9:30 Introduction

Computational Mathematics

9:40 ASSESSING NUMERICAL ERROR IN AGGREGATION PHENOMENA
Joseph Kolibal and Lynn Ladner *, University of Southern Mississippi, Hattiesburg, MS 39406, and Jefferson Davis Community College, Biloxi, MS 39530
Many aggregation phenomena such as fractals are studied using simulations involving discrete energy and spatial grids. Sampling from discrete density functions in place of the continuous density functions introduces errors into the diffusion model. More importantly, these approximations introduce possible space/angle correlation in the resulting particle distributions which alter the structure of the aggregate. In this study, the effects of numerical errors on fractal growth due to sampling from discrete pdf's is examined using model problems in diffusion limited aggregation.

10:00 TESTING MODERATELY PARALLEL ENVIRONMENTS FOR AN OCEAN MODELING APPLICATION
Jerry L. Bickham *, Germana Peggion, and Benjamin R. Seyfarth, University of Southern Mississippi, Hattiesburg, MS 39401-0002
Due to the high costs of accessing massively parallel and vector environments, as well as the overworking of high performance computers, there is now a need for a different approach to parallel computing. The feasibility of ocean modeling in a moderately parallel environment is tested using a 2-D (vertically integrated) ocean circulation model. The parallel algorithm is based on Glenda language and follows the master-worker message passing paradigm. It is evaluated on both internal and external communication environments. It is shown that the internal communication environment tested is only slightly more efficient than the external communication environment. This is due to a combination of shared memory problems in the internal communication environment, and to inefficiencies in the Glenda message-passing software. The tests also demonstrate how efficiency depends on the domain sub-divisions. And most importantly, it is shown that both environments effectively outperform their sequential counterparts, reducing the program elapsed time, and offering quicker access to the model outputs. The parallel version provided a time saving alternative to the sequential version of the same model on both internal and external communication platforms. This research supports the conclusion that both environments are a viable alternative to single-CPU machines and that moderately parallel environments are feasible computer platforms for ocean modeling applications.

10:20 Break

10:30 EXAMPLES OF NETWORK FLOW PATH ROUTING AND SCHEDULING PROBLEMS
Andrew W. Harrell, U.S. Army Waterways Experiment Station, Vicksburg, MS 39181
This problem area requires a combination of procedures using depth-first search and breath-first search. Two different C-code versions of variations of the basic Edmonds-Karp/Dinic network maximum flow/min-cost algorithms were written. These different versions enable a user to solve routing and scheduling problems interactively. The programs optimize the traffic flow (throughput) across a network of movement corridors on a digital map. They also schedule units to move through the network to perform tasks.

10:50 A SINGLE ELEMENT POISSON SOLVER
Joseph Kolibal * and Michael Eckhoff, University of Southern Mississippi, Hattiesburg, MS 39406
Using piecewise linear elements and a superconvergence result, a scheme for solving Poisson's equation using finite element methods is developed and compared with standard methods. The approach requires only a single nodal point to accurately achieve a converged solution at any point in the domain with an error independent of grid size.

2:00 HISTORICAL AND PHILOSOPHICAL FOUNDATIONS OF SINGLE-CASE RESEARCH
Richard F. Ittenbach *, and William F. Lawhead, University of Mississippi, University, MS 38677
Scientific research consists of a vast number of contributions throughout documented history. Each contribution to the broader fabric of science represents a blend of personalities and perspectives over time. Single-subject research, in union with new developments in statistical methodology and computer technology, has been used to understand the patterns of individuals' behaviors well beyond what was thought possible only a few decades ago. The purpose of the present paper is to offer a concise summary of design-related issues within the evolution of scientific thought, from the earliest of times to the design-related topics of today.

2:20 NEW MODELS TO PREDICT BODY SURFACE AREA IN DOGS
Carolyn R. Boyle *, Todd A. Tobias, Brooks A. Ahalt, and Warren W. Sullivan, Mississippi State University, Mississippi State, MS 39762-9825
Body surface area (BSA) can be used to determine doses of chemotherapeutic drugs that are safe and effective. Previously proposed models for humans, based on body weight (W) and height (H), take the forms (1) BSA=kW^(2/3) and (2) BSA=c W^a H^t, where k, a, b, and c are constants with 3 a + b = 2. Similar models have been used to predict BSA in dogs, but dosages based on these predictions tend to be too high for large, obese dogs. Previous research with various animal species has concentrated on improving estimates of BSA by obtaining better estimates of the constants k, a, b, and c; using an exponent other than 2/3 in model (1); or removing the restriction on a and b in model (2). However, we hypothesize that better estimates of BSA could be obtained by changing the form of the predictive model or by incorporating other measures of body shape and size. To test this, BSA data were collected on dogs euthanized for animal control purposes. Cadavers were wrapped in duct tape. Tape castings were harvested, cut into sections, and flattened. The sections were then scanned digitally and surface areas measured via computerized planimetry. This method of measuring BSA had been previously validated using geometric solids. Preliminary modeling results using 12 dogs indicate that growth curve models, such as the Mitscherlich three-parameter model (b_0(1-exp(-b_1 - b_2 W)), where b_0, b_1, and b_2 are constants) perform better than existing models by such criteria as larger generalized R^2 and smaller residuals for large dogs.

2:40 HYPOTHESIS TESTING IN TWO-STAGE CLUSTER SAMPLING
Sumalee Givaruangsawat *, Govinda J. Weerakkody, and Patrick D. Gerard, Mississippi State University, Mississippi State, MS 39762
Correlated observations often arise in complex sampling schemes such as two-stage cluster sampling. The resulting observations from this sampling scheme usually exhibit certain positive intracluster correlation, p*, within cluster. Due to the correlated data, the standard statistical procedures for testing Ho: \alpha'\beta = 0 may lack some of the optimal properties that these possess when the data are uncorrelated. The objective of this paper is to present exact methods for testing Ho: \alpha'\beta = 0 by combining information from the within = cluster model and the between cluster model in the same spirit as Zhou and Mathew (1993).

3:00 Break

3:10 EVALUATING THE EFFECTIVENESS OF ACT SCORES AS A PREDICTOR OF STUDENT SUCCESS IN MATHEMATICS CLASSES
Govinda J. Weerakkody * and Patrick D. Gerard, Mississippi State University, Mississippi State, MS 39762
Frequently, mathematics placement recommendations for Freshman are based on ACT scores. Effectiveness of the Composite ACT score and the ACT subscore in mathematics as predictors of student success in mathematics classes are evaluated using the Logistic Regression Analysis. This Analysis suggests that the ACT subscore in mathematics is a better predictor of student success than the Composite ACT score. Limitations of this analysis will also be discussed.

3:30 A CASE STUDY IN BIOMETRY USING MULTIPLE LOGISTIC REGRESSION
Todd G. Nick, University of Mississippi Medical Center, Jackson, MS 39216
Traditional courses in statistics teach multiple regression analysis with a series of lectures that are full of formulas and computer output. Although an occasional example relevant to the student's field may be included, these examples are usually too brief and too sanitized. In contrast, case studies motivate students to learn statistics by providing important and interesting scientific questions to address. In addition to learning about a statistical technique, students analyzing case studies learn to exercise judgment, deal with ambiguity, and communicate their findings and recommendations. In this talk, the factors that contribute to a good statistics case study are presented. A case study is described that provides biological data for students to develop a multiple logistic regression model with real-life implications. The data are from experimental aircraft overflights that were used to investigate flight response of the Pacific black brant [Erickson, Nick, and Ward (In Press)]. This model was used to recommend changes in flight paths to reduce the disruptive effect of aircraft overflights on wildlife. This case study is unique in that the main focus is on the interpretation of data, especially of the interaction effect. The case illustrates how statistical analysis is used to solve real world problems.

American Statistical Association Business Meeting

9:30 IDENTITIES INVOLVING THE ARITHMETICAL TRIANGLES OF PASCAL, EULER AND STIRLING
Bruce O'Neill, Mississippi Valley State University, Itta Bena, MS 38941
A Stirling Number of the Second Kind, S_n,m , is the number of ways of partitioning a set of n elements into m non-empty subsets. It is well known that they satisfy recurrence relations similar to those of binomial coefficients, and can be expressed in closed form in terms of binomial coefficients. Less well known, but deserving of more attention, is the fact that Stirling Numbers arise naturally when studying iterates of the differential operator zD_z. Eulerian Numbers arise in formulae involving sums of powers of integers and also in some aesthetically pleasing power series. Despite a superficial resemblance to binomial coefficients, we show that they are more closely related to Stirling Numbers, and reciprocity relations between the Eulerian and Stirling Numbers are shown. (FIGURE LEFT OUT).

9:50 POLYTOPIC STRUCTURE FOR CLASSES OF FIEDLER MATRICES
Jeffrey L. Stuart * and James R. Weaver, University of Southern Mississippi, Hattiesburg, MS 39406, and University of West Florida, Pensacola, FL 32504
A Fiedler matrix is a centrosymmetric, column stochastic, column-rhomboidal matrix with constant row sums. These matrices originally arose in work by Miroslav Fiedler on certain hypergeometric transition probability matrices for Markov-like processes. We examine the geometric structure of the class of all Fiedler matrices of a fixed size, showing that they form a set whose closure is a polytope. In addition to relating the dimension of the polytope to the matrix size, we also examine the boundary structure of the class, focusing on the inclusion of extreme points. Other results related to class containment under products will also be presented.

10:10 Break

10:20 THE NUMBER OF KNOTS THAT CAN BE BUILT WITH A REGULAR 50-SIDED POLYGON
Ama P. Fordjour and Robert Sosnoskie *, Binghamton University, and Jackson State University, Jackson, MS 39217
This research concerns the possible knotting occurring for a regular 50-sided polygon in three-dimensional space. Fifty-sided polygons in 3D space are good models for small DNA molecules as well as other small strands of polymers and macromolecules. We estimate the number of different types of knotting that can occur.

10:40 SOLVING PDE'S USING L1 APPROXIMATION OF DERIVATIVES Joseph Kolibal, University of Southern Mississippi, Hattiesburg, MS 39406 Fourier methods for computing the derivatives involved in solving partial differential equations (pde's) have proven highly accurate in many numerical applications. In this study, we investigate the use of smooth L1 functional approximations to the vector of unknowns as a mechanism for computing numerical derivatives and apply these to solving numerical problems involving model pde's.

1:30 A MULTIMEDIA APPROACH TO STUDYING SYMMETRY AND GROUP THEORY
Darren D. Wick, Millsaps College, Jackson, MS 39210
Interactive computer tutorials were developed to allow students to study the relationship between symmetry and group theory. The tutorials utilize moving images to describe the symmetries of various objects. The student is asked to connect these concrete visualizations to the more abstract notions of group theory. In particular, three tutorials were developed. The first gives a general introduction to plane symmetry, describing rotations and reflections of various two-dimensional objects. The second is a detailed analysis of the dihedral group of the equilateral triangle, including student construction of inverses, subgroups, and a multiplication table. The third tutorial gives an introduction to the symmetry of three-dimensional objects. These tutorials proved useful in helping students develop geometric intuition and insight into the structure of symmetry groups.

1:50 MULTI-LECTURING USING MULTIMEDIA IN CLASS PRESENTATIONS
R.W. McCarley, Millsaps College, Jackson, MS 39210
Multimedia may be the answer to having two lecturers and two computers running different packages during some lectures. At the introductory level of teaching Word Perfect, Lotus, Minitab, and dBase the ability to show similarities between the packages is almost impossible with one computer. The same is true for teaching the transfer of data from one package to another and showing the cause and effect of adjustments that may be required. Comparison of processes in two software packages is possible with the use of multimedia in presentations.

2:10 Break

2:20 MULTIMEDIA COURSEWARE FOR ALGORITHM ANIMATION
Andrew V. Royappa, Millsaps College, Jackson, MS 39210
Algorithm Animation is a procedure for illustrating computer algorithms by graphically showing how they manipulate data. We show animations of basic computer science concepts such as sorting by selection, sorting by merging, and the Von Neumann cycle (the Fetch/Execute machine cycle). These animations were developed using the Authorware multimedia development package. All of the animations involve user interaction and feedback to control the progress of the animation. The algorithm animation software developed through this work is useful for illustrating concepts in introductory computer science courses, including Computer Science I & II, Data Structures and Algorithms, and Machine Programming.

2:40 A MULTI-USER EVENT CALENDAR IN JAVA
Michael B. Sledge * and Andrew V. Royappa *, Millsaps College, Jackson, MS 39210
We have developed an application for posting organization-wide events and notices. The application is accessed through any Internet browser that supports applets in the Java programming language. The calendar is displayed graphically in the traditional month-by-month manner, and events on a particular day are shown as small icons. Events of a common type (e.g., sporting events, music concerts) are grouped under a single icon. The event calendar allows authorized users of an organization to post notices and schedule events. Users can also be automatically reminded by electronic mail about particular events, or notified of new event postings in a given category. The software is designed in two parts: a Java client which executes within the Internet browser and controls the user interface, and a Java server running as a separate process on an Internet host. The server serializes the way in which multiple users access a database of events. This system illustrates several advantages of Java software: client portability to numerous platforms (including Windows and UNIX), access to authorized users from anywhere on the Internet, software installation on only one host (the server), etc.

3:00 CGI PROGRAMMING USING PERL
Vijay R. Amirineni, Mississippi Valley State University, Itta Bena, MS 38941
Dynamic pages are replacing the static pages on the World Wide Web. Gateway scripts, otherwise called as Common Gateway Interface (CGI) scripts, make the interaction possible between the Web browser and the server. CGI scripts enable the user to interact with the Web pages-in filling out a form to order a product, or in searching a database by typing his/her own key words. This kind of interaction has provided a new avenue for corporations to successfully conduct their businesses on the Web. CGI programming is different from other programming in the sense that a CGI program must be extra careful about security and must be able to pass and receive data from other programs. CGI programs operate in a very insecure environment and effort should be made to protect the programs from the possible hackers. This paper concentrates on writing CGI scripts on UNIX platform using Perl programming language. UNIX is the operating system of choice on the Internet today. Perl is preferred by many programmers as it is available at no cost, relatively easy to learn, and works on many platforms. Perl 5, released this year, contains objects that make it easy to create forms and parse their contents, and has thus made the task of CGI scripting far easier.

3:20 Divisional Business Meeting

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