MATHEMATICS, COMPUTER SCIENCE AND STATISTICS.

Chair: Dale Bowman, University of Mississippi 

Vicechair: Joseph Kolibal, University of Southern Mississippi

FRIDAY MORNING

Room 2

9:00 MISSISSIPPI CENTER FOR SUPER-COMPUTING RESEARCH (MCSR) USER ADVISORY GROUP MEETING

David G. [Roach.sup.*] and Germana Peggion, University of Mississippi, University, MS 38677 and University of Southern Mississippi, Stennis Space Center, MS 39522

The Mississippi Center for Supercomputing Research was established in 1987 by the Mississippi Legislature and the Institutions of Higher Learning (IHL) in order to provide high performance supercomputing support for research and instruction at all state universities. The Mississippi Supercomputer User Advisory Committee (MSUAG) was established by the IHL Research Consortium to provide user input and advice to MCSR management and technical staff on policies and procedures for the Center's operations. It includes member representatives from all IHL institutions. The Advisory Group will meet at this MAS conference. Mr. David G. Roach, Director of the MCSR, and Dr. Germana Peggion, MSUAG Chair and Professor at USM-Stennis, will conduct the meeting. The agenda includes an update on MCSR HPC facilities and services, introduction of new MCSR staff members, and site reports and ongoing research updates by MSUAG representatives. IHL Faculty and graduate students with an interest in high performance computing are also invited to attend.

FRIDAY AFTERNOON

Room 2

12:40 BOOTSTRAP ESTIMATES OF HOME RANGE SIZE USING MINIMUM CONVEX POLYGONS

Jake H. [Olivier.sup.*] and Dale Bowman, University of Mississippi, University, MS 38677

One of the most widely used methods for computing home range size employs minimum convex polygons. This procedure is simple and quick to implement but is not probabilistic. A bootstrap procedure is proposed which retains the desirable properties of the minimum convex polygon while providing confidence intervals for the home range size. In addition the bootstrap procedure may be adjusted so that the estimated home range size is not dependent on the number of sampled points, as the minimum convex polygon generally is.

1:00 THE POWER OF AUTOTASKIENG

Germana [Peggion.sup.*], Alan Wallcraft, and Ray Sheppard Logicon, University of Southern Mississippi, Stennis Space Center, MS 39522

Ocean models are memory intensive with a relatively small ratio between computations per communications. Thus domain decompositions approach may not be efficient for simulations over small domains but for long time iterations. Under those conditions it would be still possible to achieve a good level of performance via auto tasking. The importance of such an approach is illustrated with the Princeton Ocean Model (POM). POM is a Fortran code written in the early 80s. Since then, new versions have been targeted to improve the physical formulation rather than the numerical efficiency Numerical simulations, conducted on two moderately parallel platforms: 1) Sgi Origin 2000 and 2) Sun-Enterprise 10000 illustrate how model performances can be improved by taking advantage of the f77/f90 loop parallelization. The results indicate that it is possible to migrate old vector programs to the parallel environment without writing one parallelization statement in the original code.

1:20 USING AUGMENTED SERIATION TO STUDY THE SCHOOL DATA OF THE UNITED STATES: A GEOGRAPHIC DATA ANALYSIS TOOL

Lixin [Yu.sup.*], Myke Gluck, and Abhijit Parchure, Alcorn State University, Alcorn State, MS 39096 and Florida State University, Tallahassee, FL 32306

Focusing on the tool rather than the data, this presentation demonstrates a new data analysis software which integrates map viewers and a seriation matrix. Seriation, also known as reorderable or permuted matrix, is the process of looking for univariate sequences in data. It may be used as a tool for discovering patterns in numerical data. Seriation matrix cells contain icons proportional in size to data values rather than actual data values. This feature allows users to observe and compare fields with different data ranges. For example, it is hard to compare age and salary directly since age rarely has three digits but salary has five or more. However, they become comparable after they are transformed into icons representing their relative ranks among records in each field. An icon for age 60 can be big and an icon for salary of 20,000 can be small. With this software, users can move rows and columns to visually discover graphical patterns of the data with meaningful interpretations, or use a built-in funct ion to do the seriation. It is augmented because it has other multimedia features such as map viewer and sound. The system permits simultaneous display of maps and matrices and graphically links them. These augmented features expand the use of seriation and permit users to perform a visual analysis of numerical and spatial data concurrently. State data from Common Core of Data (CCD) published by the US Department of Education are used to demonstrate the data analysis process with this system.

1:40 TESTS FOR LOCATION WITH K SAMPLES UNDER THE KOZIOL-GREEN MODEL OF RANDOM CENSORSHIP

Ke Wu, University of Mississippi, University, MS 38677

In survival analysis, one is often interested in comparing several groups (or treatments) in terms of their means, medians, or distributions when data are possibly censored. This paper considers tests for location with k samples and randomly right-censored data. Under the Koziol-Green model of random censorship in which the survival distribution of the censoring times is some power of the survival distribution of the lifetimes, one class of k sample location tests similar to those discussed by James (1987), which allows shapes do differ in the k populations, are developed. The tests are based on general estimating functions and do not require full parametric assumptions for large samples. The asymptotic distribution of the test scores is derived under the null hypothesis.

2:00 ROBUST CHARACTER OF THE RELIABILITY CHARACTERISTICS OF SOME STATIC SYSTEM MODELS WHEN THE PARAMETERS IN A LIFE TIME DISTRIBUTION ARE CONSIDERED AS RANDOM VARIABLES

Hari M. [Sharma.sup.*] and K.K. Sharma, East Mississippi Community College, Mayhew, MS 39753 and CCS University, Meerut, India

Assuming random variations in the parameters of the life time distribution, static system models are analyzed in the Baysian's framework. The random variations in parameters represented by prior distributions are updated by experimental data and are represented by posterior distributions in the Baysian's framework. The present study, however, deals with robust character of the reliability characteristics of some static system models when parameters of life time distributions are assumed to be random variables.

2:20 Break

2:30 MATHEMATICAL EXPECTATION USED IN DETERMINING AN EQUITABLE OR FAIR GAME

Garfield Burke, Jr., Mississippi Valley State University, Itta Bena, MS 38941-1400

Casinos and state-run lotteries have become big business. For example, in Mississippi, following legislation in 1990, casinos have become a major addition to the state's tourism industry. There are also over 200 different lotteries games run by over 35 different states and at least 6 interstate games. Some states run only one game each, while some run over 10 different games. Often, gamblers are motivated by the value of a successful outcome rather than the probability of success. The games they play seem to be fair because all the game participants appear to have an equal chance to win the same prize. The study of probability has become increasingly popular because it has a wide range of practical applications. Many practical applications of probability used by actuaries, insurance companies, casino gambling, etc. are embedded in the phenomena of fair games and mathematical expectation. The concept of mathematical expectation, some times called expected value, originally arose in connection with games of ch ance and is used to formally define a fair game. One of the reasons gambling is exciting is that winnings on a single play or even a few plays are uncertain. However, in the long run, as the number of plays increases and increases, the relative frequencies of outcomes get closer and closer to a theoretical (or actual) probability value. This paper will explore not only some concepts used in describing probability, but also some different kinds of probability situations using mathematical expectation concepts.

2:50 PRACTICAL APPROACHES TO ESTIMATING VARIATION FOR SAMPLE SIZE CALCULATIONS

Carolyn R. Boyle, Mississippi State University, Mississippi State, MS 39762

The most crucial component in a sample size calculation is the estimate of effect size, which relates the expected treatment differences to the expected variation in response. The exact relationship depends on the experimental design and the method of analysis; however, if the effect size is small, then the required sample size will be large. To estimate the effect size, the experimenter must decide how big a treatment difference is of practical importance and estimate how much variation in the response will be observed in the completed experiment. It is obviously difficult to predict the variation in response prior to performing the experiment. On the other hand, an estimate could be based on a pilot study, on published studies using similar protocols, on the inherent variation observed in untreated experimental units, or even on the experimenter's expert judgement. It is important to obtain a realistic estimate of the variation because it greatly influences the sample size. For example, when comparing two means using the two-sample t-test, the sample size required to detect a given treatment difference with a given power and confidence level is proportional to the square of the common standard deviation. If the common standard deviation is doubled, then the sample size quadruples and the total number of experimental units needed increases by a factor of eight (because there are two groups). This presentation will give a number of practical suggestions for obtaining a reasonable estimate of variation for use in sample size calculations.

3:10 HOW MANY EAVESDROPPERS GUARANTEE INTERCEPTION?

Jeffrey L. Stuart, University of Southern Mississippi, Hattiesburg, MS 39406

Consider a finite, loop-free undirected graph, which can be viewed as a bi-directional communications network. If one wishes to wisely deploy a team of eavesdroppers to intercept all communications between two nodes in the network, how large must that team be? This is closely related to the well-studied problem of the edge connectivity of a graph. However, in the eavesdropping scenario, one seeks the maximum over the sizes of all of the minimal cutsets of the graph rather than the minimum over the sizes. We will discuss how results on edge connectivity and on maximal clique structure can be used to produce bounds on the interception number. We will also discuss why computation of the interception number is algorithmically harder than computation of the edge connectivity.

3:30 Divisional Business Meeting

3:45 Meeting of the Mississippi Chapter of the American Statistical Association