Seminars and Colloquia by Series

Discrimination of binary patterns by perceptrons with binary weights

Series
Mathematical Biology Seminar
Time
Wednesday, November 9, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Andrei Olifer – Georgia Gwinnett College
Information processing in neurons and their networks is understood incompletely, especially when neuronal inputs have indirect correlates with external stimuli as for example in the hippocampus. We study a case when all neurons in one network receive inputs from another network within a short time window. We consider it as a mapping of binary vectors of spiking activity ("spike" or "no spike") in an input network to binary vectors of spiking activity in the output network. Intuitively, if an input pattern makes a neuron spike then the neuron should also spike in response to similar patterns - otherwise, neurons would be too sensitive to noise. On the other hand, neurons should discriminate between sufficiently different input patterns and spike selectively. Our main goal was to quantify how well neurons discriminate input patterns depending on connectivity between networks, spiking threshold of neurons and other parameters. We modeled neurons with perceptrons that have binary weights. Most recent results on perceptron neuronal models are asymptotic with respect to some parameters. Here, using combinatorial analysis, we complement them by exact formulas. Those formulas in particular predict that the number of the inputs per neuron maximizes the difference between the neuronal and network responses to similar and distinct inputs. A joint work with Jean Vaillant (UAG).

The Price of Uncertainty in Multiagent Systems with Potentials

Series
High-Dimensional Phenomena in Statistics and Machine Learning Seminar
Time
Tuesday, November 8, 2011 - 16:00 for 1.5 hours (actually 80 minutes)
Location
skyles 006
Speaker
Steven Ehrlich – School of Computer Science, Georgia tech
Multi-agent systems have been studied extensively through the lens of game theory. However, most game theoretic models make strong assumptions about agents accuracy of knowledge about their utility and the interactions of other players. We will show some progress at relaxing this assumption. In particular, we look at adversarial noise in specific potential games, and assess the effect of noise on the quality of outcomes. In some cases, very small noise can accumulate over the course of the dynamics and lead to much worse social welfare. We define the Price of Uncertainty to measure this, and we compute both upper and lower bounds on this quantity for particular games.

Regularity and decay estimates of dissipative equations.

Series
PDE Seminar
Time
Tuesday, November 8, 2011 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Hantaek Bae – University of Maryland
We establish Gevrey class regularity of solutions to dissipative equations. The main tools are the Kato-Ponce inequality for Gevrey estimates in Sobolev spaces and the Gevrey estimates in Besov spaces using the paraproduct decomposition. As an application, we obtain temporal decay of solutions for a large class of equations including the Navier-Stokes equations, the subcritical quasi-geostrophic equations.

Various simplicial complexes associated to matroids

Series
Algebra Seminar
Time
Monday, November 7, 2011 - 16:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Farbod Shokrieh – Georgia Tech –
A matroid is a structure that captures the notion of "independence". For example, given a set of vectors in a vector space, one can define a matroid. Graphs also naturally give rise to matroids. I will talk about various simplicial complexes associated to matroids. These include the "matroid complex", the "broken circuit complex", and the "order complex" of the associated geometric lattice. They carry some of the most important invariants of matroids and graphs. I will also show how the Bergman fan and its refinement (which arise in tropical geometry) relate to the classical theory. If time permits, I will give an outline of a recent breakthrough result of Huh and Katz on log-concavity of characteristic (chromatic) polynomials of matroids. No prior knowledge of the subject will be assumed. Most of the talk should be accessible to advanced undergraduate students.

Grassmannians and Random Polygons

Series
Geometry Topology Seminar
Time
Monday, November 7, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Clay Shonkwiler – UGA
In 1997 Hausmann and Knutson discovered a remarkable correspondence between complex Grassmannians and closed polygons which yields a natural symmetric Riemannian metric on the space of polygons. In this talk I will describe how these symmetries can be exploited to make interesting calculations in the probability theory of the space of polygons, including simple and explicit formulae for the expected values of chord lengths. I will also give a simple and fast algorithm for sampling random polygons--which serve as a statistical model for polymers--directly from this probability distribution.

An iterative filtering method for adaptive signal decomposition based on a PDE model

Series
Applied and Computational Mathematics Seminar
Time
Monday, November 7, 2011 - 14:00 for 30 minutes
Location
Skiles 006
Speaker
Jingfang Liu – GT Math
The empirical mode decomposition (EMD) was a method developed by Huang et al as an alternative approach to the traditional Fourier and wavelet techniques for studying signals. It decomposes signals into finite numbers of components which have well behaved intataneous frequency via Hilbert transform. These components are called intrinstic mode function (IMF). Recently, alternative algorithms for EMD have been developed, such as iterative filtering method or sparse time-frequency representation by optimization. In this talk we present our recent progress on iterative filtering method. We develop a new local filter based on a partial differential equation (PDE) model as well as a new approach to compute the instantaneous frequency, which generate similar or better results than the traditional EMD algorithm.

On the Hamilton-Jacobi variational formulation of the Vlasov equation

Series
CDSNS Colloquium
Time
Monday, November 7, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Phil Morrison – Univ. of Texas at Austin
The Vlasov-Poisson and Vlasov-Maxwell equations possess various variational formulations1 or action principles, as they are generally termed by physicists. I will discuss a particular variational principle that is based on a Hamiltonian-Jacobi formulation of Vlasov theory, a formulation that is not widely known. I will show how this formu- lation can be reduced for describing the Vlasov-Poisson system. The resulting system is of Hamilton-Jacobi form, but with nonlinear global coupling to the Poisson equation. A description of phase (function) space geometry will be given and comments about Hamilton-Jacobi pde methods and weak KAM will be made.Supported by the US Department of Energy Contract No. DE-FG03- 96ER-54346.H. Ye and P. J. Morrison Phys. Fluids 4B 771 (1992).D. Pfirsch, Z. Naturforsch. 39a, 1 (1984); D. Pfirsch and P. J. Morrison, Phys. Rev. 32A, 1714 (1985).

Discrete Mathematical Biology Working Seminar

Series
Other Talks
Time
Monday, November 7, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 114
Speaker
Todd Shayler – Georgia Tech
Continued discussion of the Allali and Sagot (2005) paper "A New Distance for High Level RNA Secondary Structure Comparison."

Atlanta Lecture Series in Combinatorics and Graph Theory IV

Series
Other Talks
Time
Saturday, November 5, 2011 - 09:30 for 1 hour (actually 50 minutes)
Location
Petit Science Center, Room 124, Georgia State University
Speaker
Featured Speaker Bela Bollobas – Cambridge University and University of Memphis

Please Note: Please contact Guantao Chen, gchen@gsu.edu if you are interested in participating this mini-conference.

Emory University, the Georgia Institute of Technology and Georgia State University, with support from the National Security Agency and the National Science Foundation, are hosting a series of 9 mini-conferences from November 2010 - April 2013. The fourth in the series will be held at Georgia State University on November 5-6, 2011. This mini-conference's featured speaker is Dr. Bela Bollobas, who will give two one-hour lectures. Additionally, there will be five one-hour talks and seven half-hour talks given by other invited speakers. See all titles, abstracts, and schedule.

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