MATHEMATICS, COMPUTER SCIENCE AND STATISTICS.

Chair: Walter T. Brehm, US Air Force/Keesler Medical Center

Vicechair: Dale Bowman, University of Mississippi 

THURSDAY MORNING

Caribbean Room

9:00 PATTERN K-POTENT RAY PATTERN MATRICES

Jeff Stuart [1][*], LeRoy Beasley [2], and Bryan Shader [3], (1.) University of Southern Mississippi, Hattiesburg, MS 39406; (2.) Utah State University, Logan, UT 84322; and (3.) University of Wyoming, Laramie, WY 82071

For a complex matrix A, the ray pattern of A is the class of all complex matrices whose the zero- nonzero pattern is specified by that of A and such that the argument of each nonzero entry is that of the corresponding entry of A. The ray pattern is called pattern k-potent if k is the smallest positive integer for which A[conjuction](k+1) = A as ray patterns. We provide a canonical form for patterns with respect to permutation similarity and signature similarity by diagonal, unitary matrices. We characterize the irreducible ray patterns that are pattern k-potent, and we provide necessary conditions for the structure of each off-diagonal block of the Frobenius normal form of a reducible, pattern k-potent ray pattern.

9:15 TILING CONVEX POLYGONS WITH EQUILATERAL TRIANGLES

John C. Mayer [1], Tameka LaShun Wilder [2][*] , John C. George [2], Lovell Agwaramgbo [2], (1.) University of Alabama at Birmingham, Birmingham, AL 35294-1150 and (2.) Tougaloo College; Tougaloo, MS 39174

The purpose of this project was to answer several questions pertaining to the tiling and tessellation of convex polygons using equilateral triangles. According to The Oxford English Dictionary, a tessellation can best be defined as an arrangement or close fitting together of minute parts or distinct colors. Convex figures are figures that if given any two points in the polygon, the entire line segment between them does lie inside the polygon. The whole objective of this project was to construct polygons, triangular, pentagonal, and hexagonal figures, with equilateral triangles. The next step was to derive and prove a formula to create these figures. In addition, this project would also thoroughly explain how to find these figures within a bigger equilateral triangle. One shall then be able to compare any given number 'k' and figure out whether or not this number 'k' can be either two of the different figures. Through the data found in this project, a number 'k' was proven not to be in any two polygons or all three polygons. However, through the substitutions of different values of 'k' one was unable to completely conclude this answer to be no due to the fact that there may exist several open-end solutions. Acknowledgements: This project was funded by NFS-AMP & MGE Programs.

9:30 INTEGRAL KERNEL/FREQUENCY SHIFT ALGORITHMS FOR IMAGE DATA COMPRESSION

Joseph Kolibal [*] and Suming Fang, University of Southern Mississippi, Hattiesburg, MS 30406

The properties of a class of computational methods, which are suitable for the purpose of data approximation, are investigated for suitability in constructing lossy compression algorithms. The specific objectives are to carry forward preliminary research and to investigate several alternative approaches to improve the performance of the algorithms with regard to image compression. Significant gains can be made from cleverly and efficiently coupling spectral shift methods with convolution operators to achieve an efficient lossy image compression method suitable for use with image data. The approach utilizes probabilistic integral kernel methods to construct approximants which serves as the core of the compression algorithm.

9:45 Break

10:00 FIP: A PATTERN RECOGNITION SOFTWARE TOOL DEVELOPED USING MATLAB FOR THE CLASSIFICATION OF GAS CHROMATOGRAPHIC DATA

Abdullah Faruque [l*], Howard T. Mayfield [2], and Barry K. Lavine [3], (1.) Mississippi Valley State University, Itta Bena, MS 38941; (2.) Armstrong Laboratory, Tyndall Air Force Base, FL 32403; and (3.) Clarkson University, Potsdam, NY 13699

This paper describes the implementation of FIP (Fuel Identification Program), a pattern recognition software tool intended to type classify fuels presented as gas chromatographic profiles by using neural network and other statistical pattern recognition techniques. Various data preprocessing techniques necessary to support the pattern recognition techniques are also provided. Data visualization tools are also provided to permit visual assessment of the data patterns and their relationships. FIP software tool has been used successfully by the Fuel Identification Research Group at Armstrong Laboratory, USAF. The development of this software system takes advantage of the high performance computational and visualization routines of the MATLAB programming environment. Data analysis component of FIP includes: (1) principal component analysis, (2) fisher and variance weight calculations and (3) feature selection. Using MATLAB's graphics routines, 2-dimensional or 3-dimensional plots of the principal components can be displayed. Classification methods in FIP include both neural network and statistical pattern recognition techniques. Neural network methods include the back propagation neural network (BPN) and radial basis function (RBF) neural network. Statistical pattern recognition component of FIP includes linear discriminant analysis (LDA), quadratic discriminant analysis (QDA), regularized discriminant analysis (RDA), soft independent modeling of class analogy (SIMCA) and discriminant analysis with shrunken covariance (DASCO). FIP provides two ways to calculate classification error rate: (1) bootstrap error rate and (2) cross-validated error rate. The neural network and statistical pattern recognition techniques used in FIP can also be used in other pattern recognition problems with little modification.

10:15 MULTIVARIATE NONLINEAR TIME SERIES MODELING

Jane L. Harvill [*] and Bonnie K. Ray, Mississippi State University, Mississippi State, Mississippi 39762 and New Jersey Institute of Technology, Newark, New Jersey 07102

A multivariate extension of the univariate nonlinearity test of Tsay (1986) is presented. Simulation results show that the multivariate test is more powerful than its univariate counterpart, especially for series having nonlinear structure involving several components of the vector process and weakly or moderately cross-correlated process error terms. Next, exploratory methods for determining appropriate lagged variables in a vector nonlinear time series model are investigated. The first is a multivariate extension of the R statistic from Granger and Lin (1994), which is based on an estimate of the mutual information criterion. The second method uses Kendall's [tau] and partial [tau] statistics for lag determination. These methods provide nonlinear analogues of the autocorrelation and partial autocorrelation matrices for a vector time series. Simulation results indicate that the methods reliably identify appropriate lags. Finally, a brief discussion of work in progress model estimation techniques in the vect or nonlinear time series case follows. Some nonparametric methods which avoid the "curse of dimensionality" are suggested as possible solutions to this problem.

10:30 ON THE ROBUST CHARACTER OF CONTROL CHARTS FOR VARIABLES WHEN STANDARDS VARY RANDOMLY

Hari M. Sharma, East Mississippi Community College, Mayhew, MS

In the process control, the control charts are used as statistical techniques. While defining control limits for these charts, standards or product qualities are considered to be constant. In the present study, in view of constant environmental stresses and other factors over a long period of time, standards are treated as random variables which are represented by Prior Distributions and are updated by using experimental data in Baysian framework, to develop Posterior Distributions. OC curves (operating characteristic functions) have been used a rational means for analyzing robustness of the system.

10:45 HYPERSPECTRAL ALGORITHM DEVELOPMENT FOR WATER APPLICATIONS

David C. Hughes [*] and Ron Holyer, University of Southern Mississippi, Hattiesburg, MS 39406

This presentation describes principal component analysis (PCA) of hyperspectral data. Hyperspectral remote sensing systems sense energy in several hundred spectral bands in the visible and near-infrared portions of the electromagnetic spectrum. These high-resolution spectral image data facilitate numerous spectroscopic applications here on Earth. Inter alia, the data are used to identify materials, detect features, and quantify environmental parameters on the Earth's surface, or along the intervening atmospheric path. We have modeled radiative transfer in the waters of the Gulf of Mexico to produce a large database of spectral curves of remote sensing reflectance and water-leaving radiance. These data are subjected to PCA so as to characterize the "important" spectral bands of radiance information for water in the Gulf. The preliminary results indicate that data set dimensionality is reduced by a factor of ten when PCA is applied.

11:00 Divisional Business Meeting

THURSDAY AFTERNOON

Caribbean Room

1:30 MINOR TRACKING PROGRAM FOR COLLEGES

Vanessa Siegal [*] and Donald R. Schwartz, Millsaps College, Jackson, MS 39210

Most college students declare a major but very few students declare a minor. It is our theory that many students, if informed that they are close to achieving a minor, would decide to "go for it" since having a minor will usually enhance a student's overall future prospects. At Millsaps College, no minor is satisfied in exactly the same way as any other minor. Minors often have a set of required courses, as well as up to four other "groups" of courses (each with their own options) that must be taken. Our major challenge was to represent these various requirements for every minor offered. We have developed a Minor Tracking System for exactly this purpose. The project required that a database be designed to determine whether classes taken by a student fulfill (or come close to fulfilling) any of the minors offered by the College, and that a user interface be developed to summarize and present this information. As an additional advising feature, our system even lists students who are any given number of hours aw ay from a specific minor. Our presentation gives the details of the database design, as well as how we merged it with a Visual Basic interface that is efficient, professional, and easy to use.

1:45 A MULTIMODE XML-BASED EDITOR FOR SMIL AUTHORING

Lindsay M. Akers [*] and Andrew V. Royappa, Millsaps College, Jackson, MS 39210

Synchronized Multimedia Integration Language (SMIL) was introduced recently by the World Wide Web Consortium. SMIL is an Extensible Markup Language (XML) system that utilizes structured text to represent multimedia presentations in a form suitable for transmission over the World Wide Web. Several programs exist for constructing SMIL presentation files. The present research is to design and implement a SMIL editor with a novel combination of features. The editor allows the user to view the SMIL presentation in different ways. First, the editor can display the actual XML code of the presentation in a treelike format that closely mirrors the structured text representation. Users may directly edit XML elements and attributes. A second mode displays an XY-slice of the presentation at any point in time, giving the user a "What You See Is What You Get" (WYSIWYG) view. Finally, the editor can also display a timeline view. The user may edit the presentation graphically using standard user interface controls in each mode. For instance, the user may change the spatial relationships of objects in the WYSIWYG mode, and change their temporal relationships in the timeline mode. A prototype for the system is under construction. It is being developed as a Windows '95 application using the Delphi rapid application development system, employing object-oriented XML components to read, write and manipulate structured text trees.

2:00 ANALYSIS OF HOME RANGE DATA USING GENERALIZED ESTIMATING EQUATIONS

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

Many procedures for analyzing home range data implicitly assume independence despite the fact that most data is not statistically independent either spatially or temporally. The procedure introduced here attempts to allow for independence in the data through correlation parameters in the covariance matrix. The method relies on generalized estimating equations to estimate a utilization distribution that is an estimate of the probability of finding the animal at a particular location within a fixed region of interest. The procedure also allows for methods of introducing covariates into the estimation process so that factors such as habitat, ground cover and other biological patterns may be included as factors affecting the utilization distribution.

2:15 DETERMINATION OF INFLUENTIAL DOSE GROUPS

Dale Bowman and Gibson Johnston [*], University of Mississippi, University, MS 38677

In a typical bioassay, one objective is to estimate a dose response curve. The designs presently used are usually predetermined by government guidelines. Here, an alternative method is proposed based on the chosen form for the dose response curve and the determination of influential dose groups. Influence depends upon both the form of the curve and the number of animals in each dose group. Once influential dose groups have been determined, the design can be changed to shift the focus to specific interests. For example, the focus can be shifted from high doses to low doses, where human exposure typically occurs. The proposed method should provide better estimates for the NOEL and confidence limits for benchmark dose levels. This paper proposes a test for influential dose groups and illustrates this test on a specific data set.

2:30 Break

2:45 A COMPARISON OF METHODS USED TO TEACH PROBABILITY IN INTRODUCTORY STATISTICS

Karen D. Morgan [*] and Dale Bowman, University of Mississippi, University, MS 38677

Recently there has been much debate about the amount of probability which should be taught in an introductory statistics course and about the manner in which probability should be presented. Studies have shown that many students have intuitive beliefs about probability which often are self-contradictory and often contradict laws of probability. These intuitions, difficult and often impossible to correct, are based in large part upon a frequentist approach to computing probabilities. The challenge of this research is to use the students' intuitive understanding of frequentist computations to teach the basic concept of probability. In this way, it may be possible to alter some misconceptions and reinforce basic concepts of probability. A study was designed to compare a new approach to teaching probability using computer simulations with a more classic method using the laws of probability.

3:00 BAYESIAN BOOTSTRAP PROCEDURES FOR ESTIMATING RISK IN DEVELOPMENTAL TOXICITY EXPERIMENTS

Gwen Aldridge [*] and Dale Bowman, University of Mississippi, Oxford, MS 38655

A typical teratological study involves a control group and several dose groups of randomly assigned females who early in gestation or prior to mating are administered fixed doses of the toxic substance being tested. Prior to term, the dams are sacrificed and the uterine contents are examined to check for either malformation of fetuses, fetal death or other event of interest. The outcome of interest is considered to be binary. Since the litter sizes vary, in studies of this type the data occur in clusters having random cluster sizes. A developmental model which not only accounts for the intralitter correlation of the fetuses, but also the possible dose effects on the size of the litter is desired. The proposed model estimates the probability of an adverse effect at a given dose level as a weighted average, where each observed proportion in the sample is weighted according to the estimated likelihood of its occurrence. A Bayesian bootstrap method is incorporated in the computation of the estimated likelihoods. The advantages of the Bayesian bootstrap over classic estimation procedures and ordinary bootstrap methods include the ability to incorporate prior information into the analysis and the ability to simulate a posterior distribution. The proposed model gives good results particularly at the lower dose levels which is desirable since the lower levels typically correspond to the level of exposure in humans.

3:15 PROPORTIONS WITH A ZERO NUMERATOR: MAKING INFERENCES USING THE "RULE OF THREE"

Carolyn R. Boyle, Mississippi State University, Mississippi State, MS 39762-9825

If p is the probability that an event will occur, the binomial distribution gives the probability of k occurrences of the event in n independent trials. When p is small, it is likely that no events will be observed even if n is relatively large. This situation often arises in biomedical research where p, for example, is the prevalence of a rare disease or the rate of occurrence of an uncommon therapeutic side effect. The normal approximation to the binomial is not appropriate for calculating an upper confidence limit for p when the point estimate of p is zero, but an upper confidence limit can be obtained using either the binomial, the F, or the Poisson distributions. Alternatively, a simple empirical rule gives a close approximation to those methods and is easily calculated using mental arithmetic. The "Rule of Three" states that (0, 3/n) is an approximate 95% confidence interval for p 0/n. For example, if n = 30, an approximate 95% confidence interval for p is (0, 0.1). This paper will review the relations hip between the "Rule of Three" and the more exact methods, discuss the use of the rule as a tool for the statistical consultant, and give an example of the use of the rule to estimate the prevalence of bovine spongiform encephalopathy ("Mad Cow Disease") in the United States' beef supply.

3:30 Business Meeting of the Mississippi Chapter of the American Statistical Association 

FRIDAY MORNING

Pre-Assembly Area

9:00-11:00 MEET THE STATISTICIAN

Walter T. Brehm, Clinical Research Laboratory, 81st Medical Group, Keesler AFB, MS 39534

The importance of considering how data will be analyzed early in the planning of an investigation or experiment cannot be overemphasized. The distinguished statistician Sir R.A. Fisher said, "To call in the statistician once the experiment is done may be no more than asking him to perform a postmortem examination: he may be able to say what the experiment died of." Don't let this happen to you! Come to the Annual meeting of the Mississippi Academy of Sciences and MEET THE STATISTICAN. The members of the Division of Mathematics, Computer Science, and Statistics will be providing free, 20 minute consultations in the areas of experimental design, statistical design & analysis selection, and sample size determination. Some analyses may be possible with advanced arrangements. Contact the division chairman, Walt Brehm, 81st Medical Group, 301 Fisher St., Rm 1A132, Keesler AFB, MS 39534 or [e-mail] to arrange an appointment. Students are welcome and walk-ins may be accepted. It could be the most important 20 minutes of you whole project.