Special Lefschetz Center for Dynamical Systems Seminar
Abstract: We prove local existence, uniqueness, and analytic dependence on the initial data of classical solutions of a nonlinear, nonlocal free-boundary problem involving the motion of a planar curve driven by its curvature function and by instantaneous diffusion, similar to that considered by Mullins and Sekerka in their work on instability of phase boundaries during solidification. We use the method of maximal regularity, together with a potential-theoretic analysis of the Dirichlet-to-Neumann map for the Laplace operator on planar domains, in spaces of functions whose Fourier transforms decay algebraically at infinity. The above is joint work with Robert L. Pego of the U. of Maryland at College Park. We will also mention a recent application of these methods to evolution by surface diffusion (the latter is joint work with Chun Liu of Carnegie Mellon U.).
Lefschetz Center for Dynamical Systems Seminar
Abstract: Patterns are frequently observed to emerge from a spatially extended system when it is driven above equilibrium by external stresses. Examples are roll patterns in Rayleigh-Benard convection and optical interference patterns in Maxwell-Bloch laser systems. Formal homogenization arguments can be used to derive macroscopic equations which model the phase structure of such patterns. We focus on one such model in 2D, the phase diffusion equation, whose stationary solutions include the minimizers of the energy
where 
is
a convex domain in
and
is
proportional to the aspect ratio of the underlying micrscopic system.
We study the limits of minimizers of 
as --> 0. This
``hyperviscosity limit'' serves to select a single-valued branch of
the multi-valued solutions of the inviscid eikonal equation. Using
Legendrian singularity theory we can further show that the generic
types of defects for the stationary phase diffusion equation
correspond to numerically observed defects.
LEMS and Electrical Sciences Seminar
Abstract: Model-based halftoning techniques exploit the properties of the display device and the human visual system to maximize the quality of the displayed images. They rely on accurate models of the display and human perception. The focus of this talk is on printers but similar techniques can be applied to other display devices. We consider two model-based techniques, the modified error diffusion and the least-squares model-based algorithm. Both algorithms produce images with high spatial resolution and visually pleasant textures. We also consider the use of printer and eye models in blue-noise screening techniques, which attempt to approximate the performance of error diffusion with minimal computation. We examine the performance of these halftoning techniques using both model-based quality metrics and subjective evaluations.
Stochastic Systems Seminar
Brown Applied Mathematics Pattern Theory and Vision Seminar
Abstract:
Automatic Target Recognition (ATR) is a problem of great
interest in both the military and the civilian applications.
In ATR, moving rigid targets are observed via
standard remote sensors (Video, Infrared, Radar)
and algorithms are developed to analyze the observations for
target detection, tracking and recognition.
We take a Bayesian approach to ATR generating
stochastic inferences on complex scenes using
Markov Jump-Diffusion Processes, extended to the non-flat
geometry of Lie groups.
In view of the recent algorithms proposed for such applications
a procedure for a comparative study becomes important.
The Bayesian approach has an added advantage in that it
provides metrics for analyzing the performances of ATR systems.
This analysis can be prognostic, i.e. given a scene-sensor
system what is the best one can perform, or
diagnostic, i.e. how well can a given algorithm perform.
We have derived Hilbert-Schmidt lower bounds for
analyzing the estimators taking values on matrix Lie groups.
Seeking an "ATR metric" the asymptotic expressions for the probabilities of
error in target detection and recognition are derived.
(This is a joint work with Ulf Grenander and Michael Miller)
LEMS and Electrical Science Colloquium
As the First Lecturer in the Electrical Engineering Distinguished Speaker Colloquium Series
| |
Abstract:
We conduct a brief historical tour of modern telecommunications,
illustrating the ways in which traditional basic research, based on
mathematical models, has dominated the major changes in the field. A
similar tour of communication networks shows a smaller influence from basic
research. We then observe that research today must proceed in parallel
with development, and point out some of the consequences for the role of
research. We illustrate this with some interesting problems in wireless
communication, high speed integrated networks, information theory, and data
compression.
BIOGRAPHY OF ROBERT G. GALLAGER:
Robert Gallager has been a Professor of Electrical Engineering at M.I.T.
since 1960 and is also Co-Director of the Laboratory for Information and
Decision Systems. He is the author of Information Theory and Reliable
Communication, co-author of Data Networks (Prentice-Hall, Ed. 2, 1992), and
author of Discrete Stochastic Processes (Kluwer, 1995). His major
research interests are wireless networks, high speed data networks,
information theory, and communication theory.
Dr. Gallager was on the IEEE Information Theory Society's Board of
Governors for many years, and was its president in 1971. He was the
chairman of the Advisory committee of the NSF Division on Networking and
Communication research and Infrastructure from Sept. 1989 to July 1992.
Dr. Gallager is a Fellow of the IEEE and received the IEEE Baker Prize
Paper Award in 1966, a U of Pa. Moore school Gold Medal award in 1973, the
Shannon Award of the IEEE IT society in 1983, and the IEEE William Bennet
Prize Paper Award in 1993. He received the IEEE Medal of Honor in 1990.
He is a member of the U. S. National Academy of Engineering and the U.S.
National Academy of Sciences.
PDE Seminar
No Seminar This Week
Department of Mathematics Colloquium
<--- 1997 Index