AN12 and FM12 Abstracts

Home , Kristin Lauter, Panagiota Daskalopoulos, Robert Ghrist

Abstracts are printed as submitted by the authors.

Society for Industrial and Applied Mathematics 3600 Market Street, 6th Floor Philadelphia, PA 19104-2688 USA Telephone: +1-215-382-9800 Fax: +1-215-386-7999 Conference E-mail: [email protected] Conference web: www.siam.org/meetings/ Membership and Customer Service: 800-447-7426 (US & Canada) or +1-215-382-9800 (worldwide) 2 2012 SIAM Annual Meeting • SIAM Conference on Financial Mathematics and Engineering

Table of Contents

Annual Meeting (AN12)

Invited Speakers...... 4

Contributed Lectures...... 7

Minisymposia...... 30

Contributed Posters...... 104

Financial Mathematics and Engineering (FM12)

Invited Speakers...... 126

Contributed Lectures...... 128

Minisymposia...... 139

Contributed Posters...... 159

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). 2012 SIAM Annual Meeting • SIAM Conference on Financial Mathematics and Engineering 3

AN12 Abstracts 4 AN12 Abstracts

IC1 emerged not only as an application domain where compu- On the Shape of Data tational mathematics provide ideas and solutions, but also in spurring new research directions (a new Computational Topology is the mathematical discipline which studies Fluid Dynamics) in geometry (Total Variation regulariza- shape. Data sets typically come with a notion of distance tion and Level Set methods), optimization (primal-dual, which formalizes notions of similarity of data points. The Bregman and Augmented Lagrangian methods, L1 convex- shape of the data is of a great deal of importance in under- iﬁcation), inverse problems (inpainting, compressive sens- standing it - cluster decompositions deﬁne subpopulations ing), and graph algorithms (high-dimensional data analy- of the data and presence of loops often is a clue to the pres- sis). This talk gives an overview of these developments. ence of periodic or recurrent behavior in it. In this talk, we will describe how topological methods can be adapted to the study of data sets, with examples. Tony Chan Department of Mathematics Gunnar E. Carlsson Hong Kong University of Science and Technology Stanford University [email protected] [email protected]

IC5 IC2 Model-Assisted Eﬀective Large Scale Matrix Com- Elliptic Curve Cryptography and Applications putations

In the last 25 years, Elliptic Curve Cryptography has be- Advanced mathematical models very often require the solu- come a mainstream primitive for cryptographic protocols tion of (sequences of) large algebraic linear systems, whose and applications. This talk will give a survey of elliptic numerical treatment should incorporate problem informa- curve cryptography and its applications, including appli- tion in order to be computationally effective. For instance, cations of pairing-based cryptography which are built with matrices and vectors usually inherit crucial (e.g., spectral) elliptic curves. No prior knowledge about elliptic curves properties of the underlying continuous operators. In this is required for this talk. One of the information-theoretic talk we will discuss a few examples where the performance applications I will cover is a solution to prevent pollution of state-of-the-art iterative linear system solvers can be attacks in content distribution networks which use network dramatically enhanced by exploiting these properties. Our coding to achieve optimal throughput. One solution is presentation will focus on structured linear systems stem- based on a pairing-based signature scheme using elliptic ming from the numerical discretization of systems of partial curves. I will also discuss some applications to privacy of differential equations, as well as of optimal control prob- electronic medical records, and implications for secure and lems constrained by partial differential equations. private cloud storage and cloud computing. Valeria Simoncini Kristin Lauter Universita’ di Bologna, Italy Microsoft Research [email protected] [email protected]

IC6 IC3 Multiscale Problems Involving Disorder: A Math- Applying Mathematics to Better Understand the ematical Perspective Ocean The talk will review a series of recent works, including The ocean still represents a realm of discovery in many works in collaboration with X. Blanc, F. Legoll, PL. Lions important respects. We do not, for example, fully under- addressing various aspects, both mathematical and numer- stand the magnitude of mixing in the ocean, and this lack ical in nature,of some multiscale problems involving non of knowledge has real consequences for our ability to model periodic and random modelling. The problems considered and predict future climate. In this talk I will describe how all originate from materials science at different scales. The we have been using ideas from dynamical systems to bring common motivation of the approaches presented is the wish a new degree of clarity to this problem. I will discuss how to keep the computational workload as limited as possible, this has improved our theoretical understanding of some despite the presence of disorder (non periodicity, defects, of the key processes driving ocean circulations and how we randomness) in the problems. have been literally applying mathematics to the ocean by deploying floats in the Southern Ocean to map unstable Claude LeBris manifolds and calculate Lyapunov exponents. CERMICS - ENPC, France [email protected] Emily Shuckburgh British Antarctic Survey, United Kingdom [email protected] IC7 Freeform Architecture and Discrete Differential Geometry IC4 Image Processing and Computational Mathematics The emergence of freeform structures in contemporary architecture raises numerous challenging research problems Image processing has traditionally been studied as a form many of which are related to the actual fabrication and of signal processing, and a subfield of electrical engineering. are of a mathematical nature. The speaker will report on Recently, with the advent of inexpensive and integrated recent progress in geometric computing for freeform archi- image capturing devices, leading to massive data and tecture, with special emphasis on the close relation to dis- novel applications, the field has seen tremendous growth. crete differential geometry. Specific topics to be addressed Within computational mathematics, image processing has include: meshes with planar quadrilateral faces and cor- AN12 Abstracts 5 responding supporting structures, semi-discrete represen- continuum model. Gradient flows on the Functionalized tations for structures from single curved panels, paneling Cahn-Hilliard energy show bi-stability of bilayer, pore, and algorithms and the design of self supporting surfaces. The micelle dominated networks. We present sharp interface transfer of research into the architectural practice will be reductions, including classes of curvature driven flows that illustrated at hand of selected projects. couple to the network structure.

Helmut Pottmann Keith Promislow King Abdullah University of Science Michigan State University [email protected] [email protected]

IC8 IP1 Computing Essentials: What SIAM Members On Mean Field Games Should Know About Emerging Architectures This talk will be a general presentation of Mean Field For most of computing history programmers have experi- Games (MFG in short), a new class of mathematical mod- enced steady performance improvement with little effort, els and problems introduced and studied in collaboration primarily due to increased clock speed and instruction level with Jean-Michel Lasry. Roughly speaking, MFG are parallelism: Riding the commodity performance curve was mathematical models that aim to describe the behavior easy. This has changed. Multicore and GPU processors of a very large number of agents who optimize their de- promise terascale laptop, petascale deskside and exascale cisions while taking into account and interacting with the center systems. But realizing this potential is challenging: other agents. The derivation of MFG, which can be justi- Riding the new commodity performance curve requires par- fied rigorously from Nash equilibria for N players games, allel execution. Furthermore, the number of components in letting N go to infinity, leads to new nonlinear systems high-end systems will increase soft and hard system errors. involving ordinary differential equations or partial differ- We discuss the essentials of how to develop algorithms and ential equations. Many classical systems are particular software in order to realize parallel performance today and cases of MFG like, for example, compressible Euler equa- prepare for the future. tions, Hartree equations, porous media equations, semilin- ear elliptic equations, Hamilton-Jacobi-Bellman equations, Michael A. Heroux Vlasov-Boltzmann models... In this talk we shall explain Sandia National Laboratories in a very simple example how MFG models are derived and [email protected] present some overview of the theory, its connections with many other fields and its applications. IC9 Pierre-Louis Lions Overcoming the Tyranny of Scales in Subsurface Collège de France Flow and Reactive Transport Simulation [email protected]

A grand challenge facing subsurface modelers is the dispar- ity between length and time scales at which fundamental IP2 processes are controlled and those at which predictions are Complex Adaptive Systems and the Challenge of needed. This presentation will describe the application of Sustainability multiscale simulation methods to this challenge. Particu- lar focus will be given to 1) hybrid multiscale simulations, The continual increase in the human population, magni- which directly couple pore- and continuum-scale models, fied by increasing per capita demands on Earth’s limited and 2) integration of genome-scale microbial metabolism resources, raise the urgent mandate of understanding the models into field-scale bioremediation analyses. We will degree to which these patterns are sustainable. The scien- present our multiscale analysis platform (or MAP), a com- tific challenges posed by this simply stated goal are enor- munity resource for navigating the breadth of multiscale mous, and cross disciplines. What measures of human wel- methods and identifying which tools are best suited to spe- fare should be at the core of definitions of sustainability, cific problems. and how do we discount the future and deal with problems of intra-generational and inter-generational equity? How Timothy D. Scheibe do environmental and socioeconomic systems become or- Hydrology Technical Group ganized as complex adaptive systems, and what are the Pacific Northwest National Laboratory implications for dealing with public goods at scales from [email protected] the local to the global? How does the increasing intercon- nectedness of coupled natural and human systems affect the robustness of aspects of importance to us, and what IC10 are the implications for management. What is the role of Network Formation and Ion Conduction in social norms, and how do we achieve cooperation at the Ionomer Membranes global level? All of these issues have parallels in evolutionary biology, and this lecture will explore what lessons Selective charge transport is an essential step in efficient can be learned from ecology and evolutionary theory for energy conversion. Ionomer membranes are formed from addressing the problems posed by achieving a sustainable cross-linked, charged polymers. They imbibe solvent to future. form nanoscaled network structures which lie at the heart of many energy conversion devices. Experimental data Simon Levin shows that the networks are hysteretic, evolving on time Princeton University, USA scales of minutes and hours, far outside the reach of molec- [email protected] ular simulations. We present a novel reformulation of the classical Cahn-Hilliard free energy that permits the inclusion of solvation energy and counter-ion entropy within a 6 AN12 Abstracts

IP3 IP6 The Isoperimetric Problem Revisited: Exposing Multifidelity Modeling for Identification, Predic- Eulers 1744 Proof of Necessity as a Proof of Suffi- tion and Optimization of Large-scale Complex Sys- ciency, as Such the First and Shortest in History tems In this talk the speaker will outline the remarkable life Often we have available several numerical models that de- of the isoperimetric problem (Determine, from all simple scribe a system of interest. These numerical models may closed planar curves of the same perimeter, the one that vary in ”fidelity” or ”skill,” encompassing different reso- encloses the greatest area) and argue that it has been the lutions, different physics, and different modeling assump- most influential mathematics problem of all time. In 1744 tions; they may also include surrogates such as reduced- Euler constructed multiplier theory to solve the isoperimet- order models. A multifidelity approach seeks to exploit ric problem; however he concluded that his theory was only optimally all available models and data. This talk dis- necessary and not sufficient to prove that the circle was the cusses the key elements of multifidelity modeling: con- solution. Some 130 years later Weierstrass constructed his structing reduced-order models, quantifying model uncer- elegant sufficiency theory for problems in the calculus of tainties, selecting models with appropriate fidelity for the variations and used it to give the first complete proof that prediction/decision task at hand, and synthesizing multi- the circle solved the isoperimetric problem. The speaker fidelity information. We show the benefit of multifidelity will demonstrate that Eulers original proof was merely an modeling for the tasks of prediction, design optimization, observation away from establishing sufficiency. As such it and uncertainty quantification. should be viewed as the first and shortest solution to the isoperimetric problem in history. Karen E. Willcox Massachusetts Institute of Technology Richard A. Tapia [email protected] Rice University Dept of Comp & Applied Math [email protected] SP1 AWM-SIAM Sonia Kovalevsky Lecture: The Role of Characteristics in Conservation Laws IP4 Complex Networks. A Tour d’ Horizon Sonya Kovalevsky, in the celebrated Cauchy-Kovalevsky theorem, made clear the significance of characteristics in The field of complex network is gently introduced. The partial differential equations. In the field of hyperbolic classical concepts of small-world and scale-freeness are conservation laws, characteristic curves (in one space di- briefly discussed. Then, the problem of communicability mension) and surfaces (in higher dimensions) dominate the in complex networks is motivated and analyzed by consid- behavior of solutions. Some examples of systems exhibit ering the use of matrix functions. The concept of network interesting, one might even say pathological, characteristic communicability is then applied to a few real-world situa- behavior. This talk will focus on ways that characteristics tions. It motivates a new Euclidean metric for networks, in systems of conservation laws give information about the which allows to embed every network into a hypersphere of systems being modeled. certain radius. Finally we discuss dynamical processes on networks. In particular we show how to extend these con- Barbara Lee Keyfitz cepts to the consideration of long-range interactions among The Ohio State University the agents in complex networks. The consequences of these Department of Mathematics extensions for real-world situations are briefly discussed. bkeyfi[email protected]

Ernesto Estrada University of Strathclyde SP2 [email protected] The John von Neumann Lecture: Liquid Crystals for Mathematicians IP5 Liquid crystals form an important class of soft matter sys- Linear Algebra Methods for Data Mining with Ap- tems with properties intermediate between solid crystals plications to Materials Science and isotropic fluids. They are the working substance of liquid crystal displays, which form the basis of a huge multi- The field of data mining is the source of many new, in- national industry. The lecture will describe these fascinat- teresting, and sometimes challenging, linear algebra prob- ing materials, and what different branches of mathematics, lems. In fact, one can say that data mining and machine such as partial differential equations, the calculus of vari- learning are now beginning to shape a ”new chapter” in ations, multiscale analysis, scientific computation, dynam- numerical linear algebra. We will illustrate the key conical systems, algebra and topology, can say about them. cepts and discuss dimension reduction methods which play a major role in machine learning. The synergy between high-performance computing, efficient electronic structure John Ball algorithms, and data mining, may potentially lead to ma- Oxford Centre for Nonlinear PDE Mathematical Institute jor discoveries in materials. We will report on our first ex- Oxford periments in ‘materials informatics’, a methodology which [email protected] blends data mining and materials science.

Yousef Saad SP3 Department of Computer Science Past President’s Address: Reflections on SIAM, University of Minnesota Publishing, and the Opportunities Before Us [email protected] Upon taking up the post of president I had, of course, for- AN12 Abstracts 7 mulated my priorities for SIAM. This talk provides a good connectivity and the way individual risk can become over- occasion to revisit some of those. One area turned out all, systemic risk when it is diversified by inter-connectivity. to play a vastly larger role than I would have anticipated, I will discuss theoretical issues that come up with mean- namely mathematical publishing and many issues associ- field and other models and will also show results of numer- ated with it, ethical, technological, economic, political, and ical simulations. scientific. The future of scholarly publishing is far from clear, but one thing seems certain: big changes are needed George C. Papanicolaou and will be coming. We, as mathematicians, are major Stanford University stakeholders. We should also be major agents in guiding Department of Mathematics these changes. I will present some of my observations and [email protected] thoughts as we confront the opportunities before us. Douglas N. Arnold CP1 School of Mathematics A-Posteriori Verification of Optimality Conditions University of Minnesota for Control Problems with Finite-Dimensional [email protected] Control Space

In this paper we investigate non-convex optimal control SP4 problems.We are concerned with a-posteriori verification of W. T. and Idalia Reid Prize Lecture: Large Alge- sufficient optimality conditions.If the proposed verification braic Properties of Riccati Equations method confirms the fulfillment of the sufficient condition then a-posteriori error estimates can be computed. A spe- In the eighties there was considerable interest in the alge- cial ingredient of our method is an error analysis for the braic properties of the following Riccati equation Hessian of the underlying optimization problem.We derive conditions under which positive definiteness of the Hessian A∗X + XA XBB∗X + C∗C =0, (1) of the discrete problem implies positive definiteness of the − Hessian of the continuous problem.The article is comple- where A, B, C A, a Banach algebra with identity, and mented with numerical experiments. the involution operation∈ . Conditions are sought to ensure that the above equation∗ has a solution in A.Theresults Saheed Ojo Akindeinde were disappointing and the problem was forgotten until Johann Radon Institute for Computational and this century when engineers studied the class of spatially Applied Mathematics (RICAM) distributed systems. One application was to control forma- [email protected] tions of vehicles where the algebraic property was essential. This case involves matrices A, B, C with components in a Daniel Wachsmuth scalar Banach algebra. Positive results are obtained for RICAM, Linz, Austria both commutative and noncommutative algebras. [email protected] Ruth Curtain University of Groningen, Netherlands CP1 [email protected] Modeling and Control of Nanoparticle Delivery to Tumor Sites with Experimental Validation SP5 Currently, experimental trials are underway to investigate I.E. Block Community Lecture: Creating Reality: the therapeutic bioavailability of nanoparticles used in the The Mathematics Behind Visual Effects treatment of certain types of cancers. This presentation will discuss the development of mathematical models to Film-makers have long realized one of the best ways to predict and controls to regulate the concentration of such convince audiences that a computer-generated effect, like a nanoparticles in a mammalian body post-injection. The stormy ocean, is real is to numerically solve physical equa- elimination of nanoparticles from the blood and into tar- tions describing the motion, bringing mathematics and geted tumors and the reticulo-endothelial system will be scientific computing into the forefront of animation. As evaluated. we progress to solving more physics more accurately and faster, a whole new way of working has emerged, ”virtual Scarlett S. Bracey, Katie A. Evans, D. Patrick O’Neal, practical effects”, where artists set up shots virtually as Isidro B. Magaña they’d want to in the real world and let simulated physics Louisiana Tech University take over. I’ll demonstrate how a little mathematical anal- [email protected], [email protected], [email protected], ysis can make a world of difference to making a film. [email protected]

Robert Bridson University of British Columbia CP1 [email protected] Discrete Approximations of Controlled Stochastic Systems with Memory

JP1 This paper considers discrete approximations of an opti- Systemic Risk mal control problem in which the controlled state equation is described by a general class of stochastic functional dif- What is systemic risk, how do we model it,how to we an- ferential equations with a bounded memory. Three differ- alyze it, and what are the implications of the analysis? I ent approximation methods, namely (i) semidiscretization will address these issues both in a larger historical context scheme; (ii) Markov chain approximation; and (iii) finite and within current research mathematical finance. The key property of systems subject to systemic risk is their inter- 8 AN12 Abstracts difference approximation, are investigated. controlled linear advection equation: Mou-Hsiung Chang ρt + ·(fρ)=χA(x)u(x, t), (2) U. S. Army Research Office ρ(x, 0) = ρ0(x); ρ Γ =0, Mathematics Division | i [email protected] where ρ is the state, u(x, t) L2([0,τ]; A)isthecontrol ∈ input, f(x)isasmoothvectorfield,Γi X is the inflow ⊂ CP1 portion of the boundary ∂X,andρ0(x) is the initial state. Steady State Sets of Non-Linear Discrete-Time The result states that the region of controllability in time Control Dynamical Systems with Singular Distur- τ is the portion of X that is touched by solutions of the bance ODEx ˙ = f(x); x(0) = x0 in time τ emanating from initial points x0 A. An explicit expression for the controllability ∈ Finding steady state sets is an important topic in the study (and by duality, the observability) gramian is shown, and of dynamical systems. In this paper, we concentrate our ef- some ideas to use the gramians for optimal placement of forts to non-linear discrete-time control dynamical systems actuators and sensors will be discussed. with large singular disturbance that are modeled by multiple valued iterative dynamical systems or set valued dy- Rajeev Rajaram namical systems. Because the traditional means of calculus Kent State University usually fails under the extensive influence of singularity, the [email protected] use of alternative methods such as multiple valued iterative dynamics modeling is necessary in general. Under the mul- CP1 tiple valued iterative dynamics modeling, the steady state sets of non-linear discrete-time control dynamical systems Solving Optimal Control Problems with Control turn out to be the locally maximal strongly full-invariant Delays Using Direct Transcription sets, and we discuss how to reach it in countable steps so Numerical solutions of optimal control problems with de- that the finite step approximation problem is well posed. lays are important in industry. Solutions to these types of We also discuss the invariant fractal structure that often problems are difficult to obtain via analytic techniques. Di- arises due to the large singular disturbance. rect Transcription is a popular numerical method used to Byungik Kahng compute the solutions of optimal control problems. In this University of North Texas at Dallas paper we report on the progress and challenges of develop- [email protected] ing a general purpose industrial grade direct transcription code that can handle problems with both state and control constraints and delays. CP1 Karmethia C. Thompson Sparsity-Promoting Optimal Control of Dis- North Carolina State Univ tributed Systems Department of Mathematics We design sparse and block sparse feedback gains that min- [email protected] imize variance amplification of distributed systems. We first identify patterns that strike a balance between the Stephen L. Campbell quadratic performance and controller sparsity. We then North Carolina State University optimize the feedback gains subject to the structural con- Department of Mathematics straints determined by the identified sparsity patterns. We [email protected] employ the alternating direction method of multipliers and exploit structure of sparsity-promoting terms to decompose John T. Betts the minimization problem into sub-problems that can be Partner of Applied Mathematical Analysis, LLC solved analytically. [email protected] Fu Lin Electrical and Computer Engineering CP2 University of Minnesota A Discrete Dynamical Systems Model to Study the [email protected] Interaction Between Arctic Sea-Surface Tempera- ture and Sea-Ice Cover Makan Fardad Electrical Engineering & Computer Science We propose a mathematical model involving discrete dy- Syracuse University namical systems to understand the interaction between [email protected] sea-surface temperature and sea-ice cover over the Arctic Ocean. In particular, we use ideas from dynamical systems Mihailo R. Jovanovic such as bifurcations and basins of attraction of equilibria Electrical and Computer Engineering along with basic probability theory to make future projec- University of Minnesota tions about the possibility of extinction of Arctic sea-ice [email protected] cover, one of the top five tipping points in the Earth’s climate. Observed data from multiple sensors will be used to validate the model. The implications and caveats of the CP1 future projections made by our model will be explored. Exact Controllability of the Linear Advection Sukanya Basu Equation with Interior Controls Grand Valley State University, An exact controllability result is discussed for the following Allendale, MI [email protected] AN12 Abstracts 9

CP2 allows for arbitrary, range-dependent sound speed data as Numerical Studies of Eor by Asp-Flooding input. Of the new techniques leading to increase oil production, Sheri L. Martinelli EOR, which uses chemical additives, is one of the most Brown University promising. Chemical flooding is a way to recover addi- Naval Undersea Warfare Center Newport tional oil after water-flooding. It involves adding sufficient [email protected] amounts of chemical species to injected fluids to change phase properties in a way that will enhance oil recovery. However, it is still a big problem that how to appropriately CP2 choose the displacing fluids based on their properties and How Do You Determine Whether The Earth Is the sequence in which these should be injected to produce Warming Up? oil out as much as possible. In this talk, we will present our results for optimal profiles on Polymer-Water flooding How does one determine whether the extreme summer tem- as well as Alkaline-Surfactant-Polymer-Water flooding. It peratures in Moscow of a few years ago was an extreme will be discussed for the cases of constant and variable con- climatic fluctuation or the result of a systematic global centrations of injected chemicals. The research reported warming trend? It is only under exceptional circumstances here has been made possible by a grant NPRP 08-777-1- that one can determine whether a climate signal belongs 141 from the Qatar National Research Fund (a member of to a particular statistical distribution. In fact, climate sig- The Qatar Foundation). The statements made herein are nals are rarely ”statistical;” other than measurement er- solely responsibility of the authors. rors, there is usually no way to obtain enough field data to produce a trend or tendency, based upon data alone. We Xueru Ding propose a trend or tendency methodology that does not Texas A&M University at Qatar make use of a parametric or statistical assumption. The [email protected] most important feature of this trend strategy is that it is defined in very precise mathematical terms. Prabir Daripa Juan M. Restrepo Texas A&M University Departments of Mathematics, Atmospheric Physics, and [email protected] Physics University of Arizona CP2 [email protected] Bregman Iterations for Geosounding Inversion Darin Comeau A novel algorithm for nonlinear inversion based on Breg- Program of Applied Mathematics man iterations is applied to electrical, electromagnetic and University of Arizona resistivity soundings. Tikhonov’s inversion method, com- [email protected] monly employed for solving inverse problems solving, produces smooth, ”smeared” models. Several techniques have Hermann Flaschka been proposed in order to improve the model development Mathematics Department in layered models, particularly in geophysics. Some change University of Arizona the norm to L1 or total variation, and others propose a fl[email protected] piecewise-continuous model. In the case of L1 optimization, a computationally expensive solver is required. Breg- man iterative method has recently proposed for L1 mini- CP2 mization problems, particularly when a sparse representa- An Adaptive Strategy with Unconditional Con- tion is required. An iterative, coordinate descent method vergence for Solving Nonlinear Coupled Flow and is implemented based on Bregman distance. Results for Transport Equations in Porous Media several data of electrical, electromagnetic and resistivity soundings are presented. We propose a new hybrid strategy for solving flow and transport equations in porous media . At each iteration, Hugo Hidalgo after updating pressure from a reduced system of linear CICESE-Ciencias de la Computacion equations, we decompose the phases flow graph into its [email protected] strongly connected components. Saturation field is updated by traversing the resulting graph from upstream to Enrique Gomez-Trevino downstream. We update pressure and saturation simulta- CICESE-Geofisica Aplicada neously in counter current flow regions identified by multi- [email protected] cell components to resolve the tight coupling. The results show that the algorithm is convergent for very large time step sizes. CP2 High Frequency Acoustic Propagation Using Level Mohammad Shahvali Set Methods Stanford University [email protected] We discuss an application of the level set method to underwater acoustic propagation. The level set model provides a Hamdi Tchelepi way to compute acoustic wavefronts on a fixed grid, so that Stanford University the user has more control over the accuracy of the final so- Energy Resources Engineering Department lution than with the standard Lagrangian approaches (i.e., [email protected] ray tracing). The method includes high order numerical boundary conditions for reflections from hard surfaces and 10 AN12 Abstracts

CP2 American Institute of Mathematics Use of Integral Transforms in Analyzing Nmr Data [email protected]

In Nuclear Magnetic Resonance (NMR) applications to Dale Olesky study porous media, the measured data is modeled as Department of Computer Science a Laplace transform of the probability density function University of Victoria (PDF) of relaxation times. In this presentation, we de- [email protected] scribe a novel method to directly compute linear functionals of the PDF without computing the PDF. This method Pauline van den Driessche involves a linear transform of the measured data using in- Department of Mathematics and Statistics tegral transforms. Diﬀerent linear functionals of the PDF University of Victoria can be obtained by choosing appropriate kernels in the in- [email protected] tegral transforms.

Lalitha Venkataramanan, Fred Gruber, Tarek Habashy CP3 Schlumberger [email protected], [email protected], Matrix Computation and Its Application to Signal [email protected] Processing First part of this presentation aims to leverage computing of the determinant of a 3 3matrixwhoseith CP3 i i i ×i 1 i 1 i 1 row is deﬁned by [a1 +a2 +a3 a1 − +a2 − +a3 − An Object-Oriented Linear System Solver for Mat- i 2 i 2 i 2 a − +a − +a − ] without expanding. Second part of lab 1 2 3 this presentation is the application to signal processing, The MATLAB backslash is an elegant interface to a suite speciﬁcally to non-uniform sampling [Yih-Chyun Jenq, of high-performance methods for solving linear systems Perfect Reconstruction of Non-Uniformly Sampled Signal, and least-squares problems. However, its simplicity pro- IEEE Trans. Inst.&Meas. 1997]. hibits the reuse of its factorization for subsequent sys- Wei-Da Hao tems. Naive MATLAB users also have a tendency to Department of Electrical Engineering and Computer translate mathematical expressions from linear algebra di- 1 Science rectly into MATLAB, so that x = A− b becomes the Texas A/&M University-Kingsville unfortunate x=inv(A)*b. To address this problem, an [email protected] object-oriented factorize method is presented. Via operator overloading, solving two linear systems can be written as F=factorize(A); x=F b; y=F c, where A is factorized Yih-Chyun Jenq only once. The selection\ of the best\ factorization method Department of Computer and Electrical Engineering 1 is hidden from the user. The expression x = A− b trans- Portland State University lates into x=inverse(A)*b, without computing the inverse. [email protected]

David H. Chiang Timothy A. Davis Department of Compuetr and Electrical Engineering University of Florida Portland State University Computer and Information Science and Engineering [email protected] [email protected]

CP3 CP3 Classiﬁcation of Potentially Eventually Exponen- Sign Patterns That Allow Strong Eventual Non- tially Positive Sign Patterns of Small Order negativity AmatrixA is eventually exponentially positive if there ex- tA A sign pattern is potentially eventually nonnegative (po- ists a positive real number t0 such that for all t t0,e > tentially strongly eventually nonnegative) if there is a ma- 0. A sign pattern is a matrix having entries in +≥, , 0 .A trix with this sign pattern that is eventually nonnegative sign pattern is potentially eventually exponentially{ − } pos- (eventually nonnegative and has some power that is both itive (PEEP)A if there exists a matrix A in the qualitative nonnegative and irreducible). The study of potentially class of such that A is eventually exponentially positive. eventually nonnegative sign patterns is hindered by nilpo- A classiﬁcationA of all 2x2 and 3x3 PEEP sign patterns is tent matrices and matrices which have powers that are re- given. ducible with a nilpotent diagonal block. This talk presents results about potentially strongly eventually nonnegative Xavier Martinez-Rivera,MarieArcher sign patterns. Iowa State University [email protected], [email protected] Craig Erickson Iowa State University Minerva Catral [email protected] Xavier University [email protected] Minerva Catral Xavier University Craig Erickson [email protected] Iowa State University [email protected] Leslie Hogben Iowa State University, Rana Haber AN12 Abstracts 11

Florida Institute of Technology paths in the topological gradient image. This coupled al- rhaber2010@my.ﬁt.edu gorithm quickly provides accurate and connected contours. We present applications to inpainting and segmentation. Leslie Hogben Iowa State University, Didier Auroux American Institute of Mathematics University of Nice, France [email protected] [email protected]

Antonio Ochoa Laurent D. Cohen California State Polytechnic University CNRS, UMR 7534 [email protected] Universite Paris-Dauphine, CEREMADE [email protected]

CP3 Mohamed Masmoudi Positive Semidefinite Zero Forcing University of Toulouse [email protected] The zero forcing number Z(G) is used to study the maximum nullity/minimum rank of the family of symmetric matrices described by a simple, undirected graph G.We CP4 study the positive semidefinite zero forcing number Z+(G) Iterative Wavefront Reconstruction in Adaptive and some of its properties. In particular, we determine Optics the maximum positive semidefinite nullity and positive semidefinite zero forcing number for a number of graph Obtaining high resolution images of space objects from families appearing in the AIM minimum rank graph cata- ground based telescopes is challenging, and often requires log. computational post processing using image deconvolution methods. Good reconstructions can be obtained if the con- Travis Peters volution kernel can be accurately estimated. The convolu- Iowa State University tion kernel is defined by the wavefront of light, and how [email protected] it is distorted as it propagates through the atmosphere. We describe the wavefront reconstruction problem - a new linear least squares model that exploits information from CP3 multiple measurements. On Estimating Hitting and Commute Times for Large Dense Digraphs Qing Chu, James G. Nagy Department of Mathematics & Computer Science Recent studies have established that the lengths of random- Emory University commutes between a source-destination pair, in large dense [email protected], [email protected] undirected-graphs, can be well approximated in terms of scaled degrees of the end-point vertices, which implicates the relevance of commute times as a distance in machine CP4 learning tasks. In this work we generalize the approxima- Parallel Markov Chain Monte Carlo Methods in tions to strongly connected directed-graphs, albeit in terms Optical Tomography of the steady-state-stationary-probability distribution. In so doing, we develop a theoretical framework for these ap- Markov Chain Monte Carlo (MCMC) is a standard sam- proximations, without resorting to the interplay between pling method in Bayesian inference. However, it is slow be- undirected graphs and electrical-networks, an analogy on cause it requires that the forward model is solved at every which previous studies rely and, more importantly, one iteration. Furthermore, the standard algorithm is inher- that does not apply to directed-graphs. ently sequential. We will discuss successful parallelization techniques involving a single and a multiple chains method Gyan Ranjan, Zhi-Li Zhang that both shorten computations and improve sample qual- University of Minnesota ity. We will then show results from applying them to a Computer Science real-world, optical tomography problem. [email protected], [email protected] Kainan Wang, Wolfgang Bangerth Daniel L. Boley Texas A&M University University of Minnesota [email protected], [email protected] Department of Computer Science [email protected] CP5 Using An Old Traffic Flow Model to Gain New In- CP4 sights into a Biological Process Contour Detection and Completion for Inpainting The use of a nonlinear PDE to model the elongation pro- and Segmentation Based on Topological Gradient cess on ribosomal RNA is discussed. Experimentally, the and Fast Marching Algorithms motion of a transcription complex experiences multiple We combine the topological gradient, a powerful method pauses, and the density of elongating complexes may be for edge detection in image processing, and a minimal path sufficiently high to experience traffic jams. The traffic flow method in order to find connected contours. The topolog- model includes the presence of non-uniform distributions ical gradient provides a more global analysis of the im- of pauses along the rrn operon and is used to estimate age than the standard gradient, and identifies the main the instantaneous elongation rate. Discontinuous Galerkin edges. Then the fast marching algorithm identifies minimal 12 AN12 Abstracts methods are used for the model simulations. CP5 Modeling Behavior: Using Game Theory and Pop- Lisa G. Davis ulation Modeling to Explain Sub-Maximal Para- Montana State University sitism [email protected] We examine the implications of spatial structure on the evolution of parasitism rates for a well-characterized in- CP5 teraction between a parasitoid wasp and host butterfly on Interior-Point Methods for An Optimal Control In- a fragmented landscape. We present multiple evolution- fluenza Model ary hypotheses, formulated as mathematical models, and show the extent to which landscape features (patch quality, We introduce a discrete optimal control problem in order density, and connectedness) and host attributes (dispersal to minimize the number of infected individuals on a single ability, reproductive success, mortality) affect the viabil- influenza outbreak. We evaluate the effect of social distanc- ity of this mechanism; thus unveiling the role of spatial ing and antiviral treatment as control policies. We solve the processes in the interaction. problem by using Forward-Backward and Interior-Point Method. Our simulations show that Interior point method Kathryn Montovan gives more robust results than Forward-Backward method. Cornell University Finally we introduce an isoperimetric constraint to con- [email protected] sider limited resources.

Paula A. Gonzalez Parra CP6 University of Texas at El Paso Modeling Cell Movement Through Collagen Using [email protected] the Level Set Method

Leticia Velazquez Cell movement affects different biological processes. In the Department of Mathematical Sciences body, cells move through a three-dimensional network of The University of Texas at El Paso collagen, filaments, and other proteins. We are modeling [email protected] cell movement through a series of deformable obstacles representing this network. We use the level set method to Sunmi Lee track the membrane of the cell and borrow concepts from Mathematical, Computational and Modeling Sciences the theory of beams to model the network. Our goal is to Center, use the simulations to model the environment within the Arizona State University, body and to investigate variations of this environment on [email protected] cell movement. Magdalena Stolarska Carlos Castillo-Chavez University of St. Thomas Arizona State University and Department of Mathematics Department of Mathematics [email protected] [email protected] Matthew Fox CP5 University of St. Thomas Modeling the Effect of a New Antibiotic on the [email protected] Transmission of Antimicrobial Resistant Bacteria in a Hospital Setting CP6 The increase in antibiotic resistance continues to pose a A Sparse Update Method for the in-Silico Manip- public health risk as very few new antibiotics are being ulation of Biological Signaling Pathways produced, and the prevalence of bacteria resistant to currently prescribed antibiotics is growing. In this talk, we use Radon Institute for Computational and Applied Mathe- both deterministic and stochastic mathematical models to matics Austrian Academy of Sciences Defective biological analyze the benefits and limitations of the introduction of a signaling pathways are linked to various pathological con- new antibiotic in both a large hospital setting and a smaller ditions and the correction of dysfunctional qualitative be- unit within a hospital under different administration pro- haviour such as oscillation or bistability is a major goal tocols. of pharmaceutical and clinical research. Based on differential equation models of the underlying biochemical re- Michele Joyner action networks we formulate nonlinear inverse problems East Tennessee State University and suggest a sparse update algorithm that determines a [email protected] comprehensible number of candidate network intervention sites. The practicability of our approach is demonstrated Cammey Manning by an example related to defective apoptotic signaling. Meredith College Philipp Kuegler [email protected] RICAM, Austrian Academy of Sciences Austria Brandi Canter [email protected] East Tennessee State University [email protected] CP6 An Unbiased Estimator of Noise Correlations un- AN12 Abstracts 13 der Signal Drift CP7 Estimation of 3D Microstructural Band Properties Estimation of correlations in noises is important in large- in Dual Phase Steel Assuming An Oriented Cylin- scale modeling and data analysis. In neuroscience, small der Model correlations in noises (trial-to-trial response variations) can decrease coding capacity by sensory neurons dramatically. Oriented cylinders in an opaque medium represent mi- Although significant noise correlation has been reported crostructural banding in steels. The medium is sliced and from almost all cortical areas, nonstationarity, such as a on the cut plane, rectangular projections of the cylinders drift in signals (mean responses) might engender artificial are observed. The marginal distributions of the cylinder correlations even if no actual correlation exists. Although radii and heights, aspect ratio, surface area and volume attempts to estimate noise correlation under changing envi- are estimated from the rectangle length and height distri- ronments have been made, they were useful only for specific butions. This estimation procedure is used on real banded cases. This study presents consideration of a bivariate nor- microstructures for which nearly 90 µm of depth have been mal distribution for activities of two neurons and advances observed via serial sectioning. the proposition of a semiparametric method for estimating its covariance matrix in an unbiased fashion, whatever the Kimberly S. McGarrity time course of the signal is. Materials innovation institute (M2i) Delft University of Technology Keiji Miura [email protected] JST PRESTO, Harvard University [email protected] Jilt Sietsma, Geurt Jongbloed Delft University of Technology CP6 [email protected], [email protected] Using Maps to Predict Activation Order in Multi- phase Rhythms CP7 We consider a network of three heterogeneous coupled Thermodynamically Compatible Model of Yield units, each described by a planar dynamical system on Stress Polymeric Fluids two timescales, motivated by recent models for respiratory rhythmogenesis. Each unit’s intrinsic dynamics supports We want to present some results on mathematical model- an active state and an inactive state. We analyze solutions ing of polymeric yield stress fluids which have the proper- in which the units take turns activating, allowing for any ties of both elastic solids and fluids. We try to investigate activation order, including multiple activations of two of this problem using the approach of multiphase continuum the units between activations of the third. The analysis mechanics. We develop the two-phase solid-fluid model proceeds via the derivation of a set of explicit maps be- which is thermodynamically compatible and its govern- tween the pairs of slow variables corresponding to the in- ing differential equations can be written in a conservative active units on each cycle. Evaluation of these maps on a form. Such a model is convenient for application of ad- few key curves in their domains can be used to constrain all vanced high-accuracy numerical methods and modeling of possible activation orders in a given network and to obtain discontinuous solutions. boundary curves between all regions of initial conditions Ilya Peshkov producing different activation patterns. Ecole Polytechnique de Montreal Jonathan E. Rubin [email protected] University of Pittsburgh Department of Mathematics Evgeniy Romenski [email protected] Sobolev Institute of Mathematics [email protected]

CP6 Miroslav Grmela The Inﬂuence of Heart Rate Variability on Alter- Ecole Polytechnique de Montreal nans Formation in the Heart [email protected]

Sudden cardiac death is caused by ventricular ﬁbrillation, which is directly linked to an alternation in action potential CP7 duration (APD) at the cellular level, i.e. alternans. A com- Temporal Coarse-Graining of High Frequency Dy- mon technique for studying the initiation and of alternans namics Using Parameterized Locally Invariant is the restitution curve, i.e. the relationship between the Manifolds APD and the preceding diastolic interval. However, this technique was derived under periodic pacing condition, i.e. A model is built for coarse representation of the dynam- in the presence of feedback. However, in the heart, more ics of phase transitions at the atomistic level. The coarse complex stimulation regimes exist, including physiological model is based on the idea of Parameterized Locally Invari- heart rate variability (HRV). Here, we investigated the ef- ant Manifolds (PLIM). By considering ﬁne dynamics as a fect of HRV on the alternans formation in the heart, both system of ODE, one generates an evolutionary set of closed at the cellular and whole heart levels. equations for the coarse quantities. With the implementation of PLIM, we observe the macroscopic features of the Elena Tolkacheva system, such as temperature, number of interfaces and the Department of Biomedical Engineering stress-strain curve. University of Minnesota [email protected] Likun Tan Carnegie Mellon University [email protected] 14 AN12 Abstracts

Amit Acharya, Kaushik Dayal Guided by these expressions, the limiting behaviors of Mori Civil and Environmental Engineering kernel, which is numerically obtained from molecular dy- Carnegie Mellon University namics simulation results of the full dynamics, are observed [email protected], [email protected] and discussed.

Changho Kim CP7 Division of Applied Mathematics Dynamics of Light Beam Interaction at the Inter- Brown University face of Nonlinear Optical Media changho [email protected]

The Dynamics of two or more light beams interacting at the George E. Karniadakis interface of linear and nonlinear optical media is studied Brown University numerically and analytically. Some interesting new results Division of Applied Mathematics have been obtained. The numerical Simulations agree with george [email protected] the results of analytical model. This results can be used to develop devices in optical beam switching. CP8 Rajah P. Varatharajah A Conjecture on the Structure of Mutually Unbi- North Carolina A ased Bases &T State University [email protected] The maximal size of a collection of mutually unbiased bases (MUBs) for a finite-dimensional, complex Hilbert space is only known for certain dimensions. We offer a conjecture CP7 concerning the structure of the space of MUBs and prove it Impact of Combined Irregularity on the Torsional for dimension 2, which provides a new proof that the max- Wave Propagation imum size of a collection of MUBs is 3. We also develop a new algorithm for generating random MUBs to numerically In this paper, we study the propagation of torsional sur- explore conjectures concerning MUBs. face wave in a homogeneous layer over an initially stressed heterogeneous half space with linearly varying directional Francis C. Motta rigidities, density and initial stress under the effect of var- Colorado State University ious combined irregularities at the interface. Dispersion [email protected] equation in a closed form has been deduced for various cases. For a layer over a homogeneous half space, the velocity of torsional surface wave coincides with that of the CP8 Love waves. The consolidated effect of combined irregular- Recursive Fermi-Dirac Operator Expansions with ity, inhomogeneity, initial stress and wave number on the Applications in Electronic Structure Theory phase velocity of torsional wave is depicted by means of graphs. Recursive Fermi-Dirac operator expansion is an efficient way to calculate the density matrix in reduced complexity Sumit K. Vishwakarma, Shishir Gupta electronic structure theory. In this work, the errors in the Indian School of Mines, Dhanbad, Jharkhand, recursive expansion methods are analyzed and schemes for India-826004 error control developed. Besides error control, a scale-and- [email protected], shishir [email protected] fold technique to accelerate the convergence of the recursive expansion for the zero temperature case will be presented. CP8 EmanuelH.Rubensson Matrices, Kirchhoff Graphs and Reaction Net- Uppsala University works [email protected] This talk introduces the concept of a Kirchhoff graph for any rational matrix. Kirchhoff graphs represent the fun- CP8 damental theorem of linear algebra for the matrix; if the Block-Sparse Matrix-Matrix Multiplication with matrix is the stoichiometric matrix for a chemical reaction Error Control for Quantum Chemistry Applica- networks, they also satisfy the Kirchhoff laws for that reactions tion network. The construction of these graphs and some of their properties will be discussed. In quantum chemistry applications such as Hartree-Fock (HF) and Kohn-Sham density functional theory (KS-DFT) Joseph D. Fehribach for large molecules, the structure of the involved matrices is Department of Mathematical Sciences such that a sparse matrix representation is advantageous. Worcester Polytechnic Institute Efficient matrix-matrix multiplication for such matrices is [email protected] needed in the computationally challenging density matrix construction operation. In this work, methods for matrix- matrix multiplication for this kind of matrices are devel- CP8 oped and evaluated, focusing on efficiency and error con- Microscopic Theory of Brownian Motion Revisited trol. A single massive particle suspended in a non-interacting Elias Rudberg solvent is studied. Microscopic expressions for the friction Division of Scientific Computing, Department of I.T. coefficient in the Langevin equation in the Brownian limit Uppsala University and the time autocorrelation function of the force on the [email protected] Brownian particle in the frozen dynamics are presented. AN12 Abstracts 15

CP9 CP9 Time Reversed Absorbing Condition (trac): Appli- The Estimation of Uncertainty in the Solution of cations to Inverse Problems Ice Sheet Inverse Problems: Gaussian Linear Case versus the Stochastic Newton MCMC Method We introduce time reversed absorbing conditions (TRAC) in time reversal methods. They enable one to “recreate We consider the estimation of uncertainty in the solu- the past’ without knowing the source which has emitted tion of ice sheet inverse problems within the framework the signals that are back-propagated. Applications in in- of Bayesian inference. When the noise and prior probabil- verse problems are presented. The method does not rely ity densities are Gaussian, and the parameter-to-observable on any a priori knowledge of the physical properties of the map is linearized, the resulting posterior probability den- inclusion. Numerical tests with the wave equation illus- sity is Gaussian, with covariance given by the inverse of the trate the eﬃciency of the method. This technique is fairly log-posterior Hessian. We compare solutions of ice sheet in- insensitive with respect to noise in the data. verse problems under the Gaussian-linear assumption with the full non-Gaussian solution obtained by stochastic New- Franck Assous ton MCMC sampling, which employs local Hessian-based Ariel University Center Gaussians as proposal densities. 40700 Ariel - Israel [email protected] Noemi Petra Institute for Computational Engineering and Sciences Frederic Nataf (ICES) Laboratoire J.L. Lions The University of Texas at Austin [email protected] [email protected]

Marie Kray James R. Martin Pierre-et-Marie Curie University, Paris, France University of Texas at Austin [email protected] Institute for Computational Engineering and Sciences [email protected]

CP9 Georg Stadler, Omar Ghattas Reducing Uncertainty in Stochastic Inverse Prob- University of Texas at Austin lems Involving Sparse Data [email protected], [email protected] This work presents an approach for augmenting the information in the posterior distribution accompanying CP9 Bayesian inverse problems. Dominant behavioral features A Comparison of Deterministic and Stochastic of a particular system, captured using snapshots from a Means for Damage Parameter Identification in a physics based model, in conjunction with a “Gappy’ in- Multiphysics Context ner product are used to generate plausible surrogate data. Such data are incorporated into the likelihood function to A means for obtaining accurate damage parameter esti- reduce the uncertainty in the joint posterior over model mates resulting from complex, multi-modal likelihood func- parameters. Numerical examples are provided for charac- tions common with multiphysics problems is presented. terization and flaw identification. Noisy data in the form of fluid pressures resulting from the vibration of a damaged structure are generated from Jose G. Cano, Christopher J. Earls sparse sensors in the fluid domain. A comparison between Cornell University a deterministic and stochastic means for solving the inverse [email protected], [email protected] problem is described. Solution existence, uniqueness and stability will be discussed.

CP9 Heather M. Reed, Christopher J. Earls An Application of Particle Swarm Optimization to Cornell University Identify the Thermal Properties of Materials [email protected], [email protected]

Input your abstract, including TeX commands, here. The Jonathan Nichols abstract should be no longer than 75 words. Only input Naval Research Laboratory the abstract text. Don’t include title or author informa- [email protected] tion here. An inverse analysis of identifying thermal properties for materials is presented. It is shown that the physical problem can be formulated as an optimization problem CP9 with differential equation constraints. A particle swarm op- 3-D Constrained Joint Inversion of Geophysical timization algorithm is developed for solving the resulting Data for Crustal and Mantle Velocities in the optimization problem. The proposed algorithm provides Southern Rio Grande Rift a global optimum with highly-improved convergence performance. Numerical results are presented to demonstrate We propose a novel approach for joint inversion of geophys- the performance of the proposed method. The comparison ical datasets to characterize velocity structure of the Rio to the modified genetic algorithm is also included. Grande Rift. The inverse problem is solved as in nonlinear programming with interior-point methods. We introduce Fung-Bao Liu physical bounds over the model parameters and a measure Department of Mechanical and Automation Engineering of differences in geological structure. Bound and structural I-Shou University constraints introduce a priori information to simulate the fl[email protected] physics of each dataset. Initial results reveal 3-D velocity structure suggesting continuation of deformation and 16 AN12 Abstracts extension of the Rift. Physics University of Arizona Anibal Sosa [email protected] Computational Science Program The University of Texas at El Paso Darin Comeau [email protected] Program of Applied Mathematics University of Arizona Aaron Velasco, Lennox Thompson [email protected] Department of Geological Sciences The University of Texas at El Paso Hermann Flaschka [email protected], [email protected] Mathematics Department University of Arizona CP10 fl[email protected] Modeling and Analysis of Plant-Seed Bank Dynam- ics of a Disturbance Specialist in a Random Envi- CP10 ronment Linear Regression Via the Singular Value Decom- A nonlinear stochastic integral projection model (SIPM) position is introduced for the dynamics of a plant population with Biased estimators for linear ill-posed problems are often ob- a seed bank. This plant population needs disturbances tained by truncating the SVD for the discrete system. The to germinate, and these disturbances are governed by a technique is generally regarded as a determination of the stochastic process. Under biologically-reasonable assump- ”numerical rank” of the matrix, even though this ”rank” tions we show that both the plant and the seed bank pop- often depends on the right hand side vector. A better ulations converge (in distribution)to a stationary distri- idea is to truncate the rotated right hand side vector to bution independent of initial populations. We also show eliminate components corrupted by measurement errors. how changes in the parameters governing disturbance (fre- The method also works well for well conditioned regression quency and intensity of disturbance)affect some of the char- problems. acteristics of the long-term stationary distribution. Bert W. Rust Eric A. Eager National Institute of Standards and Technnology University of Nebraska - Lincoln [email protected] [email protected]

CP10 CP10 Large Deviations and Importance Sampling for a Urinary Tract Infections in Meningioma Patients: Feed-forward Network Analysis of Risk Factors and Outcomes We begin by considering a feed-forward network with a sin- Urinary tract infections account for approximately 35% of gle server station serving jobs with multiple levels of prior- all nosocomial infections and 75% are associated with the ity. The service discipline is preemptive in that the server use of urethral catheters. The goal of this study was to always serves a job with the current highest priority level. evaluate pre-operative factors associated with the risk of For this system with discontinuous dynamics, we outline a UTI and estimate the impact of UTIs on patient out- that the family of scaled state processes satisfy the sample come and resource utilization. Perioperative UTIs were path large deviations principle using a weak convergence strongly associated with specific comorbidities and post- argument. In the special case where the jobs have two operative complications. They significantly increase in- different levels of priority, we explicitly identify the expo- hospital length of stay and costs. nential decay rate of the probability a rare event, namely, Miriam Nuno the total population overflow associated to the feed-forward Department of Neurosurgery network. We then use importance sampling - a variance re- Cedars Sinai Medical Center duction technique - efficient for rare event probabilities to [email protected] simulate the exact probability of interest. We conclude by confirming our theoretical results with numerical simulations. CP10 Leila Setayeshgar, Hui Wang Finding Trends in Multiscale/Non-Stationary Brown University Time Series leila [email protected], [email protected] We would like to define a trend to a a time series for which there is no information on its statistics or for which an ap- CP10 proximate or a precise functional relationship to time is not known or safely assumed. An example where this arises is Demonic Fuzzy Operators: Illustration with Fuzzy in the determination of whether meteorological variations Logic can be ascribed to simple fluctuations, or are instead man- Fuzzy relations and fuzzy relational operators can be used ifestations of changes in the global climate trend. We in- to define the fuzzy semantics of programming languages. troduce an adaptive non-parametric time series estimator The operators fuz and fuz servetogiveanfuzzy angelic that has a clear mathematical description and is capable semantics, by∪ defining a◦ program to go right when there of extracting a trend for this type of time series. is a possibility to go right. On the other hand, the fuzzy

Juan M. Restrepo demonic operators fuz and fuz do the opposite: if there Departments of Mathematics, Atmospheric Physics, and is a possibility to go wrong, a program whose semantics AN12 Abstracts 17 is given by these operators will go wrong; it’s the fuzzy the approaches in those two packages are different, they demonic semantics. We will define these operators and follow the same theme and are both highly serial. To fit illustrate them using fuzzy logic. the need for the parallel computing, a reformulation of the algorithms is inevitable. In this talk, a reformulation of the Fairouz Tchier algorithm for the mixed volume computation rooted from King saud University algorithms in graph theory will be presented. [email protected] Tsung-Lin Lee National Sun Yat-set University CP11 [email protected] Fast Computation of the Zeros of a Polynomial Tien-Yien Li We present a new method for computing the zeros of a Department of Mathematics polynomial based on a factorization of the companion ma- Michigan State University trix into a product of n 1 essentially 2 2matrices.The [email protected] zeros are computed by− a non-unitary variant× of Francis’ algorithm that preserves the matrix factorization and consequently uses only O(n) storage and produces the roots Tianran Chen in O(n2)time. Michigan State University [email protected] Jared Aurentz, David S. Watkins Washington State University Department of Mathematics CP11 [email protected], [email protected] Accelerating Iterative Linear Solvers on GPU In this talk we present new results on developing paral- Raf Vandebril lel iterative linear solvers on NVIDIA GPU. We have de- Katholieke Universiteit Leuven signed a new matrix vector multiplication kernel and other Department of Computer Science BLAS 1/2 subroutines. Based on these subroutines, seven [email protected] Krylov solvers and two algebraic multigrid solvers were implemented. ILU(k), ILUT, approximate inverse, polyno- CP11 mial, domain decomposition and algebraic multigrid preconditioners were also developed. Besides, a parallel tri- A One-Sided Convex Area Function for Improved angular solver was developed. The speedup of our solvers Variational Grid Generation was up to 20.

The use of suitable convex area functionals in the context Hui Liu,SongYu of the variational grid generation problem has been studied University of Calgary in detail. A fundamental theorem for this problem states [email protected], [email protected] that if Ω is a polygonal region for which there exists a convex grid, and f : R R is a C2 convex, strictly decreasing and nonnegative function,→ then it is possible to find a real Zhangxin Chen N University of Calgary number tsuch that the functional F : R R given by N → Department of Chemical & Petroleum Engineering F (G)= f(tα ) attains its minima in the open set q=1 q [email protected] of convex grids for Ω. Using this result, several global and local strategies for updating t have been proposed. In this Ben Hsieh, Lei Shao paper, by weakening the strictly decreasing hypothesis, we University of Calgary propose a one-sided functional, for which f(x) is constant [email protected], [email protected] for x larger that a given parameter α0. This new functional is also convex and shares many properties with the previous ones, but since it focuses only on grid cells with CP11 area values less that α , it can be used in order to increase 0 Nonoverlapping Domain Decomposition Precondi- the quality of very specific cells on convex grids. Some tioners for Isogeometric Analysis numerical experiments show the quality grids that can be obtained with this new approach. In this talk, we construct and study nonoverlapping domain decomposition preconditioners for elliptic problems Guilmer Gonzalez, Pablo Barrera discretized by NURBS-based Isogeometric Analysis. We Facultad de Ciencias - UNAM consider nonoverlapping preconditioners for the reduced [email protected], [email protected] Schur complement system, in particular BDDC preconditioners defined by primal continuity constraints across the Francisco Dominguez-Mota subdomain interface. These constraints are associated to Facultad de Ciencias Fisico-Matematicas subdomain vertices and/or averages or moments over edges UMSNH or faces of the subdomains, but have a higher multiplicity [email protected] proportional to the splines regularity. By constructing appropriate discrete norms, we are able to prove that our isogeometric BDDC preconditioner is scalable in the number CP11 of subdomains and quasi-optimal in the ratio of subdomain A Scalable Reformulation of the Parallel Algorithm and element sizes. Numerical experiments in 2D and 3D for the Mixed Volume Computation that confirm our theoretical estimates and also illustrate the preconditioner performance with respect to the polyno- Efficient algorithms for computing mixed volumes have mial degree and regularity of the NURBS basis functions, been implemented in DEMiCs and MixedVol-2.0. While 18 AN12 Abstracts as well as its robustness with respect to discontinuities of Oak Ridge National Laboratory the elliptic coefficients across subdomain boundaries. [email protected]

Luca F. Pavarino Srdjan Simunovic Department of Mathematics Computer Science and Mathemati University of Milan, Italy Oak Ridge National Laboratory [email protected] [email protected]

Lourenco Beirao Da Veiga Universita’ degli Studi di Milano CP12 [email protected] Schur Complements and Block Preconditioners for Coupled Diffusion Systems Durkbin Cho Dipartimento di Matematica Discretization of systems of coupled PDE under finite ele- Universita’ di Milano, Italy ments or finite differences gives rise to block-structured al- [email protected] gebraic systems. Expensive to solve, these systems require effective preconditioning. Many of these preconditioners Simone Scacchi are based on block LU factorizations. In such factoriza- Universita’ degli Studi di Milano tions, one obtains the Schur complement by eliminating one [email protected] field in terms of the other. Preconditioners constructed in this manner require the inverse of the Schur complement, which is very expensive to compute. We study a particular CP11 simple strategy for approximating the Schur complement Dynamic Implicit 3D Adaptive Mesh Refinement that has some general applicability, giving examples both For Non-Equilibrium Radiation Diffusion of the resulting block preconditioner and solving the Schur complement system for some coupled PDE. We describe a highly effifficient solution method for the coupled nonlinear time dependent non-equilibrium radia- Geoffrey Dillon,RobKirby tion diffffusion equations. This coupled system of nonlin- Texas Tech University ear equations exhibits multiple temporal and spatial scales geoff[email protected], [email protected] rendering it a stiffff coupled system to solve. Fully implicit time integration schemes are combined with 3D par- CP12 allel adaptive mesh refinement with the resulting nonlinear systems at each timestep being solved with a Jacobian Absolutely Stable Explicit Difference Schemes Pos- Free Newton Krylov method which employs highly efficient sessing Unconditional Approximation. Parabolic physics based multilevel preconditioners. Equation Case. Bobby Philip, Zhen Wang, Manuel Rodriguez, Mark A difference scheme is proposed that is absolutely stable Berrill as implicit schemes and require the minimum number of Oak Ridge National Laboratory arithmetic operations as explicit schemes. It also proposes [email protected], [email protected], [email protected], a version of the Du Fort - Frankel scheme possessing un- [email protected] conditional approximation. Isom Jurayev Michael Pernice Unemployed Idaho National Laboratory [email protected] [email protected]

CP12 CP11 Instability of the Finite-Difference Split-Step Recursive Schur Decomposition Method on a Non-Constant-Amplitude Back- ground in the Nonlinear Schrödinger Equation We will present a new preconditioner to solve the linear (nls) systems of equations arising from the discretization of elliptic partial differential equations (PDEs) using the finite We consider the implementation of the split-step method element method. This is a recursive algorithm that uses where the linear part of the NLS is solved by the Crank- (a) non-overlapping domain decomposition, (b) Schur de- Nicolson method employing finite-difference discretization composition, (c) Krylov subspace method and (d) a fast of the spatial derivative. The von Neumann analysis re- solver such as multigrid. We will also describe the parallel veals that this method is unconditionally stable on the implementation of this algorithm. Although the algorithm background of a constant-amplitude plain wave. However, is general enough to be applied to solve a wide variety of simulations show that the method can become unstable on elliptic PDEs, we will focus on a model Poisson problem the background of a soliton.Wepresentatheoryexplain- for demonstration purposes. The algorithm can also be ex- ing this instability. Both this theory and the instability tended to other discretizations such as finite difference or itself are substantially different from those of the Fourier finite volume methods. split-step method, which computes the spatial derivative by spectral discretization. Rahul S. Sampath ORNL Taras Lakoba [email protected] University of Vermont Department of Mathematics and Statistics Bobby Philip [email protected] AN12 Abstracts 19

CP12 CP12 Using the Reverse Heat Equation to Approximate Investigations on Performances of Electromagnetic Fields Using Gaussian Basis Functions Solvers Field interpolation is any method for approximating a Many efficient numerical methods have been developed and known field as a linear combination of basis functions. used for electromagnetic simulations in time and frequency This presentation explores a procedure using the reverse domains. Their performances are quite different based on heat equation to produce high order representations of many details of the numerical methods, such as mesh, nu- the known field. As an alternative to interpolation meth- merical orders and expansion bases, etc. This talk will ods, we will begin with a regularization of the known field investigate these factors and compare their performance in and use direct, stable, explicit finite difference methods detail. Some simulation results will be presented using the to correct the regularization using the reverse heat equa- suitable solvers. Challenges for current solvers and possible tion. This method achieves the predicted second, fourth new techniques to improve them will be discussed. and sixth order of accuracy. Jin Xu Louis F. Rossi Chinese Academy of Science University of Delaware jin [email protected] [email protected] MiSun Min Argonne National Laboratory CP12 Mathematics and Computer Science Division Uniform Numerical Approximation of Integrable [email protected] Equations via Riemann-Hilbert Problems

The Riemann–Hilbert formulations of the Korteweg–de CP13 Vries and the Painlevé II transcendent have proved to Data Mining Methods Applied to Numerical Ap- be computationally valuable. Borrowing ideas from the proximations for Pdes method of nonlinear steepest descent, the resulting numerical schemes are seen to be asymptotically reliable. Here Classical results analysis of numerical methods is very of- we derive some sufficient conditions for a numerical method ten limited to the description of tables or graphs of isoval- to maintain accuracy throughout unbounded regions of the ues. We propose a new method for numerical data analy- plane on which the differential equation is posed. sis, based on exploratory data mining techniques that have proven to be efficient in other areas producing bulimic data, Thomas D. Trogdon like biology or marketing. Our approach allows us to ana- Department of Applied Mathematics lyze and characterize the different sources of errors involved University of Washington in a given mathematical modeling process coupled with nu- [email protected] merical approximations. Sheehan Olver Joel Chaskalovic The University of Sydney UPMC - Paris 6, France [email protected] [email protected]

Franck Assous CP12 Ariel University Center On the Numerical Solution of Initial-Boundary 40700 Ariel - Israel Problem to One Nonlinear Parabolic Equation [email protected] In the presented work the numerical solution of initial- boundary problem to the following nonlinear parabolic CP13 equation Runge-Kutta Discontinuous Galerkin Method for 2D Nonlinear Moment Closures for Radiative Transfer ∂U ∂2U ∂U 2 = a (x, t, U) + b (x, t, U) + f (x, t) ∂t ∂x2 ∂x Radiative transport equation calculations have important applications in determining the interaction between high energy particle propagation and body tissue in radiation is obtained. The coefficients a (x, t, U)andb (x, t, U)are dose therapy. We apply the Runge-Kutta discontinuous required to be continuous and to have continuous partial Galerkin (RKDG) method to moment models for the ra- derivative with respect to argument U. Additionally co- diative transfer equation. Our goal is to resolve the time efficient a (x, t, U) is required to be positive. The func- evolution of isolated sources or beams of particles in hetero- tion f (x, t) is required to be continuous. For the men- geneous media on unstructured grids. The moment models tioned initial-boundary problem the difference scheme is considered are nonlinear hyperbolic balance laws. constructed and the theorem of existence of its solution and the theorem of convergence of its solution to the solution Prince Chidyagwai of the source problem are proved. The rate of convergence Temple University Department of Mathematics is established and it is equal to O τ + h2 . [email protected] Mikheil Tutberidze Ilia State University Benjamin Seibold Associated Professor Temple University [email protected] [email protected] 20 AN12 Abstracts

Philipp Monreal [email protected] Aachen University [email protected] CP13 Martin Frank Highly Accurate Algorithm for Time-Dependent RWTH Aachen University Pde’s Center for Computational Engineering Science [email protected] Standard space discretization of time-dependant pde’s usually results in system of ode’s of the form

CP13

The Ghost Solid Method Based Algorithms for ut Gu = s (3) Elastic Solid-Solid Interaction −

Three variations of Ghost Solid Method based algorithms are developed for capturing the boundary conditions at where G is a linear operator ( matrix ) and u is a the solid-solid interface of isotropic, linearly elastic mate- time-dependent solution vector. Highly accurate methods, rials, in a Lagrangian framework. The methods are exten- based on polynomial approximation of a modified expo- sively tested under 1D setting. The effect of using different nential evolution operator, had been developed already for solvers for these methods is discussed. The advantages and this type of problems where G and s are constant. In this disadvantages of each of these methods are analyzed. Pre- talk we will discribe a new algorithm for the more general liminary results show that these methods can be extended case where G and s depend on t and u. Numerical results to multi-dimensional settings. will be presented. Abouzar Kaboudian Hillel Tal-Ezer NUS Graduate School for Integrative Sciences and Academic College of Tel-Aviv Yaffo Engineering [email protected] National University of Singapore [email protected] CP14 Small Deformation Viscoplastic Dynamic Sphere Boo Cheong Khoo Problem Singapore-MIT Alliance [email protected] Developing benchmark solutions for problems in solid mechanics is very important for the purpose of verifying computational physics codes. In order to test some physics CP13 codes, we present a benchmark solution to the small de- Applying the Exterior Matrix Method to the In- formation dynamic sphere problem for an isotropic vis- clined Cable Problem coplastic material obeying the Bodner-Partom model. The solution takes the form of an infinite series of eigenfunc- We apply the Exterior Matrix Method to find the approx- tions. We demonstrate convergence under eigenmode, spa- imate eigenfrequencies for serially connected inclined ca- tial, and time refinement, and then compare to numerical bles. The dynamics of each satisfies a system of four partial results. differential equations, but even their linearization cannot be solved in closed form. However, the Exterior Matrix Brandon Chabaud Method does not require the solution of governing equa- Pennsylvania State University tions. The eigenfrequency information is embedded in a [email protected] 6 6 exterior matrix for each span, which are multiplied × together to solve for the eigenfrequencies. Jerry Brock, Todd Williams Matthew Manning, William Paulsen Los Alamos National Laboratory Arkansas State University [email protected], [email protected] [email protected], [email protected] CP14 Tensor Product Decomposition Methods for Noise CP13 Reduction, Data Compression, and Projective In- Introduction to the Exterior Matrix Method tegration

We will introduce the Exterior Matrix Method (EMM) to Tensor product decomposition (TPD) methods are a pow- compute the approximate eigenfrequencies for serially con- erful linear algebra technique for the efficient representa- nected elements, each governed by a system of four first tion of high dimensional data sets. In the simplest 2-D order linear partial differential equations. Ironically, the case, TPD reduces to the well-known singular value de- governing equations do not have to be solved to find the composition of matrices. We discuss the application of approximate corresponding 6 6 exterior matrix. We can TPD methods to data compression of 3-D Magnetohydro- solve the the approximate eigenfrequencies× by multiplying dynamic and 6-D kinetic simulations of plasmas. We also the exterior matrices together. The procedure works even discuss the application of TPD methods in noise reduc- if dissipative joints are added to the system. tion and projective integration of particle-based collisional transport computations. William Paulsen, Matthew Manning Arkansas State University Diego Del-Castillo-Negrete [email protected], Oak Ridge National Laboratory [email protected] AN12 Abstracts 21

CP14 CP14

Lime: Software for Robust and Flexible Multi- Reweighted l1 Minimization Method for SPDEs physics Coupling We propose a method for the approximation of solutions Multiphysics code coupling aims at a synergistic union of PDEs with stochastic coefficients and “sparse” solutions of existing and emerging simulation capabilities with ro- based on l1 minimization. We employ reweighted iterations bust and efficient coupling algorithms. Originally targeting to enhance the “sparsity” of the solution. Also, we use nuclear reactor performance modeling, LIME represents sampling points based on specific probability measure due a general multiphysics coupling capability. LIME’s algo- to the structure of the measurement matrix which depends rithms span fixed-point coupling, placing no restrictions on the gPC expansion of the solutions. This non-intrusive on models or methods, through Newton-based coupling, method is especially effective when the deterministic solver requiring residuals and exploiting any additional informa- is very time consuming. tion and functionality codes expose. A rich suite of linear and nonlinear solvers is provided through LIME’s interface Xiu Yang to the Trilinos Solver Framework. Brown University xiu [email protected] Russell W. Hooper, Rodney Schmidt, Kenneth Belcourt Sandia National Laboratories George E. Karniadakis [email protected], [email protected], Brown University [email protected] Division of Applied Mathematics george [email protected] CP14 Application of a Perturbation Method to Nonlinear CP15 Parabolic Stochastic PDEs Identity Issues in Radial Basis Functions: RBFs As Modulated Sinc Functions in the Near-Equivalence We have applied the perturbation method developed by of Exponentially Convergent RBF Species Zhang and Lu in 2004, making use of the Karhunen-Loève expansion, to 2D parabolic equations having stochastic On a one-dimensional uniform, infinite grid, we show that conductivity and nonlinear reaction. Some results are radial basis functions (RBFs) are well approximated by shown, demonstrating that in many cases the method pro- the product of the sinc, sin(πx)/(πx), with a modulation duces good approximations of the first and second moments πx/sinh(πx/ρ). This implies that Gaussian, sech, multi- of solutions. Some analysis of computational complexity quadric, inverse multiquadric and inverse quadratic RBFs and convergence of the approximate solutions will be pre- are the same species,modulo tiny differences that disap- sented. pear altogether in the ”flat limit”. Extensions to a nearly uniform grid and to higher dimensions are also described.. Kevin Lenth University of Wyoming [email protected] John P. Boyd University of Michigan Victor E. Ginting Ann Arbor, MI 48109-2143 USA Department of Mathematics [email protected] University of Wyoming [email protected] CP15 Peter Polyakov Error Bounds for Spline Interpolation Based Para- University of Wyoming metric Model Order Reduction [email protected] Spline interpolation technique combined with balanced truncation is considered to reduce the order of parameter CP14 dependent large LTI-systems while preserving the param- Discontinuous Galerkin Methods for Modelling and eters as variables. Linear or cubic spline interpolation is Simulation of Transcription Processes applied to transfer functions of locally reduced order models to deliver an approximation to the parameter dependent A Discontinuous Galerkin FEM is used for simulation of original transfer function. This talk presents the proce- a nonlinear PDE that models the motion of polymerases dures and the derivation of error bounds and demonstrates on ribosomal RNA. Physically relevant pauses along the the results on a numerical example. rrn operon are incorporated into the model. These pauses result in delays during the transcription process, possibly Angelika Bunse-Gerstner affecting protein production. The average delay experi- Universitaet Bremen enced by a polymerase is estimated, and sensitivity anal- Zentrum fuer Technomathematik, Fachbereich 3 ysis is used to quantify the effects that location and time [email protected] duration of pauses have on the average delay. Than Son Nguyen Jennifer Thorenson Universitaet Bremen, Germany Montana State University [email protected] [email protected] CP15 Chebyshev Interpolation for Functions with End- 22 AN12 Abstracts point Singularities. CP15 Barycentric Hermite Interpolation Functions defined on a finite interval which are bounded and singular at one or both endpoints may be effectively For long it was believed that Newton interpolation was su- dealt with by use of an exponential or double-exponential perior to Lagrange interpolation. However, the work of transform. This strategy involves transplantation of the Berrut and Trefethen has shown that Lagrange interpola- problem function to an infinite or semi-infinite interval, tion is as fast and typically more robust. Here we consider where a trade-off between domain-truncation and interpo- Hermite interpolation: finding a polynomial interpolant lation errors determines the overall rate of convergence. that matches the function values and derivatives at grid We shall systematically categorise the convergence theory points. We derive an algorithm for barycentric Hermite for these situations, with a particular focus on Chebyshev interpolation. The algorithm is identical to the recently interpolation. published version of Butcher et al. (Numerical Algorithms 2011). However our derivation is somewhat different and Mark Richardson leads to an efficient method for updating Hermite inter- University of Oxford polants. [email protected] Divakar Viswanath University of Michigan CP15 [email protected] Finite Difference Weights and Superconvergence

Let z1,z2,...,zN be a sequence of distinct grid points. A CP15 finite difference formula approximates the m-th derivative (m) Summability of Expansions on the Cylinder f (0) as wkf (zk). We derive an algorithm for finding wk which uses fewer arithmetic operations and less memory We present a result regarding the Cesàro summability of than the algorithm in current use (Fornberg, Mathematics the expansion of functions on the cylinder Bd Im in of Computation, vol. 51 (1988), p. 699-706). In addi- orthogonal polynomials with respect to a product× weight tion, the order of accuracy of the finite difference formula function. An upper bound for the critical index δ is ob- (m) forf (0) with grid points hzk, 1 k N, is typically tained. ≤ ≤ N− . However, the most commonly used finite differ- O Jeremy Wade ence formulas have an increased order of accuracy (super- Pittsburg State University convergence). Even unsymmetric finite difference formulas [email protected] can exhibit such superconvergence, as shown by the explicit algebraic condition that we derive. CP16 Burhan Sadiq Department of Mathematics Numerical Methods for High-Dimensional Pdf University of Michigan, Ann Arbor Equations [email protected] We study the evolution equation of joint excitation- response PDF obtained by the Hopf functional approach Divakar Viswanath for various stochastic systems. Adaptive Discontinuous University of Michigan Garlerkin and other methods are developed and compared [email protected] to solve this advection-type evolution equation. Also, some issues arising in this formulation are investigated including different high dimensionality in phase and parametric CP15 space, and representation of multiple correlated random Jacobi 1825, Cauchy 1826, Poisson 1827 processes. Various stochastic dynamical system such as nonlinear advection equation, tumor cell model, and Limit Fast-converging numerical algorithms are usually fast be- Cycle Oscillator are tested. cause some function is analytic, and to quantify that fast convergence, a powerful tool is contour integrals in the Heyrim Cho complex plane. We show how a formula in Jacobi’s 1825 Brown University thesis in Berlin leads to: Providence, RI fast convergence of the periodic trapezoid rule heyrim [email protected] • Hermite integral formula • Daniele Venturi Runge phenomenon • Brown University potential theory daniele [email protected] • Euler-Maclaurin formula • George E. Karniadakis Gauss quadrature • Brown University spectral methods Division of Applied Mathematics • barycentric interpolation formula george [email protected] • Chebfun • (and maybe) hyperfunctions CP16 • A Convergence Study for Spdes Using Combined Lloyd N. Trefethen Polynomial Chaos and Dynamically Orthogonal Oxford University [email protected] AN12 Abstracts 23

Schemes SPDEs driven by white noise using the Stratonovich formulation. To control the increasing dimensionality in random We study the convergence properties of the recently de- space generated by the increments of Brownian motion, we veloped Dynamically Orthogonal (DO) field equations in approximate Brownian motion with a spectral expansion. comparison with the Polynomial Chaos (PC) method. A We also use sparse grid techniques to further reduce the hybrid method with PC is introduced to tackle the sin- computational cost. Numerical examples demonstrate the gularity of the DO equations for the case of deterministic very high accuracy and efficiency of the proposed method, initial conditions. An adaptive method in the basis is also including equations driven by additive and multiplicative proposed. The computational cost of DO is found to be noises. smaller when compared to the cost of other methods including MC and PC. Zhongqiang Zhang,XiuYang Brown University Minseok Choi zhongqiang [email protected], xiu [email protected] Brown University minseok [email protected] Guang Lin Pacific Northwest National Laboratory Themis Sapsis [email protected] New Yrok University [email protected] Boris Rozovsky Brown University George E. Karniadakis Boris [email protected] Brown University Division of Applied Mathematics George E. Karniadakis george [email protected] Brown University Division of Applied Mathematics CP16 george [email protected] Variance Reduction in the Simulation of Stochastic Differential Equations CP17 Variance reduction techniques are commonly used to en- Multigrid, Adaptive Discontinuous Galerkin Meth- hance the efficiency of Monte Carlo simulations. This talk ods for the Cahn-Hilliard Equation and a Diffuse focuses on variance reduction for single and coupled sys- Interface Model of Tumor Growth tems of stochastic ordinary differential equations. Variance We present a mixed discontinuous galerkin finite element reduction techniques such as antithetic variates and control (DG-FE), convex splitting scheme for the Cahn-Hilliard variates will be described and results presented. (CH) equation. Unconditional energy stability and unique David J. Horntrop solvability, as well as optimal convergence, are proven for Dept of Mathematical Sciences, Center for Applied Math the scheme. An efficient non linear multigrid algorithm New Jersey Institute of Technology is used to solve the discrete equations. Also, a spatially [email protected] adaptive, primitive-variable DG-FE scheme for a CH-type diffuse interface model for cancer growth is presented. Con- vergence under mesh modification is demonstrated, and CP16 simulation results are provided. Variance-Reduced Equation-Free Newton-Krylov Andreas Aristotelous Methods for Stochastic Fine-Scale Simulations Duke University Equation-free methods promise a straightforward compu- Statistical and Applied Mathematical Sciences Institute tation of macroscopic steady states and their stability, [email protected] based only on appropriately initialized short bursts of microscopic simulation, which are used to compute residuals Ohannes Karakashian and Jacobian-vector products. One way to proceed is to Department of Mathematics use a Newton algorithm, in which the linear systems in each The University of Tennessee Newton iteration are solved via a Krylov method. A ma- [email protected] jor problem in a naive implementation of this approach is the amplification of statistical noise in the Jacobian-vector Steven M. Wise products when the microscopic model is stochastic. This Mathematics Department talk discusses approaches to reduce the variance on these University of Tennessee Jacobian-vector calculations significantly, yielding signifi- [email protected] cant reductions in computational effort. Giovanni Samaey CP17 Department of Computer Science, K. U. Leuven An Efficient Scheme Involving Only Constant Coef- [email protected] ficient Matrices for Coupled Navier-Stokes/Cahn- Hilliard Equations with Large Density Ratios CP16 We present an efficient scheme for simulations of the cou- Stochastic Collocation Methods for Stochastic Dif- pled Navier-Stokes/Cahn-Hilliard equations for the phase ferential Equations Driven by White Noise field approach. The scheme has several attractive features: (i) It is suitable for large density ratios, and numerical We propose stochastic collocation methods for SODEs and experiments with density ratios up to 1000 have been pre- 24 AN12 Abstracts sented; (ii) It involves only time-independent coefficient Yalchin Efendiev matrices for all flow variables, which can be pre-computed Dept of Mathematics during pre-processing, so it effectively overcomes the per- Texas A&M University formance bottleneck induced by variable coefficient matri- [email protected] ces associated with the variable density and variable viscosity; (iii) It completely de-couples the computations of Yuguang Chen the velocity, pressure, and the phase field function. Simu- Chevron Energy Technology Company lations will be presented to demonstrate the effectiveness [email protected] of current method for studying two-phase flows involving large density ratios, moving contact lines, and interfacial Louis Durlofsky topology changes. Stanford University Suchuan Dong [email protected] Purdue University [email protected] CP17 Summation-by-Parts Operators and Weak Initial CP17 Conditions for Time-Discretisation Application of Compact-Reconstruction WENO During the last decade, stable high order finite difference Schemes to the Navier-Stokes Equations methods applied to initial-boundary-value-problems have The Compact-Reconstruction WENO (CRWENO) scheme been developed. The stability is due to the use of so-called was constructed by applying the WENO algorithm on com- summation-by-parts operators (SBP), penalty techniques pact stencils and achieved high spectral resolution as well for implementing boundary and interface conditions (SAT), as non-oscillatory behavior across discontinuities. The new and the energy method for proving stability. The so called scheme was analyzed for scalar conservation laws and the SBP-SAT technique has so far only been used to discretize Euler equations. The CRWENO scheme demonstrated the initial-boundary-value-problem in space. In this talk lower dissipation and dispersion errors for smooth and dis- we will discuss the use of this technique also in time. For continuous flows, compared to the WENO scheme. In linear problems, the result will be a fully discrete and en- the present study, the CRWENO scheme is applied to the ergy stable method of very high order of accuracy. We multi-dimensional Navier-Stokes equations on curvilinear will discuss stability, accuracy and efficiency aspects of this meshes. Results are presented for steady flow over airfoils technique. as well as dynamic stall of a pitching airfoil. Flow prob- Jan Nordstrom lems representative of direct numerical simulation (DNS) of professor in scientific computing turbulent flows are attempted and the results from the CR- Department of Mathematics, Linkoping University WENO scheme are compared with those from the WENO [email protected] scheme. Debojyoti Ghosh Tomas Lundquist Applied Mathematics & Statistics, and Scientific Department of Mathematics Computation Linkoping University University of Maryland [email protected] [email protected] CP17 James Baeder Department of Aerospace Engineering Partitioned Algorithms for the Numerical Solu- University of Maryland tion of the Fluid-Structure Interaction Problem in [email protected] Haemodynamics In this work we deal with the numerical solution of the CP17 fluid-structure interaction (FSI) problem arising in the haemodynamic environment. The aim is to develop effi- A Fast Perturbation Approach in Ensemble Level cient partitioned algorithms for real haemodynamic appli- Upscaling cations, where the non-linear finite elasticity is considered Ensemble level upscaling is efficient upscaling of flow pa- for the structure subproblem. We provide theoretical and rameters for multiple geological realizations. Solving the experimental results concerning the accuracy and efficiency flow problem for all the realizations is time-consuming. Re- of the proposed schemes and finally we apply some of such cently, different stochastic procedures have been combined schemes to the case of human carotid geometries, in order with upscaling methods to efficiently compute the upscaled to compare the fluid-dynamics before and after the removal coefficients for a large set of realization. In this work, we of the atheromasic plaque. proposed a fast perturbation approach in the ensemble level Christian Vergara upscaling. We give a correction scheme to generate up- Universita’ degli Studi di Bergamo scaled parameters and use collocation and clustering tech- Bergamo, Italy niques in stochastic space, which allow us to compute the [email protected] upscaled permeabilities rapidly for all realizations. The numerical results will be present. Fabio Nobile Yan Li CSQI – MATHICSE, EPF de Lausanne, CH Chevron [email protected] [email protected] Matteo Pozzoli AN12 Abstracts 25

Universita’ degli Studi di Bergamo Bergamo, Italy optimization problems from the integer programming view- [email protected] point. A set covering-based surrogate approach is proposed to solve the sup- equation constrained optimization problem with a separableT and monotone objective function in CP18 each of the variables. This is our first trial of develop- Guaranteed Biclustering Via Semidefinite Pro- ing integer programming-based techniques to solve sup- gramming equation constrained optimization problems. Our com-T putational results confirm the efficiency of the proposed Given a set of objects and a set of features exhibited by method and show its potential for solving large scale sup- these objects, biclustering seeks to simultaneously group equation constrained optimization problems. the objects and features according to their expression lev- T els. We pose this problem as that of partitioning a weighted Cheng-Feng Hu complete bipartite graph such that the densities of the re- Dept. of Industrial Management, I-Shou university, sulting subgraphs are maximized. We consider a noncon- Taiwan vex quadratic programming formulation for this problem [email protected] and relax to a semidefinite program using matrix lifting. We show that the correct partition of the objects and features can be recovered from the optimal solution of the CP18 semidefinite relaxation in the case that the input instance A Joint Economic Production and Delivery Quan- consists of several disjoint sets of objects exhibiting similar tity Model With a General Transportation Cost features. Structure

Brendan P. Ames A joint economic production and delivery quantity model University of Waterloo in a delivery price-based supply chain is studied in this [email protected] paper. More specifically, a fixed lot sizing policy is implemented in the production system, while smaller shipping quantity with periodic dispatches is delivered to the cus- CP18 tomer. The considered cost includes setup cost to launch A Minty Variational Principle for Set-Valued Op- the batch production, inventory carrying cost, and trans- timization portation cost, where the transportation cost is a general function of the delivery quantity. A per unit time cost Set-valued optimization is proving a valuable tool in model is developed and analyzed to determine the optimal mathematical finance (see e.g. F.Heyde et al. in production quantity for the production system and the de- Math.Meth.Oper.Res (2009) 69:159-179). Besides, in livery quantity to the customer. Under some mild condi- scalar and vector optimization, Minty variational principle tions, it can be shown that the joint cost function is convex proves to be a sufficient optimality conditions and ensures and the optimal production quantity is dependent of the good properties of the primitive optimization problem. We delivery quantity. The computational study has demon- want to develop a Minty variational principle for set-valued strated the significant impact of the joint decision model optimization, defining Dini-type derivative for set-valued on the operating cost. In particular, cost savings can be functions. more than 30% when inventory carrying cost and/or transportation cost are high. Giovanni Crespi UniversitédelaVallée d’Aoste Shine-Der Lee [email protected] National Cheng Kung University Dept. of Industrial & Information Management Carola Schrage [email protected] Martin˘Luther˘University Halle˘Wittenberg [email protected] Yen-Chen Fu National Cheng Kung University Department of Industrial and Information Management CP18 [email protected] Solving Games by Differential Equations in Finite Time CP18 New method to solve symmetric matrix games by differen- Cyber-Insurance in Internet Security: The Prob- tial equations is described. It allows us to find out opti- lem of Resolving Information Asymmetry mal mixed strategy in finite time, whilst the ODE-based method, belonging to Brown and von Neumann, in general Internet users such as individuals and organizations are case consideres ODE on [0, ) and gives only the value of ∞ subject to different types of epidemic risks such as worms, game. viruses, spams, and botnets. To reduce the probability of risk, an Internet user generally invests in tradi- Koba Gelashvili tional security mechanisms like anti-virus and anti-spam Full Professor, Computer Science Department, software, sometimes also known as self-defense mecha- Ivane Javakhishvili Tbilisi State University nisms. However, such software does not completely elim- [email protected] inate risk. Recent works have considered the problem of residual risk elimination by proposing the idea of cyber- CP18 insurance. In this regard, an important research problem is resolving information asymmetry issues associated with Solving Sup- Equation Constrained Optimization T cyber-insurance contracts. In this paper we propose three Problems mechanisms to resolve information asymmetry in cyber- This work considers solving the sup- equation constrained insurance. Our mechanisms are based on the Principal- T 26 AN12 Abstracts

Agent(PA)modelinmicroeconomictheory.Weshow in a two layer miscible fluid with a sharp stratification in that (1) optimal cyber-insurance contracts induced by our density and surface tension with the drop. When the sur- mechanisms only provide partial coverage to the insureds. face tension is uniform, the drop decelerates significantly This ensures greater self-defense efforts on the part of the as it encounters the lower, denser layer. Intriguingly, when latter to protect their computing systems, which in turn the lower layer has greater surface tension than the upper, increases overall network security, and (2) the level of de- the drop may bounce and be prevented from crossing the ductible per network user contract increases in a concave transition region. In contrast, when the lower layer has manner with the degree of the user. Our methodology is lesser surface tension, the drop may accelerate through the applicable to any distributed network scenario in which a transition. framework for cyber-insurance can be implemented. Avi Shapiro, Francois Blanchette Ranjan Pal U.C. Merced University of Southern California [email protected], [email protected] [email protected] CP19 CP18 A Front-Tracking Method For Moving Fronts And Optimal Small Wind Turbine Placement in Con- Hyperbolic Conservation Laws strained Spaces We present a new high-order method for shock captur- Wind farms composed of small scale turbines can be eco- ing with tracked material interfaces. Tracking uses a level nomical for small groups interested in renewable energy set which is advected using the material interface velocity generation, however the placement of turbines is problem- obtained from interfacial Riemann problems. Each ma- atic. There are obstacles, effects of wind shear and wake terial phase is discretized independently using a uniform turbulence that are challenging to address particularly if Cartesian grid and the embedded boundary approach to the available area is limited and there are other constraints. complex geometry. Our discretization is a high-order Go- We consider a simple model of these constraints and inter- dunov method away from the interface. Near the interface ference factors and apply steepest descent techniques to it is a globally conservative and consistent finite volume optimize turbine placement within constrained spaces. approach. Vincent Winstead Mehdi Vahab Minnesota State University, Mankato University of California Davis Minnesota State University Department of Applied Science [email protected] [email protected]

Greg Miller CP19 University of California Simulation of Parachute Inflation Using the Front Department of Applied Science Tracking Method [email protected] Front Tracking is a Lagrangian tool for the propagation of material interface and is known for its excellent preser- CP19 vation of interface geometry. We use the front tracking A Nitsche Method for a Stokes Interface Problem method on a spring system to model the dynamics evolution of parachute canopies. And this mechanical structure We present a finite element method for the Stokes equa- is coupled with the incompressible Navier-Stokes solver tions involving two immiscible incompressible fluids with through the ”Impulse Method”. We will present the sim- different viscosities and with surface tension. The inter- ulation and comparison with experiments of several types face separating the two fluids does not need to align with of parachute. the mesh. We propose a Nitsche formulation which allows for discontinuities along the interface with optimal a pri- Joungdong Kim ori error estimates. A stabilization procedure is included SUNY at Stony Brook which ensures that the method produces a well conditioned Stony Brook, NY 11794 stiffness matrix. [email protected] Sara Zahedi Xiaolin Li Uppsala University Department of Applied Math and Stat [email protected] SUNY at Stony Brook [email protected] Peter Hansbo Jönköping University Yan Li [email protected] SUNY at Stony Brook Stony Brook, NY 11794 Mats G. Larson [email protected] Department of Mathematics Umea University [email protected] CP19 Drops Settling in Sharp Stratification with and Without Marangoni Effects CP20 Gpu Accelerated Greedy Algorithms for Com- We present numerical simulations of a heavy drop settling AN12 Abstracts 27 pressed Sensing gling

Greedy algorithms for compressed sensing are eﬃcient, We propose a multiobjective mesh optimization framework suboptimal algorithms to solve the combinatorial optimiza- for mesh quality improvement and mesh untangling. Our tion problem framework is able to simultaneously optimize various aspects of the mesh such as the element shape, element size, and associated PDE interpolation error; and to untangle in- min x 0 subject to y = Ax, verted elements, but is not limited to these categories. We successfully apply methods within our framework to real- · world applications, such as problems from hydrocephalus where 0 counts the nonzero entries and A is n N with and shape optimization. n

CP20 CP20 Perceptual Grouping of Characters in Antarctica Adaptive Outlier Pursuit in 1-Bit Compressive Maps Sensing and Matrix Completion

Our aim is to create a database with information about In compressive sensing (CS), the goal is to recover signals the name and location of the major geographical features at reduced sample rate compared to the classic Shannon- in maps using perceptual grouping. The first step is to Nyquist rate. However, the classic CS theory assumes the segment the characters in names from the background. The measurements to be real-valued and have infinite bit pre- centroids of these characters are grouped based on their cision. The quantization of CS measurements has been proximity and direction to other centroids. Our initial tests studied recently and it has been shown that accurate and with simulated text accurately grouped these characters stable signal acquisition is possible even when each mea- greater than 90% of the time. surement is quantized to only one single bit. There are many algorithms proposed for 1-bit compressive sensing Ravishankar N. Chityala and they work well when there is no noise in the measure- University of Minnesota ments, while the performance is worsened when there are [email protected] a lot of sign flips. We propose a robust method for recovering signals from 1-bit measurements using adaptive Sridevi Pudipeddi outlier pursuit (AOP). This method will detect the posi- South Central College tions where sign flips happen and recover the signals using [email protected] “correct’ measurements. Numerical experiments show the accuracy of sign flips detection and high performance of signal recovery for our algorithms compared with other al- CP20 gorithms. This AOP technique can also be applied to solve A Multiobjective Mesh Optimization Framework matrix completion problem when the data is damaged by forMeshQualityImprovementandMeshUntan- 28 AN12 Abstracts impulse noise. statements made herein are solely responsibility of the authors. Yi Yang,MingYan University of California, Los Angeles Prabir Daripa [email protected], [email protected] Texas A&M University Department of Mathematics Stanley J. Osher [email protected] University of California Department of Mathematics [email protected] CP21 Internal Gravity Waves and Their Generation

CP21 Time-harmonic internal gravity waves are generated in a Effect of Permeability Anisotropy on Density- stratified fluid by oscillating a rigid object. After removing the time dependence, there remains a boundary value prob- Driven Flow for CO2 Sequestration in Saline Aquifers lem for a hyperbolic partial differential equation. We solve this problem when the object is a thin horizontal elliptical We present a comprehensive study of the effect of perme- plate. ability anisotropy on the onset and subsequent develop- Paul A. Martin ment of convection for CO2 sequestration in saline aquifers. Our linear stability analysis shows that anisotropy reduces Department of Mathematical and Computer Sciences Colorado School of Mines the critical time tc and the critical wavelength λc because it amplifies all perturbation modes via an exponential growth [email protected] factor that is biased towards shorter wavelength modes. Anisotropy increases parity among the modes in such a way Stefan Llewellyn Smith that λc becomes less meaningful. We have also studied the Department of MAE behavior after tc using detailed numerical simulations. We University of California, San Diego show that anisotropy can substantially reduce the time at [email protected] which the enhanced transport from natural convection becomes significant. In addition, it permits higher mean CO2 dissolution rates to be sustained for longer periods of time. CP21 Our results give strong indication that saline aquifers with A Computational Framework for the Solution of permeability anisotropy can provide a means for safe and Multi-Material Fluid-Structure Interaction Prob- permanent storage of large amounts of CO2. lems with Crack Propagation Philip Cheng We present a high-fidelity computational framework based Yale University on the coupling of an embedded boundary method for Department of Chemical & Environmental Engineering CFD and XFEM for the coupled solution of nonlinear [email protected] fluid-structure interaction problems with large deformations and crack propagation. We illustrate this framework, Michael Bestehorn highlight its features, and assess its performance with the Brandenburg University of Technology Cottbus three-dimensional simulation of underwater implosions and Institute for Theoretical Physics II pipeline explosions for which test data is available. [email protected] Kevin Wang Institute for Compuational and Mathematical Abbas Firoozabadi Engineering Yale University Stanford University, Stanford, CA abbas.fi[email protected] [email protected]

CP21 CP21 Universal Stability Properties for Multi-Layer An Efficient Numerical Method for Solving Cou- Hele-Shaw Flows and Its Application to Instabil- pled Systems of Elliptic Interface and Hyperbolic ity Control Partial Differential Equations with Applications to Enhanced Oil Recovery With the motivation of understanding the effect of various injection policies currently in practice for chemical en- We will present a fast and efficient method for solving a hanced oil recovery, we study linear stability of displace- coupled system of elliptic and hyperbolic equations aris- ment processes in a Hele-Shaw cell involving injection of ing in the context of complex chemical flooding of porous an arbitrary number of fluid phases in succession. This media. The problem involves moving boundaries and dis- work mainly builds upon our earlier study for the three- continuous coefficients. The mathematical model we use layer case [P. Daripa, Studies on stability in three-layer is based on the Buckley-Leverett model, Darcy velocity Hele-Shaw flows, Physics of Fluids, (20), 2008]. Stability and other complex physics arising from chemicals. To be results obtained are universal in the sense that they hold more exact, we use finite volume method to solve the two- regardless of number of displacing fluids. The stability re- dimensional Riemann problem system, use the finite ele- sults have been applied here to design injection policies ment method to solve the two-dimensional elliptic inter- that are considerably less unstable than the pure Saffman- face problem, and the level set method is used to move Taylor case. This is a joint work with my postdoc Xueru the interface. The results of our numerical experiments Ding. The research reported here has been made possible will be presented and discussed. This is an ongoing work. by a grant NPRP 08-777-1-141 from the Qatar National The research reported here has been made possible by a Research Fund (a member of The Qatar Foundation). The AN12 Abstracts 29 grant NPRP 08-777-1-141 from the Qatar National Re- Whitham, Zhang-Aw-Rascle) possess traveling wave so- search Fund (a member of The Qatar Foundation). The lutions, called “jamitons’, that are analogs of detonation statements made herein are solely responsibility of the au- waves in reacting gas dynamics; (b) the occurrence of jami- thors. tons is equivalent to the instability of uniform traffic flow, i.e. jamitons serve as models for phantom traffic jams; Liqun Wang and (c) the large spread of flow rates in congested traffic 1301 Barthelow Drive, Apt 34B, College Station, regimes that is observed in fundamental diagrams can be TX,77843 explained with the simple 1979 Payne-Whitham model. [email protected] Benjamin Seibold Prabir Daripa Temple University Texas A&M University [email protected] [email protected] Rodolfo Ruben Rosales Massachusetts Institute of Technology CP22 [email protected] Supercritical And Subcritical Hopf Bifurcations On the Van Der Pol Nonlinear Differential Equation Morris Flynn University of Alberta The main purpose of this paper is to discuss following ob- mrfl[email protected] jectives with the famous Van Der Pol Nonlinear Differential Equation: (i) Development of general theory and formulae for determining Hopf Bifurcations on any non-linear Dif- Aslan R. Kasimov ferential equations (ii) Existence of Chaos , Limit Cycles , Division of Mathematical & Computer Sciences and Supercritical and Subcritical Hopf Bifurcations of Van Der Engineering Pols Oscillator and their Statistical analysis . King Abdullah University of Science and Technology [email protected] Tarini K. Dutta PROFESSOR OF MATHEMATICS, GAUHATI Jean-Christophe Nave UNIVERSITY, GUWAHATI, McGill University ASSAM STATE: 781014, INDIA [email protected] [email protected] CP23 CP22 Boundary Trace Inequalities Mathematical Analysis of Chikungunya Model With Discrete Delays This talk will describe some simple boundary trace inequalities for Sobolev functions in W 1,p(Ω) with Ω a bounded The paper presents the basic model for the transmission region in space with Lipschitz boundary ∂Ωandp N. dynamics of chikungunya. The model, which consists of The inequalities are used to provide new bounds on≤ solu- seven mutually-exclusive compartments representing the tions of inhomogeneous Robin boundary value problems. humans and vector dynamics, has a locally-asymptotically stable disease-free equilibrium (DFE) whenever the associ- Giles Auchmuty ated reproduction number () is less than unity. The analy- Department of Mathematics ses of the model show the existence of the phenomenon of University of Houston backward bifurcation (where the stable DFE of the model [email protected] co-exists with a stable endemic equilibrium when the reproduction number of the disease is less than unity). It is shown, that the backward bifurcation phenomenon can be CP23 removed by substituting the associated standard incidence Γ-Convergence of Inhomogeneous Functionals and function with a mass action incidence. Analysis of the re- Applications to Dielectric Breakdown production number of the model shows that, the disease will persist, whenever > 1. Furthermore, an increase in The asymptotic behavior of inhomogeneous functionals in the length of incubation period, increases the chikungunya Orlicz-Sobolev spaces is studied via Γ-convergence. Appli- burden in the community if a certain threshold quantities, cations to the study of (first-failure) dielectric breakdown for composites made of two isotropic phases will be dis- denoted by ∆b and ∆v are positive. On the other hand, increasing the length of the incubation period can help re- cussed. This is joint work with Mihai Mihailescu (Univer- sity of Craiova, Romania). duce disease burden if ∆b < 0and∆v < 0. Salisu M. Garba Marian Bocea Department of Mathematics Loyola University Chicago University of Pretoria [email protected] [email protected] CP23 CP22 Well-Posedness for Euler 2D in Non-Smooth Do- Connections Between Phantom Traffic Jams, Jami- mains tons, and Congested Traffic Flow The well-posedness of the Euler system has been of course the matter of many works, but a common point in all the In this presentation, we show that (a) a wide class of 1,1 “second-order’ macroscopic traffic models (e.g. Payne- previous studies is that the boundary is at least C .Ina first part, we will state the existence of global weak solu- 30 AN12 Abstracts tions of the 2D incompressible Euler equations for a large tions with Discontinuous Coefficients class of non-smooth open sets. In a second part, we will give the uniqueness if the open set is the interior or the Uniform estimate for non-uniform elliptic equations with exterior of a simply connected domain, where the bound- discontinuous coefficients in heterogeneous media is con- ary has a finite number of corners. The existence part is a cerned. The heterogeneous media considered here are peri- work in collaboration with David Gérard-Varet. odic and they consist of a connected high permeability sub- region and a disconnected matrix block sub-region with low Christophe Lacave, David Gerard-Varet permeability. Elliptic equations with diffusion coefficients Institut Mathématiques de Jussieu. depending on the permeability of the media have fast diffu- Université Paris Diderot (Paris 7) sion in high permeability sub-region and have slow diffusion [email protected], [email protected] in low permeability sub-region, and they are non-uniform elliptic equations. Let denote the size ratio of the matrix blocks to the whole domain and let the permeability ratio CP23 of the matrix block sub-region to the connected high per- Traveling Waves of an Angiogenesis Model meability sub-region be of the order 2.Itisprovedthat the Lp norm of the gradient of the elliptic solutions in the In this talk, we will study travel wave solutions for a class high permeability sub-region are bounded uniformly in of chemotaxis system modeling the initiation of tumor an- in bounded and unbounded domains. One example also giogenesis. The challenges of obtaining traveling wave solu- shows that the Lp norm of the gradient of the solutions in tions of such chemotaxis models lie in the high dimension- the disconnected subset may not be bounded uniformly in ality and the singularity. Hence the routine approaches, . It is also noted that the Lp norm of the second order such as phase plane analysis, no longer work. In the talk, derivatives of the elliptic solutions in the high permeability we shall show these challenges will be overcome by a Hope- sub-region in general are not bounded uniformly in . Cole tyoe transformation, such that the transformed system can be solved by the routine approaches. The exis- Li-Ming Yeh tence, wave speed and stability of traveling wave solutions Department of Applied Mathematics will be discussed, and open questions will be presented. National Chiao Tung University, Taiwan [email protected] Zhian Wang Department of Applied Mathematics Hong Kong Polytechnic University MS0 [email protected] Continuous and Discrete Models for Infectious Dis- eases CP23 In this talk, I will present a few representative papers that Lattice Differential Equation Analysis of Schloegls I have coauthored with Carlos Castillo-Chaves and others. Second Model for Particle Creation and Annihila- These include some of the earlier work on continuous mod- tion els for TB and influenza and more recent papers on discrete epidemic models. Schloegls stochastic models for autocatalysis on a lattice of dimension d=2 involves: (i) spontaneous annihilation of Zhilan Feng particles at lattice sites; and (ii) autocatalytic creation of Purdue University particles at vacant sites. We analyze the dynamics of in- [email protected] terfaces between populated and empty regions via discrete reaction-diffusion equations (dRDEs) obtained from approximations to the exact master equations. These dRDE MS0 can display propagation failure absent due to fluctuations From Rockstar Researcher to Selfless Mentor: An in the stochastic model. Higher-level approximations elu- Overview of the Achievements of Carlos Castillo cidate exact behavior with quantitative accuracy. Chavez Chi-Jen Wang Carlos Castillo Chavezs record of scholarship is unparal- Iowa State University, Ames Laboratory-USDOE leled, representing some of the most important contribu- [email protected] tions in the study of disease dynamics. Yet, it is a com- mitment to mentoring that has captivated his interest. In Xiaofang Guo this brief overview, I will chart how Carlos Castillo Chavez Ames LaboratoryUSDOE not only reached the pinnacle of his field, but how he then Dep of Physics & Astro and Dep of Math, Iowa State turned that same dedication to others, becoming one of the Univ most honored mentors in the sciences. [email protected] Melissa Castillo-Garsow Yale University Da-Jiang Liu tba Iowa State University dajiang@fi.ameslab.gov MS0 Jim W. Evans Modeling and Quantifying the Transmission Dy- Ames Laboratory USDOE and Iowa State University namics and Control of Infectious Diseases [email protected] I will discuss my research experience working under the su- pervision of Carlos Castillo-Chavez from my participation CP23 in the Mathematical and Theoretical Biology Institute’s Uniform Estimate for Non-Uniform Elliptic Equa- Summer Research Program to my doctoral work at Cor- AN12 Abstracts 31 nell. In addition, I will provide an overview of some recent MS1 collaborative projects with Carlos and others with a par- Title Not Available at Time of Publication ticular focus on research on the transmission and control of emerging and re-emerging infectious diseases. Abstract not available at time of publication.

Gerardo Chowell Elena Grigorescu Mathematical Modeling and Analysis Georgia Tech Los Alamos National Laboratory [email protected] [email protected] MS1 MS0 Deep-LLL Reconsidered Insights Gained from Modeling Epidemics Lattice reduction plays an important role both in coding I will review some of the insights gained from my col- theory and cryptography. For example, it has broad appli- laborations with Carlos Castillo-Chavez in creating create cations in cryptanalysis. The Deep-LLL lattice reduction new models that can anticipate the spread of a disease algorithm, as an improvement of classical LLL, was not and evaluate the effectiveness of different approaches for studied very well as it is outperformed by BKZ reduction. bringing an epidemic under control. The talk will pro- We want to argue why the concept of Deep Insertions could vide an overview, for general audiences, of what type of in- improve reduction algorithms like BKZ and provide empir- sights these models can provide. I will describe some of the ical evidence. mathematical advances needed to create the next generation of models, and share my personal experiences working Urs Wagner, Felix Fontein, Joachim Rosenthal with Carlos to create models for controlling the spread of Institut für Mathematik HIV/AIDS, SARS, dengue fever, foot and mouth disease, Universität Zürich Ebola, and preparing for a bioterrorist attack. [email protected], [email protected], [email protected] James (Mac) Hyman Tulane University [email protected] MS2 Evasion Paths in Mobile Sensor Networks

MS0 Imagine that disc-shaped sensors wander in a planar do- Influenza and Other Infectious Diseases main. A sensor can’t determine its location but does know when it overlaps a nearby sensor. We say that an evasion The complicated dynamics of influenza A exhibit fluctua- path exists in this sensor network if a moving evader can tions on multiple scales, due to the interplay of factors such avoid detection. Using tools from topology, Vin de Silva as age structure, cross-reactivity, and seasonal forcing. To and Robert Ghrist can guarantee that no evasion path ex- address this interplay, Castillo-Chavez and collaborators ists in certain networks. But what about the remaining developed a comprehensive mathematical framework, and networks? We’ll consider examples that show the existence analyzed the potential for sustained oscillations. This lec- of an evasion path depends not only on the sensor network’s ture will review this work, set it in the context of what local connectivity data but also on its embedding. came before and after, and complement with discussion of some of Carlos’s other contributions to mathematical biol- Henry Adams ogy. Stanford University [email protected] Simon Levin Princeton University, USA [email protected] MS2 Generalizing Max Flow and Min Cut: Opportuni- ties from a Topological Proof MS1 New Directions in Algebraic Coding Theory The max-flow min-cut theorem has found recent applications in image segmentation, communication, and other Abstract not available at time of publication. forms of information processing. The classical theorem and its proof can be recast in terms of the “directed homology’ Iwan Duursma of a directed graph, taking coefficients in a sheaf of con- University of Illinois at Urbana-Champaign straints. I will discuss generalizations of max-flow min-cut Department of Mathematics implied by the topological approach, and potential appli- [email protected] cations of such generalizations to real-world problems. Sanjeevi Krishnan MS1 University of Pennsylvania Title Not Available at Time of Publication [email protected] Abstract not available at time of publication. MS2 Salim El Rouayheb Sheaves and Persistence EECS University of California at Berkeley Sheaf theory brings to persistence a rich language. Us- [email protected] ing this language, I will present, through simple examples, 32 AN12 Abstracts some ongoing work on multidimensional persistence. Department of Mathematics [email protected] Amit Patel Rutgers University [email protected] MS3 Multi-moment Vortex Methods

MS2 In this talk we develop a new, high order accurate, multi- Recent Advances and Trends in Applied Algebraic moment vortex method (MMVM) using Hermite expan- Topology sions to simulate 2D vorticity. The method naturally allows the particles to deform and become highly anisotropic as Applied algebraic topology is a vibrant young field of re- they evolve without the added cost of computing the non- search, with rapid ongoing development. I will give a sur- local Biot-Savart integral. Convergence for the method vey of recent advances and results in the field includ- is proven and examples will be provided. Time permit- ing work on coordinatization, on topological inference, on ting, we will discuss the spatial accuracy and computa- topological simplification, and applications to signals, to tional costs of MMVM. cancer research, and to image analysis. I will focus, in this, on work done by young researchers in the field. David T. Uminsky UCLA Mikael Vejdemo Johansson Dept. of Mathematics Stanford University [email protected] [email protected]

MS3 MS3 A Partition of Unity Method for Divergence-free Stable Computation with Reproducing Kernels Approximation of Vector Fields on the Sphere Positive definite kernels and their associated reproducing Vector fields tangent to the surface of the sphere appear kernel Hilbert spaces provide a very flexible and powerful in many applications from the geophysical sciences. Often tool for the solution of many typical problems of numerical these fields describe the velocity of some incompressible analysis and scientific computing such as function approx- fluid and are thus divergence-free. We present a new mesh- imation, numerical integration or the numerical solution free, partition of unity method based on RBFs for approx- of PDEs. I will provide a brief introduction to positive imating these types of fields that preserves the divergence- definite reproducing kernels, mention some typical appli- free property. The method is computationally efficient, free cations, and then focus on stable computation with Gaus- of any coordinate singularities, and can be used to approx- sian kernels. The latter is motivated by the fact that, on imate surface derivatives of the field. the one hand, interpolation with flat Gaussian kernels provides a generalization of (multivariate) polynomial inter- Grady B. Wright polation with spectral convergence rates for smooth func- Department of Mathematics tions, while, on the other hand, flat Gaussian kernels lead Boise State University, Boise ID to notoriously ill-conditioned linear systems. Our work [email protected] demonstrates that this so-called uncertainty principle can be avoided by representing the space of functions used for Edward J. Fuselier the approximation by a “better” basis. A set of Matlab Department of Mathematics and Computer Science routines implementing these ideas for Gaussian kernels are High Point University available from http://math.iit.edu/˜mccomic/gaussqr [email protected] Greg Fasshauer Illinois Institue of Technology MS4 [email protected] Development of a Single Domain Framework to Model 3D L-Ion Intercalation Batteries using the Michael McCourt AMP Package Center for Applied Mathematics Cornell University Modeling of batteries involves simulation of coupled charge [email protected]; [email protected] and thermal transport, interfacial electrochemical reactions across the porous 3D structure of the electrodes (cath- odes and anodes) and electrolyte system. The resulting MS3 equations are stiffff differential algebraic systems on a sin- Refinement and Remeshing in Particle Simulations gle domain and require a robust solution methodology. These formulations are implemented in AMPERES code, Lagrangian particle simulations are often used to study an external package for AMP software. In the talk we vortex dynamics in the context of incompressible fluids. demonstrate the importance of the coupled solution proce- It is well-known that the simulation accuracy is sensi- dure using Newton Krylov iterative solvers. Experiments tive to the particle distribution, and maintaining a proper based on various preconditioning strategies are presented. distribution as the flow evolves is a challenging problem. I’ll discuss some techniques used to address this issue in two applications: (1) adaptive panel refinement for vor- Srikanth Allu tex sheets, and (2) particle remeshing for the barotropic Oak Ridge National Laboratory vorticity equations on a rotating sphere. [email protected]

Robert Krasny Sreekanth Pannala University of Michigan AN12 Abstracts 33

Computer Science and Mathematics Division reactor, and stability analysis of a magnetohydrodynamics Oak Ridge National Laboratory test problem. [email protected] Roger Pawlowski Partha Mukherjee, Bobby Philip Multiphysics Simulation Technologies Dept. Oak Ridge National Laboratory Sandia National Laboratories [email protected], [email protected] [email protected]

John Turner Eric C. Cyr Oak Ridge National Laboratory Scalable Algorithms Department Computational Engineering and Energy Sciences Sandia National Laboratotories [email protected] [email protected] John Shadid MS4 Sandia National Laboratories The Arctic Terrestrial Simulator: Developing a Albuquerque, NM Flexible Multiphysics Simulator based on Amanzi [email protected]

The Arctic Terrestrial Simulator (ATS) is being developed Eric Phipps to simulate coupled processes governing carbon releases Sandia National Laboratories from degrading permafrost, including subsurface and over- Optimization and Uncertainty Quantification Department land flow, heat transport, subsidence, and soil biogeochem- [email protected] istry. A flexible simulation capability that naturally supports strong and weak coupling of selected processes is required. Building upon Amanzi, the ASCEM simulator, we MS4 present a general strategy for dynamically managing data The Advanced Multi-Physics (AMP) Package With structures, data permissions, and process model couplings An Application to Fuel Assemblies in Nuclear Re- for the ATS. actors

Ethan T. Coon, Markus Berndt, J. David Moulton, Scott Simulations of multiphysics systems are becoming increas- Painter ingly important in many science application areas. In this Los Alamos National Laboratory talk we describe the design and capabilities of the Ad- [email protected], [email protected], [email protected], vanced Multi-Physics (AMP) package designed with multi- [email protected] domain multi-physics applications in mind. AMP currently builds powerful and flexible deterministic multiphysics simulation algorithms from lightweight operator, solver, linear MS4 algebra, material database, discretization, and meshing in- A Multiphysics PDE Assembly Engine for Non- terfaces. In this and related talks we will describe how linear Analysis using Template-based Generic Pro- AMP has been used to solve coupled multi-domain multi- gramming Techniques physics problems related to energy applications. As computational algorithms, hardware, and programming Bobby Philip,KevinClarno languages have advanced over time, computational model- Oak Ridge National Laboratory ing and simulation is being leveraged to understand, ana- [email protected], [email protected] lyze, predict, and design increasingly complex physical, biological, and engineered systems. Because of this complex- Rahul S. Sampath ity, significant investments must be made, both in terms ORNL of manpower and programming environments, to develop [email protected] simulation capabilities capable of accurately representing the system at hand. At the same time, modern analysis approaches such as stability analysis, sensitivity analy- Mark Berrill, Srikanth Allu sis, optimization, and uncertainty quantification require in- Oak Ridge National Laboratory creasingly sophisticated capabilities of those complex sim- [email protected], [email protected] ulation tools. Often simulation frameworks are not designed with these kinds of analysis requirements in mind, Gary Dilts which limits the efficiency, robustness, and accuracy of LANL the resulting analysis. In this work, we describe an ap- [email protected] proach for building a mulitphysics assembly engine that natively supports requirements for many types of analysis Pallab Barai algorithms and solution techniques. This approach lever- ORNL ages compile-time polymorphism and generic programming [email protected] through C++ templates to insulate physics experts from the complexities associated with the analysis hierarchy and solution techniques. The ideas presented here build on MS5 operator overloading-based automatic differentiation tech- Advances on the Discretizable Distance Geometry niques to transform a simulation code into one that is capa- Problem ble of providing analytic derivatives. However we extend these ideas to compute quantities that aren’t derivatives The Discretizable Distance Geometry Problem (DDGP) is such as polynomial chaos expansions, floating point counts, a subset of the DGP which can be solved using a discrete and extended precision calculations. We will show example search occurring in continuous space. Its main application use cases including turbulent flow in a light water nuclear is to find three-dimensional arrangements of proteins using 34 AN12 Abstracts

NMR data. We will talk about our efforts that have been scription of an NMR structure and its dynamic properties, directed towards adapting the DDGP to be an ever closer the same as in X-ray crystallography. The formulation of model of the actual difficulties posed by the problem of the optimization problem is given. The algorithm for solv- determining protein structures from NMR data. ing the problem is described. The test results on model proteins are presented. Carlile Lavor State University of Campinas Atilla Sit Department of Applied Mathematics University of Wisconsin - Madison [email protected] Institute for Discovery [email protected] Leo Liberti Ecole Polytechnique [email protected] MS5 An Optimal Solution to the Generalized Distance Nelson Maculan Geometry Problem Programa de Engenharia de Sistemas de Computao NMR experiments on a protein yield a set of inter-atomic COPPE Universidade Federal do Rio de Janeiro distance ranges. A number of structures satisfying the dis- [email protected] tance constraints, derived from distance range and bond information, are then generated. This ensemble of structures Antonio Mucherino is often under represented and inaccurately represents the University of Rennes 1 protein’s structural fluctuations. In this presentation we [email protected] present an alternative problem where its solution, derived from interior point optimization, provides a single representation for a protein’s conformation and its ensemble of MS5 possible structures. Coarse Grained Normal Mode Analysis vs. Refined Gaussian Network Model for Protein Residue- Zachary D. Voller, Zachary D. Voller Level Structural Fluctuations Iowa State University Department of Mathematics We investigate several approaches to coarse grained normal [email protected], [email protected] mode analysis on protein residual-level structural fluctuations by choosing different ways of representing the residues Zhijun Wu and the forces among them. The residue mean-square- Iowa State University fluctuations and their correlations with the experimental [email protected] B-factors are calculated for a large set of proteins. The extracted force constants from the Hessian are surveyed, and the statistical averages are used to build a refined Gaus- MS6 sian Network Model. Joint work with Robert Jernigan and Homogenization-based Mortar Methods for Porous Zhijun Wu. Media Jun-Koo Park For an elliptic problem with a heterogeneous coefficient in Iowa State University mixed form, nonoverlapping mortar domain decomposition [email protected] is efficient in parallel if the mortar space is small. We define a new multiscale mortar space using homogenization MS5 theory. In the locally periodic case, we prove the method achieves optimal order error estimates in the discretiza- The Determination and Refinement of Protein En- tion parameters and heterogeneity period. We assess its sembles using Inter-atomic Distance Bounds numerical performance when the coefficient is not locally A novel approach is proposed for the determination of the periodic. ensemble of structures for a protein given a set of distance Todd Arbogast bounds from NMR experiments. In this approach, simi- Dept of Math; C1200 lar to X-ray crystallography, a protein is assumed to have University of Texas, Austin an equilibrium structure with the atoms fluctuating around [email protected] their equilibrium positions. Thus, the structure determination problem can be formulated as an optimization problem, i.e., to find the equilibrium positions and maximal Hailong Xiao possible fluctuation radii for the atoms in the protein, sub- ICES ject to the condition that the fluctuations should be within The University of Texas at Austin the given distance bounds. The advantages of using this [email protected] approach are the following: (1) The mathematical problem to be solved becomes more tractable, and only a single MS6 solution to an optimization problem is required, while in conventional approaches, multiple solutions are sought for Multiscale Model Reduction for Flows in Hetero- a system of inequalities, which in general is intractable. (2) geneous Porous Media A single structure along with the estimates on the atomic For multiscale problems, some types of coarsening of the fluctuations suffices to describe the structure and its fluc- detailed model are usually performed before the model can tuation ranges that are underestimated in conventional ap- be used to simulate complex processes. In this talk, I will proaches using a finite number of structural samples. (3) describe multiscale model reduction techniques that can be A single structural model with the fluctuation radii corre- used to systematically reduce the degrees of freedoms of sponding to the B-factors can be obtained for the full de- AN12 Abstracts 35

fine-scale simulations and discuss applications to precondi- observation i.e. from core scale up. However various ex- tioners. For parameter-dependent problems, I will describe perimental techniques and discrete and continuum based how Reduced Basis approaches can be used offline to gen- computational methods are now available for the study of erate reduced local problems. phenomena at porescale. Most interesting are coupled processes whose influence on the core and field scale flow and Yalchin Efendiev transport is essential but for which upscaled models, espe- Dept of Mathematics cially for high flow rates, are lacking. We discuss our recent Texas A&M University results based on experimental as well as complex synthetic [email protected] geometries. Malgorzata Peszynska MS6 Department of Mathematics An Exponentially Convergent Approximation The- Oregon State University ory for Fields Inside Multiscale Heterogeneous Ma- [email protected] terials Anna Trykozko Large multiscale engineering systems such as airplane University of Warsaw wings and wind turbine blades are built from fiber rein- [email protected] forced composites and exhibit a cascade of substructure spread across several length scales from microns to tens of meters. The computational modeling of these hierarchi- MS7 cal and heterogeneous structures is a very large problem Composed Solution Methods for General Nonlinear that requires parallel computation. In this talk we ad- Equations dress both the problems of parallelization and dimension reduction and present an exponentially convergent approx- The numerical solution of large-scale nonlinear systems imation theory for multiscale problems. This is joint work of equations may be performed using Newton’s method, with Ivo Babuska and has appeared in Multiscale Modeling global methods, like nonlinear Krylov methods, or local and Simulation, SIAM, (2011) 9, 373 406. methods, like nonlinear Gauss-Seidel. Many problems cannot be efficiently solved using Newton-like schemes. As an Robert P. Lipton alternative, we propose a flexible framework for the com- Department of Mathematics position of local and global methods. We demonstrate the Louisiana State University effectiveness and efficiency of composable nonlinear solvers [email protected] on problems of interest from computational biology.

Peter R. Brune MS6 Mathematics and Computer Science Division Multiscale Mortar Coupling of Multiphase Flow Argonne National Laboratories and Reactive Transport on Non-matching Grids [email protected] Geochemical modeling plays an important role in designing carbon sequestration strategies, characterizing environ- Matthew G. Knepley mental site contaminations, and predicting environmental University of Chicago impacts. We formulate a multiscale model for coupling [email protected] multiphase flow and reactive transport in porous media. The flow is modeled using mortar mixed finite elements Barry F. Smith that allow for accurate and efficient parallel domain decom- Argonne National Lab position with non-matching grids. The reactive transport MCS Division equations are treated using operator splitting for decou- [email protected] pling transport and reactions. Computational results are presented. MS7 Gergina Pencheva Physics-based Preconditioning within Implicit University of Texas at Austin Simulations of Visco-resistive Tokamak Plasmas [email protected] Single-fluid resistive magnetohydrodynamics (MHD) is a Mary F. Wheeler fluid description of fusion plasmas which is often used Center for Subsurface Modeling to investigate macroscopic instabilities in tokamaks. In University of Texas at Austin MHD modeling of non-spherical tokamaks it is often desir- [email protected] able to compute MHD phenomena to resistive time scales, which can make explicit time stepping schemes computationally intractable. Our work focuses on simulations using Mojdeh Delshad a structured mesh mapped into a toroidal geometry with University of Texas at Austin a shaped poloidal cross-section, and a finite volume spatial [email protected] discretization of the PDE model. We discretize the temporal dimension using a fully implicit θ or BDF method, MS6 and solve the resulting nonlinear algebraic system using a standard inexact Newton-Krylov approach. The focus of Modeling Flow and Coupled Transport with Ad- this talk is on the construction and performance of physics- sorption from Pore to Core based preconditioning approaches for accelerating conver- Mathematical modeling of flow and transport in porous gence of these iterative solvers. We compare precondition- media until recently has been restricted to the scales of ers inspired by solvers from legacy MHD codes, though here they are used within a preconditioning context. We 36 AN12 Abstracts conclude with numerical results in the context of pellet- dominated Parabolic Problems Using an Adaptive injection fueling of tokamak plasmas. Region-swapping Approach

Daniel R. Reynolds This work couples the ﬁnite volume (FV) method with Southern Methodist University the discontinuous Galerkin (DG) method dynamically. For Mathematics Department each time-step, an eﬃcient partition of the domain between [email protected] the two methods is determined in an attempt to best preserve the high accuracy of the DG method while also taking Ravi Samtaney advantage of the low computational cost of the FV method KAUST wherever is possible. The implementation preserved the [email protected] expected numerical convergence rates, while yielding substantially smaller linear systems. Advisor: Beatrice Riv- Hilari Tiedeman iere, Rice University Southern Methodist University Joseph Huchette Mathematics Rice University [email protected] [email protected]

MS7 MS8 Anderson Acceleration of Modified Picard Itera- Spectral Properties of Neural Network Structures tion for Variably Saturated Flow I investigate how biologically relevant patterns of network We will present our investigation of the effectiveness of the connectivity affect neural activity. To encode network Anderson Acceleration method applied to the modified Pi- structure, I construct synaptic weight matrices and observe card iteration for simulations of variably saturated flow. changes in spectra and resulting dynamics. Differences in We solve nonlinear systems using both unaccelerated and spectra for small world, nearest neighbor, and random net- accelerated modified Picard iteration as well as Newton’s works affect prevalence of stable, periodic, and chaotic so- method. Since Picard iterations can be slow to converge, lutions, Lyapunov exponents, and frequencies measured by the advantage of acceleration is to provide faster conver- Fourier series approximations. The degree of asymmetry in gence while maintaining advantages of the Picard method the matrix affects radius, number of real eigenvalues, and over the Newton method. Results indicate that the ac- types of chaos achieved. Advisor: Dr. Jonathan Rubin, celerated method provides a robust solver with significant University of Pittsburgh potential computational advantages. Jeffrey Moulton Carol S. Woodward, Aaron Lott University of Pittsburgh Lawrence Livermore Nat’l Lab [email protected] [email protected], [email protected]

Homer F. Walker MS8 Worcester Polytechnic Institute The Eﬀects of Signal Delay in Gene Regulatory [email protected] Networks

Ulrike Yang Delay can qualitatively affect the dynamics of gene regu- Lawrence Livermore Nat’l Lab latory networks. It has been shown that delay can cause [email protected] oscillations and increase signal-to-noise ratios. Using analytical techniques, stochastic modeling, model reduction techniques, and simulations, we will study how delay affects MS7 the flow of information through gene regulatory networks. An Optimal Convergence Neighborhood Strategy Advisor: William Ott, University of Houston for an Implicit Timestep Solver That Converges All the Time Sarah Stanley University of Houston The Adaptively-Localized-Continuation-Newton (Younis, [email protected] R.M. et al., 2008) method is a numerical continuation scheme that applies time-step size as its homotopy parameter. The solver unifies implicit time-stepping with nonlin- MS9 ear iteration. A key component that dictates a trade-off Analysis of Nematic Liquid Crystals with Disclina- between efficiency and robustness is the choice of Conver- tions gence Neighborhood about the solution path. This work analyzes an automatically adaptive strategy for this choice We investigate the structure of nematic liquid crystal thin in order to locally optimize the progress in time advance- films described by the Landau-de Gennes tensor-valued or- ment while still guaranteeing unconditional robustness. der parameter for energy minimizers with Dirichlet boundary conditions of nonzero degree. We prove that as the Rami M. Younis elasticity constant goes to zero a limiting uniaxial texture Postdoctoral Research Fellow forms with disclination lines corresponding to a finite num- Stanford University ber of defects, all of degree one-half or minus one-half. [email protected] Patricia Bauman Purdue University MS8 [email protected] A Multi-numeric Method for Convection- AN12 Abstracts 37

Jinhae Park MS9 Seoul National University Extrinsic Curvature, and Two-dimensional Ne- Seoul, South Korea matic Order [email protected] We derive two-dimensional free energies, aimed at describ- Daniel Phillips ing the alignment of nematics deposited on curved sub- Department of Mathematics, Purdue University strates, from the conventional three-dimensional theories of [email protected] nematic liquid crystals. Both the director and the order- tensor theories are taken into account. The so-obtained surface energies exhibit extra terms compared to earlier MS9 models. These terms couple the shell geometry with the Ferronematic Liquid Crystal Composites nematic order parameters. As expected, the shape of the shell plays a prominent in the equilibrium configurations The coupling effects of nematic liquid crystals to mag- of nematics coating it. netic fields are usually weak, due to the small values of the anisotropic diamagnetic susceptibility. In their sem- Gaetano Napoli inal work, F.Brochard and P.G.de Gennes (Physique des Dipartimento di Ingegneria dell’Innovazione Solides, 1970), investigated suspensions of magnetic grains UniversitàdelSalento in liquid crystals. We discuss the roles and interaction be- [email protected] tween theoretical and experimental research works in the ensuing decades, and present a mathematical justification of the proposed models. MS10 Characterization of Discontinuities in High- Maria-Carme Calderer dimensional Stochastic Problems on Adaptive Deparment of Mathematics Sparse Grids University of Minnesota, USA [email protected] Stochastic collocation methods are an attractive choice to characterize uncertainty because of their non-intrusive na- Dmitry Golovaty ture. High dimensional stochastic spaces can be approxi- The University of Akron mated well for smooth functions with sparse grids. There Department of Theoretical and Applied Mathematics has been a focus in extending this approach to non-smooth [email protected] functions using adaptive sparse grids. This presentation will present both adaptive approximation methods and error estimation techniques for high dimension functions. Antonio De Simone SISSA-International School of Advanced Studies Rick Archibald [email protected] Computational Mathematics Group Oak Ridge National Labratory Alexander Panchenko [email protected] Washington State University [email protected] MS10 Sparse Grids for Uncertainty Quantification MS9 Recent Results on Nematic Elastomers This talk will discuss the use of sparse grids to approximate the high dimensional integrals that arise when uncertainty Abstract not available at time of publication. in problem inputs is modeled by assigning a probability density function over each range and considering the prod- Antonio De Simone uct space of all possibilities. We will consider generaliza- SISSA-International School of Advanced Studies tions of the sparse grid approach that place more emphasis [email protected] on some input factors. John Burkardt MS9 Department of Computational Science Electric-Field-Induced Instabilities in Florida State University Liquid-Crystal Films [email protected] Simple models of liquid crystals characterize orientational properties in terms of a director fie d, which can be influ- MS10 enced by an applied electric field. The local electric field is An Efficient Sparse-grid-based Method for influenced by the director field; so equilibria must be com- Bayesian Uncertainty Analysis puted in a coupled way. Equilibria are stationary points of a free energy functional,whichcanfailtobecoercivebe- Abstract not available at time of publication. cause of the nature of the director/electric-field coupling. We discuss characterizations of local stability and anoma- Max Gunzburger lous behavior in such systems. Florida State University School for Computational Sciences Eugene C. Gartland [email protected] Kent State University [email protected] MS10 A Hierarchical Adaptive Sparse Grid Stochastic 38 AN12 Abstracts

Wavelet Collocation Method for PDEs with Ran- MS12 dom Input Data Panel Discussion: Teaming Up in Tough Times Accurate predictive simulations of complex real world ap- This discussion section will be provide time for questions plications require numerical approximations to first, op- relating to the collaboration and opportunities that the pose the curse of dimensionality and second, converge speakers have addressed. quickly in the presence of steep gradients, sharp transitions, bifurcations or finite discontinuities in high-dimensional Lori A. Diachin parameter spaces. In this talk we present a novel multidi- Lawrence Livermore National Laboratory mensional multiresolution adaptive (MdMrA) sparse grid [email protected] stochastic collocation method, that utilizes hierarchical multiscale piecewise Riesz basis functions constructed from Rachel Ward interpolating wavelets. The basis for our non-intrusive Department of Mathematics method forms a stable multiscale splitting and thus, opti- University of Texas at Austin mal adaptation is achieved. Error estimates and numerical [email protected] examples will used to compare the efficiency of the method with several other techniques. Tiffani L. Williams Guannan Zhang Texas A&M University Florida State University [email protected] [email protected] MS12 Clayton G. Webster Some Perspectives on Teaming from the DOE Na- Oak Ridge National Laboratory tional Labs [email protected] I will present my perspectives on the role of teams in the Max Gunzburger current economic environment as we attempt to accomplish Florida State University more science with scarcer resources and on what has been [email protected] effective in forming and sustaining successful teams. I will call on my experiences in leading two multi-institutional mathematics teams for DOEs SciDAC program and my role MS11 as the division leader of a research organization charged Title Not Available at Time of Publication with performing multidisciplinary research.

Abstract not available at time of publication. Lori A. Diachin Lawrence Livermore National Laboratory Alexander Barg [email protected] University of Maryland [email protected] MS12 Take Initiative, Make Contacts, and Collaborate: MS11 My Journey from Graduate Student to Professor Title Not Available at Time of Publication Being a successful mathematician involves more than just Abstract not available at time of publication. knowing the math. As in other professions, taking initiative and forming collaborations are crucial in a competitive Simon Blackburn job market. These strategies can be counter-instinctual Department of Mathematics and uncomfortable in male-dominant ﬁelds such as math. Royal Holloway, University of London I will discuss my own strategies for overcoming unease in [email protected] being aggressive. I will also share other strategies and mis- takes that I made in transitioning from graduate student MS11 to professor. Sheaves on Graphs Rachel Ward Department of Mathematics Abstract not available at time of publication. University of Texas at Austin Joel Friedman [email protected] Dept. of Mathematics& Computer Science University of British Columbia MS12 [email protected] Building Relationships in the Tree of Life

MS11 The Tree of Life is a family tree showing the evolutionary relationships among all of the worlds organisms. I will dis- New Challenges in Cryptology cuss opportunities at the intersection of biology and com- Abstract not available at time of publication. puter science for constructing such an awesome representation of life. However, the Tree of Lifes impact transcends William J. Martin science. It may represent the ultimate role model for build- Department of Mathematical Sciences ing connections in a sea of diversity. Worcester Polytechnic Institute [email protected] Tiﬀani L. Williams AN12 Abstracts 39

Texas A&M University [email protected] [email protected]

MS13 MS13 Tree Based Communication for Scalable Mesh Adaptive Magnetohydrodynamics Simulations Adaptation in the SAMRAI Framework with SAMRAI SAMRAI mesh adaptation involves collective, A wide variety of plasma problems require both high res- communication-intensive operations that are challenging to olution and large spatial domains that present a problem scale. The critical clustering and partitioning operations for existing models. Adaptive Mesh Refinement (AMR) use virtual tree networks to limit communication latency provides an efficient method of obtaining both high reso- to (log P )forP processes. However, ideal performance lution and a large spatial domain. AMR allows for both is hinderedO by a number of possible causes that are dif- hi-resolution and large spatial domain computations. This ficult to examine. In this work, we use newly developed talk will focus on using structured AMR with a 3D plasma tools to analyze the complex tree-based communications, model (pixie3d). Current progress will be presented. with results leading to improved performance for SAMRAI applications. Mark Berrill, Luis Chacon, Bobby Philip, Zhen Wang, Manuel Rodriguez Brian Gunney Oak Ridge National Laboratory Lawrence Livermore National Lab [email protected], [email protected], [email protected], [email protected] [email protected], [email protected] Abhinav Bhatele, Todd Gamblin Lawrence Livermore National Laboratory MS13 [email protected], [email protected] Composable Multilevel Methods for Multiphysics Simulations MS13 Implicit solution methods for multiphysics problems are ei- Building AMR into a Multiphysics Code Using the ther monolithic (treating the coupled problem directly) or SAMRAI Framework split (solving reduced systems independently), with multilevel methods often being important for algorithmic scal- Supporting mature, evolving application requirements is ability in both approaches. We present flexible support a challenge for software frameworks. Using the SAMRAI developed in PETSc for block preconditioners, splitting framework, we have integrated adaptive mesh refinement in smoothers, related multiplicative relaxation, nonlinear (AMR) into a mature multiphysics code which is heavily and matrix-free variants, and communication/bandwidth used and under continual developed. SAMRAI provides reducing techniques. We demonstrate software modular- unique object-oriented support for parallel AMR mesh and ity without sacrificing run-time algorithmic flexibility for data management. We describe how SAMRAI allows de- applications in geodynamics and phase-field models. coupling AMR operations from the application mesh and data; SAMRAI does not own these entities, yet it manip- Jed Brown ulates them directly. Mathematics and Computer Science Division Argonne National Laboratory Richard Hornung [email protected] Lawrence Livermore National Lab [email protected] Mark Adams Columbia University Robert Anderson [email protected] LLNL Ctr for Appl Scientific Comp Peter R. Brune [email protected] Mathematics and Computer Science Division Argonne National Laboratories Noah Elliott [email protected] LLNL [email protected] Matthew G. Knepley University of Chicago Brian Gunney [email protected] Lawrence Livermore National Lab [email protected] Dave May ETH Zurich Michael Wickett [email protected] Lawrence Livermore National Laboratory [email protected] Lois Curfman McInnes Argonne National Laboratory Mathematics and Computer Science Division MS14 [email protected] Efficient Algorithms for Mesoscale Dynamics of In- teracting Particle Systems Barry F. Smith Argonne National Lab We present efficient algorithms for simulating evolution of MCS Division space-time averages of large ODE systems. Averaging pro- 40 AN12 Abstracts duces exact PDEs but they cannot be simulated without sored by ARRA-NSF-Math-Bio-0920852. solving the underlying ODEs. We approximate these PDEs by new closed form equations that can be simulated inde- Yvonne Ou pendently of solving the underlying ODEs at a fraction University of Delaware of the cost. To achieve closure we use methods from the [email protected] theory of ill-posed problems. We analyze quality of the approximation and efficiency of algorithms. MS15 Lyudmyla Barannyk Evolutionary Games with Gaussian Structures University of Idaho Department of Mathematics We consider a population playing two-strategy symmetric [email protected] games on a grid. A discrete Gaussian kernel rules out the interactions and information collection between individu- Alexander Panchenko als. We study how frequency and spatial structure of the Washington State University population change over time for Prisoner’s Dilemma game [email protected] under four different update rules. Simulation results for these rules show frequencies of the games for kernels with different deviations. It is conjectured that, if the deviation MS14 of the kernel is large enough, bifurcation diagram of mean- Flux Norm and Finite-dimensional Homogeniza- field dynamics and spatial simulations agree. This result tion Approximation with Non-separated Scales and will be justified by showing the relation between macro- High Contrast scopic and mesoscopic limits of the same microscopic rule. In joint work with Owhadi we consider the most general Ozgur Aydogmus case of arbitrary L∞ coefficients, which may contain in- finitely many scales not necessarily being well-separated. Iowa State University We establish a finite-dimensional homogenization approxi- [email protected] mation generalizing correctors in classical homogenization, and error estimates in the flux norm with an optimal error MS15 constant. We discuss recent results on localized multiscale basis and work in progress on compactness of the solution Computation and Analysis of Evolutionary Game space, and new corrector results in classical periodic ho- Dynamics mogenization problem. Biological species (viruses, bacteria, parasites, insects, Leonid Berlyand plants, or animals) replicate, mutate, compete, adapt, and Penn State University evolve. In evolutionary game theory, such a process is mod- Eberly College of Science eled as a so-called evolutionary game. We describe the [email protected] Nash equilibrium problem for an evolutionary game and discuss its computational complexity. We discuss the necessary and sufficient conditions for the equilibrium states, MS14 and derive the methods for the computation of the optimal Acoustic Propagation in a Saturated Piezo-Elastic, strategies, including a specialized Snow-Shapley algorithm, Porous Medium a specialized Lemke-Howson algorithm, and an algorithm based on the solution of a complementarity problem on a We study the problem of derivation of an effective model simplex. Computational results are presented. Theoretical of acoustic wave propagation in a two-phase, non-periodic difficulties and computational challenges are highlighted. medium modeling a fine mixture of linear piezo-elastic solid and a viscous Newtonian, ionic bearing fluid. Bone tissue is Yiping Hao an important example of a composite material that can be Department of Mathematics modeled in this fashion. We develop two-scale homogeniza- Iowa State University tion methods for this system, and discuss also a stationary [email protected] random, scale-separated microstructure. Robert P. Gilbert MS15 Department of Mathematical Sciences Within-host Dynamics of Influenza Virus Infection University of Delaware with Immune Responses [email protected] Influenza virus infection remains a public health problem worldwide. The mechanism underlying viral control during MS14 an uncomplicated influenza virus infection is not fully un- On the Integral Representation Formula (IRF) for derstood. In this talk, I will address this question by devel- a Two-parameter Family of Elastic Composites oping mathematical models that include both innate and adaptive immune responses, and fitting them to experimen- This talk focuses on the derivation/implication of the IRF tal data. This study provides a quantitative understanding for two-phase composites in which the contrasts between of the biological factors that can explain the viral and in- two set of Lame coefficients can be described indepen- terferon kinetics during a typical influenza virus infection, dently by the two parameters. This topic of research is and may provide more information for future research in inspired by the inverse problem of recovering microstruc- influenza pathogenesis, treatment, and vaccination. tural information from measurement of effective properties of finely-structured composites (dehomogenization) in Libin Rong which IRF plays an essential role. This research is spon- Oakland University [email protected] AN12 Abstracts 41

MS15 systems. Homotopy continuation methods allow one to Modeling the Dynamics of Cross-infection of Leish- compute all solutions on a given mesh, but even a moder- mania Amazonensis and Leishmania Major ate size grid may lead to an intractably high degree system. However, generally most of the solutions are nonphysical, Immune response during the course of Leishmania infec- and so filtering techniques aim to reduce the work spent on tion is a classical and crucial model in immunology and them. In this talk we discuss a new approach for forming pathology, as it revealed and claried a large number of filtering homotopies over a continuous family of numeri- critical and essential immunology factors such as binary cal schemes, which in turn allows for more robust filtering pathways of CD4+ T helper cells activations, transporta- criteria and less reliance on ad hoc threshholds. tion of pathogens by dendritic cells, and mechanisms of macrophage to clean the pathogens etc. Recently, a se- Tim M. Mccoy ries of experiments on the cross infection of Leishmania University of Notre Dame amazonensis and Leishmania major on C3HeB/FeJ and [email protected] C57BL/6 mice [Jones et.al. 06, 11] indicates critical functions of B cells during the process of cleaning the pathogen and resolving the no-healing diseases caused by Leishma- MS16 nia amazonensis. Those experimental results also demon- Real Algebraic Geometry in Combinatorics strate interesting population dynamics that the two strains of Leishmania interact indirectly through inducing differ- The talk will give an overview of several problems in Ge- ent immune responses. Using immunobiological dynamics ometric Combinatorics and will describe some approaches approach and game-theoretical approach, we propose and to these problems through Real Algebraic Geometry. compare two mutually different models to study the cross Chris Peterson, Eklund David infection of Leishmania amazonensis and Leishmania ma- Colorado State University jor based on [Jones et.al. 06, 11]. Detailed analysis and [email protected], [email protected] numerical simulation are conducted based on parameters identified from the data. Matthew Kahle Douglas Jones Institute for Advanced Study Department of Veterinary Pathology [email protected] Iowa State University [email protected] MS16 Wen Zhou Building a User Friendly Matlab Platform for Nu- Department of Mathematics and Department of Statistics merical Polynomial Algebra Iowa State University Numerical polynomial algebra and numerical algebraic ge- [email protected] ometry has enjoyed tremendous advancement in recent years with many algorithms becoming standard. A Mat- Zhijun Wu lab package Apalab, initially developed several years ago Iowa State University for numerical polynomial algebra, is in major upgrade. In Dept of Math additional to adding algorithms/implementations, we are [email protected] designing an intuitive interface so that casual users and early students can engage advanced polynomial computation easily. This talk will present those new developments MS16 toward building such a Matlab platform. Root Counts, Eigenvectors and Numerical Homo- topies Zhonggang Zeng Northeastern Illinois University We will explain how solutions to polynomial systems can Department of Mathematics be viewed as zero sets of sections of vector bundles with the [email protected] result of reducing the number of homotopy paths used in a numerical solution of the system. Specifically we will look at the tangent bundle of projective space and associated MS17 systems of polynomials. We anticipate that solving these Improvements in Adaptive Nonlinear Filtering in polynomial systems numerically amounts to a numerical Regularization Models for Incompressilbe Flows method to compute the Jordan canonical form of a matrix. We will review some recent results for adaptive nonlinear David Eklund filtering in regularization models of incompressible flow. Institut Mittag-Leffler We will then discuss some improvements in how to de- [email protected] fine the indicator functions. We will present a numerical method using these ideas, prove convergence of it to the Chris Peterson model, and give several test examples. Colorado State University [email protected] Abigail Bowers Department of Mathematical Sciences Clemson University MS16 [email protected] Filtering Homotopies for Discretized Boundary Value Problems MS17 Discretizations of boundary value problems arising from A Least Squares Approach for the Coupled Stokes- models in science and engineering often yield polynomial 42 AN12 Abstracts

Darcy System ties for the newly developed (A. Dunca, 2011) multiscale- deconvolution models of turbulence. We prove conser- We consider a linear/nonlinear Stokes flow coupled with vation laws, derive a microscale, and show the existence a porous medium flow with only flow rates specified on of global attractors. Additionally, we derive a numerical the inflow and outflow boundaries in both flow domains. scheme for the model, and show results of preliminary tests The coupled Stokes-Darcy system is formulated as an op- on some benchmark problems. timal control problem where a common force is used as a control to minimize the the jump in normal velocities of Leo Rebholz two flows across the interface and to match the given flow Clemson University rates. We analyze the optimal control problem and use a Department of Mathematical Sciences least squares approach for which a Gauss-Newton type al- [email protected] gorithm is considered. Numerical results are presented to validate convergence of the algorithm. Argus Adrian Dunca Spiru Haret University Hyesuk Lee [email protected] Clemson University Dep. of Mathematical Sciences [email protected] Monika Neda University of Nevada Las Vegas [email protected] MS17 Coupling Biot and Navier-Stokes Equations for Kara Kohler Modelling Fluid-poroelastic Media Interaction Clemson University [email protected] The interaction between a free fluid and a deformable porous medium is found in a wide range of applications: ground-surface water flow, geomechanics or blood-vessel MS18 interactions. We focus on the latest application. The Mathematical Models of Gels in Biomedical Appli- fluid-poroelastic structure interaction (FPSI) problem in cations: Drug Delivery Devices hemodynamics couples the Navier-Stokes equations for an incompressible fluid to the Biot problem, the latter govern- Abstract not available at time of publication. ing the motion of a saturated poroelastic medium. Only a limited number of works deal with this problem. The finite Maria-Carme Calderer element approximation of the FPSI problem is involved due Deparment of Mathematics to the fact that both subproblems are indefinite. We intro- University of Minnesota, USA duce a residual-based stabilization technique for the Biot [email protected] system, motivated by the variational multiscale approach. This technique allows the use of the same finite element MS18 spaces for all the velocities and pressures, greatly simpli- fying the discretization and the enforcement of coupling Immersive Visualization and Computational Cre- conditions. We choose a fixed point method for the lin- ativity for Biomedicine earization of the Navier-Stokes/Biot coupled system. To This talk will focus on recent advances in interactive vi- solve the linear FPSI system at every fixed point iteration, sualization in immersive virtual reality and on the emerg- we propose to use both a monolithic approach and par- ing research topic of computational creativity the devel- titioned procedures based on domain decomposition pre- opment of computer tools for supporting creative human conditioners (the Dirichlet-Neumann, Robin-Robin, and tasks, such as 3D design. Exciting recent interdisciplinary Robin-Neuman ones). We compare the efficiency of all the applications of this research to biomedicine at the Univer- methods on a test problem. The performance of the mono- sity of Minnesota will be described, including research on a lithic approach improves as the added-mass effect gets crit- new multi-touch 3D visualization environment for design- ical and the Robin-Neumann preconditioner proves to be ing medical devices within virtual models of the human the less sensitive to the added-mass effect. anatomy. Annalisa Quaini Daniel Keefe University of Houston University of Minnesota [email protected] [email protected]

Santiago Badia International Center for Numerical Methods in MS18 Engineering Tracking Brain and CSF Evolution via Level Universitat Polit`ecnica de Catalunya, Barcelona, Spain Set/mesh Warping Algorithm during Hydro- [email protected] cephalus Treatment

Alfio Quarteroni Hydrocephalus is a serious neurological disorder in which Ecole Pol. Fed. de Lausanne there is an abnormal accumulation of cerebrospinal fluid Alfio.Quarteroni@epfl.ch (CSF) in the brain ventricles, causing brain enlargement and tissue compression. Although hydrocephalus treatment has been performed by surgical CSF shunt inser- MS17 tion, computational models are needed to track hydro- Multiscale Deconvolution Models of Turbulence cephalic brain movement. Thus, we propose a combined level set/mesh warping algorithm and use it to simulate We will prove several mathematical and physical proper- the evolution of the brain ventricles and the CSF in pedi- AN12 Abstracts 43 atric hydrocephalic patients. MS19 Periodic Dispersion Jeonghyung Park, Suzanne M. Shontz, Corina S. Drapaca The Pennsylvania State University The evolution of linearly dispersive equations with piece- [email protected], [email protected], [email protected] wise constant initial data on periodic domains depends on the asymptotic behavior of the dispersion relation. In particular, dispersion relations with asymptotically poly- MS18 nomial growth lead to dispersive quantization, being (ap- Immunotherapy and Aging Effects in Immune proximately) quantized at rational times but fractal at ir- Modulated Tumor Growth rational times. Similar phenomena are known as Talbot effect in optics and quantum mechanics. Numerical exper- The presence of cancer in a host elicits an immune re- iments and some analysis indicate that such effects persist sponse that can be both inhibitory and stimulatory to tu- into the nonlinear regime. Advisor: Peter J. Olver, U Min- mor development. Aging decreases the effectiveness of the nesota immune response, which can alter immune modulation of tumor growth. We present a mathematical model based Gong Chen on principles of generalized logistic growth that incorpo- U Minnesota rates both pro- and anti-tumor immune processes. We then [email protected] use this model to investigate the effects of aging and immunotherapy on tumor development. MS19 Kathleen P. Wilkie Modeling Earth’s Temperature and Atmospheric Tufts University School of Medicine Carbon Dioxide Center of Cancer Systems Biology [email protected] From ice core data, it is known that over the past 400,000 years, surface temperatures and atmospheric CO2 concen- Philip Hahnfeldt trations have oscillated with a period of approximately Tufts University 100,000 years. The model introduced by Budyko (1969) is [email protected] a simple model for the temperature of the Earths surface, but it does not allow atmospheric CO2 to change. Here, the Budyko model is altered to allow CO2 to change, so as MS19 to explore the interactions between CO2 and temperature. Symplectic Methods for an Exactly Solvable Kol- Advisor: Mary Lou Zeeman mogorov Model of Two Interacting Species Emma Cutler We discuss the behavior of symplectic integration methods Bowdoin College for an exactly solvable Kolmogorov predator-prey model of [email protected] two interacting species. Using numerical experiments, we investigate the accuracy, conservation, and periodic orbits of this Hamiltonian system. In light of this, we present po- MS20 tential generalizations to other population dynamics with Multiscale Models for Coupled Flow and Elasticity bounded state variables. Advisor: Ari Stern, University of California, San Diego In this talk, a multiscale framework for fluid-structure interaction problem in an inelastic media is developed and Katherine Ball analyzed. We assume Stokes flow at the pore scale and an University of California, San Diego elasticity model for pore-level deformations. Because of the [email protected] complexity of the interaction at the pore level, an iterative macroscopic model is proposed. The constitutive relations representing media deformation is modeled via an iterative MS19 procedure. Constitutive equations are derived. Numerical CGPOP Analysis and Optimization results are presented. The CGPOP miniapp is the conjugate gradient solver from Yalchin Efendiev Los Alamos National Laboratory’s Parallel Ocean Program Dept of Mathematics (POP) version 2.0. It includes several algorithms with com- Texas A&M University bination of different communication modes and task par- [email protected] tition strategies. The main goal of the project is to study and to improve the performance the methods. It involved Peter Popov the installation, execution, performance measurement and Texas A&M University evaluation, modification and improvement to the code of mailto:[email protected] CGPOP. Students obtained better understanding on parallel computing after working on the project. Advisors: Yulia Gorb Xiaoge Wang, Yinsheng Ji, Cheng Zhang University of Houston Hongtao Cai, Xiaoxiang Hu, Haoruo Peng mailto:[email protected] Tsinghua University, Beijing [email protected], tba, tba Donald Brown Texas A&M University mailto:[email protected] 44 AN12 Abstracts

MS20 able to treat different physical processes occurring simul- Advanced Discretizations for Modeling Flow and taneously in different parts of the domain, and for compu- Reactive Transport on Highly Distorted Unstruc- tational accuracy and efficiency, should also accomodate tured Grids multiple numerical schemes. We present results demonstrating accuracy of schemes as well as applications from Abstract not available at time of publication. the Cranfield Mississippi demonstration site and core scale experiments. Konstantin Lipnikov Los Alamos National Laboratory Mary F. Wheeler [email protected] UT-Austin [email protected] MS20 Coupled and Hybrid Models for Methane Evolu- MS21 tion in Subsurface Bending, Twisting, and Snapping: Mechanics and Dynamics of Slender Structures We discuss challenges in computational modeling of processes of multicomponent adsorption and phase change Soft materials undergo volume changes and instabilities coupled to flow and transport processes in coalbed methane when subjected to external stimuli. These instabilities and and undersea methane hydrates. We report on our recent bifurcations can lead to dynamical shape changes in the results on i) implementation of solvers for PDEs with con- morphogenesis in growing soft tissues. In this work, we straints which are necessary for continuum level models, ii) present the dynamic instabilities that occur by straining handling multiscale processes in micropores using discrete an elastomer nonhomogenously with a favorable solvent. scale models, and iii) modeling of pore- to core- couplings We examine how thin elastic plates undergo rapid bend- in hybrid models which bridge between continuum and dis- ing, twisting, and snap-buckling instabilities when swollen. crete scales. Douglas Holmes Malgorzata Peszynska Engineering Science and Mechanics Department Department of Mathematics Virginia Tech Oregon State University [email protected] [email protected] Matthieu Roche, Tarun Sinha, Howard A. Stone Mechanical and Aerospace Engineering MS20 Princeton University Analysis of CO2-water Models [email protected], [email protected], [email protected] Abstract not available at time of publication.

Ralph Showalter MS21 Department of Mathematics Oregon State University An Electromechanical Model of Tubular Heart [email protected] Pumping in Ascidians Recent advancements in computational fluid dynamics MS20 have enabled researchers to efficiently explore problems such as insect flight and fish swimming that involve moving Coupling Compositional Flow, Transport, and Me- elastic boundaries immersed in fluids. These advances have chanics in Porous Media for Modeling Carbon Se- also made modeling the interaction between a fluid and an questration in Saline Aquifers elastic model of an organ that includes some aspects of its A key goal of our work is to produce a prototypical com- physiology feasible. This presentation focuses on the devel- putational system to accurately predict the fate of in- opment and implementation of coupled immersed bound- jected CO2 in conditions governed by multiphase flow, ary and electromechanical models of the tubular hearts of rock mechanics, multi-component transport, thermody- Ascidians. namic phase behavior, chemical reactions within both the Laura A. Miller fluid and the rock, and the coupling of all these phenomena University of North Carolina - Chapel Hill over multiple time and spatial scales. Even small leakage Department of Mathematics rates over long periods of time can unravel the positive ef- [email protected] fects of sequestration. This effort requires high accuracy in the physical models and their corresponding numerical approximations. For example, an error of one percent per Austin Baird, Tiffany King year in a simulation may be of little concern when deal- University of North Carolina ing with CO2 oil recovery flooding, but such an inaccu- Department of Mathematics racy for sequestration will lead to significantly misleading [email protected], tiff[email protected] results that could fail to produce any long-term predictive capability. It is important to note that very few par- MS21 allel commercial and/or research software tools exist for simulating complex processes such as coupled multiphase Anisotropic Diffusion in Swelling Polymer Gels flow with chemical transport and geomechanics. Here we When anisotropic diffusion is taken into account, special discuss modeling multicomponent, multiscale, multiphase forms of the diffusivity tensor D have to be taken into flow and transport through porous media and through wells account, with D = Dˆ (d)andd the unit vector identify- and that incorporate uncertainty and history matching and ing the preferential (higher diffusivity) direction of diffu- include robust solvers. The coupled algorithms must be AN12 Abstracts 45 sion. The solvent flux h = D µ which drives the sol- method, we use high-order summation-by- parts finite dif- vent balance equation, coupled− with∇ the equations of the ference schemes and weak enforcement of boundary condi- nonlinear three-dimensional elasticity, induces mechanical tions through the simultaneous approximation term. anisotropy, as evidenced in (DiMeo et al., Soft Matter 7, 6068, 2011). In this work, a few numerical simulations are Brittany Erickson carried out to investigate some significant cases. Stanford University [email protected] Alessandro Lucantonio Università degli Studi di Roma [email protected] MS22 A Gamma-Convergence Analysis of the Quasicon- Paola Nardinocchi tinuum Method Università degli Studi di Roma ”La Sapienza” [email protected] Continuum mechanics models of solids have certain limitations as the length scale of interest approaches the atomistic scale. A possible solution in such situations is to use Luciano Teresi a pure atomistic model. However, this approach could University Roma Tre be computational prohibited as we are dealing with bil- [email protected] lion of atoms. The quasicontinuum method is a computational technique that reduces the atomic degrees of free- MS21 dom. In this talk, we review the quasicontinuum method and present a Gamma-convergence analysis of it. Nanoscale Mechanics of Natural Soft Materials Malena Ines Espanol Nature requires soft tissue, e.g., elastomeric proteins or California Institute of Technology lipid layers, to be mechanically stable as they perform dif- [email protected] ferent tasks. In many cases, it has not been possible to replicate their mechanical properties in synthetic materials due to a lack of fundamental understanding of the mecha- MS22 nisms that the natural materials use. We present a novel Video Stabilization of Atmospheric Turbulence insight into the behavior of natural soft materials through Distortion molecular mechanics simulations. The image or the video sequence captured in a long-range Ishwar Puri system, such as surveillance and astronomy, is often cor- Engineering Science and Mechanics Department rupted by the atmospheric turbulence degradation. We Virginia Tech propose to stabilize the video sequence using Sobolev gra- [email protected] dient sharpening with the temporal smoothing. One latent image is found further utilizing the lucky-region method. Ravi Kappiyoor With these methods, without any prior knowledge, the Department of Engineering Science and Mechanics video sequence is stabilized while keeping sharp details and Virginia Tech the latent image shows more consistent straight edges. [email protected] Yifei Lou School of Electrical and Computer Engineering MS22 Georgia Institute of Technology Parametric and Other Exact Solutions to Einsteins [email protected] Equations in Terms of Special Functions

In certain cosmological models the Einstein equations of MS23 general rel- ativity reduce to a differential equation whose Hom-Polytopes solutions can be found in terms of Jacobi or Weierstrass elliptic functions. In recent joint work with Floyd L. Given full-dimensional polytopes P in Rp and Q in Rq,the Williams we find more widespread applications of special hom-polytope Hom(P, Q) is defined to be the set of affine functions for other cosmological models. I will give an maps L : Rp Rq such that L(P ) is contained in Q.It overview of techniques we employed in finding such special is not difficult→ to specify the facets of Hom(P,Q), but little solutions that may be of use to a more general audience. else is known. We prove some categorical properties and produce a range of examples in low dimensions. Even when Jennie DAmbroise P and Q are polygons, the number of vertices of the hom- Bard College polytope depends on the geometry of P and Q,notjust [email protected] on m and n. We provide experimental results for pairs of regular polygons and a structural result for generic pairs of polygons. MS22 A Method for Earthquake Cycle Simulations Tristram C. Bogart San Francisco State University We are developing a method to understand and simulate [email protected] full earthquake cycles with multiple events on geometrically complex faults, with rate-and-state friction and off- Mark Contois fault plasticity. The method advances the model over long Research in Motion interseismic periods using the quasistatic equations, and [email protected] through dynamic rupture using the elastodynamic formulation. To obtain an efficient and provably strictly stable 46 AN12 Abstracts

Joseph Gubeladze uum scale with a discrete network model that describes San Francisco State University the pore scale flow in a porous medium. We developed [email protected] single-phase flow algorithm and extended it to two-phase flow, for the situations in which the saturation profile go through a sharp transition from fully saturated to almost MS23 unsaturated states. Our coupling method for the pressure The Combinatorial Commutative Algebra of Con- equation uses local simulations on small sampled network formal Blocks domains at the pore scale to evaluate the continuum equation and thus solve for the pressure in the domain. We Vector spaces of conformal blocks are objects from confor- present numerical results for single-phase flows with non- mal field theory which have made surprising appearances linear flux-pressure dependence, as well as two-phase flow. in several moduli problems from algebraic geometry. We discuss the combinatorics underlying the dimension formu- Chia-Chieh Chu las of these spaces, and answer some questions about a University of Texas at Austin classical moduli space: the moduli of rank 2 parabolic vec- [email protected] tor bundles on a projective algebra curve. In particular, we will use a polyhedral description of conformal blocks to construct presentations for coordinate rings of these spaces. MS24 Effective Properties of a Periodic Lattice of Circu- Christopher A. Manon lar Inclusions UC Berkeley [email protected] The problem of determination of effective properties (conductivity, permittivity, etc.) of a medium containing an arbitrary doubly periodic array of identical circular cylinders MS23 within a homogeneous matrix is considered. We construct Geometry of Exceptional Divisors and the a quasiperiodic potential and determine the average field in Goemans-Williamson Algorithm the medium. The problem is then reduced to solution of an infinite system of linear equations. The effective conduc- By a result of Mukai we can associate to each Dynkin di- tivity tensor is obtained in the form of the series expansion agram Ta,b,c an algebraic variety Xa,b,c whose geometry is in terms of the volume fraction of the cylinders whose co- controlled by the combinatorics of its (finitely many) excep- efficients are determined exactly. Results are illustrated by tional divisors. In this talk we ask the question of determin- examples. ing the maximum number of pairwise intersections between two disjoint sets of such divisors. We give lower and up- Yuri Godin per bounds for this quantity and show that our bounds are University of North Carolina at Charlotte asymptotically exact for the infinite families. Our results [email protected] are a consequence of a detailed analysis of the behavior of the Goemans-Williamson random semidefinite approximation algorithm for the maxcut problem on strongly regular MS24 multigraphs. Correctors and Field Fluctuation for the p(x)- Laplacian with Rough Exponents with Sub-Linear Mauricio Velasco, Mauricio Junca Growth Universidad de los Andes [email protected], [email protected] A corrector theory for the strong approximation of fields inside composites made from two materials with different power law behavior is provided. The correctors are used to MS23 develop bounds on the local singularity strength for gra- Singularities of Schubert and Richardson Varieties dient fields inside microstructured media. The bounds are multiscale in nature and can be used to measure the ampli- This talk addresses the problem of how to analyze and dis- fication of applied macroscopic fields by the microstructure. cuss singularities of a variety X that “naturally’ sits inside The talk will focus on the case of exponents with sublinear a flag manifold. Our three main examples are Schubert growth. varieties, Richardson varieties and Peterson varieties. The overarching theme is to use combinatorics and commuta- Silvia Jimenez tive algebra to study the *patch ideals*, which encode lo- Worcester Polytechnic Institute cal coordinates and equations of X. Thereby, we obtain [email protected] formulas and conjectures about X’s invariants. We will report on projects with (subsets of) Erik Insko (U. Iowa), Allen Knutson (Cornell), Li Li (Oakland University) and MS24 Alexander Woo (U. Idaho). Inverse Born Series for the Calderon Problem Alexander Yong We propose a direct reconstruction method for the University of Illinois, Urbana-Champaign Calderon problem based on inversion of the Born series. [email protected] We characterize the convergence, stability and approximation error of the method and illustrate its use in numerical reconstructions. MS24 A Multiscale Method Coupling Network and Con- Shari Moskow tinuum Models in Porous Media Drexel University Department of Mathematics In this talk, we present a numerical multiscale method [email protected] for coupling a conservation law for mass at the contin- AN12 Abstracts 47

MS25 these approaches to large graph-valued data sets, however, Efficient Computational Methods for Thermal we must address significant theoretical and computational Imaging of Small Cracks in Plates challenges. In this talk, we discuss new techniques for statistical inference on large graphs, with application to the We present some fast computational methods and practical detection of anomalous behavior in a citation database. considerations for identifying cracks in a two-dimensional plate using thermal data from an infrared camera, based Nicholas Arcolano on the “small volume expansions’ developed Ammari, Vo- MIT Lincoln Laboratory gelius, et. al. For an applied heat flux, the plate tempera- [email protected] ture is measured over its entire surface, so we have interior data, not just on the boundary. The novelty is that the cracks we seek are near or below the single-pixel resolution MS26 of the camera. Streaming Graph Analytics for Massive Graphs Kurt Bryan Emerging real-world graph problems include detecting Rose-Hulman Institute of Technology community structure in large social networks, improving Terre Haute, Indiana USA the resilience of the electric power grid, and detecting and [email protected] preventing disease in human populations. The volume and richness of data combined with its rate of change renders monitoring properties at scale by static recomputation in- MS25 feasible. We approach these problems with massive, fine- Stochastic and Deterministic Inverse Solutions for grained parallelism across different shared memory archi- Crack and Corrosion Imaging tectures both to compute solutions and to explore the sensitivity of these solutions to natural bias and omissions Interesting mathematical issues arise when imaging tiny within the data. cracks and hidden corrosion in engineering applications using thermography. Sparse and noise pixel data “conspire’ David A. Bader with the inverse heat (parabolic) operator to furnish an ar- Georgia Institute of Technology ray of practical imaging challenges. This talk will explore [email protected] deterministic and stochastic approaches to ameliorate such difficulties and discuss the algebraic and topological con- David Ediger, Jason Riedy siderations that effect posedness in the deterministic case, Georgia Institute of Technology and informativeness within the stochastic context. School of Computational Science and Engineering [email protected], [email protected] Christopher J. Earls Cornell University [email protected] MS26 Perfect Power Law Graphs: Generation, Sampling, Construction and Fitting MS25 Application of Sparse Solutions to Underdeter- Power law graphs are ubiquitous and arise in the Inter- mined Problems in Imaging net, the Web, citation graphs, and online social networks. Deviations from the power law model do not have a large The principle of parsimony has recently been demonstrated impact on the qualitative characterization of graphs. How- useful in solving highly underdetermined systems of linear ever, the need for precise background models becomes es- equations. We first review the mathematics that make such sential in order to apply rigorous statistical signal process- solutions possible and then provide several applications of ing techniques to detect graph anomalies. This work ex- sparse (parsimonious) models in imaging. In the first we plores the power law degree distribution that is used to present results from the field of compressive sampling and model power law graphs. A simple heuristic for generat- show how high-fidelity imagery can be recovered from lowing perfect power law graphs is presented that reproduces fidelity measurements. We then demonstrate how to de- many observed phenomena. Using this model the sampling velop and use sparse image models for image processing. effects of graph construction and edge ordering are examined. Graph construction appears to be a lossy, non-linear process that generates many phenomena that are observed C. C. Olson, L. N. Smith, K. P. Judd, J. Waterman in real data (e.g., data bin scatter, low-degree tails, and Naval Research Lab high-degree tails). Likewise, the order that edges are gen- [email protected], [email protected], erated can have a strong effect on the evolution of the power [email protected], [email protected] law slope and the overall density of the graph (i.e., densifi- cation). Applying the perfect power law model to real data Jonathan Nichols (e.g., entities extracted from the Reuters Corpus) provides Naval Research Lab a self-consistent set of degree bins for measuring deviations Code 5673 from the background. Using this scheme it is possible to [email protected] identify specific edges that are typical, surplus, or deficit using standard signal processing techniques. MS26 Jeremy Kepner Statistical Models and Methods for Anomaly De- MIT Lincoln Laboratory tection in Large Graphs [email protected]

Traditional statistical models and methods provide a powerful framework for analyzing observed data. To extend 48 AN12 Abstracts

MS26 high-end scientiﬁc applications Fast Counting of Patterns in Graphs Eduardo Sanchez, Jose Castillo The occurrence of small subgraphs is a key ingredient in un- San Diego State University derstanding real networks, since local interactions can re- [email protected], [email protected] veal a lot of information about the full graph. For instance, the number of triangles indicates how well the graph is clus- tered. However, counting such small graphs can be compu- MS27 tationally intensive, preventing adoption of such techniques A Discrete Vector Calculus in Tensor Grids on massive graphs. We are developing sampling-based algorithms for counting small sugbgraphs graphs. In this The key to the success of mimetic discretization methods talk, we will present our latest results. is that they discretize some description of continuum mechanics, e.g. vector calculus or diﬀerential forms. For a Ali Pinar, C. Seshadhri discretization to be fully mimetic it must have exact dis- Sandia National Labs crete analogs of the important results from the continuum [email protected], [email protected] theory. We summarize exactly which results from vector calculus are needed to derive energy inequalities for com- Tamara G. Kolda mon initial boundary value problems, which we call the Sandia National Laboratories mimetic properties, and then produce a discrete vector cal- [email protected] culus on tensor product grids in three dimensions that is fully mimetic.

MS27 Stanly L. Steinberg University of New Mexico High Order Mimetic Methods on a Nonuniform [email protected] Mesh Mimetic Operators satisfy a discrete analog of the diver- Nicolas Robidoux gence theorem and they are used to create/design conserva- Independent Consultant tive/reliable numerical representations to continuous mod- Image Processing and Applied Mathematics els. We will present a methodology to construct mimetic [email protected] versions of the divergence and gradient operators which exhibit high order of accuracy at the grid interior as well as at the boundaries. As a case of study, we will show the MS27 construction of fourth order operators in a one-dimensional The Mimetic Spectral Element Method in the staggered grid. Mimetic conditions on discrete operators Community Atmosphere Model (CAM) are stated using matrix analysis and the overall high order of accuracy determines the bandwidth parameter. This We describe a mimetic formulation of the spectral element contributes to a marked clarity with respect to earlier ap- method and its implementation in the the Community At- proaches of construction. As test cases, we will solve 2-D el- mosphere Model (CAM). For the atmospheric hydrostatic liptic equations with full tensor coeﬃcients arising from oil primitive equations, the mimetic properties of the method reservoir models. Additionally, applications to elastic wave allow for excellent conservation on the unstructured, curvi- propagation under free surface and shear rupture bound- linear meshes used by CAM. This includes local conser- ary conditions will be given.indocument or other high-level vation (to machine precision) of quantities solved in con- commands. servation form, and semi-discrete conservation (exact with exact time-discretization) of derived quantities such as en- Jos´e E. Castillo ergy and potential vorticity. San Diego State University Department of Mathematics Mark A. Taylor [email protected] Sandia National Laboratories, Albuquerque, NM [email protected]

MS27 Aime Fournier Mimetic Library Toolkit NCAR [email protected] Mimetic Methods Toolkit (MTK) is an application programming interface that allows the intuitive implementation of Mimetic Discretization Methods for the solution MS28 of Partial Diﬀerential Equations. Mimetic Methods yield Defective Boundary Conditions for Viscoelastic numerical solution that guarantee uniform order of accu- Flow Problems racy all along the modeled physical domain, while ensur- ing the satisfaction of conservative laws. Therefore, the Abstract not available at time of publication. attained numerical solutions remain physically faithful to the underlying physics of the problem. MTK is fully de- Keith Galvin veloped in ISO C++, thus exploiting all the well-known Department of Mathematical Sciences advantages of Object Oriented Applications as for exam- Clemson University ple, providing the developer an intuitive perspective of the [email protected] theoretical framework of Mimetic Discretization Methods. Likewise, Object Orientation carries along the advantages MS28 of the extensive collection of data structures manipulation capabilities of C++, thus allowing for a clearer program- An ANOVA-based Method for High-dimensional ming methodology making MTK suitable for developing AN12 Abstracts 49

Stochastic PDEs patient-specific knowledge that can enhance significantly the reliability of numerical simulations by proper data as- The Analysis of Variance (ANOVA) expansion is often used similation procedures. We address here the variational as- to reduce the cost of evaluating multivariate functions in similation of velocity data and images for the accurate es- high dimensions. We propose an ANOVA-based method timation of hemodynamics indexes of interest with both for representation of multivariate functions, which does not a deterministic and a Bayesian approach. The latter pro- depend on the choice of the anchor point, and tracks all vides a better quantification of uncertainty and confidence the important parameters and important interactions, con- regions for the quantities of interest. structing the expansion with the minimum of the needed terms. We demonstrate a real life application where our Alessandro Veneziani method is the only usable approach. MathCS, Emory University, Atlanta, GA [email protected] Alexander Labovsky Department of Mathematical Sciences Marta D’Elia Michigan Technological University Department of Scientific Computing [email protected] Florida State University, Tallahassee, FL [email protected] Max Gunzburger Florida State University Alexis Aposporidis School for Computational Sciences Emory University, USA [email protected] [email protected]

MS28 MS29 Analysis of Long Time Stability and Errors of Two Fast Algorithms for Biophysics-based Medical Im- Partitioned Methods for Uncoupling Evolutionary age Analysis Groundwater - Surface Water Flows Abstract not available at time of publication. Abstract not available at time of publication. George Biros Catalin S. Trenchea University of Texas at Austin Department of Mathematics biros@ices. utexas.edu University of Pittsburgh [email protected] MS29 MS28 Patient-specific Mesh Generation for Improved Pulmonary Embolism Prevention An Adaptive Approach to PDE-constrained Opti- mization for Random Data Identification Problems Pulmonary embolism is a potentially fatal disease involving the blockage of an artery of the lungs, typically by a In this talk we will present a scalable mechanism for opti- blood clot. One treatment is via implantation of a mechan- mal identification of statistical moments or even the whole ical device known as an inferior vena cava filter which traps probability distribution of input random data, given the large blood clots, preventing them from reaching the lungs. probability distribution of some response of a system of In this talk, we present a computational pipeline for gen- PDEs. This novel technique integrates an adjoint-based eration of patient-specific meshes for use in CFD studies deterministic algorithm with the sparse grid stochastic col- of blood flow for improved prevention of pulmonary em- location FEM. Our rigorously derived error estimates and bolism. several numerical examples, will be described and used to compare the efficiency of the method with several other Shankar P. Sastry, Jibum Kim, Suzanne M. Shontz techniques. The Pennsylvania State University [email protected], [email protected], Clayton G. Webster [email protected] Oak Ridge National Laboratory [email protected] Brent A. Craven Penn State Applied Research Laboratory Max Gunzburger [email protected] Florida State University [email protected] Frank C. Lynch Penn State Hershey Medical Center Catalin S. Trenchea fl[email protected] Department of Mathematics University of Pittsburgh [email protected] Keefe B. Manning, Thap Panitanarak The Pennsylvania State University [email protected], [email protected] MS29 Data Assimilation in Cardiovascular Mathematics: MS29 Toward An Integration of Patient-Specific Mea- surements and Simulations Resolving Topology Ambiguity for Complicated Domain In cardiovascular sciences, images and measures provide We discuss all possible topology configurations and develop 50 AN12 Abstracts an extension of the dual contouring (DC) method which Anshu Dubey guarantees the correct topology. We analyze all the octree University of Chicago leaf cells, and categorize them into 31 topology groups by dubey@flash.uchicago.edu computing the values of their face and body saddle points based on a tri-linear representation. Knowing the correct Jonathan Gallagher categorization, we are able to modify the base mesh and Flash Center for Computational Science, Univ. of Chicago introduce more minimizer points to preserve the correct [email protected] topology. Yongjie Zhang Don Lamb, Klaus Weide Department of Mechanical Engineering University of Chicago Carnegie Mellon University lamb@flash.uchicago.edu, klaus@flash.uchicago.edu [email protected] MS30 Jin Qian A Trillion Particles: Studying Large-Scale Struc- Carnegie Mellon University ture Formation on the BG/Q [email protected] The simulation of structure formation in the Universe sits at the forefront of large-scale high-performance computing. MS30 I will discuss the unique algorithmic features employed on Results from the Early Science High Speed Com- the BG/Q in HACC, our simulation code framework for bustion and Detonation Project computational cosmology, focusing on the way in which the gravitational force is divided into short range and long The High Speed Combustion and Detonation project uses range components and how each component is efficiently an adaptive mesh refinement, reactive flow Navier-Stokes and scalably computed using both inter- and intra-node code augmented with the equation of state, microscopic parallelism. transport, and chemical kinetics required to study the detonation-to-deflagration transition in hydrogen. To David Daniel, Patricia Fasel run on future hardware, we have implemented mixed Los Alamos National Laboratory MPI/OpenMP threading, and parellelized the adaptive [email protected], [email protected] mesh refinement code. Our challenge is maintaining computational work load balance, and managing the distribu- Hal Finkel tion of ghost cells for communications performance. Argonne National Laboratory Alexei Khokhlov hfi[email protected] The University of Chicago Chicago, IL Nicholas Frontiere [email protected] University of California, Los Angeles [email protected] Charles Bacon Argonne National Laboratory Salman Habib, Katrin Heitmann [email protected] Argonne National Laboratory [email protected], [email protected]

MS30 Zarija Lukic Implementing Hybrid Parallelism in FLASH Lawrence Berkeley National Laboratory [email protected] FLASH is a component-based multiphysics scientific software which has been used for computations on some of the Adrian Pope largest HPC platforms. Simulation of turbulent nuclear Argonne National Laboratory combustion, a key process in Type Ia supernovae, is one [email protected] of the target applications on the BG/Q platform at ANL. In preparation, we have introduced hybrid parallelism to the code. We describe these modifications, and also char- MS30 acterize the performance of the modified code on our first Automatic Generation of the HPCC Global FFT BG/Q racks. for BlueGene/Q Christopher Daley We present the automatic synthesis of the HPC Challenge’s Flash Center for Computational Science, Univ. of Chicago Global FFT, a large 1D FFT across a whole supercomputer ALCF Argonne National Laboratory system. The code was synthesized with the autotuning sys- cdaley@flash.uchicago.edu tem Spiral. We run our optimized Global FFT benchmark on up to 128k cores (32 racks) of ANL’s BlueGene/P “In- Vitali Morozov trepid’ and achieved 6.4 Tflop/s. Further, we discuss the ALCF, Argonne National Laboratory necessary changes for BlueGene/Q. Our BG/P code was [email protected] part of IBM’s winning 2010 HPC Challenge Class II sub- mission. Dongwook Lee Flash Center for Computational Science, Univ. of Chicago Franz Franchetti dongwook@flash.uchicago.edu Department of Electrical and Computer Engineering Carnegie Mellon University [email protected] AN12 Abstracts 51

MS31 for static mechanical problems, has in recent years been Shape Optimization of Plasmonic Gratings applied to a number of different inverse problems involving wave-propagation. The problem formulation makes Surface plasmons are electromagnetic fields, highly local- use of element-based design variables and includes robust- ized near metal- dielectric interfaces, and associated with ness towards manufacturing variations. The presentation surface electron density oscillations. We consider a prob- will review the TopOpt-groups (www.topotp.dtu.dk) re- lem of shape design of a metallic grating interface, so that cent works within systematic design of: slow light photonic surface plasmon modes are optimized. Existence and sta- crystal waveguides; optic and acoustic cloaking devices; as bility of optimal solutions is analyzed, and a gradient-based well as structured surfaces for manipulation of visual ap- approximate solution method proposed. A numerical im- pearance. plementation which is capable of continuously tracking a changing grating interface is described, and numerical ex- Ole Sigmund amples are presented. Department of Mechanical Engineering, Solid Mechanics Nils Koppels Allé, DTU David C. Dobson [email protected] University of Utah [email protected] MS32 Mathematical Modeling of Panama Disease in MS31 Cavendish Bananas Plants Overview of Shape Optimization Problems Involv- ing Eigenvalues The Cavendish banana has served global consumers for half a century and has remained unaffected by most types of Shape optimization problems involving eigenvalues arise in Panama diseases. Currently, one type of Panama disease, many areas where one seeks to control wave phenomena, fusarium oxysproum f.sp. cubense, targets the Cavendish including mechanical vibration in structures, electromag- banana. We propose a simple mathematical system of netic waves in cavities, and population dynamics. We’ll be- ordinary differential equations, based on an SI epidemic gin this minisymposium with an overview of the field and model, describing the interactions between susceptible and survey recent results on shape and structural eigenvalue infected bananas. To lengthen survival of healthy bananas optimization problems. In particular, well discuss Krein’s plants, infected bananas plants are removed from planta- now classic problem on the optimal density distribution of tions. In our study, we consider various harvesting param- a membrane which extremizes the k-th Dirichlet-Laplacian eter values and present preliminary numerical results. eigenvalue. Blake Burkett Braxton Osting Shippensburg University University of California, Los Angeles USA [email protected] [email protected]

Chiu-Yen Kao Luis Melara, Alyssa Bumbaugh The Ohio State University Shippensburg University Claremont McKenna College [email protected], [email protected] [email protected] MS32 MS31 Simulation of Deformations and Shape Recovery Asymptotic Calculation of Resonances of Red Blood Cells Using the Lattice Boltzman Method This work is motivated by the desire to develop a method that allows for easy and accurate calculation of complex Red blood cells (RBCs) undergo substantial changes of resonances of a one-dimensional structures. We illustrate shape during blood ﬂow in vivo. In the past decade, Lattice our approach for Schrodinger’s equation whose potential Boltzmann and Immersed Boundary methods have been is a low-energy well surrounded by a thick barrier. The used to simulate the deformation of RBCs (e.g., Sui et resonance is calculated as a perturbation of the associated al, IJMPC, 2007). We introduce a more comprehensive bound state when the barrier thickness is in fnite. We show version of these models, aimed at simulating the shape re- that the error of this perturbational approach is exponen- covery of a deformed RBC. Benchmarks and preliminary tially small in barrier thickness. A similar result has been results of the model are introduced. obtained for the case of a one-dimensional ﬁnite photonic bandgap structure with a defect. This is joint work with John Gounley D. Dobson, J. Lin, S. Shipman, and M. Weinstein. Old Dominion University [email protected] Fadil Santosa School of Mathematics Yan Peng University of Minnesota Dept of Math. & Stat. [email protected] Old Dominion University [email protected] MS31 Topology Optimization for Wave-Propagation MS32 Problems Modeling of the Dynamic Delamination of L- The topology optimization method, originally developed 52 AN12 Abstracts shaped Unidirectional Laminated Composites Porosity Model

One of the widely used geometrically complex parts in Flow in carbonate reservoirs is strongly influenced by frac- advanced commercial aircraft is the L-shaped composite. tures present in the geological formations. An accurate Due to the sharp curved geometry, interlaminar opening characterization of fracture flow is needed to forecast oil stresses are induced and delamination occurs under con- recovery and optimize production. We present a general siderable mode-mixities in L-shaped beams. Dynamic phe- dual-porosity model. It is based on an unstructured finite nomena during delamination initiation and propagation of element - finite volume technique which solves the gov- L-shaped beams are investigated using dynamic (explicit) erning equations for two-phase flow fully implicitly. Mass finite element analysis in conjunction with cohesive zone transfer between fractures and matrix is computed with methods. The 2-D model consists of 24 plies of unidirec- a generalized transfer function, the only known analytic tional CFRP laminate with an initial 1 mmcrack at the solution for Darcy law with capillarity. center of the laminate at the bend. Loading is applied parallel to one of the arms quasi-statically. The loading Christine Maier type yields different traction fields and mode-mixities in Heriot-Watt University, UK the two sides of the crack in which delamination occurs [email protected] under shear stress dominated loading on one crack tip and opening stress dominated loading on the other. The speed Karen Schmid of the delamination under shear dominated loading at one Universität Stuttgart side is 800 m/s and under normal stress dominated loading [email protected] is 50 m/s. In addition radial compressive waves at the interface are observed. Finally, as the thickness is changed, Mohamed Ahmed a different failure mode is observed in which a secondary Heriot-Watt University crack nucleates at the arm and propagates towards the cen- [email protected] ter crack.

Burak Gozluklu Sebastian Geiger Middle East Technical University, Turkey Heriot-Watt University [email protected] Edinburgh [email protected] Demirkan Coker METU MS32 [email protected] An Analytical Approach to Green Oxidation Oxidation, a process in which oxygen is added to break MS32 pollutants, often uses chemicals that can result in the pro- Numerically Optimal High Order Strong Stability duction of hazardous substances. The main goal of the Preserving Multi-step Runge-Kutta Methods project is to be able to estimate the rates of the reactions based on experimental observations. We have developed We investigate the strong stability preserving (SSP) prop- perturbation techniques which allowed us to derive an ap- erty of multi-step Runge–Kutta (MSRK) methods with 2-6 proximate solution. It is expected that these techniques steps. Whereas explicit SSP RungeKutta methods have or- will yield even more far-reaching results when applied to der at most four, explicit SSP MSRK methods break this more realistic systems. order barrier. We present our algorithm for finding numerically optimal explicit MSRK methods, and methods of up Diego Torrejon to five steps and eighth order that were found using this al- George Mason University gorithm. These methods have larger SSP coefficients than [email protected] any known methods of the same order of accuracy, and may be implemented in a form with relatively modest storage requirements. The usefulness of the MSRK methods is MS33 demonstrated through numerical examples, including inte- A Second Order Virtual Node Algorithm for Stokes gration of very high order WENO discretizations. Flow Problems with Interfacial Forces and Discon- tinuous Material Properties Zachary Grant University of Massachusetts at Dartmouth We present a numerical method for the solution of the [email protected] Stokes equations that handles interfacial discontinuities due to both singular forces and discontinuous fluid proper- Sigal Gottlieb ties such as viscosity and density. The discretization cou- Department of Mathematics ples a Lagrangian representation of the material interface University of Massachusetts Dartmouth with an Eulerian representation of the fluid velocity and [email protected] pressure. The method is efficient, easy to implement and yields discretely divergence free velocities that are second- David I. Ketcheson order accurate. Numerical results indicate second order Mathematical and Computer Sciences & Engineering accuracy for the velocities and first order accuracy for the King Abdullah University of Science & Technology pressure in l-infinity. [email protected] Diego Cortegoso Assencio UCLA MS32 [email protected] Simulating Two-Phase Flows in Fractured Reser- voirs Using a Generic Transfer Function in a Dual- AN12 Abstracts 53

MS33 used over the years to characterize fragmentation, and few A Fast Method for Interface and Parameter Es- have had experimental data to aid in its construction. In timation in Linear Elliptic PDEs with Piecewise this talk, we discuss the use of 3D positional data of K. Constant Coefficients pneumoniae bacterial flocs in suspension to construct a probability density of floc volumes after a fragmentation We present a new method for the recovery of the parame- event. Computational results are provided which predict ters and interface from an observed solution to embedded that the primary fragmentation mechanism for medium to interface linear elliptic PDEs with piecewise constant co- large flocs is erosion, as opposed to the binary fragmenta- efficients. Our approach uses the linear nature of these tion mechanism (i.e. a fragmentation that results in two equations to derive a function that is approximately equal similarly-sized daughter flocs) traditionally assumed. to the coefficients across the entire domain. We recover the coefficients using split Bregman implementations of Erin Byrne standard piecewise constant segmentation methods. We Harvey Mudd College demonstrate the method on Poisson’s equation and linear [email protected] elasticity. Alejandro Cantarero MS34 UCLA Mathematics Department Modelling Cell Polarity: Theory to Experiments Los Angeles, CA [email protected] In order to migrate, cells recruit various proteins to the plasma membrance and spatially segregate them to form a front and back. I present two possible mechanisms for MS33 this symmetry breaking process, and explain how cells can Efficient Symmetric Positive Definite Second- regulate the transition from a homogeneous, ”resting cell”, Order Accurate Monolithic Solver for Fluid/Solid state to a spatially heterogeneous state corresponding to a Interactions polarized cell. I then focus on experimentally distinguish- ing between various proposed polarity models in crawling We introduce a robust and efficient method to simu- cells through perturbations of cell geometry. late strongly coupled (monolithic) fluid/rigid-body interactions. We take a fractional step approach, where the in- Alexandra Jilkine termediate state variables of the fluid and of the solid are University of Arizona solved independently, before their interactions are enforced [email protected] via a projection step. Overall, the computational time to solve the projection step is similar to the time needed to solve the standard fluid-only projection step. Numerical MS34 results indicate the method is second-order accurate in the Epidemic Spread of Influenza Viruses: The Impact l-infinity norm and demonstrate that its solutions agree of Transient Populations on Disease Dynamics quantitatively with experimental results. Recent H1N1 pandemic and recent H5N1 outbreaks have Frederic Gibou brought increased attention to the study of the role of an- University of California-Santa Barbara imal populations as reservoirs for pathogens that could [email protected] invade human populations. Here we study the interactions between transient and resident bird populations and their role on dispersal and persistence. A meta-population MS33 framework based on a system of nonlinear ordinary differ- A Second Order Virtual Node Method for Elliptic ential equations is used to study the transmission dynamics Interface Problems with Interfaces and Irregular and control of avian diseases. Epidemiological time scales Domains in Three Dimensions and singular perturbation methods are used to reduce the dimensionality of the model. Our results show that mix- We present a numerical method for the variable coefficient ing of bird populations (involving residents and migratory Poisson equation in three-dimensional irregular domains birds) play an important role on the patterns of disease with interfacial discontinuities. The discretization embeds spread. the domain and interface into a uniform Cartesian grid augmented with virtual degrees of freedom to provide ac- Karen Rios-Soto curate treatment of jump and boundary conditions. . As University of Puerto Rico at Mayaguez in Bedrossian et al, this is used in a discontinuity removal [email protected] technique that yields the standard 7-point stencil across the interface and only requires a modification to the right- hand side of the linear system. MS34 Modeling the Cofilin Pathway and Actin Dynamics Joseph Teran in Cell Motility Activity of Mammary Carcinomas UCLA [email protected] Polymerization of actin cytoskeleton leads to cell migration, a vital part of normal physiology from embryonic development to wound healing. However, it also occurs in the MS34 pathological setting of cancer metastasis. Here I present The Post-Fragmentation Density Function for Bac- mathematical models of actin regulation by cofilin which terial Aggregates has been identified as a critical determinant of metastasis. I will discuss results obtained from simulations and steady The post-fragmentation probability density of daughter state analysis and their biological implications, as well as flocs is one of the least understood aspects of modeling flocculation. A wide variety of functional forms have been 54 AN12 Abstracts modeling challenges that arise. MS35 A Mixed Finite Element Framework for the Biot Nessy Tania Model in Poroelasticity Smith College Mathematics and Statistics Department Poroelasticity is the modeling of the time-dependent cou- [email protected] pling between the deformation of porous materials and the fluid flow inside. It has been well-known that standard Galerkin finite element methods produce unstable MS35 and oscillatory numerical behavior of the pressure, which Multiscale Simulation and Upscaling Multi-Species is known as locking. We present a mixed finite element Reactive Transport from the Pore to Macro Scale formulation that has been designed to overcome locking. The formulation is based on coupling two mixed finite el- Abstract not available at time of publication. ement formulations for the flow and mechanics problems. Matthew Balhoff We discuss apriorierror estimates and show some numer- ICES ical results. The University of Texas at Austin Son-Young Yi balhoff@ices.utexas.edu The University of Texas at El Paso [email protected] MS35 Multiscale Modeling and Simulation of Fluid Flows MS36 in Deformable Porous Media Automatic Differentiation in Chebfun: Implemen- A multiscale framework for fluid-structure interaction tation and Usage problems in inelastic media will be presented. Stokes flow The implementation of Automatic Differentation (AD) in is assumed at the pore scale with a general nonlinear elas- Chebfun is described. Whereas standard AD implementa- tic model for deformations. Due to complexity of pore-level tions compute Jacobians, Chebfun works in a continuous interaction an iterative macroscopic model that consists of framework so the derivatives are Fréchet derivatives. The nonlinear Darcy equations and upscaled elasticity equa- current implementation offers automatic linearity detection tions modeled via an iterative procedure is proposed. Nu- and linearisation of differential operators, as well as interior merical results for the case of linear elastic solid skeleton point and jump conditions in differential equations through are presented for a number of model problems. AD of functionals. Examples of AD usage in Chebfun will Yuliya Gorb be given. Department of Mathematics Asgeir Birkisson University of Houston University of Oxford, Mathematical Institute [email protected] [email protected]

MS35 MS36 Coupling Modeling for Compressible Fluid Flow in Spectral Deferred Correction in Chebfun for Time- the Elastic Porous Media dependent PDEs

In this work, we consider the dynamical response of a non- Chebfun’s goal of providing automatic, accurate results for linear plate with viscous damping, perturbed in both ver- 1D problems is challenging for time-dependent PDEs. Cur- tical and axial directions interacting with a Darcy flow. rently Chebfun uses a built-in stiff integrator of order 1- We first study the problem for the non-linear elastic body 5. Huang et al. showed that spectral deferred correction with damping coefficient. We prove existence and unique- can be generalized to a Krylov iteration for a spectrally ness of the solution for the steady state plate problem. We computed error, preconditioned by low-order integration. investigate the stability of the dynamical non-linear plate This gives an A-stable, symplectic and reversible integra- problem under some condition on the applied loads. Then tion method capable of very high accuracy. It is readily we explore the fluid structure interaction problem with a implemented with Chebfun’s discretization and automatic Darcy flow in porous media. In an appropriate Sobolev differentiation capabilities. norm, we build an energy functional for the displacement field of the plate and the gradient pressure of the fluid flow. Tobin Driscoll We show that for a class of boundary conditions the energy University of Delaware functional is bounded by the flux of mass through the inlet Mathematical Sciences boundary. [email protected] Akif Ibragimov Department of Mathematics and Statistics. MS36 Texas Tech University An Overview of Differential Equations in Chebfun [email protected] Chebfun allows users to interact with functions in Matlab E. Aulisa, Y. Kaya as if they were vectors, giving ‘symbolic feel but numeric Department of Mathematics and Statistics speed’. Chebops extend this functionality to operators and Texas Tech University matrices, allowing a natural and efficient means of solv- mailto:[email protected], ing differential equations. In this introductory talk we’ll mailto:[email protected] open the chebop hood to take a look its core components, including the adaptive collocation and domain decomposition processes, and the enforcement of boundary conditions AN12 Abstracts 55 through a new technique of rectangular projection. MS37 Behavior of Droplets on a Thin Film Nick Hale Oxford U. Mathematical Inst. A drop of fluid on another fluid is modeled by a system of [email protected] fourth order nonlinear PDE derived using the lubrication approximation. We assume the two fluids are Newtonian, incompressible, and immiscible. Relevant questions to this MS36 problem include: When does the drop spread over the un- Computation of Frequency Responses of PDEs in derlying fluid? When does the drop touch the bottom sur- Chebfun face? When does the drop break through the top interface? We explore these questions analytically, numerically, and We describe how frequency responses of PDEs with one experimentally. spatial variable can be computed in Chebfun. Our method recasts the frequency response operator as a two point Ellen Peterson boundary value problem and it has two advantages over Department of Mathematics Sciences currently available schemes: first, it avoids numerical insta- Carnegie Mellon University bilities encountered in systems with differential operators [email protected] of high order and, second, it alleviates difficulty in implementing boundary conditions. We provide examples from fluid dynamics to illustrate utility of the proposed method. MS37 Fingering Instability Down the Outside of a Verti- cal Cylinder Mihailo R. Jovanovic, Binh Lieu Electrical and Computer Engineering We examine the fingering dynamics of a gravity-driven con- University of Minnesota tact line of a thin viscous film traveling down the outside [email protected], [email protected] of a vertical cylinder of radius R. A lubrication model is derived for the film height in the limit that H/R 1(H is the upstream film height). Results from a linear stability MS37 analysis of the contact line are compared to experimental Two Layer Model for Local Tear Film Dynamics data. The influence of curvature will also be discussed. Many tear film models utilize a single-layer approach that Linda Smolka represents only the aqueous layer, which constitutes the Bucknell University majority of the tear film. In such models, the layer is dom- [email protected] inated by shear stresses. Some recent models have incorporated surfactant effects at the liquid-air interface to model the effects of polar lipids there. The model presented in this MS38 talk includes a thin lipid layer between the aqueous layer Networks, Communities and the Ground-Truth and the air, which is dominated by extensional flow. Our results show that the thin extensional layer significantly The Web, society, information, cells and brain can all be perturbs the aqueous layer flow. represented and studied as complex networks of interactions. Nodes in such networks tend to organize into clusters Nicholas Gewecke and communities, which represent the fundamental struc- University of Tennessee tures for understanding the organization of complex sys- [email protected] tems. Even though detection of network communities is of significant importance for computer science, sociology and Rich Braun biology, our understanding of the community structure of Department of Mathematical Sciences large networks remains limited. We study a set of more University of Delaware than 200 large networks with the goal to understand and [email protected] identify communities in networks. We challenge the conventional view of network community structure and show that it is not exhibited by the large real-world networks. MS37 We then present a new conceptual model of network com- Defects and Heterogeneity in Liquid Coatings munity structure, which reliably captures the overall structure of networks and accurately identifies the overlapping Fluid coatings occur in situations from the manufacture of nature of network communities. semiconductors to the foam lacing left behind after drink- ing a pint of beer. Sometimes coating uniformity is de- Jure Leskovec sirable, but in many cases, coatings are heterogeneous, Stanford University with either defects or spontaneous or deliberate pattern- [email protected] ing. We examine the deposition of isolated bubbles in Landau–Levich (dip coating) flow of a pure liquid, and the self-assembly of particles in Landau–Levich flow of a sus- MS38 pension. These phenomena are explained through a com- High-Performance Metagenomic Data Clustering bination of modeling, experiment, and analysis. and Assembly Justin Kao We present a novel de Bruijn graph-based parallel assembly Massachusetts Institute of Technology approach for assembling metagenomic reads. The assem- [email protected] bler employs a maximum-likelihood framework that handles the challenges posed by increased polymorphism and over-representation of conserved regions. It also provides tolerance for errors due to the incomplete and fragmen- 56 AN12 Abstracts tary nature of the reads. We also propose a two-way, an equivalent constrained optimization problem; and solu- multi-species, multi-dimensional Poisson mixture model- tion of the resulting optimization problem either directly based method for representing reads from a metagenome. as a fully coupled algebraic system, or in the null space of We use this method to cluster metagenomic reads by their the constraints. species of origin, and to characterize the abundance of each species. Pavel Bochev Sandia National Laboratories Kamesh Madduri Computational Math and Algorithms Pennsylvania State University [email protected] [email protected] Denis Ridzal Sandia National Laboratories MS38 [email protected] Influence Propagation on Large Graphs Given a network of who-contacts-whom, will a contagious Mitchell Luskin virus/product/meme take-over (cause an epidemic) or die- School of Mathematics out quickly? What will change if nodes have partial, tem- University of Minnesota porary or permanent immunity? What if the underly- [email protected] ing network changes over time (e.g., people have different connections during the day at work, and during the MS39 night at home)? Propagation style processes can model well many real-world scenarios like epidemiology and pub- Blended Force-based Quasicontinuum Methods lic health, information diffusion etc. We present results on The development of consistent and stable quasicontinuum understanding the tipping-point behavior of epidemics (en- models for multi-dimensional crystalline solids remains a abling among other things faster simulations), predicting challenge. For example, proving stability of the force-based who-wins among competing viruses, and developing effec- quasicontinuum (QCF) model remains an open problem. tive algorithms for immunization and marketing for sev- In 1D and 2D, we show that by blending atomistic and eral large-scale real-world settings. Finally, we collected Cauchy–Born continuum forces (instead of a sharp transi- and analyzed Twitter data over multiple months, to under- tion as in the QCF method) one obtains positive-definite stand the role of external effects in how different hashtags blended force-based quasicontinuum models if and only if (topics) spread. We showed fundamental differences in the the width of the blending region scales as O(N 1/5)atomic dynamics of hashtags e.g. we found that hashtags of a 4/5 political nature are primarily driven by outside influences, lattice spacings (or the width scales as O(N − )inthe even though many people may be tweeting about them. macroscopic scale). We present computational results and analysis. Aditya Prakash CMU Xingjie Li [email protected] University of Minnesota [email protected]

MS38 Mitchell Luskin Scaling Graph Computations at Facebook School of Mathematics University of Minnesota With more than 800 million active users and 68 billion [email protected] edges, scalability is at the forefront of concerns when dealing with the Facebook social graph. This talk will discuss Christoph Ortner two recent advances. First, through the development of a University of Warwick novel graph sharding algorithm for load-balancing graph [email protected] computations, we were able to reduce the query time of a realtime system by 50%. Second, when computing the average graph distance between users on Facebook, empirical MS39 advances in the compression of the Facebook graph was a Energy-Based A/C Coupling for Pair Interaction key step in speeding up the computation. I will present a recent development in construction and John Ugander analysis of an energy-based atomistic-to-continuum cou- Cornell pling for two-body interaction (limited to zero-temperature [email protected] statics of simple crystals). Alexander V. Shapeev MS39 Swiss Federal Institute of Technology (Lausanne) Optimization-Based Decomposition of [email protected] Multiphysics Problems with Applications

We present a new, optimization-based framework for com- MS39 putational modeling. The framework uses optimization Blended Energy-based Quasicontinuum Methods and control ideas to assemble and decompose multiphysics operators and to preserve their fundamental physical prop- We present the energy-based blended quasicontinuum erties in the discretization process. Our approach relies on (BQCE) method for coupling atomistic and continuum three essential steps: decomposition of the original prob- models. We give error estimates for BQCE for 3D and lem into subproblems for which discretizations and robust multi-lattice crystals, and we give optimal choices of the solvers are available; integration of the subproblems into AN12 Abstracts 57 approximation parameters (the blending function and fi- Primary Decomposition nite element mesh) for the problem of a localized defect surrounded by a perfect crystal. Our formulation of BQCE for The goal of a numerical primary decomposition algorithm multi-lattice crystals uses a novel continuum model which is to produce an approximation to a general point on each we also discuss. Finally, we give numerical experiments component of a scheme defined by an ideal of polynomials which confirm the predictions of our error estimates. with complex coefficients. Our approach based on homotopy continuation and the concept of a deflated variety Brian Van Koten produces extraneous, the so-called pseudo-, components. University of Minnesota This talk will outline an algorithm to detect these using [email protected] approximate Macaulay dual space computation.

Mitchell Luskin Anton Leykin School of Mathematics School of Mathematics University of Minnesota Georgia Institute of Technology [email protected] [email protected]

Christoph Ortner MS40 University of Warwick Extended Precision Path Tracking in Parallel [email protected] To compensate for the overhead of extended precision (in particular: of double double and quad double arithmetic), MS40 we investigated the use of multiple cores on regular pro- Numerical Algebraic Geometry via Macaulay’s cessors and general purpose graphics processing units. Be- Perspective cause the cost of evaluating and differentiating polynomials often dominates the computational work in path tracking, F.S. Macaulay regarded theoretical solutions as prelimi- we developed and implemented multithreaded algorithms nary, a final solution to a problem is one which can actu- on multicore processors and massively parallel algorithms ally be computed. The methods he proposed in his famous for general purpose GPUs for multivariate polynomial eval- 1916 book are therefore computational but not all feasible uation and differentiation. at that time. This talk will outline the speaker’s adaptation of Macaulay’s methods, including H-bases and inverse Jan Verschelde arrays, using modern numerical linear algebra. Examples Department of Mathematics, Statistics and Computer involving the functorality of the global dual will be given. Science University of Illinois at Chicago Barry H. Dayton [email protected] Northeastern Illinois University [email protected] Genady Yoffe Dept. of Mathematics, Statistics, and CS MS40 University of Illinois, Chicago Preconditioning with H-Bases Computed Using gyoff[email protected] Dual Space Operations When solving polynomial systems using homotopy contin- MS41 uation, it is sometimes the case that we end up with a A Nonconforming Finite Element Method for an large number of paths going to . We want to precondi- Acoustic Fluid-Structure Interaction Problem tion these systems using H-bases∞ in order to remove paths going to . We calculate the H-bases numerically from In this work, we propose and analyze a nonconforming operations∞ on the dual space. When we dualize again, we finite element approximation of the vibration modes of recover H-bases with the same variety as the original ideal. acoustic fluid-structure interaction. The numerical scheme This process removes the extraneous pieces at with at is based on the irrotational fluid displacement formulation most an addition of ”junk” points. This eliminates∞ paths which eliminates the occurence of spurious eigenmodes. going to in the homotopy continuation run. Our method uses weakly continuous P1 vector fields for the ∞ fluid and classical piecewise linear elements for the fluid. Steven L. Ihde On properly graded meshes, we show optimal order error Colorado State University estimates which are validated by numerical experiments. [email protected] Susanne Brenner Department of Mathematics Daniel J. Bates Louisiana State University Colorado State University [email protected] Department of Mathematics [email protected] Aycil Cesmelioglu Jonathan Hauenstein Institute for Mathematics and Its Applications (IMA) Texas A&M University [email protected] [email protected] Jintao Cui Institute for Mathematics and its Applications MS40 University of Minnesota Elimination of Pseudo-components in Numerical [email protected] 58 AN12 Abstracts

Li-yeng Sung MS41 Department of Mathematics and CCT Uncertainly Quantiﬁcation for PDEs Louisiana State University [email protected] Abstract not available at time of publication.

Miroslav Stoyanov MS41 Florida State University Fluid-fluid Calculations using the Evolve-filter- Department of Scientific Computing relax Regularization Strategy [email protected]

Calculations for a model of two fluids coupled across a Clayton G. Webster shared interface are performed by using the evolve, then Oak Ridge National Laboratory filter and relax method, motivated by atmosphere-ocean [email protected] interaction. This method has a regularization effect and is computationally attractive since the evolution, filtering and relaxation steps can be decoupled. Different relax- MS42 ation parameters are appropriate for the two fluids. An Improving Earthquake Ground Motion Estimates algorithm is described to determine these parameters au- with Blue Gene/Q tomatically at each time step to improve model accuracy. This project aims to produce the first state-wide physics- Jeffrey M. Connors based probabilistic seismic hazard analysis (PSHA) map Lawrence Livermore National Laboratory for California, a goal only feasible with petascale com- Center for Applied Scientific Computing puting. The relevant phenomena span many orders of [email protected] magnitude in spatial scale, requiring high-resolution simulations. Furthermore, proper uncertainty estimation for PSHA requires simulations of large numbers of possible MS41 events. We will discuss the necessary optimizations to our Large Eddy Simulation of the Quasi-Geostrophic finite-element simulation codes for the Blue Gene/Q ar- Equations of Oceanic Flows chiteture.

We developed an approximate deconvolution (AD) LES Geoffrey Ely model for the two-layer quasi-geostrophic equations(QGE). Argonne National Laboratory The AD closure modeling approach is appealing for geo- [email protected] physical flows because it needs no additional phenomenological approximations to the original equations, and it can achieve high accuracy by employing repeated (computa- MS42 tionally efficient and easy to implement) filtering. We ap- Blue Gene/Q Architecture and Programming plied the AD-LES model to mid-latitude two-layer square Models oceanic basins, which are standard prototypes of stratified ocean dynamics models. Compared with a high-resolution Managing the million-way concurrency found in the Blue simulation, AD-LES yielded accurate results at signifi- Gene/Q architecture requires new thinking about algo- cantly lower computational cost. The sensitivity of the rithms and programming models. This talk will describe AD-LES results with respect to changes in input parame- the hardware architecture in detail and the connection to ters was also performed. We discovered that although the hybrid (i.e. multithreaded) programming models. Perfor- AD-LES model was robust with respect to changes in pa- mance of fundamental operations will be measured using rameters, changing the spatial filter made a huge difference. benchmarks derived from real applications. Two spatial filters were investigated in the AD-LES model: tridiagonal and elliptic differential. We found the tridiago- Jeff R. Hammond nal filter did not introduce any numerical dissipation in the Argonne National Laboratory AD-LES model. The differential filter, however, added a Leadership Computing Facility significant amount, and our numerical results show the new [email protected] AD-LES model used in with the differential filter can be employed successfully on meshes significantly coarser than the Munk scale and with an eddy viscosity coefficient that MS42 is dramatically lower than that used in the original two- Chemical Applications of the Multiresolution layer QGE. Although we do not provide a solution to the Adaptive Numerical Environment for Scientific longstanding quest for finding a rigorous derivation of the Simulation (MADNESS) eddy viscosity coefficients used in ocean modeling, we put forth a novel approach, serendipitously discovered in our MADNESS (multiresolution adaptive numerical environ- numerical investigation. The main strength of this new ment for scientific simulation) is a general numerical frame- approach is that the modeling error can be disentangled work to solve integral and differential equations in mul- from the numerical discretization error and can be stud- tiple dimensions. With its parallel runtime and numeri- ied separately in this framework. This could lead to more cal methods, MADNESS has proven to be a robust plat- robust and general LES models for large scale geophysical form for discretized problems, in particular those found flows. in quantum chemistry, nuclear physics, solid-state physics, atomic and molecular physics. In this work we will discuss Traian Iliescu asynchronous parallelism model implemented in a multi- Department of Mathematics threaded scheme and its application to energy storage and Virginia Tech conversion using linear-response density-functional theory. [email protected] Robert Harrison AN12 Abstracts 59

University of Tennessee at Knoxville formance of each of the feature vectors which in turn were [email protected] all shown to be reliable features for shape recognition. The presentation focuses on finite difference schemes for these lvaro Vázquez-Mayagoitia operators and summarizes key facts about their eigenval- Argonne National Laboratory ues that are of relevance in image recognition. (*) Joint [email protected] work with M. B. H. Rhouma and M. A. Khabou. Lotfi Hermi MS42 University of Arizona Accelerating and Benchmarking GAMESS on Department of Mathematics BlueGene/Q [email protected]

General Atomic and Molecular Electronic Structure Sys- tem (GAMESS) is a popular ab-initio quantum chemistry MS43 program. The Fragment Molecular Orbital (FMO) method Shape Optimization with the Vector Maxwell implemented in GAMESS is highly-scalable and allows Equations one to perform highly accurate calculations on very large molecular systems. We will describe our experience porting An intuitive framework is presented for shape optimiza- and optimizing GAMESS for Blue Gene/Q. The algorithm tion with the vector Maxwell equations. Through adjoint used to multithread the integral kernels in GAMESS to techniques, two simulations per iteration give both the take full advantage of the hardware capabilities of Blue shape and topological derivatives. The method is applied Gene/Q will be discussed in detail. Lastly, we will present to the design of a sub-wavelength solar cell texture, result- several benchmark results, including FMO calculations on ing in the highest reported absorption enhancement fac- water clusters. tor for high-index, thin-film media. The enhancement is achieved by shaping the bandstructure and optimizing the Maricris Mayes, Graham Fletcher in-coupling, possible only through non-intuitive, higher- Argonne National Laboratory order Fourier coefficients. [email protected], fl[email protected] Owen D. Miller, Eli Yablonovitch EECS Department Mark Gordon University of California, Berkeley Iowa State University [email protected], [email protected] [email protected]

MS43 MS43 Characterization of Weighted Graphs using Graph An Analytical Level Set Method for Eigenvalue Laplacians Shape Optimization Problems We will discuss our recent effort on characterizing and clus- We propose an eigenvalue shape optimization method tering weighted graphs using their morphological features based on representing the boundary of the domain as the extracted by spectra of their graph Laplacians. Compared zero level set of a linear combination of eigenfunctions cor- to unweighted graphs (which we studied them previously), responding to the same eigenvalue. The optimal shape is the graphs with weights pose a further challenge both in discovered by adjusting the shared eigenvalue and the co- theory and practice. We will also discuss the eigenfunction efficients of the linear combination. The method works in concentration phenomenon on a class of simple trees where any number of dimensions and is characterized by utmost such a phenomenon does not occur if unweighted. simplicity, arbitrarily high accuracy for a broad range of problems, as well as the ability to produce an exact ana- Naoki Saito lytical solution for an approximate problem. Department of Mathematics University of California, Davis Pavel Grinfeld [email protected] Drexel University [email protected] MS45 MS43 A Treecode Algorithm for N-body Interactions with Disjoint Source and Target Particles Shape Recognition Based on Eigenvalues of the Laplacian Energy and force computations are usually the bottleneck in molecular dynamics and Monte-Carlo simulations. Most Recently, there has been a surge in the use of the eigenval- algorithms for speeding up the N-body interactions are for ues of linear operators in problems of pattern recognition. a set of particles interacting with itself. We will present In this presentation, we discuss theoretical, numerical, and a treecode algorithm that offers considerable speed up for experimental aspects of using four well known linear op- (1) a set of particles interacting with itself as well as (2) erators and their eigenvalues for shape recognition. In interactions between a disjoint pair of source and target particular, the eigenvalues of the Laplacian operator un- particles while achieving high accuracy. der Dirichlet and Neumann boundary conditions, as well as those of the clamped plate and buckling of a clamped Henry A. Boateng plate are examined. Since the ratios of eigenvalues for each Department of Mathematics of these operators are translation, rotation and scale invari- University of Michigan ant, four feature vectors are extracted for the purpose of [email protected] shape recognition. These feature vectors are then fed into a basic neural network for training and measuring the per- Robert Krasny 60 AN12 Abstracts

University of Michigan lems. One such method, the singular evolutive interpolated Department of Mathematics Kalman (SEIK) filter, has been applied to the Advanced [email protected] Circulation (ADCIRC) storm surge model. Here ADCIRC along with data produced from a detailed hindcast study is used to improve hurricane storm surge forecasts. MS45 Multi-frequency It- Talea Mayo erative Integral Equations Method for the Shape University of Texas at Austin Reconstruction of an Acoustically Sound-soft Ob- [email protected] stacle Using Backscattering Troy Butler We present a method of solving the problem of obtaining Institute for Computational Engineering and Sciences a reconstruction of a planar acoustically sound-soft obsta- The University of Texas at Austin cle from the measured far-field pattern generated by plane [email protected] waves with a fixed incidence and varying frequencies. We solve iteratively the problem for each frequency, from the Muhammad Altaf lowest to the highest, using as an initial guess the solution King Abdullah University of Science and Technology given by the previous frequency. We present numerical re- [email protected] sults showing the benefits of our approach.

Carlos C. Borges Clint Dawson Worcester Polytechnic Institute Institute for Computational Engineering and Sciences [email protected] University of Texas at Austin [email protected]

MS45 Ibrahim Hoteit A Novel Multiscale Model of Glioblastoma Multi- King Abdullah University of Science and Technology forme (gbm) (KAUST) [email protected] Glioblastoma multiforme (GBM) is the most malignant, invasive, and lethal form of brain cancer; the median sur- Xiaodong Luo vival time of patients diagnosed with GBM is 15 months. King Abdullah University of Science and Technology We develop an adaptive, multiscale mathematical and nu- [email protected] merical model to study the development of GBM. We use a continuum (partial differential equation) model to describe the changes in the concentrations of important chemicals MS46 and proteins, such as glucose, oxygen, TGFα, PLCγ ,and Orbits of Projective Point Configurations an agent-based model for the tumor cells. In the development of a tumor, distinct regions evolve. There is eventu- Given an r n matrix, thought of as representing n points ally a necrotic core filled with dead cells surrounded by a in projective× (r 1)-space, we consider the closure of the or- region of quiescent (inactive) cells. The quiescent region is bit of all projectively− equivalent matrices. I will discuss the rimmed by proliferating and/or migrating cells. While one equations cutting out this variety, its finely graded Hilbert may acceptably describe the quiescent or necrotic regions series, and their relation to the matroid of the point con- of the tumor with a continuum model which would rep- figuration. resent activities on a macroscale, such a model would not capture the important details in the invasive regions where Alex Fink the cells are actively migrating and dividing. A fully mi- North Carolina State University croscale model would represent each cell as an individual arfi[email protected] entity but since a fully grown tumor has 1012 cells, this approach is too computationally expensive. We develop Andrew Berget a numerical model on adaptive quadtree grids that allows University of California, Davis for multiresolution. A phenotypic function determines the [email protected] phenotype population in each grid block as a function of the concentration of chemicals and proteins there, and cues changes in the grid resolution periodically to accurately MS46 capture the tumor structure. Finiteness Theorems and Algorithms for Polyno- mial Equations in an Infinite Number of Variables Gerardo Hernandez MathWorks We discuss the theory of symmetric Groebner bases, a con- Worcester Polytechnic Institute cept allowing one to prove Noetherianity results for sym- [email protected] metric ideals in polynomial rings with an infinite number of variables. We also explain applications of these objects to other fields such as algebraic statistics, and we present an MS45 algorithm for computing with them on a computer. Some Improving Hurricane Storm Surge Forecasting us- of this is joint work with Matthias Aschenbrener and Seth ing Data Assimilation Methods Sullivant. Uncertainty is inherent in numerical forecast models as well Christopher Hillar as in measurements of model solutions. Given both a model University of California, Berkeley and measurements, advanced data assimilation methods [email protected] can be used to improve state estimates of nonlinear prob- AN12 Abstracts 61

MS46 MS47 Stable Intersections of Ttropical Varieties Conservation Laws in Mathematical Biology Taking the stable intersection of a list of tropical hyper- In this talk I will consider conservation laws for a system surfaces is a purely combinatorial operation. The stable of hyperbolic equations, in which the coefficients are non- intersection can also be obtained by generically perturb- linear and nonlocal functions of unknown variables. I will ing the coefficients of the defining equations and taking explain how each such system arises as a mathematical the tropical variety of the ideal they generate. This ob- model of a biological process, and address the mathemat- servation leads to a new proof of Bernstein’s theorem. We ical results and, in some cases, open problems associated discuss how some combinatorial properties of stable inter- with the model equations. The examples are taken from sections can be proven either purely combinatorially or be the the areas of public health (drug resistance strains of derived from tropical varieties of ideals. bacteria), immune cell (Th cell differentiation), movement of molecules along axon, cancer, and wound healing Anders Jensen Universität des Saarlandes Avner Friedman [email protected] Department of Mathematics, Ohio State University [email protected] Josephine Yu School of Mathematics Georgia Institute of Technology MS47 [email protected] Controllability and Regularity of Some 1-d Elastic Systems with Internal Point Masses

MS46 In the case of a wave equation with an internal point mass, Computer-aided Design Algebra and Combina- it is known that exact controllability holds on an asymmet- torics ric space, where the regularity is higher on one side of the mass. We consider several variations of this problem, in- Computer Aided Design (CAD) software allows a user cluding the SCOLE beam model, but with an interior rigid to specify a finite number of rigid bodies and pair- body and thermoelastic systems with internal masses. wise coincidence, angular, and distance (cad) constraints among them. It is important to know when such a “body- Scott Hansen and-cad” framework is rigid or when the bodies may move Iowa State University relative to one another while maintaining the given con- Department of Mathematics straints. A body-and-cad framework may be specified by [email protected] an edge-colored multigraph. I will discuss a combinatorial characterization of the rigidity of a body-and-cad frame- MS47 work in which 20 of the 21 possible 3D constraints may appear. For our analysis we build on algebro-geometric Some Absolutely Continuos Schrödinger Operators methods developed by White and Whiteley to study the With Oscillating Potentials rigidity of systems consisting of a finite collection of bodies In this talk we report on the principle of limiting absorption connected by fixed-length bars using flexible joints. for a family of Schrödinger operators of the form Audrey Lee-St.John, Jessica Sidman ∆+c sin b x α/ x β . Mount Holyoke College − | | | | [email protected], [email protected] More specifically, we formulate conditions on the parameters c, b, α, β and interval which ensure that the PLA holds for such an operator overI the interval .Notethat MS47 I A Global Holmgren Theorem for Hyperbolic PDE although this potential is spherically symmetric, the validity of the PLA for the seperated operator does not imply A global uniqueness theorem for solutions to hyperbolic the PLA for the original operator. Our principal reference differential equations with analytic coefficients in a space- is the forthcoing paper of Golennia and Jecko, A New Look time cylinder Q =(0,T) Ω is established. Zero Cauchy At Mourre’s Commutator Theory. data on a part of the lateral× C1-boundary will force every solution to a homogeneous hyperbolic PDE or system Peter Rejto to vanish at half time T/2 provided that T>T.The School of Mathematics 0 University of Minnesota minimal time T0 depends on the geometry of the slowness surface of the hyperbolic operator. This theorem is an ex- [email protected] tension of an earlier result by Walter Littman from 2000. Furthermore, it is shown that this global uniqueness result MS48 holds for hyperbolic operators with C1-coefficientsaslong as they satisfy the conclusion of Holmgren’s Theorem. Modeling Evaporation and Transport in Porous Media. Comparing Models Using Different Depen- Matthias Eller dent Variables Georgetwon University Department of Mathematics Fick’s law for molecular diffusion can be used to describe [email protected] how water vapor is transported through a gas mixture. The general forms of Fick’s law can be written using gradients of either mass concentration, mole fraction, or chemical potential of the water vapor as dependent variables. Us- ing concentration as a dependent variable is more natural for the modeling process (as it appears naturally in the 62 AN12 Abstracts conservation of mass equations), but can yield unnatural [email protected] boundary conditions and nonlinear equations. Using chemical potential is less natural for modeling but yields govern- Matthew Farthing ing equations that are more mathematically tractable and US Army Engineer Research and Development Centerq boundary conditions that are more natural. In this talk we [email protected] consider evaporation and diffusion of water vapor. Depend- ing on the choice of dependent variable we derive different Clint Dawson sets of governing equations for the transport of water va- Institute for Computational Engineering and Sciences por. A careful derivation and analysis of each model will be University of Texas at Austin presented for water evaporation and diffusion in a simple [email protected] capillary tube, and comparisons of evaporation rates will be made between the models. Consequences for macroscale modeling will be discussed. Timothy Povich Department of Mathematical Sciences Lynn S. Bennethum United States Military Academy at West Point University of Colorado Denver blockedmailto:[email protected] [email protected] MS49 MS48 Delaying Wetting Failure In Coating Flows Via Title Not Available at Time of Publication Meniscus Confinement

Abstract not available at time of publication. Wetting failure brought about by air entrainment remains one of the biggest obstacles to faster operation of numer- Clint Dawson ous processes that deposit coatings of thin liquid films. Institute for Computational Engineering and Sciences Improving upon the coating speeds used in current tech- University of Texas at Austin nologies requires a better understanding of how system pa- [email protected] rameters influence wetting failure. We use both experiment and modeling to determine the effect of one such parameter—meniscus confinement—on the initiation of dy- MS48 namic wetting failure. Our experimental apparatus con- Numerical Methods for Shallow Water Models sists of a scraped steel roll that rotates into a bath of glyc- erol, and confinement is imposed via a gap formed between In this talk we will introduce and discuss numerical schemes a coating die and the roll surface. Comparison of the data for the shallow water equations. These equations are from confined and unconfined systems—obtained via flow widely used in many scientific applications related to mod- visualization—shows a clear increase in the relative critical eling of water flows in rivers, lakes and coastal areas. Fur- speed as the meniscus becomes more confined. A hydrody- thermore, many real world engineering applications require namic model for wetting failure is developed and analyzed the use of triangular meshes due to the complicated struc- with (i) lubrication theory and (ii) a two-dimensional finite ture of the computational domains of the problems being element method (FEM). Both approaches do a remarkable investigated. Therefore the development of robust and ac- job of matching the observed confinement trend, but only curate numerical methods for the simulation of shallow the two-dimensional model yields accurate estimates of the water models is important and challenging problem. In absolute values of the critical speeds due to the highly our talk we will discuss the recently developed numerical two-dimensional nature of the stress field in the displac- schemes for such models. We will demonstrate the perfor- ing liquid. The overall success of the hydrodynamic model mance of the proposed methods in a number of numerical suggests a wetting failure mechanism primarily related to examples. viscous bending of the meniscus. Yekaterina Epshteyn Satish Kumar department of mathematics Chemical Engineering and Materials Science university of utah University of Minnesota [email protected] [email protected]

MS48 Eric Vandre University of Minnesota A Comparison of Finite Element Methods for [email protected] Strongly Density Dependent Flows Saltwater intrusion is a frequent issue in coastal freshwa- Marcio Carvalho ter aquifers. We develop a Discontinuous Galerkin (DG) PUC-Rio formulation for these saltwater flow and transport prob- [email protected] lems. The transport scheme must handle sharp fronts while the flow scheme requries high accuracy. DG methods have potential advantages over continuous Galerkin models MS49 for such problems. We discretize the flow with local DG Tear Film Dynamics on an Eye Shaped Domain and the transport with Non-symmetric, Interior Penalty Galerkin. We present the formulation and comparisons for We consider a tear film dynamics model on a 2-D eye saltwater intrusion benchmarks. shaped domain with specification of the flux normal to the boundary. The domain is fixed in time, but we cy- Chris Kees cle the time dependence of the flux boundary condition. U.S. Army Engineer Research and Development Center This treatment is a drastic simplification of what occurs in Coastal and Hydraulics Laboratory vivo. Model simulations are conducted in the OVERTURE AN12 Abstracts 63 computational frame work. Results are compared with ex- MS50 isting tear film models with both 1-D and 2-D domains as Exploiting Saliency in Compressive and Adaptive well as clinical measured data. Sensing Longfei Li,RichardBraun Recent developments in compressive and adaptive sensing University of Delaware have demonstrated the tremendous improvements in sens- Department of Mathematical Sciences ing resource efficiency that can be achieved by exploiting [email protected], [email protected] sparsity in high-dimensional inference tasks. In this talk we describe how compressive sensing techniques can be extended to exploit saliency. We discuss our recent work MS49 quantifying the effectiveness of a compressive sensing strat- Tear Film Dynamics with Surfactant Transport and egy that accurately identifies salient features from compres- Osmolarity sive measurements, and we demonstrate the performance of this technique in a two-stage active compressive imaging We consider a model problem for the breakup up of the tear approach to automated surveillance. film including surface tension, Marangoni stresses, insol- uble surfactant transport, evaporation, osmolarity trans- Jarvis Haupt port, osmosis and wetting of corneal surface. Surface- University of Minnesota concentration evaporation mimics the tear film lipid. In [email protected] many, the Marangoni effect seems to eliminate a localized area of increased evaporation while the osmolarity increases because of evaporation. MS50 Sharp Recovery Bounds for Convex Deconvolution, Javed Siddique With Applications Penn State York [email protected] This work investigates the limits of a convex optimization procedure for the deconvolution of structured signals. The Richard Braun geometry of the convex program leads to a precise, yet in- University of Delaware tuitive, characterization of successful deconvolution. Cou- Department of Mathematical Sciences pling this geometric picture with a random model reveals [email protected] sharp thresholds for success, and failure, of the deconvolution procedure. These generic results are applicable to a wide variety of problems. This work considers deconvolv- MS49 ing two sparse vectors, analyzes a spread-spectrum coding Effective Slip for An Upper Convected Maxwell scheme for impulsive noise, and shows when it is possible Fluid to deconvolve a low-rank matrix corrupted with a special type of noise. As an additional benefit, this analysis re- We consider an upper convected Maxwell fluid with sol- covers, and extends, known weak and strong thresholds for vent and diffusion undergoing shear flow at a solid wall. the basis pursuit problem. We show that even for this simple model, stress diffusion may lead to plug flow and sharp boundary layers near the Michael McCoy solid wall. We discuss this for a simple channel flow con- Caltech figuration and generalize the results to lubrication models [email protected] of a thin film flowing over a solid substrate. For this free boundary problem a distinguished limit can be identified. Joel A. Tropp The lubrication models are found to correspond in part to Caltech CMS previously known lubrication models with a slip boundary [email protected] condition.

Barbara Wagner MS50 Institute of Mathematics Fast Global Convergence of Gradient Methods for Technische Universität Berlin High-dimensional Statistical Recovery [email protected] Many statistical M-estimators are based on convex opti- Pamela Cook mization problems formed by the combination of a data- Dept of Mathematical Sciences dependent loss function with a norm-based regularizer. UofDelaware We analyze the convergence rates of projected gradient [email protected] methods for solving such problems, working within a high- dimensional framework that allows the data dimension d Richard Braun to grow with (and possibly exceed) the sample size n. University of Delaware This high-dimensional structure precludes the usual global Department of Mathematical Sciences assumptions—namely, strong convexity and smoothness [email protected] conditions—that underlie much of classical optimization analysis. We define appropriately restricted versions of Andreas Muench these conditions, and show that they are satisfied with high OCIAM Mathematical Institute probability for various statistical models. Under these con- University of Oxford ditions, our theory guarantees that projected gradient de- [email protected] scent has a globally geometric rate of convergence up to the statistical precision of the model, meaning the typical distance between the true unknown parameter θ∗ and an optimal solution θˆ. This result is substantially sharper 64 AN12 Abstracts than previous convergence results, which yielded sublin- MS51 ear convergence, or linear convergence only up to the noise Massive Graphs: The Way Forward level. Our analysis applies to a wide range of M-estimators and statistical models, including sparse linear regression Large graph analytics have become an increasingly impor- using Lasso (1-regularized regression); group Lasso for tant in a wide variety of application areas such as inter- block sparsity; log-linear models with regularization; low- net search, bioinformatics, social media, and cybersecu- rank matrix recovery using nuclear norm regularization; rity. Massive graphs push the state of the art in both big and matrix decomposition. This is based on joint work compute and big data. This presentation will collect and with Alekh Agarwal and Martin Wainwright. present the outstanding questions in this field that have been raised over the course of the mini-symposium. Sahand Negahban MIT John R. Gilbert [email protected] Dept of Computer Science University of California, Santa Barbara [email protected] MS50 Robust Image Recovery via Total Variation Mini- mization MS51 Extended Sparse Matrices as Tools for Graph Com- Discrete images, consisting of slowly-varying pixel values putation except across edges, have sparse or compressible representations with respect to the discrete gradient. Despite being Sparse matrices frame a powerful graph computation ar- a primary motivation for compressed sensing, stability re- chitecture. Extensions such as complex elemental types, sults for total-variation minimization do not follow directly runtime filtering and arbitrary semiring operations greatly from the standard ”l1” theory of compressed sensing. In expand the utility of sparse matrices for graph analytics. this talk, we present near-optimal reconstruction guaran- Implementations must also match available hardware to be tees for total-variation minimization and discuss several useful. Individual shared-memory machines, distributed- relatedopenproblems. memory clusters and cloud HPC systems all raise unique challenges, but significant commonality remains among Rachel Ward them. This talk will cover how we address these challenges Department of Mathematics in our Knowledge Discovery Toolbox. University of Texas at Austin [email protected] Adam Lugowski UC Santa Barbara Deanna Needell [email protected] Department of Mathematics Claremont McKenna College [email protected] MS51 Graph Analytics for Subject-Matter Experts: Bal- ancing Standards, Simplicity, and Complexity MS51 Version 2.0 of the Parallel Boost Graph Library: Subject-matter experts needing to analyze large graphs Message-Driven Solutions to Data-Driven Prob- ideally want the abilities to incorporate data from dis- lems parate sources, perform simple analyses to find data needing deeper analysis, and execute complex analyses on that Data-driven applications, such as graph analytics, are data, all via clear, reliable, and widely-available interfaces. unique in that the computational structure of the appli- Knowledge Discovery Toolkit (KDT) enables complex anal- cations is entirely dependent on the input data. This fact yses on very large data (beyond what will reside in the makes static analysis difficult and necessitates dynamic, memory of a single cluster node) through procedural inter- lightweight, execution-time solutions. Version 2.0 of the faces, though it does not (yet) ingest numerous data for- Parallel Boost Graph Library (PBGL) demonstrates one mats. Emerging semantic-web technologies are starting to approach to building a modular, scalable, and perhaps deliver the promise of straightforward fusing of disparate most importantly, performance portable set of graph ker- data sources through standard interfaces and ontologies, nels. The PBGL 2.0 uses the AM++ active messaging li- yet the current SPARQL 1.1 language does not support brary (an implementation of the Active Pebbles program- the calculation of complex graph metrics, such as between- ming and execution model) to provide portable, generic, ness centrality. This talk will cover our work to merge thread-safe messaging support on a variety of platforms. the ease-of-use of the semantic-web technologies with the On top of AM++, PBGL 2.0 provides a variety of graph complex analytics of KDT. types, auxiliary data structures, and algorithmic kernels suitable for both shared- and distributed-memory paral- Steve Reinhardt lelism (e.g. threads and processes) with the potential for Cray, Inc. straightforward extension to various types of accelerators. [email protected] Nick Edmonds Open Systems Laboratory MS52 Indiana University Pointwise Estimates for Stokes Equation [email protected] In this talk I will describe new stability results of the finite element solution for the Stokes system in W 1 norm on general convex polyhedral domain. In contrast∞ to pre- 2 viously known results, Wr regularity for r>3, which does not hold for a general convex polyhedral domains, is not AN12 Abstracts 65 required. I will briefly describe the main ideas of the proof the first ten eigenvalues of both problems. that uses recently available sharp Holder pointwise estimates of the corresponding Greens matrix together with Pedro R. S. Antunes novel local energy error estimates, which do not involve an Group of Mathematical Physics error of the pressure in a weaker norm. University of Lisbon [email protected] Dmitriy Leykekhman Department of Mathematics University of Connecticut MS53 [email protected] Principal Eigenvalue Minimization for an Elliptic Problem with Indefinite Weight MS52 An efficient rearrangement algorithm based on Rayleigh Conforming and Divergence Free Stokes Elements quotient and rearrangement is introduced to the minimization of the positive principal eigenvalue under the con- We present a family of conforming finite elements for the straint that the absolute value of the weight is bounded Stokes problem on triangular meshes. We show that the and the total weight is a fixed negative constant. Bio- elements satisfy the inf-sup condition and converge opti- logically, this minimization problem is motivated by the mally. Moreover, the pressure space is exactly the diver- question of determining the optimal spatial arrangement gence of the velocity space. Therefore the discretely diver- of favorable and unfavorable regions for a species to sur- gence free functions are divergence free pointwise. We also vive. The optimal results are explored both theoretically show how the elements are related to a class of C1 elements and numerically. through the use of a discrete de Rham complex. Michael Hintermüller Michael J. Neilan Humboldt-University of Berlin Louisiana State University [email protected] Mathematics and Center for Computation and Technology Chiu-Yen Kao [email protected] The Ohio State University Claremont McKenna College Johnny Guzman [email protected] Brown University johnny [email protected] Antoine Laurain Humboldt-University of Berlin [email protected] MS52 Transparent Boundary Conditions and the Gap Condition for Stokes Elements MS53 Microcavity Optimization via the Frequency- In the context of a Finite Element discretization of the averaged Local Density of States Stokes equation, a gap property is the possibility of uniformly approximating velocities with discrete zero diver- Applications such as lasers and nonlinear devices require gence by exactly solenoidal fields. This property seems to optical microcavities with long lifetimes Q and small modal be rare among non-divergence-free stable Finite Element volumes V . We formulate and solve a full 3d optimization spaces for the Stokes equation. We will discuss it for some scheme, over all possible 2d-lithography patterns in a thin examples and we will prove that it implies the discrete well dielectric film. The key to our formulation is a frequency- posedness of the simplest FEM-BEM coupled schemes for averaged local density of states, where the frequency aver- Stokes. aging corresponds to the desired bandwidth, evaluated by a novel technique: solving a single scattering problem at a Francisco J. Sayas complex frequency. Department of Mathematical Sciences University of Delaware Xiangdong Liang, Steven Johnson [email protected] MIT [email protected], [email protected] Johnny Guzman Brown University johnny [email protected] MS55 Tracing the Progression of Retinitis Pigmentosa via Salim Meddahi, Virginia Selgas Photoreceptor Interactions University of Oviedo, Spain [email protected], [email protected] Retinitis pigmentosa (RP) is a group of inherited degener- ative eye diseases characterized by mutations in the genetic structure of the photoreceptors that leads to the premature MS53 death of the photoreceptors. We trace the progression of Optimal Bilaplacian Eigenvalues RP to complete blindness through each subtype via bifurcation theory. We show that the evolution of RP requires We consider the shape optimization for the clamped plate the failure of multiple components and that a delicate bal- and buckling plate eigenvalue problems. We develop a nu- ance between nutrients and the rates of shedding and re- merical method using Hadamard’s shape derivative and the newal is needed to halt its progression. Method of Fundamental Solutions as forward solver which allows to propose numerical candidates to be minimizers of Erika T. Camacho 66 AN12 Abstracts

Arizona State University form of the Ericksen-Leslie theory of liquid crystals, we Division of Mathematics and Natural Sciences have found instabilities from the trivial no-flow solution, [email protected] which lead to kink-like flow profiles and flow-aligned orientational structures. There are also other, jet-like, solutions which are often higher energy solutions but are, at least MS55 locally, stable. Oscillation Criteria for Nonlinear Dynamic Equa- tions Nigel Mottram Department of Mathematics and Statistics In this talk we consider the second-order linear delay dy- University of Strathclyde namic equation [email protected] ∆ p(t)y∆(t) + q(t)y(τ(t)) = 0 MS56 on a time scale T . By employing the Riccati transfor- Analysis of Smectic C* Films with Defects mation technique, we establish some sufficient conditions which ensure that every solution oscillates. The obtained We analyze a model for the elastic energy of planer c- results unify the oscillation of second-order delay differen- director patterns in a smectic film. Because of boundary tial and difference equations. We illustrate our results with conditions and polar fields topological defects form in these examples. patterns. We use a Ginzburg Landau model that allows the director field to have variable length and to vanish at the Raegan Higgins defect cores. We prove that if the models G-L parameter Texas Tech University is small then low energy states develop degree +(-) one de- Department of Mathematics and Statistics fects that tend to a minimal energy configuration with a [email protected] limiting far field texture. Our main contribution is that we are able to treat the case of unequal splay and bend elasticity constants. Earlier analytic work for the G-L functional MS55 had been limited to the equal constant case. Order of Events and Optimal Control in Discrete Time Biological Models Daniel Phillips Department of Mathematics, Purdue University The order of events in models with discrete time is crucial. [email protected] Two examples illustrate the effect of the order of events on optimal control of models with discrete time. One ex- Sean Colbert-Kelly ample involves augmentation of an endangered species and Purdue University the other example is a harvesting problem for an integrod- [email protected] ifference population model. Suzanne M. Lenhart MS56 University of Tennessee Shear Flow in Smectic A Liquid Crystals Department of Mathematics [email protected] The onset of a dynamic instability in the shear flow of planar aligned smectic A liquid crystals will be discussed. Os- cillatory shear will also be examined and the results will be MS55 linked to the onset of an analogous dynamic instability for A Mathematical Modeling Approach to the Rever- lipid bilayers induced by forced oscillations. Mathematical sal of Type 2 Diabetes and β-Cell Compensation modelling equivalences will be highlighted and key critical control parameters will be identified for the occurrence of Mathematically we explore fat accumulation and β-cell instabilities. function in the progression of Type 2 diabetes (T2D). Ex- tending previous models we consider a link between adi- Iain W. Stewart pose tissue and insulin sensitivity. Incorporating fat and University of Strathclyde direct effects of both insulin and β-cell sensitivity, the lat- [email protected] ter embodies a logistic response. Qualitative description on glucose-insulin-β-cell, and fat dynamics with bifurcation analysis address irreversibility of T2D and β-cell fail- MS56 ure which yield insight on clinical interventions targeted to Anisotropic Wave Propagation in Nematic Liquid certain stages of T2D. Crystals

Anarina Murillo As early as 1972, Mullen, Luthi and Stephen [1] showed AMLSS-Mathematical, Computation & Modeling experimentally that the director alignment of a nematic Sciences Center liquid crystal induces an anisotropic propagation of acous- Arizona State University tic waves. By contrast, Selinger and co-workers [2] have [email protected] studied a liquid crystal cell where the nematic molecules can be realigned by an ultrasonic wave, leading to a change in the optical transmission through the cell. The existing MS56 models for this acousto-optic effect [2,3] propose a free en- Jet Flows in Active Nematic Fluids ergy that depends on the density gradient thus describing the nematic liquid crystal as a compressible second grade We have investigated the organisation, order and flow in- fluid. In the presentation I will show how the introduction duced in an active fluid, consisting of an isotropic fluid con- in the stress tensor of the simple anisotropic term n n, n taining elongated swimming organisms. Using an adapted ⊗ AN12 Abstracts 67 being the director field, easily reproduces the experimen- the constraint that the center of the sheet deform only tal anisotropic behaviour of the sound speed, thus provid- slightly, we derive upper and lower bounds for the elastic ing a simpler first-grade model for the acousto-optic effect. energy which agree, up to a factor, with the energy of the It is worth noticing that Ericksen already considered this associated conical deformation smoothed out near its tip. term in his seminal papers but subsequently it has been For a restricted class of boundary deformations, we show neglected. This term is non-hyperelastic. However, we that similar energy scaling laws hold without a constraint show that it can be interpreted as the linear approximation on the deformation at the sheets center. of a new interaction term in the free energy for the NLC medium which couples the director field with the elastic Jeremy Brandman properties of the fluid. Some noticeable consequences of Courant Institute of Mathematical Sciences this choice are then discussed. New York Univeristy [1] M.E. Mullen, B. Luthi and M.J. Stephen, ”Sound ve- [email protected] locity in a nematic liquid crystal”, Phys. Rev. Lett. 28, 799-801 (1972). Robert V. Kohn [2] J.V. Selinger, M.S. Spector, V.A. Greanya, B.T. Wes- Courant Institute of Mathematical Sciences lowski, D.K. Shenoy, and R. Shashidhar, ”Acoustic realign- New York University ment of nematic liquid crystals”, Phys. Rev. E 66, 051708 [email protected] (2002). [3] E.G. Virga, ”Variational theory for nematoacoustics”, Hoai-Minh Nguyen Phys. Rev. E 80, 031705 (2009). Department of Mathematics University of Minnesota Antonio Di Carlo [email protected] Dipartimento di Strutture UniversitàRomaTre [email protected] MS57 Pattern Formation in Compressed Elastic Films on Paolo Biscari Compliant Substrates: An Explanation of the Her- Dipartimento di Matematica ringbone Structure Politecnico di Milano [email protected] We consider the buckling of a thin elastic film bonded to a thick compliant substrate, when the (compressive) misfit Stefano Turzi is relatively large. Previous experimental and numerical Politecnico di Milano studies suggest that a herringbone pattern minimizes the [email protected] total energy (the membrane and bending energy of the film, plus the elastic energy of the substrate). We verify this, by (i) identifying the scaling law achieved by the herringbone MS57 pattern, and (ii) proving that no structure can achieve a Quasistatic Nonlinear Viscoelasticity and Gradient better scaling law. Flows Robert V. Kohn We consider the equation of motion for one-dimensional Courant Institute of Mathematical Sciences nonlinear viscoelasticity of strain-rate type under the as- New York University sumption that the stored-energy function is λ-convex, al- [email protected] lowing for solid phase transformations. We show how this problem can be formulated as a gradient flow, leading to ex- Hoai-Minh Nguyen istence and uniqueness of solutions. By approximating gen- Department of Mathematics eral initial data by those in which the deformation gradient University of Minnesota takes only finitely many values, we show that the defor- [email protected] mation gradient is instantaneously bounded and bounded away from zero. Finally, we discuss the open problem of showing that every solution converges to an equilibrium so- MS57 lution as time t , proving by means of a new argument On the Inability of Continuum Theory to Predict that this occurs→∞ in some previously unsolved cases. the Elastic Energy of a Strained Alloy Film John Ball An explicit calculation of a ball and spring model shows Oxford Centre for Nonlinear PDE Mathematical Institute that while continuum theory can predict the average dis- Oxford placement field for an alloyed system it cannot correctly [email protected] determine the elastic energy. Implications of this result will be discussed. This is joint work with Christian Ratsch Yasemin Sengul andArvindBaskaran. Ozyegin University, Istanbul [email protected] Peter Smereka Department of Mathematics University of Michigan MS57 [email protected] Energy Scaling Laws for Conically Constrained Thin Elastic Sheets Christian Ratsc UCLA In this talk, we discuss recent work on energy scaling laws [email protected] for thin elastic sheets subject to a boundary displacement condition consistent with a conical deformation. Under 68 AN12 Abstracts

Arvind Baskaran [email protected] Institute for Pure and Applied Mathematics, UCLA University of California, Irvine [email protected] MS58 Consistency and Stability Considerations for Implicit-explicit Additive Splittings MS58 Aposteriori Analysis of Multirate and Multiscale Stability and consistency properties of operator splitting Evolution Systems time-marching are challenging to characterize and interpret due to the coupling effects, which lead to complex in- We consider analysis of numerical methods for multiscale teractions among operators. In additive splittings the right and multirate evolution models that present significantly hand side can be represented as a sum of terms that typ- different temporal and spatial scales within the compo- ically have different properties, such as stiff and nonstiff, nents of the model. We interpret the multirate method as a and require integrators with different stability properties. multiscale operator decomposition method and use this to We focus on multistage additive implicit-explicit (IMEX) conduct both an apriori and a hybrid apriori–aposteriori er- splittings and present new IMEX schemes. ror analysis. We formulate an iterative multirate Galerkin finite element method then employ adjoint operators and Emil M. Constantinescu variational analysis. We consider analyses of both ODEs Argonne National Laboratory and PDEs. Mathematics and Computer Science Division [email protected] Jehanzeb H. Chaudhry Colorado State University Department of Mathematics MS58 [email protected] Coupling for a Virtual Nuclear Reactor

Don Estep Abstract not available at time of publication. Colorado State University John Turner [email protected] Oak Ridge National Laboratory Computational Engineering and Energy Sciences Victor E. Ginting [email protected] Department of Mathematics University of Wyoming [email protected] MS59 A Problem of Boundary Controllability for a Plate Simon Tavener Colorado State University The boundary controllability problem, here discussed, [email protected] might be described by a two-dimensional space equation modeling, at the same time t, different physical phenomena in a composite solid made of different materials. These MS58 phenomena may be governed, at the same time t,forex- Quantification of Operator Splitting Effects in Fi- ample, by the heat equation and Schrödinger equation in nite Volume Calculations of Advection-diffusion two separate regions. Interface transmission conditions are imposed. Some issues are presented involving splitting effects near boundaries in operator-split finite volume calculations for Orazio Arena advection-diffusion. In applications, it is desirable to un- Universita di Firenze derstand the errors and sources of errors in calculations, Florence, Italy such as splitting effects, which may be difficult to deter- arena@unifi.it mine. One approach is presented for a posteriori error estimation to calculate the error in a quantity of interest (QoI) and investigate the effect of the splitting on the computed MS59 QoI value. Mathematical Challenges Arising from the Ques- tions of Controllability for Linked Elastic Struc- Jeffrey M. Connors tures Lawrence Livermore National Laboratory Center for Applied Scientific Computing A tremendous challenge in the study of control and sta- [email protected] bilization of dynamic elastic systems is the ability to rigorously address whether linked dynamic structures can be Jeffrey W. Banks controlled using boundary feedback alone. When a struc- Lawrence Livermore National Laboratory ture is composed of a number of interconnected elastic el- [email protected] ements or is modelled by a system of coupled partial differential equations, the behavior becomes much harder to both predict and to control. This talk focuses on a num- Jeffrey A. Hittinger ber of issues that arise when attempting to control these Center for Applied Scientific Computing complex systems. Lawrence Livermore National Laboratory [email protected] Mary Ann Horn Vanderbilt University & National Science Foundation Carol S. Woodward [email protected] Lawrence Livermore Nat’l Lab AN12 Abstracts 69

MS59 Tatiana Gambaryan-Roisman, Peter Stephan Limitations on Control and Stabilization of Certain Technische Universitaet Darmstadt Hybrid Systems [email protected], [email protected] Hybrid systems are often modeled as continuous parameter systems modeled by partial differential equations coupled to point masses. It is natural to attempt to establish MS60 exact controllability and/or uniform exponential stabiliz- A Multiple Scales Approach to Evaporation inability of the overall system using controls applied to these duced Marangoni Convection point masses. We show, using extensions of the notion of the operator trace, that the discrete mass property of such In this talk, we consider the stability of a thin liquid layer points of control application impose definite limitations on of a binary mixture of a volatile (solvent) and a non-volatile achievement of these goals. (polymer) species. Evaporation depletes the solvent near the liquid surface, which can lead to Bénard-Marangoni- David Russell type convection. Due to evaporation, the base state is time Department of Mathematics dependent, thus impeding the use of normal modes. How- Virginia Tech ever, the evaporation is slow on the diffusive time scale, and [email protected] this is exploited via a systematic multiple scales expansion.

MS59 Andreas Muench Ensemble Dynamics and Bred Vectors OCIAM Mathematical Institute University of Oxford Abstract not available at time of publication. [email protected]

George Sell Matthew Hennessy School of Mathematics Mathematical Institute University of Minnesota University of Oxford [email protected] [email protected]

MS60 MS60 Heated Tear Film in One Dimension with a Moving Asymptotics of a Thermally Driven Thin Film Boundary A flow driven up an inclined plane by thermal Marangoni We consider model problems for the tear film over multiple stresses is modeled using the lubrication approximation in blink cycles with evaporation and with heat transfer from one dimension, yielding a fourth order nonlinear PDE. Two with a model domain for the eye. The nonlinear PDE qualitatively distinct solutions to the steady-state ODE for film thickness is coupled with heat transfer under the arise when additional localized heating is introduced. Solu- film; simultaneous solution on a moving domain is via a tion type is determined by the magnitude of this localized spectral method. The numerical results reveal a similarity heating. Solution behavior as a function of this heating to quantitative in vivo observations of the film dynamics parameter is explored using asymptotic analysis and vali- and the surface temperature of the film. dated through comparison with numerical simulations.

Quan Deng Harrison Potter,ThomasP.Witelski Department of Mathematical Sciences Duke University University of Delaware Department of Mathematics [email protected] [email protected], [email protected]

MS60 MS61 Fingering Instability of Evaporating Thin Films Application of Graph Scaffolding in Approximating The fingering instability of a volatile, viscous liquid flowing the Chromatic Number down an inclined, heated surface is investigated. A lubrica- We introduce the concept of graph scaffolding, through its tion type approach is used to develop a three-dimensional application in finding the chormatic number of large-scale model of the flow, and numerical simulations are conducted networks. Graph scaffolding is a a generalized framework based on the model. Liquids of various wetting properties for working with combinatorial optimization problems that are considered. Evaporation is found to have a stabiliz- first exploits theoretical results to compute exact or near- ing influence on the flow, with the strength of evaporation exact solutions on well-defined portions of the graphthe needed to completely suppress the instability increasing scaffoldand then leverages the answer on the scaffold to with increasing apparent contact angle. construct a high-quality solution to the overall problem. Jill Klentzman We demonstrate through empirical and theoretical results University of Arizona how by using chordal graphs as a scaffold, the chormatic [email protected] number of a given graph can be closely approximated. Sanjukta Bhowmick Vladimir Ajaev Department of Computer Science Southern Methodist University University of Nebraska, Omaha [email protected] [email protected] 70 AN12 Abstracts

MS61 MS62 Sparsification Techniques for Metaphor Compre- Challenges in Isogeometric Analysis (IGA) hension IGA replaces traditional Finite Elements by watertight Comprehension of metaphors occurs at the highest level of structures of 3-variate NURBS. The introduction of language proficiency. Metaphor comprehension is compu- NURBS in FEA allows accurate representation of CAD- tationally challenging as well. The basic technique involves shapes in FEA. However, efficient technology for establish- building semantic spaces for words using relevant corpora. ing watertight IGA-models from CAD-models has to be Given large scale corpora such as English Wikipedia, spar- developed, local refinement of IGA-models has to be im- sification becomes a necessity. In this presentation, we will proved, and direct GPU-based visualization of IGA-models detail some of the sparsification techniques we have used has to be developed. IGA potentially simplifies analysis of for metaphor comprehension. as-is models as the path from measurement through CAD to analysis is shortened. Mahantesh Halappanavar Pacific Northwest National Laboratory Tor Dokken [email protected] SINTEF ICT, Department of Applied Mathematics Oslo, Norway [email protected] MS61 Graph Sparsification Methods in Cybersecurity MS62 In cybersecurity and related problem domains we often Isogeometric Analysis for Shape Optimization must deal with very large graphs. For example, consider traffic on a large computer network, a multigraph with One of the attractive features of isogeometric analysis is upwards of hundreds of thousands of nodes. In order to the exact representation of the geometry. The geometry accomplish tasks like connected component identification, is furthermore given by a relative low number of control path finding, and subgraph isomorphism in these large net- points and this makes isogeometric analysis an ideal basis work graphs we are turning to graph sparsification. We will for shape optimisation. I will describe some of the results describe the sparsification techniques we are using and give we have obtained and also some of the problems we have an analysis of their performance. encountered. One of these problems is that the geometry of the shape is given by the boundary alone. And, it is the Emilie Hogan parametrisation of the boundary which is changed by the Pacific Nortwest National Lab optimisation procedure. But isogeometric analysis requires [email protected] a parametrisation of the whole domain. So in every optimisation cycle we need to extend a parametrisation of the John Johnson, Mahantesh Halappanavar boundary of a domain to the whole domain. It has to be Pacific Northwest National Laboratory fast in order not to slow the optimisation down but it also [email protected], has to be robust and give a parametrisation of high qual- [email protected] ity. These are conflicting requirements so we propose the following approach. During the optimisation a fast linear method is used, but if the parametrisation becomes singu- MS61 lar or close to singular then the optimisation is stopped and Sparse Graph Realization from a Metric Space the parametrisation is improved using a nonlinear method. The optimisation then continues using a linear method. We present an approach for constructing a locality graph for set of points in a given metric space, without the need Jens Gravesen for an underlying geometry on the space. In addition, the Technical University of Denmark graph of all calculated distances is sparse, making our ap- [email protected] proach appropriate for very high-dimensional data. Chad Scherrer MS62 Pacific Northwest National Laboratory Locally Refined B-splines [email protected] We will address local refinement of a tensor product grid specified as a sequence of inserted line segments parallel MS62 to the knot lines. We obtain a quadrilateral grid with On Local Refinement via T-splines T-junctions in the parameter domain, and a collection of tensor product B-splines on this mesh here named an LR- We study properties of Analysis Suitable (AS) T-splines mesh. The approach applies equally well in dimensions which are needed to use T-splines within an adaptive pro- higher than two. Moreover, in the two dimensional case cedure in Isogeometric Analysis. We set up a priori and a this collection of B-splines spans the full spline space on posteriori error analysis; we study the use of AS T-splines the LR-mesh. to solve mixed problems and, more in general, non-coercive differential problems. Tom Lyche University of Oslo Annalisa Buffa Department of Informatics and CMA I.M.A.T.I. - C.N.R. tom@ifi.uio.no Pavia, Italy [email protected] AN12 Abstracts 71

MS63 Gilad Lerman The Challenges of Robustness in High Dimensions School of Mathematics University of Minnesota We consider the problem of dealing with (potentially ma- [email protected] liciously) corrupted points in the high dimensional regime. We show that even for basic problems like regression and PCA, existing techniques from robust statistics fail dra- MS63 matically. We develop new techniques designed for robust- A Novel M-Estimator for Robust PCA ness in the high dimensional regime. We formulate a convex minimization to robustly recover a Constantine Caramanis subspace from a contaminated data set, partially sampled The University of Texas at Austin around it, and propose a fast iterative algorithm to achieve [email protected] the corresponding minimum. We establish exact recovery by this minimizer, quantify the eﬀect of noise and regularization, explain how to take advantage of a known intrinsic MS63 dimension and establish linear convergence of the iterative Compressive Principal Component Pursuit algorithm. We compare our method with many other algorithms for Robust PCA on synthetic and real data sets We consider the problem of recovering target matrix that is and demonstrate state-of-the-art speed and accuracy. a superposition of low-rank and sparse components, from a small set of linear measurements. This problem arises Teng Zhang in compressed sensing of videos and hyperspectral images, Institute for Mathematics and its Applications as well as in the analysis of transformation invariant low- University of Minnesota rank matrix recovery. We analyze the performance of the [email protected] natural convex heuristic for solving this problem, under the assumption that measurements are chosen uniformly Gilad Lerman at random. We prove that this heuristic exactly recovers School of Mathematics low-rank and sparse terms, provided the number of obser- University of Minnesota vations exceeds the number of intrinsic degrees of freedom [email protected] by a polylogarithmic factor. Our analysis introduces several ideas that may be of independent interest for the more general problem of compressed sensing of superpositions of MS64 structured signals. Relaxation Results for Nematic Elastomers

Yi Ma We compute the relaxation of a free-energy functional Department of Electrical and Computer Engineering which describes the order-strain interaction in incompress- University of Illinois at Urbana-Champaign ible nematic elastomers in the regime of small strains. [email protected] Adopting the uniaxial order tensor theory (Frank model) to describe the liquid crystal order, we prove that the min- John Wright ima of the relaxation exhibit an effective biaxial nematic Department of Electrical Engineering texture (that of the de Gennes theory). The relaxed energy Columbia University density satisfies a solenoidal quasiconvexification formula. [email protected] (ARMA 197 N.3, 2010).

Pierluigi Cesana MS63 Mechanical Engineering Department Robust Locally Linear Analysis with Applications [email protected] to Image Denoising and Blind Inpainting

I will talk about the problems of denoising images cor- MS64 rupted by impulsive noise and blind inpainting (i.e., in- Title Not Available at Time of Publication painting when the deteriorated region is unknown). Our basic approach is to model the set of patches of pixels in an Abstract not available at time of publication. image as a union of low-dimensional subspaces, corrupted by sparse but perhaps large magnitude noise. For this pur- Greg Forest pose, we develop a robust and iterative method for single Department of Mathematics subspace modeling and extend it to an iterative algorithm University of North Carolina, Chapel Hill for modeling multiple subspaces. I will also cover the con- [email protected] vergence for the algorithm and demonstrate state of the art performance of our method for both imaging problems. MS64 Yi Wang A Ginzburg-Landau-type Model for Liquid Crys- School of Mathematics tals University of Minnesota [email protected] We will discuss some results regarding the Landau-De Gennes energy, often used to model liquid crystals, within the framework developed by Bethuel, Brezis and Helein Arthur Szlam for the Ginzburg-Landau energy of superconductivity. Our Department of Mathematics aim is to describe the singularities allowed by this model. NYU [email protected] Dmitry Golovaty The University of Akron 72 AN12 Abstracts

Department of Theoretical and Applied Mathematics Robert V. Kohn [email protected] Courant Institute of Mathematical Sciences New York University Alberto Montero [email protected] Departamento de Matematica Pontiﬁcia Universidad Cat´olica de Chile [email protected] MS65 Conical Singularities in Thin Elastic Sheets

MS64 When one slightly pushes a thin elastic sheet into a hol- Hypertractions and Hyperstresses in Second Gra- low cylinder, the resulting configuration of the sheet is a dient Continua so-called d-cone. D-cones have drawn some attention in the physics community in the last two decades or so, see A complete and coherent theory of second gradient con- e.g. Cerda et al., Nature 401, 46 (1999). In this talk, we tinua has not yet been fully developed. Hyperstresses and examine the scaling of the elastic energy with the sheet edge interactions are some of the key features which need thickness h in a rigorous setting and give a lower bound to be better understood. We shall review some of the main that is optimal in the leading order of h. problems and recent results in this field. Heiner Olbermann Maurizio Vianello Hausdorff Center for Mathematics & Institute for Appl. Mathematics Department Math. Politecnico di Milano University of Bonn [email protected] [email protected]

Stefan M¨uller MS65 University of Bonn Nucleation and Motion of Crystals in a Binary So- [email protected] lution

Abstract not available at time of publication. MS66 Searching for Exceptional Mechanisms with Fiber Dmitry Golovaty Products The University of Akron Department of Theoretical and Applied Mathematics Given a family of mechanisms and its parameterized sys- [email protected] tem of equations, techniques from Numerical Algebraic Ge- ometry can be used to find mechanisms with greater than expected motion. The parameters of such mechanisms can MS65 be found using the fiber product technique of Sommese Pseudo-spectral Simulations of Models for Regu- and Wampler to uncover irreducible sets that are obscured larized Dynamic Models in Nonlinear Elasticity within a larger algebraic set. Applications to particular families of mechanisms and adaptations for dealing with We discuss results of computations of two dimensional vis- large sets of defining equations will be discussed. coelastic models which arise as simplifications of models for phase transformations. These models in include dy- Daniel J. Bates namical scalar Aviles-Giga and Kohn-Muller models. We Colorado State University also discuss the resulting nature of energy minimizing solu- Department of Mathematics tions that are obtained from numerical simulations of these [email protected] models. Finally, we show that some similar results can be obtained in vectorial two dimensional models for marten- Eric Hanson sitic phase transformations. Department of Mathematics Benson K. Muite Colorado State University Department of Mathematics [email protected] University of Michigan [email protected] Jonathan Hauenstein Texas A&M University [email protected] MS65 Wrinkling of a Floating Elastic Film: Energy and Charles Wampler Pattern General Motors Research Laboratories, Enterprise Systems Lab In this talk, I discuss the floating film problem in which 30500 Mound Road, Warren, MI 48090-9055, USA a rectangle elastic film floats on the surface of a pool of [email protected] liquid and is compressed along two opposing sides. I first present the energy scaling law and then show how to use it to explain the cascade pattern at the edges of the two MS66 other sides of the film observed experimentally. Quasi Steady State Solution and Bifurcation for a Cell Cycle Model Hoai-Minh Nguyen School of Mathematics We consider a free boundary problem for a system of Unviersity of Minnestoa partial differential equations, which arises in a model of [email protected] tissue growth. For the steady state system, it depends AN12 Abstracts 73 on a positive parameter β, which describes the signals the continuous level with Uzawa and gradient type algo- from the microenvironment. Upon discretizing this model, rithms at the discrete level. The algorithms are based on we obtain a family of polynomial systems parameterized the existence of multilevel sequences of nested approxima- by β. We numerically find that there exists a radially- tion spaces that do not have to satisfy a discrete LBB sta- symmetric stationary solution with tumor free boundary bility condition. The main idea is to maintain an accurate r = R for any given positive number R. By homo- representation of the residuals at each step of the inexact topy tracking with respect to the parameter β,thereex- Uzawa algorithm at the continuous level. The residual rep- ist branches of symmetry-breaking stationary solutions. resentations at each step are approximated by projections. Moreover, we proposed a numerical algorithm based on Iteration on a fixed level corresponds to standard Uzawa or Crandall-Rabinowitz theorem to numerically verify the bi- Gradient method for solving symmetric saddle point sys- furcation points. By continuously changing µ usingaho- tems. Whenever a sufficient condition for the accuracy of motopy, we are able to compute nonradial symmetric solu- the representation for the main residual (of the first equations. We additionally discuss optimal control on β. tion) fails to be satisfied, the representation is projected on the next larger space. We emphasize on the gradient Wenrui Hao method which has the advantages of automatically select- Dept. of Applied and Comp. Mathematics and Statistics ing the relaxation parameter, lowering the number of iter- University of Notre Dame ations on each level, and improving on running time and [email protected] on global error reduction. Numerical results are presented for the Stokes system. Andrew Sommese, Bei Hu Dept. of Applied & Computational Mathematics & Constantin Bacuta Statistics University of Delaware University of Notre Dame Department of Mathematics [email protected], [email protected] [email protected]

Lu Shu MS66 University of Delaware Real Solutions to Polynomial Systems Arising in Mathematical Sciences Mechanism Design [email protected] Parameterized polynomial systems naturally arise in many applications, including mechanism design. This talk will MS67 explore using techniques from numerical algebraic geome- HDG Methods for the Vorticity-Velocity-Pressure try to attempt to compute parameters for which the poly- Formulation of the Stokes Problem nomial system has an extremal number of real solutions. An example from mechanism design will be used to demon- In this talk we discuss the hybridizable discontinuous strate the approach where there exists a set of parameters Galerkin (HDG) method for solving the vorticity-velocity- for which the corresponding system has no real solutions pressure formulation of the three-dimensional Stokes equa- and a set of parameters for which the corresponding system tions of incompressible fluid flow. The idea of the apriori has all solutions real. error analysis consists in estimating a projection of the errors that is tailored to the very structure of the numerical Jonathan Hauenstein,ZacharyGriffin traces of the method. We show that the approximated Texas A&M University vorticity and pressure, which are polynomials of degree k, [email protected], zacgriffi[email protected] converge with order k +1/2inL2-norm for any k 0. Moreover, the approximated velocity converges with order≥ k +1. MS66 Cell Decomposition of Real Surfaces Defined by Jintao Cui Mechanism Motions Institute for Mathematics and its Applications University of Minnesota This talk will describe the application of numerical alge- [email protected] braic geometry to decompose a real algebraic surface into a cell structure. A general technique for almost smooth Bernardo Cockburn algebraic surfaces will be reviewed and then applied to sev- School of Mathematics eral mechanisms. An interesting case is the study of one- University of Minnesota degree-of-freedom mechanisms with one free design param- [email protected] eter, such as a link length. The cell decomposition finds critical values of the parameter where the topology of the motion curve changes. MS67 Charles Wampler An Alternative Multigrid Method for Incompress- General Motors ible Flow R&D Center A multigrid method for H(div)-conforming DG discretiza- charles.w.wampler(at)gm.com tions of the Stokes problem is presented. It is based on an overlapping domain decomposition smoother. The MS67 smoother operates in thedivergence free subspace and thus does not require to be embedded into a block precondi- Multilevel Algorithms for Stokes Type Systems tioner for the saddle point problem. It is proven that the We analyze multilevel algorithms for symmetric saddle method is a uniform preconditioner.Its efficiency is docu- point systems. We combine inexact Uzawa algorithms at 74 AN12 Abstracts mented with numerical examples. MS68 The Peridynamic J-integral Youli Mao Texas A&M In fracture mechanics, the J-integral characterizes the en- Department of Mathematics ergy balance for a growing crack. In the nonlocal peri- [email protected] dynamic version of the J-integral, the rate of work done on the contour is replaced by a volume integral of work Guido Kanschat done on the bonds that connect the inside to the outside Department of Mathematics of the contour. The peridynamic J-integral converges to Texas A&M University the standard version in the limit of small horizon. Nu- [email protected] merical examples compare values in the peridynamic and standard theories. MS67 Stewart Silling Flow in Pebble Bed Geometries Sandia National Laboratories [email protected] Flow in complex geometries intermediate between free flows and porous media flows occurs in pebble bed reactors Florin Bobaru and in optimization of turbine placement in wind farms. University of Nebraska-Lincoln The Brinkman models have consistently shown that for [email protected] simplified settings accurate prediction of essential flow features depends on the impossible problem of meshing the Wenke Hu pores. In this paper we investigate new model to under- University of Nebraska - Lincoln stand the flow and its properties in these geometries. huwenke [email protected] Aziz Takhirov University of Pittsburgh MS68 [email protected] The Effect of Surface Tension on the Stress Field near a Curvilinear Crack MS68 In this talk, an approach to modeling fracture incorpo- The Importance of the Inner-problem in Compu- rating interfacial mechanics is applied to the example tational Models of Dynamic Brittle Fracture and of a curvilinear plane strain crack. The classical Neu- why Peridynamics Works mann boundary condition is augmented with curvature- I discuss the importance of capturing the “inner-problem’ dependent surface tension. It is shown that the considered in modeling dynamic fracture. The mechanism for crack model eliminates the integrable crack-tip stress and strain branching proposed by experimentalists suggests that when singularities of order 1/2 present in the classical linear frac- the S.I.F. becomes sufficiently high, voids grow into micro- ture mechanics solutions, and also leads to the sharp crack cracks ahead of the crack tip. I argue that computational opening that is consistent with empirical observations. models which are not able to represent the evolution of Anna Zemlyanova these microcracks, will not be able to correctly predict dy- Department of Mathematics namic brittle fracture. Peridynamics, a nonlocal extension Texas A&M University of classical mechanics, accounts implicitly for microcracks [email protected] by the way in which nonlocal damage evolves in this theory. Jay R. Walton Florin Bobaru Department of Mathematics University of Nebraska-Lincoln Texas A&M [email protected] [email protected]

MS68 MS70 Peridynamic Energy Balance and Damage Cocircuits of Linear Matroids

Our presentation reviews the recently proposed nonlocal We present a set covering problem (SCP) formulation of energy balance for peridynamic solids. Appropriate ex- the matroid cogirth problem. Addressing the matroid co- pressions for the first and second laws of thermodynamics girth problem can lead to significantly enhancing the de- are given, including a justification using the principles of sign process of sensor networks. The solution to the manon-equilibrium statistical mechanics. The first law expres- troid cogirth problem provides the degree of redundancy sion explicitly includes nonlocal interactions in a term that of the corresponding sensor network, and allows for the represents the stress power in peridynamic theory. The evaluation of the quality of the network. We provide com- second law enables restrictions to be placed on constitu- putational results to validate a branch-and-cut algorithm tive relations and is demonstrated to be a generalization of that addresses the SCP formulation. the Coleman-Noll procedure. An application to damage is presented. John David Arellano Computational and Applied Mathematics Richard B. Lehoucq Rice University Sandia National Laboratories [email protected] [email protected] AN12 Abstracts 75

MS70 gales, extending the Kolmogorov forward equation (Fokker Recent Advances in Optimization Methods for Im- Planck equation) to a non-Markovian setting. age Processing Amel Bentata Nonlinear image reconstruction based upon sparse repre- Universite Pierre & Marie Curie, France sentations of images has received widespread attention re- [email protected] cently with the advent of compressed sensing. This emerging theory indicates that, when feasible, judicious selection Rama Cont of the type of distortion induced by measurement systems CNRS (France) & Columbia University may dramatically improve our ability to perform recon- [email protected] struction. In this talk, we discuss some recent advances in large-scale optimization methods for solving these sparse signal recovery problems. MS71 Functional Ito Calculus and PDEs on Function RoummelF.Marcia Spaces University of California, Merced [email protected] The Functional Ito Calculus (Dupire 2009 ; Cont & Fournie 2010) is a calculus for non-anticipative functionals on the space of right-continuous paths, which extends the Ito cal- MS70 culus to path-dependent functionals of stochastic processes Approximate Murphy-Golub-Wathen Precondi- (Cont & Fournie 2011). This calculus, applied to function- tioning for KKT Matrices als of a martingale, leads to a new class of PDEs on the space of continuous functions, which share various prop- Karush-Kuhn-Tucker matrices arise from first order nec- erties with parabolic PDEs in finite dimensions : compar- essary conditions for nonlinear optimization. Murphy, ison principle, maximum principle, functional Feynman- Golub, and Wathen proposed a preconditioner having three Kac formula. In particular, we characterize Brownian mar- distinct eigenvalues, giving exact GMRES convergence in tingales as weak solutions of a functional heat equation. three iterations. This ideal preconditioner involves the inverse of a large submatrix, but when computed inexactly, Rama Cont GMRES will no longer converge in three steps. How will CNRS (France) & Columbia University this compromise slow convergence? Recent results on the [email protected] stability of GMRES give rigorous bounds on the number of iterations. Numerical computations verify these results for problems from optimization and fluid dynamics. MS71 Viscosity Solutions of Path Dependent PDEs Josef Sifuentes New York University We propose a notion of viscosity solutions for path depen- Courant Institute dent parabolic PDEs. This can also be viewed as viscosity [email protected] solutions of non-Markovian control problems, and thus extends the well known nonlinear Feynman-Kac formula to non-Markovian case. We shall prove the existence, unique- MS70 ness, stability, and comparison principle for the viscosity Recent Results on the Smallest Enclosing Ball solutions. The key ingredient of our approach is a func- Problem and the Smallest Intersecting Ball Prob- tional Itos calculus recently introduced by Dupire and fur- lem ther developed by Cont-Fournie. In the 19th century, J.J. Sylvester introduced the smallest Ibrahim Ekren enclosing circle problem: find a circle of smallest radius en- Department of Mathematics closing a given set of finite points on the plane. We extend University of Southern California the problem and find a ball with the smallest radius that [email protected] encloses a finite number of nonempty closed sets. Similarly, we study the smallest intersecting ball problem. Necessary Christian Keller and sufficient optimality conditions will be presented, as USC well, as numerical results. Applications exist in the field of [email protected] facility location.

Cristina Villalobos Nizar Touzi University of Texas-Pan American Ecole Polytechnique [email protected] [email protected] Jianfeng Zhang MS71 University of Southern California Markovian Projection of Stochastic Processes [email protected] We give conditions under which the flow of marginal distributions of a discontinuous semimartingale can be matched MS71 by a Markov process whose infinitesimal generator can be Control of Non-Markovian Stochastic Differential expressed in terms of its local characteristics, generaliz- Equations ing a result of Gyongy (1986) to the discontinuous case. Our construction preserves the martingale property and al- We study stochastic differential equations (SDEs) whose lows to derive a partial integro-differential equation for the drift and diffusion coefficients are path-dependent and con- one-dimensional distribution of discontinuous semimartin- trolled. We construct a value process on the canonical path 76 AN12 Abstracts space, considered simultaneously under a family of singu- ond order time accuracy. lar measures, rather than the usual family of processes indexed by the controls. This value process is characterized Samet Y. Kadioglu by a second order backward SDE, which can be seen as a Idaho National Laboratory non-Markovian analogue of the Hamilton-Jacobi-Bellman [email protected] partial differential equation. Dana Knoll Marcel Nutz Los Alamos National Laboratory Department of Mathematics [email protected] Columbia University [email protected] MS72 Operator Splitting Integration Factor Methods for MS72 Complex Biological Systems Adaptive Split-operator Methods for Modeling Flow and Transport Phenomena in Porous Medium For reaction-diffusion-advection equations, the stiffness Systems from the reaction and diffusion terms often requires very restricted time step size, while the nonlinear advection term Split-operator methods facilitate computation of large cou- may lead to a sharp gradient in localized spatial regions. pled problems. However, these methods introduce splitting It is challenging to design numerical methods that can ef- error, which is typically either ignored or controlled heuris- ficiently handle both difficulties. For reactiondiffusion sys- tically. In this work, we develop algorithms to control the tems with both stiff reaction and diffusion terms, implicit splitting error by dynamically adapting the temporal split- integration factor (IIF) method and its higher dimensional ting step based upon error estimators. The methods yield analog compact IIF (cIIF) serve as an efficient class of time- robust and efficient solutions with error control for non- stepping methods, and their second order version is linearly linear reaction problems and can be extended to Navier- unconditionally stable. Here we use splitting methods to Stokes and multiphase problems. These algorithms have incorporate different numerical methods to handle differ- widespread applicability in environmental modeling. ent terms of the equations. In particular, we apply the IIF-cIIF method to the stiff reaction and diffusion terms Sarah Gasda and the WENO method to the advection term in two dif- Center for Integrated Petroleum Research, Uni Research ferent splitting sequences. Calculation of local truncation [email protected] error and direct numerical simulations for both splitting approaches show the second order accuracy of the splitting Matthew Farthing method, and linear stability analysis and direct compari- US Army Engineer Research and Development Centerq son with other approaches reveals excellent efficiency and [email protected] stability properties. Applications of the splitting approach to several biological systems demonstrate that the overall Christopher Kees method is accurate and efficient. US Army Engineer Research and Development Center [email protected] Qing Nie University of California at Irvine Cass Miller [email protected] Environmental Sciences and Engineering Department University of North Carolina MS72 casey [email protected] Reduced Description of Reactive Flows with Tab- ulation of Chemistry MS72 Reduced description with chemistry tabulation can effec- An IMEX Method for the Euler Equations That tively reduce the simulation time of reactive flows by solv- Posses Strong Non-Linear Heat Conduction and ing the evolution equations only for represented species. Stiff Source Terms (Radiation Hydrodynamics) With operator splitting, chemical reactions are separated We present a truly second order time accurate self- into a reaction fractional step. The effect of chemical re- consistent IMEX (IMplicit/EXplicit) method for solving actions on the reduced composition is addressed through the Euler equations that posses strong nonlinear heat con- species reconstruction and the evaluation of reaction map- duction and very stiff source terms (Radiation hydrody- ping in the full composition space. ISAT is employed to namics). IMEX methodology is suggested when deal- speed chemistry calculation by tabulating information of ing with physical systems that consist of multiple physics the reduced system. or fluid dynamics problems that exhibit multiple time Zhuyin Ren scales such as advection-diffusion, reaction-diffusion, or University of Connecticut advection-diffusion-reaction. It can be challenging to pro- Department of Mechanical Engineering vide fully converged and second order time accurate nu- [email protected] merical results to these kinds of coupled systems. Order reductions in time accuracy are often reported due to inconsistent operators splitting. Our JFNK (Jacobian-Free MS73 Newton Krylov)-based IMEX method splits the operators Multiscale Engineering for Heterogeneous Media in a self-consistent way in which all-non-linearities are con- and Structures verged and second order time accuracy of different physical terms is preserved. We have applied this strategy to a Ra- In this talk, we present multiscale materials design success diation Hydrodynamics model (at diffusion approximation stories and discuss some technical barriers to using multi- limit) that posses multi-scale terms and demonstrated sec- AN12 Abstracts 77 scale simulation for rapid materials design and qualifica- MS73 tion. A paradigm for computational multiscale modeling Materials Genome: An Opportunity for Applied and simulation will be discussed which, when integrated Mathematics and Computational Science into the structural design loop, will significantly expand the design space and enable increased efficiency, performance, The recent Materials Genome Initiative seeks to accelerate and affordability by delivering materials and structures op- the process between materials discovery and their indus- timized across all engineered scales for their mission. trial application. In this talk we highlight problems where computational science and mathematics can play a role in Timothy D. Breitzman materials innovation and development. Air Force Research Laboratory [email protected] Robert P. Lipton Department of Mathematics Louisiana State University MS73 [email protected] Development of Computational Algorithms for Ma- terials Simulation and Design MS74 Supported first by NSF-ITR then by the NSF-IUCRC cen- Staggered Discontinuous Galerkin Method for ter for computational materials design, we have worked Wave Transmission Between Dielectric and Meta- on a number of mathematical and algorithmic issues that materials are related to efficient and multiscale simulation of various physical processes such as nucleation and coarsening Some electromagnetic materials exhibit, in a given fre- during phase transformations. In this talk, we will dis- quency range, effective dielectric permittivity and/or mag- cuss some of our recent works, including the development netic permeability which are negative. In the literature, of algorithms for predicting critical nuclei morphology in they are called negative index materials, left-handed ma- anisotropic elastic solids, the study of coarsening kinetics terials or meta-materials. We propose a staggered discon- of a mixture with disparate mobility and the uncertainty tinuous Galerkin method to solve a wave transmission be- quantification and statistical assessment of database used tween a classical dielectric material and a meta-material. for material property optimization. Convergence of the numerical method is proven, with the help of explicit inf-sup operators, and numerical examples Qiang Du are provided to show the efficiency of the method. Penn State University Department of Mathematics Eric Chung [email protected] The Chinese University of Hong Kong Department of Mathematics Jingyan Zhang [email protected] Department of Mathematics, Penn State University j [email protected] MS74 Lei Zhang HDG Methods for Wave Propogation Department of Math We describe the devising and analysis of the so-called hy- University of California, Irvine, bridizable discontinuous Galerkin method for the acoustic [email protected] equation in the time-continuous domain. The method provides optimal approximations for the velocity, the gradi- Long-qing Chen ent and the original scalar unknown. A superconvergence Department of Materials Science and Engineering property of the velocity allows us to obtain a new approxi- Pennsylvania State University mation to the original scalar unknown converging with one [email protected] additional order.

Zikui Liu Bernardo Cockburn Department of Materials Science and Engineering School of Mathematics Penn State University University of Minnesota [email protected] [email protected]

MS73 MS74 TheRoleofSIAMAsAnAdvocatefortheMath- Eulerian Gaussian-beams in the Viscosity Sense ematical Science Community for Multidimensional Schrodinger Equation in the Semi-classical Regime This presentation will describe the efforts of SIAM to ad- vocate for the interests of the mathematical sciences com- We design an Eulerian Gaussian-beam method for the munity with policy makers and funding agencies, including Schrodinger equation in the semi-classical regime, where the activities of the SIAM Committee for Science Policy. the Planck constant is small. The method is constructed The presentation will also detail ways in which the SIAM from a leading-order WKBJ ansatz for the quantum wave membership can participate in this effort. function, where the phase and the amplitude satisfy an eikonal and a transport equation respectively. The trans- Reinhard Laubenbacher port equation is weakly coupled to the eikonal equation in Virginia Bioinformatics the sense that one must first solve the eikonal equation to Institute provide related coefficients for the transport equation. We [email protected] use a high-order numerical scheme to evolve the set of equations to get a highly efficient and accurate approximation 78 AN12 Abstracts of the Schrodinger equation in multidimensions. University of Virginia [email protected] Susana Serna Department of Mathematics Daniel Toundykov Universitat Autonoma de Barcelona University of Nebraska-Lincoln [email protected] [email protected]

MS74 MS75 Is a Curved Flight Path in SAR Better than a Asymptotic Behavior in a 2-allele Genetic Model Straight One? with Population Control

We study the simplified model of Synthetic Aperture Radar The standard model for the evolution of the densities of imaging: recovery of singularities of a function in the plane the three genotypes aa, aA,andAA is ∂ρaa/∂t ∆ρaa = by knowing integrals along circles centered at a given curve 2 − r[2ρaa + ρaA] / 2[ρaa + ρaA + ρAA] τaaρaa ∂ρaA/∂t (the flight path). If the curve is a straight line, the symme- { }− − ∆ρaA =2r[2ρaa +ρaA][2ρAA +ρaA]/ 2[ρaa +ρaA +ρAA] try about it cannot be resolved. It has been suggested that { 2 }− τaaρaa ∂ρAA/∂t ∆ρAA = r[2ρAA + ρaA] / 2[ρaa + ρaA + a curved flight path might be better to break the symmetry. − { ρAA] τAAρaa, We show that in some sense (local measurements), a curved }− path is not better but a closed (and of course, curved) path where the parameters are constants. It has recently been offers some advantages. Our approach is based on wave shown by Souplet and Winkler that in the heterozygote intermediate case τaa τaA τAA,τaa >τAA the gene propagation methods and provides constructive algorithms ≥ ≥ fraction u := [2ρaa + ρaA]/ 2[ρaa + ρaA + ρAA] converges for reconstruction in some cases. This is a joint work with { } Gunther Uhlmann. to 0. However, the proof in the biologically interesting case depends on the fact that ρAA converges to infinity, which, Plamen Stefanov as the authors pointed out, makes the model unrealistic. Purdue University We produce a large class models of the above form with the [email protected] birth rate r replaced by a density-dependent function and no terms dropped which have the property that when the population lives in a bounded domain with impenetrable MS75 boundary and its initial conditions satisfy some reasonable Investigating through Optimal Control of Parabolic conditions, then as the time approaches infinity, the popu- PDEs: Does Movement Toward a Better Resource lation densities converge uniformly to those of a constant Benefit a Population? equilibrium in which the allele a is absent.

We investigate optimal control of the convective coefficient Hans Weinberger in parabolic parabolic partial differential equation, mod- School of Mathematics eling a population with nonlinear growth. This work is University of Minnesota motivated by the question: Does movement toward a bet- [email protected] ter resource environment benefit a population? Results on existence, uniqueness, and characterization of the optimal control will be presented along with numerical illustrations. MS75 This work is in collaboration with Tuoc Phan and Heather Quasi-Stationary Limit and Landau-Lifshitz Equa- Finotti. tions Without Exchange Energy Suzanne M. Lenhart In this paper we study a dynamic model of Landau-Lifshitz University of Tennessee equations in ferromagnetism that do not include exchange Department of Mathematics energy. The weak solution to such an equation is obtained [email protected] as the quasi-stationary limit of a simple coupled Maxwell system when dielectric permittivity approaches zero. We present a new direct proof of this quasi-stationary limit MS75 result and also establish a finite-time local L2-stability re- Stabilization of Wave Equations with Wentzell sult and thus the uniqueness for the weak solutions with Boundary Conditions bounded initial data. I will discuss uniform feedback stabilization of wave equa- Baisheng Yan,WeiDeng tions subject to second-order boundary conditions. Both Department of Mathematics dynamic (Wentzell) and static (higher derivatives in space Michigan State University only) boundary conditions will be considered. It will be [email protected], [email protected] shown how a combination of a partially localized boundary feedback and a partially localized collar feedback leads to uniform energy decay rates. The analysis combines MS76 weighted energy methods for observability of Neumann- Quadratic Sum of Squares Relaxations type wave problems and differential-geometric techniques for proving stability of waves on compact manifolds. We consider the question of minimizing a quadratic objective function over a real variety described by quadratic Marcelo Cavalcanti equations. This problem is NP-hard in general. We give Universidade Estadual de Maringa necessary and sufficient conditions in terms of Lagrange Brazil multipliers under which the first sum of squares relaxation [email protected] is exact, assuming attainment of both the SOS relaxation and the original objective. We apply the theorem when the Irena M. Lasiecka objective is squared Euclidean distance to a point, where AN12 Abstracts 79 we see that these methods can effectively tackle image re- MS77 construction problems in computer vision which motivated A Continuous Multilevel Solver for the Vertex Sep- this work. arator Problem Chris Aholt Given an undirected graph G, the vertex separator prob- University of Washington lem is to find the smallest number of nodes whose removal [email protected] disconnects the graph into disjoint subsets A and B, where A and B are subject to size constraints. We will show how this problem can be formulated as a continuous quadratic MS76 program. We use the QP as a local processor in a multi- Positive Gorenstein Ideals level scheme for solving large scale instances of the problem. Computational results will be presented. I will explain how positive Gorenstein ideals arise naturally from the dual cone to the cone of sums of squares. The James T. Hungerford, William W. Hager structure of these ideals provides a new tool for addressing University of Florida questions of nonnegative polynomials and sums of squares. Department of Mathematics I will present applications in algebraic geometry, analysis freerad@ufl.edu, hager@ufl.edu and optimization. In particular there is a simple proof of Hilbert’s result on representation of ternary forms as sums Ilya Safro of squares of rational functions. Argonne National Laboratory Greg Blekherman [email protected] University of California, San Diego [email protected] MS77 An Exact Algorithm for Graph Partitioning based MS76 on Quadratic Programming Algebraic Structure in Optimization Abstract not available at time of publication.

Solving polynomial optimization problems is known to be a Dzung Phan hard task in general. In order to turn the recently emerged IBM relaxation paradigms into efficient tools for these optimiza- [email protected] tion questions it is necessary to exploit further structure whenever presented in the problem structure. In this talk we will focus on the situation of optimization problems that MS77 are given by symmetric polynomials in order to highlight Exact Combinatorial Branch-and-bound for Graph several approaches to take advantage of symmetry. The Bisection techniques presented in the talk will also give a better understanding of the cones of symmetric sums of squares and We present a novel exact algorithm for the minimum graph symmetric non negative forms and the symmetric mean in- bisection problem, whose goal is to partition a graph equalities associated to these. In particular, we will show into two equally-sized cells while minimizing the number that in degree four, symmetric mean inequalities are char- of edges between them. Our algorithm is based on the acterized by sum of squares decomposition. branch-and-bound framework and, unlike most previous approaches, it is fully combinatorial. We present stronger Cordian B. Riener lower bounds, improved branching rules, and a new de- University of Konstanz, Germany composition technique that contracts entire regions of the [email protected] graph without losing optimality guarantees. In practice, our algorithm works particularly well on instances with rel- MS76 atively small minimum bisections, solving large real-world graphs (with tens of thousands to millions of vertices) to Regularization Methods for SDP Relaxations in optimality. Large Scale Polynomial Optimization Daniel Delling, Andrew Goldberg In this talk, we discuss how to solve semidefinite pro- Microsoft Research Silicon Valley gramming relaxations for large scale polynomial optimiza- [email protected], [email protected] tion. When interior-point methods are used, only small or moderately large problems could be solved. Here we use regularization methods on semidefinite programming with Ilya Razenshteyn block structures, and significant bigger problems could be Lomonosov Moscow State University solved on a regular computer, which is almost impossible [email protected] by interior point methods. The performance is tested on various numerical examples. Some numerical issues are Renato F. Werneck also discussed. Microsoft Corporation [email protected] Li Wang University of California, San DIego [email protected] MS77 Multi-Level Edge Separator Using a Hybrid Jiawang Nie Combinatorial-Quadratic Programming Approach University of California, San Diego [email protected] The graph partitioning problem arises in a variety of scientific and engineering domains such as VLSI design, com- 80 AN12 Abstracts puter networking, parallel computing, and sparse direct the challenges in moving from current representations and methods. In this talk, we discuss the edge separator graph datafitting techniques towards this goal and demonstrates partitioning problem and present an algorithm which com- initial results and analyses. bines aspects of multi-level combinatorial methods with a quadratic programming formulation. We discuss a novel Elaine Cohen strategies for both graph coarsening and refinement with University of Utah the goal of producing high quality cut sets. [email protected]

Nuri Yeralan University of Florida MS78 [email protected] Applications of Isogeometric Analysis at Boeing

Timothy A. Davis Isogeometric analysis at Boeing has a surprisingly long his- University of Florida tory. Univariate applications using B-splines as finite ele- Computer and Information Science and Engineering ments have existed since the late 1980s, with numerous [email protected] applications. The essence of isogeometric analysis – using a fixed parameter space to formulate a family of problems – was employed in an aeroelastic tool in the late 1990s. MS78 That application entailed solving boundary integral equa- The Geometry of Interpolation Error Estimates for tions for a family of surfaces, requiring a form of bivariate Isogeometric Analysis isogeometric analysis. We will explore those and future Boeing applications of this exciting technology. Barycentric coordinates provide a basis for linear finite elements, and underlie the definition of higher-order ba- Michael A. Epton sis functions for shape and isogeometric analysis, i.e. the Boeing Bézier triangle in computer aided-design, together with in- [email protected] terpolation and shading techniques in computer graphics and optimal convergence rates in isogeometric analysis. Thomas A. Grandine The versatility of this construction has led to barycen- Applied Mathematics tric coordinates for more general shapes; the resulting The Boeing Company functions are called generalized barycentric coordinates [email protected] (GBCs). GBCs while unique over triangles, have multiple definitions for convex polygons with four or more sides, namely Harmonic (H), Wachspress(W), Sibson (S) MS78 and Mean Value (MV) coordinates. Interpolation prop- Solid T-spline Construction from Boundary Repre- erties of H, W, S and MV have a complex dependence sentations on polygonal geometry. W exhibits the subtleties of ge- ometrical dependence: if the polygon contains interior an- We present a novel method to construct solid rational T- gles near 180 degrees, gradients of the coordinates become splines for complex genus-zero geometry from boundaries. very large. S and MV avoid this problem. In this talk we We first build a parametric mapping between the triangu- prove that given certain conditions on the geometry of the lation and a unit cube. After that we adaptively subdivide polygon, each of H, W, S and MV can obtain optimal in- the cube using an octree subdivision, pillow the subdivi- terpolation convergence estimates, and hence suitable for sion result one layer on the boundary, and use templates to isogeometric analysis. handle extraordinary nodes. The obtained solid T-spline is C2-continuous except for the local region around each Chandrajit Bajaj extraordinary node. Computer Science, ICES, CVC The University of Texas - Austin Yongjie Zhang [email protected] Department of Mechanical Engineering Carnegie Mellon University [email protected] Alex Rand The University of Texas - Austin [email protected] MS79 Posterior Rates of Contraction for Sparse Bayesian Andrew Gillette Models University of California, San Diego Department of Mathematics Sparse inverse covariance matrix modeling is an important [email protected] tool for learning relationships among different variables in a Gaussian graph. Most existing algorithms are based on 1 regularization, with the regularization parameters tuned MS78 via cross-validation. In this talk, a Bayesian formulation of Analysis Aware Representations, Parameteriza- the problem is proposed, where the regularization parame- tions, and Models ters are inferred adaptively and cross-validation is avoided. Variational Bayes (VB) is used for the model inference. Re- Isogeometric Analysis (IA) has been proposed as a method- sults on simulated and real datasets validate the proposed ology for bridging the gap between Computer Aided De- approach. In addition, a graph extension algorithm is pro- sign (CAD) and Finite Element Analysis (FEA). In order posed to include a new variable in an existing graph, which to support design and full 3D IA, new ab initio design can be used when separate testing data are available. methods must create suitable representations and approximation techniques must include parameterization method- Larry Carin ologies for volumes. This presentation discusses some of Electrical & Computer Engineering AN12 Abstracts 81

Duke University alternating optimization approach and propose solving the [email protected] subproblem using a majorization-minimization approach that yields multiplicative updates. In fact, the method we propose is a generalization of the Lee-Seung multiplica- MS79 tive updates but has the advantage of being faster and Clustering and Embedding of High-Dimensional also having provable convergence even for solutions on the Multi-Manifold Data using Sparse Representation boundary (i.e., with zeros in the factorization). Moreover, we show how to prevent the algorithm from converging to In many problems across different areas of science and en- non-stationary points (i.e., fixing the problem of getting gineering, we are dealing with massive collections of high- stuck at undesirable zero values). We will show several dimensional data. Having thousands and millions of di- examples to demonstrate the utility of the approach. mensions, the data often lie in or close to low-dimensional structures, called manifolds. Separating the data into the Tamara G. Kolda underlying low-dimensional models and finding compact Sandia National Laboratories representations for them is one of the most fundamental [email protected] problems in the high-dimensional data analysis. We address the problem of clustering and embedding of the data Eric Chi on multiple manifolds using sparse representation tech- Human Genetics Department niques. We use the collection of the data points as a self- UCLA expressive dictionary in which each point can be efficiently [email protected] represented as a sparse combination of a few other points from the same manifold with appropriate weights that encode locality information. We propose a convex optimiza- MS79 tion program whose solution is used in a spectral graph the- Performance Limits of Non-local Means ory framework to infer the clustering and embedding of the data. When the manifolds correspond to low-dimensional In this talk I describe a novel theoretical characterization subspaces, we show that under appropriate conditions on of the performance of non-local means (NLM) for noise re- the principal angles between the subspaces and the distri- moval. NLM has proven effective in a variety of empirical bution of the data, the solution of the proposed convex studies, but little is understood fundamentally about how program recovers the desired solution. We demonstrate it performs relative to classical methods based on wavelets the effectiveness of the proposed algorithm through exper- or how various parameters (e.g., patch size) should be cho- iments on several real-world problems. sen. For cartoon images and images which may contain thin features and regular textures, the error decay rates Ehsan Elhamifar of NLM are derived and compared with those of linear fil- Department of Electrical and Computer Engineering tering, oracle estimators, variable-bandwidth kernel meth- Johns Hopkins University ods, Yaroslavskys filter and wavelet thresholding estima- [email protected] tors. The trade-off between global and local search for matching patches is examined, and the bias reduction asso- Rene Vidal ciated with the local polynomial regression version of NLM Department of Biomedical Engineering is analyzed. The theoretical results are validated via simu- Johns Hopkins University lations for 2D images corrupted by additive white Gaussian [email protected] noise. This is joint work with Ery Arias-Castro and Joseph Salmon. MS79 Ery Arias-Castro Poisson Tensor Factorization for Sparse Count UCSD Data [email protected]

In data mining and analysis, we often encounter data that Joseph Salmon is indexed by three or more indices. Tensor factorizations Duke University can be used for such ”multidimensional” data and have [email protected] already found application in a variety of fields, including high-dimensional function approximations, signal process- Rebecca Willett ing, chemometrics, multi-attribute graph analysis, image Electrical and Computer Engineering recognition, and more. We consider the problem of ten- Duke University sor factorizations for sparse count data. For example, we [email protected] might have a collection of email messages and arrange them by sender, receiver, and date; the data is sparse because not all potential senders and receivers communicate and MS80 even those that do communicate do not necessarily do so Local Pointwise a posteriori Gradient Error every day. Typically, we would fit a tensor factorization Bounds for the Stokes Equations model to data by minimizing the least squares difference between the data and the tensor factorization model. Sta- We consider the standard Taylor-Hood finite element tistically speaking, we have assumed that the random vari- method for the stationary Stokes system on polyhedral ation is best described by a Gaussian distribution. We domains. We prove local a posteriori error estimates for propose, however, that the random variation may be bet- the maximum error in the gradient of the velocity field. ter described via a Poisson distribution because the count Because the gradient of the velocity field blows up near observations (especially the zeros) are more naturally ex- re-entrant corners and edges, such local error control is plained. Under this Poisson assumption, we can fit a model necessary when pointwise control of the gradient error is to observed data using the negative log-likelihood score, desirable. Computational examples confirm the utility of also known as Kullback-Leibler divergence. We discuss an 82 AN12 Abstracts our estimates in adaptive codes. Bernardo Cockburn School of Mathematics Alan Demlow University of Minnesota University of Kentucky [email protected] Department of Mathematics [email protected] MS81 Stig Larsson Math modeling as the core of Applied Math under- Department of Mathematical Sciences Chalmers graduate Curricula University of Technology and University of Gothenburg Abstract not available at time of publication. [email protected] Jeffrey Humpherys Brigham Young University MS80 jeff[email protected] Mixed Finite Elements for the Coupling of Fluid Flow with Porous Media Flow MS82 In this talk we a introduce mixed finite element method for Manycore-portable Multidimensional Arrays for the coupling of fluid flow with porous media flow. Flows Finite Element Computations are governed by the Stokes and Darcy equations, respectively, and the corresponding transmission conditions are Performance-portability to multicore-CPU and manycore- given by mass conservation, balance of normal forces, and accelerator (e.g., GPGPU) devices is a significant chal- the Beavers-Joseph-Saffman law. We consider mixed for- lenge due to device-specific programming models and per- mulations in both the Stokes domain and the Darcy re- formance characteristics. The Kokkos multidimensional gion, which yields the introduction of the traces of the array library uses C++ template meta-programming to porous media pressure and the fluid velocity as suitable provide performance-portable multidimensional array data Lagrange multipliers. Then, considering generic finite ele- structures and data parallel algorithm dispatch capabil- ment spaces with some technical conditions, we apply the ities (e.g., parallel-for and parallel-reduce). These data Babuˇska-Brezzi theory together with a classical result on structures and dispatch capabilities are demonstrated by projection methods for Fredholm operators of index zero compiling and executing the same finite element mini- to show stability, convergence, and a priori error estimates application codes on NUMA multicore-CPU (Intel and for the associated Galerkin scheme. Finally, we generalize AMD) and GPGPU manycore-accelerator (NVIDIA) de- the previous results and introduce a mixed finite element vices. method for the coupling of fluid flow with nonlinear porous H. Carter Edwards, Daniel Sunderland media flow. Sandia National Laboratories Gabriel N. Gatica [email protected], [email protected] DIM and CI2MA Universidad de Concepcion MS82 [email protected] Asynchronous, Performance-portable Krylov Methods on Accelerators Ricardo Oyarzua Universidad de Concepcion In this presentation we discuss our efforts to use the [email protected] Trilinos/Kokkos multi-dimensional array package to write portable generic code implementing the GMRES iterative Francisco J. Sayas method. Performance results from several distinct plat- Dept. Mathematical Sciences forms are presented. University of Delaware [email protected] Kurtis L. Nusbaum UIUC [email protected] MS80 A Space-Time Hybridizable Discontinuous Galerkin (HDG) Method for Incompressible Flows MS82 on Deforming Domains Auto-Tuned Hybrid Asynchronous Krylov Itera- tive Eigensolvers on Petascale Supercomputers We present the first space-time HDG finite element method for the incompressible Navier-Stokes and Oseen equations. Asynchronous hybrid parallel Krylov co-methods, such Major advantages of a space-time formulation are its ex- as the Multiple Explicitly Restart Arnoldi Method cellent capabilities of dealing with moving and deforming (MERAM), are well adapted for Petascale supercomput- domains and grids and its ability to achieve higher-order ing. Each ERAM may exploit all parallelism of a large accurate approximations in both time and space by simply number of processors and asynchronously exchange Ritz increasing the order of polynomial approximation in the elements with the other concurrent methods. Each ERAM space-time elements. may have a dedicated restart strategy to accelerate the convergence to different eigensubspaces. We study the or- Sander Rhebergen chestration of different strategies with respect to several University of Minnesota distributions along the ERAM methods. We propose to School of Mathematics overview these strategies and to evaluate experimentally [email protected] their efficiencies on a Petascale computer. As a conclusion, we propose an algorithm to auto-tune these strategies and AN12 Abstracts 83 we discuss the first results. MS83 The Implications of Different Probability Density Jerome Dubois Functions for Disease Stages from Sir Epidemiolog- CEA-DEN ical Models on the Effectiveness of Public Health [email protected] Interventions Serge G. Petiton Quantifying the uncertainty attributed to the assumed CNRS/LIFL and INRIA probability density functions for disease stages from SIR serge.petiton@lifl.fr epidemiological models is crucial. Hence, the lack of it might leads to i) limited statements with respect to the Christophe Calvin net effectiveness of intervention strategies or ii) proposing CEA-Saclay/DEN/DANS/DM2S/SERMA/LLPR the implementation of inadequate or non-optimal interven- [email protected] tion strategies and thus, these might increase the risks of high mortality and morbidity and misguide public health policy and decision makers. We illustrated that these as- France Boillod sumptions quantitatively matter greatly. CNRS/LIFL [email protected] Emmanuel J. Morales-Butler School of Human Evolution and Social Change Arizona State University MS82 [email protected] Retrofitting a Production Sparse Linear Algebra Library for Accelerators MS83 The Trilinos Epetra package provides most of the cur- Modeling the Effect of Hospital Acquired Infec- rent production quality matrix and vector services for tions in the Outcomes of Neurosurgical Patients other Trilinos packages. Although new packages have emerged (Tpetra and Kokkos) to fundamentally address Abstract not available at time of publication. the next generation of computing needs, especially support for emerging architectures, there is merit in providing Miriam Nuno some support for new architectures in Epetra. In this talk Department of Neurosurgery we discuss efforts to retrofit Epetra with support for accel- Cedars Sinai Medical Center erators, highlighting design constraints and benefits of the [email protected] effort.

Benjamin Seefeldt MS84 St John’s University Title Not Available at Time of Publication [email protected] Abstract not available at time of publication. MS83 Eray Aydil Spatio-temporal Dynamics of 2009 A/H1N1 In- Chemical Engineering and Materials Science fluenza University of Minnesota [email protected] We provide a quantitative description of the age-specific and regional 2009 A/H1N1 pandemic incidence patterns in Mexico and Peru. We analyze the geographic spread of MS84 the pandemic waves and their association with the winter Atomic Properties Database Development and school closing periods, demographic factors, and absolute Mining for Materials Genome Applications humidity. Our results indicate substantial regional variation in pandemic pattern and highlight the importance of Exploiting correlations between materials macroscopic school cycles on the transmission dynamics of pandemic properties and atomic properties of their constituents is influenza. at the heart of materials informatics whose main goal is to significantly reduce the time to unravel materials with de- Gerardo Chowell sirable properties. We have initiated a series of studies to Mathematical Modeling and Analysis explore such correlations by using data mining techniques. Los Alamos National Laboratory This talk will summarize these studies and address specif- [email protected] ically the questions: How to build the needed databases and how to use them effectively? MS83 Da Gao Game Theory and Vaccination with a Network Epi- Department of Computer Science and Engineering demiology Approach University of Minnesota [email protected] Abstract not available at time of publication. Yousef Saad Ariel Cintron-Arias Department of Computer Science Department of Mathematics and Statistics University of Minnesota East Tennessee State University [email protected] [email protected] James R. Chelikowsky 84 AN12 Abstracts

Institute for Computational Engineering and Sciences crete points in the plane. This collection of points forms University of Texas at Austin a two-dimensional spatial Poisson process, which yields a [email protected] null model for random fragment coverage. After giving an overview of this model, I will show how the successive jumps of the depth coverage function can be encoded as MS84 a random tree. This discrete, probabilistic theory can po- Renewable Polymers for a Sustainable Future tentially be of use in a wide variety of sequence census methods. Two specific applications will be presented: an Polymers are essential to myriad technologies we encounter algorithm for finding protein binding sites using ChIP-Seq every day. Over the past century an immense and highly data and a statistical test to address fragment bias in RNA- integrated knowledge base has evolved that guides the ma- Seq data. nipulation of petroleum feedstocks, the design of polymerization catalysts, and the resulting structure - property Valerie Hower relationships in a small set of relatively simple homopoly- University of California, Berkeley mers. Yet the production and disposal of these prod- [email protected] ucts presents inescapable environmental challenges that are costly to correct at a minimum and unsustainable in the long term. In response to a global mandate for sustain- MS85 ability, the development of alternatives based on renew- Some New Combinatorial Problems from RNA able feedstocks such as carbohydrates, plant oils, and ter- penes is of central importance. Realizing the tremendous In the Fall of 2011, I taught a graduate-level topics course market potential for bio-based materials hinges on creating on Combinatorial Computational Biology of RNA. There new fundamental chemistry-based foundations upon which were eleven grad students in the class, and they had diverse an industry can be established. Many known sustainable backgrounds and research areas. Our goal was to learn homopolymers have inadequate property profiles to meet some of the mathematical results and techniques from the the application requirements of modern polymeric mate- past decade and to pinpoint future research problems. In rials. Researchers in the Center for Sustainable Polymers those regards, it was quite successful. I will summarize (CSP) at the University of Minnesota (UMN) are estab- some of the main themes of the area as well as outline some lishing a comprehensive knowledge base that enables the new ideas and directions that a few graduate students from efficient and economical conversion of natural and abun- the class are currently pursuing in their research. dant molecules into tomorrows advanced polymeric materials. Members of the CSP blend efforts in polymer design, Matthew Macauley monomer synthesis, polymerization catalysis, architecture Mathematical Sciences and morphology control, and polymer property optimiza- Clemson University tion to establish the basic scientific tenants for innovative [email protected] renewable resource polymer technologies. A key and unifying concept in the CSP is that multiple renewable com- MS85 ponents, properly integrated into a single material, will yield tunable properties not achievable with either simple Non-parametric Species Delimitation Based on homopolymers or blends, which have dominated the renew- Branching Rates able polymer industry to date. Many probabilistic tests have been developed to delimit William B. Tolman species based on the coalescent model. These computa- Department of Chemistry tional efforts rely primarily on parametric models that try University of Minnesota to account for known variance found in genetic processes. [email protected] Unfortunately, this variance is difficult to model precisely. Using non-parametric tests, we develop a method to de- lineate species by estimating the time species change from MS84 growth (e.g., Yule models) to a coalescence process with- Mesoscale Description of Defected Materials out constraining the processes to a particular model. Using simulated gene trees from a known species tree, we com- A mesoscale description is necessary for a quantitative de- pare our non-parametric method to established parametric scription of defected materials, including microstructure methods. evolution. Not only they naturally incorporate defect solutions, but they also permit numerical computation on the Edward Roualdes diffusive time scales that are appropriate for overdamped Statistics defect motion. We describe the general methods involved University of Kentucky in the derivation and validation of such models, and apply [email protected] them to grain boundary motion and pinning. Jorge Vinals MS85 School of Physics and Astronomy Reverse Engineering of Regulatory Networks Using University of Minnesota Algebraic Geometry [email protected] Discrete models have been used successfully in modeling biological processes such as gene regulatory networks. When MS85 certain regulation mechanisms are unknown it is impor- Coverage Statistics for Sequence Census Methods tant to be able to identify the best model with the available data. In this context, reverse engineering of finite I will illustrate how to view fragments produced in a dynamical systems from partial information is an impor- high-throughput sequencing experiment as a set of dis- tant problem. In this talk we will present a framework and algorithm to reverse engineer the possible wiring diagrams AN12 Abstracts 85 of a finite dynamical system from data. The algorithm MS86 consists on using an ideal of polynomials to encode all pos- High Frequency Wave Propagation with Geomet- sible wiring diagrams, and choose those that are minimal rical Optics and Beyond using the primary decomposition. We will also show that these results can be applied to reverse engineer continuous We propose a new method by combining the geometri- dynamical systems. cal optics and Huygens-Kirchhoff identities to numerically solve the Helmholtz equation with single point-source con- Alan Veliz Cuba dition in high frequency regime. Data compression with Mathematics Chebyshev expansions and random sampling based pseu- University of Nebraska- Lincoln doskeleton approximations are applied to make the wave- [email protected] field reconstruction efficient. The new approach is efficient and has no pollution effects. And it can reconstruct wave- fields for a set of source points and a band of high frequen- MS86 cies. Acceleration of a Multiple Scattering High Fre- quency Iterative Method Songting Luo, Jianliang Qian Department of Mathematics A recent high frequency analysis of the Neumann series Michigan State University in the context of multiple scattering configurations shows [email protected], [email protected] that the rate of convergence converges to 1 when the distance separating scatterers converge to 0. This impairs the Krylov-subspace based iterative method that was designed MS86 especially to deal with this kind of problems. We propose Efficient Computation of the Semi-Classical Limit a preconditioner based on the Kirchhoff approximation to of the Schroedinger Equation improve this iterative solver. An efficient method for simulating the Schroedinger equa- Yassine Boubendir tion near the semiclassical limit is presented. It uses a Department of Mathematical Sciences transformation based on Gaussian wave packets and yields [email protected] a Schroedinger type equation ammenable to computation in the semi-classical limit. The number of grid points needed is small enough that computations in dimensions MS86 of up to 4 or 5 are feasible without the use of any ba- A Fast Iterative Method for Solving the Eikonal sis thinning procedures. This is joint work with Giovanni Equation on Triangular and Tetrahedral Domains Russo. using GPUs Peter Smereka In this talk we presents an efficient, fine-grained parallel al- Department of Mathematics gorithm for solving the Eikonal equation on unstructured University of Michigan triangular and tetrahedral meshes. The Eikonal equa- [email protected] tion, and the broader class of Hamilton-Jacobi equations to which it belongs, have a wide range of applications from geometric optics and seismology to biological modeling and MS87 analysis of geometry and images. The ability to solve such Discretization of Integral Operators on Compli- equations accurately and efficiently provides new capabili- cated Surfaces ties for constructing solutions on large grids, exploring and visualizing parameter spaces, and for solving inverse prob- I will describe an efficient method for the numerical eval- lems that rely on such equations in the forward model. uation of the singular integrals which arise in the dis- Efficient solvers on state-of-the-art, parallel architectures cretization of weakly singular integral operators on sur- require new algorithms that are not, in many cases, opti- faces. Standard techniques for evaluating these integrals, mal, but are better suited to synchronous updates of the while adequate in simple cases, become prohibitively ex- solution and constrained memory access patterns. In this pensivewhenappliedtointegraloperatorsgivenoncom- talk we address some particular challenges associated with plicated surfaces. The scheme I will describe, by contrast, 2D and 3D unstructured meshes, in order to extend the fast is largely insensitive to the geometry of the underlying sur- iterative method to solve the Eikonal equation efficiently on face. two-dimensional triangular and three-dimensional tetrahedral domains on parallel architectures, including graphics James Bremer processors. We propose a new local update scheme which UC Davis provides solutions of first-order accuracy on both serial and [email protected] parallel architectures, and extend that scheme to the case of inhomogeneous, anisotropic speed functions. We also propose two novel update schemes and their corresponding MS87 data structures for efficient irregular data mapping to par- Integral Equation Methods for Unsteady Stokes allel, SIMD processors. We provide detailed descriptions Flow in Two Dimensions of the implementations on a single CPU, a multicore CPU with shared memory, and SIMD architectures, with com- We present an integral equation formulation for the un- parative results against state-of-the-art Eikonal solvers. steady Stokes equations in two dimensions. This problem is of interest in its own right, as a model for slow viscous Mike Kirby flow, but perhaps more importantly, as an ingredient in University of Utah the solution of the full, incompressible Navier-Stokes equa- School of Computing tions. Using the unsteady Green’s function, the velocity [email protected] evolves analytically as a divergence-free vector field. This avoids the need for either the solution of coupled field equa- 86 AN12 Abstracts tions (as in fully implicit PDE-based marching schemes) or Department of Mathematical Sciences the projection of the velocity field onto a divergence free George Mason University field at each time step (as in operator splitting methods). [email protected] In addition to discussing the analytic properties of the operators that arise in the integral formulation, we describe Matt Gerhart a family of high-order accurate numerical schemes and il- George Mason University lustrate their performance with several examples. [email protected] Shidong Jiang Department of Mathematical Sciences MS88 New Jersey Institute of Technology A Comparison of Numerical Methods for Models [email protected] of Thin Liquid Films

Together, experiments, analytical solutions and numerical MS87 simulations have advanced our fundamental understanding Boundary Integral Methods for Inextensible Vesi- of the motion of thin liquid films. The models involve par- cle Dynamics in Two Dimensions tial differential equations that are tractable by several numerical approaches; there is no agreed-upon best scheme. A boundary integral method for simulating inextensible Many mathematicians write their own code for numerical vesicles in a 2D viscous fluid was developed by Veerapa- simulations. Open source code is uncommon. I will re- neni et. al. Recent extensions include developing precondi- view pros and cons of a variety of numerical approaches to tioners, implementing a near-singular integration strategy, thin films problems and discuss possibilities for open source allowing for vesicles with different bending moduli, and code. incoporating the Fast Multipole Method. The goal is to develop a robust method to simulate high concentrations Rachel Levy of vesicles. Harvey Mudd College [email protected] Bryan D. Quaife Institute for Computational Engineering and Sciences University of Texas at Austin MS88 [email protected] Settling of a Contact Lens

George Biros When a contact lens is placed in the eye, it is fit onto the University of Texas at Austin cornea by the action of the blink. The upper lid applies [email protected] a normal force on the lens deforming it and squeezing the tear film out between the lens and cornea. To better understand the fit performance, we model coupled fluid and MS87 solid mechanics of the settling of a soft contact lens during Fast, High-order Accurate Methods for Evaluating a blink. Layer Heat Potentials Kara L. Maki We will describe a new fast algorithm for evolving the ”his- Institute for Mathematics and its Applications tory part” of the heat potentials. It overcomes some of University of Minnesota the limitations of previous fast algorithms and lowers the [email protected] complexity constants. We will also discuss a new recursive product integration to overcome the ”geometrically David S. Ross induced stiffness” of the heat potentials. The new scheme Rochester Institute of Technology is arbitrary-order accurate and in particular, we present [email protected] results that exhibit 16th order convergence for evaluating layer potentials on time-dependent boundaries. This is joint work with Lesle Greengard, Shidong Jiang and MS88 George Biros. New Models of Two-phase Flow in Porous Media

Shravan Veerapaneni Plane waves for two phase flow in a porous medium are Courant Institute modeled by the one-dimensional Buckley-Leverett equa- New York University tion, a scalar conservation law. We analyze stability of [email protected] sharp planar interfaces to two-dimensional perturbations, which involves a system of partial differential equations. Linear stability analysis results in a criterion that distin- MS88 guishes between stable and unstable interfaces. Numerical Modeling Tear Films, Contact Lenses and Evapo- simulations of the full nonlinear system of equations, in- ration cluding dissipation and dispersion, illustrate the analytical results. We explore thin film models for the tear film on a human eye in the presence of a porous contact lens. We are in- Michael Shearer terested in pre-lens and post-lens tear film dynamics. Our Mathematics model assumes that the contact lens remains wetted upon NC State University evaporation of the pre-lens tear film and allows for contin- [email protected] ued evaporation from an exposed contact lens. Treatment of the post-lens film as a squeeze layer is also discussed. Kim Spayd Daniel M. Anderson NC State University AN12 Abstracts 87 [email protected] natorics while satisfying the constraints, are widely believed to be challenging. In this talk, I will present a Zhengzheng Hu general method to locally characterize any shape space of Department of Mathematics meshes implicitly prescribed by a collection of non-linear North carolina State University constraints and how to navigate the desirable subspaces. [email protected] Yongliang Yang, Yijun Yang King Abdullah University of Science and Technology MS89 [email protected], [email protected] Approximation on Non-Cartesian Lattices Helmut Pottmann For applications such as visualization in higher dimensions King Abdullah University of Science non-Cartesian uniform lattices outperform the Cartesian [email protected] lattice. I will present a generic framework that extends popular approximation methods, such as B-splines, from Niloy Mitra the Cartesian lattice to uniform non-Cartesian lattices. King Abdullah University of Science and Technology [email protected] Mahsa Mirzargar University of Florida [email protected]fl.edu MS90 Learning to Classify HSI

MS89 We present a sparse modeling framework for sub-pixel map- Box-Splines on Crystallographic Lattices ping that mitigates the effects of noise, spectral variability, and spectral mixing by learning material dictionaries, and The talk characterizes families of symmetric box-splines a spatialspectral coherence regularizer. Experiments with that are natural analogues of tensor-product B-splines, but synthetic and real data demonstrate the suitability of the that are shift-invariant on other crystallographic lattices method. This technique retains high-performance classifi- that appear in nature, such as the BCC and FCC lattices cation accuracy when dealing with reconstructed data from and their generalizations. In particular, the talk summa- undersampled images. Finally, we apply this technique for rizes the basic properties for computational use: the poly- HSI-LiDAR fusion. Work in collaboration with Zhengming nomial degree, the continuity, the linear independence of Xing, John Greer, Edward Bosch, and Lawrence Carin. shifts on the lattice and optimal quasi-interpolants for fast approximation of fields. Guillermo Sapiro University of Minnesota Jorg Peters Dept Electrical & Computer Engineering University of Florida [email protected] [email protected]fl.edu Alexey Castrodad Minho Kim NGA and the University of Minnesota School of Computer Science [email protected] University of Seoul [email protected] MS90 MS89 Classification of Hyperspectral Images by Varia- tional Methods Patterns in Free Form Architecture and Discrete Differential Geometry Hyperspectral classification methods have often focused on the wealth of spectral information available in each pixel. Contemporary architecture generates a stunning variety of However, the incorporation of spatial information can also new designs and patterns which are based on freeform ge- greatly aid in object identification. We will discuss the ometry. These patterns are often closely related to the adaptation of variational segmentation methods, primarily actual fabrication, for example in panel layouts and sup- designed for grayscale and color imagery, to the segmenta- porting structures. In this talk, the speaker will address the tion of hyperspectral data. We also show that multi-phase mathematical concepts behind some recent developments, segmentation finds a natural extension into the high di- which are closely linked to discrete differential geometry mensions of hyperspectral data. and concern circle patterns, geodesic patterns and patterns formed by support structures and shading systems. Alex Chen SAMSI/University of North Carolina at Chapel Hill Helmut Pottmann [email protected] King Abdullah University of Science [email protected] MS90 MS89 Social Network Clustering of High Dimensional Sparse Data Shape Space Exploration of Constrained Meshes Data mining is the mathematics, methodologies and proce- In geometry processing, meshes are often specified by a col- dures used to extract knowledge from large datasets. Spec- lection of non-linear constraints, typically associated with tral embedding uses eigenfunctions of a Laplace operator mesh faces or edges. Exploring the corresponding shape (or related graph affinity matrix) for extracting the under- space, i.e., the possible meshes sharing the same combi- lying global structure of a dataset. This talk will give an in- 88 AN12 Abstracts troduction to spectral embeddings. Applications presented Peter S Kim will include clustering LA street gang members based on School of Mathematics and Statistics sparse observations of where and who they are seen with. University of Sydney [email protected] Blake Hunter UCLA Mathematics Department Joanna R Wares [email protected] Department of Math and Computer Science University of Richmond Yves van Gennip [email protected] UCLA [email protected] MS91 TheRoleofBiomechanicsintheEarlyDevelop- MS90 ment of Breast Cancer: A Hybrid Model Robust Computation of Linear Models We investigated the role of microenvironment in an early Consider a dataset of vector-valued observations that con- development of Ductal carcinoma in situ (DCIS) and the sists of a modest number of noisy inliers, which are ex- invasion process in later stages. DCIS is an early stage non- plained well by a low-dimensional subspace, along with a invasive breast cancer that originates in the epithelial lining large number of outliers, which have no linear structure. of the milk ducts, but it can evolve into comedo DCIS and We describe a convex optimization problem that can re- ultimately the most common type of breast cancer, inva- liably fit a low-dimensional model to this type of data. sive ductal carcinoma. Understanding the progression and When the inliers are contained in a low-dimensional sub- how to effectively intervene in it presents a major scientific space we provide a rigorous theory that describes when this challenge. The extracellular matrix (ECM) surrounding optimization can recover the subspace exactly. We also for- a DCIS tumor contains several types of cells and several mulate an efficient algorithm for solving this optimization types of growth factors that are known to individually af- problem and demonstrate its effectiveness with numerical fect tumor growth. However, the complex biochemical and experiments. mechanical interactions of stromal cells with tumor cells is poorly understood. The model can predict how per- Gilad Lerman turbations of the local biochemical and mechanical state School of Mathematics influence tumor evolution via cross-talk between a tumor University of Minnesota and stromal cells such as fibroblasts. We first focus on [email protected] the EGF-TGFbeta signaling pathways and show how cell growth and proliferation can be affected by up- or down- Michael McCoy regulation of components in these pathways. We present a Caltech hybrid model for the interaction of cells with the tumor mi- [email protected] croenvironment (TME), in which epithelial cells (ECs) are modeled individually while the ECM is treated as a con- Joel Tropp tinuum, and show how these interactions affect the early CMS development of tumors. We then present an invasion model Caltech where stromal cells play a significant role in triggering the [email protected] invasion process. Our results shed light on the interactions between growth factors, mechanical properties of the ECM, Teng Zhang and feedback signaling loops between stromal and tumor Institute for Mathematics and its Applications cells, and suggest how epigenetic changes in transformed University of Minnesota cells affect tumor progression in the early and late stage of [email protected] breast cancer. Yangjin Kim MS91 University of Michigan, USA Determinants of Successful Cancer Therapy with [email protected] Cytokine-expressing Oncolytic Viruses Hans G. Othmer Oncolytic viruses selectively infect and destroy tumors University of Minnesota while largely sparing healthy cells. Many of today’s most Department of Mathematics promising oncolytic viruses express cytokines which induce [email protected] an immune attack against the tumor. Here, we systematically develop deterministic mathematical models describing the therapeutic mechanism. For model validation, we MS91 leverage in vivo measurements illustrating the antitumor Modeling Preventative Breast Cancer Vaccines us- effects of several cytokine-armed oncolytic adenoviruses in ing an Agent-based Approach melanoma cells. We present our modeling approach and preliminary findings regarding the mathematical basis for A next generation approach to breast cancer treatment fo- tumor elimination. cuses on developing preventative vaccinations to stimulate a person’s immune system to attack incipient tumors before Joseph J. Crivelli clinical detection. Relevant cell interactions would take Cornell University place on the scale of several thousands of cancer cells. To School of Medicine understand dynamics at this small scale, we develop an [email protected] agent-based model of anti-tumor immune responses that accounts for cell size, cell crowding near the microtumor, AN12 Abstracts 89 and the possibility of stochastic tumor elimination. controllability condition. We investigate how the graph theoretic concept of a zero forcing set impacts the control- Peter S. Kim lability property. In particular, we prove that if a set of ver- University of Utah tices is a zero forcing set, the associated dynamical system Department of Mathematics is controllable. Joint work with Burgarth, DAlessandro, [email protected] Severini, Young.

Peter Lee Leslie Hogben City of Hope Cancer Center Iowa State University, [email protected] American Institute of Mathematics [email protected]

MS91 Traveling Waves in a Model of Tumor Angiogenesis MS92 Lower Bounds for Minimum Semidefinite Rank In this talk, we will discuss traveling wave solutions for a chemotaxis model with logarithmic sensitivity, which de- The minimum semidefinite rank (msr) of a graph is the scribes the initiation of angiogenesis. The challenges of minimum rank among positive semidefinite matrices with analyzing traveling wave solutions of such type of chemo- the given graph. The OS-number is a useful lower bound taxis model lie in the high dimensionality and the singu- for msr, which arises by considering ordered vertex sets larity. Hence the routine approaches, such as phase plane with some connectivity properties. In this talk we present analysis, no longer work. In the talk, we shall show these two new interpretations of the OS-number. We first show challenges can be resolved by variable transformations,such that OS-number is also equal to the maximum number of that the transformed system can be solved by the regular vertices which can be orthogonally removed from a graph approaches. The existence, wave speed and stability of under certain nondegeneracy conditions. Our second in- traveling wave solutions will be discussed and open ques- terpretation of the OS-number is as the maximum possi- tions will be presented. ble rank of chordal supergraphs who exhibit a notion of connectivity we call isolation-preserving. These interpre- Zhian Wang tations not only give insight into the OS-number, but also Department of Applied Mathematics allow us to prove some new results. For example we show Hong Kong Polytechnic University that msr(G)= G 2 if and only if OS(G)= G 2. [email protected] | |− | |− Sivaram Narayan Department of Mathematics MS92 Central Michigan University The Extended Combinatorial Inverse Eigenvalue [email protected] Problem Let ( ) be the set of all real symmetric n n matrices MS92 correspondingS G to a graph G on n vertices. We× investigate Positive Semidefinite Zero Forcing the problemGiven G,avertexv of G,and2n 1real − The positive semidefinite zero forcing number of a graph, numbers Z+(G), is a variant of the (standard) zero forcing number of a graph, Z(G), which uses the same definition with a λ1 µ1 λ2 µ2 λn 1 µn 1 λn, ≥ ≥ ≥ ≥···≥ − ≥ − ≥ different color change rule. The positive semidefinite zero forcing number was introduced as an upper bound for pos- is there a matrix A ( ) such that λ1,λ2, ..., λn are the ∈S G itive semidefinite maximum nullity. This talk will discuss eigenvalues of A and µ1,...,µn 1 are the eigenvalues of − properties of Z (G) and positive semidefinite zero forcing A(v)?A complete solution can be found for a few graphs + sets. Joint work with Ekstrand, Erickson, Hall, Hay, Hog- on n vertices. ben, Johnson, Kingsley, Osborne, Peters, Roat, Ross, Row, Warnberg. Wayne Barrett Brigham Young University Michael Young [email protected] Iowa State University myoung@iastate,edu John Sinkovic, Curtis Nelson, Nicole Malloy, William Sexton, Robert Yang, Anne Lazenby Department of Mathematics MS93 Brigham Young University Assessing Beliefs and Content Knowledge in First [email protected], [email protected], Semester Biocalculus [email protected], [email protected], talent- [email protected], [email protected] Many colleges and universities struggle with finding ways to meet the quantitative needs of their biology and life science majors. Here I will share my experiences in the MS92 development and implementation of a first semester cal- Zero Forcing, Minimum Rank, and Applications to culus course for biology majors. I will discuss assessment Control of Quantum Systems of student beliefs and attitudes about mathematics pre- and post-biocalculus, their performance as compared to We study the dynamics of systems on networks from a lin- students in traditional calculus, and the similarities and ear algebraic perspective. Under appropriate conditions, differences in their styles of learning mathematics. there is a connection between the quantum (Lie theoretic) property of controllability and the linear systems (Kalman) Hannah L. Callender 90 AN12 Abstracts

Institute for Mathematics and its Applications researchers and pracitioners a rich set of possibilities, in- University of Minnesota cluding deep recursive solves and mixed-precision primi- [email protected] tives. We demonstrate hybrid-parallel multi-precision iterative linear and eigenvalue solvers using the generic programming library support in Trilinos. MS93 Calculus II for Biology Students Christopher G. Baker Oak Ridge National Laboratory Abstract not available at time of publication. [email protected] David Gammack Marymount University MS94 [email protected] Design and Development of Sustainable Libraries for Numerical Computation on Many Core Archi- tectures MS93 Introducing Quantitative Thinking into an Intro- The new supercomputers have millions of cores intercon- ductory Biology Curriculum nected hierarchically by high-speed networks. The hierar- chic and massive parallelism present in these architectures Introducing quantitative thinking in introductory biology imply that the numerical libraries have to be defined ac- classes presents challenges from students and instructors. cording to an adequate design model and the existing ones To address these, we have identified quantitative concepts would have to be adapted to this design. In this talk, we that support introductory biology concepts; designed tu- present a model for numerical library allowing reusability torials and exercises placing them in biological contexts; and sustainability. Some experiments on large scale many- designed an instrument to assess the effectiveness of this core platforms validating the approach will be presented. approach; and piloted the approach in a small section of introductory biology. This work is supported by a grant to the University of Arizona from the Howard Hughes Medical Nahid Emad Institute (52006942). University of Versailles, PRiSM Laboratory [email protected] Susan Hester University of Arizona Makarem Dandouna [email protected] University of Versailles [email protected] Lisa Elfring, Lisa Nagy Arizona State University Molecular and Cellular Biology MS94 [email protected], [email protected] Incorporation of Multicore FEM Integration Rou- tines into Scientific Libraries MS93 We have developed a system for integration of the finite A New Quantitative Modeling Course for First- element residual and Jacobian arising from a given weak year Biology Students form. This system is based upon the Ignition code generation package and ideas from the FEniCS project, and In the last few decades biological and medical fields have generates code targeting GPUs. Since this is merely a part undergone a profound transformation into data-driven, of the overall PETSc library framework, we discuss the de- quantitative sciences. The standard calculus courses which sign decisions made in order to incorporate these routines traditionally constitute the quantitative training for biol- with a minimum of user input, generation of debuggable ogy majors do not adequately prepare students for these code, and smooth integration into the PETSc build pro- needs. A new course developed at the University of cess. Chicago takes the place of the last course in the required calculus sequence. It combines mathematical modeling, Matthew G. Knepley computational implementation, and basic statistics, all ap- University of Chicago plied to specific biological and medical problems. I will [email protected] present the results of assessments, both of student learning and of their evaluations of the course effectiveness. Andy Terrel Texas Advanced Computing Center Dmitry A. Kondrashov University of Texas University of Chicago [email protected] [email protected]

MS94 MS94 Cray Scientific Library for Accelerators Multi-precision Inner/outer Solvers via Generic Programming Libraries We will present Cray Scientific Libray for accelerators designed for Cray XK family. This library provides the Multi-precision and mixed-precision techniques combine same interface of the original BLAS and LAPACK that inefficient high-precision types with efficient low-precision can be executed on accelerators and CPUs together. For types in order to provide fast and high-precision solvers and the performance enhancement, we have applied an auto- preconditioners. Traditional approaches typically utilize a adaptation mechanism to select the best implementation high precision solver preconditioned using a lower precision for different problem size, type of host memory allocation solve, but modern generic programming techniques allow AN12 Abstracts 91 and data location. These features deliver immediate speed lation that generates a family of successively tighter lower up for existing applications with relatively light coding ef- bounds, all solvable in polynomial time, and compare these forts. new bounds to the well-known Held-Karp bound.

Keita Teranishi,AdrianTate Alejandro Toriello Cray Inc. Industrial and Systems Engineering [email protected], [email protected] University of Southern California [email protected] MS95 Resilience of Small Social Networks with Multiple MS96 Relations Eulerian Approaches for Transmission Traveltime Tomography with Discontinuous Slowness The ability of a network to retain a given property under perturbation of its structure is referred to as resilience.We We propose an Eulerian approach for transmission trav- focus on the resilience of small social networks with multi- eltime tomography with discontinuous slowness. The ap- ple types of relations. Here, we describe the multirelational proach is to minimize the mismatch between the measure- structure as a partially ordered semigroup, represented by ments and the Eulerian solutions of the eikonal equation. its Hasse diagram. We discuss qualitative differences be- To accurately incorporate the contributions from discon- tween networks with connected and disconnected Hasse di- tinuity in the slowness, we propose a level-set formula- agrams, and we illustrate the resilience formulation with a tion to describe the discontinuity in the velocity model. number of empirical examples. This results in a shape recovery problem. In the first part of the talk, we match only the first arrivals from point Taniecea Arceneaux sources. Even though the algorithm is computationally ef- Mathematics ficient, such approach discards all information from later Princeton University arrivals. In the second part of the talk, we consider us- [email protected] ing multivalued Eulerian traveltime solutions. We propose a novel algorithm to compute such multivalued solutions of the eikonal equation without doing any computation in MS95 the phase space. Preliminary numerical results will also be Matroidal Branchwidth given. Abstract not available at time of publication. Wenbin Li Department of Mathematics, Illya Hicks Hong Kong University of Science and Technology Texas A&M University [email protected] [email protected]

MS96 MS95 Simulation of Light Waves in Large Scale Photonic Price Optimization under the Nested Logit Model Crystal Devices With Multiple No-Purchase Options Photonic crystals (PhCs) are periodic structures with a pe- We consider a pricing problem under the Nested Logit riod on the scale of the wavelength of light. Devices can be Model in which nests represent agencies acting as amal- created in a PhC by introducing various types of defects gamators of product offerings from several firms, rather and they are usually connected by waveguides that serve as than being wholly controlled by a single firm. We consider input and output ports. A large scale PhC device may have a revenue maximization problem from the perspective of a a length scale that is much larger than the wavelength. We single firm utilizing n channels and show that the optimal present some techniques for simulating lightwaves in PhC revenue can be obtained by an iterative procedure which devices. These techniques can take advantage of the exis- adjusts prices sequentially over each nest. tence of many identical unit cells, the partial periodicity of William Z. Rayfield the structure and the locality of some nonlinear processes, Operations Research and Information Engineering etc. Cornell University Ya Yan Lu [email protected] City University of Hong Kong Dept of Mathematics Paat Rusmevichientong [email protected] Marshall School of Business University of Southern California [email protected] MS96 Unformization of WKB Solutions via Wigner Transform MS95 Optimal Toll Design: A Lower Bound Framework We propose a renormalization process of a two phase WKB for the Traveling Salesman Problem solution, which is based on an appropriate surgery of local uniform asymptotic approximations of the Wigner trans- We propose a framework of lower bounds for the asymmet- form of the WKB solution. We explain in details how this ric traveling salesman problem based on approximating the process provides the correct spatial variation and frequency dynamic programming formulation, and give an economic scales of the wave field on the caustics where WKB method interpretation wherein the salesman must pay tolls as he fails. The detailed analysis is presented in the case of a fun- travels between cities. We then introduce an exact reformu- damental problem, that is the semiclassical Airy equation, 92 AN12 Abstracts which arises from the model problem of acoustic propaga- the solver has optimal ( ) complexity, where N is the O N / tion in a layer with linear variation of the sound speed. system size; in 3D, it incurs an ( ∈) precomputation cost, followed by ( log )solves.Numericalexperi-O N George Makrakis ments suggest theO utilityN ofN our method as a direct solver, Department of Applied Mathematics a generalized fast multipole method, and as a precondi- University of Crete tioner for complex problems. [email protected] Kenneth L. Ho Courant Institute MS96 [email protected] Randomized Structured Direct Solvers for Seismic Problems Leslie Greengard We consider the solution of 2D and 3D inhomogeneous Courant Institute acoustic wave equation in the frequency domain, by solv- New York University ing Helmholtz equations via a new set of structured ma- [email protected] trix methods. Randomized techniques are used to facilitate the structured matrix operations. The advantages of such MS97 solvers include: 1. For a single frequency, all solution steps share a common Helmholtz operator, which can be quickly Fast Methods for Boundary Integral Equations on factorized so as to solve linear systems with multiple right- the Sphere hand sides, each in nearly linear time and storage. We Models describing physical or biological phenomena con- take advantage of certain hidden rank structures in the strained to evolve on subsurfaces of compact manifolds can operators. 2. For different frequencies, the same adjacency be reformulated in terms of integral equations. Examples pattern is used, so that only one step of matrix ordering is of such models include point vortices moving on the sur- needed. 3. The factorizations are relatively insensitive to face of the earth, or polar-driven chemotactic migration the frequencies. We try to justify such insensitivity. The on cell membranes during mitosis. The use of integral efficiency and accuracy are demonstrated by various impor- equation strategies in this context is fairly new, and re- tant numerical examples, such as 2D (BP2004 & BP2007 quires a careful examination of the relevant parametrices TTI) and 3D (SEAM) models. This is joint work with for the elliptic operator of concern. In this talk we first Maarten V. de Hoop, Xiaoye S. Li, and Shen Wang. describe reformulations of a boundary value problem for Jianlin Xia the Laplace-Beltrami operator in terms of layer potentials. Department of Mathematics We then describe a class of fast methods based on the fast Purdue University multipole method. [email protected] Nilima Nigam Dept. of Mathematics MS97 Simon Fraser University [email protected] Fast Computation of Eigenfrequencies of Planar Domains via the Spectrum of the Neumann-to- Dirichlet Map Mary-Catherine Kropinski Simon Fraser University We present a new method for the spectrum and eigenfunc- [email protected] tions of a planar star-shaped Dirichlet domain. It is ‘fast’ since it is computes a cluster of eigenfunctions (number- ing of order the square-root of the eigenvalue) with the MS97 effort usually taken to find a single one. For a domain 400 Mathematical and Numerical Aspects of the Adap- 10 wavelengths across, and relative error 10− , the resulting tive Fast Multipole Poisson-Boltzmann Solver speed-up is 103. Its error analysis is rigorous, and it achieves higher-order∼ accuracy than the ‘scaling method’. We present recent progress on the development of the adap- I will also discuss a new technique for evaluation of poten- tive fast multipole Poisson-Boltzmann solver. We briefly tial fields close to their source curves. review previous efforts on integral equation reformulation, mesh generation and discretization, and new versions of the Alexander H. Barnett fast multipole methods. We introduce our recent progress Mathematics Department on parallelization based on the dynamic prioritization tech- Dartmouth College nique for large-scale problems and on-going work on time- [email protected] marching schemes for long-time simulations. Jingfang Huang Andrew Hassell Department of Mathematics Australian National University University of North Carolina, Chapel Hill [email protected] [email protected]

MS97 Bo Zhang A Fast Direct Solver for Non-oscillatory Integral Duke University Equations [email protected]

We present a fast direct solver for non-oscillatory integral Xiaolin Cheng equations via multilevel matrix compression and sparse Oak Ridge National Laboratory matrix embedding. For boundary integral equations in 2D, [email protected] AN12 Abstracts 93

Benzhuo Lu practices that have emerged, and some questions that re- Institute of Computational Mathematics, China main. [email protected] Jennifer Pearl Nikos Pitsianis Division of Mathematical Sciences Department of Electrical and Computer Engineering National Science Foundation Aristotle University [email protected] [email protected] MS98 Xiaobai Sun Multidisciplinary Undergraduate Research Department of Computer Science in Computational Mathematics and Nonlinear Dy- Duke University namics of Biological, Bio-inspired and Engineering [email protected] Systems J. Andrew McCammon In this talk, we will describe a multidisciplinary under- Howard Hughes Medical Institute graduate research program in computational mathematics University of California, San Diego and nonlinear dynamics of biological, bio-inspired and en- [email protected] gineering systems that has not only helped to enhance ongoing interaction among communities of people including students, educators and academicians, but also serve as a MS98 catalyst to help reinforce and drive reform across the insti- Undergraduate Research on the Fast Track: From tution. Nothing to Publication in Eight Weeks Padmanabhan Seshaiyer Since Summer 2010, we have been hosting the REU Site: George Mason University Interdisciplinary Program in High Performance Comput- [email protected] ing. It introduces undergraduate students to scientiﬁc, statistical, and parallel computing with MPI and conducts research with application scientists from industry, academia, MS99 and government agencies in only eight weeks. We will share Mapping the Connectome with Convex Algebraic our experiences of how to make this program work through Geometry team work and by involving several layers of support from graduate students to faculty, with lessons that are useful The human brain connectome project seeks to provide a for anyone interested in running an REU Site. complete map of neural connectivity. Just as the human genome represents a triumph of marrying technology (high Matthias K. Gobbert throughput sequencers) with theory (dynamic program- University of Maryland, Baltimore County ming for sequence alignment), the human connectome is Department of Mathematics and Statistics the result of a similar union. The technology is that of [email protected] diﬀusion magnetic resonance imaging while the requisite theory, we shall argue, comes from a combination of har- Nagaraj Neerchal monic analysis and convex algebraic geometry. Department of Mathematics and Statistics University of Maryland, Baltimore County Lek-Heng Lim [email protected] University of Chicago [email protected]

MS98 Thomas Schultz Building An Applied and Computational Math De- Max Planck Institute for Intelligent Systems gree Program from the Ground Up [email protected] We are developing a new undergraduate degree program in applied and computational mathematics, scheduled to MS99 commence Fall 2013. Each year, this major will admit a co- Klein’s Idea and Identities for Powers of Polynomi- hort of up to 40 students into a two-year lock-step curricu- als lum commencing at the beginning of their junior year and continuing through to graduation. This carefully planned In his famous book on the icosahedron, Felix Klein con- educational experience will provide students with a tightly sidered the identification of a point on the unit sphere u, with the linear form x vy,wherev is the image of u un- integrated combination of coursework and computer labs, − together with a capstone project and close mentoring. der the Riemann map. If you start with the vertices of a nice polytope inscribed in the sphere, and take quadratic Jeffrey Humpherys forms corresponding to products of linear forms associated Brigham Young University with antipodal pairs of vertices, you get interesting sets jeff[email protected] of quadratic forms. For example, the octahedron corresponds to xy, x2 y2,x2 + y2 (the Pythagorean parameterization), the cube− to four quadratic forms whose 5-th MS98 powers are dependent and the icosahedron to six quadratic Models for Undergraduate Research, Best Prac- forms whose 14-th powers are dependent. We’ll give more tices, and Questions examples and try to explain this phenomenon. This talk will highlight some successful models that fac- Bruce Reznick ulty have used to foster undergraduate research, some best University of Illinois, Urbana-Champaign 94 AN12 Abstracts [email protected] erndesignshopinwhichsuchtoolsdon’tplayavitalrole.

Thomas A. Grandine MS99 Applied Mathematics Linearization Functors on Real Convex Sets The Boeing Company [email protected] We prove that linearizing certain families of polynomial optimization problems leads to new functorial operations in real convex sets. We show that under some conditions MS100 these operations can be computed or approximated in ways Knot Theorems and Counterexamples for Splines amenable to efficient computation. These operations are convex analogues of Hom functors, tensor products, sym- For piecewise linear approximation of spline curves, it is metric powers, exterior powers and general Schur functors well-known that repeated subdivision produces a control on vector spaces and lead to novel constructions even for polygon that converges to the spline under the Hausdorff polyhedra. metric. Little has been shown about the relationship of topological properties between the control polygon and its Mauricio Velasco spline curve. We i) provide sufficient conditions for sub- Universidad de los Andes division to yield a control polygon ambient isotopic to the [email protected] curve, and ii) show examples of topological differences between a spline and its control polygon. MS99 Thomas Peters A Sums of Squares Relaxation for Hyperbolicity University of Connecticut Cones [email protected] Hyperbolic programming a useful generalization of semidefinite programming. Here we will investigate the MS100 relationship between them. Using derivative cones, I will Volume Rendering Verification Using Discretiza- give an inner approximation of a hyperbolicity cone using tion Errors Analysis sums of squares. In particular, this will give an inner approximation of the hyperbolicity cone by the feasible set of Much recent research has been dedicated to direct volume an SDP. As a bonus, this relaxation is exact for hyperbolic rendering (DVR). In disciplines such as image-based med- polynomials already coming from an SDP. ical diagnosis or material science, images generated using DVR require high accuracy and precision. Unfortunately, Cynthia Vinzant little research has been dedicated to assess volume ren- University of California, Berkeley dering correctness. We propose a technique for volume [email protected] rendering verification based on an analysis of the volume rendering integral. We apply order-of-accuracy and con- Daniel Plaumann vergence analysis - well-established verification techniques University of Konstanz, Germany - to volume rendering implementations, and derive the the- [email protected] oretical foundations of our verification approach. Tiago Etiene Queiroz MS100 New York University Spline Operators for Subdivision and Differentia- [email protected] tion The discrete derivatives of a Bezier curve are known to con- MS101 verge to the continuous derivative under subdivision. So Non-modal Amplification of Disturbances in Chan- after a sufficient number of subdivisions one can obtain a nel Flows of Viscoelastic Fluids: A Possible Route ‘good’ approximation of the derivative. Here a tight error to Elastic Turbulence? bound for this approximation is derived and the number of subdivisions required for a prescribed error tolerance is Abstract not available at time of publication. calculated. This is done considering the subdivision algo- Satish Kumar rithm as an operator acting on the control points of the Chemical Engineering and Materials Science curve. University of Minnesota Hugh Cassidy [email protected] University of Connecticut [email protected] MS101 Title Not Available at Time of Publication MS100 Abstract not available at time of publication. The Case Against Interactivity in Geometric De- sign Thomas Pence Michigan State University Interactive geometric design tools are now a firmly en- Department of Mechanical Engineering trenched means of building geometric models suitable for [email protected] product definition and engineering analysis. Such tools have seemingly been a boon to mechanical engineering and product design worldwide, and it is hard to imagine a mod- AN12 Abstracts 95

MS101 with the Hadwiger conjecture are also considered. Regularized Two-phase Models for Gels Thomas Milligan Abstract not available at time of publication. Department of Mathematics and Statistics University of Central Oklahoma Longhua Zhao [email protected] University of Minnesota [email protected] MS102

A Colin de Verdiere-type Invariant and odd-K4- 2 MS102 and odd-K3 -free Signed Graphs 2-Matching Covered Loopy Graphs A signed graph is a pair (G, Σ) where G is an undi- A 1, 2 -factor is a spanning subgraph consisting of pair- rected graph (we allow parallel edges, but no loops) and wise{ vertex} disjoint edges and cycles. Tutte has character- Σ E(G). A cycle C of G is called odd if C has an ized graphs which have a 1, 2 -factor. We investigate min- odd⊆ number of edges in common with Σ. A signed graph is imal 2-matching covered graphs,{ } i.e. graphs in which every called bipartite if it has no odd cycles. We have introduced edge is in some 1, 2 -factor and removal of any edge yields ν(G, Σ), which generalizes the Colin de Verdière invariant a graph without{ this} property. We will discuss some classes ν(G). The invariant ν characterizes bipartite signed graphs of minimally 2-matching covered loopy graphs (graphs in as those signed graphs (G, Σ) with ν(G, Σ) 1, and signed 2 ≤ which vertices may have a loop), where loops are cycle of graphs with no odd-K4- and no odd-K3 -minor as those length one. signed graphs (G, Σ) with ν(G, Σ) 2. In this talk we will discuss these results. Joint work with≤ Marina Arav, Frank Adam Berliner Hall, and Zhongshan Li. Department of Mathematics St. Olaf College Hein van der Holst [email protected] Department of Mathematics Georgia State University Richard A. Brualdi [email protected] University of Wisconsin Department of Mathematics [email protected] MS103 Dynamic Density Functional Theory (DDFT) Model for Freezing of a Pair Potential Fluid: The MS102 Effect of Fluid Flow Spectrally Arbitrary Patterns over Finite Fields The Classical Density Functional Theory (CDFT) and the A zero-nonzero pattern is a square matrix where each entry Phase Field Crystal (PFC) models have proven to be good is either a zero or a star. A realization of a zero-nonzero approaches to model crystal growth from a fluid phase. pattern over a specified field is a matrix where each of the These models capture atomic level details including defects stars is replaced by a nonzero entry from the field. A pat- and grain boundaries. However these approaches usually tern is said to be a Spectrally Arbitrary Pattern over the involve a phenomenological gradient descent based time specified field if for every monic polynomial(with degree evolution. and do not take the convection of the fluid phase corresponding to the size of the matrix) with coefficients (fluid flow) into consideration. In this work we start with from the field, there exists a realization whose character- the Revised Enskog Theory (RET) (an effective kinetic the- istic polynomial is the given polynomial. We will look at ory) as the definition of time evolution. Then exploiting the interplay between pattern structure and field stucture the connection to CDFT of freezing, we develop evolution in determining whether or not a pattern turns out to be equations for the macroscopic density and flow fields. The spectrally arbitrary over a given field. over damped limit provides us a DDFT model for time evolution of the density field. Some studies of this model and Judith J. McDonald results on crystal growth from fluid phase will be discussed. Washington State University Department of Mathematics [email protected] Arvind Baskaran Institute for Pure and Applied Mathematics, UCLA University of California, Irvine MS102 [email protected] Minor Monotone Floors and Ceilings of Graph Pa- rameters Aparna Baskaran Brandeis University A graph parameter is minor monotone if it preserves the Department of Physics minor relation. We consider the transformation of real- [email protected] valued graph parameters into related minor monotone graph parameters using two different methods. The mi- John Lowengrub nor monotone floor of well-ordered graph parameter p is Department of Mathematics defined by p =minp(H) G H with a similar def- { | } University of California at Irvine inition for the minor monotone ceiling. We consider the [email protected] minor-monotone floor and ceiling of a number of graph parameters, with particular attention given to parameters that relate to the zero-forcing number. Results dealing MS103 Liquid Crystal Phase Transitions in Elastic Net- 96 AN12 Abstracts works MS104 Failure of Random Materials: Asymptotic Analysis We develop a modelling approach to anisotropic, nonlinear and Importance Sampling elasticity using ideas from the liquid crystal theory. We consider highly compressible elastic networks with embed- We study the problem of estimating small failure probabili- ded rigid units. The work is motivated by the structure ties for elastic random material which is described by a one and functionality of actin and collagen networks found in dimensional stochastic elliptic partial differential equation inter-connective tissue. We analyze the phase transition with certain external force and boundary conditions. Gaus- behavior of these systems under compression and shear, sian random function is used to model the spatial variation and found a range of nematic phases and a soft-elasticity of the material property parameters. The failure event of regime, according to geometric properties of the network. the bulk material is simply characterized by the exceeding of certain thresholds for the max stress or load in any spa- Maria-Carme Calderer tial location. With the large deviation heuristics, we pro- Deparment of Mathematics vide a intuitive description of the most probable realization University of Minnesota, USA of the random material parameters which could lead to the [email protected] critical situation of material failure in engineering. An efficient Monte Carlo method to compute such probabilities Chong Luo is presented. Oxford University [email protected] Jingchen Liu department of statistics Columbia University MS103 [email protected] A General Framework for High Accuracy Solutions to Energy Gradient Flows from Material Science Xiang Zhou Models Division of Applied Mathematics Brown University Abstract not available at time of publication. xiang [email protected] Brian R. Wetton University of British Columbia MS104 Department of Mathematics [email protected] Sampling Transition States Using Gentlest Ascent Dynamics

MS103 The dynamics of complex systems often involve thermally activated barrier-crossing events that allow the system to Energy Stable Scheme for Phase Field Models move from one basin of attraction on the energy surface Abstract not available at time of publication. to another. Such events are ubiquitous, but difficult to simulate using conventional simulation tools like molecular Zhengfu Xu dynamics. We present an extension of the gentlest ascent Michigan Technological University dynamics (GAD) under which the system evolves in a man- Dept. of Mathematical Sciences ner opposite to that of the steepest descent method. [email protected] Amit Samanta Program in Applied and Computational Mathematics MS104 Princeton University, Princeton Nucleation Events in Soft Condensed Matter Using [email protected] the String Method Weinan E Within the self-consistent field theory, we develop an “on- Princeton Univesity the-fly’ string method to compute nucleation events in soft- Department of Mathematics condensed matter systems. Several applications of the [email protected] method are given, including: membrane pore formation and rupture, particle translocation, and the budding of a micelle from a rod-like micelle. Where applicable, the MS104 method is compared against classical nucleation theory. Some Interacting Particle Methods for Sampling Complex Energy Landscapes Daniel Appelo Division of Engineering and Applied Science This talk will survey my efforts with coworkers to develop California Institute of Technology and analyze Monte Carlo sampling algorithms for complex [email protected] (usually high dimensional) probability distributions. These sampling problems are typically di?cult because they have Christina Ting multiple high probability regions separated by low proba- Biochemistry and Molecular Biophysics bility regions and/or they are badly scaled in the sense that California Institute of Technology there are strong unknown relationships between variables. [email protected] The dimensionality and complexity of the problems neces- sitate a Monte Carlo approach (as opposed to numerical Zhen-Gang Wang quadrature) but standard MC schemes converge extremely Caltech slowly in the presence of barriers or bad scalings. New [email protected] methods designed to address these issues directly have the potential to significantly accelerate the solution of impor- AN12 Abstracts 97 tant problems in many areas of science. I’ll discuss some SR16000/M1. very preliminary work on geophysical and chemical applications. Takahiro Katagiri, Satoshi Itoh, Satoshi Ohshima The University of Tokyo Jonathan Weare [email protected], [email protected], University of Chicago satoshi ohshima ([email protected] Department of Mathematics [email protected] MS105 ppOpen-HPC: Open Source Infrastructure for De- MS105 velopment and Execution of Large-Scale Scientific Parametric Steering for Autotuning Numerical Applications with Automatic Tuning Kernels and Scientific Codes in Multicore Environ- ments ppOpen-HPC is an open source infrastructure for development and execution of optimized and reliable simula- Our goal is to find a way to represent the correlation tion codes with capabilities of automatic tuning (AT) on between different performance tuning parameters, auto- post-peta (pp) scale parallel computers using heteroge- tuning techniques and understand their relevance for im- neous computing nodes which consist of multicore CPUs plementing different numerical kernels in multicore envi- and co-processors. ppOpen-HPC consists of various types ronments. Our goals are to find some trends in perfor- of libraries, which covers various types of procedures for mance driving parameters and form a criteria for the case- scientific computations. In this talk, current status of based selection of kernels at runtime. ppOpen-HPC and results of recent developments are described. Leroy A. Drummond Computational Research Division Kengo Nakajima Lawrence Berkeley National Laboratory The University of Tokyo [email protected] Information Technology Center [email protected] Serge G. Petiton CNRS/LIFL and INRIA Masaki Satoh serge.petiton@lifl.fr Atmospheric and Ocean Research Institute The University of Tokyo Christophe Calvin [email protected] Commissariat l’Energie Atomique [email protected] Takashi Furumura Earthquake Research Institute University of Tokyo MS105 [email protected] Promise Chaining for Automatic Kernel Fusion and Avoiding Data Movement on Accelerators Hiroshi Okuda Research into Artifacts, Center for Engineering (RACE) Performance optimizations for discrete compute accelera- The University of Tokyo tors (like GPUs) cut across computational kernels. For [email protected] example, launching a single kernel is expensive, which motivates ”fusing” multiple kernels. Moving data from the accelerator to the CPU is slow, which forces programmers to Takeshi Iwashita track data placement. Cross-kernel optimizations clutter Academic Center for Computing and Media Studies interfaces, confuse algorithm developers, and hinder evolu- Kyoto University tion of kernel optimizations. We propose a programming [email protected] model that uses dataflow and promise chaining to hide data placement and fuse kernels automatically. Hide Sakaguchi Japan Agency for Marine-Earth Science and Technology Mark Hoemmen [email protected] Sandia National Laboratories [email protected] MS106 Self-assembly of Islands during the Initial Stages of MS105 Film Growth: Sizes and Spatial Arrangements Adaptation of ppOpen-AT To Numerical Kernels on Explicit Method Atoms deposited on a flat surface at the onset of film growth diffuse and aggregate into islands (whose locations ppOpen-AT is an auto-tuning (AT) language for code op- impact subsequent multilayer film morphologies). The size timization in 5 kinds of crucial numerical methods pro- distribution and spatial arrangement of islands reflect the vided by ppOpen-HPC project. In this presentation, we stochastic nature of the self-assembly process. Mean-field present preliminary result by adapting ppOpen-AT to a treatments fail to describe this behavior prompting devel- numerical kernel derived by explicit method on Finite Dif- opment of alternative formalisms. We describe recent anal- ference Method. We have developed a new AT function ysis for the distribution of capture zones, where the surface on ppOpen-AT for its code optimization; loop fusion and is tessellated so that one capture zone surrounds each is- loop split. Performance evaluation is performed by using land. the T2K Open Supercomputer (U.Tokyo) and HITACHI Jim W. Evans 98 AN12 Abstracts

Ames Laboratory USDOE and Iowa State University MS107 [email protected] NumericalSolutionofAnInverseDiffractionGrat- ing Problem MS106 In this talk, we consider the diffraction of a time-harmonic On the Dynamics of Crystal Facets in Materials plane wave incident on a perfectly reflecting periodic sur- Surface Relaxation face. A continuation method on the wavenumber will be proposed for the inverse diffraction grating problem, which Below the roughening temperature, crystal surfaces relax reconstructs the grating profile from measured reflected through the motion of line defects (steps); and develop waves on a constant height away from the structure. Nu- macroscopically flat surface regions (facets). A challeng- merical examples will be presented to show the validity and ing problem is to reconcile step motion, which is described efficiency of the proposed method. by discrete schemes, with a viable continuum theory, based on variational principles and Partial Differential Equations, Gang Bao near facets. In this talk, I will discuss recent progress in Michigan State University formulating and analyzing an evaporation step model that [email protected] is fully consistent with a continuum thermodynamics approach. Peijun Li Department of Mathematics Dionisios Margetis Purdue University University of Maryland, College Park [email protected] [email protected] Haijun Wu Kanna Nakamura Department of Mathematics Department of Mathematics Nanjing University University of Maryland, College Park [email protected] [email protected]

MS107 MS106 Resoance of 1D Phototic Crystal with Finite Ex- Strain Dependence of Microscopic Parameters and tent its Effect on Ordering during Epitaxial Growth Abstract not available at time of publication. Strain is often the driving force behind self-organization of quantum dots and other nanoscale structures. I present Junshan Lin a DFT analysis of the effect of strain on key microscopic University of Minnesota growth parameters. I then illustrate in growth simulations [email protected] that employ the level-set technique how such strain dependence affects growth. This approach includes a variable Fadil Santosa (and strain dependent) potential energy surface for adatom Institute for Mathematics and its Applications diffusion, and an additional step-edge barrier via a mixed University of Minnesota Robin boundary condition. [email protected] Christian Ratsch UCLA MS107 Department of Mathematics [email protected] Numerical Methods for the Complex Helmholtz Equation and Scattering from a Lossy Inclusion

MS106 I will discuss a new method for solving the Helmholtz equation in lossy materials that is based on the variational Kinetic Monte Carlo Simulation of Heteroepitaxial principles developed by Milton, Seppecher, and Bouchitté. Growth: Wetting Layers, Quantum Dots, Capping, This method results in a system of equations which can be and NanoRings reduced to a symmetric positive-definite system, and can A KMC algorithm efficiently accounting for elastic strain be solved using conjugate gradient and Cholesky factoriza- is developed for heteroepitaxial growth. It exploits the ob- tion. Also, I will discuss the application of this method servation that adatoms are essentially decoupled from the to the problem of scattering from an inclusion filled with elastic field. The film is therefore decomposed into weakly lossy material, which requires the application of a trans- and strongly bonded portions. The first evolves indepen- parent boundary condition. dent of the elastic field which is updated infrequently. We Russell B. Richins show that faceted quantum dots form from layer-by-layer Michigan State University nucleation of pre-pryamids. Capping simulations provide [email protected] insights into dot erosion and ring formation. Joint with T.P. Schulze. MS107 Peter Smereka Department of Mathematics Mathematical Analysis in Quantifying Mechanical University of Michigan Properties for Nano-Materials [email protected] Nanotechnology deals with structures sized between 1 to 100 nanometer and involves investigating and designing materials or devices within that scale. Due to its small AN12 Abstracts 99 size, it is difficult to quantify the mechanical properties an easy task. Then, once data is acquired, what insights of nanomaterials which significantly rely on measurement can be gained? In this talk, we consider the observations techniques, conditions and environment. In this talk, we and scientific hypothesis around two historic transitions propose a novel model based on Euler-Bernoulli equation in Earth’s history. Approximately 650 million years ago, with a stochastic source term accounting for the effect of Earth is likely to have been completely covered in ice in initial bending, surface roughness and white noise during what is called ”Snowball Earth”. Additionally we’ll con- the measurement. The forward problem is demonstrated sider an abrupt transition (PETM) when atmospheric car- to have a unique and explicit path-wise solution. Further- bon sky rocketed nearly 55 million years ago. more, the inverse problem consists of identifying the elastic modulus of nanobelt and reconstructing the random source Samantha Oestreicher structure, i.e., the mean and the variance. Based on the University of Minnesota explicit formula of the direct problem, the inverse problem School of Mathematics can be reduced into a first kind of Fredholm type integral [email protected] equation. Two kinds of regularization techniques are introduced to obtain stable solutions. Numerical examples are presented to illustrate the validity and effectiveness of MS108 the proposed methods. Climate Tipping Points: Overview and Outlook Xiang Xu I will provide some overview of investigations of potential Michigan State University tipping elements in Earths climate, highlighting challenges [email protected] of developing early warning signs for impending critical transitions. Drawing on material covered in our “virtual seminar” on this topic, I will survey mathematical mech- MS107 anisms for tipping, some of which depart from classical Phase Retrieval for Diffractive Imaging bifurcation theory. Parts of the discussion will be framed in terms of case studies associated with conceptual models Abstract not available at time of publication. of (1) Arctic sea-ice retreat, and (2) desertification. Chao Yang Mary Silber Lawrence Berkeley National Lab Northwestern University [email protected] Dept. of Engineering Sciences and Applied Mathematics [email protected]

MS108 Climate Transitions in a Conceptual Model with MS109 Multiple Time Scales Optimality of the Neighbor Joining Algorithm and Faces of the Balanced Minimum Evolution Poly- Techniques from dynamical systems are used to analyze tope a multiple timescale conceptual model incorporating temperature, glacial motion, and the carbon cycle. Within Balanced minimum evolution (BME) is a statistically con- this framework, we examine how both ice-albedo and sistent distance-based method to reconstruct a phyloge- greenhouse gas feedback effects can cause a wide vari- netic tree from an alignment of molecular data. In 2000, ety of glacial oscillations, including variations between ice- Pauplin showed that the BME method is equivalent to op- covered and ice-free states. timizing a linear functional over the BME polytope, the convex hull of the BME vectors obtained from Pauplins Anna Barry formula applied to all binary trees. The BME method is Mathematics related to the popular Neighbor Joining (NJ) algorithm, Boston University now known to be a greedy optimization of the BME prin- [email protected] ciple. In this talk I will elucidate some of the structure of the BME polytope and strengthen the connection between the BME method and NJ Algorithm. I will show MS108 that any subtree-prune-regraft move from a binary tree to A Dynamical Systems Perspective on Period Tran- another binary tree corresponds to an edge of the BME sitions in Glacial Cycles polytope. Moreover, I will describe an entire family of faces parametrized by disjoint clades. Finally, given a phy- About one million years ago, the Earth’s glacial cycles logenetic tree T, I will show that the BME cone and every changed character, increasing in amplitude and moving NJ cone of T have intersection of positive measure. from a period of about 40 thousand years to a period of about 100 thousand years. Various theories attempting to David Haws explain this transition can be expressed as dynamical sys- University of Kentucky tems phenomena. [email protected] Richard McGehee University of Minnesota MS109 [email protected] WNT Signaling in Melanoma Cells Experimental evidence suggests that retinoic acid deacti- MS108 vates canonical WNT signaling in early stage melanoma Abrupt and Gradual Transitions from the Deep cells, thereby affecting cell division. More agressive Past melanoma cell lines are not responsive to retinoic acid. The question then arises how such a switch in signaling could be Gaining information about ancient Earth climates is not affected in these unresponsive cell lines. This talk will dis- 100 AN12 Abstracts cuss a time- and state-discrete mathematical model of the timization of Partially Separable Functions two pathways and its use in identifying potential effectors of a switching mechanism. Optimization problems often exhibit partial separability (PS). A function f is partially separable if f can be rep- m Reinhard Laubenbacher resented in the form f(x)= i=1 fi(x)wherefi depends Virginia Bioinformatics on pi n variables. The sparsity of the Jacobian (and Institute Hessian) of f can be exploited by computing the sparse [email protected] Jacobians of the elemental functions first. We present PS support in ADIC2 by using the ColPack coloring toolkit and demonstrate it with a TAO optimization example. MS109 A Differential Algebra Method for Finding Identi- Boyana Norris, Sri Hari K. Narayanan fiable Parameter Combinations of Nonlinear ODE Argonne National Laboratory Models [email protected], [email protected]

Parameter identifiability analysis for dynamic system ODE Todd Munson models concerns finding which unknown parameters can be Argonne National Laboratory quantified from given input-output data. If all the param- Mathematics and Computer Science Division eters of a model have a finite number of solutions, then the [email protected] model is said to be identifiable. However, many models are unidentifiable, i.e. the parameters can take on an infinite Assefaw H. Gebremedhin number of values and yet yield identical input-output data. Purdue University This problem has been especially apparent in Systems Bi- [email protected] ology. In this talk, we examine unidentifiable models and a differential algebra method for finding globally identifiable parameter combinations using Groebner Bases. We also MS110 discuss computational difficulties in finding these identifi- An Efficient Overloaded Method for Computing able parameter combinations and explore possible improve- Analytic Derivatives of Mathematical Functions in ments to our algorithm. MATLAB Nicolette Meshkat An operator-overloaded method is presented that gener- Department of Mathematics ates analytic derivatives of mathematical functions defined Santa Clara University by MATLAB computer code. The method implements for- [email protected] ward more automatic differentiation in a manner that produces a source code that contains the derivative of the orig- MS109 inal function. Because a new source code is produced, the method can be applied recursively to generate derivatives Disentangling Phylogenetic Mixture Models of any order. A description of the method is given and its Mixture models are used to model the heterogeneity inher- effectiveness is demonstrated on three examples. ent in evolutionary processes. A mixture model is specified Michael Patterson by a collection of trees (possibly with repetitions). I will Aerospace Engineering discuss ongoing work on the identifiability of phylogenetic University of Florida mixture models. The best results in this area require a mix mpatterson@ufl.edu of techniques from algebraic geometry and discrete mathematics. Matthew Weinstein Seth Sullivant Department of Mechanical and Aerospace Engineering North Carolina State University University of Florida [email protected] mweinstein@ufl.edu

Anil Rao MS110 Mechanical and Aerospace Engineering Exploiting Sparsity in Derivative Computation University of Florida anilvrao@ufl.edu Jacobian and Hessians matrices that arise in large-scale computations are typically sparse. We discuss combinatorial algorithms and software we have developed for making MS110 the computation of such matrices using Automatic Differ- Computing Higher-order Derivatives: Approaches, entiation efficient in terms runtime and memory usage. We Tools and Uses illustrate the advantages the methods afford using a numerical optimization problem in chemical engineering as The approximation errors of finite difference schemes for an example. computing higher-order derivatives make their use in practical applications unattractive. Except for cases where an- Assefaw H. Gebremedhin alytical derivatives are available, only algorithmic differen- Purdue University tiation (AD) can provide derivatives of an arbitrarily high [email protected] order with machine precision. The talk will cover the basic approaches used in the AD context for computing such derivatives, cover the most relevant AD tool implementa- MS110 tions, and the computational complexity. It will briefly Automating Sparse Gradient Computations in Op- highlight current developments addressing heterogeneous AN12 Abstracts 101 computing hardware. The talk will conclude with example MS111 uses of higher-order derivatives and practical tool applica- Undergraduate CSE Programs in the U.S. tions from ODE solvers, model reductions, path continuation methods, and others. In this talk, a brief survey of some of the different models of undergraduate computational science and engineering Jean Utke programs will be presented. This will highlight some cur- Argonne National Laboratory rent best practices that can be extended to applied mathe- [email protected] matics in general. relevant activities of SIAM’s Education Committee will also be presented including possibilities for outreach into the K-12 community. MS111 Weather, Uncertainty, Supercomputing, and Can- Peter R. Turner cer: Research Experiences for Math Majors at Ari- Clarkson University zona State University School of Arts & Sciences [email protected] This talk describes innovative programs that involve mathematically talented students at the sophomore through se- nior level. Interdisciplinary group projects and related MS112 courses in modern applications of mathematics, including Addressing the Materials Genome Initiative ensemble forecasting, biomedical models, state estimation, through the AFLOWLIB.ORG Consortium: Ther- finance, and high-performance computing, are offered to moelectric Properties of Sintered Compounds with 11 to 16 juniors each year (with beneficial impacts on the High-throughput Ab-initio Calculations graduate program as well). I will also discuss efforts to develop a 21st Century undergraduate mathematics cur- In this presentation we will describe the aflowlib.org con- riculum. sortium and give some examples of its use including scintil- lator, thermoelectrics and topological insulators research. Eric J. Kostelich Arizona State University Department of Mathematics Stefano Curtarolo [email protected] Duke University [email protected]

MS111 Experiences in Running the STAGE Program MS112 Data Mining Applications for Knowledge Discov- ’Smooth Transition for Advancement to Graduate Edu- ery in Materials Science: Promises and Challenges cation’ (STAGE), is a multi-year NSF-funded eight-week summer research experience for underrepresented minority Extensive materials databases are available for new knowl- undergraduate students which intends to immerse the par- edge discovery. However, in spite of considerable advances ticipants, mainly from the HBCUs, in an intensive train- in data mining techniques, materials scientists still lack ing program that includes (a) crash courses,(b) guided re- practical data mining tools to manage and transform the search, and (c) professional developments. This talk is data into actionable knowledge. We have initiated a series based on the rewarding experience of managing STAGE of computational experiments with various materials data in 2011 which can help other researchers in running simi- in an attempt to create such tools. An overview of promises lar programs nationwide. as well as challenges of such studies will be presented. Nabendu Pal Da Gao Mathematics Department Department of Computer Science and Engineering University of Louisiana at Lafayette University of Minnesota [email protected] [email protected]

Yousef Saad MS111 Department of Computer Science Excel-lent Experiences: Computational Research University of Minnesota Internships [email protected] Professors can help undergraduates excel through obtaining meaningful CSE research internships. Such internships James R. Chelikowsky can enhance students’ professional and personal lives and Institute for Computational Engineering and Sciences can add new dimensions to a school’s program. With University of Texas at Austin students’ inexperience, active involvement by professors is [email protected] usually a crucial. Using numerous ”success stories,” this talk explores how advisors can help students obtain and MS112 benefit from computational research experiences. Informatics for the Materials Genome: a Minimal- Angela B. Shiflet ist Perspective Chair of Computer Science and Director of Computational Sci. The recently announced Materials Genome Initiative raises Wofford College a fundamental question of whether materials can in fact shifletab@wofford.edu have a ”gene”. Implied in the term of ”genome” is the idea for the need for large quantities of data. This talk ventures to show, however, that we in fact need to seek 102 AN12 Abstracts the minimal amount of data . Applications of statistical MS113 inference integrated into a variety of data mining tools for Computational Issues for Multi-physics, Multi- materials design are presented. Phase Equations Krishna Rajan Abstract not available at time of publication. Iowa State University Department of Materials Science and Engineering Andrew Chrislieb [email protected] Dept. of Mathematics Michigan State University [email protected] MS112 USPEX: Evolutionary Crystal Structure Predic- Keith Promislow tion as a Tool in Materials Design Michigan State University [email protected] The evolutionary methodology USPEX for crystal structure prediction [1] provides, with high reliability and efficiency, the stable and low-energy metastable structures MS113 of a given compound at given P-T-conditions. Theory of Using GPUs to Compute Solutions to the Func- energy landscapes of solids [2] gives tools that greatly en- tionalized Cahn-Hilliard Equation hance structure prediction. The following results will be discussed: 1. Theoretical and experimental evidence for a We present a nonlinear semi-implicit numerical scheme for new stable high-pressure phase of boron, γ-B [3], showing computing solutions to the evolution equation, superhardness and charge transfer between boron. 2. New 2 2 2 high-pressure phase, a transparent insulator, was found for ut =∆( ∆ W (u)+ η)( ∆u W (u)), (4) sodium [4]. 3. High-pressure phases of group IV hydrides − − methane CH4 [5], silane SiH4 [6], germane GeH4 [7] and that describes pore network formation in a functionalized stannane SnH4 [8]. We found much more stable phases polymer/solvent system as described by the Functional- of SiH4 and SnH4 than previous random-sampling predic- ized Cahn-Hilliard Model. The physical process is defined tions, and unusual structure of the superconducting phase by multiple time-scales: short time phase separation, long of GeH4 with high Tc= 64. CH4 decomposes into diamond time network growth, and slow evolution to steady state. and hydrogen within interiors of giant planets; this process This requires very long simulations, so our scheme is de- is important for understanding the energy balance of Nep- signed to be unconditionally gradient stable allowing for tune. Our method has been extended to enable efficient adaptivity in the time stepping while preserving the dis- prediction of the structure of nanoparticles and surface re- crete energy law. The gradient stability derives from the constructions, which opens doors for many geochemical ap- semi-implicit splitting of the chemical potential into con- plications, as well as predictive studies of nanomaterials tractive and expansive components. We present a novel and catalysis. References [1] Oganov A.R., Glass C.W., iteration for solving the nonlinear equation with a Fourier J.Chem.Phys. 124, 244704 (2006) [2] Oganov A.R., Valle spectral method, and numerical results are shown with a M., J.Chem.Phys. 130, 104504 (2009) [3] Oganov A.R., 10x speedup using Graphics Processing Units (GPUs). Chen J., Gatti C., et al., Nature 457, 863 (2009) [4] Ma Y., Eremets M.I., Oganov A.R., et al., Nature 458, 182 Jaylan S. Jones, Andrew Christlieb, Keith Promislow (2009) [5] Gao G., Oganov A.R., et al., J.Chem.Phys. 133, Michigan State University 144508 (2010). [6] Martinez-Canales M., Oganov A.R., et [email protected], [email protected], al., Phys.Rev.Lett. 102, 087005 (2009) [7] Gao G., Oganov [email protected] A.R., et al., Phys.Rev.Lett. 101, 107002 (2008). [8] Gao G., Oganov A.R., et al. (2010). Proc.Natl.Acad.Sci. 107, MS113 1317 (2010). Variational Multiscale Models for Biomolecular Qiang Zhu Systems State University of New York, Stony Brook [email protected] A major feature of biological science in the 21st Century will be its transition from a phenomenological and descriptive discipline to a quantitative and predictive one. MS113 I will discuss the use of differential geometry theory of sur- Efficient Spectral-Galerkin Methods for High-order faces for coupling microscopic and macroscopic scales on an Equations and Systems of Coupled Elliptic Equa- equal footing. Based on the variational principle, we derive tions with Applications to Phase-field Models the coupled Poisson-Boltzmann, Nernst-Planck (or Kohn- Sham), Laplace-Beltrami and Navier-Stokes equations for Abstract not available at time of publication. the structure, dynamics and transport of ion-channel systems. As a consistency check, our models reproduce ap- Feng Chen propriate solvation models at equilibrium. Moreover, our Purdue University, West Lafayette model predictions are intensively validated by experimen- [email protected] tal measurements. Mathematical challenges include the well-posedness and numerical analysis of coupled partial Jie Shen differential equations (PDEs) under physical and biologi- Dept. of Mathematics cal constraints, lack of maximum-minimum principle, effec- Purdue University tiveness of the multiscale approximation, and the modeling [email protected] of more complex biomolecular phenomena. Guowei Wei Department of Mathematics Michigan State University AN12 Abstracts 103 [email protected] would be the migration of a defect through a crystal. Par- allel replica dynamics accelerates this by simulating many replicas simultaneously, concatenating the simulation time MS114 spent of the ensemble, as thought it were a single long tra- A Dynamic Model of Polyelectrolyte Gels jectory. This leads to several numerical analysis questions: Is parallel replica dynamics doing what we think it is? For Abstract not available at time of publication. what systems will it be useful? How do we implement it efficiently? In this talk, I will thoroughly describe the algo- Yoichiro Mori rithm and report on progress towards rigorous justification. School of Mathematics Open questions will also be highlighted. University of Minnesota [email protected] Gideon Simpson University of Toronto [email protected] MS114 Models with Increasing Complexity for Hydro- Mitchell Luskin gel/enzyme Feedback Oscillations School of Mathematics Abstract not available at time of publication. University of Minnesota [email protected] Ronald Siegel University of Minnesota Department of Pharmaceutics and Biomedical MS115 Engineering Escape from An Attractor: Importance Sampling [email protected] and Rest Point We discuss asymptotically optimal importance sampling MS114 schemes for the estimation of finite time exit probability Computations of Moving and Deforming Objects of small noise diffusions that involve escape from an equi- in Biological Flows librium point. The appearance of the rest point compli- cates the prefactor of the second momentum of the ordi- Abstract not available at time of publication. nary state-dependent importance sampling estimator. Our analysis points out a useful and efficient scheme to obtain a Lingxing Yao nice prefactor by using the linear quadratic regulator near University of Minnesota the rest point. [email protected] Xiang Zhou Aaron L. Fogelson Division of Applied Mathematics University of Utah Brown University [email protected] xiang [email protected]

Paul Dupuis, Konstantinos Spiliopoulos MS115 Division of Applied Math Noise-induced Transitions of Barotropic Flow over Brown University Topography paul dupuis ¡[email protected]¿, konstantinos [email protected] We study the noise-induced transitions in a climate system modeled by the barotropic quasi-geostropic equations with topography. The stochastic dynamic is constrained on a MS116 constant energy surface and it exhibits metastable behav- The Adaptive Finite Element Simulations for the ior: The system is likely to stay trapped for a long time Electronic Structures near one state until it switches to another. The metastable states are characterized by the strength of the zonal ﬂow. Abstract not available at time of publication. We compute the maximum likely-hood transition paths and the transition rates between the metastable states us- Guanghui Hu ing the string method. We ﬁrst study a truncated one- Michigan State University mode ODE model, then generalize the results to the full [email protected] PDE model. This is a joint work with Xu Yang and Eric Vanden-Eijnden. MS116 Weiqing Ren Multiscale Modeling and Model Computation for Courant Institute of Mathamatical Sciences Scanning Near-Field Optical Microscopy [email protected] Abstract not available at time of publication.

MS115 Songting Luo Department of Mathematics Analysis of Parallel Replica Dynamics Michigan State University Parallel replica dynamics was ﬁrst proposed by A.F. Voter [email protected] as a numerical tool for accelerating molecular dynamics simulations characterized by a sequence of infrequent, but rapid, transitions from one state to another. An example 104 AN12 Abstracts

MS116 Opportunities Scattering and Resonances of Thin High Contrast Dielectrics The emergence of scalable manycore computing systems presents fundamental challenges and opportunities for lin- Abstract not available at time of publication. ear equation solvers. In this talk we discuss the role of processor and memory architecture, system faults and problem Shari Moskow size in guiding linear solver algorithms research and devel- Drexel University opment. In particular, we discuss new opportunities for Department of Mathematics making linear solvers faster, more robust and resilient to [email protected] system faults. Michael A. Heroux MS116 Sandia National Laboratories Some Reconstruction Algorithms in Quantiative [email protected] Photoacoustic Tomography

In quantitative photoacoustic tomography (qPAT) we aim MS117 at reconstructing physical parameters of biological tissues A Heterogenous Scale-bridging Kinetic Solver for from “measured’ data of absorbed radiation inside the tis- Emerging Architectures sues. Mathematically, qPAT problems can be regarded as inverse problems related to some elliptic partial differential The advent of modern parallel architectures, and the equations. We present in this talk some new reconstruc- promise of exascale computing resources, brings new chal- tion strategies for inverse problems in qPAT with different lenges to computational science. Dependably taking ad- types of available data. vantage of billion-way parallelism and distinct levels of parallelism will stress solver algorithms. We are develop- Kui Ren ing a broadly applicable scale-bridging solver algorithm to University of Texas at Austin help meet some of this challenge. Development of simi- [email protected] lar moment-based acceleration methods can be found in a variety of application areas such as neutron transport, thermal radiation (photon) transport, kinetic plasma sim- MS117 ulation. We will provide algorithm fundamentals and open Liszt: A Domain Specific Language for Partial Dif- research questions. We will provide some indication of al- ferential Equations gorithm performance on emerging architectures.

Liszt is a domain specific language to simplify solving par- Dana Knoll tial differential equations (PDE) on parallel computers and Los Alamos National Laboratory graphics processing units (GPU). Liszt is a high level lan- [email protected] guage that contains constructs specific to PDE solvers such as finite-volume or finite-element methods on unstructured C.N. Newman, H. Park, R. Rauenzahn grids. Topological objects like mesh, cell, face, edge and LANL vertex are part of the language. Knowledge of the mesh [email protected], [email protected], [email protected] connectivity allows the compiler to automatically reason about data dependency and schedule communication (eg, L. Chacon, G. Chen MPI calls). As a result Liszt code does not contain any ORNL explicit parallel instruction, such as inter-node communi- [email protected], [email protected] cation, aside from the use of parallel for loops to iterate over mesh objects. A Liszt code is very portable. The source to source compiler can take the same code as in- W. Taitano put and produce MPI code for clusters, openMP code for UNM multicore processors, and CUDA code for GPUs. The per- [email protected] formance of Liszt matches or in some cases exceeds hand tuned code. Jeffrey A. Willert North Carolina State University Eric F. Darve [email protected] Stanford University Mechanical Engineering Department [email protected] MS117 Co-Design and You Zach Devito Stanford University In this talk I will give a high-level, general discussion of [email protected] the DOE ASCR Exascale Co-Design Centers and the role of applied mathematics in extreme-scale scientific computing.

Niels Joubert, Pat Hanrahan Karen I. Pao Stanford Office of Science [email protected], [email protected] US Department of Energy [email protected] MS117 Linear Solvers at Extreme Scale: Challenges and PP1 A Gpu Implementation of Von Mises-Fisher Distri- bution Algorithm for Polymer Conformation Anal- AN12 Abstracts 105 ysis tioned for moments of highly anisotropic distributions. We resolve this difficulty by adaptively selecting the polyno- The statistical representation of polymer conformations is mial basis defining the moments, and when the optimiza- very important because it is impossible to track all relevant tion problem cannot be solved in finite precision, we find a microscopic variables for each polymer in a polymer-laden physically similar solvable problem. solution due to the huge number of degrees of freedom. In our study we consider one of the most descriptive kinetic Graham Alldredge models of polymer, Kramers’ bead-rod model, where the University of Maryland, USA probability density function models the angle of each rod [email protected] with respect to the fixed coordinate axes. Towards this goal we apply von Mises-Fisher distribution for a polymer Cory Hauck conformation distribution. The hard and soft assignment Oak Ridge National Laboratory methods of clustering of the Expectation-Maximization al- [email protected] gorithm are used to cluster the mixture model which have been implemented in parallel using CPU and GPU based AndréTits platforms. We demonstrate that the GPU-accelerated ver- University of Maryland at College Park sion of the clustering algorithm is significantly faster than [email protected] the CPU version.

Bakytzhan Kallemov Dianne P. O’Leary Center for Energy Research University of Maryland, College Park Nazarbayev University, Astana Department of Computer Science [email protected] [email protected]

Aidos Abzhanov PP1 Nazarbayev University Astana Alternate Powers in Serrin’s Swirling Vortex Solu- [email protected] tions We consider a modification of the fluid flow model for a PP1 swirling vortex developed by J. Serrin, where velocity decreases as the reciprocal of the distance from the vortex Pollutants Transport Simulation in Atmospheric axis. Recent studies, based on radar data of selected se- Boundary Layer Using Stabilized Finite Element vere weather events, indicate that the angular momentum Formulations in a tornado may not be constant with the radius, and thus This work deals with a numerical method based on the suggest a different scaling of the velocity/radial distance Galerkin Least Square scheme for a two-dimensional model dependence. Motivated by this suggestion, we consider of pollutant dispersion in the atmosphere. The model, Serrin’s approach with the assumption that the velocity which is described through a diffusion-convection equation, decreases as the reciprocal of the distance from the vortex accounts for pollutant emission from the soil and from an axis to the power b with a general b>0. This leads to a elevated source. It also accounts for diurnal changes in the boundary-value problem for a system of nonlinear differ- atmospheric stability conditions via parametric models for ential equations. We analyze this problem for particular turbulent diffusion and wind speed. Numerical results are cases, both with nonzero and zero viscosity, discuss the obtained and compared with results available in the liter- question of existence of solutions, and use numerical tech- ature. niques to describe those solutions that we cannot obtain analytically. Roseane A. Albani PEM/COPPE- Universidade Federal do Rio de Janeiro Doug Dokken [email protected] University of St. Thomas [email protected] Antônio Cruz PEM/COPPE/UFRJ Pavel Belik [email protected] Mathematics Department Augsburg College [email protected] Eduardo carmo PEN/COPPE/UFRJ [email protected] Kurt Scholz, Misha Shvartsman University of St. Thomas [email protected], [email protected] Fernando Duda PEM/COPPE/UFRJ [email protected] PP1 High Order Numerical Method for the Nearly Sin- PP1 gular Integration of the Stokes Kernel Advanced Optimization Techniques for Entropy- Simulating Stokesian particulate flows using integral equa- BasedClosuresinSlabGeometry tions requires the resolution of nearly singular integrals (evaluation of the fluid variables near the surface of a parti- Entropy-based moment closures are a parallelizable simu- cle), which are inaccurate using standard quadrature rules. lation technique with attractive theoretical properties for We propose a method to resolve this numerical difficulty. reducing the state-space of the kinetic equation, but the We partition the space around a particle into two different defining optimization problem is arbitrarily poorly condi- 106 AN12 Abstracts zones: we use quadrature in the far zone and we interpo- Total Boundary Flux late in the nearly singular zone. We present results in two dimensions. We study a time asymptotic of the non-linear Forchheimer flows in porous media with given total flux and constraints Walid Ben Romdhane on the pressure trace on the boundary. We prove that Institute for Computational Engineering and Sciences if total flux stabilizes then the difference between pressure University of Texas at Austin average inside domain and on the boundary stabilizes as [email protected] well. The refined comparison of fully transient and certain time-invariant pressure was performed. These results George Biros can be applied in reservoir engineering and other problems University of Texas at Austin modeled by diffusive equations. [email protected] Lidia Bloshanskaya Texas Tech University Bryan D. Quaife Department of Mathematics and Statistics Institute for Computational Engineering and Sciences [email protected] University of Texas at Austin [email protected] PP1 PP1 Faraday Waves on Surfactant-Covered Thin Films An Axisymmetric Boundary Element Method for Liquid layers under vertical vibration give rise to a surface Modeling Biphasic Articular Cartilage Mechanics wave pattern known as Faraday waves. In this work, the effects of surfactants on Faraday waves are explored under In comparing the stress, strain, and deformation of healthy the assumption that the depth of the liquid layer is small. and osteoarthritic cartilage under an applied load, differ- Owing to the importance of inertial effects, the standard lu- ences in parameter values can give insight into the na- brication approximation is not suitable and extended thin ture and progression of osteoarthritis. An axisymmetric film type approximation must be used. Numerical simu- Laplace-domain boundary element method is presented for lations and linearized analysis of this modified model are solving the boundary integral equations modeling the represented. sponse of biphasic cartilage tissue under mechanical loading, which involve fundamental solutions of the governing Lake Bookman PDEs. Simulation of confined compression stress relax- North Carolina State University ation of a biphasic cartilage cell is shown. [email protected] Brandy A. Benedict Merrimack College Michael Shearer [email protected] Mathematics NC State University [email protected] PP1 Predicting Bifurcations in Dynamical Systems Karen Daniels, Stephen Strickland North Carolina State University Nonlinear dynamical systems, which include models of the [email protected], [email protected] Earths climate, financial markets and complex ecosystems, often undergo abrupt transitions that lead to radically different behavior. The ability to predict such qualitative PP1 and potentially disruptive changes is an important problem Multi-Frequency Iterative with far-reaching implications. For a nonlinear dynamical Integral Equations Method for the Shape Recon- system with multiple parameters, we combine Conley instruction of An Acoustically Sound-Soft Obstacle dex theory with machine learning techniques to accurately in the Presence of Multiple Scatterers predict global bifurcations. We present a method to solve the problem of obtaining Jesse Berwald a reconstruction of a planar acoustically sound-soft obsta- Department of Mathematics cle from the measured far-field pattern generated by plane College of William and Mary waves with a fixed incidence and varying frequencies. We [email protected] solve iteratively the problem for each frequency, from the lowest to the highest, using as initial guess the solution Tomas Gedeon given by the previous frequency. We present numerical re- Montana State University sults showing the benefits of our approach. Department of Mathematics [email protected] Carlos C. Borges Worcester Polytechnic Institute [email protected] Kelly Spendlove Department of Mathematical Sciences Montana State University Marcus Sarkis [email protected] Worcester Polytechnic Institute Instituto de Matematica Pura e Aplicada (Brazil) [email protected] PP1 AWM - Time Asymptotic of Non-Darcy Flows with AN12 Abstracts 107

PP1 [email protected] Particle Methods for Geophysical Flows on the Sphere Johannes Tausch Southern Methodist University We develop a fluid dynamics solver for spherical domains Department of Mathematics with a focus on applications related to the “dynami- [email protected] cal cores” of global circulation models. We use a tree- structured Lagrangian grid and intermittent interpolation of the Lagrangian flow map to avoid inaccuracies caused by PP1 mesh distortion without introducing significant mass error. Stochastic Approximated-Gradient Optimization Interpolation is carried out using integral convolution with Methods for Oilfield Well Placement a regularized delta kernel. Fluid equations are solved using Green’s function integral solutions for the velocity stream Well placement is critical to optimal hydrocarbon resource function and potential. management. This work compares the performance of Ensemble-based Optimization (EnOpt) and Fixed-Gain Peter A. Bosler SPSA (FSP) for optimal well placement. These algorithms University of Michigan belong to the broad class of stochastic approximated- [email protected] gradient methods and offer several practical benefits: They combine the advantages of both gradient-based and Robert Krasny stochastic optimization algorithms without the correspond- University of Michigan ing computation effort, do not require access to simulator Department of Mathematics code and the gradient approximation is independent of the [email protected] problem dimensions.

Christiane Jablonowski Yuqing Chang, Deepak Devegowda University of Michigan Mewbourne School of Petroleum and Geological Ann Arbor MI 48109-2143 Engineering [email protected] University of Oklahoma [email protected], [email protected]

PP1 PP1 Software Development for a Three Dimensional Gravity Inversion and Application to Study of the Spatio-Temporal Calcium Smoothing in Dendritic Border Ranges Fault System, South Central Alaska Trees Our research involves the testing of several plausible den- To understand how animals learn it is necessary to study sity models of structure along the Border Ranges Fault changes in the strength of synaptic connections between System in South-Central Alaska by developing a novel, 3D neurons. It is thought that synaptic plasticity underlies inversion software package. The inversion utilizes gravity learning and memory at a cellular level. Therefore the data constrained with geophysical, borehole, and surface mechanisms of synaptic plasticity have been a key ques- geological information to produce a density solution. The tion in neuroscience. However, current imaging techniques novel inversion approach involves directly modeling known are limited in their ability to capture the electric proper- geology, initially free-air corrected data, and revising ”a ties of a neuron at the fine scales necessary to address this priori” uncertainties on the geologic model to allow com- problem. We use fast, random access, fluorescent multi parisons to alternative interpretations. photon microscopy to indirectly measure calcium concentration from different locations on a cell. The recordings of Rolando Cardenas,DianeDoser light intensity of the probe molecules (fluorophore) is spa- University of Texas at El Paso tially sparse and have low signal to noise ratio. Therefore, [email protected], [email protected] we propose two methods to infer the underlying calcium signal across the entire dendritic tree from such record- Mark Baker ings. The first method is a simple least squares estimate, Geomedia R&D which recovers the signal at isolated spatial locations, fol- [email protected] lowed by spatial interpolation using splines. The second method uses Bayesian inference to smooth signal. Both algorithms have the ability to infer the underlying calcium PP1 signal up to some affine transformation. Each approach Numerical Solution of Integral Equations in Solid- has advantages and disadvantages in complexity and com- ification and Laser Melting puting time. However, we show how the recovered traces from each algorithm can provide insight into the mecha- We consider the evolution of the liquid-solid interface in nisms that underlie synaptic plasticity a freezing or laser-induced melting process. Using the Green’s representation theorem for the heat equation and Rebecca Chen,KresimirJosic the Stefan condition we obtain a system of nonlinear University of Houston integro-differential equations in space and time. The in- Department of Mathematics tegral equations are discretized with the Nyström method [email protected], [email protected] which leads to an efficient time stepping scheme to determine the position and velocity of the interface with given Peter Saggau material properties. Baylor College of Medicine Neuroscience Department Elizabeth Case [email protected] Southern Methodist University 108 AN12 Abstracts

Keith Kelleher design is carried out on the area under blood pressure wave- Department of Biology and Biochemistry form during breath holds and the results will be presented. University of Hoston [email protected] Hyung Wook Chun University of Texas at Arlington Liam Paninski [email protected] Statistics Department Columbia University PP1 [email protected] Modeling and Simulating Flow-Induced Fluctua- tions in Polymer Solutions Eftychios Pnevmatikakis Columbia University Polymer solutions under flow exhibit anisotropically ampli- Statistics Department fied concentration fluctuations due to stress/concentration [email protected] coupling. The full model incorporates a two-fluid approach with polymer stress described by the Rolie-Poly equations together with thermal noise, introduced consistently by ap- PP1 plication of the fluctuation-dissipation theorem. Pertur- AWM - Tumor Growth in Complex, Evolving Ge- bations of the resulting Langevin equations about homo- ometries: A Diffuse Domain Approach geneous, in particular extensional, flow are examined. A method of characteristics solver is developed and the pre- In this poster, we present a new diffuse domain method dictions are compared with experiments on a polystyrene for simulating tumor growth in complex, evolving geome- solution in extensional flow. tries, taking into account homotype adhesion between tumor cells and heterotype adhesion between the cells and Michael Cromer, Michael Villet, Glenn Fredrickson the basement membrane. We develop an adaptive energy- University of California, Santa Barbara stable nonlinear multigrid method to solve the governing [email protected], [email protected], equations efficiently. Two and three dimensional simula- [email protected] tions are performed. This provides a model for ductal carcinoma in situ. Gary Leal Ying Chen Department of Chemical Engineering University of California, Irvine University of California, Santa Barbara [email protected] [email protected]

John Lowengrub PP1 Department of Mathematics AWM - Curve Matching Using Discrete Integral University of California at Irvine Invariants [email protected] As a result of its use in medical imaging, aerial photog- raphy, and handwriting recognition, curve matching is a PP1 significant problem in the field of image analysis. Previ- Singular Limits of Geophysical Fluid Dynamics in ous works propose integral invariants as a robust solution Spherical and Bounded Domains for the curve matching problem. However, these invariants rely on a parametric equation fit to the curve and in many We study 2D geophysical fluid models in physically rel- real world applications, this fit requires a fair amount of evant, fast rotating domains. The initial data are un- computational work. We generate discrete invariants that prepared. The first model is the rotating shallow wa- require only an ordered set of points. We apply our dis- ter equations with solid-wall boundary conditions. We crete invariants to the fields of image recognition and ob- prove convergence rates of a singular limit problem as the ject assembly. In this poster, we present examples of curve Rossby number goes to zero. The second model is incom- matching used for handwriting recognition and puzzle compressible Euler equations on a fast rotating sphere. The pletion. time-averages of solutions are shown to be approximately longitude-independent zonal flows, which is due to the non- Susan Crook flat geometry. North Carolina State University [email protected] Bin Cheng (SoMSS) School of Mathematical and Statistical Sciences Arizona State University PP1 [email protected] A Finite-Element Mmoc Groundwater Model for Gpu’s on the Cloud

PP1 We use finite-elements with a modified method of charac- Crossover Design for Studying Obstructive Sleep teristics to model a reaction-diffusion problem with advec- Apnea tion. Our application of interest is in the area of Ground- water flow with contaminant transport where biofilms are The physiological response to sleep apnea was determined present. The linear system of equations developed from the from beat to beat blood pressure in 16 healthy subjects by PDEs governing this physical model are solved on a cluster a series of breath hold maneuvers. The experiments were of GPUs accessed over the Cloud. done for both sitting and supine posture of the subject. For finding the difference in breath hold related physiological Mark C. Curran changes during different protocols and posture, crossover University of St Thomas AN12 Abstracts 109

St. Paul, MN tions with Applications to Biology [email protected] In this poster we present a numerical method for delay differential equations with application to some biology prob- PP1 lems. Two different applications are presented. The first AWM - Polyhedral Combinatorics For Phyloge- one is R.V Culshaw and S. Ruan s DDE model of cell- netic Trees free viral spread of human immunodeficiency virus ( HIV ) in a well-mixed compartment such as the bloodstream. A Tree agglomeration methods such as Neighbor-Joining and discrete time delay was introduced to describe take into ac- UPGMA continue to play a significant role in phylogenetic count the time between infection of a CD4+ T-cell and the research. Polyhedral combinatorics offers a robust toolkit emission of viral particles at the cellular level. We present for analyzing the natural subdivision of Euclidean space an analytic stability analysis of the endemically infected induced by classifying the input vectors according to tree equilibrium. we then present a numerical analysis of the topologies returned by an agglomerative algorithm. We stability and bifurcation process of the same equilibrium give a closed form for the extreme rays of UPGMA cones using numerical tools. The second application is the DDE on n taxa via the partition lattice Πn. We also study the model proposed by Barlett and Wangersky. Their model cones induced by the NJ algorithm. is a Non-Kolmogorov-Type predator prey model with two discrete times delay. We again present an analytic and a Ruth E. Davidson, Seth Sullivant numerical analysis of the stability and bifurcation process North Carolina State University of the steady state solutions. Numerical simulations are [email protected], [email protected] presented to illustrate the results.

Ibrahim O. Diakite, Benito Chen-Charpentier PP1 Department of Mathematics Stochastic Heterogeneous Multiscale Modeling of University of Texas at Arlington Single Phase Flow in a Porous Media [email protected], [email protected] Risk assessment for carbon sequestration applications requires detailed analysis of multiphase flow through porous PP1 media. We present a stochastic Heterogeneous Multiscale A Predictive Model for Geographic Statistical Data Method (HMM) with iterative coupling to model the distributions of macroscopic pressure based upon statistical- Any planar map may be transformed into a graph. If we based random pore-throat size probability density. We an- consider each country to be represented by a vertex (or alyzed its impact in a one dimensional macroscopic model, node), if they are adjacent they will be joined by an edge. coupled to a two dimensional microscale network model. To consider how trends migrate across boundaries, we ob- We further propose a domain decomposition strategy with tain relevant measures of the statistic we want to consider; a highly efficient implementation for large scale simula- namely, the index of prevalence, and the index of incidence. tions. We define a cycle by a given unit of time, usually a year. We then propose various alternate equations whereby, by Paul M. Delgado parametrizing various variables, such as population size, UTEP birth rate, death rate, and rate of immigration/emigration, [email protected] we calculate a new index of prevalence/index of incidence, for the next cycle. For a given data set, each statistic we consider may propagate by a different equation, and/or a PP1 different set of parameters; this will be determined empiri- Probabilistic Divide-and-Conquer: a New Method cally. What we are proposing is, technically, to model how for Exact Sampling with Integer Partitions as an a discrete stochastic process propagates geographically, ac- Example cording to geographical proximity. Very often, statistics that depend on geographical proximity are tabulated by For us, the random objects S whose simulation might ben- variables that are not; i.e., alphabetically. Such a predic- efit from a divide-and-conquer approach are those that can tive model would be relevant in areas such as public health; be described as S =(A, B), where there is some abil- and/or crime mapping, for law enforcement purposes. We ity to simulate A and B separately. Specifically, we represent an application using a GIS (geographic information quire that A , B , and that there is a function system). h : ∈A, ,sothatfor∈B a , ∈B, h(a, b)isthe A×B→{ ∞} ∈A indicator that “a and b fit together to form an acceptable Jorge Diaz-Castro s.’ Furthermore, we require that A and B be indepen- University of P.R. School of Law dent, and that the desired S be equal in distribution to University of P.R. at Rio Piedras ((A, B) h(A, B) = 1). This description, independent ob- [email protected] jects conditional| on some event, may seem restrictive, but very broad classes — combinatorial assemblies, multisets, and selections — fit into this setup. PP1 Investigations of Cai’s Power Law for Strong Tor- Stephen Desalvo nados University of Southern California [email protected] We investigate the consequences of power laws and self similarity in mesocyclones and tornados as presented in the work of H. Cai. We give a model for tornado genesis and PP1 maintenance using the 3-dimensional vortex gas theory of Numerical Methods for Delay Differential Equa- Chorin. High energy vortices with negative temperature in the sense of Onsager play an important role in the model. 110 AN12 Abstracts

We speculate that the high temperature vortices formation drugs are unnecessary. We use data that contain health is related to the helicity they inherit as they form or tilt into insurance claims to attempt to detect the unnecessary pro- the vertical. We also exploit the notion of self similarity cedures and drugs. It isn´t explicitly obvious from the data to give justification for power laws corresponding to weak which claims are wasteful, so we must use unsupervised and strong tornados given by Cai. Doing a nested grid methods. These methods include developing a measure- simulation using ARPS we find results consistent with Cai’s ment of similarity between different procedures. scaling. Ben Ehlert Doug Dokken Brigham Young University University of St. Thomas [email protected] [email protected]

Pavel Belik PP1 Mathematics Department Three-Dimensional High-Resolution Simulation of Augsburg College Convective Mixing [email protected] Dissolution by convective mixing is an essential trapping mechanism during CO2 sequestration. The injected CO2 Kurt Scholz, Misha Shvartsman mixes with brine and creates mixture denser than both University of St. Thomas initial fluids, leading to a Rayleigh-Benard type instabil- [email protected], [email protected] ity, which greatly accelerates the dissolution process.While 2D analyses on this phenomenon have elucidated various PP1 aspects of this mechanism, full 3D studies are scarce. We present high-resolution, 3D simulations of convective dis- Convergence in Mallows-Wasserstein Distance of solution, and discuss the validity of quantitative results Randomly Indexed Partial Sums and Upper derived from lower-dimensional models. Bounds for the Ruin Probabilities Xiaojing Fu Abstract: Classical risk processes are modelled with a Pois- MIT son arrival process along with light-tailed claim variables. [email protected] However, some real data measurements may not be compatible with the assumption of the finiteness of the second moment. In this case, heavy-tailed rewards may arise Luis Cueto-Felgueroso as a suitable approach. By considering a heavy-tailed re- MIT newal reward dependent process and by making use of Civil and Environmental Engineering the Mallows-Wasserstein distance, we study the asymptotic [email protected] properties of the resulting randomly indexed partial sums and obtain upper bounds for ruin probabilities. Applica- Ruben Juanes tions to data traffic in cumulative broadband networks as MIT well as buffer overflow probabilities are also presented. tba

Chang C. Dorea Universidade de Brasilia PP1 [email protected] Fast Algorithms for Inverse Problems of Reaction- Diffusion-Advection Equations PP1 We present a method for the solution of an inverse prob- Statistical Methods for Detecting Fraudulent Pre- lem with parabolic PDE constraints. The constraint is a scriptions reaction-diffusion-advection equation. We discuss two numerical methods to solve the associated least squares in- In the medical field, fraud, waste, and abuse are prevalent. verse problem, one based on a direct solve and one based on A large percentage of medical expenditures are for pro- a randomized SVD. Numerical tests are performed to show cedures later deemed unnecessary. In order to cut down the effectiveness of the methods for different cases, that is this rate, this project focuses on detecting unneeded pre- to compare the speed of calculations and the accuracy of scriptions by comparing insurance claims against normal the predicted data. behavior patterns. The prescriptions are sorted by similar medical claims and analyzed within these groups. Abnor- Amir Gholaminejad mal transactions are then detected and flagged for human PhD Student, Institute for Computational Engineering review. and Sciences, University of Texas at Austin [email protected] Jessica Doud Brigham Young University George Biros [email protected] University of Texas at Austin [email protected] PP1 Unsupervised Methods to Detect Health Care PP1 Waste A Fast Algorithm to Solve Slow Incompressible Steady Flows Detecting fraud is a big part of credit card management. We are trying to apply similar methods to detect waste in We present a high order fast algorithm to solve the bound- health care. A good portion of health care procedures and ary value problems associated with the inhomogeneous Bi- AN12 Abstracts 111 harmonic equation in the interior of a unit disk of the com- special case, these two optimizations are always equiva- plex plane using uniform and non-uniform grid. The fast lent when there are no constraints. We also investigate the algorithm is based on the representation of the solution in relations between the achievabilities of their optima. The terms of Green functions, uniform and non-uniform fast exact Jacobian SDP relaxation proposed by Jiawang Nie Fourier transforms and some recursive relation derived in is employed to solve the polynomial optimization obtained the Fourier space. Performance of this algorithm on non- by homogenization. We also prove that the assumption of uniform mesh and with singular source terms are some of the smoothness in Nie’s paper under which the Jacobian the attractive features of this algorithms. This algorithm SDP relaxation is exact can be weakened as the finiteness has been implemented, validated and applied to solve sev- of real singularities. Some numerical examples are given in eral interesting applied problems from fluid mechanics and the end to illustrate the efficiency of our method. electrostatics. Feng Guo Aditi Ghosh University of California, San Diego Texas A&M University [email protected] [email protected] Li Wang University of California, San DIego PP1 [email protected] Analysis of Interfaces for the Nonlinear Diffusion- Convection Equations Guangming Zhou The problem of determining the short-time behavior for in- Department of Mathematics and Computational Science, terfaces of nonlinear diffusion equations, known as a Baren- Xiangtan University blatt problem, was first formulated in the 1950s. A full [email protected] solution of the Barenblatt problem for the related problem of reaction-diffusion was given in 2000 [Abdulla and PP1 King, SIAM J. Math. Anal.] but the problem remains open for the diffusion-convection case. In this work we Statistics of Solar Cycle-La Nina Connection: Cor- first identify the regions in the parameter space relevant relation of Two Autocorrelated Time Series. for the expanding, shrinking and stationary interfaces. We Both the 11-year solar cycle and the El Nino-Southern Os- fully characterize the case when diffusion dominates over cillation (ENSO) phenomena are quasi-periodic, with pe- the convection. We prove explicit asymptotic formulae for riods of 9-11 years and 3-4 years, respectively. There have the expanding interface and local solution. The methods been claims that the two are correlated, with the Sun at its used are maximum principle for the weak solutions, com- peak in Sunspot number presumably forcing a cold event parison theorems and scaling techniques. We also analyze in the equatorial Pacific. However both phenomena are self-similar solutions and travelling waves in the borderline also highly auto-correlated. Caution should be exercised case. when testing for statistical significance of the correlation Jonathan Goldfarb, Nathan Mertins of two autocorrelated time series. Even if the two time Florida Institute of Technology series are independent, the solar peak years can coincide jgoldfar@my.fit.edu, nmertins2008@my.fit.edu with cold-ENSO by chance, and then persist for many cycles due to their autocorrelation, before drifting apart. We demonstrate that this is indeed the case using the Quinn PP1 El Nino Index going back to 1525, which is a chronicle of Identifying Fraud with Bayesian Networks observation of El Nino related events, and Sunspot Num- ber (SSN) series, which goes back to 1750. Appropriate Detecting fraud, waste, and abuse in healthcare is an im- statistical tests are suggested that can test for correlation portant topic. Our approach aims to identify anomalies in taking into account autocorrelation and are applicable to medical insurance claims data by combining a prior fraud the shorter instrumental records. There is so far no solar likelihood rating with Bayesian network classification. We peak-La Nina connection found that is statistically signifi- calculate the probability of an insurance claim with the cant at 95% confidence level. help of a Bayesian network and compare this probability with the probabilities of other claims. By assuming that Eddie Haam most insurance claims are legitimate, we can use this com- Harvard University parison to tag low probability claims for further investiga- [email protected] tion. Ka-Kit Tung Ryan Grout University of Washington Brigham Young University [email protected] [email protected] PP1 PP1 Topic Analysis and Grouping of Insurance Claims Minimizing Rational Functions by Exact Jacobian SDP Relaxation Applicable to Finite Real Singu- Latent Semantic Analysis and Latent Dirichlet Allocation larities are fairly new tools for document and topic analysis. With some simple modifications, these tools can be used for This paper consider the minimization of rational functions grouping clusters of medical insurance claims to get some with or without polynomial constraints. We reformulate interesting results. This process of grouping claims is also this problem as polynomial optimization by homogeniza- helpful in building models for disease progression. Our tion. We give some conditions under each of which we goal with these tools is to better predict future medical show the equivalence of these two optimizations. As a 112 AN12 Abstracts costs given a patient’s claim history. PP1 AWM - Inferring Gang Affiliation for Violent Danielle Hanks, Mason Victors Events with Incomplete Data Brigham Young University [email protected], [email protected] Data sets are often plagued with portions of incomplete data. In this case, the data are assumed to be associated with one of N self-exciting point processes that lie on a PP1 network. The time and geographical location for all events Computation and Analysis of Evolutionary Game are known, however the process affiliation is not known for Dynamics some events. This work proposes an iterative method with a directly calculable score function assigning weights for Biological species (viruses, bacteria, parasites, insects, process affiliation and approximating the process parame- plants, or animals) replicate, mutate, compete, adapt, and ters. evolve. In evolutionary game theory, such a process is modeled as a so-called evolutionary game. We describe the Rachel Hegemann Nash equilibrium problem for an evolutionary game and University of California, Los Angeles discuss its computational complexity. We discuss the nec- [email protected] essary and sufficient conditions for the equilibrium states, and derive the methods for the computation of the optimal strategies, including a specialized Snow-Shapley algorithm, PP1 a specialized Lemke-Howson algorithm, and an algorithm A Bayesian Approach to Uncertainty Quantifica- based on the solution of a complementarity problem on a tion for Stochastic Epidemic Models simplex. Computational results are presented. Theoretical difficulties and computational challenges are highlighted. We present a method to quantify the uncertainty in predictions made by stochastic models of epidemics. For these Yiping Hao types of simulations random events cause important fac- Department of Mathematics tors, such as epidemic size and duration, to vary over a Iowa State University wide range of values. This makes it difficult for policy mak- [email protected] ers to base decisions on these types of epidemic models. In this research we use Bayesian techniques to construct dis- Wen Zhou tributions for important epidemic quantities from sample Department of Mathematics and Department of Statistics runs of the simulation. Once a distribution is found for Iowa State University an output quantity of interest the quality of the model’s [email protected] predictions can be evaluated. We propose a measure to quantify the effectiveness of a stochastic epidemic models Zhijun Wu predictive ability using these distributions. Iowa State University [email protected] Kyle S. Hickmann,MacHyman Tulane University [email protected], [email protected] PP1 Explicit Update Scheme for Inverse Elliptic Prob- PP1 lems A Family of Euler-Maclaurin Formulae for N-Point We introduce an efficient method to recover piecewise con- Gaussian Quadrature stant coefficients occurring in elliptic PDEs as well as the interface where these coefficients have jump discontinuities. The Euler-Maclaurin Formula is a powerful and well-known We use an output least squares approach with level set and result from classical numerical analysis relating discrete augmented Lagrangian methods. Our formulation incorpo- sums to integrals. One way to establish this equation rates the inherent nature of the piecewise constant coeffi- is by utilizing periodic Bernoulli Polynomials, which can cients, which allows us to obtain an explicit update formula be derived using a generating function, and performing a for them. Numerical examples of Poisson’s equation and straight-forward integration by parts. The obtained for- linear elasticity are given. mula relates the standard trapezoid rule (or the zero-point Gauss Method) of numerical integration to a series of terms Jan Hegemann involving the Bernoulli Numbers, the derivatives of the University of Muenster function at the endpoints and an error term. My aim in University of California, Los Angeles this presentation is to show one can derive an analogous [email protected] formula based on the midpoint (1-point Gauss Method), 2-point Gauss method, and, in turn, a general family of Alejandro Cantarero Euler-Maclaurin formulae for N-Point Gaussian-Legendre UCLA Quadrature. [email protected] Andrew M. Hofstrand Hunter College–City University of New York Casey Richardson [email protected] Johns Hopkins University [email protected] PP1 Joseph Teran A Slow Pushed Front in a Lotka-Volterra Compe- UCLA tition Model [email protected] We study invasion speeds in the Lotka-Volterra competi- AN12 Abstracts 113 tion model when the rate of diffusion of one species is small. University of Texas Our main result is the construction of the selected front Department of Mathematics and a rigorous asymptotic approximation of its propaga- [email protected] tion speed, valid to second order. From a perspective of linear versus nonlinear speed selection, this front provides an interesting example as the propagation speed is slower PP1 than the linear spreading speed. However, our front shares AWM Variance Reduction for Monte Carlo Simu- many characteristics with pushed fronts that arise when the lation for European Call Options Under the Cou- influence of nonlinearity leads to faster than linear speeds pled Additive-Multiplicative Noise Model of propagation. We show that this is a result of the linear spreading speed arising as a simple pole of the resolvent We propose a variance reduction method for Monte Carlo instead of as a branch pole. Using the pointwise Green’s computation of option prices in the context of the Cou- function, we show that this pole poses no a priori obsta- pled Additive-Multiplicative Noise model. Four different cle to marginal stability of the nonlinear traveling front, schemes are applied for the simulation. The methods select thus explaining how nonlinear systems can exhibit slower control variates which are martingales in order to reduce spreading that their linearization in a robust fashion. the variance of unbiased option price estimators. Numer- ical results for European call options are presented to il- Matt Holzer lustrate the effectiveness and robustness of this martingale School of Mathematics control variate method. University of Minnesota [email protected] Wanwan Huang Florida State University Arnd Scheel [email protected] University of Minnesota [email protected] Brian Ewald Department of Mathematics Florida State University PP1 [email protected] Convergence of a Gauss Pseudospectral Method for Optimal Control PP1 A convergence theory is established for approximations of Device Modeling for Organic Solar Cells continuous-time optimal control problems using a Gauss pseudospectral method. Specifically, it is shown that, Organic solar cells (OSCs) have great potential to play an under assumptions of coercivity and smoothness, the important role in addressing our future energy needs. A Gauss pseudospectral method has a local minimizer that drift-diffusion model is developed to describe the dynamics converges in the sup-norm to a local minimizer of the of excitons and free charge carriers in OSC. Our model pre- continuous-time optimal control problem. The convergence dicts the performance of OSC devices by calculating their theory is summarized and examples are provided that agree quantum efficiency and current-voltage curves, as well as with the theoretical results. many other important physical quantities, such as electric field, and the carrier concentration. Hongyan Hou, William Hager Department of Mathematics Lunmei Huang,RobertKrasny University of Florida University of Michigan hhongyan@ufl.edu, hager@ufl.edu Department of Mathematics [email protected], [email protected] Anil Rao Mechanical and Aerospace Engineering Kyle Renshaw University of Florida Department of Physics, University of Michigan anilvrao@ufl.edu [email protected]

Stephen Forrest PP1 Department of Physics, Department of Electrical A Fast Spectral Algorithm for the Quantum Boltz- Engineering mann Collision Operator [email protected] Numerically solving the quantum Boltzmann equation (Nordheim-Uehling-Uhlenbeck equation) is challenging due PP1 to the multidimensional structure of the collision integral. Shortest Path for High-Dimensional Data Repre- Comparing to its classical counterpart, the main difficulty sentation comes from the cubic interaction term. We propose a fast spectral algorithm based on a special decomposition of the We show that the power-weighted shortest path length collision kernel. Numerical results in 2-D and 3-D for both through random points reflects metric deformation affected the Bose gas and the Fermi gas are presented to illustrate by the probability density function. Such metric defor- the accuracy and efficiency of the method. mations adapt the data structure of the random sample for machine learning purposes. We reason how the power- Jingwei Hu weighted shortest path length achieves asymptotic consis- The University of Texas at Austin tency in data clustering and connects to classical single- [email protected] linkage clustering. Furthermore, the deformation metric framework will be proposed to encompass and connect Lexing Ying 114 AN12 Abstracts

spectral methods and shortest paths. blocks in ( ) time, where nzb is the number of non– zeros in aO block,\‡ is developed. Performance comparisons Sung Jin Hwang with Intel MKL sparse BLAS and with standard CSR and University of Michigan BSR implementations are presented. [email protected] Ramaseshan Kannan Steven Damelin University of Manchester, UK and Arup Ltd. UK Georgia Southern University [email protected] [email protected] PP1 Alfred Hero University of Michigan AWM - A Stochastic Delay Model for Pricing [email protected] In the business world, in addition to equity, corporate bonds are also a main source of funds for many com- PP1 panies. However, depending on the ability of the managers or other reason, it can happen that a company faces Analysis of Optimal Mortgage Termination Under bankruptcy. When a company becomes insolvent, the stock the Cox-Ingersoll-Ross Model value decreases to zero and the equity-holders lose their We consider mortgage contracts where the borrower has investments. Naturally, debt-holders would like to make the option to pay the outstanding balance at any time. sure that their investments are secured. In order to sup- In theory, the decision to terminate depends on the yield port companies in this situation and encourage new in- curve. Assuming the Cox-Ingersoll-Ross model for inter- vestments, some government agencies provide loan guar- est rates, the problem can be formulated as a variational antees. In this presentation, we give a formula for the inequality or an equivalent free boundary problem. Exis- price of an option used for the pricing of corporate default- tence and uniqueness of a solution as well as regularity of able bonds satisfying a stochastic delay differential equa- the free boundary will be presented. tion (SDDE). Assuming that the company value satisfies a SDDE as above, we evaluate government loan guarantees Christopher S. Jones for companies in financial distress. University of Pittsburgh [email protected] Elisabeth Kemajou Southern Illinois University Carbondale [email protected] PP1 Computing Characteristic Classes in Algebraic Ge- PP1 ometry Deforming Cylindrical Hypersurfaces in Hyper- Characteristic classes, i.e., Chern and Segre classes of va- bolic Space by Their Harmonic Mean Curvature rieties are important invariants in algebraic geometry. We present a method to compute them which works either We show that under harmonic mean curvature flow cylin- symbolically using Gröbner bases or numerically using ho- drically symmetric hypersurfaces about a closed geodesic in motopy continuation methods for polynomial equation sys- hyperbolic space contract to the geodesic and the shape of tems. It has been implemented using Macaulay2 and the evolving hypersurface becomes like a round cylinder. Bertini. A novel approach is developed to distinguish the radial and angular principal curvatures of the evolving hypersur- Christine Jost face by their qualitative behavior using parabolic maximum Stockholm University principle. The evolution equation is a fully nonlinear de- [email protected] generate parabolic PDE. Chris Kim David Eklund University of Minnesota Institut Mittag-Leffler [email protected] [email protected] Robert Gulliver Chris Peterson University of Minnesota Colorado State University School of Mathematics [email protected] [email protected]

PP1 PP1 Minimizing Communication in Sparse Matrix- Deforming Cylindrical Hypersurfaces in Hyper- Vector Multiplication Using a Novel Representa- bolic Space by their Harmonic Mean Curvature tion We show that under harmonic mean curvature ﬂow rota- We consider the problem of multiplying a sparse matrix n n n tionally symmetric hypersurfaces about a closed geodesic in A R × with a dense matrix X R × with the aim of ∈ ∈ hyperbolic space contract to the geodesic and the shape of increasing register reuse. A new block compressed format the evolving hypersurface becomes like a round cylinder. that is shown to have less loads compared with compressed A novel approach is developed to distinguish the radial sparse row and block compressed sparse row formats, is and angular principal curvatures of the evolving hypersur- proposed. The format stores blocks as bitmaps and is less face by their qualitative behavior using parabolic maxi- sensitive to the non–zero structure (in comparison with mum principle. The evolution equation is a fully nonlinear blocked formats). A C++ based algorithm that decodes AN12 Abstracts 115 parabolic PDE. [email protected]

Christopher Kim Rafail Abramov Cornell University Department of Mathematics, Statistics and Computer [email protected] Science University of Illinois at Chicago Robert Gulliver [email protected] University of Minnesota School of Mathematics [email protected] PP1 Accuracy-Enhancing Moving Grid Method for Stratified Flow Calculations PP1 Mechanism of Default Contagion with Graph Rep- We present the moving grid method an r-adaptive dis- resentations cretization of the underlying system of PDEs. This grid adaptivity allows to dynamically increase resolution in the We consider a mechanism of contagion of default following areas of interest (an interface or a rapid flow variation) default of Greek banks, in which creditor banks in Euro- while keeping the size of computational mesh unchanged. pean countries give proportional haircuts to their creditors, The method was tested on several stratified flow configu- in a sequence of stages. Net liabilities are represented by rations with sharp density discontinuities and consistently simple weighted directed graphs and bilateral liabilities by outperformed its static-grid counterpart. Scalability and multigraphs. We compare with current data. This includes parallel performance of our solver on a supercomputer will work by undergraduate student Shuangshi Han, with fac- be discussed. ulty sponsor Katherine Kime. Sergey Koltakov Katherine Kime Stanford University University of Nebraska at Kearney [email protected] Department of Mathematics and Statistics [email protected] Oliver Fringer Environmental Fluid Mechanics Laboratory Shuangshi Han Stanford University University of Nebraska Kearney [email protected] Lanzhou University of Finance and Economics (P.R. China) [email protected] PP1 Reduced Order Modeling for Dynamic Earthquake Simulations PP1 A Delay-Differential Equation Approach to Deter- Motivated by the devastating earthquake and tsunami last mine Insulin Sensitivity year in Japan, we explore the use of reduced order models for subduction zone, megathrust earthquake simulations. After initial research by Bergman et al. (1985) using math- The technique we employ uses a few parallel, full physics ematical models to determine insulin sensitivity in diabet- simulations to build a surrogate model which can be sam- ics, the insulin sensitivity question has largely been ignored pled to explore the parameter space. The quantities of in preference of directly modeling the glucose/insulin dy- interest are the total slip on the fault, slip at the trench namics in the human body. These models have greatly axis (where the fault meets the seafloor), and seafloor de- increased in their complexity and ability to explain clin- formation. ically observed data. This research aims to reopen the insulin sensitivity question using the more sophisticated Jeremy E. Kozdon techniques that have recently been applied to this field. Stanford University Geophysics Stephen M. Kissler [email protected] University of Colorado Boulder [email protected] Paul Constantine Stanford University PP1 Mechanical Engineering [email protected] Linear Response Closure Approximation for Mul- tiscale Systems PP1 Many physical processes involve multiscale dynamics, characterized by time and space scale separation with a large A POD Study for a Coupled Burgers Equation set of rapidly evolving variables and a smaller set of slowly We study the coupled Burgers Equation that share similari- evolving variables. We present a method to obtain a closed ties with the Boussinesq equations that are commonly used system for the slow variables, requiring only a simple cal- in thermal-fluid dynamics. A training set” of FE solutions culation of statistics of the fast variables and use of the is generated and a POD model reduction scheme is applied. fluctuation-dissipation theorem. We apply this method to However, the actual dynamics of the system can vary from a two-scale model with linear coupling. the dynamics that are contained in the training set. Hence, Marc Kjerland we investigate the dependence of the reduced order model University of Illinois at Chicago on the input parameters(especially the Reynolds number). 116 AN12 Abstracts

PP1 Vector-Valued Parametric Kernel-Based Interpola- Boris Kraemer tion for Two-Dimensional Facial Animations Virginia Tech [email protected] This paper explores a scattered-data, interpolation-based approach, which uses a vector-valued parametric interpo- John A. Burns lation method for creating tween frames. Using the blend- Virginia Tech shapes method, a 27-frame, two-dimensional, facial anima- Interdisciplinary Center for Applied Mathematics tion was generated. Key-frames 1, 3, and 27 were then used [email protected] to produce similar animations with the following interpolation methods: Gaussian RBF,Inverse multiquadratic, C2 Mate rn, Multiquadratic, and the Distance Function. PP1 All methods were then compared and performance adjust- Approximating the Singularities of a Function by ments made. Means of Its Fourier-Jacobi Coefficients: An En- hanced Power Method Barrett A. Leslie Illinios Institute of Technology We modify the method suggested earlier by us and over- [email protected] come its main deficiency. The method enables the approximation of the locations of jump discontinuities of a function, one by one, by means of ratios of so called higher order PP1 Fourier-Jacobi coefficients of the function. It is shown that A Neuronal Network Model of Drosophila Anten- the location of singularity of a piecewise constant function nal Lobe with one discontinuity is recovered exactly and the locations of singularities of a piecewise constant function with We construct a conductance based neuronal network model multiple discontinuities are recovered with exponential ac- of the Drosophila antennal lobe with the aim of proposing curacy. Unlike the previous one, the modified method is possible interactions within the antennal lobe that account robust, since its success is independent of whether or not for the variety of projection neuron activity observed in a location of the discontinuity coincides with a root of a experimental data. Computational studies using olfactory Jacobi polynomial. In addition, some numerical examples receptor neuron inputs that mimic experimental recordings are presented. demonstrate the possible roles of excitatory local neurons in spreading excitation among glomeruli and in recruiting George Kvernadze inhibition. Weber State University [email protected] Dori Luli Arizona State University [email protected] PP1 Computational Docking of Molecular Wires to the Sharon M. Crook Reaction Center of Rhodobacter Sphaeroides Dept of Mathematics and Statistics & School of Life Sciences Given the worldwide interest in renewable energy, scien- Arizona State University tists have been exploring the possibility of using bacterial [email protected] photosynthetic reaction centers to build a new generation of highly efficient photovoltaic devices. To build such devices, molecular wires (MWs) that serve as good conduc- PP1 tors to transport electrons from and to the reaction cen- SmartGrid Pricing and Consumer Privacy Con- ters are needed. The MWs must dock at specific binding straints sites within the reaction centers. We explore computational models of docking MWs to the reaction centers. The widespread adoption of SmartGrid technologies promises to radically change the way electricity is delivered Byong Y. Kwon and priced, in part by enabling the collection of fine-grained George Mason University data on customer power consumption. Unfortunately, this [email protected] usage data can be linked by adversaries to other behaviors, seriously threatening consumer privacy. We explore schemes for maintaining privacy, investigate tradeoffs be- PP1 tween privacy and fairness, and model the game that arises Mixed Methods of Viscoelastic Wave Propagation between providers and strategic, privacy-conscious electricity consumers. We present new mixed finite element methods for wave propagation in viscoelastic solids. We use recently devel- Shaudi Mahdavi Hosseini oped mixed finite elements for elasticity with weak sym- University of Pennsylvania metry of stress for which we have proved optimal a priori [email protected] error estimates. We present numerical results which support our error analysis and demonstrate the performance of the methods on problems of practical interest. PP1 Massively Parallel Jeonghun Lee Adaptive Fast Multipole Method for Volume Po- University of Minnesota tentials [email protected] FMM is traditionally used to solve N-body problems with AN12 Abstracts 117 point sources. Here, we present a FMM based solver for is based on a consistency condition that reproduces ex- volume potentials in 3D, using piecewise polynomials and actly the integration by parts formula for polynomials of adaptive octree to represent source distribution and output degree higher than one. This formulation requires different potential. We use OpenMP and MPI for shared and dis- kinds of degrees of freedom, like moments of polynomials tributed memory parallelism, and BLAS, FFTW and SSE or normal derivatives at edges. Optimal convergence rate is optimizations are used to get high FLOP rates. We present proved in a mesh-dependent H 1 norm for meshes with very convergence results for various kernels and show scalability general shaped elements and experimental results confirm to over 100,000 processor cores. this behavior. This presentation is based on joint works with L. Beirao da Veiga and K. Lipnikov. Dhairya Malhotra Institute of Computational Engineering and Sciences Gianmarco Manzini The University of Texas at Austin Los Alamos National Laboratory [email protected] [email protected]

George Biros University of Texas at Austin PP1 [email protected] Meshfree Quadratures for Planar Regions Radial Basis Function (RBF) methods have gained signif- PP1 icant attention in the last decade as robust and highly A Network-Patch Model for the Transmission and accurate alternatives to classical polynomial methods for Emergence of Mosquito-Borne Pathogens function approximation. Here, we present a novel quadrature scheme to approximate integrals in smooth planar re- We derive a network-patch model for the spread of gions using RBFs. Preliminary numerical results show the mosquito-borne diseases that couples to agent-based spa- scheme to be spectrally (exponentially) convergent and ro- tial epidemic models. The new model accounts for environ- bust with respect to node location. mental factors, such as rainfall and temperature, and for variations in mosquito-related parameters, including the Jordan M. Martel emergence rates and incubation period of the pathogen. It University of Colorado at Boulder considers spatial heterogeneity in vector populations with- Department of Applied Mathematics out modeling individual mosquitoes, thus reducing compu- [email protected] tational expense while maintaining accuracy. Our simulations quantify the importance of heterogeneity in predict- PP1 ing the spread of vector-borne diseases. Numerical Modeling of Flow Over Flexible Vegeta- Carrie A. Manore,JamesHyman tion Tulane University [email protected], [email protected] Understanding the interaction of currents, waves, and storm surge with coastal vegetation is important for coastal and environmental engineering. The existence of vegeta- Christopher Mores tion greatly affects flow resistance, but modeling vegetation Louisiana State University at small scales is challenging. In particular, plant flexibil- [email protected] ity is often an important factor in the resistance characteristics. We numerically model the interaction of complex Sarah DelValle, Susan Mniszewski flow fields with flexible vegetation, utilizing the immersed Los Alamos National Laboratory boundary method and stabilized finite element methods on [email protected], [email protected] highly-resolved computational meshes.

Kyle S. Hickmann Steven A. Mattis Tulane University The Institute for Computational Engineering and Sciences [email protected] University of Texas at Austin [email protected] Rebecca Christofferson Louisiana State University Clint Dawson [email protected] Institute for Computational Engineering and Sciences University of Texas at Austin Helen Wearing [email protected] University of New Mexico [email protected] Christopher Kees US Army Engineer Research and Development Center Reid Priedhorsky [email protected] Los Alamos National Laboratory [email protected] Matthew Farthing US Army Engineer Research and Development Centerq [email protected] PP1 High-Order Nodal Formulation of the Mimetic Fi- nite Difference Method for Elliptic Problems PP1 Systems of Conservation Laws for Thermodynam- The high-order nodal formulation of the Mimetic Finite ically Consistent Adsorption with Subscale Diffu- Difference Method for two-dimensional elliptic problems 118 AN12 Abstracts sion Rockefeller University Laboratory of Molecular Genetics Multicomponent adsorption is typically described by a [email protected] system of conservation laws in which the nonlinear flux terms come from explicit functional relationships called Christoph Borgers isotherms. Unfortunately the most popular extended Tufts University Langmuir isotherm is thermodynamically inconsistent. We [email protected] discuss analysis and numerical approximation of multicomponent adsorption system where the thermodynamically consistent isotherms are given only implicitly. Addition- PP1 ally, we consider subscale diffusion coupled to the transport Highly Accurate 3D Nearly Singular Integration and the associated nonlocal in time effects which smooth out the solutions. Boundary integral methods often give rise to nearly singular integrals in which the integrand is very steep at a Francis P. Medina, Malgorzata Peszysnka point. Standard integration techniques on such integrals Oregon State University suffer from low accuracy. We develop a highly accurate [email protected], method for 3D surface integrals with near singularities. [email protected] The method involves isolation and smoothing of the near singularity with two changes of variables. Stokes flow is PP1 used as a test case. Multiscale Seismic Imaging Mike Nicholas Carthage College Imaging the Earth’s interior requires estimation of mechan- [email protected] ical parameters (velocities and densities) that describe a region of the subsurface. Numerical solution of the wave equation involves discretization and a choice of a particular PP1 scale of interest. The Earth contains interesting features at Application of Fractional Calculus to Domain Wall many scales (from the millimeter to the kilometer scale). Motion We describe an algorithm for solving the wave equation in which sub-wavelength heterogeneities are captured and The equation of motion carrying the domain wall motion incorporated into the macro-scale solution. inside a ferromagnetic material has been solved fractionally using Laplace transform technique for a fractional deriva- Susan E. Minkoff tive of the damping term. The solution reduces to the well University of Maryland, Baltimore County known result of the simple harmonic oscillator when alpha Dept of Mathematics and Statistics =0 and to the damping result when alpha =1 where the sminkoff@umbc.edu damping term is proportional to the viscosity of the suspension. Results for different values of alpha and damping PP1 ratio are drawn and discussed under special initial conditions. Pandemic Influenza:Best Strategies to Minimize Transmission Despite Parameter Uncertainty Abdalla A. Obeidat, Wesam Al-Sharoa, Manal Al-Ali Jordan University of Science and Technology When under the threat of Pandemic Influenza countries [email protected], [email protected], etu- decide to take certain measures in order to contain the [email protected] transmission of the virus. Given that the parameters of the transmission might not be accurate, the scenarios might be far from reality. We employed the robust optimization PP1 framework to determine the most efficient strategies that Applying Stochasticity to Models of Rotavirus Dis- mitigate the adverse effects of Pandemic Influenza. ease and Vaccination Romarie Morales Despite significant advances in water quality and hygiene Arizona State University around the world, rotavirus diarhhea continues to be the [email protected] main cause of severe gastroenteritis across the globe. A two-strain continuous-time Markov chain model of ro- PP1 tavirus infection is formulated. This model considers natural immunity from subsequent infections and the effects of The Case for Exponential Time Differencing for vaccination are analyzed. Although, the disease can not be Neuronal Network Simulations completely eradicated without perfect vaccination, differ- Exponential time differencing (ETD) has been used for ent scenarios for the reduction of morbidity and mortality Hodgkin-Huxley-like ODEs by several authors, and is the are evaluated and compared. default integrator in the popular neuronal simulation pack- Omayra Ortega age GENESIS. We show that the effectiveness of ETD for Arizona State University Hodgkin-Huxley-like ODEs comes from the fact that it pre- [email protected] vents overshoot during the very fast rising phase of the action potential, allowing simulations that sacrifice accurate resolution of action potentials without significant loss PP1 of overall accuracy. We also propose a second-order ETD Cost Benefit Analysis of Vector Control Strategies scheme. for Dengue in Bangkok Alexander Nectow We use the data from Queen Sirkit National Institute of AN12 Abstracts 119

Child Health (QSNICH) from 1973-1999 to estimate the droplets on superhydrophobic surfaces by presenting a nu- true prevalence of Dengue disease in Bangkok, Thailand merical study that finds MEPs in configuration space, crit- using Monte Carlo Markov Chain Simulations. We present ical droplet morphologies and free-energy barriers which preliminary results of a cost benefit analysis on three vector in turn give us a greater understanding of the free-energy control strategies: Larvicide and Adult control, Blocking landscape. transmission and Reducing mosquito biting. Kellen Petersen Abhishek Pandey Courant Institute of Mathematical Sciences Clemson University New York University [email protected] [email protected]

Anuj Mubayi Northeastern Illinois University PP1 [email protected] Exact Chirped Soliton Solutions for 1D Gross- Pitaevskii Equation with Time-Dependent Param- Jan Medlock eters Oregon State University The Gross-Pitaevskii equation describing the dynamics of a [email protected] Bose-Einstein condensates at absolute zero temperature, is a generalized form of the Nonlinear Schroedinger equation. PP1 In this work, the exact one bright soliton solution of 1D GP equation with time-dependent parameters is directly The Behaviour of a Thin Ridge Or Rivulet of Fluid obtained by using the well known Hirota method under the Two problems involving a thin ridge or rivulet of fluid are same conditions as Ref (10). In addition the two-soliton discussed. Firstly, a ridge on an inclined planar substrate solution is also constructed effectively. subject to an external airflow directed tangentially to the Zhenyun Qin substrate is considered; in particular, the effect of increas- Fudan university ing the strength of the airflow is analysed. Secondly, the [email protected] gravity-driven draining of a rivulet of fixed width around a large horizontal cylinder is considered; qualitatively different behaviour is exhibited depending on whether the Gui Mu rivulet is “narrow’ or “wide.’ Qujing Normal University [email protected] Colin Paterson, Stephen Wilson, Brian Duffy University of Strathclyde [email protected], [email protected], PP1 b.r.duff[email protected] Small Steady Self-Similar Inviscid Flow We consider solutions of the 2-d compressible Euler equa- PP1 tions that are steady and self-similar. Examples arise nat- Use of the String Method to Find Minimal Energy urally at interaction points in genuinely multi-dimensional Paths of Droplets on Superhydrophobic Surfaces flow, and we are able to classify all possible solutions that are L∞-close to a constant supersonic background. As a Interest in superhydrophobic surfaces has increased due to special case we prove that solutions of 1-d Riemann prob- a number of interesting advances in science and engineer- lems are unique in the class of small L∞ functions, and ing. Here we use a diffuse interface model for droplets more generally that all solutions are necessarily BV . on topographically and chemically patterned surfaces in the regime where gravity is negligible. We then apply Joseph P. Roberts, Volker W. Elling the constrained string method to examine the transition of University of Michigan droplets between different metastable/stable states. The [email protected], [email protected] string method finds the minimal energy paths (MEPs) which correspond to the most probable transition pathways PP1 between the metastable/stable states in the configuration space. In the case of a hydrophobic surface with posts Computing An Approximation to the Helmholtz of variable height and separation, we determine the MEP Equation with a High Contrast Thin Scatterer corresponding to the transition between the Cassie-Baxter Present and Wenzel states. Additionally, we realize critical droplet In this poster, we present new computations stemming morphologies along the MEP associated with saddle points from the work of Moskow, Santosa, and Zhang [S. Moskow, of the free-energy potential and the energy barrier of the F. Santosa, J. Zhang. An Approximate Method for Scat- free energy. We analyze and compare the MEPs and free- tering by Thin Structures. SIAM J. Appl. Math. 66, pp. energy barriers for a variety of surface geometries, droplets 187-205]. We compute solutions to the Helmholtz equation sizes, and static contact angles ranging from partial wetting with a high contrast thin scatterer present where the di- to complete wetting. We also introduce an unbiased double aelectic constant is discontinuous. We then compare the well potential in the diffuse interace model by introducing accuracy of a leading term approximation under such con- a chemical potential that is fixed for a given simulation. ditions. We find that the energy barrier shifts toward the Wenzel state along the MEP as the height of the pillars increases Scott Rome in the topographically patterned case while a shorter en- Drexel University ergy barrier exists and is more centered along the MEP Department of Mathematics for pillars of shorter height. More importantly, we demon- [email protected] strate the string method as a useful tool in the study of 120 AN12 Abstracts

PP1 Modularity Maximization Snakes and Ladders: Stability of Fronts and Pulses Community detection through modularity maximization, The subject of this poster are localized patches composed of is an important objective in large-scale network analysis. spatially periodic structures. These patterns often exhibit However, the value of the modularity and consequently the snaking: in parameter space, the localized states lie on a community membership is affected by vertex ordering of vertical sine-shaped bifurcation curve so that the width of the network. We define a stable community as an invari- the underlying periodic pattern increases as one moves up ant group of vertices that are always assigned to the same along the bifurcation curve. The issue addressed here is the community. We present an algorithm to identify stable stability of these structures as a function of the bifurcation communities and show that combining stable communities parameter. as a preprocessing step leads to higher modularity. . Bjorn Sandstede Sriram Srinivasan,SanjuktaBhowmick Brown University Department of Computer Science bjorn [email protected] University of Nebraska, Omaha [email protected], [email protected] PP1 AWM Physiologically-Based Pharmacokinetic (pbpk) Modeling of Metabolic Pathways of Bro- PP1 mochloromethane in Rats. Quantized Vortex Dynamics in Complex Ginzburg- Landau Equation in Bounded Domain An updated PBPK model for bromochloromethane is generated and applied to two different metabolic hypotheses: In this presentation, I will present efficient and accurate 1) a two-pathway model using CYP2E1 and glutathione numerical methods for studying the quantized vortex dy- transferase enzymes, and 2) a two-binding site model where namics and their interaction of the two-dimensional (2D) metabolism occurs only with CYP2E1. Our computer sim- complex Ginzburg-Landau equation (CGLE) with a dimen- ulations show that both hypotheses describe the experi- sionless parameter ε>0 in bounded domains under either mental data in a similar manner. In addition, we explore Dirichlet or homogeneous Neumann boundary condition. I the sensitivity of different parameters for each model using will begin with a review of various reduced dynamical laws our obtained optimized values and explore their applica- for time evolution of quantized vortex centers and show tions to risk assessment. how to solve these nonlinear ordinary differential equations numerically. Then, I will present some results on the Megan Sawyer quantized vortex interaction under various different initial North Carolina State University setup, and identify the cases where the reduced dynamical [email protected] laws agree qualitatively and/or quantitatively as well as fail to agree with those from CGLE. Some other interesting phenomena will also be presented. PP1 On the Spectral Stability of Soltion Solutions of the Qinglin Tang Vector Nonlinear Schrödinger Equation National University of Singapore Singapore We consider a system of coupled cubic nonlinear [email protected] Schrödinger (NLS) equations

2 n PP1 ∂ψj ∂ ψj 2 i = + αjk ψk ψj j =1, 2,...,n ∂t − ∂x2 | | Statistical Test and Simulation for Multi-Scale k=1 Computation of 2D Polymer Model where αjk = αkj are real. The stability of solitary wave Multi-scale computation is an accurate and highly efficient solutions is examined numerically using Hill’s method (De- computing method involving simulation and analysis of in- coninck, B. and J. N. Kutz. J. Comput. Phys., 219: 296- formation at different resolutions. Due to its common ap- 321, 2006). Our results extend the analysis of Nguyen plications, many mathematicians expect to ameliorate the (Commun. Math. Sci., 9: 997-1012, 2001.) to incorpo- levelofaccuracyandefficiencytoanevenhigherlevel.One rate solitons with nontrivial phase profile. potential way is to analyze the statistics of data, and en- Natalie Sheils hance the algorithm by knowing the trend of data. Here Department of Applied Mathematics we discuss the statistical methods involving in 2D polymer University of Washington model. [email protected] Sunli Tang Rensselaer Polytechnic Institute Bernard Deconinck Department of Mathematical Sciences University of Washington [email protected] [email protected]

Nghiem Nguyen, Rushun Tian PP1 Utah State University An Analytical Approach to Green Oxidation [email protected], [email protected] In this poster, we study the problem of suicidal inactivation of oxidation catalysts. We formulate a system of differen- PP1 tial equations that models chemical reactions and analyze Detecting And Using Stable Communities For its numerical and analytical properties. Noticing its sim- AN12 Abstracts 121 ilarity with Michaelis-Menten system, we have been able position is one of the most commonly used methods to gen- to develop quasi-state approximation that together with erate reduced-order models for turbulent flows dominated perturbation techniques has allowed us to derive an ap- by coherent structures. To balance the low computational proximate solution. The main goal is to estimate the rates cost required by a reduced-order model and the complexity of the reactions for deeper understanding of the system. of the targeted turbulent flows, appropriate closure modeling strategies need to be employed. In this paper, we will Diego Torrejon present several new nonlinear closure methods for proper George Mason University orthogonal decomposition reduced-order models. We will [email protected] also present numerical results for the new models used in realistic applications such as energy efficient building design and control, and climate modeling. PP1 Conditional Stochastic Simulations and Error Esti- Zhu Wang, Traian Iliescu mates for Flow and Transport in Porous Media Department of Mathematics Virginia Tech We use stochastic parameterizations to describe the prop- [email protected], [email protected] erties of the coefficients of flow and transport model; then we use stochastic collocation or Monte Carlo simulations Jeff Borggaard to solve the system of PDEs. The novelty is that we are Virginia Tech able to include prior data for which conditional parame- Department of Mathematics terizations are obtained. We provide comparison with un- [email protected] constrained simulations. Additionally, we derive error estimates for the quantities of interest in the coupled system. Imran Akhtar Virginia Tech Veronika S. Vasylkivska [email protected] Department of Mathematics Oregon State University [email protected] PP1 Computing Positive Semidefinite Minimum Rank Mina E. Ossiander for Small Graphs Math Dept The positive semidefinite minimum rank (mr+)ofasim- Oregon State University ple graph G is the smallest possible rank over all posi- [email protected] tive semidefinite real symmetric matrices whose ijth ( i not equal to j) entry is nonzero whenever ij is an edge, Malgorzata Peszynska and zero otherwise. We programmed an implementation Department of Mathematics of known bounds in the open-source mathematical software Oregon State University Sage. The program, along with orthogonal representations, [email protected] establishes mr+ for all graphs of order 7 or less. Nathan Warnberg,StevenOsborne PP1 Iowa State University A Method of Lines Approach to Solving Pdes on [email protected], [email protected] Surfaces Partial differential equations (PDEs) posed on surfaces PP1 appear often in mathematical modelling. The Closest Improving Hidden Markov Models that use Classi- Point Method is a numerical technique for solving these fied Observations types of equations, by embedding the surface in a higher- dimensional space. We present a new way to formulate A Hidden Markov Model looks at observations generated an embedding equation which leads to a simple method of by a ”hidden” Markov process. When the observed data lines approach. We also include a variety of computational is complex, it must first be classified before it can be used examples. in such a model. We use classification methods borrowed from natural language processing to prepare observation Ingrid Von Glehn data to train a Hidden Markov Model. As an example we University of Oxford consider grouping clients based on health insurance claims. [email protected] Matthew Webb, Danielle Hanks, Mason Victors, Jared Colin Macdonald Webb Oxford University Brigham Young University [email protected] [email protected], [email protected], ma- [email protected], [email protected]

PP1 Proper Orthogonal Decomposition Reduced Order PP1 Models For Complex Flows Improving Certainty Using Informed Markov Mod- els Reduced-order models are frequently used in the simulation of complex flows to overcome the high computational Hidden Markov Models are a powerful tool for analysis cost of direct numerical simulations, especially for three di- when a Markov Process is not directly observable. How- mensional nonlinear problems. Proper orthogonal decom- ever, in a complicated model the sequence of observable 122 AN12 Abstracts states with maximum likelihood may have a probability Boise State University, Boise ID very near to zero. We examine how these probabilities are [email protected], [email protected] affected as we add information to the model, either via the hidden Markov process, or through the observation probability matrix. PP1 Grain Boundaries in Turing Patterns Jared Webb Brigham Young University Our main results show the existence of grain boundaries, [email protected] describe their shapes, and exhibit bifurcations where grain boundaries split into pairs of concave and convex disclina- tions. Our work is split into two parts. In the first part, we PP1 show that universally, for any pattern-forming system near Diversification Effect of Distributed Solar Energy onset, that is, for small-amplitude patterns, the shape of Upon Energy Generation Volatility grain boundaries is determined by a system of coupled ordinary differential equations. Those equations are obtained High levels of volatility are a significant impediment to the by recently developed reduction theorems for ill-posed el- integration of solar energy into the electric grid. Combining liptic partial differential equations. The key observation is the output of geographically distributed solar systems re- that those reduced equations are universal once put in nor- sults in a diversification effect that reduces the aggregated mal form, that is, after a suitable change of coordinates. volatility. This diversification effect has been previously They contain only very few parameters and their solutions proposed, but it has undergone limited validation under can be fully analyzed despite the fact that the dimension of controlled conditions. We have quantified and validated the system of equations is at least 12, and tends to infinity this diversification effect across a large fleet of distributed when the angle between rolls becomes small. solar installations in the field using highly granular data. Qiliang Wu Matthew K. Williams, Shawn Kerrigan, Alex Thornton, University of Minnesota Sergey Koltakov [email protected] Locus Energy [email protected], Arnd Scheel [email protected], [email protected], University of Minnesota [email protected] School of Mathematics [email protected] PP1 Restructuring the Ppm Gas Dynamics Algorithm PP1 for Many-Core Cpu Devicces Parallel Cardiac Image Segmentation with Random The latest CPU devices contain a large number of cores Projection Tree (over 50 on Intels new MIC processors) that all must work Due to noise, artifacts and high accuracy requirement, together in order to achieve the best performance. Tech- medical image segmentation is always a challenging prob- niques and tools for restructuring fluid dynamical com- lem. We proposed a data-driven approach, which classified putations to allow all the cores on a single CPU chip to each pixel based on the similarity along the low dimen- work cooperatively on data that they share in the proces- sional parameterization of the feature space. In particu- sor caches will be described, using the PPM gas dynamics lar, our framework discovers the intrinsic structure of high algorithm as an example. dimensional wavelet features using a random projection Paul R. Woodward tree structure, which is built on top of MPI and OpenMP Laboratory for Computational Science and Engineering for massive dataset, and shows excellent scalability and University of Minnesota speedup. [email protected] Bo Xiao School of Computational Science and Engineering Jagan Jayaraj, Pei-Hung Lin Georgia Institute of Technology University of Minnesota [email protected] [email protected], [email protected] Geroge Biros PP1 The Institute for Computational Engineering and Sciences University of Texas at Austin A Radial Basis Function Partition of Unity Method [email protected] for Transport on the Sphere

The transport process dominates geophysical fluid motions PP1 on all scales making the numerical solution of the transport problem fundamentally important for the overall accuracy Local Convergence of Newton-Type Methods for of any flow solver. We present a new high-order, computa- Degenerate Eigenvalues of Nonlinear Algebraic tionally efficient method for this problem that uses radial Eigenvalue Problems basis functions in a partition of unity framework. Results We analyze the local convergence rates of several Newton- of the method are presented for several well-known test type methods for the computation of a semi-simple or de- cases that probe the suitability of numerical methods for fective eigenvalue of general nonlinear algebraic eigenvalue modeling transport in spherical geometries. problems of the form T (λ)v = 0. We show that the con- Grady B. Wright,KevinAiton vergence for semi-simple eigenvalues is similar to that for Department of Mathematics simple ones. For defective eigenvalues, Newton-type meth- AN12 Abstracts 123 ods converge only linearly. A class of accelerated methods stability, accuracy and speed. is proposed and shown to exhibit quadratic convergence. Maryam Yashtini Fei Xue University of Florida Temple University Mathematics Department [email protected] myashtini@ufl.edu

Daniel B. Szyld William Hager, Yumni Chen Temple University Department of Mathematics Department of Mathematics University of Florida [email protected] hager@uﬂ.edu, [email protected]ﬂ.edu

Xiaojing Ye PP1 School of Mathematics Computation of Harmonic Forms of the Vector Georgia Tech Laplacian [email protected] The vector Laplacian arises in electromagnetics and other applications, and an important role is played by its null PP1 space, the space of harmonic forms. I present an algorithm Stochastic Simulation and Power-Law Relaxation to compute a basis of this space. The algorithm combines of Highly Entangled Wormlike Micellar Solutions mixed finite elements for discretization, algorithms from computational geometry to analyze the topology, and a Wormlike micelles, long flexible self-assembled aggregates variation of the power method suitable for multiple eigen- of surfactant molecules, form entangled networks in solu- values. I also consider various ways to approximate localize tion. These mixtures exhibit two relaxation mechanisms, the harmonic basis functions. reptation and reversible breaking. Experiments in concentration regimes in which the worms are highly entangled Bo Yang show power law stress relaxation instead of the exponential School of Mathematics, University of Minnesota relaxation predicted by most traditional models (Johnson- [email protected] Segalman, Giesekus, VCM). In this poster, we present flow predictions, using stochastic simulations, to understand the PP1 mechanisms of the power-law relaxation regime. AWM - A New Approach to Understanding the Yun Zeng Dynamics of the Formation of Magnetic Domains Department of Mathematical Sciences, University of Delaware Traditionally, ferromagnetism is studied using the Ising Newark, DE 19716, USA model, which is exactly solvable in one or two dimensions [email protected] and of limited use in the infinite- dimensional mean field case. While preserving the classic energy arguments, our model uses techniques previously applied to sociophysics to Pamela Cook allow for arbitrary coupling between particles. By predict- Dept of Mathematical Sciences ing the dynamics of the approach to magnetic equilibrium, UofDelaware we hope to improve the understanding of phase transitions [email protected] in materials of various lattice structures. Lin Zhou Haley Yaple Department of Mathematics, New York City College of Northwestern University Technology, Brooklyn, NY 11201, USA [email protected] [email protected]

PP1 PP1 Partially Parallel Magnetic Resonance Image Re- AWM - Min-Max Game Theory Problem for the construction Using Bregmanized Operator Split- Fluid-Structure Interaction Model: An Applica- ting with Variable Stepsize tion to the Medicine Effect on Blood Flow in Hu- man Body This paper proposes a Bregman operator splitting algorithm with variable stepsize (BOSVS) for solving nons- The min-max game theory problem for the fluid-structure mooth and nonlinear optimization problems of the form interaction model is considered. We apply the model to 2 minu φ( u)+1/2 Au f 2 ,whereφ is a nonsmooth func- a biological scenario, where the medicine and the bacte- tion.{ This∇ algorithm− uses a} line search to achieve better ria/viruses become two players counteracting on the blood efficiency. The stepsize rule starts with a Barzilai-Borwein flow and blood cells inside the human body. The motions (BB) step, and increases the nominal step until a termi- of the blood flow and blood cells are described by Navier- nation condition is satisfied. Theoretically, this algorithm Stokes equation and elastic equation respectively. Our goal converges globally to the optimal solution of the optimiza- is to find the optimal dose of the medicine for the patient tion problem. Numerically, we get significantly better re- that can kill worst possible bacteria/viruses in his body. sults compared to original BOS algorithm with fixed stepsize and SBB algorithm with BB stepsize. Experimental Jing Zhang results in partially parallel magnetic resonance image re- University of Virginia construction displays that BOSVS algorithm gives greater [email protected] 124 AN12 Abstracts

PP1 Mathematics and Statistics How to Compute Transition States/saddle Points? [email protected]

Exploring complex energy landscape is a challenging issue Curtis R. Menyuk in many applications. Besides locating equilibrium states, UMBC it is often also important to identify transition states given Baltimore, MD by saddle points. In this talk, we will discuss existing [email protected] and new algorithms for the computation of such transition states with a focus on the newly developed Shrinking Dimer Dynamics and present some related mathematical theory on stability and convergence. We will consider a number of applications including the study of frustrations of interacting particles and nucleation in solid state phase transformations. Jiangyan Zhang Department of Mathematics Penn State University j [email protected]

Qiang Du Penn State University Department of Mathematics [email protected]

PP1 Multi-Layer and Multi-Resolution Large Popula- tion Stochastic Games Game theory has been used to understand and design complex systems with many interacting independent decision- making agents in changing environments. In this work, we study a class of large population stochastic games with multi-layer (ML) and multi-resolution (MR) structures. We first look at ML games in which the players have hybrid dynamics where the continuous dynamics model the interactions at the physical layer of the system, and the discrete dynamics model the behavior at the cyber layer. In the second part of the work, we study MR games where players face competitions within their group as well as interact with members outside their groups through global parameters such as price, temperature, etc. We adopt a mean-field approach to characterize the mean-field Nash equilibria of ML and MR games. We apply the framework and results to study complex systems such as molecular transport and demand response in the smart grid. Quanyan Zhu,TamerBasar University of Illinois at Urbana-Champaign [email protected], [email protected]

PP1 Dynamics and Noise Minimization of Femto- Second Similariton Pulses in a Fiber Laser with Zero Average Disperion

Various experimental designs have recently been proposed for ultra-short pulse mode-locked fiber lasers with applications to optical clocks, time and frequency transfer, generation of arbitrary optical waveforms, and frequency-comb spectroscopy. We will present simulation results (independently confirmed by laboratory experiments) demonstrating the existence of self-similar femto-second pulses near zero average dispersion in a laser with a Ytterbium fiber, and show that timing jitter is minimized when the average dispersion is close to zero. John W. Zweck University of Maryland Baltimore County FM12 Abstracts 126 FM12 Abstracts

IC1 which happens in applications to barrier option pricing or Optimal Execution in a General One-Sided Limit structural credit risk models. In this talk, I will present Order Book novel adaptive discretization schemes for the simulation of stopped Lvy processes, which are several orders of magni- We construct an optimal execution strategy for the pur- tude faster than the traditional approaches based on uni- chase of a large number of shares of a financial asset over form discretization, and provide an explicit control of the a fixed interval of time. Purchases of the asset have a non- bias. The schemes are based on sharp asymptotic estimates linear impact on price, and this is moderated over time by for the exit probability and work by recursively adding dis- resilience in the limit-order book that determines the price. cretization dates in the parts of the trajectory which are The limit-order book is permitted to have arbitrary shape. close to the boundary, until a specified error tolerance is The form of the optimal execution strategy is to make an met. initial lump purchase and then purchase continuously for some period of time during which the rate of purchase is Peter Tankov set to match the order book resiliency. At the end of this Université Paris-Diderot (Paris 7) period, another lump purchase is made, and following that [email protected] there is again a period of purchasing continuously at a rate set to match the order book resiliency. At the end of this second period, there is a final lump purchase. Any of the IC4 lump purchases could be of size zero. A simple condition is Talk Title TBA - Avellaneda provided that guarantees that the intermediate lump purchase is of size zero. This is joint work with Gennady Abstract not available at time of publication. Shaikhet and Silviu Predoiu. Marco Avellaneda Steven E. Shreve Courant Institute Carnegie Mellon University New York University Dept of Mathematical Sciences [email protected] [email protected] IC5 IC2 Optimal Order Placement in Limit Order Books Stable Diffusions With Rank-based Interactions, Abstract not available at time of publication. and Models of Large Equity Markets Xin Guo We introduce and study ergodic diffusion processes inter- University of California, Berkeley acting through their ranks. These interactions give rise to [email protected] invariant measures which are in broad agreement with stability properties observed in large equity markets over long time-periods. The models we develop assign growth rates IC6 and variances that depend on both the name (identity) Quantitative Absence of Arbitrage and Equivalent and the rank (according to capitalization) of each individ- Changes of Measure ual asset. Such models are able realistically to capture critical features of the observed stability of capital distri- It is well known that absence of arbitrage is a highly desir- bution over the past century, all the while being simple able feature in mathematical models of financial markets. enough to allow for rather detailed analytical study. The In its pure form (whether as NFLVR or as the existence of methodologies used in this study touch upon the question a variant of an equivalent martingale measure R), it is qual- of triple points for systems of interacting diffusions; in par- itative and therefore robust towards equivalent changes of ticular, some choices of parameters may permit triple (or the underlying reference probability (the ”real-world” mea- higher-order) collisions to occur. We show, however, that sure P). But what happens if we look at more quantitative such multiple collisions have no effect on any of the sta- versions of absence of arbitrage, where we impose for in- bility properties of the resulting system. This is accom- stance some integrability on the density dR/dP? To which plished through a detailed analysis of collision local times. extent is such a property robust towards changes of P? We The models have connections with the analysis of Queue- discuss these questions and present some recent results. ing Networks in heavy traffic, and with competing par- The talk is based on joint work with Tahir Choulli (Uni- ticle systems in Statistical Mechanics (e.g., Sherrington- versity of Alberta, Edmonton). Kirkpatrick model for spin-glasses). Their hydrodynamic- limit behavior is governed by generalized porous medium Martin Schweizer equations with convection, whereas limits of a different ETH Math kind display phase transitions and are governed by Poisson- Zurich, Switzerland Dirichlet laws. [email protected]

Ioannis Karatzas Columbia University SP1 [email protected] AWM-SIAM Sonia Kovalevsky Lecture : The Role of Characteristics in Conservation Laws IC3 Sonya Kovalevsky, in the celebrated Cauchy-Kovalevsky Simulation Schemes for Stopped Lvy Processes theorem, made clear the significance of characteristics in partial differential equations. In the field of hyperbolic Jump processes, and Lvy processes in particular, are noto- conservation laws, characteristic curves (in one space di- riously difficult to simulate. The task becomes even harder mension) and surfaces (in higher dimensions) dominate the if the process is stopped when it crosses a certain boundary, behavior of solutions. Some examples of systems exhibit FM12 Abstracts 127 interesting, one might even say pathological, characteristic scalar Banach algebra. Positive results are obtained for behavior. This talk will focus on ways that characteristics both commutative and noncommutative algebras. in systems of conservation laws give information about the systems being modeled. Ruth Curtain University of Groningen, Netherlands Barbara Lee Keyfitz [email protected] The Ohio State University Department of Mathematics bkeyfi[email protected] SP5 I.E. Block Community Lecture: Creating Reality: the Mathematics Behind Visual Effects SP2 The John Von Neumann Lecture: Liquid Crystals Abstract to follow. for Mathematicians Robert Bridson Liquid crystals form an important class of soft matter sys- University of British Columbia tems with properties intermediate between solid crystals [email protected] and isotropic fluids. They are the working substance of liquid crystal displays, which form the basis of a huge multi- national industry. The lecture will describe these fascinat- SP6 ing materials, and what different branches of mathematics, SIAG/FME Junior Scientist Prize: Market-Based such as partial differential equations, the calculus of vari- Aapproach to Modeling Derivatives Prices ations, multiscale analysis, scientific computation, dynamical systems, algebra and topology, can say about them. Most of the existing quantitative methods in Finance rely on the assumptions of the underlying mathematical models. The problem of choosing the appropriate model as- John Ball sumptions is one of the cornerstones of modern Financial Oxford Centre for Nonlinear PDE Mathematical Institute Engineering. I am interested in developing modeling frame- Oxford works that facilitate the use of historical observations when [email protected] making the choice of model assumptions. It turns out that, in the markets with a large family of liquid derivative contracts, it is rather hard to construct a model that exploits SP3 the information contained in the historical prices of these Past President’s Address: Reflections on SIAM, derivatives. In fact, constructing such models requires the Publishing, and the Opportunities Before Us use of the so-called Market-Based Approach. The idea of this approach is to treat the liquid derivatives as generic Upon taking up the post of president I had, of course, for- financial assets and prescribe the joint evolution of their mulated my priorities for SIAM. This talk provides a good prices in such a way that any future arbitrage-free combi- occasion to revisit some of those. One area turned out nation of prices is possible. In this presentation, I will out- to play a vastly larger role than I would have anticipated, line the main difficulties associated with the construction of namely mathematical publishing and many issues associ- market-based models and will present a general methodol- ated with it, ethical, technological, economic, political, and ogy that bypasses these difficulties. Finally, I will illustrate scientific. The future of scholarly publishing is far from the theory by describing (both mathematically and numer- clear, but one thing seems certain: big changes are needed ically) a family of market-based models for the European and will be coming. We, as mathematicians, are major call options of multiple strikes and maturities. stakeholders. We should also be major agents in guiding these changes. I will present some of my observations and Sergey Nadtochiy thoughts as we confront the opportunities before us. Oxford University Oxford-Man Institute Douglas N. Arnold [email protected] School of Mathematics University of Minnesota [email protected] JP1 Systemic Risk SP4 What is systemic risk, how do we model it, how to we an- W. T. and Idalia Reid Prize Lecture: Large Alge- alyze it, and what are the implications of the analysis? I braic Properties of Riccati Equations. will address these issues both in a larger historical context and within current research mathematical finance. The key In the eighties there was considerable interest in the alge- property of systems subject to systemic risk is their inter- braic properties of the following Riccati equation connectivity and the way individual risk can become overall, systemic risk when it is diversified by inter-connectivity. A∗X + XA XBB∗X + C∗C =0, (1) I will discuss theoretical issues that come up with mean- − field and other models and will also show results of numer- where A, B, C A, a Banach algebra with identity, and ical simulations. the involution operation∈ . Conditions are sought to ensure that the above equation∗ has a solution in A.Theresults George C. Papanicolaou were disappointing and the problem was forgotten until Stanford University this century when engineers studied the class of spatially Department of Mathematics distributed systems. One application was to control forma- [email protected] tions of vehicles where the algebraic property was essential. This case involves matrices A, B, C with components in a 128 FM12 Abstracts

CP1 approximations already proposed in the literature. Pricing Interest Rate Derivatives in a Multifactor Hjm Model with Time Dependent Volatility Joao Pedro V. Nunes ISCTE-IUL Business School We investigate the partial differential equation (PDE) for [email protected] pricing interest rate derivatives in a multi-factor Cheyette Model, that involves time-dependent volatility functions Pedro Prazeres with a special structure. The high dimensional parabolic Sociedade Gestora dos Fundos de Pensoes do Banco de PDE that results is solved numerically via a sparse grid Portugal approach, that turns out to be both accurate and efficient. [email protected] The results are compared to the analytical solution for bonds and caplets and also the Monte Carlo simulation solution for Bermudan Swaptions. CP1 Pricing and Hedging the Smile with Sabr: Evi- Ingo Beyna dence from the Interest Rate Caps Market Frankfurt School of Finance & Management [email protected] This is the first comprehensive study of the SABR (Stochastic Alpha-Beta-Rho) model (Hagan et. al (2002)) Carl Chiarella on the pricing and hedging of interest rate caps. We imple- Professor, School of Finance and Economics, University of ment several versions of the SABR interest rate model and Technology, Sidney, Broadway NSW 2007, Australia analyze their respective pricing and hedging performance [email protected] using two years of daily data with seven different strikes and ten different tenors on each trading day. In-sample Boda Kang and out-of-sample tests show that in addition to having University of Technology Sydney stochastic volatility for the forward rate, it is essential to [email protected] recalibrate daily either the vol of vol or the correlation between forward rate and its volatility, although recalibrat- ing both further improves pricing performance. The fully CP1 stochastic version of the SABR model exhibits excellent A Paradigm Shift in Interest-Rate Modeling pricing accuracy and more importantly, captures the dynamics of the volatility smile over time very well. This This research starts with a solution for modeling non- is further demonstrated through examining delta hedging negative interest rates in an incomplete bond market. It performance based on the SABR model. Our hedging is the stochastic-splines model, in which instantaneous for- result indicates that the SABR model produces accurate ward rates are almost surely finite and approximately log- hedge ratios that outperform those implied by the Black normal under both the real-world and the risk-adjusted model. measures. A unique term structure of convenience yield for the default-free bond market is introduced for the Tao L. Wu first time to compensate idiosyncratic risk. Addressing Illinois Institute of Technology on the market completeness issue, the stochastic-volatility tw33 [email protected] stochastic-splines model is presented whereby bond convenience yield vanishes. Under this framework, the market CP2 price of volatility risk can be computed endogenously. Var- ious applications are given. Swing Options in Commodity Markets: A Model with Multidimensional Jump Diffusions Peter Lin Johns Hopkins University The objective of this talk is to study the optimal exercise [email protected] policy of a swing option in the electricity markets. We formulate a model in terms of a stochastic control problem in continuous time, subjected to a total volume constraint. CP1 The underlying price process is a linear function depend- Pricing Swaptions under Multifactor Gaussian Hjm ing on a multidimensional Lévy diffusion. The results are Models illustrated with examples. Several approximations have been proposed in the liter- Marcus Eriksson ature for the pricing of European-style swaptions under Ph.D Student multifactor term structure models. However, none of them [email protected] provides an estimate for the inherent approximation error. Until now, only the Edgeworth expansion technique Jukka Lempa of Collin-Dufresne and Goldstein (2002) is able to char- Centre of Mathematics for Applications acterize the order of the approximation error. Under a University of Oslo multifactor HJM Gaussian framework, this paper proposes [email protected] a new approximation for European-style swaptions, which is able to bound the magnitude of the approximation er- Trygve Nilssen ror and is based on the conditioning approach initiated by School of Management Curran (1994) and Rogers and Shi (1995). All the pro- University of Agder posed pricing bounds will arise as a simple by-product of [email protected] the Nielsen and Sandmann (2002) setup, and will be shown to provide a better accuracy-efficiency trade-off than all the CP2 Decomposing the Risk from Investing in Foreign FM12 Abstracts 129

Commodities CP3 Basket and Spread Options in a Variance Gamma Several papers show that FX rates and commodity prices Model are interlinked. When investing in commodities traded in a foreign currency, the investor faces both price risk and Financial asset returns exhibit higher skewness and kurto- FX risk. We investigate how exchange-traded contracts on sis than those implied by the Normal distribution. Price WTI crude oil and EUR/USD correlate. We propose and paths can also exhibit jumps, which is particularly true for estimate a model that accounts for the stochastic correla- emerging and commodity markets. In this case, the Vari- tion between the two. This can be used to price and risk ance Gamma (VG) process is more realistic than the geo- manage foreign commodity positions, e.g., quanto options metric Brownian motion (GBM) to model the asset price or oil-linked gas contracts. dynamics. However, valuation of basket and spread options (common derivatives in commodity, FX and other markets) Nina Lange under this model is a very challenging and time-consuming Copenhagen Business School task. We propose a novel and elegant method for valuation nl.fi@cbs.dk of basket and spread options under VG model, by conditioning the VG processes on a realization of the stochastic CP2 Gamma time change and combining it with the Generalized LogNormal (GLN) approximation. We consider a simpler A Real-Time Pricing Model for Electricity Con- (and easily tractable) case of the identical stochastic time sumption change for all underlying assets, as well as the more gen- Input your abstract, including TeX commands, here. The eral case of dierent (but dependent) Gamma time changes. California electric company, i.e., PGE (Pacific Gas and Numerical study shows that the proposed method performs Electric Co.,), has recently announced its intentions to remarkably well in term of option pricing, even for a sim- charge small businesses in the state with dynamic prices pler model. Our method is intuitive, computationally very for electricity consumption. In this regard, we study a fast, ecient and exible enough to allow for basket options on real-time electricity pricing model in the paper and com- arbitrary number of assets and negative portfolio weights. pare it with two static pricing models. We show that realtime pricing outplays static pricing when it comes to jointly Svetlana Borovkova maximizing provider andconsumerwelfare. Vrije Universiteit Amsterdam Ranjan Pal [email protected] University of Southern California [email protected] CP3 High-order Short-time Expansions for ATM Op- CP2 tion Prices Under the CGMY Model A Resampling Particle Filter Parameter Estima- In this presentation, we derive a novel second-order ap- tion For Electricity Prices With Jump Diffusion proximation for ATM option prices under the CGMY Lvy In this paper we propose a particle ?lter for parameter es- model, and then extend to a model with an addition Brow- timation of jump diffusion models employed for modelling nian motion. The third-order asymptotic behavior of the electricity prices 1,2,3,4,5. We consider a jump-diffusion option prices as well as the asymptotic behavior of the cor- model 4. The jumps has the possibility to give a better ex- responding Black-Scholes implied volatilities are also ad- planation of the behaviour of electricity prices, however es- dressed. Our numerical results show that in most cases timation of parameters becomes more complicated 4.Com- the second-order term significantly outperform the first or- plications in parameter estimation will be introduced by der approximation. the inclusion of the jump component. The inclusion of Ruoting Gong jumps will add several new parameters 4. These parame- School of Mathematics ters will describe the jump frequency and distribution. The Georgia Institute of Technology jump models are non-Gaussian and this increases the com- [email protected] plexity of the models 1,2,3,4. A known ?ltering technique for these models is particle ?lter 1,2,3. Particle ?lter (PF) is a fully non-linear ?lter with Bayesian conditional prob- CP3 ability estimation, compared here with the well-known en- Efficiently Simulating the Double-Barrier First- semble Kalman lter (EnKF). A Gaussian resampling (GR) Passage Time in Jump-Diffusion Models method is proposed to generate the posterior analysis ensemble in an effective and efficient way 3. The performance We present a fast and accurate Monte-Carlo simulation of gaussian particle ?lter to model the jump frequency and to obtain double-barrier first-passage time probabilities in distribution parameters will be investigated and bench- a jump-diffusion model with arbitrary jump size distri- marked to other maximum likelihood state estimators. bution; extending single-barrier results by Metwally and Atiya [2002]. The presented algorithm is unbiased and sig- Bahri Uzunoglu nificantly faster than a brute-force Monte-Carlo simulation Gotland University on a grid. As an application, we discuss corridor bonus cer- [email protected] tificates, floor certificates, and digital first-touch options.

Dervis Bayazit Federal Home Loan Bank of Atlanta Peter Hieber [email protected] University of Toronto [email protected] 130 FM12 Abstracts

Lexuri Fernandez CP4 Universidad Aut´onoma de Madrid A New Perspective on Dependence Within Finan- [email protected] cial Markets

Matthias Scherer Many financial instruments are inherently multivariate Technische Universität München in their origination. A rigorous empirical valuation re- Chair of Mathematical Finance quires simultaneous analysis of many components. Nonlin- [email protected] ear and inter-temporal dependencies, extreme events, and large datasets introduce additional challenges. Indepen- dent component analysis is an indispensable tool for find- CP3 ing suitable representations of the complex multivariate in- Numerical Solution of Jump-Diffusion SDEs formation within financial markets. We introduce a novel statistical framework for independent component analysis Jump-diffusions are ubiquitous in finance and economics. of financial data and illustrate its use on several important This paper develops, analyzes and tests a discretization financial applications. scheme for multi-dimensional jump-diffusion SDEs with general state-dependent drift, volatility, and jump inten- David S. Matteson sity function. Unlike conventional schemes, our scheme Cornell University allows for an unbounded jump intensity–a feature of many Department of Statistical Science standard jump-diffusion models in credit, equity, FX and [email protected] commodity markets. The convergence of the discretization error is proved to be of weak order one. Numerical experiments illustrate our results. CP4 The Herd Behavior Index: a New Measure for the Gerald Teng Implied Degree of Co-Movement in Stock Markets Stanford University [email protected] We introduce a new measure for the implied degree of herd behavior, one of the driving factors of systemic risk. Kay Giesecke This forward looking Herd Behavior Index (HIX) is model- Stanford University independent and based on observed option data. As an Dept. of Management Science and Engineering illustration, we determine historical values of the 30-days [email protected] HIX for the Dow Jones Industrial Average. David Vyncke CP4 Ghent University Department of Applied Mathematics and Computer Model Risk Based on the Distribution of the Hedge Science Error [email protected] When pricing and hedging a derivative, we face model risk, that is, the risk of choosing the wrong dynamics for the fi- Jan Dhaene, Daniel Linders, Wim Schoutens nancial market. We propose a measure of model risk based University of Leuven on the hedge error that can be interpreted as a capital [email protected], charge. This has several positive implications beyond esti- [email protected], mating the riskiness of a claim in terms of model risk. We [email protected] calculate these model risk measures for several examples and derive its general properties. CP5 Nils Detering Incorporating Parameter Risk into Derivatives Frankfurt School of Finance and Management Prices - An Approach to Bid-Ask Spreads [email protected] We present a new method based on convex risk measures to incorporate parameter risk (e.g. estimation and calibration CP4 risk) into derivative prices. As an application we calculate WhyIsItSoHardtoEstimateExpectedReturns? parameter risk-implied bid-ask spreads of exotics, enabling us to compare the parameter risk of different models and A key part of experiment design is determining how much different exotics. Furthermore, we introduce a nonpara- data to collect. When the data comes in the form of a metric calibration procedure to real bid-ask prices using timeseries, the sample size is expressed both by the count distortion risk measures, compare our results to given para- N of the observations and the duration T of the historical metric distortion calibrations and present a new parametric period over which observations were made. For an asset family. whose price has continuous sample paths, we demonstrate that the standard error of any unbiased estimator of the Karl F. Bannör, Matthias Scherer price of risk is bounded below by 1/√T . Technische Universität München Chair of Mathematical Finance John A. Dodson [email protected], [email protected] University of Minnesota Center for Financial and Actuarial Mathematics [email protected] CP5 Analytical Calculation of Risk Measures for Vari- FM12 Abstracts 131 able Annuity Guaranteed Benefits Nils Detering Frankfurt School of Finance and Management With the increasing complexity of investment options in life [email protected] insurance, more and more insurers have adopted stochastic modeling methods for the assessment and management of Uwe Wystup insurance and financial risks, with the most prevalent being MathFinance AG Monte Carlo simulation. In this paper we propose an al- u.wystup@mathfinance.com ternative analytical method for the calculation of risk measures for variable annuity guaranteed benefits. The techniques for analytical calculations are based on the study of CP6 an integral of geometric Brownian motion as well as asymp- Optimal Cash Holdings in a Firm totic analysis of special functions. As we demonstrate by numerous examples on quantile risk measure and condi- The precautionary principle of cash-holdings is empirically tional tail expectation, the numerical algorithms developed well analysed. However, the quantitative modelling of such in this paper appear to be accurate and computationally cash holdings is exceptionally sparse. This is due to the efficient. path dependent nature of the problem and the fact that cash holdings may both increase and decrease in time. As Runhuan Feng,HansWVolkmer such, novel numerical solutions to the problem are required. University of Wisconsin-Milwaukee We show how to model endogenous cash holdings within a Department of Mathematical Sciences Firms valuation and extract numerical solutions. In doing [email protected], [email protected] so we provide a solid basis by which Real Options analysis, dividend payments, debt issuance, cash holdings, and CP5 corporate finance decisions (investments) can finally all be viewed in a consistent, non-contradictory and more realis- Fair Valuation of Drawdown Insurance tic fashion. This analysis and need for consistency has been Drawdowns are path-dependent measures of risk and have called for within many papers, and we hope our (economi- been used extensively in the description of market crashes. cally robust) approach shows how mathematics can provide We evaluate the market price of a market crash as mea- a more unifying approach to the theory of the Firm. sured through drawdowns by considering an investor who Paul V. Johnson, Geoff Evatt, Mingliang Cheng wishes to insure herself against the risk of a market crash University of Manchester and does so by purchasing insurance claims against draw- School of Mathematics downs. We further examine the fair valuation of drawdown [email protected], insurance in the possibility of early cancellation and iden- geoff[email protected], tify optimal cancellation strategies. [email protected] Olympia Hadjiliadis Graduate Center of CUNY, New York CP6 Brooklyn College, CUNY [email protected] Risk Aversion and Managerial Cash-Flow Esti- mates in Real Options Tim Leung While there are a number of academic papers discussing Department of Operations Research and Industrial the importance of accounting for risk aversion in real option Engineering valuation, none of them are applicable to discrete cash-flow Columbia University estimates supplied by managers. Here, we develop an ap- [email protected] proach which explicitly incorporates managerial cash-flow estimates and accounts for risk-aversion through indiffer- Hongzhong Zhang ence valuation. Interestingly, we find that the real option Department of Statistics value not only deteriorates as risk-aversion increases, it Columbia University dropstozeroaboveacriticalrisk-aversionlevel. [email protected] Yuri Lawryshyn University of Toronto CP5 [email protected] Diversification and Crash-Protection Using Vari- ance Swap Calendar Spreads CP6 Volatility can be also considered an asset class. Variance Irreversible Investment with Regime Switching : swaps, one of the main investment vehicles, provide expo- Revisit with Linear Algebra sure to realized volatility. Implied volatility is often higher than the realized volatility will turn out to be. We ex- We consider irrevesible investment problems with regime plain how a variance swap calendar spread benefits from switching feature under a monopoly setting. Several pa- both negative risk premium and negative correlation with rameters describing the economic environment varies ac- the underlying stock index. Via backtesting we show how cording to a regime switching with general number of the strategy added to a stock/bond portfolio significantly states. We present the derivation of the value function diversifies crash risk. via solving a system of simultaneous ordinary differential equations with knowledge of linear algebra. It is found that Qixiang Zhou the functional form of the value function depends on the MathFinance AG decomposition of a coefficient matrix. qixiang.zhou@mathfinance.com Keiichi Tanaka 132 FM12 Abstracts

Tokyo Metropolitan University Markus Mocha [email protected] Humboldt-Universit¨at zu Berlin [email protected]

CP6 Nicholas Westray Embedded Currency Exchange Options in Roll- Imperial College London over Loans [email protected] In ship and aircraft financing long term roll-over loans are often equipped with the right to change the currency every CP7 quarter at spot. The loan taker then pays LIBOR of the A Continuous Time Bank Run Model for Insol- respective currency plus a pre-determined constant sales vency, Recovery and Rollover Risks margin. If the capital outstanding exceeds 105% calculated in the original currency, the amortization is required We propose a continuous time bank run model for incor- to the level of 105% of the original currency. By clever cur- porating insolvency, recovery and rollover risks. The firm rency management the loan taker can amortize the loan finances by issuing both long and short term debt, and the faster and terminate the loan early. Essentially the loan short term debt holders need to decide whether to roll over taker owns a series of options on the cross currency ba- or to withdraw their debt (i.e. to run the bank) when their sis spread with unknown notional amounts. We determine contracts expire. We show there exists a threshold strat- the key drivers of risk, an approach to valuation and hedg- egy (i.e. the bank run barrier) for the short-term creditors ing, taking into consideration the regulatory constraints to decide when to run. We decompose the total credit risk of a required long term funding. We present a closed-form into an insolvency component and an illiquidity component approximation to the pricing problem and illustrate its sta- based on such an endogenous bank run barrier together bility. with an exogenous insolvency barrier. The short term debt in our model can have either a discrete tenor structure, or Uwe Wystup a more realistic staggered tenor structure. The problem Frankfurt School of Finance & Management is reduced to an optimal stopping time problem with con- MathFinance AG straint, which is solved by the BSDE method. uwe.wystup@mathfinance.com Gechun Liang University of Oxford CP7 [email protected] Dynamic Quadratic Hedging in the Presence of Partially Hedgeable Assets and Liabilities CP7 We consider an incomplete market where an investor who Quadratic Reflected Bsdes with Bounded Condi- owns a partially hedgeable asset faces a liability at time T. tions. Application to American Options. The investor’s aim is to minimize the terminal replication error based on a quadratic loss criterion in this setting. In this talk, I present an elementary and totally pertur- We investigate the solution to the quadratic hedging prob- bative method for dealing with the well-posedness of some lem using the stochastic linear-quadratic optimal control reflected BSDEs : existence, uniqueness and stability. It approach through the corresponding (stochastic Riccati) works for a smooth coefficient f which has a growth at BSDEs and provide some examples. most quadratic in z, when the terminal condition as well as the lower obstacle are bounded. I then connect these Coskun Cetin equations with the problem of pricing american options in California State University, Sacramento an incomplete market. [email protected] Arnaud Lionnet Oxford-Man Institute for Quantitative Finance, CP7 University of Oxford BSDEs with BMO Market Price of Risk [email protected] We study quadratic semimartingale BSDEs arising in power utility maximization when the market price of risk is CP7 of BMO type. In a Brownian setting we provide a necessary A Simple Proof of BichtelerDellacherieMokobodzki and sufficient condition for the existence of a solution but Theorem show that uniqueness fails to hold in the sense that there exists a continuum of distinct square-integrable solutions. We give a simple and quite elementary proof of the cel- This feature occurs since, contrary to the classical Ito rep- ebrated BichtelerDellacherieMokobodzki Theorem, which resentation theorem, a representation of random variables states that a process is a good integrator if and only if it is in terms of stochastic exponentials is not unique. We study a semi-martingale. Moreover we reformulate its statement when the BSDE has a bounded solution and derive a new in a way that -we believe- is more natural. dynamic exponential moments condition which is shown to be the minimal sufficient condition in a general filtration. Pietro Siorpaes The main results are complemented by several interesting University of Vienna (Universität Wien) examples which illustrate their sharpness as well as impor- math department tant properties of the utility maximization BSDE. [email protected] Christoph Frei University of Alberta Mathias Beiglböck [email protected] University of Vienna (Universität Wien) math department [email protected] FM12 Abstracts 133

CP8 CP8 InferencefortheFractionalHestonModelUsing Stochastic Calibration to Implied Volatility Sur- the Auxiliary Particle Filter faces The fractional Heston Model is a generalization of the Hes- This paper provides a two-step method to fully calibrate ton Model obtained by replacing Brownian motion by frac- the implied volatility surface in the environment of ran- tional Brownian motion in the two equations that define dom volatility. The first step consists of the Fourier trans- the Heston model. After defining the fractional Heston form method (Malliavin and Mancino (2009)) for estimat- model and showing its representation as a Dynamic state ing model parameters of stochastic volatility models, and space model, we will use that auxiliary particle filter both the second step solves an optimization problem by means to sample the volatility process and to update the posterior of Monte Carlo simulation with variance reduction tech- distribution of the parameters sequentially as data arrive niques. We compare fitting accuracies with the fast Fourier over time. We apply our approach to simulated and real transform method (Carr and Madan (1999)) and perturba- data with success. Keywords:- Fractional Heston Model, tion method (Fouque et al. (2003, 2011)). In addition, it maximum likelihood estimation, particle filter, auxiliary is natural to generalize our calibration procedure to the particle filter, sequential Bayesian inference. implied volatility surface of American options. Muhannad Al-Saadony Chuan-Hsiang Han University of Plymouth National Tsing-Hua University United Kingdom [email protected] [email protected]

CP8 CP8 Understanding Jumps in the High-Frequency VIX Non-Parametric Calibration of the Local Volatility Surface for European Options This article provides a comprehensive nonparametric high- frequency analysis of jumps in the VIX (S&P500 volatility Assuming the volatility surface is smooth, a second or- index). A comparison of the VIX and the S&P500 futures der Tikhonov regularization is applied to the calibration time series (1992-2010) shows that 97% of jumps in the VIX problem. Additionally a new approach for choosing the are spurious. This finding not only leads to a new interpre- Tikhonov regularization parameter is proposed. Using the tation of the broadly used VIX dataset but also extends the TAPENADE automatic differentiation tool in order to ob- literature on volatility jumps and on the return-volatility tain adjoint code of the direct model is employed as an relationship. efficient way to obtain the gradient of cost function with respect to the local volatility surface. Finally we perform Inna Khagleeva four numerical tests aimed at assessing and verifying the University of Illinois at Chicago aforementioned techniques. [email protected] Jian Geng Department of Mathematics Florida State University CP8 [email protected] Implied Volatiltiy from Black-Scholes and Other Formulas Michael Navon Florida State University We show that if the parameters of an arbitrary stock price [email protected] model are used in the Black-Scholes formula for calculating option prices for finitely many strikes, the implied volatility (a function of time t) will be bounded by a value which Xiao Chen depends only on strikes. Our model-free results, which can Lawrence Livermore National Laboratory be used in calibration, provide sets of constraints limiting Center for Applied Scientific Computing the acceptable values of the implied volatility parameters. [email protected] We use the Heston model for illustration. Olivia Mah CP8 Monash University Small-time Asymptotics For Some Stochastic [email protected] Volatility Models In the paper SMALL-TIME ASYMPTOTICS FOR Kais Hamza, Fima Klebaner FAST MEAN-REVERTING STOCHASTIC VOLATIL- School of Mathematical Sciences ITY MODELS they investigate two rates for the mean- Monash University, Clayton Campus Victoria 3800 reversion time δ in terms of the maturity , namely δ = γ Australia for γ =2, 4. Looking at this model and a few others we [email protected], fi[email protected] characterize the behaviors for γ>2andfor1<γ<2and show how this relates to Moderate Deviations and Super- CP9 large Deviations, respectively. This argument also shows why γ = 2 is special. Extensions of the Lt Method for Option Pricing Jerome Grand’maison Monte Carlo (MC) and quasi-Monte Carlo (QMC) meth- University of Southern California odsareoftenusedinpricingcomplexderivatives.The [email protected] merit of QMC is that, theoretically at least, higher convergence rates can be obtained than regular MC. The payoff function is usually high-dimensional and non-smooth, elim- 134 FM12 Abstracts inating the advantage of using QMC. Imai & Tan (2006) method to the pricing of Asian options. In this setting, the introduced the LT method which minimizes the effective approximation relies on the discretization of the integral dimension of the problem by transforming the normal vari- of the price process over a time interval. We also analyze ates using an orthogonal transformation, thereby improv- the error process and prove a stable functional central limit ing the QMC method. We extended their method for valu- theorem. Finally, We use our result in order to optimize ing options that have a barrier feature on an underlying the choice of the parameters, which are different from the asset, incorporating and extending an idea from Staum & ones in the Euler scheme. Numerical simulations were pro- Glasserman (2001). These options have a payoff that de- cessed. pends on whether the asset does or does not cross a certain level during the life of the option. If the probability of (not) Ahmed Kebaier, Ben Alaya Mohamed hitting is large enough, then much more paths have to be University Paris XIII sampled for reliable results. Our method greatly reduces [email protected], [email protected] the required number of paths and our aim is to extend this method to Levy market models. CP9 Nico Achtsis A Hybrid Pricing Method for Options with Multi K.U.Leuven Assets [email protected] A numerical method is studied for options with multi- Ronald Cools, Dirk Nuyens underlying assets. Instead of imposing artificial boundary Dept. of Computer Science condition for the multi-dimensional Black-Scholes equa- K.U.Leuven tion, we calculate certain one-dimensional model equation [email protected], [email protected] at each time-step using pre-simulated Monte-Carlo time series. With standard finite difference method using nine point stencil, our method reduce the computational do- CP9 main of the governing equation (the two dimensional Black- Variance Reduction for Monte Carlo Simulation Scholes equation) exceedingly. As benchmark tests, we of European Call Options Under the Coupled consider the call on the maximum option which has an Additive-Multiplicative Noise Model analytic solution, and a complicated structured note from the derivative market. We propose a variance reduction method for Monte Carlo computation of option prices in the context of the Cou- Yongsik Kim pled Additive-Multiplicative Noise model. Four different Department of Mathematics schemes are applied for the simulation. The methods select Yonsei University control variates which are martingales in order to reduce [email protected] the variance of unbiased option price estimators. Numer- ical results for European call options are presented to il- Hyeong-Ohk Bae lustrate the effectiveness and robustness of this martingale Department of Financial Engineering control variate method. Ajou University [email protected] Wanwan Huang Florida State University Tae-Chang Jo [email protected] Inha University [email protected] Brian Ewald Department of Mathematics Florida State University CP9 [email protected] Control Variate Methods and Applications in Asian and Basket Options Pricing and Hedging under Jump-Diffusion Models CP9 Central Limit Theorem for the Multi-Level Monte We discuss control variate methods with applications to Carlo Algorithm and Applications to Option Pric- Asian and basket option pricing under exponential jump ing diffusion models for the underlying asset prices. We first revisit the single control variate method and then discuss This paper deals with the problem of the multi-level Monte the multivariate control variate method in detail. Con- Carlo method, introduced by Giles (Multilevel Monte Carlo ditions which ensure the variance of an m variate con- path simulation Operations Research, 2008; 56:607-617) as trol variates is smaller than that of a k variate− control an extended method of the statistical Romberg one intro- variates (1 k

Zhongfei Li sequential transaction costs. The prices of the assets are Lingnan (University) college modeled as a discrete random walk perturbed by both tem- Sun Yat-Sen University poral and permanent impacts induced by the trading vol- [email protected] ume. We show that the optimal strategy is time-consistent and deterministic if the dynamic risk measure satisfies a Yan Zeng Markovian property. We also show that our optimal ex- Lingnan (University) College ecution problem can be formulated as a convex program, Sun Yat-Seng University and propose an accelerated first-order method that com- [email protected] putes its optimal solution. The efficiency and scalability of our approaches are illustrated via numerical experiments.

CP9 Qihang Lin Taylor-Like Anova Expansion for High Dimensional Carnegie Mellon University Pdes Arising in Finance Tepper School of Business [email protected] The solution of high dimensional problems in short time as well as with high precision is of great importance in fi- Javier Pena nance. For this purpose we propose an approximation to Carnegie Mellon University an ANOVA decomposition of the problem, which is only of [email protected] linear order in the dimension of the full problem and supe- rior in precision. We will call this approximation Taylor- like ANOVA. We develop this approximation up to higher CP10 orders and show its efficiency by numerical experiments. An Optimal Trading Rule under Switchable Mean Reversion Market Philipp Schroeder Goethe Center for Scientific Computing This work provides an optimal trading rule that allows Goethe University Frankfurt buying or selling of an asset whose price is governed by [email protected] mean-reversion model. In the model, the equilibrium level is controlled by an 2-state Markov chain. With the slippage Thomas Gerstner cost imposed, the goal is to maximize the overall return. Goethe University Frankfurt The value functions are characterized by considering the [email protected] associated HJB equations. This paper also shows that the solution of the original optimal problem can be obtained by Gabriel Wittum solving four quasi-algebraic equations. Finally, numerical Goethe Center for Scientific Computing examples are given for demonstration. Goethe University Frankfurt Duy Nguyen [email protected] University of Georgia [email protected] CP10 Optimal Order Routing in Limit Order Markets CP10 When executing a trade, traders in electronic equity mar- Price Impact and Market Indifference Prices with kets can choose to submit a limit order or a market order, Power Utilities as well as the venue to submit this order, if the stock is We investigate the price impact of large transactions in an traded in several exchanges. This decision is influenced by equilibrium pricing model with HARA utility functions. the order flow characteristics and queue sizes in each limit A market maker trades with a large investor at a price order book, as well as the structure of transaction fees and that allows him to preserve his expected utility, the so- rebates across exchanges. We show that this optimal order called market indifference price. In this setting we look at routing problem may be formulated as a convex optimiza- marginal prices and illiquidity premia in comparison to the tion problem and propose a stochastic algorithm for solving Black-Scholes model as well as hedging and replication of it. We study this problem under various statistical assump- non-traded (OTC) claims. tions on the order flow and show the interplay between the fee structure, the order flow and the risk preferences of the Nadim Sah trader in determining the optimal routing decision. TU Berlin [email protected] Arseniy Kukanov Columbia University [email protected] CP10 A Self-exciting Point Process Model for Limit Or- Rama Cont der Books CNRS (France) & Columbia University [email protected] The statistical properties of events affecting a limit order book -market orders, limit orders and cancellations- reveal strong evidence of clustering in time, significant CP10 cross-correlation across event types and significant depen- Optimal Trade Execution with Dynamic Risk Mea- dence of the order flow on the bid-ask spread. We show sures that these dependencies may be adequately represented by a multi-dimensional self-exciting point process, for which We propose a model for optimal trade execution in an illiq- a tractable parameterization is proposed. Using high- uid market that minimizes a coherent dynamic risk of the 136 FM12 Abstracts frequency data from the Trades and Quotes database, we Kiel University perform a Maximum Likelihood Estimation of the model [email protected] and assess its predictive performance for a variety of stocks.

Ekaterina Vinkovskaya CP11 Columbia University Indifference Pricing with Uncertainty Averse Pref- Dept of Statistics erences [email protected] We consider the indifference valuation of an uncertain mon- Allan Andersen etary payoff from the perspective of an uncertainty averse Copenhagen Business School decision-maker. We study how the indifference valuation aa.fi@cbs.dk depends on the decision-maker’s attitudes toward uncertainty. We obtain a characterization of comparative uncer- Rama Cont tainty aversion and various characterizations of increasing, CNRS, France, and Columbia University decreasing, and constant uncertainty aversion. [email protected] Flavia Giammarino, Pauline Barrieu London School of Economics CP10 [email protected], [email protected] Evolutionary Game Dynamics Using a Non- Equilibrium Price Formation Rule for Trading with CP11 Market Orders Portfolio Optimization Based on Independent Sets Markets have dynamics that may result in excess volatility of Market Cliques and other phenomena that are a challenge to explain us- We consider the problem of selecting an optimal mar- ing rational expectation models. Following Farmer (2002) ket portfolio that maximizes expected return and includes and identifying trading strategies with species and capital highly correlated disjoint market cliques (i.e., members invested in a strategy with a population, we use the repli- within a clique are pairwise highly correlated) which are cator equation to identify the evolutionary game dynamics pairwise anticorrelated based on a correlation function de- between the relevant agents. We then extend the dynamics fined on the set of cliques. We present integer program- spatially in order to examine the progression toward mar- ming models that can be effectively used to construct such ket efficiency caused by the evolution of capital. We ob- an optimal portfolio that satisfies given clique correlation serve interesting dynamics including the phenomenon that thresholds. the market becomes efficient as new strategies find them and cause them to disappear. Athula D. Gunawardena University of Wisconsin-Whitewater Gareth Q. Witten [email protected] University of Cape Town Pontificia Universidad Católica del Per, CENTRUM Católica Robert Meyer [email protected] Computer Science Department University of Wisconsin-Madison [email protected] CP11 On the Existence of Shadow Prices. Thisath Kularatna OptSolv LLC. For utility maximization problems under proportional [email protected] transaction costs, it is known that the original market with transaction costs can sometimes be replaced by a friction- Michael Monaghan less shadow market that yields the same optimal strategy Blackthorne Capital Management, LLC and utility. In this paper we present a counterexample [email protected] which shows that shadow prices may fail to exist. We then prove that short selling constraints are a sufficient condi- Joseph Haske tion for their existence, even in very general multicurrency University of Wisconsin-Whitewater market models with discontinuous bid-ask-spreads. [email protected] Giuseppe Benedetti CREST CP11 [email protected] Portfolio Optimization under Convex Incentive Schemes Luciano Campi Paris 13 University We consider the utility maximization problem of terminal [email protected] wealth from the point of view of a portfolio manager paid by an incentive scheme given as a convex function g of the Johannes Muhle-Karbe terminal wealth. The manager’s own utility function U Departement Mathematik is assumed to be smooth and strictly concave, however the ETH Zürich resulting utility function U g fails to be concave. As a con- [email protected] sequence, this problem does◦ not fit into the classical portfolio optimization theory. Using duality theory, we prove Jan Kallsen wealth-independent existence and uniqueness of the optimal wealth in general (incomplete) semimartingale markets FM12 Abstracts 137 as long as the unique optimizer of the dual problem has a Investment-Consumption Models for Retirees continuous law. In many cases, this fact is independent of the incentive scheme and depends only on the structure of We consider the optimal investment-consumption problem the set of equivalent local martingale measures. We pro- for retirees with uncertain lifespan. We assume that their vide explicit examples for complete and incomplete market initial wealth can spread between both risky and riskless models. (liquid) investments and an income-producing (irrevoca- ble) life annuity with default risk. We examine whether Stephan Sturm default risk (or the perception of default risk) rationally ORFE Department affects a retirees decision to purchase an annuity upon re- Princeton University tirement. We formulate our problem as a Hamilton-Jacobi- [email protected] Bellman equation and do a thorough numerical study for CRRA investors. Maxim Bichuch Department of Operations Research and Financial Jeffrey Humpherys Engineering Brigham Young University Princeton University jeff[email protected] [email protected] David Babbel University of Pennsylvania CP11 Wharton School of Business Optimal Portfolios for Hedge Funds and Their [email protected] Managers Craig Merrill Hedge fund managers receive fees proportional to profits, Brigham Young University and may reinvest them. We find the fund and personal Marriott School of Business portfolio that maximize managers’ expected utility from craig [email protected] personal wealth, when relative risk aversion is constant, and investment opportunities constant and separate, but correlated. Managers do not reinvest fees, allocating ex- CP12 cess personal wealth in Merton portfolio. But they man- Voluntary Retirement and Annuity Contract age funds like Merton investors with risk aversion shrunk towards one. Managers do not hedge fund exposure with We consider an optimal financial planning problem of an personal positions. economic agent who has an option to retire from labor voluntarily. The economic agent with labor income deter- Gu Wang mines his/her investment strategy, consumption, and re- Boston University, Department of Mathematics and tirement strategy along with annuity. We investigate the Statistics relation between the annuity contract and the condition for [email protected] the voluntary retirement. We also analyze how the presence of voluntary retirement option affects the purchase of Paolo Guasoni an annuity and the annuity market. Boston University Dublin City University Minsuk Kwak [email protected] Korea Advanced Institute of Science and Technology [email protected]

CP11 Yong Hyun Shin An Equilibrium Approach to Utility-Based and In- Sookmyung Women’s University difference Pricing [email protected] The utility-based and utility indifference pricing are frameworks for pricing contingent claims. Since these principles CP12 are based on utility maximization principle, prices are op- Bang-Bang Controls on Some Optimal Insurance timal for each investor with utility function. Our purpose Problems is to expand these frameworks for deducing the equilibrium price. Another purpose is to clarify the relationship In this talk, we are interested in finding an optimal solution between utility-based and utility indifference framework. for a large class of optimal insurance problems. This class This discussion will be also done in the setting of the mar- of problems includes those whose risks are measured by ket with transaction costs. Value at Risk, Average Value at Risk, Conditional Tail Expectation and law-invariant convex risk measures. We Daisuke Yoshikawa have found that Bang-Bang controls are optimal to all of Mizuho-DL Financial Technology co., ltd. them. This result also holds for multi-dimensional optimal daisuke-yoshikawa@fintec.co.jp insurance problems such as those in adverse selections.

Mark Davis Siu Pang Yung Impreial College london Math. Dept., University of Hong Kong [email protected] [email protected]

CP12 CP12 Optimal Decumulation: An Optimal Consumption and Portfolio Choice with Life Insurance under Uncertainty and Borrowing 138 FM12 Abstracts

Constraints for Credit Risk Applications

We develop a duality approach to study a family’s optimal Calculation of portfolio loss distributions for large numbers consumption, portfolio choice and life insurance purchase of correlated losses (e.g. credit risk applications) typically when the family receives deterministic labor income which use brute force Monte Carlo simulation. We use an asymp- may be terminated due to premature death or retirement totic probabilistic model based on the Central Limit The- of the family’s wage earner. The family faces a borrowing orem for solving the portfolio risk aggregation problem for constraint and the wage earner has an uncertain lifetime. credit risky portfolios. We then prove a theorem that en- We establish the existence of an optimal solution to the ables eﬃcient computation of the conditional expectation optimization problem and solve the problem explicitly for of the default rate for any subportfolio, conditioned on the several cases. total portfolio loss. This theorem enables us to solve the capital allocation problem (using expected shortfall as the Xudong Zeng risk measure) without resorting to Monte Carlo simulation. Shanghai University of Finance and Economics The approach is very eﬃcient, even for portfolios with sev- [email protected] eral million positions.

Andrew Barnes CP12 General Electric Optimal Dividend Payments for the Piecewise- Global Research Center Deterministic Compound Poisson Risk Model [email protected] This work deals with optimal dividend payment problem for a piecewise-deterministic compound Poisson insurance CP13 risk model. The objective is to maximize the expected Measure Changes for Reduced-Form Affine Credit discounted dividend payout up to ruin time. When the Risk Models dividend payment rate is restricted, the value function is shown to be a solution of the corresponding HJB equa- We consider a reduced-form credit risk model, with default tion. For the case of unrestricted payment rate, the value intensity driven by an affine process. We fully character- function and an optimal barrier strategy are determined ize the family of all locally equivalent probability measures explicitly with exponential claim size distributions. which preserve the structure of the model, providing necessary and sufficient conditions on their density process. Runhuan Feng In particular, this allows for a rigorous treatment of dif- University of Wisconsin-Milwaukee fusive and jump-type risk premia. As an application, we Department of Mathematical Sciences characterize the family of all risk-neutral measures for a [email protected] jump-to-default Heston model.

Shuaiqi Zhang Claudio Fontana Central South University University of Padova School of Mathematical Science and Computing [email protected] Technology [email protected] CP13 Chao Zhu Killed Brownian Motion with a Prescribed Lifetime University of Wisconsin-Milwaukee Distribution and Models of Default [email protected] The inverse first passage time problem asks for some distribution whether there is a barrier such that the first time CP13 a Brownian motion crosses the barrier has the given distribution. We consider a ‘smoothed’ version of this prob- On the Credit Risk of Secured Loans lem in which the first passage time is replaced by the first We use stochastic control techniques to analyze the credit instant that the time spent below the barrier exceeds an risk of secured revolving loans, whose collateral cannot be independent exponential random variable. We show that liquidated immediately. The objective function is a trade- any distribution results from some unique barrier. off between the expected loss due to a liquidation event and Alexandru Hening, Steven Evans, Boris Ettinger the shortfall due to the borrower drawing on the credit line UC Berkeley less than the full amount available. We exhibit the lender’s [email protected], [email protected], et- optimal strategies and compare them with the standard [email protected] LTV-based lending policy favored by practitioners.

Agnes Tourin CP13 Polytechnic Institute of NYU [email protected] Analysis of Recovery Rate of Non-Performing Con- sumer Credit

Fabian Astic There have been more studies on recovery rate modeling of Moody’s Investors service bonds than on recovery rate modeling of personal loans and Credit policy/research retail credit. Little to no research have been conducted on [email protected] recovery rates in non-performing retail credit with emphasis on third-party buyers. From an empirical point of view, in order to analyze the recovery rate distributions across CP13 the different industries, over nine million defaulted or non- Conditional Expected Default Rate Calculations performing consumer credit data provided by a German FM12 Abstracts 139 debt collection company are used. A variety of statistical arrivals is large, the intraday dynamics of the limit order and data mining methods will be examined with respect to book may be approximated by a Markovian jump-diffusion prediction and classification. A two-stage model which first process in the positive outhunt, whose characteristics are classifies debts as extreme or non-extreme with respect to explicitly described in terms of the statistical properties of recovery rate is applied; then, the extreme debts are clas- the underlying order flow [Cont Larrard 2011]. This result sified into full payment and non-payment. Moreover, the allows to obtain analytical expressions for the probability of non-extreme recovery rates are predicted in the entire unit a price increase or the distribution of the duration until the interval [0,1]. next price move, conditional on the state of the order book and characterize various other quantities as solutions of el- Markus Hoechstoetter liptic PDEs in the positive orthant [Cont Larrard 2012]. Chair of Statistics, Econometrics and Mathematical Our results allow for a wide range of distributional and de- Finance pendence assumptions in the orders and apply to a wide Karlsruhe Institute of Technology (KIT), Germany class of stochastic models proposed for order book dynam- [email protected] ics, including Poisson point processes, self-exciting point processes [Cont, Andersen Vinkovskaya 2011] and models Abdolreza Nazemi of the ACD-GARCH family. Karlsruhe Institute of Technology (KIT), Germany [email protected] Rama Cont CNRS (France) & Columbia University Svetlozar T. Rachev [email protected] Department of Applied Mathematics at Stony Brook University Adrien DE LARRARD New York, USA Laboratoire de Probabilités & Modeles Aleatoires [email protected] Universite Pierre & Marie Curie (Paris VI) [email protected] CASLAV Bozic Informatics Institute, Faculty of Business Engineering, MS1 Karlsruhe Institute of Technology, Germany [email protected] Information and the Value of Guaranteed Trade Execution

CP13 In many markets, uncertainty about whether a trade is executed can be removed by paying a price premium. We Maximum Likelihood Estimation for Large Inter- use financial markets as a particular setting in which to acting Stochastic Systems study this trade-off. In particular, we assess the role of Parameter estimation for a large system is facilitated by information in the choice between certain trade at a price use of the asymptotic SPDE to which the system weakly premium in an intermediated market such as a dealer mar- converges. Standard particle filtering methods are often ket or a limit order book and contingent trade in a dark not applicable for parameter estimation of the SPDE. A pool. Our setting consists of intrinsic traders and specula- method of moments reduces the SPDE into an SDE sys- tors, each endowed with heterogeneous fine-grained private tem. We then develop a particle filtering method for the information as to an assets value, that endogenously decide SDE system. Theoretical convergence of the finite sys- between these two venues. We solve for an equilibrium in tem’s likelihood to the asymptotic likelihood is discussed. this setting, and address three main questions: First, we Important credit risk and mortgage applications motivate illustrate how the choice between certain and contingent the method. trade depends on information available to an individual agent, as well as the overall distribution of information Justin Sirignano across all agents. Second, we analyze how the premium for Stanford University certain trade over contingent trade affects the strategic be- [email protected] havior of traders. Finally, we demonstrate how the option for contingent trade affects the ability of intermediating Gustavo Schwenkler market makers to set transaction costs to maximize profit. Stanford University Krishnamurthy Iyer, Ramesh Johari Dep. of Management Science and Engineering Stanford University [email protected] [email protected], [email protected]

Kay Giesecke Ciamac C. Moallemi Stanford University Columbia U Dept. of Management Science and Engineering [email protected] [email protected]

MS1 MS1 Mean-variance Optimal Adaptive Order Execution Price Dynamics in Limit Order Markets: Limit and Dawson-Watanabe Superprocesses Theorems and Diffusion Approximations It is well-known that the mean-variance optimization of We propose a queueing model for the dynamics of a limit adaptive order execution strategies is not dynamically con- order book in a liquid market where buy and sell orders sistent. By localizing the mean-variance criterion, one is are submitted at high frequency. We derive a functional led to the optimization of the mean versus quadratic vari- central limit theorem for the joint dynamics of the bid and ation, which is a dynamically consistent stochastic control ask queues and show that, when the frequency of order problem with fuel constraint. We show how this latter 140 FM12 Abstracts problem can be solved by means of Dawson-Watanabe su- Department of Mathematics perprocesses. University of Texas at Austin [email protected] Alexander Schied University of Mannheim Gordan Zitkovic [email protected] The University of Texas at Austin Department of Mathematics MS1 [email protected] Optimal Liquidation in a Limit Order Book Mihai Sirbu We consider an asset liquidation problem at the market mi- University of Texas at Austin crostructure level, conditional on observing the limit order [email protected] book. The optimization problem is formulated in terms of a sequence of stopping times, at which we submit market sell orders. We describe the shape of the trade and no MS2 trade regions for various assumptions on the price process Optimal Investment with Small Transaction Costs and the latency of the trader. In the empirical section, and General Stochastic Opportunity Sets we show that our optimal policy significantly outperforms a benchmark TWAP algorithm on US treasury bonds. In For an investor with constant absolute risk aversion, we in- addition we can efficiently calculate the cost of latency in formally derive the first-order asymptotics of the optimal the trade execution. investment strategy as the bid-ask spread becomes small. For general Itô processes, the first order correction term is Sasha F. Stoikov, Rolf Waeber expressed in terms of the quadratic variation of the friction- Cornell University less optimizer. This result allows to quantify the impact [email protected], [email protected] of, e.g., predictability and stochastic volatility on portfolio choice in the presence of transaction costs. Applied to an investor holding a random endowment, it also leads MS2 to a generalization of the asymptotic utility-based hedging Pricing a Contingent Claim Liability with Transac- strategies determined by Whalley and Wilmott (1997) for tion Costs Using Asymptotic Analysis for Optimal a constant opportunity set. This is joint work with Jan Investment Kallsen.

We price a contingent claim liability using the utility in- Johannes Muhle-Karbe difference argument. We consider an agent, who invests Departement Mathematik in a stock and a money market account with the goal of ETH Zürich maximizing the utility of his investment at the final time [email protected] T in the presence of a proportional transaction cost in two cases with and without the liability. In both cases, we pro- Jan Kallsen vide a rigorous derivation of the asymptotic expansion of Kiel University the value function and obtain a “nearly optimal” strategy. [email protected] Additionally, we derive the asymptotic price of the contingent claim liability. MS2 Maxim Bichuch The Optimal Use of Options to Reduce the Effect Department of Operations Research and Financial of Transaction Costs in a Portfolio Engineering Princeton University Options are redundant in a portfolio of cash and stock if [email protected] we assume the market of Black and Scholes, which includes no transaction costs. When we include transaction costs, however, options, when used correctly, can become quite MS2 useful in reducing the ill-effects these costs create. Specif- Shadow Prices and Well Posedness in the Optimal ically, let ε represent the scale of a small proportional loss Investment and Consumption Problem with Trans- from any trade. Given an investor’s utility preference, the action Costs loss in expected utility due to transaction costs in a cash 2 We revisit the optimal investment and consumption model and stock portfolio is, at best, O ε 3 . However, by in- of Davis and Norman (1990) and Shreve and Soner (1994), cluding options in the portfolio, we can improve this to following a shadow-price approach similar to that of 6 O ε 7 , which is much closer to the O (ε) loss guaranteed Kallsen and Muhle-Karbe (2010). Making use of the completeness of the model without transaction costs, we re- by even one trade. We detail the specific optimal strategy formulate and reduce the HJB equation for this singular that accomplishes this. stochastic control problem to a free-boundary problem for a first-order ODE with an integral constraint. Having shown Dan Ostrov that the free boundary problem has a twicely differenciable Santa Clara University solution, we use it to construct the solution of the origi- [email protected] nal optimal investment/consumption problem without any recourse to the dynamic programming principle. Further- Jonathan Goodman more, we provide an explicit characterization of model pa- Courant Institute rameters for which the value function is finite. USA [email protected] Jin Hyuk Choi FM12 Abstracts 141

MS3 MS3 Modeling and Simulation of Systemic Risk in Default and Systemic Risk in Equilibrium Insurance-Reinsurance Networks In a finite horizon continuous time market model, we con- We propose a dynamic insurance network model that al- sider risk averse utility maximizers who invest dynamically lows to deal with reinsurance counter-party default risks in a risk-free money market account, a stock written on with a particular aim of capturing cascading effects at the a default-free dividend process, and a defaultable bond. time of defaults.An equilibrium allocation of settlements is Prices are determined via equilibrium. We analyze conta- found as the unique optimal solution of a linear program- gion arising endogenously between the stock and the de- ming problem. This equilibrium allocation recognizes 1) faultable bond via the interplay between equilibrium be- the correlation among the risk factors, which are assumed havior of investors, risk preferences, and cyclicality prop- to be heavy-tailed, 2) the contractual obligations, which erties of the default intensity. The equilibrium price of are assumed to follow popular contracts in the insurance the stock experiences a jump at default, despite that the industry (such as stop-loss and retro-cesion), and 3) the default event has no causal impact on the dividend pro- interconnections of the insurance-reinsurance network. We cess. We characterize the direction of the jump in terms are able to obtain an asymptotic description of the most of a relation between investor preferences and the cyclical- likely ways in which the default of a specific group of in- ity properties of the default intensity. A similar analysis is surers can occur, by means of solving a multidimensional performed for the market price of risk and investor wealth Knapsack integer programming problem. Finally, we pro- processes. The impact of heterogeneity of preferences on pose a class of provably strongly efficient estimators for the default exposure carried by different investors is also computing the expected loss of the network conditioning investigated. the failure of a specific set of companies. Martin Larsson Jose Blanchet Cornell University Columbia University [email protected] [email protected] Agostino Capponi Yixi SHI School of Industrial Engineering IEOR Dept, Columbia University Purdue University [email protected] [email protected]

MS3 MS3 Pricing of Path-Dependent Vulnerable Claims in Filtered Likelihood for Point Processes Regime Switching Markets We develop likelihood estimators of the parameters of a We study pricing of path-dependent vulnerable claims in marked point process and of incompletely observed ex- regime-switching markets. The key theoretical tool under- planatory factors that influence the arrival intensity along lying our results is a Poisson series representation of vulner- with the point process itself. The factors follow jump- able claims, which we develop using a change of probabil- diffusions whose drift, diffusion, and jump coefficients are ity measure technique. We employ such a representation, allowed to depend on the point process. We provide condi- along with a short-time asymptotic expansion of the claim’s tions guaranteeing consistency and asymptotic normality price in terms of the Laplace transforms of the symmetric as the sample period grows. We also establish an approxi- Dirichlet distribution, to develop an efficient method for mation to the likelihood and analyze the convergence and pricing claims which may depend on the full path of the un- asymptotic properties of the associated estimators. Nu- derlying Markov chain. The proposed approach is applied merical results illustrate our approach. to price not only simple European claims such as defaultable bonds, but also a new type of path-dependent claims Gustavo Schwenkler that we term self-decomposable, as well as the important Stanford University class of vulnerable call and put options on a stock. We Dep. of Management Science and Engineering provide a detailed error analysis and illustrate the accuracy [email protected] and computational complexity of our algorithms on market traded instruments, such as defaultable bond prices, Kay Giesecke barrier options, and vulnerable European options. Stanford University Dept. of Management Science and Engineering Agostino Capponi [email protected] School of Industrial Engineering Purdue University [email protected] MS4 Excursions in Atlas Models of Equity Market Jose E. Figueroa-Lopez Purdue University Let us consider an equity market of finite number of stocks fi[email protected] where behavior of their capitalization is a multidimensional diffusion characterized with their rankings. Such model can Jeff Nisen capture flows of market capitalizations as it was observed Purdue University by Fernholz et al. In this talk we consider some questions Statistics Department on excursion measure and time-reversibility for these flows [email protected] of market capitalization with application to portfolio management under such abstract equity market. Tomoyuki Ichiba 142 FM12 Abstracts

University of California, Santa Barbara Mark Fees Department of Statistics [email protected] In this talk, we consider the Merton problem for an agent who may invest in a money market fund, a stock, and a hedge fund that is subject to a performance fee. This fee MS4 is assessed each time the cumulative profit-to-date derived Optimal Investment for All Time Horizons and from the investment in the hedge fund reaches a new run- Martin Boundary of Space-time Diffusion ning maximum. We will study the associated HJB equation and examine some qualitative properties of the opti- I review the definition and basic properties of the forward mal strategy. performance processes, including their relation to the more standard investment criteria, and the associated SPDE Gerard Brunick characterization. I, then, concentrate on the problem of University of California constructing the forward investment performance processes Santa Barbara in a Markovian setting. In this case, the problem reduces [email protected] to the so-called ”forward Hamilton-Jacobi-Bellman equation”, which, in some cases, can be transformed into a time- Karel Janecek reversed linear parabolic equation. I characterize the so- RSJ algorithmic trading lutions of this (ill-posed) problem explicitly, extending the [email protected] classical Widders theorem on positive solutions to the time- reversed heat equation. Finally, I consider closed-form ex- Mihai Sirbu amples of the Markovian forward performance processes University of Texas at Austin in some specific stochastic volatility models, including the [email protected] mean-reverting log-price (Schwartz) model.

Sergey Nadtochiy MS5 Oxford University A Uniqueness Theorem for a Degenerate QVI Ap- Oxford-Man Institute pearing in An Option Pricing Problem [email protected] We prove the missing uniqueness theorem for the viscosity solution of a degenerate quasi-variational inequality, which MS4 makes the probability-free theory of option pricing in the Volatility-Stabilized Markets interval market model, essentially complete.

We consider models which generalize the Volatility- Na¨ıma El Farouq stabilized markets introduced in Fernholz and Karatzas University Blaise Pascal, Clermont-Ferrand, France (2005). We show how to construct a weak solution of the [email protected] underlying system of stochastic differential equations, express the solution in terms of time changed squared-Bessel Pierre bernhard processes, and argue that this solution is unique in distri- INRIA-Sophia Antipolis-Méditerranée bution. Moreover, we discuss sufficient conditions for the France existence of a strong solution and show that strong relative [email protected] arbitrage opportunities exist in these markets.

Radka Pickova MS5 Columbia University [email protected] Existence, Uniqueness, and Global Regularity for Degenerate Obstacle Problems in Mathematical Fi- nance MS4 The Heston stochastic volatility process, which is widely Generalizations of Functionally Generated Portfo- used as an asset price model in mathematical finance, is a lios paradigm for a degenerate diffusion process where the de- I will present generalizations on functionally generated generacy in the diffusion coefficient is proportional to the portfolios (FGPs) of stochastic portfolio theory. The as- square root of the distance to the boundary of the half- sets and the benchmark may be any strictly positive wealth plane. The generator of this process with killing, called processes, as opposed to merely the stocks and the market the elliptic Heston operator, is a second-order degenerate portfolio, respectively. Another generalization is that the elliptic partial differential operator whose coefficients have generating function may be stochastic, so that the gen- linear growth in the spatial variables and where the degen- erated portfolio can be adjusted to changing market con- eracy in the operator symbol is proportional to the distance ditions. These FGPs can be applied to arbitrary cointe- to the boundary of the half-plane. With the aid of weighted grated market modes exploiting their mean-reversion in a Sobolev spaces, we prove existence, uniqueness, and global risk-controlled manner. regularity of solutions to stationary variational inequalities and obstacle problems for the elliptic Heston operator on Winslow C. Strong unbounded subdomains of the half-plane. In mathematical University of California Santa Barbara finance, solutions to obstacle problems for the elliptic He- [email protected] ston operator correspond to value functions for perpetual American-style options on the underlying asset.

MS5 Paul Feehan Optimal Investment in the Presence of High-water Rutgers University [email protected] FM12 Abstracts 143

Panagiota Daskalopoulos stochastic volatility model. For smooth density functions, Columbia University the method converges exponentially in the number of terms [email protected] in the Fourier cosine series summations.

Marjon Ruijter, Kees Oosterlee MS5 CWI - Center for Mathematics and Computer Science Approximate Solutions to Second Order Parabolic [email protected], [email protected] Equations with Time-dependent Coefficients We consider second order parabolic equations with co- MS6 efficients that vary both in space and in time (non- Risk-Neutral Valuation of Real Estate Options autonomous). We derive closed-form approximations to the associated fundamental solution by extending the We propose a novel and intuitive risk-neutral valuation Dyson-Taylor commutator method that we recently es- model for real estate derivatives. The resulting index be- tablished for autonomous equations. We establish error havior can easily be analyzed and closed-form pricing so- bounds in Sobolev spaces and show that by including lutions are derived for forwards, swaps and European put enough terms, our approximation can be proven to be ac- and call options. We demonstrate the application of the curate to arbitrary high order in the short-time limit. We model by valuing a put option on a house price index. Au- show how our method extends to give an approximation of tocorrelation in the index returns appears to have a large the solution for any fixed time and within any given toler- impact on the option value. We also study the effect of ance. Some applications to option pricing are presented. In an over- or undervalued real estate market. The observed particular, we perform several numerical tests, and specif- effects are significant and as expected. ically include results on Stochastic Volatility models. Stefan Singor Victor Nistor Ortec-Finance Pennsylvania State University Stefan.Singor@ortec-finance.com [email protected] David van Bragt Anna Mazzucato Aegon Department of Mathematics, Penn State University [email protected] [email protected] Marc Francke Wen Cheng Ortec Finance Penn State university marc.francke@ortec-finance.com [email protected] Antoon Pelsser University of Maastricht MS6 [email protected] Mixed Deterministic Monte-Carlo Simulations for Finance MS6 Mixing Monte-Carlo and PDE methods can substantially Efficient Option Pricing of Asian Options based on speed-up computations because it allows use of closed Fourier Cosine Expansions form solutions for some of the components. It can also solve problems like unknown boundary conditions for com- In this talk we present an efficient pricing method for Asian plex stochastic volatility models. Applying the method options under Lévy processes, based on Fourier–cosine ex- combined with Longstaff-Schwartz projection can lead to pansions and Clenshaw–Curtis quadrature. The pricing efficient computations of early exercise contracts. The method has been developed for both European–style and convergence of the methods will be established with er- American–style Asian options, written on different types ror estimates and we shall report performance on multi- of average (arithmetic, geometric and harmonic), and for dimensional problems. discretely and continuously monitored versions. Fast convergence of Fourier cosine expansions and Clenshaw–Curtis Olivier Pironneau quadrature ensures exponential convergence in the Asian University of Paris VI (Pierre et Marie Curie) option prices in most cases, which reduces the computing [email protected] time of the method to milliseconds for geometric Asian options and a few seconds for arithmetic Asian options. The Gregoire Loeper method’s convergence behavior is explained by an error Natixis analysis. Its performance is further demonstrated by vari- [email protected] ous numerical examples, where we also show the power of an implementation on the Graphics Processing Unit (GPU) where hundreds of speedup is achieved for pricing early– MS6 exercise Asian options, in particular. Two-dimensional Fourier Cosine Series Expansion Method for Pricing Financial Options Bowen Zhang Delft University of Technology The COS method for pricing European and Bermudan op- [email protected] tions with one underlying asset was developed by Fang and Oosterlee (2008, 2009). We extend the method to higher Cornelis W. Oosterlee dimensions, with a multi-dimensional asset price process. Delft University of Technology The algorithm can be applied to, for example, pricing two- Centrum Wiskunde en Informatica (CWI) color rainbow options, but also to pricing under the Heston [email protected] 144 FM12 Abstracts

MS7 Regime Shifts and Levy Jumps Sampling Error of the Supremum of a Levy Process We develop a tractable dynamic term structure models un- Lvy processes are often used in finance to model the dy- der jump-diffusion with Levy Jumps and regime shifts with namics of asset prices. The supremum of a Lvy process time varying transition probabilities. The model allows for is of interest when one is pricing financial contracts whose regime-dependent jumps while both jump risk and regime- payoffs depend on the supremum of the underlying asset switching risk are priced. Two types solutions, including price process. While the maximum of a discretely sampled (log-linear) approximate solutions and exact solutions for Lvy process can often be handled very efficiently using nu- the term structure are obtained for affine-type models un- merical methods, not much is known about the continuous der different conditions. For the approximate solutions, we supremum of a general Lvy process. We present results on derive the error bound, which is in the first order only. For the discrepancy between the discrete maximum and contin- the exact solutions, we further obtain closed-form expres- uous supremum of a Lvy process. Using Spitzers identity sions for special cases. Joint work with Xiangdong Liu, and results from analytic number theory, we derive explicit Lawrence C. Evans, and Shu Wu. expressions for the sampling errors for various commonly used Lvy processes. The results help us better understand Yong Zeng the error of approximating the continuous supremum of a University of Missouri at Kansas City Lvy process by a discrete maximum. Department of Mathematics and Statistics [email protected] Liming Feng Department of Industrial and Enterprise Systems Xiangdong Liu Engineering Jinan University University of Illinois at Urbana-Champaign [email protected] [email protected] Lawrence Evans University of Missouri MS7 [email protected] Positive Subordinate CIR Processes with Two- Sided Mean-Reverting Jumps Shu Wu We present the SubCIR jump-diffusion process. The University of Kansas SubCIRsdiffusion dynamics are those of a CIR pro- [email protected] cess. The SubCIRs jump componentincludes two-sided mean-reverting (state-dependent) jumps. The process re- MS8 mainsstrictly positive if the CIR process satisfies Fellers condition. Theanalytical tractability of the SubCIR pro- Risk Measures and Fine Tuning of High Frequency cess makes it a richer extension tothe CIR process (com- Trading Strategies pared to previous models) and it is also a naturalalternative for interest rates and credit models. Alvaro Cartea Universidad Carlos III Rafael Mendoza-Arriaga [email protected] University of Texas at Austin [email protected] Sebastian Jaimungal University of Toronto, Canada MS7 [email protected] Default Swap Games We consider the valuation of game-type credit default MS8 swaps that allow the protection buyer and seller to raise or New Models for Optimal Execution and High- reduce the respective position once prior to default. Under frequency Market Making a structural credit risk model based on spectrally negative Levy processes, we analyze the existence of the Nash equi- Two related papers will be presented that rely on the same librium and derive the associated saddle point. Using the mathematical finding. The first one ”Dealing with the in- principles of smooth and continuous fit, we determine the ventory risk” solves the Avellaneda-Stoikov problem. It buyer’s and seller’s equilibrium exercise strategies, which corresponds to the case of a market maker who has to are of threshold type. continuously set a bid and a ask quote and we derive the optimal quotes with closed-form approximations based on Kazutoshi Yamazaki spectral ideas. The second one deals with the classical Osaka University subject of optimal liquidation and is one of the first at- [email protected] tempts to solve the problem with limit orders instead of liquidity-consuming market orders. This second paper will Tim Leung be presented for very general intensity functions. Johns Hopkins University Olivier Gueant [email protected] Université Paris-Diderot UFR de Mathématiques MS7 [email protected] Multifactor Term Structure of Interest Rates under FM12 Abstracts 145

MS8 MS9 Optimal HF Trading in a Prorata Microstructure Optimal Consumption and Investment in Incom- plete Markets with General Constraints We propose a framework to study optimal trading policies in a one-tick pro-rata limit order book, as typically We study an optimal consumption and investment problem arises in short-term interest rate futures contracts. The in a possibly incomplete market with general, not neces- high-frequency trader has the choice to trade via market sarily convex, stochastic constraints. We give explicit solu- orders or limit orders, which are represented respectively by tions for investors with exponential, logarithmic and power impulse controls and continuous controls. We model and utility. Our approach is based on martingale methods discuss the consequences of the two main features of this which rely on recent results on the existence and uniqueness particular microstructure: first, the limit orders sent by of solutions to BSDEs with drivers of quadratic growth. the high frequency trader are only partially executed, and therefore she has no control on the executed quantity. For Patrick Cheridito this purpose, cumulative executed volumes are modelled by Princeton University compound Poisson processes. Second, the high frequency [email protected] trader faces the overtrading risk, which is the risk of bru- tal variations in her inventory. The consequences of this risk are investigated in the context of optimal liquidation. MS9 The optimal trading problem is studied by stochastic con- Dynamic Portfolio Choice with Multiple Decentral- trol and dynamic programming methods, which lead to a ized Agents characterization of the value function in terms of an integro quasi-variational inequality. We then provide the as- Abstract not available at time of publication. sociated numerical resolution procedure, and convergence Andrew Lim of this computational scheme is proved. Next, we exam- Industrian Engineering and Operations Research ine several situations where we can one one hand simplify University of California, Berkeley the numerical procedure by reducing the number of state [email protected] variables, and on the other hand focus on specific cases of practical interest. We examine both a market making problem and a best execution problem in the case where MS9 the mid-price process is a martingale. We also detail a high Constructing Sublinear Expectations on Path frequency trading strategy in the case where a (predictive) Space directional information on the mid-price is available. Each of the resulting strategies are illustrated by numerical tests. We provide a general construction of time-consistent sublinear expectations on the space of continuous paths. It Huyen Pham yields the existence of the conditional G-expectation of a University Paris Diderot Borel-measurable (rather than quasi-continuous) random huyn pham ¡[email protected]¿ variable, a generalization of the random G-expectation, and an optional sampling theorem that holds without ex- Fabien Guilbaud ceptional set. University Paris Diderot [email protected] Marcel Nutz Department of Mathematics Columbia University MS9 [email protected] Stochastic Perron’s Method and Verification without Smoothness using Viscosity Comparison: Ob- Ramon Van Handel stacle Problems and Dynkin Games Princeton University [email protected] We adapt the Stochastic Perron’s method in Bayraktar and Sirbu (to appear in the Proceedings of the American Math- ematical Society) to the case of double obstacle problems MS10 associated to Dynkin games. We construct, symmetrically, Resilience to Contagion in Financial Networks a viscosity sub-solution which dominates the upper value of the game and a viscosity super-solution lying below the Propagation of balance-sheet or cash-flow insolvency across lower value of the game. If the double obstacle problem financial institutions may be modeled as a cascade process satisfies the viscosity comparison property, then the game on a network representing their mutual exposures. We de- has a value which is equal to the unique and continuous vis- rive rigorous asymptotic results for the magnitude of conta- cosity solution. In addition, the optimal strategies of the gion in a large financial network and give an analytical ex- two players are equal to the first hitting times of the two pression for the asymptotic fraction of defaults, in terms of stopping regions, as expected. The (single) obstacle prob- network characteristics. Our results extend previous stud- lem associated to optimal stopping can be viewed as a very ies on contagion in random graphs to inhomogeneous di- particular case. This is the first instance of a non-linear rected graphs with a given degree sequence and arbitrary problem where the Stochastic Perron’s method can be ap- distribution of weights. We introduce a criterion for the plied successfully. (Joint work with Mihai Sirbu. Available resilience of a large financial network to the insolvency of a on ArXiv.) small group of financial institutions and quantify how contagion amplifies small shocks to the network. Our results Erhan Bayraktar emphasize the role played by ”contagious links’ and show University of Michigan that institutions which contribute most to network insta- Department of Mathematics bility in case of default have both large connectivity and a [email protected] large fraction of contagious links. The asymptotic results 146 FM12 Abstracts show good agreement with simulations for networks with empirical data. realistic sizes. Lakshithe Wagalath Hamed Amini Universite Pierre & Marie Curie Swiss Finance Institute, Ecole´ polytechnique fédérale de [email protected] La hamed.amini@epfl.ch Rama Cont CNRS (France) & Columbia University Rama Cont [email protected] CNRS (France) & Columbia University [email protected] MS11 Andreea Minca Dynamic Modeling of Systemic Risk Cornell University We generalize the Eisenberg-Noe model to allow for multi- [email protected] ple clearing dates, as well as uncertainty in future liabilities and cash inflows. The clearing payment vectors are sequen- MS10 tially recovered as the solutions of robust linear programming problems solved over the planned horizon. We show Coupled Diffusions, Swarming and Systemic Risk existence and uniqueness of the clearing payment vectors Abstract not available at time of publication. over time. We perform a sensitivity analysis of the loss and payment vector with respect to borrowing and equity Jean Pierre Fouque constraints. We employ the Shapley value methodology University of California Santa Barbara to dynamically attribute the systemic risk to the individ- [email protected] ual nodes in the network. We conclude with a numerical assessment of the proposed methodology on a systemic network consisting of a large number of highly interconnected MS10 financial institutions. FailureandRescueinanInterbankNetwork PengChu Chen This paper is concerned with systemic risk in the inter- Purdue University bank market. We model this market as a directed graph [email protected] in which the banks represent the nodes and the liabilities between the banks represent the edges. Our work builds Agostino Capponi on the modelling paradigm of Eisenberg and Noe (2001), School of Industrial Engineering extending it by introducing default costs in the system. Purdue University We provide a rigorous analysis of those situations in which [email protected] banks have incentives to bailout distressed banks. Such incentives exist under very mild conditions. We illustrate our results with some simple examples, and go on to dis- MS11 cuss possible measures of soundness of a financial system, Estimating Hedge Fund Risk Factors together with possible policy implications for resolution of distress. The estimation of hedge fund returns and the risk factors that impact them is a critical step in the construction of Luitgard Veraart portfolios. In particular, so called fund-of-funds have the Department of Mathematics arduous task of building portfolios of hedge fund strategies London School of Economics based on limited and low frequency observations. This is [email protected] quite daunting in the hedge fund space due to the generally small sample sizes and opaque nature of that in- Chris Rogers dustry’s data. To overcome these difficulties, it is desired Chair of Statistical Science to estimate risk factors based on market observables and Cambridge University reverse engineer a hedge fund exposure to those factors. [email protected] The model that we propose will be used to analyze and decompose the risk of various hedge fund indices on common factors at a high frequency (e.g., daily, or intra-day) MS10 based on their habitual low frequency observations (typi- Feedback Effects and Endogenous Risk in Financial cally monthly). Specifically, we will jointly model the risk- Markets factors (e.g., stock returns) and the asset returns (e.g., a hedge fund strategy) in a fat-tailed, stochastic volatil- We present a mathematical model which allows to quan- ity environment implemented with a Bayesian approach tify the impact of fire sales of assets of a fund undergoing via a Rao-Blackwellised (R-B) particle filter. We utilize a losses on the volatilities and correlations of assets held by vector Stochastic-Volatility model with smoothed observ- the fund. Our model shows that the liquidation of large able returns to extract the potentially time-varying ex- positions by funds may result in spikes in volatilities and posure of low frequency hedge fund performance on high correlations, even in absence of liquidity dry-up, and gives frequency data. By making use of a particle filter with plausible explanations for the large hedge fund losses of Rao-Blackwellization, we reduce the parameter space sig- August 2007. We show that our model can be used for nificantly resulting in a more accurate estimate of the dis- forensic analysis of financial data, to recover characteris- tibution of the parameter state. This approach can be tics of the portfolio undergoing fire sales from public data, used for analyzing hedge fund performance and their ad- by solving an inverse problem. We show the consistency vertized strategies as well as in forensic risk-management. of the estimator obtained and apply it to simulated and The latter of which is a critical need given the generally FM12 Abstracts 147 low transparency of the hedge fund industry. ticular, how past performances may impact the present assessment of risk. Illustrative examples will be discussed. Douglas Johnston Quantalysis, LLC Martin Karliczek [email protected] Department of Mathematics, Humboldt University Berlin Germany Petar Djuric [email protected] Stony Brook University [email protected] MS12 Minimal Supersolutions of BSDEs and Robust MS11 Hedging Smooth and Monotone Covariance Estimation for Elliptical and Generalized Hyperbolic Distribu- We study minimal supersolutions of BSDEs - related to tions Peng’s g-expectation - which can be seen as superhedging functionals. We prove existence, uniqueness, mono- We consider the problem of high-dimensional covariance tone convergence, Fatou’s Lemma and lower semicontinuity estimation from severely limited observations. Strong as- of our functional. Unlike usual BSDE methods, based on sumptions on the structure of the underlying random vec- fixed point theorems, the existence relies on compactness tor have to be made for the problem to be well-defined. methods. We then study some robust extensions which Some examples developed in the literature include: covari- correspond to the problem of superhedging under volatility ance selection models with sparse inverse covariances, low- uncertainty. The talk is based on joint works with Samuel rank structures (PCA models and factor analysis), sparse Drapeau and Gregor Heyne. plus low-rank structures, multi-scale structures. We consider another assumption which is important for a variety Michael Kupper of applications including term-rate risk-modeling in com- Humboldt University Berlin putational finance: smoothness and monotonicity. We re- [email protected] view our previous formulation for multivariate Gaussian random vectors based on semi-definite programming, and MS12 extend the method for elliptical and generalized hyperbolic distributions. We use efficient convex optimization algo- Set-valued Dynamic Risk Measures in Markets rithms and compare the methods using various penalized with Transaction Costs Bregman divergences as objective functions with examples Set-valued risk measures appear naturally when markets from interest rate modeling. with transaction costs are considered and capital require- Dmitry Malioutov ments can be made in a basket of currencies or assets. DRW Holdings In this talk we study dual representation and time con- [email protected] sistency properties of dynamic set-valued risk measures. It turns out that only a stronger time consistency called multi-portfolio time consistency is equivalent to a recur- Xiaoping Zhou sive form of the risk measure as well as to an additive Stony Brook University property for the acceptance sets, which is a central result [email protected] in the scalar case. Birgit Rudloff MS11 Princeton University Nonparametric Prediction in a Limit Order Book brudloff@princeton.edu We propose a novel non-parametric approach to short-term forecasting of the mid-price in a limit order book. We in- MS12 troduce a state vector describing the state of the order Portfolio Choice with Time-consistent Dynamic book at each time. The predictor is based on two features, Risk Measures computed for each value of the state vector. Implicit assumptions of our method are very mild and are supported We study portfolio selection based on time-consistent dy- by our preliminary real-data experiments on NYSEs Open- namic risk measures in a general continuous-time setting. Book which yield promising empirical results. The setting features discontinuities in the asset price processes, with a general and possibly infinite activity jump Ilya Pollak, Deepan Palguna part besides a continuous diffusion part, and general and Purdue University possibly non-convex trading constraints. We character- [email protected], [email protected] ize the minimal risk processes as solutions to Backward Stochastic Differential Equations (BSDEs). We prove ex- MS12 istence and uniqueness of the solution in the general class of jump BSDEs having a driver function that grows at most Dynamic Assessment Indices quadratically. We further compute these solutions in a few Measuring performance and risk of cash flows is a crucial examples by numerically solving the corresponding BSDEs issue in finance. A Dynamic Assessment Index (DAI) is a using regression techniques. quasiconcave, monotone function, mapping cash flows into Mijda Stadje processes which represent their risk or performance evalu- 0 Department of Econometrics and Operations Research ations in time. Using L -separation theorems, we provide Tilburg School of Economics and Management, an upper semicontinuous robust representation and study Netherlands the impact of different time consistency conditions; in par- [email protected] 148 FM12 Abstracts

Roger Laeven asset follows a jump-diffusion process. The main challenge Department of Quantitative Economics lies in the efficient treatment of the jump term resulting a University of Amsterdam full matrix. We discuss some efficient, robust, and accurate [email protected] time discretization methods including schemes treating the jump term explicitly.

MS13 Santtu Salmi The Valuation of Double Barrier Options under University of Jyvaskyla Multifactor Pricing Models santtu.salmi@jyu.ﬁ

The (vast) literature on the pricing of barrier options is Jari Toivanen mainly focused on the valuation of European-style con- Stanford University tracts under single-factor option pricing models (such as [email protected] the geometric Brownian motion and the CEV processes). This paper extends the literature in two directions. First, European-style (double) barrier options are priced under MS13 a multifactor and Markovian financial model that is able Pricing American Options Under Jump-diffusion to accommodate stochastic volatility, stochastic interest Models rates, endogenous bankruptcy, and time-dependent barriers. Second and more importantly, quasi-analytical pric- Under jump-diffusion models, a linear complementarity ing solutions are also proposed for American-style (double) problem (LCP) with a partial-integro differential opera- barrier option contracts under the same general financial tor can formulated for the price of an American option. As model. The proposed pricing solutions are shown to be the discretization of the jump term leads to a full matrix, accurate, easy to implement, and efficient. it preferable to use special techniques to solve the resulting LCPs. We discuss various efficient methods for these JoséC.Dias LCPs. ISCTE-IUL Business School [email protected] Jari Toivanen Stanford University Joo Nunes [email protected] BRU-UNIDE and ISCTE Business School [email protected] Santtu Salmi University of Jyvaskyla santtu.salmi@jyu.fi MS13 Exponential Time Differencing Methods for Pric- ing and Hedging American Options MS14 Efficient Laplace Inversion, Wiener-Hopf Factor- Exponential time differencing (ETD) methods based on the ization and Pricing Lookbacks Cox and Matthews approach are developed to solve a nonlinear BlackScholes model for pricing and hedging Ameri- We construct very fast and accurate methods of approx- can options with transaction cost. Each of these methods imate Laplace inversion, calculation of the Wiener-Hopf avoids solving nonlinear systems, whilst, well known stan- factors for wide classes of Levy processes with exponen- dard methods would require solving nonlinear systems at tially decaying Levy densities, and pricing lookback op- each time step. Numerical experiments are performed on tions. In all cases, we use appropriate conformal changes exotic path-dependent American options with transaction of variables, which allow us to apply the simplified trape- cost to demonstrate the computational efficiency, accuracy zoid rule with small number of terms. The same technique and reliability of the methods. is applicable for calculation of pdf’s of the supremum and infimum processes, and prices and sensitivities of options Abdul M. Khaliq with lookback and barrier features. Middle Tennessee State University Department of Mathematical Sciences Svetlana Boyarchenko [email protected] , Department of Economics, University of Texas at Austin, Mohammad Yousuf 1 University Station C3100, Austin,TX 78712–0301, USA King Fahd University of Petroleum and Minerals [email protected] Saudi Arabia [email protected] MS14 Britta Kleefeld Quadratic Hedging of Barrier Options under Lep- Brandenburgische Technische Universitat Cottbus tokurtic Returns Driven by an Exponential Lvy Germany Model [email protected] We examine quadratic hedging of barrier options in a model realistically calibrated to reflect the leptokurtic nature of MS13 equity returns. We compute the hedging error of the optimal hedging strategy andevaluate prices that yield reason- Efficient and Robust Time Stepping Under Jump- able risk-adjusted performance for the hedger. Our main diffusion Models finding is that the impact of hedging errors on prices is sev- Partial-integro differential (PIDE) formulations are often eral times higher than the impact of other pricing biases used to solve option pricing problems where the underlying studied in the literature, in particular the effect of barrier FM12 Abstracts 149 misalignment and of discrete monitoring. on the risk of the CCP and the incentives for CDS clearing.

Ale Cern Cass Business School, London JinBeom KIM [email protected] IEOR Dept, Columbia University [email protected]

MS14 Rama Cont Exact Simulation of the Heston Jump-Diffusion CNRS (France) & Columbia University [email protected] In this talk, we extend the Heston stochastic volatility model to include state-dependent jumps in the price and the volatility, and develop a method for the exact simu- MS15 lation of this model. The jumps arrive with a stochastic Central Clearing of OTC Derivatives : Bilateral vs intensity that may depend on time, price, volatility and Multilateral Netting jump counts. They may have an impact on the price or the volatility, or both. The random jump size may depend on We study the impact of a central counterparty (CCP) for the price and volatility. Numerical experiments illustrate OTC derivatives on expected interdealer exposures. The the features of the exact method. This is a joint work with results are sensitive to assumptions on heterogeneity of Prof. Erhan Bayraktar at the University of Michigan and risk across asset classes as well as correlation of exposures Prof. Kay Giesecke at Stanford University. across asset classes; empirically plausible specifications of these parameters lead to the conclusion that the gain from Xueying Hu, Erhan Bayraktar multilateral netting in a CCP largely overweighs the loss of University of Michigan netting across asset classes in bilateral netting agreements. Department of Mathematics [email protected], [email protected] Thomas KOKHOLM Aarhus University Kay Giesecke [email protected] Stanford University Dept. of Management Science and Engineering Rama Cont [email protected] CNRS (France) & Columbia University [email protected] MS14 Efficient Pricing and Reliable Calibration in the MS15 Heston Model and its Generalizations Measuring Contagion in Financial Networks We suggest a general scheme for improvement of FT- Liabilities between financial entities form a network. The pricing formulas for European option and give efficient rec- clearing of liabilities and thereby contagion of risk and ommendations for the choice of the parameters of the nu- default depend on this network structure. We provide a merical scheme, which allow for very accurate and fast cal- mathematical model to understand clearing and propaga- culations. We demonstrate that an indiscriminate choice tion of default in such financial networks. This yields a of parameters of a numerical scheme leads to an inaccu- precise measure for the systemic risk induced by individ- rate pricing and calibration. As applications, we consider ual financial entities. The model allows to compute opti- the Heston model and its generalization, and several other mal bailout strategies that either minimize the cost of the affine models. For many parameter sets documented in em- intervention or maximize the stabilizing effect for a given pirical studies of financial markets, relative accuracy bet- bailout budget. Finally, the computational efficiency of the ter than 0.01 % can be achieved by summation of less than model allows to analyze large scale networks quickly. 10-20 terms even in the situations in which the standard approach requires more than 200. In some cases, the one- Sebastian Stiller term formula produces an error of several percent, and the Technische Universitat Berlin summation of two terms — less than 0.5 %. Typically, 10 [email protected] terms and fewer suffice to achieve the error tolerance of several percent and smaller.high-level commands. MS15 Sergei Levendorskii Are CDS Auctions Biased? University of Leicester [email protected] We study settlement auctions for credit default swaps (CDS). We find that the one-sided design of CDS auctions used in practice gives CDS buyers and sellers strong incen- MS15 tives to distort the final auction price, in order to maximize Central Clearing Mechanisms for Credit Default payoffs from existing CDS positions. Consequently, these Swaps auctions tend to overprice defaulted bonds conditional on an excess supply and underprice defaulted bonds condi- Central clearing of Credit default swaps through Central tional on an excess demand. We propose a double auction Counterparties (CCPs) has been proposed as a tool for to mitigate this price bias. We find the predictions of our mitigating systemic risk and counterpart risk in CDS mar- model on bidding behavior to be consistent with data on kets. The design of CCPs for CDS involves the implemen- CDS auctions. tation of margin requirements and a clearing fund (or default fund), for which various designs have been proposed. Haoxiang ZHU We study the impact of the design of these requirements Stanford University 150 FM12 Abstracts [email protected] Justin Sirignano Stanford University SongZi DU [email protected] Graduate School of Business Stanford University [email protected] MS16 Branching and Interacting Particle Models of Sys- temic Risk MS16 Endogenous Equilibria in Liquid Markets with Fric- We propose an interacting particle system description of tions and Boundedly Rational Agents the banking system. While net bank assets evolve independently under normal conditions, defaults trigger a We propose a simple binary mean field game, where N mean-field type interaction that creates systemic risk. We boundedly rational agents may decide to trade or not a work with a stochastic size of the economy, with new banks share of a risky asset in a liquid market. Agents’ utility added spontaneously according to a mean-field birth pro- depends on returns, which are endogenously determined cess. We present some preliminary results about system taking into account observed and forecasted demand and stability and the properties of the corresponding mean-field an exogenous transaction cost. The explicit dependence on limit. past demand generates endogenous dynamics of the system. It is shown that pure strategy Nash equilibria exist. Michael Ludkovski We study under a rather general setting (risk attitudes, UC Santa Barbara pricing rules and noises) the aggregate demand for the as- [email protected] set, the emerging returns and the structure of the equilibria of the asymptotic game. We prove that boom and crash cy- Tomoyuki Ichiba cles may arise and that transaction costs have a stabilizing University of California, Santa Barbara effect on the market. Department of Statistics [email protected] Paolo Dai Pra university of Padua [email protected] MS16 Most Likely Path to Systemic Failure Fulvio Fontini Department of Economics and Management In this talk, I will present recent results on modeling the University of Padova dynamics of correlated default events in the financial mar- [email protected] ket. An empirically motivated system of interacting point processes is introduced and we study how different types of risk, like contagion and exposure to systematic risk, com- Elena Sartori, Marco Tolotti pete and interact in large-scale systems. Large deviation Department of Management arguments are used to approximate the tail of the default Ca’ Foscari University of Venice loss in large portfolios and to identify the way that atyp- [email protected], [email protected] ically large (i.e. “rare’) default clusters are most likely to occur. The results give insights into how different sources MS16 of default correlation interact to generate atypically large portfolio losses. Large Portfolio Asymptotics for Loss From Default Konstantinos Spiliopoulos We prove a law of large numbers for the loss from default Brown University and use it for approximating the distribution of the loss [email protected] from default in large, potentially heterogenous portfolios. The density of the limiting measure is shown to solve a non-linear SPDE, and the moments of the limiting mea- Kay Giesecke sure are shown to satisfy an infinite system of SDEs. The Stanford University solution to this system leads to the distribution of the limit- Dept. of Management Science and Engineering ing portfolio loss, which we propose as an approximation to [email protected] the loss distribution for a large portfolio. Numerical tests illustrate the accuracy of the approximation, and highlight Richard Sowers its computational advantages over a direct Monte Carlo Department of Mathematics simulation of the original stochastic system. University of Illinois [email protected] Kay Giesecke Stanford University Dept. of Management Science and Engineering MS17 [email protected] Quasi-convex Dynamic Programming for Storage Evaluation Konstantinos Spiliopoulos Brown University The value of a storage facility can often be represented [email protected] as a quasi-convex function of the market price and current capacity utilization. This talk will describe a dynamic programming procedure to take advantage of this struc- Richard Sowers ture. The method relies on progressive refinement of outer University of Illinois at Urbana-Champaign approximations of the sub-level sets of the value function [email protected] FM12 Abstracts 151 in each stage. credit risk.

John Birge Matt Thompson University of Chicago Queen’s University Booth School of Business Queen’s School of Business [email protected] [email protected]

MS17 MS18 A Kernel Based Approach to Gas Storage and Small-time Expansions for Stochastic Volatility Swing Contracts Valuations in High Dimensions Models with Lévy Jumps We are expanding upon our previous work [Boogert and We analyze the short-time (equivalently, near expiration) Mazieres, “A Radial Basis Function Approach to Gas Stor- behavior of the tail distributions and option prices of a age Valuation”, 2011], by introducing multi-factor price class of stochastic volatility (SV) models obtained by su- and volume dimensions encountered in both gas storage perposing a classical continuous SV process (say, the Hes- and swing contracts. This is achieved by introducing new ton process) with an independent pure-jump Lévy process. multivariate methods (Kernel based: Radial Basis Func- Polynomial expansions in time of arbitrary order are ob- tions and the Tensor of Radial Basis Functions) to the tained for the tail distributions and out-of-the money op- multi-dimensional Least-Squares Monte Carlo method used tion prices, assuming certain smoothness conditions on the to value these contracts with the spot approach. Lévy density of the jump component and a small-time large deviation principle for the continuous component. As a re- Denis Mazieres sult, we are able to disentangle the effects of the various London University model parameters in the short-time behavior of the option Birkbeck prices and rank their contribution according to the first [email protected] power at which they appear in the polynomial expansion. This talk is based on a joint work with C. HoudréandR. Alexander Boogert Gong. EnergyQuants BV [email protected] Jose E. Figueroa-Lopez Purdue University fi[email protected] MS17 Approximate Linear Programming Relaxations for Commodity Storage Real Option Management MS18 Large Deviations and Stochastic Volatility with The real option management of commodity conversion as- Jumps: Asymptotic Implied Volatility for Affine sets based on high dimensional forward curve evolution Models models commonly used in practice gives rise to intractable Markov decision processes. Focusing on commodity stor- We consider the implied volatility of European options in age, we derive approximate dynamic programs from re- an affine stochastic volatility model with jumps, as time laxations of approximate linear programs formulated using tends to infinity. We show that under a simultaneous low dimensional value function approximations. We evalu- rescaling of the option strike a non-degenerate limiting ate the performance of our approximate dynamic programs volatility smile exists and describe it by a formula which on natural gas and oil instances. can be expressed in terms of the parameters of the underlying model. The result is based on a large-deviation prin- Selvaprabu Nadarajah, Francois Margot ciple for affine stochastic volatility models, that is derived Carnegie Mellon University via the Gärtner-Ellis theorem. We exhibit some specific ex- Tepper School of Business amples including a Heston model with and without jumps, [email protected], [email protected] Bates’ model with state-dependent jump intensity and the Barndorff-Nielsen-Shephard model. Nicola Secomandi Carnegie Mellon Martin Keller-Ressel Tepper School of Business TU Berlin [email protected] [email protected] Antoine Jacquier, Aleksandar Mijatovic MS17 Imperial College London Natural Gas Storage Valuation, Optimization, [email protected], [email protected] Market and Credit Risk Management We present a model for the valuation, optimization, and MS18 pricing of the credit risk of gas storage contracts. A re- A New Look at Short-term Implied Volatility in duced form term structure model of the curve dynam- Models with Jumps ics is derived that facilitates dimension reduction without sacrificing realism. A system of PDEs is derived and This talk analyses the behaviour of the implied volatil- solved using RBF collocation. When the number of injec- ity smile for short-dated options in semimartingale models tion/withdrawal opportunities is large, RBF-PDE method with jumps. We introduce a new renormalization of the can solve problems where heuristic approaches would be strike variable such that the implied volatility for short- impractical. The RBF expansions facilitate pricing of maturity options converges to a nonconstant finite limit, characterised by the diffusion and jump components of the 152 FM12 Abstracts model. This limit yields calibration algorithms for short- small-time asymptotics, (ii) tails of the distribution and dated options and sheds new light on the difference between (iii) small-noise expansions. In the context of stochastic finite and infinite variation jumps in pricing models. volatility models, we recover the Busca-Berestycki-Florent formula (applying (i)) and Gulisashvili-Stein expansion Aleksandar Mijatovic (from (ii)). This is a joint work with J.D. Deuschel (TU Imperial College London Berlin), P. Friz (TU Berlin) and S. Violante (Imperial Col- [email protected] lege London).

Peter Tankov Antoine Jacquier Paris 7 Imperial College London [email protected] [email protected]

Peter Friz MS18 TU Berlin Parametric Inference and Dynamic State Recovery Weierstrass Institute from Option Panels Jean-Dominique Deuschel We develop parametric estimation procedure for option TU Berlin panels observed with error. We provide semiparametric tests for the option price dynamics based on the distance between the spot volatility extracted from the options and Sean Violante the one obtained nonparametrically from high-frequency Imperial College London data on the underlying asset. We further construct new formal tests of the model fit for specific regions of the MS19 volatility surface and for the stability of the risk-neutral dynamics over a given period of time. Asymptotics of Implied Volatility to Arbitrary Or- der Viktor Todorov Kellogg School of Management In a unified model-free framework that includes long- Northwestern University expiry, short-expiry, extreme-strike, and jointly-varying [email protected] strike-expiry regimes, we find asymptotic implied volatility and implied variance formulas in terms of L, with rigorous error estimates of order 1/L to any given power, where L Torben G. Andersen, Nicola Fusari denotes the absolute log of an option price that approaches Northwestern University zero. Our results therefore sharpen, to arbitrarily high [email protected], [email protected] order of accuracy, the model-free asymptotics of implied volatility in extreme regimes. We then apply these general MS19 formulas to particular examples: Lévy and Heston. Joint work with Kun Gao. A Decomposition Formula for Option Prices in the Heston Model and Applications to Option Pricing Roger Lee,KunGao Approximation University of Chicago [email protected], [email protected] By means of classical Its calculus we decompose option prices in the Heston volatility framework as the sum of the classical Black-Scholes formula with volatility param- MS19 eter equal to the root-mean-square future average volatil- Multi-Factor Stochastic Volatility Models for Op- ity plus a term due to correlation and a term due to the tions and Options on Variance volatility of the volatility. This decomposition formula allows us to construct first and second order option pricing Through perturbation methods we reconcile skews of im- approximation formulas that are extremely easy to com- plied volatilities for options and options on variance in the pute, as well as to study their accuracy for short maturi- context of multi-scale stochastic volatility models. ties. Moreover we see the corresponding approximations for the implied volatility are linear (first-order approxima- Jean Pierre Fouque tion) and quadratic (second-order approximation) in the University of California Santa Barbara log-stock price variable. [email protected]

Elisa Alos Yuri Saporito Universitat Pompeu Fabra UC Santa Barbara [email protected] [email protected]

MS19 Jorge P. Zubelli Small-noise Expansion for Projected Diffusions and IMPA Implied Volatility Asymptotics [email protected] Given a diffusion in Rn, we prove a small-noise expansion for the density of its projection on a subspace of di- MS20 mension p n. Our proof relies on the Laplace method On the Multi-Dimensional Controller and Stopper on Wiener≤ space and stochastic Taylor expansions in the Games spirit of Azencott-Benarous-Bismut. Our result (assuming Hörmander’s condition on the vector fields) applies to (i) We consider a zero-sum stochastic differential controller- and-stopper game in which the state process is a controlled FM12 Abstracts 153 diffusion evolving in a multi-dimensional Euclidean space. Johns Hopkins University In this game, the controller affects both the drift and the [email protected] volatility terms of the state process. Under appropriate conditions, we show that the game has a value and the Qingshuo Song value function is the unique viscosity solution to an obsta- City University of Hong Kong cle problem for a Hamilton-Jacobi-Bellman equation. [email protected] Yu-Jui Huang University of Michigan, Department of Mathematics MS20 [email protected] Optimal Trend-following Trading Rules under a Three-state Regime-switching Mode Erhan Bayraktar University of Michigan Assume the market follows a regime switching model with Department of Mathematics three states, a set of sufficient conditions are developed to [email protected] guarantee the optimality of trend-following trading strategies. A dynamic programming approach is used to verify these optimality conditions. The value functions are char- MS20 acterized by the associated HJB equations. The results in Numerical Solutions of Optimal Risk Control and this paper will help an investor to identify market condi- Dividend Optimization Policies tions and to avoid trades which might be unprofitable even under the best market information. This work develops numerical methods for finding optimal dividend pay-out and reinsurance policies. The surplus Jie Yu is modeled by a regime-switching process subject to both Roosevelt University regular and singular controls. Markov chain approximation [email protected] techniques are used to approximate the value function and optimal controls. The proofs of the convergence of the ap- Qing Zhang proximation sequence to the surplus process and the value University of Georgia function are given. Examples are presented to illustrate Department of Mathematics the applicability of the numerical methods. [email protected] Zhuo Jin University of Melbourne, Australia MS21 [email protected] Evaluating Callable and Putable Bonds: An Eigen- function Expansion Approach George Yin Wayne State University Abstract not available at time of publication. Department of Mathematics [email protected] Dongjae Lim Northwestern Chao Zhu [email protected] University of Wisconsin-Milwaukee [email protected] MS21 Building Financial Models with Time Changes MS20 Abstract not available at time of publication. Outperformance Portfolio Optimization via the Equivalence of Pure and and Randomized Hypoth- Vadim Linetsky esis Testing Northwestern University [email protected] We study the portfolio problem of maximizing the outperformance probability over a random benchmark through dynamic trading with a fixed initial capital. Under a gen- MS21 eral incomplete market framework, this stochastic control Pricing Derivatives on Multiscale Diffusions: An problem can be formulated as a composite pure hypothesis Eigenfunction Expansion Approach testing problem. We analyze the connection between this pure testing problem and its randomized counterpart, and Using tools from spectral analysis, singular and regu- from latter we derive a dual representation for the maxi- lar perturbation theory, we develop a systematic method mal outperformance probability. Moreover, in a complete for analytically computing the approximate price of a market setting, we provide a closed-form solution to the derivative-asset. The payoff of the derivative-asset may problem of beating a leveraged exchange traded fund. For be path-dependent. Additionally, the process underlying a general benchmark under an incomplete stochastic fac- the derivative may exhibit killing (i.e. jump to default) as tor model, we provide the Hamilton-Jacobi-Bellman PDE well as combined local/nonlocal stochastic volatility. The characterization for the maximal outperformance probabil- nonlocal component of volatility is multiscale, in the sense ity. that it is driven by one fast-varying and one slow-varying factor. The flexibility of our modeling framework is con- Jie Yang trasted by the simplicity of our method. We reduce the University of Illinois at Chicago derivative pricing problem to that of solving a single eigen- [email protected] value equation. Once the eigenvalue equation is solved, the approximate price of a derivative can be calculated Tim Leung 154 FM12 Abstracts formulaically. To illustrate our method, we calculate the Money Illusion approximate price of three derivative-assets: a vanilla option on a defaultable stock, a path-dependent option on a We use the portfolio selection model presented in He and non-defaultable stock, and a bond in a short-rate model. Zhou (2011, Management Science, Volume 57, Issue 2, pages 315–331) and the NYSE equity and U.S. treasury Matthew Lorig bond returns for the period 1926-1990 to provide a rigor- Princeton University ous treatment of Benartzi and Thaler’s myopic loss aver- ORFE Department sion theory. We find that in addition to the agent’s loss [email protected] aversion and evaluation period, his reference point also has a significant effect on optimal asset allocation. We demonstrate that the agent’s optimal allocation to equities is con- MS21 sistent with the market observation when he has reasonable Closed-form Expansions of Option Prices under values of degree of loss aversion, evaluation period, and ref- Time-changed Dynamics erence point. We also find that the optimal allocation to equities is sensitive to these parameters. We then examine We consider a broad class of option pricing models and the implications of money illusion for asset allocation and derive a simple closed-form expansion of option prices in pricing. Finally, we extend the model to a dynamic setting. these models in terms of Black-Scholes prices and higher- order Greeks. The expansion provides a transparent and informative decomposition of option prices. Moreover, it Xuedong He can be used for a large class of flexible models which allow Columbia University for both stochastic volatility and jumps. Finally, it allows Department of Industrial Engineering and Operations for fast model calibration. Research [email protected] David Pedersen Aarhus University Xunyu Zhou [email protected] University of Oxford and The Chinese University of Hong Kong Elisa Nicolato [email protected] University of Aarhus [email protected] MS22 Consumption-based Behavioral Portfolio Selection MS22 in Continuous Time Optimal Portfolios under Worst Case Scenarios We study the optimal consumption-investment problem in Standard portfolio theories such as Expected Utility The- a continuous-time financial market with behavioural cri- ory, Yaari’s Dual Theory, Cumulative Prospect Theory and teria featured by S-shaped utility function and probability Mean-Variance optimization all assume that investors only distortions. Different formulations of the problem are stud- look at the distributional properties of strategies and do ied. When optimal solutions exist, we get explicit forms not care about the states of the world in which the cash- basedonsomealgebraicequations. flows are received. In a very interesting paper, Dybvig (1988a, 1988b) essentially showed that in these instances Hanqing Jin optimal portfolios are decreasing in the state-price density, Oxford University also pointing indirectly to the important role of diversified [email protected] portfolios. In this paper we first observe that the worst outcomes for optimal strategies exactly occur when the market declines (i.e. during a financial crisis), but this is at odds MS22 with the aspirations and requirements of many investors. Utility Maximization with Addictive Consumption Hence we depart from the traditional behavioral setting Habit Formation in Incomplete Markets and study optimal strategies for investors who do not only care about the distribution of wealth but, additionally, also We study the utility maximization problem of consumption impose constraints on its interaction with the (stressed) fi- with addictive habit formation in the general incomplete nancial market. Preferences become state-dependent and semimartingale market. By introducing the auxiliary state we are able to assess the impact of these on trading deci- and dual processes and defining the value function both on sions. We construct optimal strategies explicitly and show initial wealth and initial habit, we embed our original path how they outperform traditional diversification strategies dependent problem into an abstract time separable opti- under worst-case scenarios. mization problem with the shadow random endowment. We establish existence and uniqueness of the optimal solu- 0 Carole Bernard,Jit-SengChen tion using convex duality approach on L+ spaces. University of Waterloo [email protected], [email protected] Xiang Yu Department of Mathematics, Steven Vanduffel The University of Texas at Austin Vrije Universiteit Brussel, Belgium. [email protected] steven.vanduff[email protected] MS23 MS22 The Log Optimal Portfolio under Transaction Myopic Loss Aversion, Reference Point, and Costs and the Shadow Price: The Geometric Ornstein-Uhlenbeck Process and a Counterexam- FM12 Abstracts 155 ple asymptotically but not for all times. A turnpike theorem shows it is a limit of numeraire strategies on finite hori- As in (Gerhold/Muhle-Karbe/Schachermayer 2011) we zons (joint work with Constantinos Kardaras and Eckhard find the growth optimal portfolio for the geometric Platen). Ornstein-Uhlenbeck process under proportional transaction costs by constructing a shadow price. This is a price Jan Obloj process, such that the optimization problem without fric- Mathematical Institute, University of Oxford tions for that price has the same solution as the one under and the Oxford-Man Institute of Quantitative Finance transaction costs. This technique allows us to explicitly [email protected] compute fractional Taylor expansions of arbitrary order for all quantities of interest. Similar results have (to the best of our knowledge) so far only been obtained for the Black Sc- MS23 holes model. Moreover, we present a counterexample that Wealth vs Risk in a Continuous Time Model shadow prices may not exist in general even in discrete time and for “well-behaved’ markets. We discuss a continuous time optimization problem which combines two conflicting objectives of maximizing the port- Christoph Czichowsky, Philipp Deutsch folio wealth up to a level and minimizing the conditional U of Vienna value-at-risk of the portfolio wealth loss. The associated [email protected], utility function is not differentiable nor strictly concave [email protected] and does not satisfy Inada’s condition. We use the dual control method to show that there is a classical solution to Johannes Muhle-Karbe the HJB equation and that the optimal value function is Departement Mathematik smooth if the optimal control satisfies an exponential mo- ETH Zürich ment condition. We find the closed-form optimal feedback [email protected] control and optimal value function for a wealth maximization problem. Walter Schachermayer Harry Zheng U of Vienna Imperial College London [email protected] [email protected]

MS23 MS24 Market Depth and Trading Volume Dynamics Stress Tests: From Arts to Science (Overview)

We derive the process followed by trading volume, in a Expectations on stress tests are high in the financial in- market with finite depth and constant investment oppor- dustry: they should measure the resilience of individual tunities. A representative investor, with a long horizon and financial institutions and of the whole banking system as constant relative risk aversion, trades a safe and a risky as- part of an economy. Additionally, they should act as a set with a liquidity cost proportional to trading speed. An calmative for nervous markets. It is time to assess the ordinary differential equation identifies the trading policy expectations about what information can realistically be and welfare. In the high-liquidity limit, trading volume obtained from stress tests. How should we choose scenar- follows approximately an Ornstein-Uhlenbeck process, and ios which are at the same time plausible and informative increases with liquidity, volatility, and risk aversion. of potential weaknesses? How can we assess the validity Paolo Guasoni of our models and the potential consequences where our Boston University models break down? How can we adequately discriminate Dublin City University adverse external shocks and dangerous endogenous effects? [email protected] Thomas Breuer Marko Weber Research Centre PPE, Fachhochschule Vorarlberg Dublin City University Austria Scuola Normale Superiore [email protected] [email protected]

MS24 MS23 Finding Stress Scenarios That Get the Job Done, Long-run Investment under Drawdown Con- with Credit Risk Applications straints: optimal portfolios and numeraire property We introduce new methods to generate finite representative collections of plausible yet severe scenarios. We apply We consider long-run investment problems under draw- these methods to generate credit risk scenarios and demon- down constraints: the current wealth can not fall below strate, via numerical experiments, that with respect to cer- a given function of its past maximum. We work in a gen- tain performance measures, our method is better able to eral semimartingale setting. First, we show that this prob- discover (ex ante) scenarios close to those that occurred lem is equivalent to an unconstrained problem but with a (as determined ex post), than previously described meth- modified utility function: both the value and the optimal ods. Moreover, our methods discover these scenarios at portfolio are given explicitly in terms of their unconstrained substantially lower computational cost. counterparts (joint work with Vladimir Cherny). Second, we analyse in more detail the growth optimal portoflio un- Craig A. Friedman der linear drawdowns. We show it enjoys the numeraire Standard & Poors property along specific sequences of stopping times and [email protected] 156 FM12 Abstracts

MS24 Discontinuous Semimartingales Stress Testing Model Risk We derive a forward partial integro-differential equation for Abstract not available at time of publication. prices of call options in a model where the dynamics of the underlying asset under the pricing measure is described by Paul Kupiec a -possibly discontinuous- semimartingale. A uniqueness FDIC theorem is given for the solutions of this equation. We [email protected] relate this result to the construction of a Markovian projection - a Markov process which mimics the marginals distributions of the semimartingale. This result gener- MS24 alizes Dupire’s forward equation to a large class of non- Must Stress Tests be Credible? Markovian models with jumps. Abstract not available at time of publication. Amel Bentata Universite Pierre & Marie Curie, France Til Schuermann [email protected] Oliver Wyman [email protected] Rama Cont CNRS (France) & Columbia University MS25 [email protected] Utility Indifference Pricing in Energy Markets MS26 Abstract not available at time of publication. Functional Ito Calculus and the Pricing and Hedg- Luciano Campi ing of Path-dependent Derivatives Paris 13 University [email protected] We provide a brief overview of the Functional Ito Calcu- lus [Dupire 2009; Cont & Fournié 2010], which provides a convenient mathematical framework for analyzing path- MS25 dependent functionals of Ito processes, and show that it Probabilistic Approach to Mean Field Games and may be used to derive a ’universal’ pricing equation which the Control of McKean Vlasov Dynamics holds for a wide class of path-dependent options on an underlying asset whose price follows an Ito process. This uni- Abstract not available at time of publication. versal pricing equation is a functional analog of the backward Kolmogorov equation: we present a uniqueness re- Rene Carmona sult for solutions of this equation and show that it verifies Princeton University a comparison principle. Finally, we provide a unified ap- Dpt of Operations Research & Financial Engineering proach to the computation of hedging strategies for path- [email protected] dependent options. Rama Cont MS25 CNRS (France) & Columbia University Levy Semistationary Processes with Applications [email protected] to Electricity Markets David Fournie So called Levy semistationary processes (LSS processes) Morgan Stanley constitute a rather general class of continuous time mov- [email protected] ing average processes. Our motivation is employing these processes to model electricity and commodity forwards and spots. We discuss and analyze numerical simulation MS26 procedures for LSS processes and energy forward random Local Vs Non-Local Forward Equations for Option fields, by means of stochastic partial differential equations, Pricing Fourier methods and finite dimensional approximations. When the underlying asset is a continuous martingale, Heidar I. Eyjolfsson,FredEspenBenth call option prices solve the Dupire equation, a forward University of Oslo parabolic PDE in the maturity and strike variables. By [email protected], [email protected] contrast, when the underlying asset is described by a discontinuous semimartingale, call price solve a partial integro-differential equation (PIDE), containing a non- MS25 local integral term. We show that the two classes of equa- Forward-Backward SDE Games and Stochastic tions share no common solution: a given set of option prices Control under Model with Uncertainty is either generated from a continuous martingale (”diffusion”) model or from a model with jumps, but not both. Abstract not available at time of publication. In particular, our result shows that Dupires inversion for- Agnès Sulem mula for reconstructing local volatility from option prices INRIA does not apply to option prices generated from models with [email protected] jumps. Yu Gu MS26 Columbia University [email protected] Forward Equations and Mimicking Theorems for FM12 Abstracts 157

Rama Cont CNRS (France) & Columbia University [email protected] Martin Summer OeNB, Austrian Central Bank [email protected] MS26 Degenerate Parabolic PDEs, Martingale Problems Thomas Breuer, Martin Jandacka and a Mimicking Theorem for Itô Processes Research Centre PPE, Fachhochschule Vorarlberg Austria We prove existence, uniqueness and regularity of solutions [email protected], [email protected] in weighted Hölder spaces for a certain class of degenerate parabolic partial differential equations with unbounded Javier Mencia coefficients on the half space. We show that the mar- Financial Stability Department tingale problem associate with the differential operator is Banco de Espana well-posed, which implies existence and uniqueness of weak [email protected] solutions to the corresponding stochastic differential equations. The weak solutions match the one-dimensional probability distributions of a certain class of Itô processes. MS27 Camelia A. Pop,PaulFEEHAN Lessons and Limits of Stress Tests as a Macropru- Rutgers University dential Supervisory Tool [email protected], [email protected] Abstract not available at time of publication. Konstantinos Tsatsaronis MS27 Bank for International Settlements Credit Risk Concentration under Stress [email protected] We present a general approach to implementing stress scenarios in multi-factor credit portfolio models, which is MS28 based on the truncation of risk factors. We derive ana- Derivatives on Non-Storable Renewable Resources: lytic formulae for credit correlations under stress and ana- Fish Futures and Options, Not So Fishy after All. lyze their asymptotic behavior in normal variance mixture (NVM) models. It turns out that correlations in heavy- We study forward prices and prices of European call op- tailed NVM models are less sensitive to stress than in tions, which are written on a non-storable renewable re- medium- or light-tailed models. source. An example for such derivatives is provided by futures and options on fresh salmon traded in large volumes Michael Kalkbrener at Fish Pool (Norway) since 2008. The introduction of sim- Deutsche Bank ilar exchanges in the United States and other countries is Frankfurt currently discussed. The pricing formulas are derived from michael kalkbrener ¡[email protected] first principles, starting of by modeling the dynamics of the resource reserves, and assuming that resource extraction MS27 is managed as open access. We derive closed form solutions for the forward price of the renewable resource and Risk Assessment Modelling of Systemic Institu- study its dynamics. In contrast to Black (1976) we show tions that forward prices do not evolve according to a geomet- The Bank of England has developed a top-down stress test- ric Brownian motion, but follow a more complex process. ing and systemic risk model (RAMSI). The model contains For the case of an option we show that the Black (1976) a network of banks, with each bank modelled in consider- formula needs to be adapted in such a way, that the nor- able detail. RAMSI allows the banks to be shocked by mal distribution is replaced by a reciprocal Γ-distribution, (deterministic or stochastic ) macroeconomic scenarios to to get at least a very good approximation of the true op- determine the resilience of the system under stress. The tion price. We include numerical evidence to underline this banks can themselves propagate stress around the system statement. Finally, we derive pricing formulas for options through second round effects. We present the model and written on forward contracts, and show how forward con- an illustration of its use. tracts can be hedged under the assumption that there is a spanning asset. The full paper is available at SSRN: Jack McKeown http://ssrn.com/abstract=1469135 The presentation will Bank of England also include material from a second working paper, which [email protected] includes more empirical analysis. Christian Ewald MS27 Department of Economics, University of Glasgow A Systematic Approach to Multi-period Stress [email protected] Testing of Portfolio Credit Risk

We propose a new method for analysing multiperiod stress MS28 scenarios for portfolio credit risk more systematically than Adaptations of Least-squares Methods to Convex in current macro stress tests. The plausibility of a scenario Control Problems is quantiﬁed by its distance from an average scenario. For a given level of plausibility, we search systematically for Abstract not available at time of publication. the most adverse scenario. We show how this method can Juri Hinz be applied to some models already in use by practitioners. 158 FM12 Abstracts

ETH Zurich, Department of Mathematics, University of Padova Institute for Operations Research [email protected] [email protected]

MS29 MS28 Generalized Aﬃne Transform Formulae and Exact Dark Pools and Hidden Markets Simulation of the WMSV Model

Abstract not available at time of publication. The aim of this talk is to introduce transform formulae for linear functionals of affine processes and their bridges Ulrich Horst whose state space is a set of positive semidefinite matrices. Humboldt University Particularly, we investigate the relationship between such [email protected] transforms and certain integral equations. We are, then, able to derive analytic expressions for Laplace transforms of some functionals of Wishart bridges. As an application, MS28 we suggest an exact simulation method of Wishart multi- A Feedback Model for the Financialization of Com- dimensional stochastic volatility model. modity Prices Chulmin Kang,WanmoKang Abstract not available at time of publication. Departement of Mathematical Sciences, KAIST Republic of Korea Ronnie Sircar [email protected], [email protected] ORFE Princeton University [email protected] MS29 Calibration of Multivariate Affine Stochastic MS29 Volatility Models A Flexible Matrix Libor Model with Smiles We provide a new calibration algorithm for multivariate affine stochastic covariance models using both option and We present a flexible approach for the valuation of inter- timeseries data. The option data is used to recover the pa- est rate derivatives based on Affine Processes. We extend rameters determining the drift of the covariance process, the methodology proposed in Keller-Ressel et al. (2009) by while the timeseries allows us to identify the volatility of changing the choice of the state space. We provide semi- the covariance process and its correlation to the price pro- closed-form solutions for the pricing of caps and floors. We cesses. The procedure relies only on the knowledge of the then show that it is possible to price swaptions in a multi- first moments of log-prices and an estimation of volatility factor setting with a good degree of analytical tractability. using Fourier series. This is done via the Edgeworth expansion approach developed in Collin-Dufresne and Goldstein (2002). A numeri- Christa Cuchiero cal exercise illustrates the flexibility of the Wishart Libor University of Vienna, Faculty of Mathematics model in describing the movements of the implied volatility [email protected] surface.

Alessandro Gnoatto Elisa Nicolato LMU Munich University of Aarhus [email protected] [email protected]

Jose Da Fonseca David Skovmand Auckland University of Technology Aarhus University, Department of Economics and [email protected], Business [email protected] Martino Grasselli University of Padova Josef Teichmann [email protected] Department of Mathematics ETH Z [email protected] MS29 The Explicit Laplace Transform for the Wishart MS30 Process Calibrating Volatility Surfaces for Commodity We derive the explicit formula for the joint Laplace trans- Derivatives form of the Wishart process and its time integral which extends the original approach of [Bru, M. F. (1991): Wishart Commodities and their derivatives have become key players processes. Journal of Theoretical Probability, 4:725751]. in the portfolios of many corporations, especially for those We compare our methodology with the alternative results working in the energy sector. In this talk we shall discuss given by the variation of constants method, the lineariza- the calibration of local volatility surfaces for commodity tion of the Matrix Riccati ODEs and the Runge-Kutta al- derivatives. In order to obtain stable and robust results gorithm. The new formula turns out to be fast, accurate we shall make use of regularization techniques to handle and very useful for applications when dealing with stochas- the inverse problem. In particular we shall present some tic volatility and stochastic correlation modelling. results with Brent oil (WTI) and Natural Gas (HH) data. Martino Grasselli FM12 Abstracts 159

the calibration problem.

Vinicius Albani Jorge P. Zubelli IMPA IMPA Rio de Janeiro, Brazil [email protected] [email protected] PP1 MS30 Adjoint Monte-Carlo Technique for Calibration of Volatility Surface Calibration and Financial Market Models Relative-Entropy Minimization We present a Monte-Carlo based adjoint technique for solv- In this talk we will survey the research developed jointly ing calibration problems of financial market models like the with a number of collaborators during the past few years Heston model with time-dependent parameters. Any effi- in connection with the calibration of Black-Scholes models cient optimization method for calibration requires at least under stochastic volatility. We shall start with the rela- gradient information. The major advantage of the adjoint tion between uncertain volatility models, Hamilton-Jacobi technique lies in the fact that the calculation time required equations, and the Kullback-Leibler distance. Then, we for a gradient computation stays nearly constant, indepen- shall discuss calibration and entropy. Finally we will dis- dent of the number of parameters. Our numerical results cuss weighted Monte Carlo methods and applications. confirm this improved speed-up. Marco Avellaneda Bastian Gross Courant Institute University of Trier New York University [email protected] [email protected] Ekkehard W. Sachs University of Trier MS30 Virginia Tech Calibrating Self-exciting Marked Point Processes [email protected] for Algorithmic Trading

Recently, marked point processes have been used to model PP1 the dynamics of assets at ultra-high frequencies. Cartea, On Efficient Option Pricing Under Jump Diffusion Jaimungal and Ricci (2011) develop a multi-factor self- exciting model accounting for the arrival of market orders Merton’s jump-diffusion model leads to partial-integro dif- that influence activity, trigger one- and two-sided cluster- ferentialequations(PIDE),whichcanbesolvedinorder ing of trades, and induce temporary changes in the shape of to price options. Discretization of the integral in the PIDE the LOB. The classification of trades as influential versus leads to non-local terms and dense matrices. The presen- non-influential induces hidden state variables and makes tation will discuss ways to solve the PIDE, avoiding dense online calibration a necessity in high frequency trading a matrices. This is applied to European-style options. challenging endeavor. Here, we develop quasi-maximum- likelihood parameter estimators and a Sequential Monte Ruediger U. Seydel Carlo estimator of the activity path for use in algorithmic University of Cologne trading strategies. Mathematical Institute [email protected] Sebastian Jaimungal University of Toronto, Canada [email protected] PP1 The Impact of Constraints on the Views of the Jason Ricci Black-Litterman Model University of Toronto [email protected] The Black-Litterman model is a Bayesian portfolio optimization model that allows investors to impose prior views on the expected returns of assets in the portfolio. Con- MS30 straints can be considered as prior views on the optimal An Overview of Calibration Methods of Local portfolio weights. Constraints distort the views expressed Volatility Surfaces by the investor, resulting in sub-optimal portfolio weights. Our research shows that a mild relaxation of the long-only Local volatility models are extensively used and well rec- constraint results in Black-Litterman views that are more ognized for hedging and pricing in financial markets. They efficiently represented in the portfolio weights. are frequently used, for instance, in the evaluation of exotic options so as to avoid arbitrage opportunities with respect Byron Wilson to other instruments. Yet, the ill-posed character of local University of Cape Town volatility surface calibration from market prices requires [email protected] the use of regularization techniques either implicitly or explicitly. Such regularization techniques have been widely Gareth Q. Witten studied for a while and are still a topic of intense research. University of Cape Town In this talk we shall review different attempts that have Pontificia Universidad Católica del Per, CENTRUM been made in order to tackle the local volatility calibration Católica problem. In particular, we shall discuss convex regulariza- [email protected] tion tools and recent inverse problem advances to deal with