Colloquia — Fall 2000
Friday, September 8, 2000
| Title |
The Elementary Solution of Hilbert's Third Problem |
| Speaker |
Mr. David Benko
University of South Florida |
| Time |
3:00-4:00 p.m. |
| Place |
PHY 013 |
| Sponsor |
Professor Masahiko Saito |
Abstract
If two polygons have the same area, it is always possible to decompose one
of them into a finite number of parts which can be rearranged to form the second
polygon. This is the Bolyai-Gerwien theorem. One might ask whether this is still
true for polyhedra; in fact, Farkas Bolyai and Gauss already asked this around
1830.
Hilbert raised this question again; it was the third problem of his celebrated
list of 23 problems in 1900. The negative answer was first given by Max Dehn
in the same year. Even today (after 170 years), the simplest proof of the problem
uses Dehn's idea.
Not any more! In my talk I will show that the solution of this seemingly elementary
question is indeed elementary. My proof does not use vector spaces or additive
functions. In fact, the proof finally boils down to the pigeon hole principle...
Monday, September 18, 2000
| Title |
Image Modeling and Its Impact on Image/Video Compression,
Metrics, and Indexing |
| Speaker |
Dr. Anastase Nakassis
National Bureau of Standards & Technology |
| Time |
3:00-4:00 p.m. |
| Place |
PHY 013 |
| Sponsor |
Professor Arunava Mukherjea |
Abstract
There is a multiplicity of techniques (in use, former and actual wannabes)
for image compression, metrics, and indexing. These techniques reflect modeling
choices (most often those underlying signal processing) and exhibit the strengths
and weaknesses of the underlying model.
The talk will be a survey of the state of the practice and of the technological
challengers with emphasis on the underlying models and on the consequences of
the modeling choices.
Examples (images,simulated clips, other) will be included as often as possible.
Underlying mathematical theories (Fourier, Wavelets, Catastrophe theory/Topology,
Fractals) will be briefly mentioned and explained in apopthegmatic/telegraphic
style with emphasis on the properties that are relevant to image modeling. Proofs,
details, and alternate interpretations will be left as an exercise to the audience.
Sparse references to the literature will be included.
Friday, October 6, 2000
| Title |
Reflections on Mirrors |
| Speaker |
Professor Anthony Quas
University of Memphis |
| Time |
3:00-4:00 p.m. |
| Place |
PHY 013 |
| Sponsor |
Professor Natasha Jonoska |
Abstract
We consider a random spatial process in which mirrors are placed randomly on
the lattice at +/- 45 degrees to the axes. A light is then shone from a point
on the lattice and the resulting light beam is studied. The talk uses techniques
from ergodic theory and percolation theory and these will be explained as needed.
The results of computer experimentation will be presented.
Friday, October 13, 2000
| Title |
Biodiversity and Statistics: We Can't Save the Planet if we
Don't Know What's Going On |
| Speaker |
Professor A. K. Dewdney
University of Waterloo |
| Time |
3:00-4:00 p.m. |
| Place |
PHY 013 |
| Sponsor |
Professor Edwin Clark |
Abstract
The term “biodiversity” has many meanings, mathematically speaking,
no two the same. The outcome of biodiversity measures depends on what measure is
being used, yet the preservation of natural areas may well hinge on such
measurements. An unacknowledged crisis in theoretical biology has resulted from
the lack of sound research in natural communities, particularly the patterns
(i.e., distributions) of species abundance that prevail in them. I demonstrate the
presence of a uniform J-shaped abundance distribution which I call the
Logistic-J Distribution. I show how I discovered it by computer, how I
tested it against 100 randomly-selected biosurveys, and what it tells us about
“biodiversity”, as well as the twin phenomena of speciation and
extinction.
Friday, October 27, 2000
| Title |
On Hierarchical Bayesian Neural Networks: An Application to
Prostate Cancer Study |
| Speaker |
Professor Malay Ghosh
Distinguished Professor of Statistics
University of Florida |
| Time |
3:00-4:00 p.m. |
| Place |
PHY 013 |
| Sponsor |
Professor Arunava Mukherjea |
Abstract
Prostate cancer is one of the most common cancers in American men. Management
depends on the staging of prostate cancer. Only cancers that are confined to
organs of origin are potentially curable. The paper considers a hierarchical
Bayesian neural network approach for posterior prediction probabilities of certain
features indicative of non-organ confined prostate cancer. The Bayesian procedure
is implemented by an application of the Markov Chain Monte Carlo numerical integration
technique. For the problem at hand, the hierarchical Bayesian neural network
approach is shown to be superior to the one based on hierarchical Bayesian logistic
regression model.
Friday, November 3, 2000
| Title |
Combinatorial Dynamics: Directed Graphs and Maps of the Interval |
| Speaker |
Professor Ethan M. Coven
Wesleyan University |
| Time |
3:00-4:00 p.m. |
| Place |
PHY 013 |
| Sponsor |
Professor Natasha Jonoska |
Abstract
Combinatorial Dynamics deals with periodic orbits of self-maps of
one-dimensional spaces. The language and concepts of directed graphs are
particularly useful for stating and proving results about periodic orbits of
continuous self-maps of the interval. We will illustrate this by discussing
“minimal combinatorial models” for some periodic point properties of
continuous self-maps of the interval.
Wednesday, November 8, 2000
| Title |
Pure Multigrades |
| Speaker |
A. W. Goodman
Professor Emeritus |
| Time |
3:00-4:00 p.m. |
| Place |
PHY 013 |
Abstract
The talk and the topic uses only the elementary theory of numbers of the positive
integers. If you wish to learn what a pure multigrade is you must attend the
lecture for at least 5 minutes. The lecture will mention a number of open problems
that may be attractive for future research.
Friday, November 17, 2000
| Title |
Resolutions of Some Conjectures of Saffari on Ultraflat Polynomials |
| Speaker |
Professor T. Erdelyi
Texas A&M University |
| Time |
3:00-4:00 p.m. |
| Place |
TBA |
| Sponsor |
Professor Vilmos Totik |