threshold. We present tational cost demanded in these applications, the proper joint anomaly detection algorithms for the control center orthogonal decomposition (POD) method has been widely CT13 Abstracts 161

and vehicle routing policies. MS24 Stability of Numerical Methods for Jump Diffusion Francesco Bullo Systems Mechanical & Environmental Engineering University of California at Santa Barbara This work is devoted to stability analysis of numerical solu- [email protected] tions for jump diffusions and jump diffusions with Marko- vian switching. Different from the existing treatment of Vaibhav Srivastava Euler-Maurayama methods for solutions of stochastic dif- Princeton University ferential equations, we use techniques from stochastic ap- [email protected] proximation. We analyze the almost sure exponential stability and exponential p-stability. The benchmark test Fabio Pasqualetti model in numerical solutions, namely, one-dimensional lin- University of California at Santa Barbara ear scalar jump diffusion is examined first and easily ver- [email protected] ifiable conditions are presented. Then Markovian regime- switching jump diffusions are dealt with. Moreover, analysis on stability of numerical methods for linearizable and MS23 multi-dimensional jump diffusions is carried out. This is a Smart Realizations of Sparse Transfer Matrices joint work G. Yin and Haibo Li.

Abstract not available. Zhixin Yang Wayne State University Ali Jadbabaie Department of Mathematics Department of Electrical and Systems Engineering [email protected] University of Pennsylvania [email protected] MS24 Stock Trading Rules under a Switchable Market MS23 Solving a Linear Equation Across a Network This work provides an optimal trading rule that allows buy- ing and selling of an asset sequentially over time. The This talk describes a very simple distributed algorithm for asset price follows a regime switching model involving a solving a system of linear equations of the form Aix = geometric Brownian motion and a mean reversion model. bi,i=1, 2,...,n where Ai is a mi × m matrix and bi The objective is to determine a sequence of trading times is an mi vector. The system is recursively solved by n to maximize an overall return. The corresponding value agents assuming that agent i knows only the pair (Ai,bi) functions are characterized by a set of quasi variational and its neighbors’ current estimates of a solution. All n inequalities. Closed-form solutions are obtained. estimates converge exponentially fast to a solution to the system provided only that the time-varying graph G(t) Qing Zhang characterizing neighbor relations is strongly connected for University of Georgia all t. Department of Mathematics [email protected] A Stephen Morse Yale University Duy Nduyen, Jingzhi Tie Dept of Syst Science/Elect Eng University of Georgia [email protected] [email protected], [email protected]

MS24 MS25 Discrete Time Linear Quadratic Control with Ar- Toward Adaptive Control of the Systemic Inﬂam- bitrary Correlated Noise matory Response

A control problem for a discrete time linear stochastic sys- Optimizing therapeutic treatment for the critically ill is a tem with a general correlated noise process and a cost challenge that clinicians face due to the complexity of the functional that is quadratic in the state and the control inflammatory response. This talk will report on the use of is solved. An optimal control is given explicitly as the state estimation methods and nonlinear model predictive sum of the well known linear feedback control for the asso- control for finding optimal inputs for a reduced but highly ciated deterministic linear-quadratic control problem and nonlinear system of inflammation. We further discuss the the prediction of the response of a system to the future progress and challenges toward implementing strategies to noise process. The optimal cost is also given explicitly. adapt this system to the patient system and improve predictability of the response. Tyrone E. Duncan University of Kansas Judy Day Department of Mathematics University of Tennessee [email protected] [email protected]

Bozenna J. Pasik-Duncan Seddik Djouadi University of Kansas Department of Electrical Engineering and Computer [email protected] Science University of Tenneessee, Knoxville [email protected] 162 CT13 Abstracts

Wassim Bara [email protected] Department of Electrical Engineering and Computer Science Balaji Yegneswaran University of Tennessee Department of Critical Care Medicine [email protected] University of Pittsburgh byegneswaran Greg Zitelli Department of Mathematics Robert Parker University of Tennessee Department of Chemical and Petroleum Engineering [email protected] University of Pittsburgh [email protected] MS25 Multiple Model Predictive Control Approach to MS25 Personalized Anemia Management Characterization and Control of the Erk/MAPK Signaling Pathway in T Lymphocytes This presentation introduces a new algorithm, based on the principles of Multiple Model Predictive Control The ability to characterize and selectively control signal- (MMPC), for personalized dosing of Erythropoiesis Stim- ing pathways within T cells will generate new approaches ulating Agents (ESA) in hemodialysis patients. The al- for therapeutic design and research tools in medicine and gorithm learns patients dose-response profile from data in systems biology. We characterize the signaling pathways real time and generates new doses by combining outputs using model-based design of experiments and use the re- from individual MPCs. Results of the first human study fined mathematical models to inform open-loop control of show that this algorithm significantly improves stability the Erk/MAPK intracellular signaling. This integrated ap- of hemoglobin concentration over a standard population- proach was evaluated using experiments with Jurkat cells based paper protocol approach. to track trajectories with short, moderate and extended durations of Erk phosphorylation. Adam E. Gaweda University of Louisville Jeffrey Perley, Thembi Mdluli Health Sciences Center Weldon School of Biomedical Engineering [email protected] Purdue University [email protected], [email protected] MS25 Judith Mikolajczak, Marietta Harrison Model-Based Estimation and Control for Personal- 2Department of Medicinal Chemistry & Molecular ized Real-Time Glucose Control in Intensive Care Pharmacology The benefits of targeted glucose control in post-surgical in- Purdue University tensive care is a topic of debate, which we hypothesize is a [email protected], [email protected] result of increased hypoglycemia and interpatient variability. We synthesize: (i) a model-based receding horizon con- Gregery Buzzard troller; (ii) an output regulator to eliminate hypoglycemia Purdue University and penalize large insulin infusions; and (iii) an on-line [email protected] moving horizon estimator to update the controller model to match individual patient dynamics as they evolve. The Ann E. Rundell resulting system was tested using actual intensive care pa- Weldon School of Biomedical Engineering tient data. Purdue University [email protected] Stanislaw Gawel Department of Chemical and Petroleum Engineering University of Pittsburgh MS26 [email protected] H∞-Stability Analysis of Delay Systems of Neutral Type Gilles Clermont University of Pittsburgh The stability of linear neutral systems with commensurate [email protected] delays has been largely studied in the literature. However, the critical case where neutral poles approach the imagi- Thang Ho nary axis has not been fully understood. In this work, we Department of Chemical and Petroleum Engineering consider some classes of these systems, which furthermore University of Pittsburgh have formal polynomials of multiple roots. First, the lo- [email protected] cation of neutral poles with respect to the imaginary axis is determined through approximation of the poles. Then, H∞-stability conditions are derived in the cases where all Brandi Newman the poles of the system are in the left half-plane. Department of Chemical Engineering Iowa State University Catherine Bonnet,LeHaVyNguyen [email protected] Inria [email protected], [email protected] John Maalouf Department of Chemical and Petroleum Engineering University of Pittsburgh CT13 Abstracts 163

MS26 MS27 Solution of An Infinite Dimensional Two-Point Tropicalizing the Simplex Algorithm Boundary Value Problem Via the Principle of Least Action We present an analogue of the simplex algorithm, allowing one to solve tropical (max-plus) linear programming A new approach for solving two point boundary value prob- problems. This algorithm computes, using signed tropi- lems for conservative infinite dimensional systems is inves- cal Cramer determinants, a sequence of feasible solutions tigated. This new approach seeks to exploit the principle which coincides with the image by the valuation of the se- of least action in reformulating and solving such problems quence produced by the classical simplex algorithm over in the framework of optimal control. A specific and highly the ordered field of Puiseux series. This is motivated in simplified problem involving a one dimensional wave equa- particular by deterministic mean payoff games (which are tion is considered. The construction of a solution to the equivalent to tropical linear programming). attendant optimal control problem is identified as crucial in applying this new approach. Xavier Allamigeon CMAP, Ecole Polytechnique William M. McEneaney [email protected] Dept. of Mechanical and Aerospace Engineering University of California, San Diego [email protected] MS27 A Max-plus Method for the Approximate Solution Peter Dower of Discrete-time Linear Regulator Problems with The University of Melbourne Non-quadratic Terminal Payoff [email protected] A new max-plus based method is developed for the approximate solution of discrete time linear regulator problems MS26 with non-quadratic terminal payoff. This new method is Root Locus of Infinite-Dimensional Systems underpinned by the development of fundamental solutions to such discrete time linear regulator problems. In com- The root locus is an important tool for analysing the sta- parison with typical grid-based approaches, a substantial bility of linear finite-dimensional systems as a parameter reduction in computational effort is observed in applying is varied. However, many systems are modelled by partial this new method. A number of simple examples are pre- differential equations or delay equations. A rigorous defini- sented that illustrate this and other observations. tion of the root locus appropriate for a wide class of systems is developed. As for finite-dimensional systems, any limit Huan Zhang, Peter Dower point of a branch of the root locus is a zero. However, the The University of Melbourne general asymptotic behaviour can be quite different. The [email protected], [email protected] theory will be illustrated with an delay equation. Kirsten Morris MS27 Dept. of Applied Mathematics Contraction of Riccati Flows Applied to the Con- University of Waterloo vergence Analysis of a Max-Plus Curse of Dimen- [email protected] sionality Free Method The approximation error of McEneaney’s curse-of- Birgit Jacob dimensionality free method for√ solving HJB equations was Universität Wuppertal, Germany shown to be O(1/(Nτ))+O( τ)whereτ is the time dis- [email protected] cretization size and N is the number of iterations. Here we use a recently established contraction result for the indefi- MS26 nite Riccati flow in Thompson’s metric to show that under different technical assumptions, still covering an important Numerical Computation and Implementation of H- class of problems, the error is only of O(e−Nατ)+O(τ) Infinity Controllers for Infinite-Dimensional Sys- where α is related to the convergence rate of the Riccati tems flow.

The mixed sensitivity minimization is considered for SISO Zheng Qu inﬁnite dimensional plants with low order weights. Pre- Ecole Polytechnic viously it was shown that the optimal controller can be [email protected] computed from singular values and vectors of a square matrix whose dimension is + n1,where is the number of unstable modes of the plant and n1 isthedegreeofthesen- MS28 sitivity weight. This presentation shows that the dimen- Convex Lyapunov Functions and Duality for Con- sion of the square matrix in question can be reduced n1. vex Processes Hence a connection of the skew Toeplitz approach with the Zhou-Khargonakar formulation can established. Examples Concepts of weak and strong asymptotic stability of con- from systems with time delays, as well as systems repre- vex processes, generalizing asymptotic controllability and sented by partial diﬀerential equations, will be given and detectability of linear systems in presence of constraints, implementation issues are discussed. are studied through convex Lyapunov functions. Duality between the two concepts is established, through convex Hitay Ozbay conjugacy between a weak Lyapunov function for a convex Bilkent University, Turkey process and Lyapunov function for the adjoint process. [email protected] Rafal Goebel 164 CT13 Abstracts

Loyola University Chicago tion problems in complex networks based on algebraic USA graph theory. We present a novel synchronization condi- [email protected] or [email protected] tion applicable to a general coupled oscillator model. We rigorously establish that our condition is exact for various interesting network topologies and parameters. Via statis- MS28 tical studies we show that our condition predicts accurately Numerical Computation of Nonsmooth Lyapunov the existence of stable synchronous solutions for generic Functions for Differential Inclusions networks as well as various power network test cases. We present a method for the computation of piecewise lin- Florian Dorfler ear Lyapunov functions for strongly asymptotically stable Mechanical Engineering differential inclusions. The method relies on converting the University of California at Santa Barbara usual Lyapunov function inequalities into the constraints dorfl[email protected] of a linear optimization problem on the nodes of a grid covering a subset of the state space. Contrary to other Francesco Bullo numerical approaches, the resulting function does not only Mechanical & Environmental Engineering yield a numerical approximation to a Lyapunov function University of California at Santa Barbara but indeed a (nonsmooth) real Lyapunov function. [email protected] Robert Baier, Lars Gruene Mathematical Institute, University of Bayreuth MS29 [email protected], Coordination and Synchronization of Weakly Cou- [email protected] pled Harmonic Oscillators Sigurdur Hafstein We propose an approach for the analysis and design of School of Science and Engineering, Reykjavik University weakly coupled harmonic oscillators for coordination and [email protected] synchronization. Through a coordinate transformation and averaging, a sufficient condition is given for orbital stability of a targeted limit cycle, in terms of linear matrix in- MS28 equalities on the coupling matrix. The condition guaran- Robust Non-Zenoness of Piecewise Affine Systems tees orbital stability when the coupling is sufficiently weak. with Applications to Complementarity Systems However, for design, the coupling can be strengthened for faster convergence through a line search to minimize the In this talk, we discuss non-Zenoness, referred to as the ex- magnitude of the Floquet multiplier with the largest mod- istence of finitely many mode switchings on finite time, of a ulus. Our method allows for multiple oscillation patterns family of piecewise affine systems (PASs) subject to param- to be embedded as stable limit cycles into a single coupling eter and initial state uncertainties/perturbations. In par- matrix with a local distributed structure. ticular, we show that there is a uniform bound on the number of mode switchings for a family of Lispchitz PASs, as Tetsuya Iwasaki, Xinmin Liu along as their subsystem matrices are uniformly bounded. UCLA Its applications to linear complementarity systems will be [email protected], [email protected] discussed. Further, we present preliminary results for robust non-Zenoness of non-Lipschitz PASs, under the assumption of well-posedness. MS29 Determining Steady-State Patterns and Their Sta- Jinglai Shen bility in Lateral Inhibition Networks University of Maryland Baltimore County [email protected] We analyze spatial patterns on networks of cells where adjacent cells inhibit each other through contact signaling. The network is represented as an interconnection of identi- MS28 cal individual dynamical systems. To predict steady state Control Problems for a Class of Set Valued Evolu- patterns we identify equitable partitions of the graph ver- tions tices, assigning them into disjoint classes. We use results from monotone systems theory to prove the existence of The talk studies controllability problems for the reachable patterns with this structure. We study their stability prop- set of a differential inclusion. These were originally moti- erties and provide a small-gain type criterion. vated by models of control of a flock of animals. Conditions are derived for the existence or nonexistence of a strategy Ana Sofia Rufino Ferreira which confines the reachable set within a given bounded University of California, Berkeley region, at all sufficiently large times. Steering problems [email protected] and the asymptotic shape of the reachable set are also investigated. Murat Arcak University of California-Berkeley Dongmei Zhang, Alberto Bressan [email protected] Pennsylvania State University zhang [email protected], [email protected] MS29 MS29 Weighted L2 Norm Contractions in Diffusively- Coupled Systems Synchronization in Complex Oscillator Networks We present conditions using contraction theory that guar- This talk proposes an insightful approach to synchroniza- CT13 Abstracts 165

antee synchrony in diffusively-coupled systems. The condi- MS30 tions we derive generalize and unify existing theory about A Utility Model of Learning How to Consume Ef- asymptotic convergence of trajectories of reaction-diffusion fectively partial differential equations as well as compartmental ordinary differential equations, and furthermore may be numer- This paper proposes a utility model in which agents require ically verified using linear matrix inequalities. Our analysis effort to learn how to consume effectively. In this model, also provides a useful perspective for studying spatial pat- there is an ideal utility function of consumption that re- tern formation arising from diffusion-driven instability. We quires skill to achieve. At each time, there is a range of discuss examples relevant to enzymatic cell signaling and consumption levels for which the agent can consume at the coupled oscillators. full potential described by this ideal utility function, and consuming outside this range generates less than the po- Sayed Y. Shafi tential utility. There is an optimal policy for expending UC Berkeley effort to move the boundaries of the range of consumption [email protected] levels at which the agent is skilled at consuming. When the range is narrow, the presence of this learning induces Zahra Aminzare a kind of risk aversion in the large, and makes the indirect Rutgers University utility function more concave than it would otherwise be. [email protected] Hyeng Keun Koo Murat Arcak Ajou University, Suwon, Korea University of California-Berkeley [email protected] [email protected] Philip Dybvig Eduardo Sontag Washington University Rutgers University [email protected] [email protected] Bong Gyu Jang POSTECH MS30 [email protected] A Nonlocal Free Boundary Problem and Financial Pricing for Retirement Benefits MS30 We study a nonlocal parabolic variational inequality which Weak Necessary and Sufficient Stochastic Maxi- is from the financial valuation of defined benefits retirement mum Principle pension plan that allows early retirement. The paid benefits on retirement dependent on the salary at that time. In this paper we prove a weak necessary and sufficient max- The underlying salary is assumed to follow a jump-diffusion imum principle for Markov modulated stochastic optimal process. We characterize the financial value of the retire- control problems. Instead of insisting on the maximality ment benefits as the solution of an optimal stopping time condition of the Hamiltonian, we show that 0 belongs to problem, which corresponds to a variational inequality or the sum of Clarke’s generalized gradient of the Hamilto- a free boundary problem of an integro-differential operator nian and Clarke’s normal cone of the control constraint of the parabolic type. The existence and uniqueness of the set at the optimal control. Under a joint concavity con- solution to the variational inequality are proved and the dition on the Hamiltonian and a convexity condition on properties for related free boundary are discussed. the terminal objective function, the necessary condition becomes sufficient. We give examples to demonstrate the Baojun Bian weak stochastic maximum principle. Tongji University [email protected] Harry Zheng Imperial College London [email protected] MS30 A Law of the Iterated Logarithm for Sublinear Ex- pectations MS31 On Time-optimal Trajectories for a Car-like Robot In this paper, with the notion of independent identically with One Trailer distributed (IID) random variables under sub-linear expectations initiated by Peng, we investigate a law of the In addition to the theoretical value of challenging optimal iterated logarithm for capacities. It turns out that our control problmes, recent progress in autonomous vehicles theorem is a natural extension of the Kolmogorov and the mandates further research in optimal motion planning for Hartman-Wintner laws of the iterated logarithm. wheeled vehicles. Since current numerical optimal control techniques suffer from either the curse of dimensionality, Zengjing Chen e.g. the Hamilton-Jacobi-Bellman equation, or the curse of Shandong University, Jinan, China complexity, e.g. pseudospectral optimal control and max- [email protected] plus methods, analytical characterization of geodesics for wheeled vehicles becomes important not only from a the- Feng Hu oretical point of view but also from a practical one. Such Qufu Normal University an analytical characterization provides a fast motion plan- Qufu, China ning algorithm that can be used in robust feedback loops. [email protected] In this work, we use the Pontryagin Maximum Principle to characterize extremal trajectories, i.e. candidate geodesics, for a car-like robot with one trailer. We use time as the 166 CT13 Abstracts

distance function. In spite of partial progress, this prob- MS32 lem has remained open in the past two decades. Besides The Non Occurrence of the Lavrentiev Gap for straight motion and turn with maximum allowed curva- Scalar Multidimensional Variational Problems ture, we identify planar elastica as the third piece of motion that occurs along our extremals. We give a detailed We consider an autonomous integral functional deﬁned in characterization of such curves, a special case of which, the space of Sobolev functions on an open and bounded set, called merging curve, connects maximum curvature turns and that agree with a prescribed Lipschitz function on the to straight line segments. The structure of extremals in boundary of the domain. Jointly with Pierre Bousquet and our case is revealed through analytical integration of the Giulia Treu we show, without assuming growth conditions, system and adjoint equations. that the Lavrentiev gap does not occur for a wide class of Lagrangeans. Hamidreza Chitsaz Wayne State University Carlo Mariconda [email protected] Universit`a degli Studi di Padova [email protected]

MS31 Sampling-Based Algorithms for Optimal Motion MS32 Planning Necessary and Sufficient Second-Order Optimality Conditions for Strong Solutions of Optimal Control Sampling-based algorithms, such as the RRT and PRM, Problems with Pure and Mixed Constraints have revolutionized motion planning. In this talk, we analyze these algorithms in terms of convergence to optimal We provide optimality conditions for strong solutions of solutions, and we introduce two novel algorithms called optimal control problems with pure and mixed constraints. the RRT* and the PRM* that guarantee asymptotic opti- Second-order necessary conditions are obtained by combin- mality, i.e., almost-sure convergence to optimal solutions. ing the sliding mode approach of Dmitruk and the condi- Moreover, we extend the application domain of sampling- tions obtained by Bonnans and Hermant for weak solu- based algorithms to a variety of other control problems, in- tions. Sufficient conditions and a characterization of the cluding differential games, stochastic optimal control, and quadratric growth are obtained by extending the decom- planning with complex task specifications. position principle of Bonnans and Osmolovski˘ı. Sertac Karaman Laurent Pfeiffer,Frédéric Bonnans, Xavier Dupuis Massachusetts Institute of Technology Inria-Saclay and CMAP, Ecole Polytechnique [email protected] laurent.pfeiff[email protected], [email protected], [email protected] MS31 Title Not Available MS32 Abstract not available. (Sup + Bolza)-Control Problems As Dynamic Dif- ferential Games Steven LaValle University of Illinois at Urbana-Champaign Minimum problems are considered where the payoff is the [email protected] sum of a sup functional and a classical Bolza functional. Owingtothe L1,L∞ duality, the (L∞+Bolza)-control problem is rephrased in terms of a static differential game, MS31 where a new variable k plays the role of a maximizer.In Kinodynamic Rrt*: Asymptotically Optimal Mo- this framework 1 − k is regarded as the available fuel for tion Planning for Robots with Linear Dynamics the maximizer. The relevant (and unusual) fact is that this static game is equivalent to the corresponding dynamic dif- We present Kinodynamic RRT*, an incremental sampling- ferential game, which allows the (upper) value function to based approach for asymptotically optimal motion plan- verify a rather simple boundary value problem. ning for robots with linear dynamics. Our approach extends RRT*, which was introduced for holonomic robots, Franco Rampazzo by using a fixed-final-state-free-final-time controller that Universita di Padova optimally connects any pair of states, where the cost func- Dept di Math Pura e Applicata tion is expressed as a trade-off between the duration of a [email protected] trajectory and the expended control effort. Our approach generalizes earlier work on RRT* for kinodynamic systems, as it guarantees asymptotic optimality for any system with MS32 controllable linear dynamics, in state spaces of any dimen- Approximate Maximum Principle for Systems with sion. In addition, we show that for the rich subclass of Nonsmooth Endpoint Constraints systems with a nilpotent dynamics matrix, closed-form solutions for optimal trajectories can be derived, which keeps In this talk we report necessary optimality conditions for the computational overhead of our algorithm compared to finite-difference approximations of continuous-time control traditional RRT* at a minimum. systems with nonsmooth endpoint constraints and cost function. These results justify stability of the Pontrya- Jur van den Berg,DustinWebb gin Maximum Principle for continuous-time systems with University of Utah partially nonsmooth data under discrete approximations. [email protected], [email protected] Boris Mordukhovich Wayne State University CT13 Abstracts 167

Department of Mathematics linear output-feedback systems with time delays is given. [email protected] Zhong-Ping Jiang, Tengfei Liu Ilya Shvartsman Dept of Electrical and Computer Eng Penn State Harrisburg Polytechnic Institute of NYU Middletown, PA [email protected], [email protected] [email protected] MS33 MS33 Robustness of Nonlinear Systems with Respect to Time-Varying Input and State Delay Compensa- Delay and Sampling of the Controls tion for Uncertain Nonlinear Systems Sampling and delays in nonlinear controllers present chal- A predictor-based controller is developed for nonlinear sys- lenges that are beyond the scope of standard Lyapunov tems under time-varying (unknown) state and (known) in- or small gain methods. Here we consider continuous time put delays and additive disturbances. A desired trajectory- nonlinear time varying systems that are globally asymp- based predictor structure of previous control values facili- totically stabilizable by state feedbacks. We study their tates the control design. A Lyapunov-Krasovskii functional closed loop stability under controls that are corrupted by analysis guarantees semi-global tracking when the delays delay and sampling. We establish robustness through a are bounded and slowly varying. Numerical simulations il- Lyapunov approach of a new type. We illustrate our work lustrate improved performance over previous time-varying using the kinematics of a wheeled mobile robot. input delay control designs and robustness to combinations Frederic Mazenc of simultaneous input and state delays. INRIA Nic Fischer, Serhat Obuz, Rushi Kamalapurkar, [email protected] Warren Dixon Department of Mechanical and Aerospace Engineering Michael Malisoff University of Florida Louisiana State University nic.fischer@ufl.edu, serhat.obuz@ufl.edu, Department of Mathematics rkamalapurkar@ufl.edu, wdixon@ufl.edu malisoff@lsu.edu

Thach Dinh MS33 INRIA Numerical Implementation of Predictor Feedback Supelec, France for Nonlinear Plants with Input Delays [email protected] For nonlinear plants with large input delays, numerical approximation of the predictor mapping is the central prob- MS34 lem for implementation of predictor-based feedback. We Semilinear Differential Inclusions with Non- show that a numerical scheme for the predictor, in conjunc- Compact Evolution Operators: Solution Existence tion with a hybrid feedback that uses sampled measure- Results and Controllability ments, achieves global stabilization of all forward complete nonlinear systems that are globally asymptotically stabiliz- As it was pointed out by Triggiani in [R. Triggiani, A note able and locally exponentially stabilizable in the delay-free on the lack of exact controllability for mild solutions in case. Special results are provided for the linear time in- Banach spaces, SIAM J. Control Optim. 15 (1977), no. 3, variant case. 407-411], the exact controllability in finite time for linear control systems in infinite dimensional Banach spaces us- Iasson Karafyllis ing locally Lp- controls, for p>1, is in contradiction with Department of Environmental Engineering the compactness of the associated C0-semigroup. Thus, it Technical University of Crete is meaningful to introduce conditions assuring exact con- [email protected] trollability for semilinear equations and not requiring the compactness of the semigroups or evolution operators gen- Miroslav Krstic erated by the linear part. In this talk two approaches are University of California, San Diego described. The first one is related with a regularity as- Dept of Mechanical & Aerospace Engineering sumption on the non-linear term, formulated through a [email protected] measure of non-compactness, see [V. Obukhovski, P. Zecca, Controllability for systems governed by semilinear differential inclusions in a Banach space with a non-compact MS33 semigroup, Nonlinear Anal. 70 (2009), no. 9, 3424-3436], Stability and Distributed Control for Dynamic [I. Benedetti, V. Obukhovskii, P. Zecca, Controllability for Networks with Time-Delays: Some New Results impulsive semilinear functional differential inclusions with a non-compact evolution operator, Discuss. Math. Dif- Dynamic networks are pervasive across engineering and sci- fer. Incl. Control. Optim., 31 (2011), 39-69]. The other ence. Their importance and complexity continues to chal- one exploits the weak topology of the state space, see [I. lenge us to develop new stability criteria. Time delays Benedetti, L. Malaguti, V. Taddei, Nonlocal semilinear are often unavoidable when there is information exchange evolution equations without strong compactness: theory across large-scale dynamic networks. Here we report on and applications, BVP, 2013]. our recent work on small-gain methods to ensure stability for dynamic nonlinear networks with time-delays. Then, Irene Benedetti an application to distributed control for networks of non- Dip. Matematica e Informatica, Universita di Perugia [email protected] 168 CT13 Abstracts

MS34 tion Optimizing Spectral Parameters in Nonlinear Wave Equation Arising in High Intensity Ultra- We consider fluid flows governed by the Navier-Stokes sound equations and we are interested in the stabilization of a flow about an unstable stationary solution in the case of Input your abstract, including TeX commands, here. We partial information. This means that we have some mea- consider a third order in time equation which arises as a surements and that we look for a control expressed in terms model of wave propagation in viscous thermally relaxing of an estimate of the velocity of the flow. In the case of a fluids. The nonlinear PDE model under consideration dis- control acting in a Dirichlet boundary condition and when plays two important characteristics: (i) it is quasilinear and the observation is expressed in terms of the stress tensor or (i) it is degenerate in the principal part. The main goal of of the pressure at the boundary, the observation involves this talk is to present results on existence-nonexistence and the derivative of the control at the boundary. This hap- decay rates for the solutions as a function of physical pa- pens not only for the continuous system but also for dis- rameters in the equation. crete models obtained by finite element methods. This leads to unsual filltering and control problems. We shall Irena M. Lasiecka present a new approach for determining a feedback control University of Virginia law and an estimator of finite dimension for the velocity of [email protected] the flow. This work is in collaboration with J.-M. Buchot, M. Fournie’, P. A. Nguyen, L. Hosseini, J. Weller. Barbara Kaltenbacher University of Klagenfurt, Austria Jean-Pierre Raymond [email protected] Universite’ Paul Sabatier, Toulouse [email protected] Jason Knapp University of Virginia MS35 [email protected] Lp Parameter Differentiability in Diffuse Optical Tomography MS34 In this talk, an elliptic PDE coefficient inverse problem A New Numerical Method Based on Shape Calcu- for image reconstruction in Diffuseff Optical Tomography lus for State-Constrained Optimal Control Prob- (DOT) will be presented. We will motivate the need for lems with Pdes regularization with sparsity constraints for the ill-posed inverse problem which requires Lp regularity with respect to The talk is devoted to the analysis and the numerics of the parameters. We will formulate a trilinear form to prove pointwisely state-constrained elliptic optimal control prob- L differentiability of the forward operator in DOT. lem. The transfer of an idea from the field of ODE optimal p control is the starting point. A geometrical splitting of the Taufiquar R. Khan constraints is necessary to carry over this approach. This Clemson University leads to an equivalent reformulation of the model problem [email protected] as a new class of optimization problem: a hybrid of optimal control and shape-/topology optimization, a so–called set optimal control. This class is integrated into the ab- MS35 stract framework of optimization on vector bundles. By Solution of Ill-Posed Inverse Problems Through Lo- a comparison of the new optimality conditions with those cal Variational Filtering known form literature it becomes apparent that the new approach involves higher regularity. Newton- and trial al- The method of local regularization has been shown to lead gorithms are presented and discussed in detail. The new to fast numerical algorithms for inverse problems with method can be formulated in function space without any special structure (e.g., Volterra problems) and the possi- regularization. Some numerical tests illustrate its perfor- bility for improved resolution of fine details of solutions. mance. We present recent developments on the extension of this method to more general inverse problems through the so- Michael Frey, Simon Bechmann lution of local variational problems with both quadratic University of Bayreuth and nonquadratic penalties (such as those associated with [email protected], sparsity constraints). [email protected] Patricia Lamm Hans Josef Pesch Department of Mathematics University of Bayreuth, Germany Michigan State University Chair of Mathematics in Engineering Sciences [email protected] [email protected] MS35 Armin Rund Institute for Mathematics and Scientific Computing Discrete-Time Blind Deconvolution for Distributed University of Graz Parameter Systems with Dirichlet Boundary In- [email protected] put and Unbounded Output with Application to a Transdermal Alcohol Biosensor

MS34 A scheme for the blind deconvolution of blood or breath alcohol concentration from biosensor measured transder- Stabilization of Fluid Flows with Partial Informa- mal alcohol concentration based on a parabolic PDE with Dirichlet boundary input and point-wise boundary output CT13 Abstracts 169

is developed. The estimation of the convolution ﬁlter cor- ter. responding to a particular patient and device is formulated as a nonlinear least squares ﬁt to data. The deconvolution Vladimir Gaitsgory is then formulated as a regularized linear-quadratic pro- CIAM gramming problem. Numerical results involving patient University of South Australia data are presented. [email protected]

I. Gary Rosen Department of Mathematics MS36 University of Southern California Explicit Solutions for Singular Inﬁnite Horizon Cal- [email protected] culus of Variations

Susan Luczak We consider a one dimensional infinite horizon calculus Department of Psychology of variations problem (P), where the integrand is linear University of Southern California with respect to the velocity. The Euler-Lagrange equa- [email protected] tion, when defined, is not a differential equation as usual, but reduces to an algebraic (or transcendental) equation C(x) = 0. Thus this first order optimality condition is Weiwei Hu not informative for optimal solutions with initial condition University of Southern California x0 such that C(x0) = 0. To problem (P) we associate [email protected] an auxiliary calculus of variations problem whose solutions connect as quickly as possible the initial conditions to some Michael Hankin constant solutions. Then we deduce the optimality of these Department of Mathematics curves, called MRAPs (Most Rapid Approach Path), for University of Southern California (P). According to the optimality criterium we consider, we [email protected] have to assume a classical transversality condition. We observe that (P) possesses the Turnpike property, the Turn- pike set being given by the preceding particular constant MS35 solutions of the auxiliary problem. An Inverse Problem Involving Words Eladio Ocana Abstract not available. Instituto de Matematica y Ciencias Afines (IMCA) - Lima [email protected] Fadil Santosa School of Mathematics University of Minnesota MS36 [email protected] Results and Experiments of LMBFGS in High Di- mensional nonlinear optimization on WORHP

MS36 Discretized optimal control problems typically lead to high A Decomposition Technique for Multi-agent Pur- dimensional nonlinear optimization. To solve these prob- suit Evasion Games lems we need to determinate the Hessian matrix, which requires a lot of memory consumption. We present an We present a decomposition technique for a class of dif- ffiefficient algorithm for calculating the Hessian matrix, ferential games and find a relation between the regularity namely. the limited memory BFGS method (LMBFGS). of the solution and the possibility to decompose the prob- Afterwards the results from the experiments on a software lem. We have used this technique to solve a pursuit evasion library for mathematical nonlinear optimization WORHP game with multiple agents. are shown. Furthermore several examples from space ap- Adriano Festa plications are presented. Imperial College London Sonja Rauski [email protected] Astos Solutions, Germany [email protected] Richard B. Vinter Imperial College, Exhibition Road, London SW7 2AZ, UK [email protected] MS36 Necessary and Sufficient Conditions for Turnpike Properties of Solutions of Discrete-Time Optimal MS36 Control Systems Linear Programming and Averaging Approaches to Singularly Perturbed Optimal Control Problems We discuss necessary and sufficient conditions for turnpike properties of approximate solutions of nonautonomous It is known that equating of the singular perturbations discrete-time optimal control systems arising in economic parameter to zero may not lead to ”near optimality” in dynamics which are determined by sequences of lower semi- nonlinear singularly perturbed (SP) optimal control prob- continuous objective functions. To have these properties lems (OCPs) and that, if this is the case, then an appro- means that the approximate solutions of the problems are priate way of dealing with such problems is an averaging determined mainly by the objective functions, and are es- approach. In this presentation, we will revisit some of the sentially independent of the choice of intervals and end- existing results and discuss new results on averaging of SP point conditions, except in regions close to the endpoints. OCPs based on linear programming relaxations of the lat- Alexander Zaslavski The Technion Israel Institute of Technololy 170 CT13 Abstracts

[email protected] our approach through several examples.

Sam Coogan MS37 University of California Causal Domain Restriction Techniques Berkeley [email protected] For shortest path problems on graphs, the techniques to restrict the computational domain are well-known. We con- Murat Arcak sider similar domain restriction techniques for continuous University of California-Berkeley optimal trajectory problems. Unlike in the discrete case, [email protected] this results in additional errors depending on grid size and the aggressiveness of restriction. We explore computational efficiency and accuracy of several such techniques. MS38 The resulting methods are particularly useful for higher- Challenges in Computational Nonlinear Control dimensional problems, for which refining the mesh in the Theory: An Overview entire domain is prohibitively costly. Abstract not available. Zachary D. Clawson Cornell University Fariba Fahroo [email protected] Air Force Office of Scientific Research [email protected] MS37 Simplicial A* Algorithm for Optimal Feedback MS38 Planning Partial Observability for the Shallow Water Equa- tions The problem of robot navigation along the shortest path among obstacles on a n-dimensional smooth manifold is We discuss a quantitative measure of partial observability considered. An approximate shortest path is computed us- for the shallow water equations. A first order approxima- ing the Simplicial Dijkstra Algorithm (SDA). Its heuristic- tion of an unobservability index using empirical gramian driven variation, called Simplicial A* Algorithm (SAA), is discussed. For linear systems with full state observabil- avoids a costly omnidirectional wave-front propagation ity, the empirical gramian is equivalent to the observabil- by using heuristics that ”steer” the computation towards ity gramian. We present algorithms for computing par- robot initial position but ensure optimality. Experiments tial observability using the nonlinear system and the lin- show, however, that the SAA completes computations in earized system given by the tangent linear model. This roughly half the time that is required by the SDA. This work has applications to optimal sensor placement for nu- performance improvement renders the SAA advantageous merical weather prediction. over the SDA for practical robotics applications. Sarah King Dmitry Yershov Naval Research Laboratory University of Illinois, Urbana-Champaign Monterey, CA [email protected] [email protected]

Steven LaValle Wei Kang University of Illinois at Urbana-Champaign Naval Postgraduate School [email protected] Department of Applied Mathematics [email protected]

MS38 Liang Xu The Hamilton-Jacobi Bellman Approach for Solv- Naval Research Laboratory ing State-Constrained Optimal Control Problems [email protected] Abstract not available. MS39 Olivier Bokanowski Lab. Jacques-Louis Lions, Univ. Paris-Diderot (Paris 7) Extensions of Chronological Calculus and Chow- Commands, Inria Saclay, France Rashevskii Theorem in Infinite Dimensions [email protected] We present an extension of the Chronological Calculus, originally developed by Agrachev and Gamkrelidze, which MS38 is valid for the study of control systems on infinite- dimensional Ck-smooth manifolds with Ck-smooth dynam- Sum-of-Squares Approach to Synthesis of Switch- ics and controls which are merely measurable in time. Us- ing Guards in Hybrid Systems ing techniques of nonsmooth analysis on smooth manifolds, We propose a numerically-based technique for synthesiz- we derive a generalization of the Chow-Rashevski theo- ing switching guards for hybrid systems to satisfy a given rem for control problems on infinite-dimensional manifolds state-based safety constraint. In particular, we employ sum modeled over smooth Banach spaces. of squares (SOS) programming to design guards defined by Robert J. Kipka semialgebraic sets that trigger mode switches, and we guar- Western Michigan University antee that the synthesized switching policy does not allow [email protected] Zeno executions. We use an iterative algorithm to solve the resulting bilinear SOS program and we demonstrate CT13 Abstracts 171

Yuri S. Ledyaev of an infinite horizon singular stochastic control problem, Department of Mathematics where the state process is a controlled two-dimensional Western Michigan University Lévy process. In our model the controlled process is al- [email protected] lowed to be a general two-dimensional Lévy process, in particular to have jumps. This makes that the HJB equation has an integral term coming from the jumps of the MS39 controlled process, and which is naturally related to the Distributed Continuous-Time Dynamics for Linear integral term of its infinitesimal generator. This is a joint Programming with D. Hernandez and V. Rivero. We consider a general linear programming problem with Harold Moreno-Franco equality and inequality constraints whose information CIMAT structure is distributed across a multi-agent system. We [email protected] develop a distributed algorithmic solution where, in contrast to existing methods, each agent converges to its local component of a global minimizer. Our solution is scalable MS40 with the problem dimension and is based on saddle-point On HJB Equation for a Finite Time Optimal Con- methods for augmented Lagrangians. The stability anal- sumption Problem ysis uses nonsmooth analysis, Lyapunov techniques, and set-valued analysis for dynamical systems. We consider a finite time optimal consumption problem where an investor wants to maximize the expected HARA Dean Richert, Jorge Cortes utility of consumption and terminal wealth. We treat a Department of Mechanical and Aerospace Engineering stochastic factor model that the means returns and the University of California, San Diego volatilities of the risky assets depend on the underlying eco- [email protected], [email protected] nomic factors formulated as the solutions of stochastic differential equations. Using dynamic programming approach we can derive the Hamilton-Jacobi-Bellman (HJB) equa- MS39 tion. We show the existence of a solution for HJB equa- Hybrid Control Systems and Variational Analysis tion. The uniqueness of the solution with certain growth condition will be also proved. Tools from variational analysis are employed to design control laws for the stabilization of hybrid dynamical sys- Shuenn-jyi Sheu tems. Key regularity properties of the set-valued mappings National Cenrtal University, Taiwan emerging from Lyapunov inequalities permitting the con- [email protected] struction of state-feedback laws are determined. In particular, conditions guaranteeing the existence of stabilizing controllers given by continuous functions of the state and MS40 by functions with minimum norm are presented. Examples Shadow Prices and Well Posedness in the Prob- illustrate the conditions and controller constructions. lem of Optimal Investment and Consumption with Transaction Costs Ricardo G. Sanfelice University of Arizona We revisit the optimal investment and consumption model [email protected] of Davis and Norman (1990) and Shreve and Soner (1994), following a shadow-price approach similar to that of Kallsen and Muhle-Karbe (2010). Making use of the com- MS39 pleteness of the model without transaction costs, we re- Variational Analysis and Stochastic Hybrid Sys- formulate and reduce the Hamilton-Jacobi-Bellman equa- tems tion for this singular stochastic control problem to a nonstandard free-boundary problem for a first-order ODE We use results from variational analysis to propose a mod- with an integral constraint. Having shown that the eling framework for a class of stochastic hybrid systems. free boundary problem has a smooth solution, we use it Randomness appears only in the jump map of the hy- to construct the solution of the original optimal invest- brid dynamics. Systems with non-unique solutions are ment/consumption problem in a self-contained manner and handled in the framework. Connections are made to a without any recourse to the dynamic programming princi- recently-developed modeling approach for non-stochastic ple. Furthermore, we provide an explicit characterization hybrid systems that also relies heavily on concepts from of model parameters for which the value function is finite. variational analysis. Time permitting, stability concepts will be described and sufficient Lyapunov conditions provided for stability. Mihai Sirbu University of Texas at Austin Andrew Teel [email protected] University of California Santa Barbara [email protected] Jin Hyuk Choi Carnegie Mellon University MS40 [email protected] Existence of the Value Function for Controlled Two-Dimensional Lévy Processes Gordan Zitkovic The University of Texas at Austin The main purpose of this work is to establish the exis- Department of Mathematics tence, and study the regularity, of a solution to a Hamilton- [email protected] Jacobi-Bellman (HJB) equation arising in the minimization 172 CT13 Abstracts

MS40 Predictive Control The Valuation of Banxico Put Option We address the inherent robustness properties of nonlinear Banco de Mexico (Banxico) issues a novel instrument to systems controlled by suboptimal model predictive control, buy US dollars. They allow to implement Monetary Policy i.e., when a suboptimal solution of the (generally noncon- and control reserve levels. They give the right to sell dollars vex) optimization problem, rather than an element of the back to Banxico with strike price indexed to the FIX. The optimal solution set, is used for the control. We extend option can be exercised ONLY if the current FIX is below existing results by relaxing the continuity conditions of the its own last 20-day moving average. We will discuss the feasible set, and we establish inherent robustness of an ex- arbitrage free price of Banxico’s put option through a new ample featuring both a discontinuous feedback control law stopping problem with constraints. and a discontinuous optimal MPC cost function. Erick Treviño-Aguilar James Rawlings Department of Economics and Finance University of Wisconsin, Madison University of Guanajuato [email protected] [email protected] Gabriele Pannocchia Universiyt of Pisa MS41 [email protected] Online Computation of Backwards-Reachable Sets for Robust Linear Discrete-Time MPC Stephen Wright University of Wisconsin We propose a method of computing feasible sets of states Dept. of Computer Sciences and inputs for linear robust MPC based on locally explor- [email protected] ing parametric solutions of a sequence of linear programming problems. The approach avoids the computationally demanding problem of determining entire backwards MS41 reachable subsets of state space. Instead we use active con- Stability Robustness in Stochastic Model Predic- straints of the feasibility problem to construct constraints tive Control That Generates Discontinuous Feed- for a family of robust MPC solvers via an online algorithm backs with complexity that scales linearly with horizon length. We consider robustness of stochastic stability for discrete- Mark Cannon time stochastic systems under discontinuous control laws, Department of Engineering Science including MPC. For controlled deterministic, discrete-time University of Oxford, UK systems the existence of a continuous Lyapunov function [email protected] for the closed-loop system establishes nominal robustness of asymptotic stability, even with discontinuous control Johannes Buerger, Basil Kouvaritakis law. Under basic regularity assumptions, we show that for Department of Engineering Science discrete-time stochastic systems under discontinuous con- University of Oxford trol laws, asymptotic stability in probability is robust to [email protected], sufficiently small strictly causal perturbations. [email protected] Sergio Grammatico ETH MS41 [email protected] Separable Prediction Structures in Model Predic- tive Control Under Uncertainty Anantharaman Subbaraman UCSB The talk discusses the notion of separable prediction struc- [email protected] ture, which formalizes the deployment of separable state and control action predictions and allows for a theoretically sound and computationally efficient synthesis of model Andrew Teel predictive control (MPC) under uncertainty. The pro- University of California Santa Barbara posed paradigm outperforms the existing robust MPC ap- [email protected] proaches in the linear-polytopic case. Furthermore, it is shown that the framework can be extended, with a relative MS42 ease, to the settings of linear time-varying and nonlinear systems under uncertainty. Pseudospectral Computational Optimal Control for Multiscale Systems Sasa Rakovic St Edmunds Hall In aerospace control applications, systems with multiple University of Oxford, UK time scales are frequently encountered. Since standard [email protected] pseudospectral methods apply the same discretization grid on all state trajectories and controls, it reduces computational efficiency in dealing with dynamical systems with William S. Levine multiple time scales. We will present some recent devel- University of Maryland, College Park opments in pseudospectral computational optima control [email protected] algorithms, which allow states with different time scales to de discretized on different grids. Simulation results on MS41 space applications will also be presented. On the Inherent Robustness of Suboptimal Model Qi Gong CT13 Abstracts 173

Univ. of California, Santa Cruz iments. [email protected] Dejan Milutinovic I. M. Ross Department of Applied Mathematics and Statistics Naval Postgraduate School University of California, Santa Cruz [email protected] [email protected]

Veronica Pellegrini MS43 Dept. of Applied Math & Stats Sparse Controls in State-Constrained Elliptic Op- University of California, Santa Cruz timal Control Problems [email protected] This talk deals with pointwise state-constrained optimal control problems governed by semilinear elliptic equations. MS42 We look for optimal controls that are sparse. To this end, Experimental Implementation of Pseudospectral the L1-norm of the control is added to the cost functional. Motion Planning From the ﬁrst order optimality conditions we deduce the sparsity of the optimal control as well as some new regu- Pseudospectral (PS) motion planning is a version of PS op- larity results for the Lagrange multiplier associated to the timal control theory developed for solving navigation prob- state constraints. Second order conditions and stability lems in robotics. In this talk, we discuss the mathematics properties are also analyzed. of the PS motion planning algorithm and the experimental implementation of the approach on an autonomous ground Eduardo Casas robot. Recent work aimed at developing a small form factor Universidad de Cantabria embedded system for deploying the PS motion planning al- ETSI Ind y de Telecomm gorithm as part of an on board navigation system will also [email protected] be discussed. Mark Karpenko Fredi Tr¨oltzsch Department of Mechanical and Astronautical Engineering Techn. University of Berlin Naval Postgraduate School Department of Mathematics [email protected] [email protected]

Travis Bateman, I. Michael Ross MS43 Naval Postgraduate School Sparse Controls for the Optimization of Traveling [email protected], [email protected] Wave Fronts We consider optimal sparse control problems for reaction MS42 diffusion equations, like the Schlögl equation in spatial di- Iterative Svd Algorithm for Optimal Ensemble mension one and two as well as the FitzHugh-Nagumo sys- Control Synthesis tem in spatial dimension two. Both have in common, that their solutions form pattern of travelling wave fronts or Designing optimal controls for manipulating an ensemble even spiral waves. We derive first-order necessary optimal- of bilinear systems is imperative for wide-ranging appli- ity conditions for the associated control problems as well cations in quantum control and robotics. We develop an as sparsity of the controls and present various numerical iterative optimization-free algorithm for synthesizing op- examples. timal ensemble controls for bilinear systems based on the singular value decomposition. At each step, the bilinear Christopher Ryll ensemble system is approximated by a time-varying linear Technical University of Berlin ensemble system. The convergence of the algorithm is illus- Faculty II Mathematics and Natural Sciences trated theoretically and through examples of pulse design [email protected] in quantum control.

Jr-Shin Li, Anatoly Zlotnik Fredi Tröltzsch Washington University in St. Louis Technical University Berlin, Germany [email protected], [email protected] [email protected] Eduardo Casas MS42 Universidad de Cantabria Stochastic Optimal Control of Nonholonomic Vehi- ETSI Ind y de Telecomm cles [email protected] While stochastic processes are useful models for wind disturbances influencing the dynamics of small unmanned MS43 aerial vehicles, in our work we also use them to model possi- Sparse Optimal Controls for the Linear Wave Equa- ble vehicles paths. Based on this, we compute target track- tion ing controllers, decentralized multi-vehicle formation con- Optimal control problems for the linear wave equation are trol and resolve the spatio-temporal conflict of vehicle tra- 2 jectories. This talk reviews several years of research in my investigated with L (I,M(⊗)) for the space of controls. group and is illustrated by examples, including unmanned Here M(⊗) denotes the space of regular Borel-measures. aerial vehicles, airport traffic and scaled-down robot exper- Its Fenchel-dual problem involves a smooth cost and bi- lateral box-constraints, which are amenable for numerical 174 CT13 Abstracts

realisation. On the basis of the KKT-conditions sparsity routes to perform tasks that are generated over time by properties of the optimal controls can be derived. The nu- an exogenous stochastic process. We consider a variety of merical discretization is based on mixed finite elements in scenarios relevant for applications in robotics and trans- space and a Petrov-Galerkin method in time. The controls portation networks, based on different models for tasks are discretized by Dirac-measures in space. The resulting and/or vehicles. In each DVR scenario, we adopt a rig- optimization problems are solved by a semi-smooth New- orous technical approach that relies upon methods from ton method queueing theory, combinatorial optimization, and stochastic geometry. Karl Kunisch Karl-Franzens University Graz Emilio Frazzoli Institute of Mathematics and Scientific Computing Massachusetts Institute of Technology [email protected] [email protected]

Philip Trautmann Department of Mathematics MS44 University of Graz, Austria Autonomous Data Collection in Underwater Sen- philip.trautmann sor Networks This talk considers two problems related to path planning MS43 for Autonomous Underwater Vehicles (AUVs): (1) data A Priori Error Analysis for Discretization of Sparse gathering from an underwater sensor network equipped Elliptic Optimal Control Problems in Measure with acoustic modems and (2) autonomous inspection of Space the submerged portion of a ship hull. I will present path planning methods that extend variants of the TSP to these In this talk we consider an optimal control problem, where domains, and I will show how nonparametric uncertainty the control variable lies in a measure space and the state modeling can be used to optimize the efficiency of mobile variable fulfills an elliptic equation. This formulation leads data collection. to a sparse structure of the optimal control. For this problem we prove a new regularity result for the optimal so- Geoffrey A. Hollinger lution and derive a priori error estimates for a finite ele- University of South Carolina ment discretization, which significantly improve the esti- [email protected] mates known from the literature. Numerical examples for problems in two and three space dimensions illustrate our Urbashi Mitra results. Electrical Engineering Department University of Southern California Boris Vexler [email protected] Technische Universitaet Muenchen Centre for Mathematical Sciences, M1 Gaurav Sukhatme [email protected] Computer Science Department University of Southern California Konstantin Pieper [email protected] Technische Universitaet Muenchen [email protected] MS44 Procrustes Based Approximations to the Traveling MS44 Salesman Problem Efficient Tracking and Pursuit of Moving Targets by Heuristic Solution of the Traveling Salesman We present a novel heuristic approach for computing the Problem solution of the traveling salesman problem (TSP). We relax the TSP to the Procrustes problem and compute the We consider a problem in which a large number of moving resulting optimal solution. We then construct a homotopy targets must be intercepted by a single agent as quickly between the solution of the Procrustes problem and the as possible. Decision-making about which target to pur- distance matrix to improve the original solution. The solu- sue next is driven by the repeated heuristic solution of the tion of the homotopy is then used to bias the Lin-Kernighan traveling salesman problem (TSP), which is compared to a approach. We find that this approach provides significant greedy algorithm over different problem parameterizations. improvement over the standard approach of using mini- The proposed method is superior when the targets move at mum spanning trees. In particular, for randomly generated low speeds, and its relative performance improves as sensor TSPs, our approach is found to find lower cost solutions in noise worsens. 85% of the problems. For TSPLIB challenge problems, we find lower cost solutions in nearly all tested examples. Brendan Englot, Tuhin Sahai United Technologies Tuhin Sahai [email protected], [email protected] United Technologies [email protected]

MS44 Stefan Klus Stochastic and Dynamic Vehicle Routing Problems United Technologies Research Center in Robotics and Transportation Systems [email protected] This paper surveys recent results in dynamic vehicle routing (DVR) problems, aiming at the on-line planning of Michael Dellnitz University of Paderborn CT13 Abstracts 175

[email protected] Christopher Ryll Technical University of Berlin Faculty II Mathematics and Natural Sciences MS45 [email protected] A Priori Error Estimates for Parabolic Optimal Control Problems with Pointwise Controls MS45 We consider a parabolic optimal control problem with a Adjoint Consistent Gradient Computation with the pointwise control in space, but variable in time, in two Damped Crank-Nicolson Method space dimensions. W use the standard continuous piecewise linear approximation in space and the first order dis- The talk is concerned with a damped version of the Crank- continuous Galerkin method in time to approximate the Nicolson (CN) Method for the solution of parabolic partial problem numerically. Despite low regularity of the state differential equations. As it is well known, the CN-Methods equation, we show almost optimal h2 + k convergence rate needs to be damped in order to cope with irregular initial for the control in L2 norm. The main ingredients of the data, due to the missing smoothing property. Since the ad- analysis are the new global and local error estimates in joint of the CN-Method is again a CN-Method, shifted by L2([0,T]; L∞(Ω)) norms. half a timestep, it is not surprising that a similar problem occurs for the adjoint time stepping scheme. In this talk, Dmitriy Leykekhman we will derive an adjoint consistent damped CN-Scheme Department of Mathematics that ensures sufficient damping of the dual problem. The University of Connecticut necessity of these modifications will be discussed along the [email protected] use of the dual-weighted residual (DWR) method for the adaptive solution of the Black-Scholes equation. The con- Boris Vexler sequences for optimization problems with parabolic PDEs Technische Universitaet Muenchen will be discussed. Centre for Mathematical Sciences, M1 [email protected] Christian Goll University of Heidelberg [email protected] MS45 On a Class of Semi-Infinite Optimization Problems Rolf Rannacher Arising in Pde-Constrained Optimal Control Heidleburg University, Germany [email protected] Many practical applications of PDE-constrained optimization are influenced by finitely many, possibly time- Winnifried Wollner dependent, control parameters rather than by control func- University of Hamburg, Department of Mathematics tions that can vary arbitrarily in space. Oftentimes, point- [email protected] wise state constraints are also part of a problem formulation. The associated active sets then typically admit a certain structure that can be used in the numerical analy- MS46 sis of such problems. In the recent past, Merino, Tröltzsch, Cooperative Control for Flocking of Mobile Agents Vexler, and the speaker have worked on convergence results Using L1 Adaptive Architecture for the finite element discretization of problems with finite- dimensional control space and obtained higher rates than This talk discusses an adaptive cooperative control frame- for control functions. In this talk, we present some related work for a system of multiple mobile agents with nonlin- theoretical results as well as some numerical experiments. ear dynamics. The adaptive cooperative control framework is an extension of L1 adaptive control architecture to Ira Neitzel multi-agent systems, which consists of three components: Technische Universität München, state predictors for extended dynamics of agents, adaptive Department of Mathematics laws, and decentralized control laws. The state predictors [email protected] provide the estimation of each agents extended dynamics which includes its own local dynamics and interacted dy- MS45 namics with other agents. The adaptive laws can make the estimated states from state predictors arbitrarily close Optimal Control Methods for the Schlögl Model to the real states by reducing the time step of integration. Optimal control problems for a class of semilinear parabolic Each control law is a combination of a velocity consensus equations with cubic nonlinearity are considered. This term, a gradient-based term on an artificial potential func- class is also known as the Schlögl model. Main empha- tion, and an uncertainties canceling term. Rather than sis is laid on controlling traveling wave fronts as typical reproducing the flocking motion, this cooperative control solutions to the state equation. We discuss the analysis framework provides a general decentralized coordination of the problem and report on the application of nonlinear method for achieving velocity consensus and regulation of conjugate gradient methods to a variety of numerical test relative distances among nonlinear dynamical agents. 2- examples. Moreover, the performance of model reduction D flocking simulation with nonlinear dynamics is provided by POD is studied. to demonstrate the presented adaptive cooperative control algorithm. Fredi Tröltzsch Techn. University of Berlin Jie Luo Department of Mathematics University of Connecticut, Storrs [email protected] [email protected] Chengyu Cao 176 CT13 Abstracts

Department of Mechanical Engineering MS46 University of Connecticut L1Simplex for Co-Stability in [email protected] Computer-Controlled Systems As the complexity of systems increases, it becomes very MS46 challenging to ensure system reliability in the presence of L∞ Adaptive Control of High Speed Personal Wa- failures. To address this issue, we propose L1Simplex ar- tercraft chitecture, which contains the safety monitor, the high- performance-controller (HPC), the L1-adaptation-based Reliable and effective use of high-speed watercraft for un- high-assurance-controller (HAC), and the control switch- manned operations relies on advanced control systems ca- ing logic. When failures are detected by the safety mon- pable to govern it across its entire operational spectrum. itor, the controller will be switched from the HPC to the The complex nonlinear time-varying dynamics of the wa- HAC. We show that L1Simplex can efficiently handle both tercraft can be partly identified through full scale sea tri- software and physical failures. als, which calls for robust controllers able to manage large system’s uncertainties. The L∞ adaptive control enforces Xiaofeng Wang the desired maneuvering and positioning features into the Department of Electrical Engineering watercraft, providing uniform performances despite of op- University of South Carolina erational and environmental conditions. [email protected]

Roberto Galeazzi Department of Electrical Engineering MS47 Technical University of Denmark The Principle of Least Action and Solution of Two- [email protected] Point Boundary Value Problems on a Limited Time Horizon Niels Ole Holck Image House A conservative system follows a trajectory according to the [email protected] principle of least action. The dynamics may be posed as an optimal control problem. Solution of this allows one Casper Svendsen to convert two-point boundary-value problems into initial MAN Diesel & Turbo value problems through idempotent convolution with the [email protected] fundamental solution. We consider the n-body problem. Representing the gravitational potential as a maximum of quadratic forms, one obtains a differential game. The fun- Lukas R. S. Theisen, Mogens Blanke damental solution is a set of Riccati solutions. Department of Electrical Engineering Technical University of Denmark William M. McEneaney [email protected], [email protected] Dept. of Mechanical and Aerospace Engineering University of California, San Diego [email protected] MS46 Regulation of Anesthesia Delivery via L1-Adaptive Peter Dower Control The University of Melbourne In this paper, we present an application of L1-adaptive [email protected] control design to anesthesia delivery during surgery. Our main objectives are the design of feedback controllers en- MS47 suring that the patient’s Bispectral Index profile tracks a prespecified reference trajectory, and demonstrating ro- Informational Issues in Deterministic Dynamic bustness to inter-patient variability. For the design of the Games controllers we developed patient models based on clinical In deterministic dynamic games the relevant information trial data. Controller switching mechanisms and specific patterns are either open-loop control or state feedback con- safety measures are considered in the paper. Simulation trol. In games where the players use open-loop control the results are provided demonstrating the effectiveness of the optimal controls are obtained using the necessary condi- control methods. tions of optimal control and in games where the players Evgeny Kharisov have perfect information and state feedback action is used University of Illinois at Urbana-Champaign the solution is obtained using the method of dynamic pro- [email protected] gramming. In this talk deterministic two person dynamic games are considered where one player is constrained to use open-loop control whereas his opponent uses feedback Carolyn Beck action we shall refer to mixed games. The solution of Department of General Engineering mixed games requires an adaptation of the method of dy- University of Illinois at Urbana-Champaign namic programming. The difficulties associated with the [email protected] solution of mixed games are discussed and the solution of mixed linear-quadratic games is derived. Marc Bloom School of Medicine of the New York University Meir Pachter [email protected] Air Force Inst of Technology Dept of Electrical Engineering Meir.Pachter@afit.edu CT13 Abstracts 177

MS47 lem will be equivalent to a min-max equilibrium associated Max-Plus Methods for Optimal Attitude Estima- to the game. Our analysis is based on the dynamic pro- tion on So(3) gramming technique. In this work we introduce the use of recently developed Hector Jasso-Fuentes min/max-plus techniques in order to solve the optimal at- CINVESTAV-IPN titude estimation problem in filtering for nonlinear systems [email protected] on the special orthogonal (SO(3)) group. This work helps obtain computationally efficient methods for the synthesis of deterministic filters for nonlinear systems - i.e., optimal MS48 filters which estimate the state using a related optimal con- Stochastic Games Against Nature: Applications to trol problem. The technique indicated herein is validated Finance using a set of optimal attitude estimation example problems on SO(3). We develop a pure game-theoretic approach to option pricing in a multi-dimensional market (rainbow options), Srinivas Sridharan where risk-neutral probabilities emerge automatically from Dept. of Mech. and Aero. Eng. the robust control evaluation. The process of invest- UC San Diego ment is considered as a zero-sum game of an investor [email protected] with the Nature. The talk will be based mostly on my paper http://arxiv.org/abs/1105.3053 (to appear in “Risk and Decision Analysis’) and my Chapter 4 of the MS47 joint monograph P. Bernhard et al “The Interval Market Stochastic Games, Nonexpansive Operators and O- Model in Mathematical Finance: Game-Theoretic Meth- Minimal Structures ods.’ Birkhäuser, 2012, p. 217-290.

We show that the normalized iterates of a non-expansive Vassili Kolokoltsov operator converge (as the number of iterations tends to Statistics Dept, University of Warwick infinity) as soon as this operator is definable in some o- [email protected] minimal structure. This implies convergence of the values, as the horizon tends to infinity, for some classes of zero-sum stochastic games with finitely many states and definable MS48 payoffs and transitions . We also give some applications Average Optimal Strategies for Zero-Sum Markov to risk sensitive control and non-linear Perron-Frobenius Games with Poorly Known Payoff Function on One theory. Side Guillaume Vigeral We are concerned with two-person zero-sum Markov games Université Paris-Dauphine, CEREMADE with Borel spaces under a long-run average criterion. The [email protected] payoff function is possibly unbounded and depends on a parameter which is unknown to one of the players. The Jérôme Bolte parameter and the payoff function can be estimated by im- TSE, UniversitéToulouse1Capitole plementing statistical methods. Thus, our main objective [email protected] is to combine such estimation procedure with a variant of the so-called vanishing discount approach to construct an average optimal pair of strategies for the game. Our results Stéphane Gaubert are applied to a class of zero-sum semi-Markov games. INRIA-Saclay & CMAP Ecole Polytechnique J. Adolfo Minjarez-Sosa [email protected] Departamento de Matemáticas, Universidad de Sonora [email protected] MS48 Fernando Luque-Vásquez The Hamiltonian Cycle Problem and Markov De- Departamento de Matematicas, Universidad de Sonora cision Processes fl[email protected] Abstract not available.

Jerzy Filar MS49 Flinders University Quickest Detection and Sequential Classification in jerzy.filar@flinders.edu.au Systems with Correlated Noise We address the problems of sequential classification and MS48 quickest detection in Brownian channels with correlated Stochastic Differential Games Against Nature: An noise. In the former we demonstrate that the maximum Application to Optimal Control with Unknown Pa- of two SPRTs is asymptotically optimal in identifying the rameters channel with signal as the error probabilities decrease to zero, while in the latter, asymptotic optimality of the min- In this talk we will describe a problem regarding the op- imum of two CUSUM stopping rules in detecting the first timal control of Markov diffusion processes with unknown instance of a signal as the frequency of false alarms de- parameters. Our approach is to rewrite the problem as a creases to zero. game against nature, where player 1 is the controller and player 2 selects, from a given set, the values of the unknown Olympia Hadjiliadis parameter. Hence, an optimal policy for the original prob- Graduate Center of CUNY, New York Brooklyn College, CUNY 178 CT13 Abstracts

[email protected] having fewer constraints determines the optimal value and identiﬁes an optimal impulse control policy.

MS49 Richard Stockbridge A Mean Field Stochastic Growth Model and Its University of Wisconsin - Milwaukee Out-of-Equilibrium Behavior [email protected]

This work introduces a framework of mean field Kurt Helmes consumption-accumulation optimization, where the pro- Humboldt University of Berlin duction dynamics are generalized from stochastic growth [email protected] theory by addressing the negative mean field effect on efficiency. The HARA utility is adopted by the agents. We Chao Zhu construct decentralized strategies by the Nash certainty University of Wisconsin-Milwaukee equivalence approach. We further investigate the out- [email protected] of-equilibrium behavior of the mean field dynamics and identify interesting nonlinear phenomena, including stable equilibria, limit cycles and chaos. PP1 Minyi Huang Modeling Carleton University and Analysis of Adaptive-Conversion-Ratio-Based [email protected] Bidirectional Switched-Capacitor Converter This research deals with the modeling and analysis MS49 of a new adaptive-conversion-ratio-based bidirectional switched-capacitor converter (BSCC) for the bidirectional Apply Stochastic Optimal Control to Invest- step-up/down DC-DC conversion and regulation. The ment and Consumption Problems with Regime- power part consists of one mc-stage cell and one nc-stage Switching cell in cascade between low-voltage (LV) and high-voltage This presentation is concerned with optimal investment (HV) sides to obtain a step-up gain of (mc x nc) from LV and consumption problems in continuous-time Markov to HV sides, or a step-down gain of 1/(mc x nc) from HV regime-switching models. An investor distributes his/her to LV at most. Here, the adaptive-conversion-ratio (ACR) wealth between a risky asset (a stock) and a risk-less asset control with adapting stage number m,n is suggested to (a bond) and consumes at a non-negative rate from the change the topological path for a proper step-up/down bond account. The market parameters (the interest rate, gain: (m x n) or 1/(m x n) (m=1,2,...,mc, n=1,2,...,nc) the appreciation rate and the volatility rate of the stock) so as to improve efficiency, especially for the lower desired are assumed to depend on a continuous-time Markov chain voltage. Finally, the performance of this converter is ver- with finite number of states (the regimes). The objective ified experimentally on a BSCC prototype, and all results of the optimization problem is to maximize the expected are illustrated to show the efficacy of this scheme. total utility of consumption. Due to regime-switching, the Yuen-Haw Chang, Kun-Wei Wu Hamilton-Jacobi-Bellman (HJB) equation for this optimal Department of Computer Science and Information control problem is given by a system of coupled nonlinear Engineering, partial differential equations. We apply the stochastic op- Chaoyang University of Technology, Taichung, Taiwan, timal control methods to study the value functions and the R.O.C. optimal control policies. These results extend that for the [email protected], [email protected] cases without regime-switching.

Ruihua Liu PP1 University of Dayton Department of Mathematics Nonlinear Model Reduction and Control [email protected] In many physical systems, real time or near real time controllers must be computed using a reduced order model. MS49 Furthermore, parameter dependent systems introduce another layer of complexity to the selection and develop- A Measure Approach to Impulse Control Problems ment of the reduced order model. In this presentation, we Only finitely many actions will occur in any bounded inter- demonstrate both the online and offline computation cost val of time for control problems in which each action incurs of several controllers each based on a different paramet- a positive cost. Typically these problems are formulated so ric model reduction technique. Finally, the performance of that the decision-maker selects sequences of stopping times each is measured in a high fidelity simulation. { ∈ } { ∈ } τ := τk : k N andjumpamountsY := Yk : k N Christopher Jarvis, Boris Kramer, John Burns such that at time τk the state process X instantaneously − − Virginia Tech jumps from X(τk )toX(τk )+Yk. The paired sequeneces [email protected], [email protected], [email protected] (τ,Y ) form an impulse control policy. A criterion is then used to compare the efficacy of the policies. This talk establishes a general formulation of impulse control problems PP1 for state processes characterized as solutions to martingale Pseudo-Real Time Monitoring and Control of Ab- problems for their generators. It shows how to reformulate normal Occurrences of Fire Incidents with the Min- a discounted control problem in terms of expected occu- ing of the National Fire Data System (NFDS) pation measures, resulting in an imbedding in an infinite- dimensional linear program. Specific examples are con- Fire prevention/control is a global issue for sustainability. sidered in which the analysis of auxiliary linear programs Every outbreak of fire is analyzed and recorded into NFDS CT13 Abstracts 179

(or similar systems in other countries) on a daily basis. [email protected] Through data-mining, we develop a prediction model considering the context related to fire occurrences and an ef- Guo-Cheng Yang, Qi-Yi Liu, Rui Jiang fective monitoring system for proactive alarm generations, School of Engineering Science based on control charts. Multi-scale monitoring select- University of Science and Technology of China ing appropriate space and time is adapted to reduce false [email protected], [email protected], alarms. Multivariate context-sensitive monitoring is inves- [email protected] tigated with adjusting control limits on-line, based on the predicted moving bandwidth of fire incidents. PP1 Kidon Joo Markowitz’s Mean-Variance Asset-Liability Man- Dept. of Chemical Engineering agement With Regime Switching: A Time- Myongji University Consistent Approach [email protected] In this work, we consider the mean-variance asset-liability Dongil Shin management problem under a continuous time Markov Myongji University regime switching model. This regime switching feature is Dept. of Chemical Engineering good in capturing the bull-bear market feature but no- [email protected] torious in yielding a time-inconsistent optimal solution. This time-inconsistent feature means that the dynamic pro- Jeongpil Park gramming identity is no longer valid and so are its sub- Myongji University, Cheoingu sequence derivations in finding the optimal solution. By [email protected] using an extended Hamilton-Jacobi-Bellman equation, we can successfully solve the problem via finding the equilibrium value function and equilibrium feedback control. PP1 This equilibrium control will be time-consistent in the sense Tip Position Estimation and Control of a Flexible that it is also an equilibrium control for any subproblems. Cantilever with Kalman Estimator Using An Ac- We have also shown that the equilibrium value function is celerometer quadratic in liability and affine in surplus; and the equilibrium control is affine in liability. This is a joint work with Tip position control of a flexible cantilever is difficult due J.Q.Wei,K.C.WongandS.C.P.Yam. to the non-minimum phase dynamics that result from the finite propagating speed of a mechanical wave along the Siu Pang Yung cantilever. In this research, tip position estimation and Math. Dept., University of Hong Kong control using a light and cheap accelerometer that does [email protected] not bring any significant change to the dynamics of the cantilever is studied. A Kalman estimator is designed with the flexible cantilever model to estimate tip position based PP1 on tip acceleration information. The estimated tip position Cauchy Integral Formula to Compute the Expo- is used to a fuzzy logic controller to verify reliability. Also, nential of a Matrix the performance of the estimator with the accelerometer is presented and discussed. In this paper we derive a kind of formula for computing the exponential of a matrix by symbolic computation. This Soon-Geul Lee formula can exactly express each element of the desired Kyung Hee University exponential function of a matrix as a Cauchy integral of Deptartment of Mechanical Engineering some known functions. A numerical solution can be given [email protected] by computing the value of the Cauchy integral by numerical computation.

PP1 Zhinan Zhang Phase Transition and Optimization of Granular College of Mathematics and System Science Flow Down a Chute with Successive Turning Points Xinjiang University, Xinjiang, P.R.China znz [email protected] Granular materials are ubiquitous in industrial, mining and pharmaceutical processes. This paper studies the phase Jianning Zhang transition and optimization of granular flow down a chute College of Mathematics and System Science,Xinjiang with successive turning points with experiments and dis- Universit crete element simulations. The dependence of flux on chan- Urumqi,XinJiang P.R.China 830046 nel width show dilute to dense flow trantision. A remark- znz [email protected] able bistable state appears near the transition point, depending on the original condition. Base on this discovery, one can optimize the flow rate along such channels.

Qing-Song Wu School of Engineering Science, University of Science and Technology of China [email protected]

Mao-Bin Hu University of Science and Technology of China, P.R. China