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Upcoming Seminars
MONDAY, February 18, 2008
GRADUATE STUDENT RESEARCH SEMINAR PSA 103 12:00 p.m.
Russ Park, Department of Mathematics and Statistics
"Optimal Compression and Numerical Stability of Gegenbauer
Reconstructions"
ABSTRACT: Image reconstruction methods are characterized by the
source data space on which they operate, the range space and
the degree to which objectives such as artifact suppression,
compression and numerical stability are optimized. The
Gegenbauer reconstruction method operates on Fourier source
data, projecting it onto a finite set of Gegenbauer polynomials.
Gegenbauer data is then expanded on sub-domains of physical
space segmented by presumed jump discontinuities in the source
data. The absence of jump discontinuities within each sub-domain
assures spectral convergence as long as reconstruction
parameters lambda and m linearly track the resolution N as it
approaches infinity. The implicit benefit of Gegenbauer
reconstruction is source data compression, unfortunately the
process is also limited by numerical instability as either
lambda or m, or both, increase.
Early studies on this issue assumed lambda and m to be
linearly tied to N and then characterized the bounds of
instability as well as recommended safe reconstruction
parameter combinations. Subsequent work demonstrated how to
automatically predict the source data smoothness parameters, of
which apriori knowledge is required for accurate
reconstruction. This study performs asymptotic analyses on the
predicted error bounds as N goes to infinity while fixing
either m or lambda, leading to the discovery of reconstruction
parameters optimized for an objective of either compression or
numerical stability. Finally, the effectiveness of this new
approach is illustrated by extensive numerical experiments.
Bagels, coffee and tea will be served in PSA 103 at 11:50 a.m.
TUESDAY, February 19, 2008
MATHEMATICS AND COGNITION SEMINAR PSA 206 12:45 p.m.
Joel Gereboff, Department of Religious Studies
Christopher Duncan, Department of Religious Studies,
School of Global Studies
"Social Identity"
ABSTRACT: The term "social identity" is related to the
propensity of individuals to conflate identity as membership in
a social group. This talk will discuss theories of social
identity and discuss assumptions at the foundation of these
theories.
Cookies and coffee will be served at 12:30 p.m.
APPLIED ANALYSIS AND PDE READING SEMINAR PSA 546 3:00 p.m.
For more information, contact Svetlana Roudenko.
WEDNESDAY, February 20, 2008
COMPUTATIONAL AND APPLIED MATHEMATICS PROSEMINAR
GWC 487 2:00 p.m.
Russ Park, Department of Mathematics and Statistics
"Optimal Compression and Numerical Stability of Gegenbauer
Reconstructions
ABSTRACT: Image reconstruction methods are characterized by the
source data space on which they operate, the range space and
the degree to which objectives such as artifact suppression,
compression and numerical stability are optimized. The
Gegenbauer reconstruction method operates on Fourier source
data, projecting it onto a finite set of Gegenbauer polynomials.
Gegenbauer data is then expanded on sub-domains of physical
space segmented by presumed jump discontinuities in the source
data. The absence of jump discontinuities within each sub-domain
assures spectral convergence as long as reconstruction
parameters lambda and m linearly track the resolution N as it
approaches infinity. The implicit benefit of Gegenbauer
reconstruction is source data compression, unfortunately the
process is also limited by numerical instability as either
lambda or m, or both, increase.
Early studies on this issue assumed lambda and m to be
linearly tied to N and then characterized the bounds of
instability as well as recommended safe reconstruction
parameter combinations. Subsequent work demonstrated how to
automatically predict the source data smoothness parameters, of
which apriori knowledge is required for accurate reconstruction.
This study performs asymptotic analyses on the predicted error
bounds as N goes to infinity while fixing either m or lambda,
leading to the discovery of reconstruction parameters optimized
for an objective of either compression or numerical stability.
Finally, the effectiveness of this new approach is illustrated
by extensive numerical experiments.
CRESMET COLLOQUIUM University Center 201 3:30 p.m.
1130 E. University Dr. (behind Chompies)
(Hosted by Center for Research on Education in Science,
Mathematics, Engineering and Technology)
Brett van de Sande, University of Pittsburgh
"Andes: An Intelligent Tutor Homework System for Introductory
Physics"
ABSTRACT: Andes (www.andes.pitt.edu) is an intelligent tutor
homework system designed for students taking an introductory
physics course. It encourages students to use sound problem-
solving techniques and provides immediate feedback on each
student entry, along with hints on request. I will discuss how
Andes works, from the perspective of a student, and summarize
research demonstrating its effectiveness as a pedagogical tool.
I will also discuss Andes as a vehicle for conducting education
research, focusing on a study of individual versus pair problem
solving while using Andes.
COMPUTATIONAL AND APPLIED MATHEMATICS PROSEMINAR
GWC 487 3:30 p.m.
Kangyu Ni, University of California, Los Angeles
"Local Histogram Based Segmentation Using the Wasserstein
Distance
ABSTRACT: We propose and analyze a nonparametric region-based
active contour model for clutter segmentation. This
segmentation model is unsupervised and assumes pixel intensity
is independently identically distributed. The proposed energy
functional consists of a geometric regularization term that
penalizes the length of region boundaries, and a region-based
image term that uses the probability density function (or
normalized histogram) of pixel intensity to distinguish
different regions. More specifically, the region term attempts
to find a partition so that the local histograms at each pixel
in each region are similar to one another. The similarity
between normalized histograms is measured by the Wasserstein
distance with exponent 1.
We employ a fast global minimization method based on Bresson
et al.'s work to solve the proposed model. The advantages of
this method include the ability to find a global minimize and
less computational time compared with the standard minimization
method by the gradient descent of the associated Euler-Lagrange
equation. Moreover, our proposed model has several desired
properties due to the use of the Wasserstein distance with
exponent 1. For instance, the proposed model is contrast
invariant and intrinsically insensitive to noise. Both the
proofs of these properties and experimental results will be
presented. We further propose a variant of the proposed model
that deals with local illumination changes in an image.
THURSDAY, February 21, 2008
ADAPTIVE NEURAL SYSTEMS SEMINAR AND
MATH BIOLOGY SEMINAR COOR L1-20 4:00 p.m.
(Jointly hosted by Center for Adaptive Neural Systems and
Department of Mathematics & Statistics)
John Rinzel, Center for Neural Science,
Courant Institute of Mathematical Sciences,
New York University
"Dynamics of Perceptual Bistability"
ABSTRACT: When visualizing an ambiguous scene (such as the
Necker cube) one may perceive ongoing temporal alternation
between the possible interpretations. Various dynamical models
lead to alternating mutual exclusivity with neuronal
competition implemented as reciprocal inhibition between
neuronal populations. Slow negative feedback sets the basic
time scale (seconds) for switching. We will describe two
mechanistic frameworks for the switching behavior. If the
negative feedback is strong enough it can overcome dominance
and alternations occur intrinsically and periodically; noise
perturbs the regularity. In an alternative, attractor-based,
framework negative feedback is relatively weaker and switches
are induced by noise operating on a bistable system. Statistics
of the observed alternations provide constraints that favor an
operating range near the transition zone between the two
mechanisms.
FRIDAY, February 22, 2008
COLLOQUIUM (SCHOOL DIRECTOR CANDIDATE) PSF 101 1:30 p.m.
Wayne Raskind, University of Southern California
"Public Key Cryptography, Number Theory and Arithmetic
Geometry"
ABSTRACT: Many public key cryptographic systems are based on
the discrete logarithm problem for finite abelian groups. In
this talk, we will briefly review how this works and present
some of our research (joint with Ming-Deh Huang of the USC
Computer Science Department) on a general method for treating
this problem for abelian algebraic groups over finite fields.
We will then describe in some detail the cases of the
multiplicative group and elliptic curves over finite fields,
which reveal some surprising connections between the discrete
logarithm problem and some fundamental problems in number
theory and arithmetic geometry.
Refreshments will be served in PSA 206 at 1:00 p.m.
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