Department Colloquium
Talks in Spring 2003
Time and place: January 21 (Tuesday),
2:00 p.m. Jones 131.
Speaker: Cameron Parker (Department of
Mathematics, University of California, San Diego)
Title: Unit Root Testing via the Stationary
Bootstrap
Abstract: A nonparametric, residual-based
stationary bootstrap procedure is proposed
for testing for the presence of a unit root in a given time
series. The procedure gives a way
of generating a pseudo series which mimics the original
in terms of dependence structure but
that has the property of having a unit root. To develop
this test a brief introduction to the
bootstrap and time series analysis is given as well as defining
both the
stationary bootstrap and unit root processes.
Time and place: February 10 (Monday),
3:00 p.m. Jones 131.
Speaker: Jeff Moehlis (Program
in Applied and Computational Mathematics, Princeton University)
Title: Response of Neurons in the Brain
Region Locus Coeruleus to Stimuli
Abstract: Experimental data shows that
neurons in a region of the brain known as the locus coeruleus (LC)
can exhibit two distinct firing patterns which are strongly correlated
with performance on cognitive tasks. In the phasic mode, associated
with good performance, the baseline firing rate is lower and the neurons
show enhanced reponse. In the tonic mode, associated with poor
performance, the average baseline firing rate is higher and the neurons
are less reponsive. From membrane voltage and
ion channel equations, we derive a phase oscillator model
for LC neurons. Average firing probabilities of a pool of neurons in
response to stimuli over many trials are then computed via a probability
density formulation. Using this, we show that: (1) Response is elevated
in populations with lower baseline firing rates; and (2) Response decays
due to noise and distributions of neuron frequencies. These results
may account for much of the experimental response variability.
Time and place: February 14 (Friday), 3:00
p.m. Jones 131.
Speaker: Loius Tao (Courant Institute
of Mathematical Sciences, New York University)
Title: A Neuronal Network Model of the
Primary Visual Cortex
Abstract: Visually responsive neurons
in the primary visual cortex (V1) are generally separated into two broad
classes: those that show approximately linear responses (Simple cells)
and those that do not (Complex cells). It is an open problem as
to how these differing responses actually arise within V1. Guided
by simulations of a large-scale, biologically realistic neuronal network
model, I offer an explanation. My results suggest that a broad
spectrum of balances between visual stimulation and network excitation
underlies the Simple-Complex response diversity as is seen in recent
experiments. I will also discuss future directions for large-scale
cortical modeling.
Time and place: February 17 (Monday), 3:00
p.m. Jones 131.
Speaker: William Casey (Courant Institute
of Mathematical Sciences, New York University)
Title: Graph Embeddings with Application
to Genomic Experiments
Abstract: Inference of global structure
from data which are accurate only on a local scale is common to many
problems in mathematical biology. In an application called `probe-mapping',
motivated by goals to characterize gene copy events in cancer cells, we
address an NP-hard problem concerning Graph Embeddings with efficient heuristics.
We provide model-based analysis of the heuristic argument and prove the
correctness of its result with probability very close to 1 on a relevant
set of inputs. The result is a design for realistic experiments
capable of characterizing genome structure.
Time and place: February 20 (Thursday), 4:00
p.m. Morton 20.
Speaker: Michael Gertz (Northwestern
University)
Title: Interior-Point Optimization through
Trust Regions
Abstract: We describe a trust-region
approach to non-convex, nonlinear optimization. The method, based on
a merit function of Forsgren & Gill, handles non-convexity correctly
and has excellent convergence properties. The algorithm uses off-the-shelf
linear equation solvers, allowing us to leverage years of research in
numerical linear algebra.
Time and place: March 14 (Friday), 4:00 p.m. Jones
131.
Speaker: Alexander Pankov (Department
of Mathematics, Texas A&M University)
Title: Traveling waves in lattice dynamical
systems
Abstract: We consider the following class
of 1-dimensional lattice dynamical
systems: chains of particles with nearest neighbor interaction. We
prove
the existence of spatially periodic traveling waves with prescribed
speed
and an arbitrary period. We also study the asymptotic behavior of such
waves
for large values of periods and show that they converge in an appropriate
topology to a solitary traveling wave. As a consequence, the existence
of
solitary waves is obtained.
Time and place: March 21 (Friday), 4:00 p.m. Jones
131.
Speaker: Simon Gindikin (Department
of Mathematics, Rutgers University)
Title: Complex geometry of real symmetric spaces
Abstract: The discovery of symmetric spaces
by E. Cartan is one of the most brilliant achievements of geometry of
XX century. These spaces possess a very expressive non Euclidean geometry
and as a result they are a field for very deep multidimensional analysis.
In XIX century Poncelet and Pluecker found that complex geometry is responsible
for many facts of real geometry. I will discuss several new examples of
such nature in geometry of symmetric spaces. It was shown that
each (real) Riemannian symmetric space has a canonical complex neighborhood
- a complex crown , which universally appears in geometric and analytic
problems. In special cases this construction reduces to some problems about
matrices, partly classical, partly new ones.
See also Cissy Patterson Lecture
by Professor Gindikin
Time and place: April 25 (Friday), 3:00 p.m. Jones
131
Speaker: Ratnasingham Shivaji
(Deptment of Mathematics and Statistics, Mississippi State University)
Title: An Existence result on positive solutions for
a class of semilinear elliptic systems.
Abstract: Consider the system
-\Delta u=\lambda f(v)\text{ \ in }\Omega \\
-\Delta v=\lambda g(u)\text{ \ in }\Omega \\
u=v=0\;\text{\ on }\partial \Omega ,
where $\lambda $ is a positive parameter and $\Omega $ is a bounded domain
in $R^{N}.\;$We prove the existence of a large positive solution for $\lambda
$ large when lim$_{x\rightarrow \infty }\frac{f(Mg(x))}{x}=0$ for every $M>0.$
In particular, we do not need any monotonicity assumptions on $ f,g$ nor any
sign conditions on $f(0),g(0).$
Time and place: May 14th (Wednesday), 3:00 p.m. Jones
301
Speaker: Tiancheng Ouyang (Deptment of
Mathematics, Brigham Young University)
Title: Periodic Orbits of N-body Problems in
Celestial Mechanics and Computer Simulation
Abstract: The classical N-body problem of celestial
mechanics concerns the motion of N point masses governed by the universal
gravitation law in the Euclidean space. In this talk I will introduce a new
approach for the existence and the construction of preassigned orbits.
This approach uses variational method to minimize an energy functional and
optimize the corresponding boundary value problem. Many interesting
periodic and quasi-periodic solutions in two and three dimensional spaces
with different topological structures have been constructed. Our numerical
simulation shows many interesting properties of those orbits.
Talks in Fall 2002
Time and place: September 27 (Friday), 3:00 p.m. Jones
131.
Speaker: Peter W. Bates (Professor and
Chairman, Department of Mathematics, Michigan State University)
Title: A new class of evolution equations
suggested by phase transition in materials
Abstract: Starting with the basic idea
of energy and the need to decrease energy (increase entropy) during
the evolution of a state one may derive some mathematically interesting
equations. I will show this derivation and attempt to justify the word
"interesting". If there is time, I will discuss homotopy methods,
spectral theory, and the use of weak convergence to be employed in the
analysis of the equations.
Time and place: November 1 (Friday),
3:00 p.m., Jones 131.
Speaker: Robert Reams (Instructor, Department
of Mathematics, College of William and Mary)
Title: Constructions of trace zero symmetric
stochastic matrices for the inverse eigenvalue problem
Time and place: November 8 (Friday),
3:00 p.m., Jones 131.
Speaker: John H. Lowenstein
(Professor, Department of Physics, New York University)
Title: Computer-assisted analysis of
two-dimensional piecewise isometries with rational rotation number.
Time and place: November 11 (Monday),
1:00 p.m., Jones 302.
Speaker: James R. Wilson (Professor and
Head, Department of Industrial Engineering, North Carolina State University)
Title: Using nonhomogeneous Poisson processes
to drive the UNOS Liver Allocation Model (UNOS is the Organ Sharing
organization headquartered in Richmond and a large-scale simulation
model was developed to determine optimal distribution policies)
Time and place: November 22 (Friday),
3:00 p.m., Jones 131.
Speaker: Sivaram Narayan
(Professor, Department of Mathematics, Central Michigan University
and College of William and Mary)
Title: Nonnegative matrices with prescribed
spectra
Time and place: December 9th (Monday),
3:00 p.m., Jones 131.
Speaker: Percy Deift, (Professor,
Courant Institute of Mathematical Sciences, New York University)
Title: Perturbation theory for infinite
dimenional integrable systems. A case study |
