AN4 Abstracts
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AN4 Abstracts 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) AN14 Abstracts 1 IC1 Laplacians of graphs. The talk will describe these tech- Equilibrium Analysis of Large Populations Dynam- niques, starting with Vaidya’s 1991 solver and ending with ics very recent algorithms by Kelner and others. The talk will focus on how the graph-matrix isomorphism is used The first part of the talk will review several applica- in these solvers, on the class of matrices that they can be tions, including bird flocking, information percolation in applied to, and on the gap between theory and practice in social networks, valuation of exhaustible resources, high this area. frequency market making, emissions regulation, , for which models of large populations dynamics can be brought to Sivan A. Toledo bear. These models will be framed in the context of the Tel Aviv University theory of mean field games. The second part of the talk [email protected] will present recent equilibrium existence results, and dis- cuss some of the nagging computational challenges raised by the need for reasonable numerical approximations to IC5 these equilibria. Optimization Algorithms for Machine Learning Rene Carmona The extraordinary success of search engines, recommenda- Princeton University tion systems, and speech and image recognition software Dpt of Operations Research & Financial Engineering suggests that future advances in these technologies could [email protected] have a major impact in our lives. In this talk, we discuss modern intelligent-algorithmic systems based on sophisti- cated statistical learning models and powerful optimization IC2 techniques. One can envision new algorithms that operate Solving Stochastic Inverse Problems Using Sigma- in the stochastic or batch settings, and that take full ad- Algebras on Contour Maps vantage of parallelism. We review our remarkable under- standing of classical stochastic approximation techniques, We describe recent work on the formulation and numerical and pose some open questions. The lecture concludes with solution of stochastic inverse problems for determining pa- a discussion of modern neural nets and the demands they rameters in differential equations with stochastic data on impose on optimization methods. output quantities. The new approach involves approximat- ing the generalized contour maps representing set-valued Jorge Nocedal inverse solutions, using the approximate contour maps to Department of Electrical and Computer Engineering define a geometric structure on events in the sigma-algebra Northwestern University for the probability space on the parameter domain, and [email protected] exploiting the structure to define and approximate proba- bility distributions in the space. We will present various examples, including high-dimensional problems involving IC6 spatially varying parameter fields in storm surge models. The Mathematical Problems of Isotropic-Nematic Interface Donald Estep Colorado State University Liquid crystals represent a vast and diverse class of [email protected] or [email protected] anisotropic soft matter materials which are intermediate between isotropic liquids and crystalline solids. The vari- ous liquid crystal phases can be characterized by the type IC3 of ordering,one of the most common liquid crystal phases Computational Biology in the 21st Century: Mak- is the isotropic phase, another is the nematic phase. In ing Sense out of Massive Data this talk, a wide spectrum of mathematical problems of isotropic-nematic interface will be considered. One set of The last two decades have seen an exponential increase problems to be considered is the relationship between these in genomic and biomedical data, which will soon outstrip different levels of modeling, for example how one can make advances in computing power to perform current methods a rigorous passage from molecular/statistical descriptions of analysis. Extracting new science from these massive to continuum theories. Special consideration will be given datasets will require not only faster computers; it will re- to the existence, uniqueness and regularity of the solutions quire smarter algorithms. We show how ideas from cutting- of the Landau-de Gennes theory. edge algorithms, including spectral graph theory and mod- ern data structures, can be used to attack challenges in Pingwen Zhang sequencing, medical genomics and biological networks. Peking University [email protected] Bonnie Berger Department of Mathematics Massachusetts Institute of Technology IC7 [email protected] The Statistics Behind the Discovery of the Higgs Boson IC4 The standard model of particle physics is a wildly suc- The Evolution of Combinatorial Solvers for Lapla- cessful theory of fundamental particles and their interac- cian Linear Systems tions. The Higgs boson is a particle that was predicted nearly 50 years ago to address a serious theoretical consis- Fast solvers that are based on combinatorial techniques tency issue in the Standard Model of particle physics, but have been investigated for more than two decades now. it has never been observed. The Large Hadron Collider is a The most successful of these (at least theoretically) solve multi-national, multi-billion dollar experiment to search for symmetric diagonally linear systems, a class that includes the Higgs boson and other new phenomena. I will discuss 2 AN14 Abstracts the statistical aspects of the recent discovery of the Higgs information on model parameters. Based on this property boson, including the collaborative statistical modeling of we design MCMC methods that adapt to the structure of the data and the statistical procedures we employ. With the posterior probability and exploit an effectively-reduced multi-petabyte datasets and complex statistical models, we parameter dimension, thereby rendering Bayesian inference are arguably pushing a frontier of statistical analysis and tractable for high-dimensional Antarctic ice sheet flow in- quickly outstripping our most advanced tools. verse problems. Kyle Cranmer Omar Ghattas New York University The University of Texas at Austin [email protected] [email protected] IC8 IP3 Random Braids Pattern Recognition with Weakly Coupled Oscilla- tory Networks Braids are mathematical objects closely related to knots. They consist of a set of strings embedded in three dimen- One outstanding property of biological neural networks is sions, anchored at both ends. Plotted in a spacetime di- the ability to perform pattern recognition tasks. To mimic agram, trajectories of two-dimensional systems naturally this property with a man-made device that processes in- form braids. When the trajectories correspond to peri- formation in parallel has been a great challenge. Tradi- odic orbits they form closed braids, and there are powerful tional approaches employ many interconnected units and mathematical techniques available to analyze the dynam- are inherently difficult to construct. In the lecture, we will ics. If the trajectories are chaotic, then the analysis is not focus on neural network models of weakly coupled oscilla- so simple. I will describe the types of braids that arise tors with time-dependent coupling. In these models, each when dealing with chaotic orbits, and discuss their connec- oscillator has only one or a few connections to a common tion to surface dynamics. I will also discuss applications support, which makes them predestinated for hardware im- to sparse trajectory datasets. plementation. We will discuss the dynamics of different network architectures, compare their scalability, present Jean-Luc Thiffeault experimental realizations of the networks and point out Dept. of Mathematics open challenging mathematically problems. University of Wisconsin - Madison [email protected] Katharina Krischer Technische Universit¨at M¨unchen [email protected] IP1 Age of Networks IP4 Networks are becoming increasingly relevant in a host of Scientific Computing in Movies and Virtual domains. In the tech industry, we see the Internet, the Surgery WWW, and many online social networks. In economics, we are experiencing both the positive and negative effects New applications of scientific computing for solid and fluid of a global networked economy. In biomedical applications, mechanics problems include simulation of virtual materials the structure of gene regulatory networks is relevant for for movie special effects and virtual surgery. Both disci- the treatment of many human diseases. In this talk, I de- plines demand physically realistic dynamics for such mate- scribe quite generally models we are using to describe these rials as water, smoke, fire, and brittle and elastic objects. networks, processes we are studying on the networks, algo- These demands are different than those traditionally en- rithms we have devised for the networks, and finally, meth- countered and new algorithms are required. This talk will ods we are developing to indirectly infer network structure address the simulation techniques needed in these fields and from measured data. I then focus on a couple of specific some recent results including: simulated surgical repair of applications, including one to cancer genomics. biomechanical soft tissues, extreme