ABSTRACT Recently, there has been rather intense research activity related to various forms of extensions of standard parametric family of distributions to obtain more flexible classes, possibly retaining at least some of the appealing formal properties of the original family. While this exercise makes sense also in the scalar case, it is the multivariate setting that provides the more interesting and stimulating context, since here only a limited number of alternatives to the multivariate normal family are currently in use. In this talk, first the univariate skew-normal distribution and some of its properties, including the result that the square of a skew-normal random variable is chi-square, will be given. A characterization result, which is a generalization of a well-known result is given. Two applications to the stock returns data and the data on twins will be presented. Then a skew multivariate normal distribution will be defined and its properties will be studied in some detail. A stochastic representation of the skew multivariate normal random vector will be given which is useful for computer simulation. Further generalization to the matrix case will be indicated and some unsolved problems in this area will also be pointed out.

September 17, 2004
W. Charles HOLLAND, Bowling Green State University
"Small Varieties of Lattice-Ordered Groups and MV-Algebras"

ABSTRACT Lattice-ordered groups have been studied for more than a hundred years for their intrinsic interest, and because of their connections to other subjects such as "soft" analysis, and measurement theory (in social sciences). MV-algebras are algebraic models of multi-valued logic, which has applications in quantum mechanics, quantum computing, and similar areas. It has recently been discovered that there is an intimate connection between MV-algebras and lattice-ordered groups. In this talk, we will discuss that connection, and the implications this has for future research in the area.

September 24, 2004
Ray Heitger, Bowling Green State University
"Parents Preparing Preschool Pupils"

ABSTRACT I will discuss some ideas I have developed during 39 years in the classroom (all anecdotal), will look at some of the existing educational problems, will look at what some are doing to solve them, and suggest some areas of research for mathematics educators. Public schools really are doing a great job! Blaming our educational problems on schools is not where the true problem lies. I feel that parents need to become full partners with the academic community in accepting responsibility and assist in preparing students for an academic life.

October 1, 2004
Davd Hemmer, University of Toledo
"Specht module filtrations for representations of symmetric group"

ABSTRACT The representation theories of the symmetric group and general linear group have been closely related since the work of Schur in the early 1900's. This talk will illustrate a recent application of Schur's ideas in joint work with Dan Nakano. The complex irreducible representations of the symmetric group are called Specht modules. In characteristic p, the Specht modules may no longer be irreducible. Certain modules (e.g. Young modules) are known to have filtrations where the quotients are Specht modules. Unfortunately, the multiplicities may depend on the choice of filtration, i.e. there is no ``Jordan-Holder type'' theorem. This is in stark contrast to the situation for the general linear group, where the corresponding notion is of a ``good filtration.'' Not only are the multiplicities in such a filtration well-defined, but there is a nice cohomological criterion for when such a filtration exists and a formula for the multiplicities. We use the Schur and inverse Schur functors to demonstrate the situation for the symmetric group is much better than previously believed. Namely, for primes p>3 the multiplicities in a filtration by Specht modules are well-defined. We give a criterion for such a filtration to exist, and a formula for the multiplicities. As a corollary we give a new construction of Young modules, analogous to the Ringel-Donkin construction of tilting modules.The talk will be accessible to graduate students and advanced undergraduates.

October 8, 2004
NO COLLOQUIUM, Fall Break Weekend

October 15, 2004
Truc T. Nguyen, Bowling Green State University
"Exact EDF goodness-of-fit tests for inverse Gaussian distributions"

ABSTRACT Several characterizations of inverse Gaussian distributions are studied. Exact EDF goodness-of-fit tests for inverse Gaussian distributions using these characterization results as transformations are constructed. The powers of these tests at several alternative distributions are estimated by Monte-Carlo method.

October 22, 2004
Daniel Mihalko, Western Michigan University
"On Similarity Indices for Comparing Clustering Results"

ABSTRACT Many similarity indices have been introduced in the literature for comparing the results of different clusterings of the same data set. This work shows that after correction for chance agreement, many of these indices are actually equivalent. Potential uses of similarity indices in the analysis of gene expression experiments will also be discussed.

October 29, 2004
Dale H. Mugler, University of Akron
"Wavelets and the Time-Frequency Analysis of Musical Instruments"

ABSTRACT What makes the sound of a horn playing a middle C seem different from the sound of a flute playing the same note? Nearly everyone likes to listen to some kind of music, but rarely do we think of a piece we listen to as a time-frequency function. Fourier analysis, based on sines and cosines of different frequencies, has been used for many years to analyze the spectrum of a signal. But there is a relatively new mathematical tool that has taken over in many related areas, and that involves the theory of wavelets. Wavelets provide a basis made of functions that are non-zero only on a small time interval, yet represent very general functions. This talk will be a general overview to introduce the theory of wavelets and many of its applications, including the new JPEG 2000 standard for image compression, but will concentrate on time-frequency representations.

November 5, 2004
Richard Little, Baldwin Wallace College & BGSU "An Introduction to and Call for Help With the Ohio Resource Center for Mathematics, Science and Reading (Notice the disciplines are NOT in alphabetical order!)"

ABSTRACT The ORC is a virtual resource sponsored by the Ohio Board of Regents for "promising practice" and "best practice" lesson plans that are aligned with the national and Ohio standards in these three disciplines. We will introduce the plethora of lessons presently available on or via the ORC site for grades K -> 12 classes. There is a distinct dearth of lesson plans for college classes now available. Your help is needed in locating and developing more lesson plans which are relevant to the standards and which promote inquiry strategies for teaching the concepts. Of course we want these additional lesson plans to be attractive to college/university teachers so that they might try them in their classes which include prospective K -> 12 teachers. Please join us for the colloquium and join in the pursuit of more college level resources on the ORC site.

November 12, 2004
NO COLLOQUIUM

November 19, 2004
Michael J. Collins, Oxford University and Ohio State University "Bounds for Finite Groups of Matrices"

ABSTRACT In 1878, Jordan showed that there was a function f on the natural numbers such that, if G is a finite group of complex n x n matrices, then G has a normal abelian subgroup of index bounded by f(n). Explicit functions were given by Frobenius and Schur, but they are very far from optimal, and it was only after the classification of finite simple groups was announced that a near-best result was announced by Weisfeiler; using more powerful group theoretic methods in place of his analytic estimates, precise bounds can now be given. I will discuss these and related questions.

November 26, 2004
NO COLLOQUIUM - Thanksgiving Break

December 3, 2004
Theodore Chang, University of Virginia "Statistics of Tectonic Plate Reconstructions"

ABSTRACT In 1960, Hess proposed the theory of sea floor spreading: that new ocean crust is formed by magma welling up from the interior of the earth and cooling as it reached the surface at mid-ocean ridges. This crust is carried across the bottom of the ocean floor until it is subducted in trenches. Thus the surface of the earth is, to first approximation, composed of tectonic plates which move rigidly away from the mid-ocean ridges. The molten magma acquires a magnetization whose direction depends upon the Earth's magnetic field at the time that it reaches the surface. Periodically in the past the North magnetic pole has flipped to close to the South geographic pole, resulting in the so called marine magnetic anomaly lineations. These marine magnetic anomaly lineations provide the best information to reconstruct the past position of tectonic plates. We will discuss the statistical errors in these reconstructions. The relative position of two tectonic plates at a fixed time in the past is given by a 3-dimensional rotation matrix. Similar statistical issues arise in the estimation of an unknown 3 dimensional coordinate system, a problem which has arisen in other engineering contexts and in image analysis. We will focus on some general statistical principles that apply in this group of problems. In estimating these reconstructions, the shapes of the lineations become a nuisance parameter and a parsimonious model for their shapes becomes desirable. Previous models assumed a piecewise great circular shape, however, as the data density has increased, these models become untenable. We will discuss some recent results on the use of an Ornstein-Uhlenbeck process to model these shapes. No geophysical background will be needed. If time allows, we will show that statisticians can also have fun with some slides of a geophysical data collection cruise in the Indian Ocean.

January 21, 2005
Ignacio Zalduendo, Universidad Torcuato Di Tella and Kent State University "Orthogonally Additive polynomials over $C(K)$"

ABSTRACT Two continuous functions on the compact set $K$ are called orthogonal if their product is zero. A continuous homogeneous polynomial over $C(K)$ is said to be orthogonally additive if $P(u+v)=P(u)+P(v)$, for all orthogonal $u$ and $v$. In two recent papers Benyamini-Llavona-Lassalle and Perez-Villanueva characterize such polynomials using Borel measures on $K$. The two proofs are different and both very technical. In this talk we provide a third proof of the result. Our proof uses the Aron-Berner extension, a linearization procedure (which will be explained in the talk) and elementary topology and functional analysis. The proof is far shorter than those mentioned above.

Gennady Puninskiy, Ohio State University-Lima "Pure-Injective Modules Over String Algebras"

ABSTRACT String algebras form a class of finite dimensional algebras over a field $k$ which are tame, that is, it is possible to classify indecomposable finite dimensional modules over them. An example of a string algebra is a Gelfand-Ponomarev algebra $G_{2,3}$ which is isomorphic to the factor of the polynomial ring $k[x,y]$ by the ideal generated by $xy$, $x^2$, and $y^3$. Pure-injective modules over string algebras can be defined as direct summands of direct products of finite-dimensional modules. For instance, we usually have pure-injective modules which are analogs of `adic', `Prüfer' and `generic' abelian groups. In this talk we consider a classification problem of pure- injective modules over string algebras and its connections with complexity of the category of modules. For instance, we will discuss Ringel's conjectural classification of indecomposable pure-injective modules over domestic string algebras, and Schröer's conjecture that the Krull-Gabriel dimension of a domestic string algebra is finite.

March 2, 2005
V. Seshadri, McGill University "Some New Independence Properties of the Inverse Gaussian Distribution"

ABSTRACT This talk is motivated by the classical result of Tweedie about the weighted sum of reciprocals of inverse Gaussian random variables which, besides being independent of the sample mean , also follows a gamma law. The result goes as follows. Let a, t_1 , ......t_n be real positive constants. Let Y_1 , ......., Y_n be n independent inverse Gaussian random variables, such that L(Y_i) = IG (a t_i, a(t_i)^2) , i = 1,....,n. Define by b_i = [(t_i)^2 / Y_i], and c = ( T^2 / Y ) where T is the sum of all the t_i's and Y is the sum of all the Y_i's . Then we have the result that Q= a [{ b_1 + ......+ b__n} - c] is independent of Y. Moreover, Q has a chi-square law with (n-1) degrees of freedom and the law of Y, namely L(Y) = IG [aT,aT^2]. This talk explores what happens when the t_i 's are considered random. We also consider a generalization to the Generalized inverse Gaussian law. Finally we show a connection to the Wishart distribution.

March 18, 2005
Alexander Izzo, BGSU "Algebras of Functions of One Complex Variable via Several Complex Variables"

ABSTRACT Some results concerning algebras of bounded functions on a planar domain will be discussed. Some of the ingredients in the proofs, which involve a combination of techniques from functional analysis and complex analysis, will also be described. Although the results concern only functions of one complex variable, in many cases the only known proofs make essential use of several complex variables.

Nadini Kannan, University of Texas at San Antonio "Estimation of the Linear Array Model"

ABSTRACT The area of array processing has received considerable attention in the past several decades. The Array Model consists of an array of sensors used to detect the presence of one or more radiating point sources. Sensor arrays are widely used in radar and sonar, geophysics, and tomography. The main problem of interest is estimation of the parameters associated with the signals including their directions of arrival (DOA), the number of signals, and their crosscorrelations. The Array Model is highly nonlinear, and traditional estimation methods like maximum likelihood and least squares are numerically difficult. We will discuss some alternative methods of estimation of the model parameters using eigendecompositions of the sample covariance matrix. These eigenspace methods are high resolution techniques that exploit the inherent structures in the model and are computationally much more tractable then the traditional methods. We will also discuss the problem of identifying the number of signals which may be formulated as a model selection problem. Some extensions to estimating the parameters for wideband signals will also be discussed.

April 1, 2005
Pamela Richardson, University of Virginia-Richmond "Centroids of Quadratic Jordan Superalgebras"

ABSTRACT The centroid of a Jordan superalgebra consists of the natural "superscalar multiplications'' on the superalgebra. The basic examples of Jordan superalgebras are the simple Jordan superalgebras with semisimple even part, which were classified over an algebraically closed field of characteristic not 2 by M. L. Racine and E. I. Zelmanov. In this talk, we discuss the centroids of these superalgebras over a general ring of scalars.

April 8, 2005
Satish Iyengar, University of Pittsburgh "Models for Integrate-and-Fire Neurons"

ABSTRACT Stochastic models of neural activity are a well developed application in biology. Diffusion models for integrate-and-fire neurons hold a prominent place because of the many synaptic inputs to a neuron, and because these models arise out of noisy versions of differential equations for the neural membrane's electrical properties. While the probabilistic aspects of such models have been well studied, inferential and computational procedures for them are not as well developed. In this talk, I outline the physiological background leading to these models. I then describe recent progress in parameter estimation and the computational problems that arise.

April 22, 2005
Tong Sun, Bowling Green State University "Error Control in Numerical PDEs"

ABSTRACT General ideas and methods of error estimation and control in numerical solutions of partial differential equations will be discussed. That is, we are going to introduce the concepts of local error, global error, consistency, stability, convergence, and error bound. In addition, we also need to understand error propogation and error pollution. What are the mathematical tools we need to work on all these problems?

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