| MathStat Home | USA Home |
| Date/Time | Speaker | Title/Abstract |
|---|---|---|
| Tuesday May 9, 2000 3:30 PM in ILB 370 |
Louis H. Kauffman
University of Illinois, Chicago |
Virtual Knot Theory |
| Abstract: TBA | ||
| Thursday April 27, 2000 3:30 PM in ILB 370 |
Carroll Dougherty
University of South Alabama, Dept. of Mechanical Engineering |
Harmonic Analysis of Flow and Pressure Traces in Perfusion Circuits |
| Abstract: TBA | ||
| Thursday April 13, 2000 3:30 PM in ILB 370 |
Joe Borzellino
Pennsylvania State University |
Determining the topological structure of an orbifold from algebraic information about its group of orbifold diffeomorphisms. |
| Abstract: Given a topological space X, one can consider X endowed with many different geometric structures and the subgroup of the homeomorphism group of X that preserves that structure. For example, one might give X a differentiable structure and consider the group of diffeomorphisms of X. The question is: Do algebraic properties of the group of structure preserving automorphisms of X determine the structure? A question of this type is the following: Let M and N be two differentiable manifolds with groups of diffeomorphisms Diff(M) and Diff(N). Suppose there is a group isomorphism I: Diff(M) --> Diff(N). Is there a diffeomorphism f:M --> N such that I(g)=(f o g o f^{-1}) for all g in Diff(M)? An affirmative answer implies in particular that M and N are diffeomorphic. In this talk, I will discuss the analogous question when X carries the structure of an orbifold. The talk will include relevant history, definitions and examples. There is no guarantee that the information provided will increase the chances of a hefty tax refund and will in no way expedite the filling out of tax returns before the April 17 deadline. Individual results may vary. | ||
| Wednesday April 12, 2000 3:30 PM in ILB 140,refreshements at 3:00PM |
John Lefante
Tulane University |
Approximating Poisson Regression with Logistic Regression |
| Abstract: The number of occurrences of an event in a fixed period of time or space can be modeled as a Poisson random variable, Y. The Poisson probability distribution, f(y) =P(Y = y| mu) = (e^(-mu) (mu^y))/y! , for y = 0, 1, 2, ..., , where mu = the mean number of occurrences in the time or space interval, is used to describe the likelihood of rare events. Some common applications include estimating the annual incidence rate of a rare disease, the number of catastrophic work related accidents per year in an industry, and annual mortality rates. When the mean number of occurrences change within the levels of some dependent covariate Poisson regression is used. The expected number of occurrences can be modeled as mu_i=l_i p_i, i = 1, 2 , where l_i represents the population size or person-years for the ith group, and p_i represents the population risk in the ith group. The Poisson regression model relates p_i to an independent variable x, by ln(p_i)= beta_0 +beta_1 x_i. Maximum likelihood estimation is used to estimate the beta's. The model can also estimate relative risk, RR =exp(beta_1). Logistic regression, where ln(p(x)/(1-p(x))=beta_0+beta_1 x , can be used to approximate poisson regression when the incidence rates p_i are small and the l_i, population size or person-years for the ith group, are large. Odds ratios, estimated from this model, can approximate relative risk. An example is presented, applying both Poisson and Logistic regression to a data set, modeling the risk of new onset asthma in paper plant workers exposed to low levels of irritant chemicals in the work place. | ||
| Thursday April 6, 2000 3:30 PM in ILB 370 |
Mimmo Iannelli
Purdue University and University of Trent |
The mathematical modeling of epidemics with age structure |
| Abstract: Age is actually one of the most natural and important parameters structuring a population. In fact many internal variables, at the level of the single individual, strictly depend on the age because different ages mean different reproductive and survival capabilities and, also, different behaviors. In particular, when modeling epidemics, it is important to consider age-structure because the infection mechanisms may be dependent on the age of the individuals and may interact with the demographic processes of the population. In the case of epidemics, age may be intended as "chronological age", i.e., the age of the individuals, or as "class age", i. e. the time elapsed since an individual has been infected. This leads to two different classes of models that try to describe the behaviour of diseases like measles, rubella, ghonorrhea, T.B. , AIDS. The mathematical problems involved consist in some nonlinear first order PDE hyperbolic problems with non local boundary conditions that make the problem somewhat related to the theory of integro-differential equations of Volterra type. In this talk we will review the formulation of the models, their mathematical implications and their help in the study of epidemics. | ||
| Friday March 31, 2000 3:30 PM in ILB 370 |
Vladimir Troitsky
University of Texas,Austin |
Spectral radii of bounded operators on topological vector spaces |
| Abstract: We develop a version of spectral theory for bounded linear operators on topological vector spaces. We show that the Gelfand formula for spectral radius and Neumann series can still be naturally interpreted for operators on topological vector spaces. Of course, the resulting theory has many similarities to the conventional spectral theory of bounded operators on Banach spaces, though there are several important differences. The main difference is that an operator on a topological vector space has several spectra and several spectral radii, which fit a well-organized pattern. | ||
| Thursday March 30, 2000 3:30 PM in ILB 370 |
Sytska Kimball
University of South Alabama, Dept. of Meteorology |
The evolution of model hurricanes in three-dimensional flow |
| Abstract: It is believed, from observational studies, that when hurricanes interact with upper level troughs, or upper level low pressure systems, the storms' potential for rapid intensification increases. The exact mechanisms that lead to hurricane intensification after trough interaction are not well understood. One of the complicating factors arises because troughs are associated with strong vertical wind shear. Strong vertical wind shear has long been known to hamper hurricane intensification and, in some cases, even destroy storms all together. In this paper, a non-hydrostatic, three dimensional numerical weather model (MM5) is used to investigate the complex problem of hurricane-trough interaction. The basic equations and parameterizations underlying the model are introduced and the results from a number of idealized hurricane simulations are presented. An idealized hurricane will be placed in vertically sheared flow and will be allowed to interact with three different idealized upper level lows. The upper lows vary in intensity and size, while the initial hurricane is the same in each case. The low is initially positioned 800 km west of the storm. A weak, vertically sheared, westerly flow allows the systems to approach one another gradually. Each of the hurricanes undergoes a very different evolution. The ultimate rainfall and windspeed distributions, and hence damage potential, of the hurricanes differ dramatically. These differences will be discussed in the presentation. | ||
| Thursday Mar. 23, 2000 3:30 PM in ILB 370 |
Charles Zheng
University of South Alabama, Dept. of Mechanical Engineering |
Examples of Applied Mathematics in Fluid Mechanics Research |
| Abstract: In this presentation, a sound radiation problem from turbulent boundary layers is used to demonstrate several applied mathematical techniques employed in fluid mechanics research. The analysis starts from Lighthill's acoustic analogy. With integral expressions for turbulent boundary layers, dominant sound radiation sources from low Mach number turbulent boundary layers are identified. Using Green's function combined with integral transforms, orders of magnitude of each source can be compared. Subsequently, a mathematical model of the cross-correlation function of fluctuation wall pressure in turbulent boundary layers (by assuming turbulence as a steady stochastic process) is employed to obtain analytical solutions for the power spectra of radiated sound field. | ||
| Friday Mar. 17, 2000 2:30 PM in ILB 370(subject to change) |
Eriko Hironaka
Florida State University |
The Geometry of Salem numbers |
| Abstract: A Salem number is a real algebraic integer larger than one all of whose conjugates lie on or inside the unit circle, with at least one conjugate on the unit circle. A long outstanding problem is whether there are Salem numbers arbitrarily close to one. The smallest known Salem number was found by Lehmer in 1933 and is a root of the 10th degree polynomial x^10 + x^9 - x^7 - x^6 - x^5 - x^4 - x^3 + x + 1. In this talk we will discuss some approaches to solving this problem which arise from an interesting interplay between knot theory, geometric group theory, and arithmetic hyperbolic surfaces. | ||
| Tuesday Mar. 14, 2000 (subject to change) 3:30 PM in ILB 370 |
Carlos Coelho
Lisbon Technical University |
The concept of near-exact distribution. Some of its applications. |
| Abstract: The concept of 'near-exact' distribution although being a simple one, its use enables us to obtain distributions which lay very close to the exact distribution but which are far more manageable. The concept may be used whenever the characteristic function of the random variable or statistic under study may be expressed as the product of two or more factors. Indeed, in a number of cases by replacing just a small part of the characteristic function of a random variable by an asymptotic result with very good convergence properties one will be able to get a distribution extremely close to the exact distribution but much easier to handle and yet far better than any of the usual asymptotic distributions. Further, using such procedure one may usually choose which component parts of the characteristic function one wants to replace. Since a number of times we just have to replace a given number of components in order to obtain a fairly manageable distribution, we may choose the most adequate ones to replace in terms of the asymptotic result used, giving yet more control over the process to the researcher and the possibility to obtain very good near-exact distributions. Examples are given with the application of the concept to the distribution of the product of an odd number of particular independent Beta random variables and to the distribution of the generalized Wilks Lambda statistic when two or more sets of variables have an odd number of variables. | ||
| Thursday Mar. 2, 2000 3:30 PM in ILB 370 |
Tony Robbin
Mathematical Artist, New York City |
The one culture theory |
| Abstract: When we consider artists such as van Gogh and Monet, the idea of space in their art and the idea of space in contemporary mathematics are the same. My own work is based on the visualizations of four-dimensional geometry that were made possible by computer graphics. | ||
| Thursday Feb. 24, 2000 3:30 PM in ILB 370 |
Masakazu Teragaito
Univ. of Tx, and Hiroshima Univ. |
Toroidal Dehn fillings and lens spaces |
| Abstract: For a hyperbolic 3-manifold with a torus boundary component, there are only finitely many Dehn fillings yielding non-hyperbolic 3-manifolds. In this talk, we examine the situation that one filling yields a lens space and the other yields a toroidal manifold. For such two fillings, Cameron Gordon gave an upper bound for their distance, but he also conjectures that it is not best-possible. We will give a partial improvement of Gordon's upper bound. The arguments are quite elementary, and are based on the analysis of graphs of intersections. | ||
| Friday Feb. 4, 2000 3:30 PM in ILB 370 |
Mark Brittenham Univ. of Nebraska-Lincoln |
Tying surfaces up in knots |
| Abstract: This talk will explore the many ways in which a surface F (with boundary) can be embedded in 3-space. The boundary of F forms a knotted circle (AKA a knot) in space, and the many different ways to embed F give rise to many different knots K. Our main focus will be to provide answers to the questions: given a knot K, what kinds of surfaces F in space have K as their boundary, and what can such surfaces tell us about our knot K? | ||
|
Wednesday Dec 15, 1999 2:00 PM in ILB 370 |
Mausumi Bose Indian Statistical Institute |
|
| Abstract: The multinomial selection problem is considered in its most general form where the objective is to select a subset of s cells which contain the t best cells, s > t >1. The least favourable configuration(LFC) is obtained and two interesting conjectures about the LFC by Chen and Hwang (Commun. Statist. -Theor. Meth 13(10), 1289-98, 1984) are settled in the affirmative. An expression for the efficiency of the inverse-sampling procedure with respect to the fixed-sample-size procedure is obtained and bounds are derived for this efficiency. | ||
| Tuesday Dec 14, 1999 2:00 PM in ILB 370: Refreshments at 1:30 |
Prof. Laurent Baratchart Institut National de Recherche en Informatique et Automatique |
|
| Abstract:
The problem of recovering an analytic function in a simply connected domain
from partial boundary data is an old one, that arises in many applications
of
harmonic analysis to inverse problems. On the one hand,
asymptotic formulae involving singular
integrals were proposed already by T. Carleman, and subsequently refined by
Patil,
but their contructiveness is questionable since the problem is ill-posed.
On another hand, one can ask for a best approximation of (possibly
non-analytic)
partial boundary data
by an analytic function out of some restricted class, which makes for a
well
posed problem that was first considered by M.G. Krein and N. Nudel'man. It
turns
out that,
in case the boundary of the domain of analyticity is smooth
and for some appropriate choice of the kernel, Carleman asymptotic formulae
solve such a problem already by minimizing a weighted L2 criterion.
We shall discuss these facts, together with the sharp rate of convergence to boundary data with $L^2$ derivative; the analysis of the rate relies on the constructive spectral theory of Toeplitz operator of M.Rosenblum and J. Rovnyak. |
||
| Monday Dec 13, 1999 3:30 PM in ILB 370: Refreshments at 3:00 |
E.B. Saff University of South Florida |
|
| Abstract:
The problem of placing a large number of points
uniformly over the surface of a sphere has not only inspired
mathematical researchers, it has attracted the attention
of biologists, chemists, and physicists working in such
fields as viral morphology, crystallography, molecular
structure , and electrostatics. The research presented concerns
the generation of such points via optimization with respect
to certain "generalized energy" criteria.
Computer results for optimal configurations involving up to 200 points reveal graphical patterns that have features in common with the standared soccer ball design: i.e. they produce tilings of the sphere involving hexagons and pentagons. Larger numbers of optimal points appear also to generate heptagons in the tiling. The research conducted has two main aspects. First, the theoretical investigation of the energy associated with optimal configurations when the number N of points on the sphere grows large and, second, the creation of simple algorithms for quickly generating any number of points on the sphere that are "near optimal". For the former, methods of potential theory are utilized and for the latter a simple geometric approach is described. |
||
| Thursday Nov. 11, 1999 3:30 in ILB 370 |
Xin Minh Zhang University of South Alabama |
|
| Abstract: We shall take a new look at some old problems in elementary geometry from a dynamical systems point of view, and briefly introduce some new ideas and questions. In particular, we construct different sequences of polygons via iterative procedures and study their limiting behavior. The underlying analysis and algebra are accessible to undergraduates, and the revealed problems and proposed questions motivate people to further understand some fundamentals in dynamic systems and geometric analysis. (This talk is partially based a joint work by Drs. Hitt and Zhang on "Dynamic Geometry of Polygons). Undergraduates and Graduates are encouraged to come. | ||
| Thursday Oct. 28, 1999 3:30 in ILB 370 |
Robert Ghrist Georgia Tech. |
|
| Abstract: One of the best places to find interesting topological spaces is in an automated factory. We will consider the topology of configuration spaces associated to certain manufacturing problems. When coupled with some ideas from dynamical systems, knowing what these spaces look like can yield practical algorithms for collision-avoidance. | ||
| Thursday Oct. 7, 1999 3:30 in ILB 370 |
Tahl Nowik Columbia Univ. |
|
| Abstract: For F a closed surface, M a 3-manifold and i,i':F\to M two regularly homotopic generic immersions, we will be interested in the number mod 2 of quadruple points occurring in generic regular homotopies between i and i'. We will ask under what conditions is this number (in Z/2) the same for all generic regular homotopies between i and i'? If so, we will want an expicit formula for this number. | ||
| Thursday Sept. 23, 1999 3:30 in ILB 370 |
Masahico Saito University of South Florida |
|
| Abstract: Knots can be distinguished by coloring their diagrams. The rule of coloring is generalized to an algebraic system called quandles. New knot invariants defined from quandles will be discussed. The talk is intended for general audience. | ||
|
Department of Mathematics and Statistics |
|
