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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)

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.

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.

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 &amp; 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&#039;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.

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

Yang, "Predictor-based tracking for neuromuscular electrical

stimulation," International Journal of Robust and Nonlinear Control, to

appear. doi: 10.1002/rnc.3211

Friday, April 17, 2015 - 14:05 ,
Location: Skiles 005 ,
Stephen Sprigle ,
Schools of Industrial Design and Applied Physiology, Georgia Tech ,
Organizer: Guillermo Goldsztein

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.

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.

Monday, April 13, 2015 - 14:00 ,
Location: Skiles 005 ,
Seong Jun Kim ,
Georgia Tech ,
skim396@math.gatech.edu ,
Organizer:

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.

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.