Monday, November 16, 2015 - 14:05 , Location: Skiles 005 , Gil Ariel , Bar-Ilan University , Organizer:
Collective movement is one of the most prevailing observations in nature. Yet, despite considerable progress, many of the theoretical principles underlying the emergence of large scale synchronization among moving individuals are still poorly understood. For example, a key question in the study of animal motion is how the details of locomotion, interaction between individuals and the environment contribute to the macroscopic dynamics of the hoard, flock or swarm. The talk will present some of the prevailing models for swarming and collective motion with emphasis on stochastic descriptions. The goal is to identify some generic characteristics regarding the build-up and maintenance of collective order in swarms. In particular, whether order and disorder correspond to different phases, requiring external environmental changes to induce a transition, or rather meta-stable states of the dynamics, suggesting that the emergence of order is kinetic. Different aspects of the phenomenon will be presented, from experiments with locusts to our own attempts towards a statistical physics of collective motion.
Monday, November 2, 2015 - 14:05 , Location: Skiles 005 , Professor James von Brecht , Cal State University, Long Beach , Organizer: Martin Short
In this talk, I will discuss mathematical models and tools for analyzing physical and biological processes that exhibit co-dimension one characteristics. Examples include the assembly of inorganic polyoxometalate (POM) macroions into hollow spherical structures and the assembly of surfactant molecules into micelles and vesicles. I will characterize when such structures can arise in the context of isotropic and anisotropic models, as well as applications of these insights to physical models of these behaviors.
Thursday, October 29, 2015 - 11:00 , Location: Skiles 006 , Philippe Chartier , INRIA Rennes, Université de Rennes I, ENS Rennes , Philippe.Chartier@inria.fr , Organizer: Molei Tao
Joint with School of Math Colloquium. Special time (colloquium time).
In this talk, I will introduce B-series, which are formal series indexed by trees, and briefly expose the two laws operating on them. The presentation of algebraic aspects will here be focused on applications to numerical analysis. I will then show how B-series can be used on two examples: modified vector fields techniques, which allow for the construction of arbitrarly high-order schemes, and averaging methods, which lie at the core of many numerical schemes highly-oscillatory evolution equations. Ultimately and if time permits, I will illustrate how these concepts lead to the accelerated simulation of the rigid body and the (nonlinear) Schrödinger equations. A significant part of the talk will remain expository and aimed at a general mathematical audience.
Tuesday, October 27, 2015 - 12:30 , Location: Skiles 005 , Venkat Chandrasekaran , Cal Tech , Organizer: Greg Blekherman
Due to its favorable analytical properties, the relative entropy function plays a prominent role in a variety of contexts in information theory and in statistics. In this talk, I'll discuss some of the beneficial computational properties of this function by describing a class of relative-entropy-based convex relaxations for obtaining bounds on signomials programs (SPs), which arise commonly in many problems domains. SPs are non-convex in general, and families of NP-hard problems can be reduced to SPs. By appealing to representation theorems from real algebraic geometry, we show that sequences of bounds obtained by solving increasingly larger relative entropy programs converge to the global optima for broad classes of SPs. The central idea underlying our approach is a connection between the relative entropy function and efficient proofs of nonnegativity via the arithmetic-geometric-mean inequality. (Joint work with Parikshit Shah.)
Monday, October 26, 2015 - 14:00 , Location: Skiles 005 , Professor Maarten de Hoop , Rice University , email@example.com , Organizer:
We consider an inverse problem for an inhomogeneous wave equation with discrete-in-time sources, modeling a seismic rupture. We assume that the sources occur along an unknown path with subsonic velocity, and that data is collected over time on some detection surface. We explore the question of uniqueness for these problems, and show how to recover the times and locations of sources microlocally first, and then the smooth part of the source assuming that it is the same at each source location. In case the sources (now all different) are (roughly speaking) non-negative and of limited oscillation in space, and sufficiently separated in space-time, which is a model for microseismicity, we present an explicit reconstruction, requiring sufficient local energy decay. (Joint research with L. Oksanen and J. Tittelfitz)
Simultaneous Random and Optimized Sources and Detectors for Efficient Optimization in Inverse ProblemsMonday, October 19, 2015 - 14:00 , Location: Skiles 005 , Eric de Sturler , Department of Mathematics, Virginia Tech , firstname.lastname@example.org , Organizer: Sung Ha Kang
In nonlinear inverse problems, we often optimize an objective function involving many sources, where each source requires the solution of a PDE. This leads to the solution of a very large number of large linear systems for each nonlinear function evaluation, and potentially additional systems (for detectors) to evaluate or approximate a Jacobian. We propose a combination of simultaneous random sources and detectors and optimized (for the problem) sources and detectors to drastically reduce the number of systems to be solved. We apply our approach to problems in diffuse optical tomography.This is joint work with Misha Kilmer and Selin Sariaydin.
Wednesday, October 14, 2015 - 14:00 , Location: Skiles 270 , Vira Babenko , The University of Utah , email@example.com , Organizer: Sung Ha Kang
A wide variety of questions which range from social and economic sciences to physical and biological sciences lead to functions with values that are sets in finite or infinite dimensional spaces, or that are fuzzy sets. Set-valued and fuzzy-valued functions attract attention of a lot of researchers and allow them to look at numerous problems from a new point of view and provide them with new tools, ideas and results. In this talk we consider a generalized concept of such functions, that of functions with values in so-called L-space, that encompasses set-valued and fuzzy functions as special cases and allow to investigate them from the common point of view. We will discus several problems of Approximation Theory and Numerical Analysis for functions with values in L-spaces. In particular numerical methods of solution of Fredholm and Volterra integral equations for such functions will be presented.
Monday, October 5, 2015 - 14:00 , Location: Skiles 005 , Felix Lieder , Mathematisches Institut Lehrstuhl für Mathematische Optimierung , firstname.lastname@example.org , Organizer:
Survival can be tough: Exposing a bacterial strain to new environments will typically lead to one of two possible outcomes. First, not surprisingly, the strain simply dies; second the strain adapts in order to survive. In this talk we are concerned with the hardness of survival, i.e. what is the most eﬃcient (smartest) way to adapt to new environments? How many new abilities does a bacterium need in order to survive? Here we restrict our focus on two speciﬁc bacteria, namely E.coli and Buchnera. In order to answer the questions raised, we ﬁrst model the underlying problem as an NP-hard decision problem. Using a re-weighted l1-regularization approach, well known from image reconstruction, we then approximate ”good” solutions. A numerical comparison between these ”good” solutions and the ”exact” solutions concludes the talk.
Monday, September 28, 2015 - 14:05 , Location: Skiles 005 , Dr. Christina Frederick , GA Tech , Organizer: Martin Short
I will discuss inverse problems involving elliptic partial differential equations with highly oscillating coefficients. The multiscale nature of such problems poses a challenge in both the mathematical formulation and the numerical modeling, which is hard even for forward computations. I will discuss uniqueness of the inverse in certain problem classes and give numerical methods for inversion that can be applied to problems in medical imaging and exploration seismology.
Monday, September 14, 2015 - 14:00 , Location: Skiles 005 , Associate Professor Hongchao Zhang , Department of Mathematics and Center for Computational & Technology (CCT) at Louisiana State University , email@example.com , Organizer:
In this talk, we discuss a very efficient algorithm for projecting a point onto a polyhedron. This algorithm solves the projeciton problem through its dual and fully exploits the sparsity. The SpaRSA (Sparse Reconstruction by Separable Approximation) is used to approximately identify active constraints in the polyhedron, and the Dual Active Set Algorithm (DASA) is used to compute a high precision solution. Some interesting convergence properties and very promising numerical results compared with the state-of-the-art software IPOPT and CPLEX will be discussed in this talk.