Seminars and Colloquia by Series

Math Modeling of Biological Memory

Series
Mathematical Biology Seminar
Time
Tuesday, March 8, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Vadim L. StefanukRussian Academy of Sciences
Some properties of biological memory are briefly described. The examples of short term memory and extra long term memory are drawn from psychological literature and from the personal experience. The short term memory is modeled here with the two types of mathematical models, both models being special cases of the Locally Organized Systems (LOS). The first model belongs to Prof. Mikhail Tsetlin of Moscow State University. His original ?pile of books? model was independently rediscovered a new by a number of scientists throughout the World. Tsetlin?s model demonstrates some very important properties of a natural memory organization. However mathematical study of his model turned out to be rather complicated. The second model belongs to the present author and has somewhat similar properties. However, it is organized in a completely different manner. In particular it contains some parameters, which makes the model rather interesting mathematically and pragmatically. The Stefanuk?s model has many interpretations and will be illustrated here with some biologically inspired examples. Both models founded a number of practical applications. These models demonstrate that the short term memory, which is heavily used by humans and by many biological subsystems is arranged reasonably. For humans it helps to keep the knowledge in the way facilitating its fast extraction. For biological systems the models explain the arrangement of storage of various micro organisms in a cell in an optimal manner to provide for the living.

Isospectral Graph Reductions, Estimates of Matrices' Spectra, and Eventually Negative Schwarzian Systems

Series
Dissertation Defense
Time
Tuesday, March 8, 2011 - 09:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Benjamin WebbSchool of Mathematics, Georgia Tech
Real world networks typically consist of a large number of dynamical units with a complicated structure of interactions. Until recently such networks were most often studied independently as either graphs or as coupled dynamical systems. To integrate these two approaches we introduce the concept of an isospectral graph transformation which allows one to modify the network at the level of a graph while maintaining the eigenvalues of its adjacency matrix. This theory can then be used to rewire dynamical networks, considered as dynamical systems, in order to gain improved estimates for whether the network has a unique global attractor. Moreover, this theory leads to improved eigenvalue estimates of Gershgorin-type. Lastly, we will discuss the use of Schwarzian derivatives in the theory of 1-d dynamical systems.

Arithmetic of the Legendre curve

Series
Algebra Seminar
Time
Monday, March 7, 2011 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Doug UlmerGeorgia Tech
Let k be a field (not of characteristic 2) and let t be an indeterminate. Legendre's elliptic curve is the elliptic curve over k(t) defined by y^2=x(x-1)(x-t). I will discuss the arithmetic of this curve (group of solutions, heights, Tate-Shafarevich group) over the extension fields k(t^{1/d}). I will also mention several variants and open problems which would make good thesis topics.

Lecture series on the disjoint paths algorithm

Series
Graph Theory Seminar
Time
Monday, March 7, 2011 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 168
Speaker
Paul WollanSchool of Mathematics, Georgia Tech and University of Rome
The k-disjoint paths problem takes as input a graph G and k pairs of vertices (s_1, t_1),..., (s_k, t_k) and determines if there exist internally disjoint paths P_1,..., P_k such that the endpoints of P_i are s_i and t_i for all i=1,2,...,k. While the problem is NP-complete when k is allowed to be part of the input, Robertson and Seymour showed that there exists a polynomial time algorithm for fixed values of k. The existence of such an algorithm is the major algorithmic result of the Graph Minors series. The original proof of Robertson and Seymour relies on the whole theory of graph minors, and consequently is both quite technical and involved. Recent results have dramatically simplified the proof to the point where it is now feasible to present the proof in its entirety. This seminar series will do just that, with the level of detail aimed at a graduate student level.

Statistical Shape Analysis of Target Boundaries in 2D Sonar Imagery

Series
Applied and Computational Mathematics Seminar
Time
Monday, March 7, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Darshan Bryner Naval Surface Warfare Center/FSU
There are several definitions of the word shape; of these, the most important to this research is “the external form or appearance of someone or something as produced by its outline.” Shape Analysis in this context focuses specifically on the mathematical study of explicit, parameterized curves in 2D obtained from the boundaries of targets of interest in Synthetic Aperture Sonar (SAS) imagery. We represent these curves with a special “square-root velocity function,” whereby the space of all such functions is a nonlinear Riemannian manifold under the standard L^2 metric. With this curve representation, we form the mathematical space called “shape space” where a shape is considered to be the orbit of an equivalence class under the group actions of scaling, translation, rotation, and re-parameterization. It is in this quotient space that we can quantify the distance between two shapes, cluster similar shapes into classes, and form means and covariances of shape classes for statistical inferences. In this particular research application, I use this shape analysis framework to form probability density functions on sonar target shape classes for use as a shape prior energy term in a Bayesian Active Contour model for boundary extraction in SAS images. Boundary detection algorithms generally perform poorly on sonar imagery due to their typically low signal to noise ratio, high speckle noise, and muddled or occluded target edges; thus, it is necessary that we use prior shape information in the evolution of an active contour to achieve convergence to a meaningful target boundary.

From the "slicing problem" to "KLS Conjecture": The concentration of measure phenomenon in log-concave measures

Series
Joint ACO and ARC Colloquium
Time
Monday, March 7, 2011 - 13:30 for 1 hour (actually 50 minutes)
Location
Klaus 1116W
Speaker
Grigoris PaourisTexas A &M University

Please Note: Tea and light refreshments 2:30 p.m.  in Room 2222

We will discuss several open questions on the concentration of measure on log-concave measures and we will present the main ideas of some recent positive results.

Ramified optimal transportation in geodesic metric spaces

Series
CDSNS Colloquium
Time
Monday, March 7, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Qinglan XiaUniversity of California Davis
An optimal transport path may be viewed as a geodesic in the space of probability measures under a suitable family of metrics. This geodesic may exhibit a tree-shaped branching structure in many applications such as trees, blood vessels, draining and irrigation systems. Here, we extend the study of ramified optimal transportation between probability measures from Euclidean spaces to a geodesic metric space. We investigate the existence as well as the behavior of optimal transport paths under various properties of the metric such as completeness, doubling, or curvature upper boundedness. We also introduce the transport dimension of a probability measure on a complete geodesic metric space, and show that the transport dimension of a probability measure is bounded above by the Minkowski dimension and below by the Hausdorff dimension of the measure. Moreover, we introduce a metric, called "the dimensional distance", on the space of probability measures. This metric gives a geometric meaning to the transport dimension: with respect to this metric, the transport dimension of a probability measure equals to the distance from it to any finite atomic probability measure.

Complexity and criticality of the Ising problem

Series
Combinatorics Seminar
Time
Friday, March 4, 2011 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Martin LoeblCharles University, Prague, Czech Republic
The Ising problem on finite graphs is usually treated by a reduction to the dimer problem. Is this a wise thing to do? I will show two (if time allows) recent results indicating that the Ising problem allows better mathematical analysis than the dimer problem. Joint partly with Gregor Masbaum and partly with Petr Somberg.

A Filtration of the Magnus Representation

Series
Geometry Topology Working Seminar
Time
Friday, March 4, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Taylor McNeillRice University
While orientable surfaces have been classified, the structure of their homeomorphism groups is not well understood. I will give a short introduction to mapping class groups, including a description of a crucial representation for these groups, the Magnus representation. In addition I will talk about some current work in which I use Johnson-type homomorphisms to define an infinite filtration of the kernel of the Magnus representation.

Discussion of Gender Issues and Authority in Academics

Series
Other Talks
Time
Friday, March 4, 2011 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 257
Speaker
Open DiscussionsSchool of Mathematics, Georgia Tech
Are there gender differences in authority in mathematics? For instance, do students treat male and female professors differently and what can we do to overcome any negative consequences? Also, what might some positive differences be? We may also discuss issues surrounding respect and authority in research. All are welcome, but if possible, please let Becca Winarski rwinarski@math.gatech.edu know if you plan on attending, so she can get an approximate head count.

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