Colloquia — Spring 2000
Friday, April 28, 2000
| Title |
U-Statistics and Imperfect Ranking in Ranked Set Sampling |
| Speaker |
Professor Brett Presnell
University of Florida |
| Time |
3:00-4:00 p.m. |
| Place |
PHY 108 |
| Sponsor |
Professor Shanti Gomatam |
Abstract
Ranked set sampling has attracted considerable attention as an efficient
sampling design, particularly for environmental and ecological studies. A number
of authors have noted a gain in efficiency over ordinary random sampling when
specific estimators and tests of hypotheses are applied to rank set sample data.
We generalize such results by deriving the asymptotic distribution for random
sample U-statistics when applied to ranked set sample data. Our results
show that the ranked set sample procedure is asymptotically at least as efficient
as the random sample procedure, regardless of the accuracy of judgement ranking.
Some errors in the ranked set sampling literature are also revealed, and
counterexamples provided. Finally, application of majorization theory to these
results shows when perfect ranking can be expected to yield greater efficiency
than imperfect ranking. (Note: This work is joint with Lora L. Bohn.)
Friday, April 21, 2000
| Title |
Diagrams of Knotted Arcs and Quandles |
| Speaker |
Professor J. Scott Carter
University of S. Alabama |
| Time |
3:00-4:00 p.m. |
| Place |
PHY 108 |
| Sponsor |
Professor Masahiko Saito |
Abstract
A quandle is an algebraic structure that imitates the moves in classical knot
theory. We examine the structure in terms of examples of knotted arcs and circles.
From several examples, we hope to develop some intuition about quandle homology.
The talk will be elementary with lots of pictures, and the author hopes to make
it accessible to beginning graduate students.
Friday, April 14, 2000
| Title |
Constructing the Identities and the Central Identities of
the Square Matrix Rings |
| Speaker |
Professor Siamack Bondari
Saint Leo's University |
| Time |
3:00-4:00 p.m. |
| Place |
PHY 108 |
| Sponsor |
Professor Masahiko Saito |
Abstract
In this talk I present a procedure to compute all the multilinear identities
and the multilinear central identities of the m × m
matrices over a field of characteristic zero or large enough prime. The method
uses group representation theory and relies heavily on computational techniques.
Some knowledge of linear algebra (multiplication of matrices, nullspace of a
matrix, etc.) is needed to follow the presentation.
Friday, April 7, 2000
| Title |
Bounded Variation and its Generalizations |
| Speaker |
Prof. Dan Waterman
Syracuse University |
| Time |
3:00-4:00 p.m. |
| Place |
PHY 108 |
| Sponsor |
Professor J. Ratti |
Abstract
We begin by defining the notion of bounded variation and explain various directions
in which it can be generalized. Bounded variation arose in the context of Fourier
series and made its first appearance in the Dirichlet-Jordan theorem on the
convergence of Fourier series. Most (one-dimensional) generalizations of bounded
variation came into being in attempts to improve this theorem. We will also
discuss a recent failed attempt to generalize this notion. A more complete description
of this talk can be found here.
Friday, March 31, 2000
| Title |
The Refinement Equation: Multi-wavelets and Subdivision |
| Speaker |
Professor Sherman D. Riemenschneider
West Virginia University |
| Time |
3:00-4:00 p.m. |
| Place |
PHY 108 |
| Sponsor |
Professor Mourad Ismail |
Abstract
This talk will center on the refinement equation for multi-wavelets and subdivision
schemes. This is the relationship connecting the wavelets on adjacent levels
of a multiresolution analysis. In particular we will focus on the information
contained in the “refinement mask”, the finitely suppported sequence of coefficients
appearing in this equation for vector subdivision schemes. How can one decode
information about the existence of a solution to the functional equations defined
by the equation, about the convergence to that solution, about the polynomials
that can be reproduced with the scheme, and about the smoothness of the underlying
solution? Most of the information is found from linear algebra applied to certain
finite matrices formed from the refinement mask and should be accessible to
non-experts.
Friday, March 24, 2000
| Title |
Superlinear 3 point boundary value problems |
| Speaker |
Professor Bruce Calvert
Auckland University
New Zealand |
| Time |
3:00-4:00 p.m. |
| Place |
PHY 108 |
| Sponsor |
Professor Athanassios Kartsatos |
Abstract
We consider second order 3-point boundary value problems involving superlinear
and sublinear terms. We show that there exist solutions with arbitrarily large
number of oscillations. The methods involve applications of the Leray-Schauder
degree theory. This is joint work with Professor Chaitan Gupta.
Monday, March 20, 2000
| Title |
The Fastest Systolic Designs |
| Speaker |
Professor Marjan Gusev
University “St. Cyril and Methodius”
Skopje, Macedonia |
| Time |
3:00-4:00 p.m. |
| Place |
LIF 260 |
| Sponsor |
Professor Natasa Jonoska |
Abstract
The fast systolic computation was designed by the author to achieve implementations
that use fewer processors to execute the algorithm in less time then the conventional
systolic algorithms. In 1978, H. T. Kung and C. S. Leiserson proposed systolic algorithms
realized on a bidirectional linear array where two data streams flow in opposite
directions. The data flow introduced for this solution requires data elements
to appear in the data stream at each second time step, which is the only way
to meet all the elements from the other data stream.
One way to speedup the solution is to use the regular folding procedure. This
is achieved by a procedure called regular folding that consists of determination
of symmetry planes and vector of interlocking properties and implementation
of the translated folding. These solutions use up to 40% less processors and
have double efficiency. However, these solutions do not execute the algorithms
in less time and use a little bit more complex processors. To execute the algorithms
in less time the author invented fast systolic designs.
The main idea to achieve fast systolic designs is based on algorithm partitioning,
remapping, interlocking translation and composition of relevant parts. An additive
splitting is obtained if partitioning is performed on input data. This is possible
only if the operations used in the algorithm are associative and commutative.
However we do not use partitioning to map large size algorithms onto small processor
arrays, but use it organize the computation execution in a more efficient way.
We partition the data stream into odd and even parts similar to the idea of
partitioning the output data stream result in better solutions, since partitioning
the input data stream requires an additional summation cell.
The best improvement achieved by the fast systolic designs is 33% less processors
and 33% less time using the same type of processors and communication. Actually
the same processor array used to solve a problem of dimension N can be used
to solve a problem of dimension 3N/2 in the same array and the same time.
If further partitioning is implemented then the solutions are double pipelines.
The algorithm can now be solved in half the time and the speed up is increased
by a factor of 2. Two versions are identified for all four types of linear pipelines
whether retiming or relocation is used. The fastest systolic design is a derivation
of the last double pipeline solution and it uses 50% less processors and 50%
less time. To achieve this solution an extra memory cell is required per cell.
No increase in communications and processor design is required.
Friday, March 10, 2000
| Title |
Variational integrators, the Newmark Algorithm, and Collisions |
| Speaker |
Professor Jerry Marsden
California Institute of Technology |
| Time |
3:00-4:00 p.m. |
| Place |
PHY 108 |
| Sponsor |
Nagle Lecture Committee |
Abstract
This lecture surveys a number of recent results in the analysis of the Newmark
algorithm and related issues for nonlinear systems, both conservative and nonconservative.
In particular, it is shown that the conservative Newmark algorithm is variational
and hence symplectic. This analysis is believed to underly the reason that the
second order accurate Newmark algorithm has excellent energy behavior for both
conservative and dissipative systems. The variational approach is also studied
in the context of collision algorithms using techniques from nonsmooth analysis,
avoiding the use of gap functions. We will also briefly discuss some related
issues, such as the fact that finite element elasticity using the Newmark algorithm
is both variational and multisymplectic in a spacetime sense. The theory as
well as simulations will be discussed. (Based on joint work with Michael Ortiz,
Couro Kane, Anna Pandolfi, and Matt West).
Thursday, March 9, 2000
| Title |
Nonparametric Models and Methods for ANOVA and ANCOVA Designs |
| Speaker |
Professor Michael G. Akritas
Penn State University |
| Time |
3:00-4:00 p.m. |
| Place |
CHE 204 |
| Sponsor |
Professor Chris Tsokos |
Abstract
The talk will review some of the most common models used for the analysis of
continuous and discrete ordinal data. Some drawbacks of these models will be
highlighted in order to motivate the need for fully nonparametric approaches.
Such nonparametric models and procedures will be presented and illustrated with
the analysis of several data sets. The material for the talk is taken from Akritas,
Arnold and Brunner (1997, JASA) and Akritas, Arnold and Du (2000, Biometrika,
in press).
Friday, February 11, 2000
| Title |
A new classification of nilpotent groups, and some non-cancellation
results |
| Speaker |
Professor Peter Hilton
SUNY Binghamton/University of Central Florida |
| Time |
3:00-4:00 p.m. |
| Place |
PHY 108 |
| Sponsor |
Professor Natasha Jonoska |
Abstract
The Mislin genus classifies nilpotent groups of a certain type. By studying
the Mislin genus of a group N and of its k-fold direct power,
non-cancellation results for direct products are obtained.
Friday, January 28, 2000
| Title |
A Survey of Double-Torus Knots |
| Speaker |
Professor Kunio Murasugi (Professor Emeritus)
University of Toronto |
| Time |
3:00-4:00 p.m. |
| Place |
PHY 108 |
| Sponsor |
Professor Masahiko Saito |
| Acknowledgement |
Supported by CAS Faculty Development Program |
Abstract
A double-torus knot is a knot in a 3-sphere that can be embedded in the standard
orientable closed surface of genus 2. The class of these knots is not new, but
the systematic study of these knots started quite recently. In this talk, I
explain the background and main objectives of this research, and discuss the
connections with other prpblems in knot theory.
Wednesday, January 26, 2000
| Title |
Bifurcations, Chaos, and the Ultimate Fate of the Galaxy |
| Speaker |
Professor Antonio Elipe
Department of Astronomy
University of Zaragoza, Spain |
| Time |
4:00-5:00 p.m. |
| Place |
PHY 130 |
| Sponsor |
Professor Carol Williams |
Abstract
TBA.
Friday, January 7, 2000
| Title |
Domination in Cartesian Products and Vizing’s Conjecture, Part I |
| Speaker |
Professor Douglas F. Rall
Furman University |
| Time |
1:00-2:00 p.m. |
| Place |
PHY 120 |
| Sponsor |
Professor Edwin Clark |
Abstract
An Introduction: A well-known problem in domination theory is the long
standing conjecture of V. G. Vizing from 1963 that the domination number of the
Cartesian product of two graphs is at least as large as the product of the domination
numbers of the individual graphs. Although limited progress has been made this
problem essentially remains open. In this introductory talk, a brief survey
of progress will be outlined.
Refreshments will be served from 2:00-2:30 p.m. in PHY 209
(Faculty Lounge)
| Title |
Domination in Cartesian Products and Vizing’s Conjecture, Part II |
| Speaker |
Professor Bert Hartnell
Saint Mary’s University |
| Time |
2:30-3:30 p.m. |
| Place |
PHY 120 |
| Sponsor |
Professor Stephen Suen |
Abstract
Some recent results: As explained in the previous talk on this topic,
2-packings have long been recognized as playing a useful role in obtaining a
lower bound for the domination number of the Cartesian product of two graphs.
Here we will outline more recent attempts to exploit the nature of 2-packings
more fully to establish improved lower bounds.