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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 ,
mdehoop@purdue.edu ,
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)

Monday, October 19, 2015 - 14:00 ,
Location: Skiles 005 ,
Eric de Sturler ,
Department of Mathematics, Virginia Tech ,
sturler@vt.edu ,
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 ,
babenko@math.utah.edu ,
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 ,
lieder@opt.uni-duesseldorf.de ,
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 ,
hozhang@math.lsu.edu ,
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.

Monday, April 20, 2015 - 15:05 ,
Location: Skiles 005 ,
Dr. Antonio Cicone ,
L'Aquila, Italy ,
Organizer: Haomin Zhou

Given a finite set of matrices F, the Markovian Joint Spectral
Radius represents the maximal rate of growth of products of matrices in
F when the matrices are multiplied each other following some Markovian law.
This quantity is important, for instance, in the study of the so called
zero stability of variable stepsize BDF methods for the numerical
integration of ordinary differential equations.
Recently Kozyakin, based on a work by Dai, showed that, given a set F of
N matrices of dimension d and a graph G, which represents the admissible
products, it is possibile to compute the Markovian Joint Spectral Radius
of the couple (F,G) as the classical Joint Spectral Radius of a new set
of N matrices of dimension N*d, which are produced as a particular
lifting of the matrices in F. Clearly by this approach the exact
evaluation or the simple approximation of the Markovian Joint Spectral
Radius becomes a challenge even for reasonably small values of N and d.
In this talk we briefly review the theory of the Joint Spectral Radius,
and we introduce the Markovian Joint Spectral Radius. Furthermore we
address the question whether it is possible to reduce the exact
calculation computational complexity of the Markovian Joint Spectral
Radius. We show that the problem can be recast as the computation of N
polytope norms in dimension d. We conclude the presentation with some
numerical examples.
This talk is based on a joint work with Nicola Guglielmi from the
University of L'Aquila, Italy, and Vladimir Yu. Protasov from the Moscow
State University, Russia.

Monday, April 20, 2015 - 14:00 ,
Location: Skiles 005 ,
Professor Michael Malisoff ,
Louisiana State University ,
Organizer: Haomin Zhou

Speaker’s Biography:Michael Malisoff received his PhD in 2000 from

the Department of Mathematics at Rutgers University in New Brunswick,

NJ. In 2001, he joined the faculty of the Department of Mathematics at

Louisiana State University in Baton Rouge (LSU), where he is now the Roy

Paul Daniels Professor #3 in theLSU College of Science. His main

research has been on controller design and analysis for nonlinear

control systems with time delays and uncertainty and their applications

in engineering. One of his projects is joint with the Georgia Tech

Savannah Robotics team, and helped develop marine robotic methods to

help understand the environmental impacts of oil spills. His more than

100 publications include a Springer monograph on constructive Lyapunov

methods. His awards include the First Place Student Best Paper Award at

the 1999 IEEE Conference on Decision and Control, two three-year

NationalScience Foundation Mathematical Sciences Priority Area

grants, and 9 Best Presentation awards in American Control Conference

sessions. He is an associate editor for IEEE Transactions on Automatic

Control and for SIAM Journal on Control and Optimization.

We present a new tracking controller for neuromuscular electrical stimulation, which is an emerging technology that can artificially stimulateskeletal muscles to help restore functionality to human limbs. We use a musculoskeletal model for a human using a leg extension machine. The novelty of our work is that we prove that the tracking error globally asymptotically and locally exponentially converges to zero for any positive input delay andfor a general class of possible reference trajectories that must be tracked, coupled with our ability to satisfy a state constraint. The state constraint is that for a seated subject, the human knee cannot be bent more than plus or minus 90 degrees from the straight down position. Also, our controller only requires sampled measurements of the states instead of continuousmeasurements and allows perturbed sampling schedules, which can be important for practical applications where continuous measurement of the states is not possible. Our work is based on a new method for constructing predictor maps for a large class of nonlinear time-varying systems, which is of independent interest. Prediction is a key method for delay compensation that uses dynamic control to compensate for arbitrarily long input delays. Reference: Karafyllis, I., M. Malisoff, M. de Queiroz, M. Krstic, and R.
Yang, "Predictor-based tracking for neuromuscular electrical
stimulation," International Journal of Robust and Nonlinear Control, to
appear. doi: 10.1002/rnc.3211