Fall 2007 GSS Schedule

Date Speaker Topic Abstract
September 3 Labor Day    
September 10 Free Snacks Day Party Time We investigate whether graduate students in mathematics can have a good time.
September 17 Dennis Smith Title: Star Trek : Generations
Subtitle: (If we define Star Trek to mean Random Test Networks)		 Empirical testing of network flow algorithms often requires the generation of a large number of random instances having fixed characteristics. In order to generate a directed network that is useful in testing shortest path algorithms, it is desirable for the network to be root-connected. We may need to generate and subsequently reject large numbers of networks while attempting to find "useable " ones. As one example, it was necessary to generate 2,122,478 random networks with 100 nodes and 250 edges in order to find 200 that were root-connected. This is a computationally unsatisfying position. We can achieve a computationally feasible method by ensuring root-connectivity through the generation process. The big question is, "Do we have to sacrifice the uniform selection of root-connected networks to do so? " This talk will provide both theoretical and computational results that shed light on this question. Attempts to actually discuss Star Trek will be not be tolerated.
September 24 Surprise Presenter:
Bonnie McAdoo 		The Inverse Source Problem with Applications to Optical Tomography Recovering the coefficients of a PDE given information about the solution is in general ill-posed. However, by choosing the optimal source term in the equation, we can make this inverse problem more robust.

In this talk I'll discuss possible directions for this problem and two applications.
October 1 Frank Volney AI in Short What exactly is Artifcial Intelligence (AI)? It's one of those multidisciplinary fields where you'll get a different definition from each person you ask. I recently finished a pretty good book on the subject, so I'd like to give you a description of some of the topics, or subfields, in AI and the types of math that go along with it. After our very brief tour, we'll talk about the A* search and apply it to a toy problem - the 15-puzzle.
October 8 Tom Fisher Introduction to the R Project for Statistical Computing R is a free (GNU-style) software environment for statistical computing and graphics designed for a wide variety of computing systems. It is currently growing in popularity amongst research statisticians and the general academic populous due to its availability. Much like the famous MATLAB, it consist of a programming language and run-time environment. It borrows many programming elements from MATLAB, and classical languages such as C and Fortran and is based on the popular statistical language S-Plus. In this talk, we will introduce the basic operations of R and its overall structure. Specific examples of linear regression, test for normality, and general probability methods will be covered time permitting. Statistics students and those who may have the need for some basic computational statistical analysis are encouraged to attend.
October 15 Fall Break    
October 22 Ferebee Tunno Simple Interval Estimation for Autoregressive Parameters My talk is concerned with interval estimation of an autoregressive parameter. Many confidence intervals appearing in the literature require a high level of numerical computation, but applied practitioners always have a need for reliable intervals that are easy to compute. The intervals proposed in this talk possess simple formulas and no numerical calculation or approximation is needed. Coverage is exact when the errors are symmetric normal, and remains very good for symmetric non-normal errors. A simple AR(1) model is initially considered, but then extended to time series models possessing a parametric trend.
October 29 J. Bowman Light Graph Theory... In Disquise Many problems in mathematics can be solved using the principles of graph theory. In this Halloween talk, we will explore how this versatile branch of mathematics can be found in common problems in other branches, including algebra, number theory, and stochastics.
November 5 Sharon Darby Software for Linear and Nonlinear Programming In this presentation, we will explore LINGO, MATLAB, R and how they can be used for solving linear and nonlinear programs. We will consider examples of binary integer programming, linear programming and nonlinear programming.
November 12 Jeff Beyerl Not Real, but Surreal Numbers A rigorous set theoretic development of numbers by John Horton Conway resulted in a generalization that includes real numbers, ordinals, and game theory. I will illustrate the foundations of this theory. The topics to be discussed include numbers, their ordering, arithmetic operations, properties of the resulting class, as well as looking at a few numbers in specific including but not limited to 0, 1, ½, ω (the first limit ordinal), and 1/ω.
November 19 Faculty Candidate    
November 26 Chinthaka Kuruwita A Bayesian Approach for Bandwidth Selection in Kernel Density Estimation We propose a modifcation to the regular kernel method using asymmetric kernels (like lognormal) to circumvent the spill-over problem when estimating densities with positive support. Further, we develop a data-driven bandwidth selection method based on a Bayesian criterion. Strong convergence of the proposed estimator is established. For suitable choices of prior parameters our local bandwidths converge to zero almost surely. Simulation results establish the superiority of the proposed estimator over two competing estimators. A real data example reveals more precise features of the proposed estimator over existing methods.