Selected Abstracts from Student Papers
 

Candace Porter, Michael Sotelo, Brandon McKenzie and Lindsay Kellam took a statistical look at the spread of sexually transmitted diseases.   Each year, thousands of federal and state dollars are allocated for STD education programs, medical treatments, and preventative measures. These four students used the STD situation to illustrate how multivariate classification methods can be used. First, they used principal component analysis to simplify the interpretation and summary of those variables which aid in predicting STD rates. Principal component analysis allowed them to depict a set of data using a number of descriptive factors that was less than the number of variables. They began with measurements of ten racial, ethnic, socioeconomic, and educational variables for each case and were able to combine them into four components that provide a clearer picture of the factors that predict the rate of STDs. Second, using discriminant analysis, they created a model that consisted of two groups: a group with a high rate of STDs and another with a low rate of STDs. Members (cases) in each group share similar racial, ethnic, socioeconomic, and educational variables. Using this discriminant model, they can predict an unknown observation's group classification.	Candace, Dr. Waikar, Mike, Brandon and Lindsay discuss their findings
Dana Thompson and Lawrence Garcia (SUMSRI 2000) examined an extension of the problem by allowing the position of the home point to vary. They fixed four points, representing cities, on a Cartesian grid and allowed the coordinates of the home point to change. For each position, as the home point moves throughout the plane, the salesman has several possible paths from which to choose. The path with the shortest length is determined and called the best path for that home point.  They assigned each possible best path a color and then colored each home point according to its best     path, creating colored regions on the graph. A Matlab program was used to create colored graphs for different arrangements of the four cities. They chose to examine cases that involved placing the four points on the grid to form certain quadrilaterals including a rhombus, a kite, and a trapezoid. Melissa Dejarlais proved in her unpublished 1999 SUMSRI paper that there are four, five, or six distinct best         paths for any configuration of four distinct cities. For each of our quadrilaterals, they examined the conditions necessary for a fifth or sixth color to be present in the graph.	Dana Thompson and Lawrence Garcia
In the summer of 2000, Betsy LaPlant, Beth McLemore and Victoria Pace Wood continued this research. A latin transversal is defined as a collection of n distinct entries of an n×n matrix, no two of which are in the same row or column. They showed that every 4×4 submatrix contains a latin transversal. Additionally, they proved that any n-2×n-2 submatrix contains a latin transversal when n is prime. These results, together with the previous years findings establish the existence of at least one latin transversal in any 4×4 or smaller submatrix as well as in many n-2×n-2 submatrices and any n-1×n-1 submatrix of the Z_n Cayley addition table where n is odd.	Algebraists Vicky, Beth & Betsy pose for the camera
Jennifer Hebert looked at the travelling salesman problem for three cities with the use of Sperner's Lemma in which there is always a coordinate for homeport where all paths of travel are equal in distance.  It is possible to compute this point (the Sperner Point) in the case that the cities form an equilateral or an isosceles triangle.  However when the cities are in a scalene formation, the Sperner Point is not easily computable.  Using Newton's Method, a good estimation of the Sperner Point can be found; with the use of the centroid of the triangle formed by the cities to fuel Newton's Method, it is possible to always find a convergent answer.