Spring 2004 GSS Schedule

Organizers: Jason Howell and Mark Liu

Date Speaker Topic Abstract
January 19 MLK Holiday
January 26 Postponed
February 2 Thomas McCoy Infidelity, French fish, and Deviance: An Introduction to Applied GLM with SAS GLM stands for Generalized Linear Models, which include widely-applied statistical tools like Logistic and Poisson regression. In this talk, we will be introduced with some basic SAS GLM modeling using Fair's famous data set for infidelity, a classic example often used to motivate use of Poisson and Negative Binomial Regression. We'll compare the Poisson and Negative Binomial Regression models with regular linear regression by talking about the assumptions involved, analogs for checking model fit, and using diagnostics such as examining appropriate residuals and such. In this discussion, we'll also explore details of the recent literature that argues the model validity of Fair's results on cheating.
February 23 Tim Flowers Partial Sums of Hurwitz Class Numbers The definition of a class number of quadratic forms with a certain discriminant can be modified for a number $N$ to produce what is known as the Hurwitz class number, $H(N)$. For any odd prime $p$, Kummer's Theorem states $\sum H(4p-r^2)=2p$, where the sum is taken over all integers $r$ such that $4p-r^2>0$. We are interested in splitting this sum apart into the congruence classes of $r$ modulo some number $q$. Since some of these partial sums can be viewed as counting $q$-torsion points on elliptic curves, it is not a surprise that these certain sums exhibit predictable patterns. However, we have also found patterns for several other cases. In this talk we will demonstrate the computations that lead to the patterns we have found. We will also point out which of the patterns we can prove and which are still open questions. (This work was done in the summer of 2003 here at Clemson for the ``REU in Computational Number Theory and Combinatorics'' funded by NSF with program participants Brittany Brown and Amy Stout and supervisor Kevin James).
March 1 Grad Student Meeting
March 8 John Chrispell An Introduction to LaTeX Since its introduction in 1985, LATEX has made it possible for authors of scientific papers, especially mathematicians, to typeset their own documents. LATEX works works as a markup language with simple commands and environments used for document processing. In this presentation we introduce the basic commands and environments commonly used in LATEX. Starting with the fundamentals we learn how to prepare an input file, how to compile the input file, and how to view the compiled file. No previous knowledge of LATEX is assumed. As time permits we will cover formating of the documents and explore some of the commonly used environments in LATEX and how they can be used to typeset Mathematical formulas, and tables to give documents the professional touch.

Files used in this presentation are: the source file talk.tex, the figure talk.ps, and the bibliography file bibmaster.bib.
March 15 Spring Break
March 22 John Paul Roop Fractional Directional Derivatives and the n-Dimensional Fractional Advection Dispersion Equation In this talk, we will introduce the concept of a fractional directional derivative for a function $u: R^{n} -> R$. We prove many useful properties of these operators and show how they can be used in order to generalize the fractional advection dispersion equation to many dimensions.
April 5 Mark Liu The Linear Diophantine Problem of Frobenius MacDonalds sells chicken nuggets in the amounts of 6, 9, and 20. You can buy 12: (2*6) or 21:(2*6 + 9) pieces but you can't buy 17 or 22 pieces. It is well known that after a certain value N, you can buy nuggets in quantity of N+1, N+2,.... What is the largest quantity of nuggets you can not buy? This number is known as the Frobenius Number of {6, 9, 20}, denoted by g(6, 9, 20). The question generalizes to asking: Given a set {a_1, ..., a_k} with gcd(a_1, ..., a_k) = 1, determine g(a_1, ..., a_k). J. J. Sylvester solved the problem for k = 2 in 1884. For the case of k>2, very little is known. In this talk we will discuss some results known about this problem.
April 19 Sathish Indika Scheduling Aircraft Maintenance Programs By Integer Programming In this talk we will discuss a mixed-integer quadratic programming model (MIQP) that is used to schedule different types of aircraft maintenance programs. Here we concentrate on a single facility (hangar) which is equipped with several work stations (bays). It is assumed that there are a number of scheduled jobs with specified starting times, job durations and specified work station assignments for the next planning horizon. We are interested on how best to schedule a number of new jobs that the facility will be anticipating in the near future. A MIQP is used to obtain a generalized model for the scheduling problem. The MIQP gives an exact schedule which optimizes the overall facility allocation. As time permits we will discuss a simplified heuristic procedure which often gives a near optimal allocation.