Seminars and Colloquia by Series

Wednesday, October 21, 2009 - 12:00 , Location: Skiles 171 , Doron Lubinsky , School of Mathematics, Georgia Tech , Lubinsky@math.gatech.edu , Organizer:
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.
Wednesday, October 21, 2009 - 11:00 , Location: Skiles 269 , Klas Udekwu , Biology, Emory University , ikeche@gmail.com , Organizer:
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.  
Series: PDE Seminar
Tuesday, October 20, 2009 - 15:05 , Location: Skiles 255 , Hongqiu Chen , University of Memphis , Organizer: Zhiwu Lin
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.
Tuesday, October 20, 2009 - 15:00 , Location: Skiles 269 , Daniel Bauer , Georgia State University , Organizer: Liang Peng
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.
Tuesday, October 20, 2009 - 12:05 , Location: Skiles 255 , Gelasio Salazar , Universidad Autonoma de San Luis Potosi , Organizer: Robin Thomas
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
Monday, October 19, 2009 - 14:00 , Location: Skiles 255 , Brett Wick , Georgia Tech , Organizer:
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.
Monday, October 19, 2009 - 14:00 , Location: Skiles 269 , Inanc Baykur , Brandeis University , Organizer: John Etnyre
We will introduce new constructions of infinite families of smooth structures on small 4-manifolds and infinite families of smooth knottings of surfaces.
Monday, October 19, 2009 - 13:00 , Location: Skiles 255 , Helga S. Huntley , University of Delaware , Organizer:
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.
Monday, October 19, 2009 - 11:00 , Location: Skiles 269 , Redouane Qesmi , York University, Canada and SoM, Georgia Tech , Organizer: Yingfei Yi
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.
Friday, October 16, 2009 - 15:05 , Location: Skiles 255 , Nina Balcan , Computing Science & Systems, Georgia Tech , Organizer: Prasad Tetali
There has been substantial work on approximation algorithms for clustering data under distance-based objective functions such as k-median, k-means, and min-sum objectives. This work is fueled in part by the hope that approximating these objectives well will indeed yield more accurate solutions. That is, for problems such as clustering proteins by function, or clustering images by subject, there is some unknown correct "target" clustering and the implicit assumption is that clusterings that are approximately optimal in terms of these distance-based measures are also approximately correct in terms of error with respect to the target. In this work we show that if we make this implicit assumption explicit -- that is, if we assume that any c-approximation to the given clustering objective Phi is epsilon-close to the target -- then we can produce clusterings that are O(epsilon)-close to the target, even for values c for which obtaining a c-approximation is NP-hard. In particular, for the k-median, k-means, and min-sum objectives, we show that we can achieve this guarantee for any constant c > 1. Our results show how by explicitly considering the alignment between the objective function used and the true underlying clustering goals, one can bypass computational barriers and perform as if these objectives were computationally substantially easier. This talk is based on joint work with Avrim Blum and Anupam Gupta (SODA 2009), Mark Braverman (COLT 2009), and Heiko Roeglin and Shang-Hua Teng (ALT 2009).

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