Seminars and Colloquia by Series

Uniqueness of seismic inverse source problems modeling microseismicity and ruptures

Series
Applied and Computational Mathematics Seminar
Time
Monday, October 26, 2015 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Professor Maarten de Hoop – Rice University –
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 Problems

Series
Applied and Computational Mathematics Seminar
Time
Monday, October 19, 2015 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Eric de Sturler – Department of Mathematics, Virginia Tech –
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.

(unusual date and room) Numerical Analysis in Metric Spaces

Series
Applied and Computational Mathematics Seminar
Time
Wednesday, October 14, 2015 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 270
Speaker
Vira Babenko – The University of Utah –
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.

Survival of the Smartest: Sparse Recovery in Biology

Series
Applied and Computational Mathematics Seminar
Time
Monday, October 5, 2015 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Felix Lieder – Mathematisches Institut Lehrstuhl für Mathematische Optimierung –
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.

Methods for multiscale inverse problems

Series
Applied and Computational Mathematics Seminar
Time
Monday, September 28, 2015 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Dr. Christina Frederick – GA Tech
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.

Projection on a Polyhedron

Series
Applied and Computational Mathematics Seminar
Time
Monday, September 14, 2015 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Associate Professor Hongchao Zhang – Department of Mathematics and Center for Computational & Technology (CCT) at Louisiana State University –
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.

What is and how to compute efficiently the Markovian Joint Spectral Radius?

Series
Applied and Computational Mathematics Seminar
Time
Monday, April 20, 2015 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Dr. Antonio Cicone – L'Aquila, Italy
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.

Tracking Control for Neuromuscular Electrical Stimulation

Series
Applied and Computational Mathematics Seminar
Time
Monday, April 20, 2015 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Professor Michael Malisoff – Louisiana State University

Please Note: 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

Pressure Ulcers and Applied Mathematics

Series
Applied and Computational Mathematics Seminar
Time
Friday, April 17, 2015 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Stephen Sprigle – Schools of Industrial Design and Applied Physiology, Georgia Tech
The Rehabilitation Engineering and Applied Research Lab (REARLab) performs both experimental research and product development activities focused on persons with disabilities. The REARLab seeks collaboration from the School of Mathematics on 2 current projects. This session will introduce wheelchair seating with respect to pressure ulcer formation and present two projects whose data analysis would benefit from applied mathematics. 3D Tissue Deformation- Sitting induces deformation of the buttocks tissues. Tissue deformation has been identified as the underlying cause of tissue damage resulting from external loading. The REARLab has been collecting multi-planar images of the seated buttocks using MRI. This data clearly shows marked differences between persons, as expected. We are interested in characterizing tissue deformation as a combination of displacement and distortion. Some tissues- such as muscle- displace (translate within the sagittal, coronal and transverse planes) and distort (change shape). Other tissue such as skin and subcutaneous fat, simple distorts. We seek a mathematical means to characterize tissue deformation that reflects its multi-planar nature. Categorizing Weight-shifting behaviors - many wheelchair users have limitations to their motor and/or sensory systems resulting in a risk of pressure ulcers. Pressure ulcers occur when localized loading on the skin causes ischemia and necrosis. In an attempt to reduce risk of pressure ulcer occurrence, wheelchair users are taught to perform weight-shifts. Weight shifts are movements that re-distribute loads off the buttocks for short periods of time. The REARLab is measuring weight shifting behaviors of wheelchair users during their everyday lives. We seek a means to classify patterns of behavior and relate certain patterns to healthy outcomes versus other patterns that result in unhealthy outcomes.

Parareal methods for highly oscillatory ordinary differential equations

Series
Applied and Computational Mathematics Seminar
Time
Monday, April 13, 2015 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Seong Jun Kim – Georgia Tech –
We introduce a new parallel in time (parareal) algorithm which couples multiscale integrators with fully resolved fine scale integration and computes highly oscillatory solutions for a class of ordinary differential equations in parallel. The algorithm computes a low-cost approximation of all slow variables in the system. Then, fast phase-like variables are obtained using the parareal iterative methodology and an alignment algorithm. The method may be used either to enhance the accuracy and range of applicability of the multiscale method in approximating only the slow variables, or to resolve all the state variables. The numerical scheme does not require that the system is split into slow and fast coordinates. Moreover, the dynamics may involve hidden slow variables, for example, due to resonances.

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