Seminars and Colloquia by Series

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.

Spin Bundles

Series
Geometry Topology Student Seminar
Time
Monday, April 20, 2015 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Shane Scott – Georgia Tech
Spin bundles give the geometric data necessary for the description of fermions in physical theories. Not all manifolds admit appropriate spin structures, and the study of spin-geometry interacts with K-theory. We will discuss spin bundles, their associated spectra, and Atiyah-Bott-Shapiro's K orientation of MSpin--the spectrum classifying spin-cobordism.

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.

Veering Dehn surgery

Series
Geometry Topology Seminar
Time
Friday, April 17, 2015 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Henry Segerman – Oklahoma State University –
This is joint work with Saul Schleimer. Veering structures onideal triangulations of cusped manifolds were introduced by Ian Agol, whoshowed that every pseudo-Anosov mapping torus over a surface, drilled alongall singular points of the measured foliations, has an ideal triangulationwith a veering structure. Any such structure coming from Agol'sconstruction is necessarily layered, although a few non-layered structureshave been found by randomised search. We introduce veering Dehn surgery,which can be applied to certain veering triangulations, to produceveering triangulationsof a surgered manifold. As an application we find an infinite family oftransverse veering triangulations none of which are layered. Untilrecently, it was hoped that veering triangulations might be geometric,however the first counterexamples were found recently by Issa, Hodgson andme. We also apply our surgery construction to find a different infinitefamily of transverse veering triangulations, none of which are geometric.

Bounding the density of packing objects: a symmetry-based optimization perspective

Series
ACO Student Seminar
Time
Friday, April 17, 2015 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Cristóbal Guzmán – Georgia Tech –
How much of space can be filled with pairwise non-overlapping copies of a given solid? This is one of the oldest problems in mathematics, intriguing since the times of Aristotle, and remaining remarkably elusive until present times. For example, the three-dimensional sphere packing problem (posed by Kepler in 1611) was only solved in 1998 by Ferguson and Hales. In this talk, I will provide some historical and modern applications of geometric packing problems, and I will introduce a methodology to derive upper bounds on the maximal density of such packings. These upper bounds are obtained by an infinite dimensional linear program, which is not computationally tractable. However, this problem can be approximated by using tools from sums of squares relaxations and symmetry reduction (harmonic analysis and representation theory), leading to rigorous computational upper bounds on the density. Time permitting, I will present ongoing work with Maria Dostert, Fernando de Oliveira Filho and Frank Vallentin on the density of translative packings of superspheres (i.e., ell_p balls). This is an introductory talk: no previous knowledge of sums of squares relaxations or symmetry reduction is assumed.

Chi, Omega, MAD

Series
Graph Theory Seminar
Time
Thursday, April 16, 2015 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Luke Postle – University of Waterloo
We discuss the relationship between the chromatic number (Chi), the clique number (Omega) and maximum average degree (MAD).

Polynomial Inequalities

Series
School of Mathematics Colloquium
Time
Thursday, April 16, 2015 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Prof. Vili Totik – Szeged University (Hungary) and University of South Florida –
Bernstein's inequality connecting the norms of a (trigonometric) polynomial with the norm of its derivative is 100 years old. The talk will discuss some recent developments concerning Bernstein's inequality: inequalities with doubling weights, inequalities on general compact subsets of the real line or on a system of Jordan curves. The beautiful Szego-Schaake–van der Corput generalization will also be mentioned along with some of its recent variants.

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