Schedule:

Speakers:

• Douglas N. Arnold, “Mathematics in a Dangerous Time”
  Director of the Institute of Mathematics and its Applications, Mathematics Department, University of Minnesota

  In view of recent events many mathematical scientists have begun to apply their expertise to problems connected with homeland security and antiterrorism. Moreover there are increasing calls from many of those involved for the help of the mathematical community. But how does mathematics relate? What can it offer? This talk we will some of the history of mathematics and security, current efforts, and some of the challenges and opportunities that face us.

• Yoram Bresler, “Fast Algorithms for Tomography”
  Electrical and Computer Engineering,  University of Illinois at Urbana-Champaign

  Computer Tomography is the primary non invasive means for examining the internal structure of the human body. The revolutionary nature of this imaging technology was recognized by the 1979 Nobel Prize in Medicine.Tomographic reconstruction underlies nearly all diagnostic imaging modalities, including x-ray computed tomography (CT), positron emission tomography, single photon emission tomography, and certain acquisition methods for magnetic resonance imaging. It is also widely used for nondestructive evaluation in manufacturing, and more recently for airport baggage security. The reconstruction problem in tomography is recovery (inversion) from samples of either the x-ray transform (set of the line-integral projections) or of the Radon transform (set of integrals on hyperplanes)of an unknown distribution. The method of choice for tomographic reconstruction is filtered backprojection (FBP), which uses a backprojection step. This step is the computational bottleneck in the technique, with computational requirements of O(N^3) for an NxN pixel image in two dimensions, and at least O(N^4) for an NxNxN voxel image in three dimensions. We present a family of fast hierarchical tomographic backprojection algorithms, that reduce the complexities to O(N^2 log N) and O(N^3 log N), respectively. For image sizes typical in medical applications or airport baggage security, this results in speedups by a factor of 50 or greater. Such speedups are critical for next-generation real-time imaging systems.

• Susan Friedlander, “The Ubiquity of Fluid Instability”
  Mathematics Department, University of Illinois at Chicago

  The unstable nature of fluid motion is a classical problem whose mathematical roots go back to the 19th Century. It has important applications to many aspects of our life from such disparate issues as predicting the weather to regulating blood flow. Instabilities might lead to turbulence or to new nonlinear flows which themselves might become unstable. We will discuss some of the mathematical techniques that can be used to gain insight into fluid instabilities. These tools include nonlinear PDE, spectral theory and dynamical systems.

• David Terman, “Neuronal Dynamics”
  Mathematics Department, Ohio State University

  Oscillations and other patterns of neuronal activity arise throughout the central nervous system. This activity has been observed in sensory processing, motor activities, and learning, and has been implicated in the generation of sleep rhythms, epilepsy, and parkinsonian tremor. Mathematical models for neuronal activity often display an incredibly rich structure of dynamic behavior. In this lecture, I describe how the neuronal systems can be modeled, various types of activity patterns that arise in these models, and mechanisms for how the activity patterns are generated.

Workshop activities include posters and a Discussion Session in the afternoon that will focus on applied mathematics programs and funding of collaborative applied mathematics activities. Peter March, Mathematics Department, Ohio State University; and Hans Kaper, NSF and Argonne Research Laboratory, will join the above speakers in this discussion session.

Applied Mathematics Program Advisory Committee:

Joseph Rosenblatt
Professor and Chair
Department of Mathematics
University of Illinois at Urbana-Champaign
Urbana, IL 61801
Email: jrsnbltt@math.uiuc.edu
Phone: 217-333-3352
Fax: 217-333-9576

Last modified May 13, 2003