Seminars and Colloquia Schedule

A Hepatitis B virus model with age since infection that exhibits backward bifurcation

Series
CDSNS Colloquium
Time
Monday, October 19, 2009 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Redouane Qesmi – York University, Canada and SoM, Georgia Tech
Despite advances in treatment of chronic hepatitis B virus (HBV) infection, liver transplantation remains the only hope for many patients with end-stage liver disease due to HBV. A complication with liver transplantation, however, is that the new liver is eventually reinfected in chronic HBV patients by infection in other compartments of the body. We have formulated a model to describe the dynamics of HBV after liver transplant, considering the liver and the blood of areas of infection. Analyzing the model, we observe that the system shows either a transcritical or a backward bifurcation. Explicit conditions on the model parameters are given for the backward bifurcation to be present, to be reduced, or disappear. Consequently, we investigate possible factors that are responsible for HBV/HCV infection and assess control strategies to reduce HBV/HCV reinfection and improve graft survival after liver transplantation.

Normal Mode Analysis for Drifter Data Assimilation to Improve Trajectory Predictions from Ocean Models

Series
Applied and Computational Mathematics Seminar
Time
Monday, October 19, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Helga S. Huntley – University of Delaware
Biologists tracking crab larvae, engineers designing pollution mitigation strategies, and climate scientists studying tracer transport in the oceans are among many who rely on trajectory predictions from ocean models. State-of-the-art models have been shown to produce reliable velocity forecasts for 48-72 hours, yet the predictability horizon for trajectories and related Lagrangian quantities remains significantly shorter. We investigate the potential for decreasing Lagrangian prediction errors by applying a constrained normal mode analysis (NMA) to blend drifter observations with model velocity fields. The properties of an unconstrained NMA and the effects of parameter choices are discussed. The constrained NMA technique is initially presented in a perfect model simulation, where the “true” velocity field is known and the resulting error can be directly assessed. Finally, we will show results from a recent experiment in the East Asia Sea, where real observations were assimilated into operational ocean model hindcasts.

Interpolation in Bergman Spaces

Series
Analysis Working Seminar
Time
Monday, October 19, 2009 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Brett Wick – Georgia Tech
In this working seminar we will give a proof of Seip's characterization of interpolating sequences in the Bergman space of analytic functions. This topic has connection with complex analysis, harmonic analysis, and time frequency analysis and so hopefully many of the participants would be able to get something out of the seminar. The initial plan will be to work through his 1993 Inventiones Paper and supplement this with material from his book "Interpolation and Sampling in Spaces of Analytic Functions". Notes will be generated as the seminar progresses.

Sylvester's Four Point Constant: closing in (or are we?)

Series
Graph Theory Seminar
Time
Tuesday, October 20, 2009 - 12:05 for 1.5 hours (actually 80 minutes)
Location
Skiles 255
Speaker
Gelasio Salazar – Universidad Autonoma de San Luis Potosi
In 1865, Sylvester posed the following problem: For a region R in the plane,let q(R) denote the probability that four points chosen at random from Rform a convex quadrilateral. What is the infimum q* of q(R) taken over allregions R? The number q* is known as Sylvester's Four Point Problem Constant(Sylvester's Constant for short). At first sight, it is hard to imagine howto find reasonable estimates for q*. Fortunately, Scheinerman and Wilf foundthat Sylvester's Constant is intimately related to another fundamentalconstant in discrete geometry. The rectilinear crossing number of rcr(K_n)the complete graph K_n is the minimum number of crossings of edges in adrawing of K_n in the plane in which every edge is a straight segment. Itis not difficult to show that the limit as n goes to infinity ofrcr(K_n)/{n\choose 4} exists; this is the rectilinear crossing numberconstant RCR. Scheinerman and Wilf proved a surprising connection betweenthese constants: q* = RCR. Finding estimates of rcr(K_n) seems like a moreapproachable task. A major breakthrough was achieved in 2003 by Lovasz,Vesztergombi, Wagner, and Welzl, and simultaneously by Abrego andFernandez-Merchant, who unveiled an intimate connection of rcr(K_n) withanother classical problem of discrete geometry, namely the number of

Modeling the forward surface of mortality

Series
Mathematical Finance/Financial Engineering Seminar
Time
Tuesday, October 20, 2009 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Daniel Bauer – Georgia State University
In recent literature, different mothods have been proposed on how to define and model stochastic mortality. In most of these approaches, the so-called spot force of mortality is modeled as a stochastic process. In contrast to such spot force models, forward force mortality models infer dynamics on the entire age/term-structure of mortality. This paper considers forward models defined based on best-estimate forecasts of survival probabilities as can be found in so-called best-estimate generation life tables. We provide a detailed analysis of forward mortality models deriven by finite-dimensional Brownian motion. In particular, we address the relationship to other modeling approaches, the consistency problem of parametric forward models, and the existence of finite dimensional realizations for Gaussian forward models. All results are illustrated based on a simple example with an affine specification.

Boundary Value Problems for Nonlinear Dispersive Wave Equations

Series
PDE Seminar
Time
Tuesday, October 20, 2009 - 15:05 for 1.5 hours (actually 80 minutes)
Location
Skiles 255
Speaker
Hongqiu Chen – University of Memphis
Under the classical small-amplitude, long wave-length assumptions in which the Stokes number is of order one, so featuring a balance between nonlinear and dispersive effects, the KdV-equation u_t+ u_x + uu_x + u_xxx = 0 (1) and the regularized long wave equation, or BBM-equation u_t + u_x + uu_x-u_xxt = 0 (2) are formal reductions of the full, two-dimensional Euler equations for free surface flow. This talk is concerned with the two-point boundary value problem for (1) and (2) wherein the wave motion is specified at both ends of a finite stretch of length L of the media of propagation. After ascertaining natural boundary specifications that constitute well posed problems, it is shown that the solution of the two-point boundary value problem, posed on the interval [0;L], say, converges as L converges to infinity, to the solution of the quarter-plane boundary value problem in which a semi-infinite stretch [0;1) of the medium is disturbed at its finite end (the so-called wavemaker problem). In addition to its intrinsic interest, our results provide justification for the use of the two-point boundary-value problem in numerical studies of the quarter plane problem for both the KdV-equation and the BBM-equation.

Antibiotics: Efficacy 'measures' and physiological state effects

Series
Mathematical Biology Seminar
Time
Wednesday, October 21, 2009 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Klas Udekwu – Biology, Emory University –
Treatment of bacterial infections with antibiotics is universally accepted as one of (if not THE) most significant contributions of medical intervention to reducing mortality and morbidity during last century. Surprisingly, basic knowledge about how antibiotics kill or prevent the growth of bacteria is only just beginning to emerge and the dose and term of antibiotic treatment has long been determined by clinicians empirically and intuitively. There is a recent drive to theoretically and experimentally rationalize antibiotic treatment protocols with the aim to them and to design protocols which maximize antibiotics’ efficacy while preventing resistance emergence. Central to these endeavors are the pharmacodynamics of the antibiotic(s) and bacteria, PD (the relationship between the concentration of the antibiotic and the rate of growth/death of bacteria), and the pharmacokinetics of the antibiotic, PK (the distribution and change in concentration of the antibiotics in a treated host) of each bacteria. The procedures for estimating of PD and PK parameters are well established and standardized worldwide. Although different PK parameters are commonly employed for the design of antibiotic treatment protocols most of these considerations, a single PD parameter is usually used, the minimum inhibitory concentration (MIC). The Clinical and Laboratory Standards Institute (CLSI) approved method for estimating MICs defines testing conditions that are optimal for the antibiotic, like low densities and exponential growth, rarely obtain outside of the laboratory and virtually never in the bacteria infecting mammalian hosts. Real infections with clinical symptoms commonly involve very high densities of bacteria, most of which are not replicating, and these bacteria are rarely planktonic, rather residing as colonies or within matrices called biofilms which sometimes include other species of bacteria. Refractoriness (non-inherited resistance) is the term used to describe an observed inefficacy of antibiotics on otherwise antibiotic-susceptible bacterial populations. This talk will focus on our efforts to describe the pharmacodynamic relationship between Staphylococcus aureus and antibiotics of six classes in the light of antibiotic refractoriness. I will begin by addressing the effects of cell density on the MIC index, after which I intend to present unpublished data descriptive of physiology-related effects on antibiotic efficacy. Additionally, we will explore the potential contribution of such in vitro results, to observed/predicted clinical outcomes using standard mathematical models of antibiotic treatment which also serve to generate testable hypotheses.

Title: Orthogonal and Biorthogonal Polyonmials

Series
Research Horizons Seminar
Time
Wednesday, October 21, 2009 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 171
Speaker
Doron Lubinsky – School of Mathematics, Georgia Tech –
Orthogonal polynomials are an important tool in many areas of pure and applied mathematics. We outline one application in random matrix theory. We discuss generalizations of orthogonal polynomials such as the Muntz orthogonal polynomials investigated by Ulfar Stefansson. Finally, we present some conjectures about biorthogonal polynomials, which would be a great Ph.D. project for any interested student.

The Grothendieck definition of sheaf cohomology

Series
Other Talks
Time
Wednesday, October 21, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Farbod Shokrieh – Ga Tech
As we have seen already, the global section functor is left exact.  To get a long exact sequence, I will first give the construction of derived functors in the more general setting of abelian categories withenough injectives. If time permits, I will then show that for any ringed space the category of all sheaves of Modules is an abelian category with enough injectives, and so we can construct sheaf cohomology as the right derived functors of the global section functor. The relation with Cech cohomology will be studied in a subsequent talk.

Inequalities for Derivatives and their Applications

Series
Analysis Seminar
Time
Wednesday, October 21, 2009 - 14:00 for 8 hours (full day)
Location
Skiles 269
Speaker
Yuliya Babenko – Sam Houston State University
In this talk we will discuss Kolmogorov and Landau type inequalities for the derivatives. These are the inequalities which estimate the norm of the intermediate derivative of a function (defined on an interval, R_+, R, or their multivariate analogs) from some class in terms of the norm of the function itself and norm of its highest derivative. We shall present several new results on sharp inequalities of this type for special classes of functions (multiply monotone and absolutely monotone) and sequences. We will also highlight some of the techniques involved in the proofs (comparison theorems) and discuss several applications.

ARC-ACO Colloquium - Concentration under Heavy Tails

Series
Other Talks
Time
Wednesday, October 21, 2009 - 14:00 for 1 hour (actually 50 minutes)
Location
Klaus, Room 1116
Speaker
Ravi Kannan – Microsoft Research Labs, Bangalore India

Tea and light refreshments 1:30 in Room 2222. Organizer: Santosh Vempala

Concentration results for the TSP, MWST and many other problems with random inputs show the answer is concentrated tightly around the mean. But most results assume uniform density of the input. We will generalize these to heavy-tailed inputs which seem to be ubiquitous in modern applications. To accomplish this, we prove two new general probability inequalities. The simpler first inequality weakens both hypotheses in Hoffding-Azuma inequality and is enough to tackle TSP, MWST and Random Projections. The second inequality further weakens the moment requirements and using it, we prove the best possible concentration for the long-studied bin packing problem as well as some others. Many other applications seem possible..

Theory and Applications of Model Equations for Surface Water Waves

Series
School of Mathematics Colloquium
Time
Thursday, October 22, 2009 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Jerry Bona – University of Illinois at Chicago
After a brief account of some of the history of this classical subject, we indicate how such models are derived. Rigorous theory justifying the models will be discussed and the conversation will then turn to some applications. These will be drawn from questions arising in geophysics and coastal engineering, as time permits.

Jacobians of Nearly Complete Graphs

Series
Graph Theory Seminar
Time
Thursday, October 22, 2009 - 12:05 for 1.5 hours (actually 80 minutes)
Location
Skiles 255
Speaker
Peter Whalen – Math, GT
The Jacobian of a graph, also known as the Picard Group, Sandpile Group, or Critical Group, is a discrete analogue of the Jacobian of an algebraic curve. It is known that the order of the Jacobian of a graph is equal to its number of spanning trees, but the exact structure is known for only a few classes of graphs. In this talk I will present a combinatorial method of approaching the Jacobian of graphs by way of a chip-firing game played on its vertices. We then apply this chip-firing game to explicitly characterize the Jacobian of nearly complete graphs, those obtained from the complete graph by deleting either a cycle or two vertex-disjoint paths incident with all but one vertex. This is joint work with Sergey Norin.

Interacting particles, series Jackson networks, and non-crossing probabilities

Series
Stochastics Seminar
Time
Thursday, October 22, 2009 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Ton Dieker – (ISyE, Georgia Tech)
In this talk, we study an interacting particle system arising in the context of series Jackson queueing networks. Using effectively nothing more than the Cauchy-Binet identity, which is a standard tool in random-matrix theory, we show that its transition probabilities can be written as a signed sum of non-crossing probabilities. Thus, questions on time-dependent queueing behavior are translated to questions on non-crossing probabilities. To illustrate the use of this connection, we prove that the relaxation time (i.e., the reciprocal of the ’spectral gap’) of a positive recurrent system equals the relaxation time of a single M/M/1 queue with the same arrival and service rates as the network’s bottleneck station. This resolves a 1985 conjecture from Blanc on series Jackson networks. Joint work with Jon Warren, University of Warwick.

From transfinite diameter to order-density to best-packing: the asymptotics of ground state configurations

Series
Analysis Seminar
Time
Friday, October 23, 2009 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Doug Hardin – Vanderbilt University
I will review recent and classical results concerning the asymptotic properties (as N --> \infty) of 'ground state' configurations of N particles restricted to a d-dimensional compact set A\subset {\bf R}^p that minimize the Riesz s-energy functional \sum_{i\neq j}\frac{1}{|x_{i}-x_{j}|^{s}} for s>0. Specifically, we will discuss the following (1) For s < d, the ground state configurations have limit distribution as N --> \infty given by the equilibrium measure \mu_s, while the first order asymptotic growth of the energy of these configurations is given by the 'transfinite diameter' of A. (2) We study the behavior of \mu_s as s approaches the critical value d (for s\ge d, there is no equilibrium measure). In the case that A is a fractal, the notion of 'order two density' introduced by Bedford and Fisher naturally arises. This is joint work with M. Calef. (3) As s --> \infty, ground state configurations approach best-packing configurations on A. In work with S. Borodachov and E. Saff we show that such configurations are asymptotically uniformly distributed on A.

Introduction to Heegaard Floer Homology

Series
Geometry Topology Working Seminar
Time
Friday, October 23, 2009 - 15:00 for 2 hours
Location
Skiles 269
Speaker
Amey Kaloti – Georgia Tech

This is a 2 hour talk.

Abstract: Heegaard floer homology is an invariant of closed 3 manifolds defined by Peter Ozsvath and Zoltan Szabo. It has proven to be a very strong invariant of 3 manifolds with connections to contact topology. In these talks we will try to define the Heegaard Floer homology without assuming much background in low dimensional topology. One more goal is to present the combinatorial description for this theory.

Random regular graphs: from spectrum to geometry and back

Series
ACO Seminar
Time
Friday, October 23, 2009 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Eyal Lubetzky – Microsoft Research, Redmond, WA
The class of random regular graphs has been the focus of extensive study highlighting the excellent expansion properties of its typical instance. For instance, it is well known that almost every regular graph of fixed degree is essentially Ramanujan, and understanding this class of graphs sheds light on the general behavior of expanders. In this talk we will present several recent results on random regular graphs, focusing on the interplay between their spectrum and geometry. We will first discuss the relation between spectral properties and the abrupt convergence of the simple random walk to equilibrium, derived from precise asymptotics of the number of paths between vertices. Following the study of the graph geometry we proceed to its random perturbation via exponential weights on the edges (first-passage-percolation). We then show how this allows the derivation of various properties of the classical Erd\H{o}s-R\'enyi random graph near criticality. Finally, returning to the spectrum of random regular graph, we discuss the question of how close they really are to being Ramanujan and conclude with related problems involving random matrices. Based on joint works with Jian Ding, Jeong Han Kim and Yuval Peres, with Allan Sly and with Benny Sudakov and Van Vu.

Theory Day Speaker 1 - What Makes an Algorithm Great?

Series
Other Talks
Time
Saturday, October 24, 2009 - 12:30 for 2 hours
Location
LeCraw Auditorium
Speaker
Richard Karp – Electrical Engineering and Computer Sciences, University of California, Berkeley
From time to time a new algorithm comes along that causes a sensation in theoretical computer science or in an area of application because of its resolution of a long-standing open question, its surprising efficiency, its practical usefulness, the novelty of its setting or approach, the elegance of its structure, the subtlety of its analysis or its range of applications. We will give examples of algorithms that qualify for greatness for one or more of these reasons, and discuss how to equip students to appreciate them and understand their strengths and weaknesses.

Theory Day Speaker 2 - Computational Aspects of Equilibria

Series
Other Talks
Time
Saturday, October 24, 2009 - 13:50 for 3 hours
Location
LeCraw Auditorium
Speaker
Mihalis Yannakakis – Computer Science, Columbia University
Many models from a variety of areas involve the computation of an equilibrium or fixed point of some kind. Examples include Nash equilibria in games; price equilibria in markets; optimal strategies and the values of competitive games (stochastic and other games); stable configurations of neural networks; analysis of the evolution of various types of dynamic stochastic models. It is not known whether these problems can be solved in polynomial time. Despite their broad diversity, there are certain common computational principles that underlie different types of equilibria and connect many of these problems to each other. In this talk we will discuss some of these common principles and the corresponding complexity classes that capture them; the effect on the complexity of the underlying computational framework; and the relationship with other open questions in computation.

Theory Day Speaker 3 - Disjoint paths, isoperimetric problems, and graph eigenvalues

Series
Other Talks
Time
Saturday, October 24, 2009 - 15:10 for 1.5 hours (actually 80 minutes)
Location
LeCraw Auditorium
Speaker
Noga Alon – Mathematics and Computer Science, Tel Aviv University
The spectral properties of a graph are intimately related to its structure. This can be applied in the study of discrete isoperimetric problems and in the investigation of extremal and algorithmic questions for graphs. I will discuss several recent examples illustrating this theme.

Can (Theoretical Computer) Science come to grips with Consciousness

Series
ACO Distinguished Lecture
Time
Saturday, October 24, 2009 - 17:00 for 1 hour (actually 50 minutes)
Location
LeCraw Auditorium, College of Management
Speaker
Manuel Blum – Computer Science, Carnegie Mellon University

Preceded with a reception at 4:10pm.

To come to grips with consciousness, I postulate that living entities in general, and human beings in particular, are mechanisms... marvelous mechanisms to be sure but not magical ones... just mechanisms. On this basis, I look to explain some of the paradoxes of consciousness such as Samuel Johnson's "All theory is against the freedom of the will; all experience is for it." I will explain concepts of self-awareness and free will from a mechanistic view. My explanations make use of computer science and suggest why these phenomena would exist even in a completely deterministic world. This is particularly striking for free will. The impressions of our senses, like the sense of the color blue, the sound of a tone, etc. are to be expected of a mechanism with enormously many inputs categorized into similarity classes of sight, sound, etc. Other phenomena such as the "bite" of pain are works in progress. I show the direction that my thinking takes and say something about what I've found and what I'm still looking for. Fortunately, the sciences are discovering a great deal about the brain, and their discoveries help enormously in guiding and verifying the results of this work.