Past colloquia

Colloquium Schedule for Spring 2006

Date	Speaker	Topic
January 18	Dr. Selwyn Hollis	Nuts and Bolts of Nonlinear Optimization Abstract: In the latter half of the 20th century, advances in computing technology spurred numerous scientific and mathematical fields. Among them is the field of optimization, which in its broadest sense overlaps significantly with operations research, numerical analysis, the calculus of variations, and optimal control theory. However, the field known to today's applied mathematics community as optimization is essentially a subfield of numerical analysis that deals with algorithms for optimization (minimization or maximization) of functions, with emphasis on efficiency and applicability to large-scale problems, i.e., problems involving a large number of variables. While linear programming is a fairly common topic in a variety of settings, nonlinear optimization/programming is a relatively small discipline that seems oddly obscure within the broader mathematics community, even though multivariable calculus, linear algebra, and basic real analysis provide sufficient background for its study. In this talk, Dr. Hollis describes some of the fundamental problems and algorithms in nonlinear optimization and gives a brief outline of its history.
February 1	Tim Ellis	The Complete Dummy's Guide to teh Greatest Unsolved Problem in Mathematics Abstract: In 1859, Bernhard Riemann was appointed a corresponding member of the Berlin Academy, based on his 1851 doctoral dissertation and his 1857 work on abelian functions. In response to this honor, he submitted a paper entitled "Son the Number of Prime Numbers Less Than a Given Quantity". In this paper, he presented an educated guess (since known as the Riemann Hypothesis), which is arguably the greatest unsolved problem in all of mathematics. The purpose of this presentation is to explore the background of the Riemann Hypothesis, to shed some light on its meaning, to delve into the history of attempts to prove or disprove it, and to describe the current prognosis of a solution. This presentation will be fully understandable by anyone possessing a passing familiarity with complex numbers and Calculus I.
February 8	Jim Brawner	The Marriage Problem Abstract: As Valentine's Day approaches, you may be wondering about a strategy for finding the spouse of your dreams (Then again, you may consider advice on dating from a mathematician to be about as helpful as an ethics seminar conducted by Jack Abramoff). In this talk we will discuss the problem of finding an optimal strategy for pairing men and women into stable marriages based on their preferences for the members of the opposite sex. In addition to offering at least one genuine piece of advice for marriage seekers, we will discuss why this problem might be of particular interest to pre-med, pre-law, and economics majors.
February 15	Dr. Charles W. Champ GSU	Properties of Multivariate Control Charts with Estimated Parameters Abstract: In this presentation, Dr. Champ will discuss his and co-author L. Allison Jones-Farmer's research into Hotelling's T^2, multivariate exponentially weighted moving average (MEWMA), and several multivariate cumulative sum (MCUSUM) charts. Traditionally, these types of charts track varying attributes of a product or service over time. He will present two descriptions of each chart, with estimated parameters for monitoring the mean of a vector of quality measurements. For each chart, one description explains how the chart can be applied with estimated parameters in practice and the other description is useful for analyzing the run length performance of the chart. Run lengths are important in quality control because they offer information about the expected time until a false alarm (i.e. a stop-the-manufacturing-line signal that is erroneous). Dr. Champ demonstrates that, if the covariance matrix is Sin control, the run length distribution of most of these charts depends only on the distributional parameters through the size of the process shift in terms of statistical distance. Simulation is used to provide performance analyses and comparisons of these charts. Dr. Champ presents an example to illustrate the MCUSUM and MEWMA charts when parameters are estimated.
February 22	Amy Chambers University of Colorado at Boulder	*Certain Subalgebras of the Tensor Product of Graph C-algebras**
March 1	Ray Hashemi	A Signature-Based Predictive System for Liver Cancer Abstract: A hybrid predictive system is presented to improve the prediction of liver cancer caused by a group of chemical agents. The system employs both SOM net and Hopfield net. The SOM net performs the clustering of the training set and delivers a signature for each cluster. Hopfield net treats each signature as an exemplar made up of 2,717 X 2,717 digits and then learns the exemplars. Each record of the test set is also converted into a vector of 2,717 elements and is considered a corrupted signature. The Hopfield net tries to un-corrupt the test record through several iterations using its associative memory property and map it to one of the signatures and consequently to the prediction value associated with the mapped signature.
March 8	The Armstrong Putnam Exam Team	Reflections on the 2005 Putnam Exam Abstract: The Armstrong student team for the 2005 Putman Exam in Mathematics will present a synopsis of their experiences in taking this challenging national examination. Each of the three team members will discuss a solution for one of the problems on the examination.
March 22	Dr. Robert L. Taylor Clemson University	Fun and Opportunities in Probability and Statistics Abstract: Probability and statistics problems have intrigued and puzzled people for many years. Dr. Taylor will analyze some of these problems to determine logical solutions and to illustrate facetious approaches to solutions. He will present Monty Hall's "Let's Make a Deal" puzzler as one example of illogical and logical solutions. In addition, Dr. Taylor will discuss career opportunities for students in the mathematical sciences, especially probability and statistics.
April 5 Cancelled	Elijah Allen	Prime Constellations Abstract: Consider a k-tuple of prime numbers in ascending order. Such a k-tuple is considered inadmissible if there are no other k-tuples of prime numbers that match its intervals between successive primes exactly. Thus, admissible k-tuples of primes establish a pattern that is repeatable with other k-tuples of primes. An admissible k-tuple with the smallest possible difference between the last and the first terms is defined to be a prime constellation with k terms. The prime k-tuple conjecture states that every admissible pattern for a prime constellation occurs infinitely often. In this talk, Elijah Allen will discuss his research into this still-open question and his results so far. Note: This talk has been cancelled. Colloquia will resume April 12.
April 12	Elijah Allen	Prime Constellations Abstract: Consider a k-tuple of prime numbers in ascending order. Such a k-tuple is considered inadmissible if there are no other k-tuples of prime numbers that match its intervals between successive primes exactly. Thus, admissible k-tuples of primes establish a pattern that is repeatable with other k-tuples of primes. An admissible k-tuple with the smallest possible difference between the last and the first terms is defined to be a prime constellation with k terms. The prime k-tuple conjecture states that every admissible pattern for a prime constellation occurs infinitely often. In this talk, Elijah Allen will discuss his research into this still-open question and his results so far.

Colloquium Schedule for Fall 2005

Date	Speaker	Topic
August 31	Dr. Sean Eastman	The Irrationality of Pi Abstract: It is well known that the number Pi is irrational, and there are a number of websites devoted to studying the digits in the decimal expansion. But, whereas proofs for other well known irrational numbers (such as sqrt(2) and e) are relatively straightforward, proving that Pi is irrational is more difficult. In this talk, Dr. Eastman will present a proof of the irrationality of Pi due to Ivan Niven in 1947. The proof relies only on the calculus of a single variable, so this talk is appropriate for students who have taken one semester of calculus.
September 6	Jim Brawner and Tim McMillan	Sudoku Puzzles Abstract: Sudoku is a number puzzle game. In the past year, Sudoku~Rs popularity has exploded internationally. In this colloquium we will introduce the game and its history. Sudoku suggests many interesting mathematical and computational problems. Some of these problems, and what is known about their solutions, will be presented.
September 14	Paul Hadavas	Graph Theory Abstract: In this talk, three graph theoretic problems will be explored. The first will be the classic coloring problem. Then, the question of saving a bus driver's sanity will be put in a graph framework with appropriate weights given to the vertices and edges of the network (the bus driver's route). Finally, the problem of optimizing over a graph where each edge has two attributes of concern (time & cost or time & safety) will be introduced.
September 21	Sungkon Chang	The Magic of Elliptic Curves, II Abstract: This talk is a sequel of Dr. Brawner's colloquium talk, the magic of elliptic curves, (given two years ago); no prerequisites from his talk are required but some concepts in abstract algebra such as fields and Galois groups. Class Field Theory is a highlight of algebraic number theory, which explicitly describes the Galois group of the maximal abelian extension of a number field. Nevertheless, actually generating abelian field extensions is a difficult problem. In number theory, quadratic imaginary fields are an active research subject, and generating the abelian field extensions of these number fields is an interest to many number theorists. While this problem comes from a purely algebraic setup, an answer comes from a seemingly unrelated geometric context: there is an elliptic curve such that some special points on it generate the abelian field extensions. In this talk, introduced are Class Field Theory, some basics of elliptic curves, and the connection between an elliptic curve and the abelian extensions of a quadratic imaginary field.
October 5	Dr. Lewis VanBrackle Faculty Fellow Center for Excellence in Teaching and Learning Kennesaw State University	An Alternative to the Least Squares Estimator in Statistics Abstract: The slope mean is defined as the tangent of the mean of the angles between the x-axis and the lines from the origin through statistical data points. Examining the statistical properties of the slope mean is an excellent exercise for undergraduate mathematics and statistics majors. In the process of evaluating the statistical properties of the slope mean and comparing them to the properties of the ordinary least squares estimator, students can apply techniques they have learned in a variety of mathematics and statistics courses. In this presentation, Dr. VanBrackle will show how the Fundamental Theorem of Calculus, the Central Limit Theorem, the Gauss-Markov Theorem, Taylor's series approximations, and calculation of probabilities by numerical integration and simulation can all be applied in deriving the statistical properties of the slope mean.
October 19	Lorrie Hoffman and Jaree Hudson	Famous Women Mathematicians Abstract: Lorrie Hoffman and Jaree Hudson take you on a journey from the work of one 18th century mathematician, Sophie Germain, to the research of a present-day mathematician, Nan Laird. This talk discusses the link between these women, their findings, and their fame. The presentation will address mathematical topics ranging from prime numbers to missing numbers. In addition, the talk will include information on research inquiry tools, including those used to trace academic genealogy and to track journal article citations.
November 2	Dr. Joe Fu Chair of Mathematics at University of Georgia	1. The Convex - Convex Valuations 2. The Complex - The Graduate School Admission Process Abstract: A convex valuation is a finitely additive measure on the family of all compact convex subsets of a euclidean space. Phi is a valuation if it assigns a number Phi(A) to every compact convex set in such a way that if A and B are convex sets, and their union happens to also be convex, then Phi(A union B) = Phi(A) + Phi(B) - Phi(A intersection B). Three common and foundational examples of convex variations are volume, perimeter, and the constant valuation Chi(A) = 1for all convex sets A. H. Hadwiger's classical (1957) theorem states that these three valuations, and a few others very much like them, span the vector space of all valuations that are continuous in a certain inevitable sense, and invariant under the euclidean group (i.e. the numerical value assigned by the valuation to a convex body [IMAGE] is the same as that assigned to any rotation or translation of A). Over the past five years or so, mathematicians have produced some amazing and beautiful results concerning the structures on the space of all convex valuations. Dr. Fu will discuss the new understanding that these results have produced, along with some of the new puzzles they have posed. Following his talk on convex valuations, Dr. Fu will provide helpful hints and insights into the graduate school admission process and will conduct a Q&A session on this important topic. If you are thinking of applying to graduate school anytime soon, be sure to attend this session!
November 9	Jatin Patel	Teaching and learning sorting/searching algorithms by animation Abstract: The primary goals of the presentation are two-fold. The first one is to provide a basic knowledge about three sorting algorithms (Bubble Sort, Insertion Sort, and Selection Sort) and two searching algorithms (Binary Search and Linear Search). The second goal is to provide a visual tool for beginning computer science students to understand these algorithms and for teachers to use it as a teaching tool in supplement to the textbooks. The application will be easily available and will be in Java hence will be platform-independent. Thus students can use it anytime with their own inputted values and thus be able to understand the concept of these algorithms much easily.

Colloquium Schedule for Spring 2005

Date	Speaker	Topic
January 19	Cynthia Y. Young	Mathematical Modeling of Atmospheric Effects on Laser Beams Abstract: Scientists and engineers are interested in using optical (laser) systems as opposed to conventional radio frequency systems. The two main types of systems that are of special interest are laser communications and laser radar systems. The advantages of laser communications systems is that they enable 1000 times higher data rates and require less space and power which makes them ideal for satellite systems. The advantages of laser radar systems is that they provide secure channels for military target identification applications. Of course, with advantages also come disadvantages. The disadvantage is that the Earth's atmosphere has deleterious effects on optical waves that it does not have on radio waves. Star twinkle is an example of intensity (or brightness) fluctuations which correspond to a fade in a communication system. In order to take advantage of laser systems we must first have a solid understanding of the magnitude of the disadvantages such as amplitude and phase fluctuations, power loss, error rates, etc. The Earth's atmospheric effects are random and therefore statistical quantities are investigated. In this talk, mathematical models of atmospheric effects on laser beams and their corresponding engineering consequences will be discussed.
January 26	Ed Wheeler	Weighted Voting Systems Abstract: Following a series of weighty talks on topics such as The Geometry of Gaussian Elimination and the Rook's Pivoting Strategy and Mathematical Modeling of Atmospheric Effects on Laser Beams, Wheeler will deliver a real creampuff showing how a little arithmetic can shed light on a potentially important issue related to political processes. Though the mathematics will be light, Wheeler might manage to say a word or so at the end indicating some of the important contributions that persons trained in mathematics can make in lots of different work environments. Comments might be useful to students currently undecided about whether a major in mathematics might contribute to their career goals.
February 2	Jim Brown University of Michigan	L-functions and Arithmetic Abstract: A large number of very beautiful theorems in number theory arise from the study of L-functions, in particular, their special values. It is a general philosophy that one can get arithmetic information about a "motivic" object by studying the L-function that is associated to it. I will illustrate this concept through several examples. We will start with the basic Riemann zeta function and work our way to elliptic curves and modular forms. I will assume a basic knowledge of complex analysis (i.e., what it means to be holomorphic) and some basic abstract algebra (i.e., what a field extension is) and work from there to develop the theory.
February 9	Farrah Jackson North Caroline State University	P-adic Symmetric Spaces Abstract: This presentation we will introduce p-adic Symmetric Spaces, which are a generalization of the real symmetric spaces. Before we discuss these we will first introduce the concept of a p-adic absolute value and a metric. Then we will discuss the construction of the p-adic numbers and how arithmetic is performed in the p-adic field. Next we briefly describe the connection between involutions and symmetric spaces. Finally, we will discuss the classification of involutions and the corresponding symmetric spaces of SL(2,k) for various fields k.
February 16	Hong Zhang	Lost treasures of Mathematics that every Computer Scientist should know Abstract: Pure mathematical discoveries often take a long time to find any practical applications. The development of computer science and technology has revived many such ancient mathematical beauties. Examples such as Boolean algebra in digital design and entropy in information theory are well known. In this talk, I would like to point out several other old and simple mathematics problems, including Discrete Green's theorem, Chinese remainder theorem, quaternion and others, and their new lives in computer science.
February 23	Sean Eastman Colorado State University	Linearization Error for Computational Error Estimates, and the Perturbed Power Method Abstract: A-posteriori error estimates for nonlinear equations based on residuals and variational analysis are subject to an error of linearization. It is not well understood what effect the linearization has on the estimate, and in this talk I will present some ideas for ways in which to bound the effect of linearization. The primary computational tool is very closely related to the Power Method for finding the dominant eigenvalue and eigenvector of a square matrix.
March 23	Ram N. Mohapatra University of Central Florida	Power and Frontiers of Mathematics Abstract: In this lecture, we shall consider how mathematics is used to model physical systems. We shall also take a brief tour of some of the emerging areas of mathematics viz. Fractals, Wavelets and Neural Nets. Some application of each of these will also be mentioned. As much as possible the talk will be self contained.
March 30	Wayne Johnson & Priya Thamburaj	Vibrations: a Couple of Applications Abstract: The principles of vibration analysis can be applied to numerous situations based on a simple spring-mass-damper-system model. First, we present the underlying principles of vibrations associated with rotating tire imbalances and discuss how they can be eliminated. The system will be modeled as a single degree of freedom system subject to harmonic force excitation. Next, we look at a large-scale application ~V the response of structures to earthquakes. This ground motion during an earthquake is measured and represented by a set of accelerations, which serve as the input for vibration analysis of the structure. This talk will present the response of simple structures to such excitations. The basic concepts behind design considerations of such structures will also be discussed.
April 5 1:30-2:30	Dr. Terrence Fries Coastal Carolina University	Fuzzy Genetic Motion Planning for an Autonomous Mobile Robot Abstract: Optimal motion planning is critical for the successful operation of an autonomous mobile robot. Many approaches have been proposed using either fuzzy logic or genetic algorithms (GAs). Most approaches offer only path planning or trajectory planning, but not both. The GA-based approach presented in this paper provides both path and trajectory planning, and has the advantage of allowing terrain conditions to be included in determining the optimal path. The terrain conditions are modeled using fuzzy linguistic variables to allow for the imprecision and uncertainty of the terrain data. Although a number of methods have been proposed using GAs, few are appropriate for a dynamic environment or provide response in real-time. The method proposed in this paper is robust, allowing the robot to adapt to dynamic conditions in the environment. Note: This talk will take place in SC-1505A
April 8, 2005 2:30-3:30	Dr. Venu Dasigi	Information Retrieval and Text Mining: Applications Abstract: This colloquium will summarize the presenter's work on some aspects of text information retrieval and classification, and some applications of the techniques. Some of the issues, such as the number and quality of features will be introduced, and our approach to address them will be described, along with a brief evaluation of the information fusion techniques used. The presenter's work with students in applying information retrieval techniques to program selection through an analysis of closed captions in video transmissions will also be summarized. A brief exposition to the joint work with some researchers at Georgia Tech and Emory University in mining biomedical literature for identifying relationships among genes will also be made. Note: This talk will take place in SC-1503A
April 13, 2005 1:00-2:00	Dr. John Talburt	Aspect-Oriented Information Management Abstract: Aspect-Oriented Information Management (AOIM) is an object view of data in which the "data objects" encapsulate a uniform method for handling a common set of data characteristics or concerns (the "aspects"). It is the data analog of Aspect-Oriented Programming (AOP). Discussion to include: A method for encapsulating aspects using XML wrappers Application of AOIM to ETL Process AutomationApplication of AOIM to file management Note: This talk will take place in SC-129
April 13	Bud Sanders	On the Axiom of Choice Abstract: In the elementary theory of sets, one happens upon the inadequacy of the usual axioms for assembling sets that allow for certain constructions involving infinite sets. This inadequacy has led to an additional axiom, labeled the Axiom of Choice. Now, while axioms are statements that are meant to be accepted by and large without qualms, the innocuous-seeming Choice Axiom leads to deeper and more perplexing mathematical results. Indeed, when introduced, these results caused much discussion in the mathematical world and created a divide amongst mathematicians as to the role and of and the acceptance of the Choice Axiom. Mathematicians today, in general, accept the Axiom of Choice without reservation and invoke its power without hesitation. I will discuss this axiom and some of its consequences in this forum.
April 20	Jonathan Kish	Cyclotomic Fields and Reciprocity Abstract:
April 25 11 am	Venu Dasigi	Information Retrieval and Text Mining: Applications Abstract: This colloquium will summarize the presenter's work on some aspects of text information retrieval and classification, and some applications of the techniques. Some of the issues, such as the number and quality of features will be introduced, and our approach to address them will be described, along with a brief evaluation of the information fusion techniques used. The presenter's work with students in applying information retrieval techniques to program selection through an analysis of closed captions in video transmissions will also be summarized. A brief exposition to the joint work with some researchers at Georgia Tech and Emory University in mining biomedical literature for identifying relationships among genes will also be made. Note: This talk will take place in SC-1503A

Colloquium Schedule for Fall 2004

Date	Speaker	Topic
August 25	Dr. Lorrie Hoffman	Mathematical Modeling and Its Role in Computer Performance Analysis Abstract: Variously trained mathematicians, computer scientists, engineers, and statisticians are employed by a large cross-section of industry to maintain, enhance and create computer networks that are performance-optimized. Speedy response times are necessary on United Airlines travel reservation systems. Quick data retrieval is mandatory on mini-computers built by companies like AT&T. The Army issues RFPs (request for proposals) to fund researchers who can find mechanisms for synchronizing performance-mismatched simulators. Mathematical modeling is one tool used to study problems in this area of Computer Performance Analysis. Both analytical and simulation techniques are used to understand the behavior of these business environments. Many of the analytical solutions are derived by using knowledge from the area of Stochastic Processes and in particular the sub-field referred to as Markov Chains and Queueing. These academic concentrations provide powerful mechanisms to investigate industrial problems of this type. We will examine the contribution of the Chapman-Kolmogorov equation and apply the results to producing a cost effective selection of a disk subsystem for a computing network
September 15	Dr. Jim Brawner	Color My World Abstract: How many colors does it take to color a map? It was conjectured over 150 years ago that four colors suffice (for a sufficiently nice map) and the problem has attracted the attention of amateurs as well as professional mathematicians ever since. An incorrect proof was published in 1879 and went unchallenged for the next ten years. In 1978 Appel and Haken published a proof that was somewhat controversial because it used a computer to check a large (but finite) number of special cases. In this talk we will give a brief history of the problem and discuss related colorings of all sorts of objects: maps, graphs, polyhedra, doughnuts, and more.
September 22	Dr. Mark Burge	Pervasive Computing Abstract: How do we prepare our students today to develop applications for tomorrow's most widely available computing platforms? In fact, pervasive computing devices like cell phones and personal digital assistants (PDAs) are now more numerous then PCs. Cheap and ubiquitous, these compact mobile devices are the computing platforms of tomorrow. During the last four years, with the support of IBM, Motorola, and the NSF, we have started to address the unique software engineering challenges (e.g., small memory models, cross-platform development, and wireless networking) of these platforms in our curriculum. Topics to include: secure computing using Java Card smartcards, wireless Personal Area Networks (PANs) using Bluetooth, and advanced J2ME application development using real hardware.
October 13	Dr. Paulius Micikevicius	Protein Structure Prediction from Inter-atomic Distances Abstract: Determining the three-dimensional structure of a protein molecule (or any other large biomolecule) is an extremely important and computationally challenging problem. One of the most widely used approaches relies on NMR (nuclear magnetic resonance) spectroscopy, through which a small subset of the inter-atomic distances in an n-atom- molecule is determined. Furthermore, these distance measurements are not exact, but each lies within an upper and a lower bound. In this talk we will review the computational problems and approximate solutions employed to solve them when distance-bounds are used to predict atom coordinates in the 3D Euclidean space.
October 27	Dr. Ray Greenlaw	The Fastest Hike: A Lesson in Leadership Abstract: The Pacific Crest Trail (PCT) is a 2,659-mile-long national scenic trail that winds over mountains from the Mexican border at Campo to the Canadian border near Manning Park. Completing such a hike tests and develops one's leadership skills. We examine perspective, creative thinking, problem solving, and other leadership issues in the this context. Schedule building equipment selection, logistics, and stories from the trail will be presented.
November 3	Dr. Mark Budden	A Brief History of Reciprocity Abstract: Euler and Legendre were the first to consider the problem of determining when an integer is a square modulo an odd prime. Although Legendre gave an explicit description of what we now refer to as the Law of Quadratic Reciprocity, Gauss was the first to provide a complete proof. During his lifetime, he provided eight different proofs of the law and stated several generalizations of it. The development of algebraic number theory can be traced through the attempts of mathematicians to provide an all-encompassing generalization of the Law of Quadratic Reciprocity. Among the mathematicians whose names have been attached to Reciprocity laws since Gauss are Kummer, Eisenstein, Hilbert, and Artin. In this talk, we will discuss the criteria for determining what can be classified as a Reciprocity law and look at some of the developments in Reciprocity since the time of Gauss.
November 10	Dr. Andi Kivinukk	Fast Computation of Pi Abstract: In the nineteenth century, Karl Friedrich Gauss developed an elementary iterative technique for computing pi. This method influenced many new and modern methods which can be shown briefly.
November 17	Dr. George Poole	The Geometry of Gaussian Elimination and the Rook's Pivoting Strategy Abstract: A geometric analysis of Gaussian elimination is presented to better understand several difficulties encountered when this algorithm is applied in a finite-precision environment (computers). Based on this geometric analysis, a better understanding of Gaussian elimination (GE) is achieved which leads to a better understanding of the subject of scaling. These new insights also lead to a new pivoting strategy, Rook^Òs Pivoting (RP), which encourages stability in the back-substitution phase of GE while controlling the growth of round-off error during the sweep-out. In fact, Foster has already shown that RP, as with Complete Pivoting, cannot have exponential growth error. Empirical evidence will be presented to show that RP produces computed solutions with consistently greater accuracy than Partial Pivoting, but with comparable costs. That is, Rook's Pivoting is, on average, more accurate than Partial Pivoting, and the cost of implementing Rook's Pivoting in a scalar or serial environment is only about three times the cost of Partial Pivoting.

Colloquium Schedule for Spring 2004

Date	Speaker	Topic
January 28	Bud Sanders	Iterated Function Systems: A Geometric Introduction Abstract: An Iterated Function System (IFS) consists of a finite number of contraction mappings on a complete metric space. An elegant and well-understood fact about IFSs is that that there is a unique compact set associated with a given IFS; it's called the attractor of the IFS. The speaker will provide an overview of the mathematical theory of IFSs including their utility in image compression as well as new thoughts on their use in image recognition problems. Open questions regarding the mathematical nature of such systems will also be addressed.
February 4	Mark Budden	P-ADIC FIELDS AND THEIR RISE IN NUMBER THEORY Abstract: The p-adic numbers were invented/discovered by Kurt Hensel in the early 1900s. His idea was to introduce into number theory the method of power series expansion. We will take a look at the construction of a p-adic field Qp, where p is a fixed prime number, and define the p-adic absolute value. With respect to such an absolute value, Qp can be thought of as a completion of the rational numbers (similar to the way in which one completes the rational numbers to obtain the real numbers). Additionally, the rational numbers are a subset of Qp for every prime p. A brief survey will be given on the properties of p-adic fields and their importance in number theory. Note: the mathematical notation in the abstract was modified to use ASCII characters only. Namely, Qp stands for Q subscript p.
February 11	Paulius Micikevicius	An interactive framework for rendering forest scenes Abstract: Interactive rendering of a forest containing a large number of unique trees and other vegetation is a challenging and important problem in computer graphics and visual simulation. While methods for rendering near photo-realistic vegetation scenes have been described in the literature, they require tens of minutes or even hours of computation. In order to support interactive forest walk-throughs, we implement a method for reducing the level of detail (LOD) for a given tree, as well as a runtime framework for choosing the appropriate LOD based on a combination of visibility and projected size metrics. Live demos will be shown to illustrate the concepts.
February 25	Dr. Cathy Meadows Naval Research Laboratory, Washington D.C.	Formal Methods in Cryptographic Protocol Analysis Abstract: A cryptographic protocol is meant to provide secure services in an insecure network. But if the protocol is not designed correctly, it may fail to achieve these goals. A hostile intruder may be able to subvert the protocol by feeding false messages to honest users of the system. If the protocol fails to identify this behavior correctly, then the intruder's action may result in some security failure such as key compromise or false authentication. Such security flaws in a protocol can be subtle and hard to find. A number of examples exist in the literature of flaws that were not found for some time in protocols that had received extensive scrutiny. Thus, analysis of cryptographic protocols seems particularly suited to the application of formal methods, and a growing body of research exists in that area. In this talk we give a survey of of the use of formal methods in the analysis of cryptographic protocols. We outline some of the major threads of research in this area, and also document some emerging trends.
March 3	Gregory T. Knofczynski University of Northern Colorado	Minimum Sample Size Issues Using Kaiser-Guttman Rule For Factor Extraction in Exploratory Factor Analysis Abstract: This study helped establish guidelines for determining minimum sample sizes in exploratory factor analysis by focusing on the sample sizes needed to determine the correct number of factors when applying the eigenvalue-greater-than-one criterion, known as the Kaiser-Guttman (K-G) rule. The goal was to compare the results of this study with the results of a study completed by T. L. Ke (2001). The study by Ke established minimum sample sizes needed to produce the correct factors in exploratory factor analysis when the correct number of factors was known. Another objective of this research was to investigate the relationships between minimum sample size, number of factors, level of communality, and average number of variables per factor, when utilizing the K-G rule. This study consisted of a Monte Carlo simulation that examined 180 different population scenarios involving different numbers of factors, variables per factor ratios, and levels of communality. For each scenario, 100 population correlation matrices were created. For each population correlation matrix, 100 sample correlation matrices were created and examined to determine if the Kaiser-Guttman rule correctly determined the number of factors at least 95% of the time. For a majority of the scenarios examined, the minimum sample sizes suggested by Ke were higher than the sample sizes obtained in this study. As a result, for most scenarios examined, a researcher using Ke's sample sizes will confidently obtain not only the correct factors, but also the correct number of factors. Generally, the minimum sample size needed to determine the correct number of factors, using the K-G rule, increases when the number of factors increases, when the variables per factor ratio increases, and when the level of communality decreases. Almost 95% of the variation in these minimum sample sizes can be accounted for by the variation in the number of factors, variables per factor ratio, and the level of communality. Additionally, the K-G rule was shown to be unreliable for certain population scenarios, even with a sample size of 5,000.
March 10	Dr. Selwynn Hollis	A Tour of Calculus with Graphics and Animations Abstract: Using Mathematica-generated graphics and animations, we will demonstrate/illustrate a variety of concepts from calculus, ranging from limits to vector fields.
March 31	Michael Ariotti Duc Huynh Min-Jung "Jenny" Seo Brent Watson	The William Lowell Putnam Mathematical Competition Abstract: The William Lowell Putnam Mathematical Competition is an annual contest for college students established in 1938 in memory of its namesake. Cash prizes for the top five teams in recent years ranged from $25,000 to $5,000. Recent cash prizes for the top five individuals have been $2,500 each. The Elizabeth Lowell Putnam Prize was established in 1992 to be "awarded periodically to a woman whose performance on the Competition has been deemed particularly meritorious". Recent winners of the Elizabeth Lowell Putnam prize have received $1,000. Over the years many of the winners of the Putnam competition have become distinguished mathematicians. A number of them have received the Fields Medal and several have won the Nobel Prize in Physics. Reports by recent AASU Putnam exam takers will be given.
April 7	Cassandra Paff	IT Senior Project: Dynamic Web Site Design Abstract: This talk will present NorhtCorp Accountants^Ò web site and discuss its implementation. NorthCorp Accountants is a small-to-medium sized accounting firm located in Port Macquarie, Australia. As my Senior Project in the Bachelor of Information Technology program, I have developed a dynamic web site for marketing and information purposes that both clients and employees will benefit from. The Web site was completed using Macromedia Dreamweaver MX 2004, Microsoft Visual Studio.NET (using VB.NET as the code behind the Web pages), and Microsoft SQL Server 2000 as the backend database. I will describe the two main dynamic features of the Web site: an Employee Portal with file upload and download functionality, and a Football Tipping competition section.
April 14	Dr. Glenn Ray	The Role of UML State Machines in Rigorous Object-Oriented Modeling Abstract: The Unified Modeling Language (UML) is the adopted standard for visualizing OO systems. Although it offers a useful suite of diagrams, it lacks a formal foundation. As a result, UML models are not suitable for rigorous analysis. Furthermore, attempts to develop an executable UML (models that can be compiled into a programming language) require, at a minimum, the formal specification of a UML subset (i.e., kernel). Among UML 2.0 diagrams, this study identifies Protocol State Machines (PSM) as a promising candidate for the kernel. A PSM specifies an object lifecycle in terms of transitions between states. Transitions are fired by the invocation of an allowed operation. Ambiguities in PSMs are identified and semantic clarifications are proposed. PSMs are extended (XPSM) to include a token that marks the object^Òs current state, enabling visual simulation of systems. The XPSM is formally specified and some examples show their use in OO modeling.
April 21	Dr. Dale Kilhefner	Much Ado About Nothing: The History of Zero Abstract: Today we take the number zero for granted, but much of mathematics and civilization developed without a zero. In this talk we will look at theories on where, when, and how the concept of zero began, what effect it had on mathematics, and some of the difficulties it still causes.

Colloquium Schedule for Fall 2003

Date	Speaker	Topic
September 10	Paulius Micikevicius	General Computation on Commodity Graphics Hardware Abstract: Commodity graphics cards, intended for accelerating computer games, have recently surpassed modern CPUs in computation power and complexity. Programmability, parallelism, and IEEE-standard floating point arithmetic make these cards an attractive platform for general computation, not just computer graphics. However, certain hardware limitations pose interesting problems for algorithm implementation. This talk will give a high-level overview of the current graphics hardware architecture and will discuss in detail the implementation of Warshall-Floyd algorithm for the all-pairs shortest paths problem in graph theory. Additional problems, amenable to graphics hardware, will be mentioned.
September 17	Selwyn Hollis	Reaction-Diffusion Models of the Formation of Animal Pigmentation Patterns Abstract: In a seminal 1952 paper, The Chemical Basis of Morphogenesis, Alan Turing theorized that, under certain conditions, chemicals can diffuse and react in such a way as to produce spatially heterogeneous patterns of chemical concentration. Models of reacting and diffusing chemicals lead to systems of parabolic partial differential equations known as reaction-diffusion systems. In the years since Turing's work, certain reaction-diffusion models have been proposed as models for the formation of pigmentation patterns in animals. In this talk we will describe the basic mechanisms involved and show numerous computer simulations of pattern formation.
September 24	Ray Hashemi	Data Mining: An Overview Abstract: A broad range of disciplines, from science and medicine to sports and business, generate exponentially expanding amount of data that are offered to people through various means including the World Wide Web. People cannot absorb or use such enormous amount of data unless the data is offered to them in a consolidated form suitable to their particular needs. Data Mining is a multi-disciplinary field of study that dedicates itself to automatic analysis of huge volumes of data for the purpose of discovering knowledge, finding trends and exceptions, summarizing, and categorizing of data.
October 1 & 8	Cancelled	Cancelled Due to time conflicts with university events, there will be no CS/Math colloquia October 1, and October 8.
October 15	Mark Burge	Video Games: Old School and New Wave Abstract: The first talk in this two part series promises to be a real adventure. In this week's talk we will discover all the secrets of the very first action-adventure video game. If we survive the quest then next week we will visit CarrionCity and delve into Unreal Tournament, arguably the most advanced realtime 3D action game engine ever. Playing Unreal requires great reflexes, big guns, and tremendous computing resources. So come find out how the earliest games ran in realtime on 1.2 MegaHertz processors with only 4096 bytes (4K) available for the game code and 128 bytes for program variables. Next week's talk will be hosted by the development team of CarrionCity.com led by Armstrong CS grad student Ruslan Hristov.
October 22	Ruslan Hristov	Welcome To Carrion City ROOM CHANGE TO UH156 (this week only) Abstract: Last week you saw some of the challenging problems and their solutions in the development of the very first action-adventure video game. Today, game development has become an even more challenging and demanding job. New games have gone a long way with more intelligence, extensive graphics, and complex game play. It takes 5-10 years for a team of 30 people to develop a cutting edge game like Half-Life II. However, time, technology, and staff are just a few components that not every small development company can afford. That is why more and more computer games are designed to be easily modified. Many companies buy game technology, and base their products on already developed game engines, thus creating a new product. A successful example is Unreal Tournament, a 3D first person shooting game, similar to Doom and Quake. The game's originality comes from its extensively complex "game engine". Its object oriented design and simple scripting language (UnrealScript) allow for easy modification, which creates many opportunities not only for large game development companies, but also for small game developers. In this coming talk, we will look at the Unreal engine and especially UnrealScript, discuss its features and capabilities, and see how it can be used to create a total conversion -- a new game, called Carrion City. Following is a quote from the Carrion City Web site that gives an introduction to the Carrion City game [www.carrioncity.com]. Carrion City clings to the atmosphere like ashen smoke. The town is an evil frame, hanging in mockery of another time. Sickening heat, like the fumes of burst entrails fills the air. It's almost as if the town itself were issuing forth from the charred remains of an ancient fiery giant, it's carcass flung from hell's crevasse. Six figures can be seen in the sweltering heat. They are like mirages of men, flickering through the streets with reckless determination etched on their faces. A faint whisper can be heard in Carrion City. A single thought murmured on the six fighter's cracked lips as they hunt each other. The words fall, muted by the stagnant air. Lost in the roar of gunfire, they bounce in a jumble of hot shells that are kicked into the dust. "I must get out of town at all costs."
October 29	Jim Brawner	The Magic of Elliptic Curves Abstract: One of the most elegant topics in algebraic geometry, the theory of elliptic curves brings together ideas from such disparate branches of mathematics as abstract algebra, complex analysis, number theory, and topology. An elliptic curve is not an ellipse (its name arises from efforts to calculate the arc length of an ellipse), but a geometric object equipped in a natural way with the algebraic structure of a group. Elliptic curves are used in algorithms for factoring large integers, and played a key role in the work of A. Wiles and others in proving Fermat's Last Theorem. In this talk we will explore some of the highlights of these fascinating curves.
November 12	Larry Davis	Conformal Tracking in Virtual Environments Abstract: What do the movies Minority Report, The Matrix, Star Wars, Die Another Day, and Mission Impossible 2 have in common, besides huge budgets, special effects, and stunt doubles? The movies all utilize or portray various aspects of virtual environments. A virtual environment is a set of surroundings that appears to exist to a user through sensory stimuli provided by a computer. Subsets of virtual environment systems include Virtual Reality, where the environment presented to the user is completely computer-generated (e.g., The Matrix, Die Another Day, Mission Impossible 2), and Augmented Reality, which enhances the user's perception of the real world with additional computer-generated data (e.g., Minority Report, Star Wars). A necessity for virtual environments is accurate and precise knowledge of the location of the user and/or objects in the environment, which is obtained by tracking. Objects may be tracked in a variety of ways, one of which is placing markers upon the object(s) of interest. This collection of markers on an object is called a tracking probe. When tracking objects with markers, we find that the accuracy and precision of tracking are linked to the characteristics of the tracking probe. The number of markers, how the markers are arranged, and the accuracy with which the markers can be detected are all constraints within the process of tracking probe design. We must also account for the possibility that the markers may move relative to each other, implying a non-rigid tracked object. In this talk, we will examine steps toward formalizing a framework for dynamic conformal tracking in virtual environments. The framework includes algorithms for predicting tracking probe performance, optimization methods for probe design, and optimization methods for tracking in the case of semi-deformable objects.
November 19	Chris Pretz	Minimum sample size recommendations for a two-group discriminant analysis Abstract: The goal of this study was to provide minimum sample size recommendations for performing a two-group discriminant analysis under a variety of conditions. Sample size recommendations were determined by conducting a series of Monte Carlo simulations. For each simulation, data were generated from two multivariate normal distributions and an estimate of the OER was calculated. This process was repeated 5000 times resulting in the production of 5000 different estimates of the OER. For each sample size considered, a sample size was determined to be the minimum necessary sample size when 95% of the estimates fell within a specified range of the OER. This range was determined by a tolerance level. Three tolerance levels were used in this study; .02, .03, and .05. It was discovered that sample size is a function of the optimum error rate (OER), also known as the total probability of misclassification. Based upon the relationship between sample size and OER, three conclusions regarding sample size were drawn from the data: (1) as the value of the OER increases the sample size increases (2) as the value of k (the number of variates) increases the sample size increases (3) and as the tolerance level increases the sample size decreases. Sample size recommendations for this study are presented based upon the value of the OER, the number of variates, where k = 2, 3, 5, and 8, and each tolerance level. Findings of this study will enable researchers to use appropriate sample sizes, thereby ensuring resources are not wasted by taking a sample that is larger than necessary, or, that inaccurate results are obtained by taking a sample that is too small.
December 3	Senior Projects	Cancelled No colloquia until next semester.

Colloquium Schedule for Spring 2003

Date	Speaker	Topic
January 22	Jarrett Walsh	Checking for Substructures in Graphs of Bounded Pathwidth and Treewidth Abstract: Using a previously developed algebraic representation system for graphs of bounded pathdwidth and treewidth, efficient membership algorithms are built for subgraph, minor and topological-minor partial orders. Semi-automatic procedures for these problems are presented through numerous explanatory figures and source code. An enumeration scheme for building automata for fixed graph substructures of graphs of bounded width will also be introduced.
January 29	Dr. Joy Reed	Introduction to Computer Networks and Security Abstract: Have you ever wondered what TCP/IP means is plain English? Where do firewalls reside? How does distributed denial-of-service come about? I will give a gentle introduction to computer networks with focus on security. This is a talk I gave as the kick-off presentation for last spring's Science in Savannah Symposium: A Regional Approach to Cyber Security.
February 5	Cancelled	Cancelled Note: Because of the University meeting, the colloquium on 02/05 has been cancelled.
February 19	Robert Gadd	Inside the Entrepreneurial Mind Abstract: Robert Gadd, cofounder of seven different technology-oriented startups over the past twenty years, offers insights into his personal motivations and many lessons learned launching new businesses. Mr. Gadd will review his experiences in good times and bad times, some successful and other less than fully realized. Through these many ventures, Mr. Gadd has designed and licensed software solutions to leading companies including Cisco Systems, IBM, NCR, AT&T, Intel and many others. Now President of Savannah-based OnPoint Digital, Mr. Gadd leads a small team of developers and creative talent building a next generation offering of e-learning and performance improvement tools for corporate customers.
February 26	Dr. Selwyn Hollis	How the Work of an Engineer at the Renault Auto Company in 1962 Affects Your Life Every Day Abstract: Pierre Bezier died on November 15, 1999. He had retired from Renault in 1975 after a 42-year career there, during which one seminal idea in the early 1960s made him the father of computer-aided design. In 1977, at the age of 67, he was awarded a Doctorate of Science degree from the Université de Paris. In this talk we will describe his astonishingly simple breakthrough and how it permeates modern life.
March 5	Dr. Elena Braynova	Preference Queries Abstract: The handling of user preferences is becoming an increasingly important issue in present-day information systems. Among others, preferences are used for information filtering and extraction to reduce the volume of data presented to the user. They are also used to keep track of user profiles and formulate policies to improve and automate decision making. In this talk I will present a logical framework for formulating preferences as preference formulas and discuss some open problems in this field.
March 12	Armstrong's 2002 Putnam team	Problems from the Putnam Abstract: The Putnam Exam is a national intercollegiate mathematics competition. Members of Armstrong's 2002 Putnam team will discuss problems from the Putnam Exam. Elijah Allen, Bobby Griffin, Jarrett Walsh, and Brent Watson will each present solutions to problems. They hope to convey the flavor and fun of the challenge that the Putnam presents.
April 2	Dr. Manuel "Bud" Sanders	Topology is ... Abstract: Topology is a (relatively recent) foundational branch of pure mathematics that is related to geometry in a rather loose sense. While topological concepts involving Euler's formula for polyhedra, the Four-color theorem, the Mobius strip, the Klein bottle, seven bridges in Konigsburg, and the shape of the universe all widely contribute to the popularity and intrigue of topology within mathematical culture, the fact remains that topology is curiously hard to define in a precise, yet succinct, manner. Nevertheless, topological ideas permeate the study of modern mathematics. The goal of this talk is to provide a view of topology that paints a realistic picture of point-set topology, of geometric topology, and of algebraic topology in a manner suited for an audience with varying interests.
April 9	Ralph G. Smith, Chemist Savannah Customs Laboratory	Determination of Country of Origin of Agricultural Products Abstract: An overview of the U.S. Customs Service (Customs and Border Protection) will be presented. Customs is interested in determining the country-of origin of agricultural products in order to enforce existing laws and to collect appropriate tariffs. The use of trace metal profiles and multivariate statistical analysis to determine the country-of-origin of agricultural products will be discussed. Trace metal analyses were accomplished using high resolution ICP/MS and the multivariate statistical methods used include stepwise discriminant analysis, discriminant analysis, and canonical discriminant analysis. Methods of sample preparation, validation of analyses, and discriminatory techniques used to determine the country-of origin will also be presented.
April 16	Dr. Cameron Coates	On the Dynamic Characteristics of Thin-Walled Extension-Twist Composite Beams Abstract: The dynamic characteristics of six optimally coupled and near optimally coupled extension-twist thin-walled closed section composite beams are examined experimentally and with Finite Element Analysis (FEA). FEA predictions are compared with experimental results as well as a closed form analytical solution. It is observed that for higher modes, in plane warping significantly affects mode shapes and natural frequencies. This results in the appearance of shell modes not predicted by the analytical method, as in plane warping was neglected in the formulation. For initial bending modes, the global optimum natural frequency is found to be 1.5% to 5% more sensitive to a three-degree perturbation in lay-up than the local optimum.

Colloquium Schedule for Fall 2002

Date	Speaker	Topic
August 28	Mary Thornton	Data Mining by Wavelet Fractal Analysis Abstract: For many years, wavelets and fractals have been the domain of pure mathematics and physics. Exciting new research is revealing many applications for these structures in an increasingly data-driven scientific world. The challenge for scientists today is the extraction of information about trends, relationships, and patterns from immense amounts of seemingly chaotic data. Wavelets and fractals are proving to be very useful in meeting this challenge. We will offer a brief history and description of these structures and discuss novel techniques using wavelets and fractals in pattern recognition and data mining. Lunch will be served.
September 18	Dr. Sergio De Agostino	Lossless Image Compression by Block Matching Abstract: Block matching is a lossless compression method which extends Lempel-Ziv text compression to bi-level images and is suitable for high-speed applications. Sequential and parallel implementations of the method will be described.
September 23 (Monday)	Dr. Jim Brawner	Playing with Polyhedra Abstract: A colorful romp through the world of polyhedra, visiting the solids of Plato, Archimedes, Kepler, Johnson, and others. We will take a virtual tour through a variety of polyhedra, examine their history and applications, and pay particular attention to the notions of duality and symmetry.
September 26 (Thursday)	Dr. Azita Hashemi	Computer Literacy This talk will take place at 1:30 p.m. in Science Center - Room 2505. Abstract: People around the world use technology of varying types every day for both professional and personal purposes. In the USA in recent years, PC computers have become necessary tools for every one. That is why educational institutions in general and universities in particular are moving toward making Computer Literacy one of the mandatory general education courses. This presentation focuses on understanding what computer literacy is and how it empowers people to conveniently and accurately take care of their various affairs.
September 27 (Friday)	Dr. Ray Hashemi	Web Mining: Identification and Classification of Suspicious Web Sites This talk will take place at 10:00 a.m. in Science Center - Room 2505. Abstract: The goal of this research effort is to develop a software system that crawls into the World Wide Web and identifies those web sites that contains suspicious materials that may undermine the security of the United States and/or a minority group within the United States. The suspicious web sites are classified based on their threat level conveyed by their contents. At this point of our research, the system is able to analyze a web site for a set of limited concepts including Actions, Places, Titles, People, and Organizations. We use the ontology technology to determine the relevancy (in form of weights) of the content (sentences) of a site in reference to the above five concepts and then quantify the threat level of each sentence accordingly. A neural network using backpropagation training paradigm learns the relationship between the threat level and the relevancy weights and tries to predict the threat level for the suspicious sentences that the system has not encountered before. If a web site includes at least one threatening sentence, then it is considered as a suspicious one. The highest threat level among the sentences of a web site represents the threat level of the site. The findings reveal that the combination of ontology and neural network in this type of investigation is extremely effective.
October 2	Dr. Paul Hadavas	Operations Research: The Joy of Optimization Abstract: The field of Operations Research has been around for about 60 years and in that time the science of optimization has sprouted solutions to a multitude of diverse "real world" problems. In this talk, we will examine three classes of problems: linear programming, integer programming, and network flows. Specific examples will be presented and techniques for their respective solutions discussed.
October 11 (Friday)	Dan Lipsa	Open Source Software - The Engine Behind an Internet-Era Start-Up Company This talk will take place at 9:00 a.m. in University Hall - Room 105. Abstract: Open source software is an ubiquitous term nowadays. We define what open source software is, and explain its relationship with free software. In this context, two ways of using open source software in a business environment emerge: internal use, and use in a commercial product as a standalone module or library. Both of these, were successfully pursued in an actual company. Our presentation includes the use of open source software in their IT infrastructure (internal use), as well as in their product. We conclude that open source software, can provide real value to businesses that are willing to explore its possibilities.
October 23	Dr. Mark Burge	What can I do with my Palm?! Abstract: In the last two years the market for handheld and ubiquitous computing (HUC) and Personal Digital Assistants (PDAs) has grown at a compound annual rate of 30 percent (www.idc.com, 2001). This rapid growth has resulted in a field with few experts, little teaching material, and tremendous demand for trained professionals. I will present results from the first year of a NSF funded grant (CCLI Burge, Jodis) to develop curriculum materials to prepare our students, now, for handheld and ubiquitous computing careers. No technical background required, the talk will feature student written games and a live demonstration of a new generation of networked, handheld gaming.
October 30	Dr. Manuel "Bud" Sanders	A Dunce Hat, a House with Two Rooms, and the Whitehead Group: A Geometric Introduction to Simple-homotopy Theory Abstract: The speaker will introduce selected aspects of a beautiful and elegant area of mathematics known as simple-homotopy theory. Simple-homotopy theory blends algebra and geometry magnanimously to form intricate mathematical structure which is rich in both beauty and complexity. Fundamental notions of the theory such as expanding and collapsing polyhedra (as well as more general complexes) will be highlighted for aesthetic and motivational reasons in order to convey the flavor and central ideas of the theory. Concepts will be exhibited from a, decidedly, geometric perspective and will primarily be developed intuitively. The speaker will introduce the Whitehead Group of a complex from an entirely geometric viewpoint and will state several algebraic consequences. Several low-dimensional complexes including a topologist's dunce cap and RH Bing's well-known house-with-two-rooms will be discussed in the exposition. More exotic spaces may also be introduced.
November 13	Dr. Robert P. Cook, GSU Yamacraw Distinguished Speaker	The Phoenix Operating System Architecture
November 20	Dr. Chunyan Li, SKIO	Initial Observations of a Penetrating Shelf Front in the Central Georgia Bight Observed with Terra MODIS Ocean Color Abstract: A low temperature front often penetrates across the continental shelf in the Georgia Bight in winter. Observations from the recently validated 1-km resolution Terra MODIS SST and ocean color parameters showed that the front had a distinct acute shape protruding from the shelf to the edge of the Gulf Stream. Data from Dec. 2001 to Mar. 2002 indicated a dramatic change of features of these fronts. An analysis of five consecutive SST images separating by 11-13 hours showed some along-shelf advection of the front. The SST gradient in Dec. ranged from 0.3 to 1.0 C/km. In contrast, the SST gradient from Jan. to Mar. ranged from 0.3 to 2.4 C/km. The southern boundaries of the filaments had larger SST gradients and the strongest gradients were at the tip of the filaments near the edge of the Gulf Stream, suggesting a sinking point of cold water in the front.
December 4	Various Speakers	Presentation of Senior Projects Students: Brian Concepcion (Dr. Su) Catherine Carter (Dr. Su) Mary Thornton (Dr. Burge) Michael Walters (Dr. Su)

Colloquium Schedule for Spring 2002

Date	Speaker	Topic
January 9	Dr. Larry Lesser	Interdisciplinary Investigations in Mathematics, Statistics, and Ethics Abstract: Dr. Larry Lesser explores connections between mathematics, statistics and philosophy, particularly ethics. Lesser will discuss the module he developed for the Mathematics Department's debut participation in AASU's Interdisciplinary Ethics and Values course (ETHC 2000), which was one aspect of his freshly-completed year as Gignilliat Professor and the subject of a paper he presented at the recent national meeting of the American Statistical Association. Examples will be shared that can be adapted for a variety of courses and students.
January 14	Dr. Joel Best	Damned Lies and Statistics: Thinking About Numbers and Social Problems AbstractDr. Best is the head of the Department of Sociology at the University of Delaware, and the author of the best-selling book "Damned Lies and Statistics." His talk is sponsored by the College of Arts and Sciences, the Department of Criminal Justice, Social and Political Science, and the Department of Mathematics.
January 23	Dr. Mark Burge and Dr. John Kraft	A Java Client server architecture for studying human social behavior Abstract: Group Choice is our term for describing the behavioral phenomenon in which a group of individuals chooses between two alternatives over time. We use the Ideal Free Distribution (IFD; Fretwell & Lucas, 1970) analysis from behavioral ecology to account for Group Choice. The IFD theory suggests that the ratio of foragers at two resource sites should equal the ratio of obtained resources. Group Choice is a social phenomenon analogous to individual choice, and the IFD is analogous to the Matching Law account of individual choice. In this talk, we present several experiments that investigate earlier IFD research with flocks of pigeons and more recent work with groups of humans that made choices via networked computers. In most cases, the groups failed to match the distribution of resources, but they were sensitive in an orderly manner. In addition to presenting the original pigeon and human experiments, we present a novel computer based environment for group choice experimentation. The environment uses the java programming language to create an interactive graphical client, which enables real time interaction over the Internet with other members of the group. Design decision (e.g., multithreaded servers versus peer-to-peer, the use of multicasting, UDP, and TCP/IP) behind the client server architecture which led to its real time performance will be presented.
January 25	Dr. Darren A. Narayan, RIT	Sequences of Matrix Determinants Noon in UH 158 Abstract: We investigate families of nested matrices whose successive determinants form sequences that are strikingly familiar. In particular we shall focus on families of n x n matrices {M_n, n >= 1} where M_n is the (1,1)-cofactor of M_{n+1} and the determinants of the successive matrices form a strictly increasing subsequence of the Fibonacci sequence. The talk will be accessible to undergraduates and should include several entertaining exercises from [N. D. Cahill, J. R. Derrico, D. A. Narayan and J. Y. Narayan, Fibonacci Determinants, to appear in the College Mathematics Journal]. Dr. Narayan is visiting us from the Department of Mathematics at Rochester Institute of Technology. No lunch will be served.
January 30	Dr. Tamara Burton	Domination Dot Critical Graphs Abstract: For a graph G, a dominating set is a set of vertices such that every vertex belongs to that set or is adjacent to a vertex in that set. The domination number of a graph is the smallest possible cardinality of a dominating set. Agraph G is dot-critical with respect to the domination number if identifying any two adjacent vertices causes the domination number of the graph to drop. We show these graphs include previously-studied domination edge-critical and vertex-critical graphs. We provide additional examples of these graphs including a characterization of 2-dot-critical graphs. Many properties of dot-critical graphs are presented, and we close with some results on dot-critical trees including a constructive characterization of all such trees.
January 31	Dr. Bill Roscoe	CSP and Security Research Room UH111 @ 3:15pm Bill Roscoe joins us from Oxford University, England. In computer security we are typically thinking about interaction: between systems in a distributed environment; between a system and its users; between a system and an "attacker". There is therefore much to be said for using process algebras in security research. In this talk Professor Roscoe will describe how CSP has been used to model security problems and reason about them. Two rather different threads of work will be described: the modelling of cryptographic protocols and the analysis of information flow. Very different features of CSP make it an excellent tool for both.
February 6	Dr. Sergio De Agostino	Static and Dynamic Data Compression Abstract: Huffmann coding, Tunstall coding and arithmetic coding are the main data compression techniques when the probabilities of the alphabet characters are known (static methods). Lempel-Ziv coding is the main technique when such probabilities are unknown (dynamic method) and it works with a purely combinatorial approach. We will survey these techniques. Then, we will see a reinterpretation of Lempel-Ziv coding using a probabilistic approach.
February 13	Dr. Geir Agnarsson	The Science of Secrecy This talk will take place at noon in UH 157. Abstract: Throughout history secrecy has has been of uttermost importance, to deliver sensitive messages, to plan a surprise attack and so forth. In this talk, we survey the most common enciphering methods and how to crack them. Including the basic Caesar Shift, the German Enigma, the notion of a public key, and the Holy Grail of encryption.
February 27	Prof. Jane Barnard	Teaching and Learning in South Africa . . . Changing My World Abstract: Experiences of learning and teaching mathematics in South Africa during August 2001 in K-12 schools and universities through pictures and artifacts . . . Bryandale Elementary School and Wits University in Johannesburg, University of South Africa in Pretoria, Hilton College (boys' boarding school) and Shayabantu (Zulu township school) in Kwazulu-Natal, Stellenbosch University, and Hermanus Montessori School.
March 4 (Monday)	Dr. Robert Taylor, UGA	Graduate Work and Career Opportunities in Statistics
March 28 (Thursday)	Dr. James L. Clark, P.E.	A Collage of Industrial Research University Hall - 156, Noon Dr. Clark has spent the past twenty-four years on the faculty at Georgia Tech, teaching and conducting applied research projects in industrial technologies and processes. In this seminar, he will discuss five of his projects, beginning with four, brief "teaser" presentations covering: Energy conservation for compressed air utilization in textile weaving Analysis and experiments in two-component fluid flow inside a porous felt Recycling opportunities/challenges for fibrous solid waste, and Development of new automation technology for the food processing industry. Dr. Clark will then present in greater detail a university/industry/government collaboration in which he directed a student/faculty team developing a process for automated reuse of the chemical baths used in batch dyeing of carpeting.
March 29 (Friday)	Dr. Dennis Lambert, P.E.	Fracture of Engineering Materials University Hall - 103, Noon Mechanical engineers design mechanical devices-devices that convert energy to motion, transform motion from one type to another, or magnify forces. The designs must be economical and effective at performing the task for which they were designed. Safety cannot be ignored in the considerations. A great deal of effort is expended to understand the response of materials to applied forces and environmental effects in order to make sure that the design performs as expected. Failure can occur in many different ways, but it is especially important to avoid fracture of loaded parts, which usually is catastrophic in nature, and results in the transfer of input energy in an uncontrolled manner-occasionally, people get hurt. Fracture can be identified to result from the force input, relative to the size of the object, but it is also greatly influenced by the presence and size of discontinuities and flaws. Early efforts to insert fracture resistance into design focused on linear-elastic behavior. Materials used at the time responded to forces with linear "stretch". Upon removal of the load, the object returns to the original shape-this is termed an elastic response. A simple approach allowed the point where fracture would occur, so that this could be avoided in the resulting design. In the time since World War II, many materials have been developed that cannot be considered linear elastic. These materials are much tougher, i.e., more tolerant to the presence of flaws while being subjected to forces. These materials still express linear elastic behavior, but the determination of the point of fracture requires extremely large and expensive specimens. New approaches have been developed to account for the fracture of these new "elastic-plastic" materials, but severe restrictions remain. The current effort is to remove these restrictions to more appropriate limits. Approaches presented in this presentation will include energet approaches.
April 1 (Monday)	Dr. Cameron Coates	A Proposed Methodology for Structural Health Monitoring of Commercial Airlines
April 2 (Tuesday)	Dr. Thomas Murphy	The Control of Synchronous Sequential Machines with Races University Hall - 156, Noon The problem of overcoming the effects of critical races on asynchronous sequential machines is considered in a control theoretic framework. State feedback controllers that eliminate the effects of critical races are developed. The results include necessary and sufficient conditions for the existence of such controllers, as well as algorithms for their design. When the controllers exist, they eliminate the critical race effects and control the machine to match a desirable race-free asynchronous model.
April 3	Dr. Charlesworth R. Martin	Multi-Sensor Data Fusion - An Informed Approach University Hall - 103, Noon Multi-Sensor Data Fusion is becoming increasingly important in autonomous vehicle design as challenging operating environments and cost have given impetus to designers to investigate the capabilities and processing requirements of various multi-mode sensor designs. To meet this requirement, engineers and scientists are working to make these systems fault tolerant to certain types of error, namely, incompleteness, inaccuracy and/or tardiness in the data supplied by individual system elements such as sensors or processors. The why and how of Multi-Sensor Data Fusion are explored and an example from my research on a dual IR-RF sensor suite is presented to illuminate the discussion.
April 10	Dr Selwyn Hollis	An Overview of Oscillators An oscillator (by our definition) is any physical system that is capable of stable periodic behavior. We will survey several examples that include mechanical, electrical, chemical, and ecological oscillators. Mentioned briefly in the talk will be three Nobel laureates, a handful of Russians, a giant squid, and millions of little creatures like the one on the right.
April 17	Dr. Jane Sinclair University of Warwick England	Z: Specification, Refinement and Proof Dr. Sinclair is widely known for her research into formal methods. Her book about the specification language Z, Introduction to Formal Specification and Z, published by Prentice Hall, Int. is in its second edition. Dr Sinclair will give a general overview of formal methods. She will describe how the world of logic, sets and relations form the basis for specification and verification techniques of realistic systems. Location & Time: Room UH 103, 3:00 PM
April 24	Dr. Paulius Micikevicius, UCF	Prufer-like Codes for Labeled Tree In 1918 Prüfer showed a one-to-one correspondence between n-node labeled trees and (n ^Ö 2)-tuples of node labels. The proof implies a tree code computed by iteratively deleting the leaf with the smallest label and appending its neighbor to the code. Since then other tree codes have been proposed, based on different node deletion sequences. These codes have additional properties, interesting and useful in graph theory and computer science. For example, a number of graph-theoretic results for labeled trees can be proved quite simply using Prüfer-like codes. These codes are also of interest in genetic algorithms. In the presentation we survey these Prüfer-like codes, as well as describe the proposed classification. Some graph-theoretic results for random labeled trees, derived with the use of Prüfer-like codes will also be presented.
May 3rd (Friday)	Dr. Paul Goransson	Securing the Wireless Lan Wireless technologies applied to Local Area Networking are undergoing unprecedented growth both in deployment and technical advances. The convenience of high-speed Internet access without wires in airports, universities and homes, ensures accelerating deployment of wireless LANs. This technology, while fueling the next wave in networking growth, creates a plethora of new security problems. This talk will provide a brief review of the security "Pandora's Box" that is opened by IEEE 802.11 wireless LANs and the initial approaches to mitigating these problems. We will also discuss future directions in solutions to these problems and explain why a single solution is likely to remain elusive. This talk will be held in the Science Center - Room 1407 at 11:30 a.m.

Colloquium Schedule for Fall 2001

Date	Speaker	Topic
September 12	Dr. Geir Agnarsson	Geometric and Graph Theoretical Methods for Measuring Complexity in Biochemical Networks Biochemical networks are in general very large and complex and therefore hard to analyze. In this talk we mention a couple of these difficulties and how any measure of their complexity are of value. We will mention some graph theoretical and geometrical objects arising from these networks, and talk about their topology and some invariants.

Note: Sergio de Agostino's flight was delayed. His talk, originally scheduled for September 19, will take place in the Spring.



September 19	Prof. Carolyn Smith	The Use of SPRT in the Search for UXO Many locations in the US ara contaminated with unexploded ordnance (UXO). In a few istances, UXO has been discovered, has functioned, and as a result, tragedies have occurred. Taxpayer funds are utilized in the clean-up efforts. Techniques to estimate contamination levels (thus exposure levels for residents) were developed. One technique utilized in the estimation process is the Sequential Probability Ratio Test (SPRT). The development and use of automated tools incorporating the method(s) will be discussed.

September 26	Maria Watts	The Wireless Internet

October 10	Dr. Hongjun Su	Internet Quality of Service and the Differentiated Service Network Approach With the rapid emergence of real-time multimedia applications in the internet, there are urgent needs to bring Quality of Service (QoS) to the Internet. This presentation will give a general introduction of Internet Qos and Differentiated Service Network (DiffServ). First, it will explain what Internet QoS is and why we need it. Then it will introduce the Differentiated Service Network (DiffServ), one of IETF's current efforts in adding QoS to the Internet. It will explain the basic concepts of DiffServ as well as how DiffServ achieves its QoS goals. Finally, the performance issues of DiffServ will be addressed and some research results will be discussed.

October 10	Dr. Mark Burge, Dr. John Craft	CANCELLED The colloquium talk scheduled for this week on Wednesday, October 10 is cancelled so that we can attend the Commemorative Tree Planting honoring the inauguration of President Jones. The talk will be rescheduled soon. A Java Client server architecture for studying human social behavior Group Choice is our term for describing the behavioral phenomenon in which a group of individuals chooses between two alternatives over time. We use the Ideal Free Distribution (IFD; Fretwell & Lucas, 1970) analysis from behavioral ecology to account for Group Choice. The IFD theory suggests that the ratio of foragers at two resource sites should equal the ratio of obtained resources. Group Choice is a social phenomenon analogous to individual choice, and the IFD is analogous to the Matching Law account of individual choice. In this talk, we present several experiments that investigate earlier IFD research with flocks of pigeons and more recent work with groups of humans that made choices via networked computers. In most cases, the groups failed to match the distribution of resources, but they were sensitive in an orderly manner. In addition to presenting the original pigeon and human experiments, we present a novel computer based environment for group choice experimentation. The environment uses the java programming language to create an interactive graphical client, which enables real time interaction over the Internet with other members of the group. Design decision (e.g., multithreaded servers versus peer-to-peer, the use of multicasting, UDP, and TCP/IP) behind the client server architecture which led to its real time performance will be presented.

October 17	Greg Geller	The Path to Intelligence / Intelligent Artifacts and the Human Mind The field of Artificial Intelligence has been a roller coaster ride ever since its beginnings in the 1950s. The majority of research in the field has followed a distinct pattern. Initial success in building a system that can "reason" in an abstract or specialized world, followed by extreme optimism, followed by the discovery of deep problems when trying to generalize these systems, followed by the failure to solve these problems. Perhaps we haven't discovered the right sort of algorithms that are used by Reason. Perhaps we need to study the brain and unlock more of its secrets. Perhaps it is simply a matter of getting faster computers with parallel architectures. These are questions that might pop into the minds of a computer scientist trying to solve the problem of creating an intelligent artifact. On the other hand, what about the philosophical question of the algorithmic nature of Reason? Does the mind operate by gathering facts that are "out there", internally representing them "in here", manipulate these internal symbols formalistically until finally the output is given to the body to execute? Is there really something like a computer program going on in our brains? If there is, what does that say about the body? Does it make sense to think about Reason and Intelligence as being disembodied? These are questions that have mostly been ignored or tacitly affirmed as being self-evidently true by most members of the scientific community. Recently however, the emerging field of Cognitive Science has been questioning the validity of these traditional beliefs and believe they have shown hard EMPIRICAL evidence that contradict these beliefs. If the evidence turns out to be real, then the traditional approach to AI leads NECESSARILY to failure and we should jump ship immediately and start looking for other approaches to building intelligent artifacts. During the an explain of the traditional approach to AI and some objections to that approach, including the evidence given by Cognitive Science will be given. I will explain why this evidence, if valid and true, is devastating to the traditional conception of Intelligence which AI research has largely assumed. Finally, a presentation of an alternate approach to AI coming from the field of robotics will be given. Audience participation is encouraged and there will be a question and answer session following the talk.

October 24	Vladimir Gorelik	Neuron: One biologically plausible model. The concept of a neuron as a nonlinear summing element with adjustable weight coefficients is commonly accepted as the basic building block for Artificial Neural Networks. This concept evolved from early work in neurophysiology and was relatively easy integrated into many neural network architectures. Lately much more intricate properties of neurons have been discovered and at the same time ANN theories are facing computational problems associated with training. As the result, new science of Neuromorphic Engineering is emerging as a less formal and more intuitive approach to simulating computational living tissue. In the talk I will introduce a model of an artificial neuron. This model allows both temporal and spatial processing of sensory information presented at the neuron's receptive field. An attempt will be made to bring the discussion into the framework of existing knowledge about the physiology of biological neurons. A brief history of the field will be provided and difficulty of temporal processing in traditional Artificial Neural Networks will also be discussed. Finally several examples of possible integration of the proposed model into neural processing circuitry will also be provided.

October 31	Prof. Jane Barnard	Tickled by Trapezoids: What do you MEAN? One often speaks of the average or mean of a set of numbers. However, these words are actually ambiguous when we consider that there are many types of average. By nature, means are numerical or algebraic; but they have application and models in geometry. Trapezoids provide a vehicle for combining algebraic and geometric problem-solving techniques in addition to introducing some Vocabulary and notions generally not connected in geometry classes.

November 5	Dr. Guillermo Martínez	Borges and Mathematics Dr. Martinez is professor of mathematics at the University of Buenos Aires, and has authored the novels "Regarding Roderer" (1993, 1999 second edition) and "The Woman Master" (1999). At age 20, Dr. Martinez earned Argentina's National Short Story Award for "La jungla sin bestias" in 1982, has performed post-doctoral work in mathematics at Oxford University and has a related novel "The Oxford Series" in the works. This fall he is serving as the Elena Diaz-Verson Amos Eminent Scholar in Latin American Studies at Columbus State University.

November 14	Dr. Sigmund Hudson	Logic, Computers, and Truth The present logical system used in mathematics, computer science, and the natural sciences is not as powerful as one would hope. A discussion is presented on the ideas used to show that there are true statements of mathematics which are not provable using the present logical system, revolutionary ideas developed by Kurt Goedel in the 1930's. The discussion is fully understandable by beginning mathematics and computer science students.

~~November 28~~ December 5	Dr. Steve Damelin	Quadrature on d, d>1, spheres, energy and weighted approximation We discuss a new method for distributing points on d-spheres using finite fields as well as new results dealing with quadrature error bounds involving extremal energy. This is a joint work with Mullen (PSU) and Grabner (Graz).

Note: Due to an unforeseen event, Dr. Steve Damelin will not be able to give his talk on 11/28.
His talk is postponed to Wednesday December 5 at noon in room 157.