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MONDAY, May 1, 2000
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MATHEMATICAL BIOLOGY SEMINAR
PSA 307 12:40 p.m.
(Co-sponsor: Systems Science and Engineering Research Center)
S.A.L.M. Kooijman, Free University, Amsterdam
"The Synthesizing Unit as Model for the Interaction of
Substrates in the Uptake by Organisms"
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TUESDAY, May 2, 2000
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COMPUTATIONAL AND APPLIED MATH PROSEMINAR GWC 604
12:30 p.m.
Rosemary Renaut, Department of Mathematics
"Kinetic Parametric Estimation Using Positron Emission
Tomographic Data"
ABSTRACT: In this talk I will present a simple model that
describes FDG dynamics in the brain. Using PET data to estimate
the output from this model, we obtain an inverse problem for
the determination of kinetic rate constants for different
tissue types in the brain. I will describe several solution
techniques based on least squares, and total least squares
algorithms. This is initial work on which the development of a
whole brain parametric imaging technique will be based. The
research is joint with Cristina Negoita in our department, and
Dr. Kewei Chen of the Good Samaritan PET Center in Phoenix.
See http://plato.la.asu.edu/compsem.html
Talks Given
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FRIDAY, January 28, 2000
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MATHEMATICAL BIOLOGY SEMINAR
PSA 106 12:40 p.m.
(Co-sponsor:
Systems Science and Engineering Research Center)
Yang
Kuang, Department of Mathematics
"Theoretical Frameworks for Ecological Dynamics Subject to
Stoichiometric Constraints"
ABSTRACT:
All organisms are composed of multiple chemical
elements
such as carbon, nitrogen, and phosphorus. Although
the
relative abundance of these chemical constituents is known
to
vary considerably among species and across trophic levels,
most
ecological studies have until very recently ignored the
sources
and consequences of this chemical heterogeneity.
However,
rapidly accumulating evidence suggests that the
dynamic
implications of chemical heterogeneity among species
deserves
much more study than it has yet received. This body of
research,
which is to date chiefly empirical in nature, places
major
emphasis on the consequences of chemical heterogeneity
among
species for consumer-resource dynamics and nutrient
recycling
in ecosystems.
In this talk, we will outline a theoretical framework for
ecological
dynamics that explicitly incorporates stoichiometric
constraints.
The base model involves a stoichiometric counterpart
of
the familiar Rosenzweig-MacArthur equations in which the
effective
carrying capacity of the resource species and the
transfer
efficiency of the consumer species are constrained by
stoichiometric
principles. Introduction of stoichiometric
considerations
in these equations (here, akin to "food quality")
allows
for a rich array of ecologically realistic dynamics,
including
deterministic extinction of the consumer species when
resources
are abundant but of poor quality.
We will expand this model in several different directions, to
explore
ecological realities whose consideration has proved
illuminating
in other, non-stoichiometric settings.
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FRIDAY, February 4, 2000
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MATHEMATICAL
BIOLOGY SEMINAR
PSA 106 12:40 p.m.
(Co-sponsor:
Systems Science and Engineering Research Center)
Horst
Thieme, Department of Mathematics
"What can we Learn from the Most Elementary Stage-Structured
Population Model?"
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February 14, 2000
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Note different day and time for
this seminar:
MATHEMATICAL BIOLOGY SEMINAR
PSA 103 3:40 p.m.
(Co-sponsor: Systems Science and Engineering Research Center)
Duane Nykamp, Courant Institute of Mathematical Sciences, NYU
"A Population Density Approach That Facilitates Large-Scale
Modeling of Neural Networks"
ABSTRACT: The neural networks of even small functional units
in the brain are enormously complex. Conventional simulation
methods, where one models thousands of individual neurons, can
take large amounts of computer time even for models of small
cortical areas. The population density approach can be used
to speed up large-scale neural network simulations. In this
method, ones groups neurons into large populations of similar
neurons. By calculating the evolution of a probability density
function for each population, one obtains population firing
rates and the distribution of neurons over state space.
I demonstrate a population density method for simulating
networks of integrate-and-fire neurons with instantaneous
synapses or with slow inhibitory synapses. Through comparisons
with conventional Monte-Carlo simulations for a model of a
hypercolumn in cat visual cortex, I demonstrate the speed and
accuracy of the population density method.
FRIDAY, March 3, 2000
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Joint
MATHEMATICAL BIOLOGY SEMINAR
DYNAMICAL SYSTEMS SEMINAR
PSA 106 12:40 p.m.
(Co-sponsor: Systems Science and Engineering Research Center)
Eugene Izhikevich, Department of Mathematics
"Classification of Bursting Dynamics"
ABSTRACT: A neuron is said to exhibit bursting dynamics when its
behavior alternates between spiking (oscillation) and rest
(quiescence). The history of formal classification of bursters
starts from the seminal paper by Rinzel (1987), who contrasted
the bifurcation mechanism of the "square-wave", "parabolic", and
"elliptic" bursters. We use geometric bifurcation theory to
extend the existing classification of bursters, including many
new types. We show how the type of burster affects its
neuro-computational properties.
Additional Information:
http://math.la.asu.edu/~eugene/publications/nesb.htm
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FRIDAY, March 10, 2000
MATHEMATICAL BIOLOGY SEMINAR
PSA 106 12:40 p.m.
(Co-sponsor: Systems Science and Engineering Research Center)
Horst Thieme, Department of Mathematics
"When can a Cannibalistic Strain Invade a Tiger Salamander
Population?"
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FRIDAY, March 24, 2000
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MATHEMATICAL BIOLOGY SEMINAR
PSA 106 12:40 p.m.
(Co-sponsor: Systems Science and Engineering Research Center)
Diana Verzi, Claremont Graduate University
"A Nonlinear Cable Model for Activity-Dependent Spine
Densities"
ABSTRACT: The spread of electrical activity in a dendritic
tree is shaped, in part, by its morphology (its branching
structure, geometry, spine distribution). Conversely,
experimental evidence is growing that electrical activity can
slowly shape the morphology of the dendrite and regulate the
density of dendritic spines. In this talk a nonlinear cable
model is formulated to explore how activity-dependent changes
in spine densities (minutes to hours) can influence patterns
of electrical activity; and how electrical activity due to
synaptic events and excitable membrane properties can, over
time, influence the spine distribution and hence the morphology
of the dendrite. In the model, the distribution of spines is
treated as a continuum rather than discretely, and the spine
density is modeled as a slow dynamic variable. The system of
differential equations is autonomous. A minimal model is
proposed where the local change in spine density depends on
local electrical activity, measured by current flow between
the spine head and the dendritic shaft. For spines with
passive spine head membrane, we show how spine densities can
increase in regions of sustained synaptic activity, and how
existing spines can wither away when deprived of synaptic
activity. For excitable spines, we demonstrate how pathways
for impulse propagation can be forged over time, due to the
recruitment of distal spines.
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FRIDAY, April 14, 2000
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MATHEMATICAL BIOLOGY / STATISTICAL GENOMICS SEMINAR
NOTE DIFFERENT ROOM AND TIME:
ECA 221 12:40 p.m.
(Co-sponsor: Systems Science and Engineering Research Center)
Laura Salter, University of New Mexico
"A Stochastic Search Strategy for Estimation of Maximum
Likelihood Phylogenetic Trees"
ABSTRACT: A common goal in the analysis of nucleotide sequence
data sets is the inference of the phylogenetic history of the
sequences under consideration. Although many criteria for the
selection of a phylogenetic representation of the data are
available, the maximum likelihood method of phylogenetic tree
construction has several advantages over other criteria.
These include the interpretability of the underlying models,
consistency in the statistical sense, and the possibility of
statistical testing of hypotheses using the likelihood framework.
However, use of the maximum likelihood method in practice has
been limited by two significant difficulties in its
implementation. The first is that existing implementations of
the method can be quite time-consuming when the number of
sequences under consideration is large. The second is that
current algorithms used to implement the method seem to be
prone to entrapment in local maxima when the data are
sufficiently complex. To overcome these difficulties, we
propose a stochastic search strategy for estimation of the ML
tree which incorporates ideas from both the simulated annealing
algorithm and the stochastic probing algorithm. The algorithm
works by moving through tree space via a "local rearrangement"
strategy so that topologies that improve the likelihood are
always accepted, while those that decrease the likelihood are
accepted with a probability that is related to the
proportionate decrease in likelihood. In addition to greatly
reducing the time required to estimate the ML tree, the
stochastic search strategy is much less likely to become
trapped in local optima than are existing algorithms for ML
tree estimation. The success of the algorithm will be
demonstrated by comparison to two existing algorithms
(Felsenstein's DNAMLK and Swofford's PAUP*) for several
theoretical and real data examples. Extensions of the current
algorithm to include simultaneous estimation of the parameters
in the underlying nucleotide substitution models will also be
discussed.
This is joint work with Dennis Pearl (Ohio State University).
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MONDAY, April 24, 2000
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MATHEMATICAL BIOLOGY SEMINAR
PSA 307 12:40 p.m.
(Co-sponsor: Systems Science
and Engineering Research Center)
Dung Le, University of Texas
at San Antonio
"On a Time Dependent
Cross Diffusion System"
ABSTRACT: Long time
dynamics of solutions to a strongly
coupled system of parabolic
equations modelling the
competition in bio-reactors
with chemotaxis will be studied.
If the parameters of the
system are periodic, sufficient
conditions for positive
periodic solutions will be derived
in terms of parabolic eigenvalue
problems.
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NONLINEAR DYNAMICS / MATHEMATICAL BIOLOGY SEMINAR
PSA 103 3:40 p.m.
(Co-sponsor: Systems Science
and Engineering Research Center)
Ira Schwartz, Naval Research
Laboratory, Washington
"Noise Induced
Chaos in Population Dynamics"
ABSTRACT: In many
model models of population dynamics, which
include epidemics and lasers
in the semi-classical limit,
quadratic nonlinearities
play an important role in the global
behavior of dynamical transients.
That is, when population
models are modeled deterministically
using estimated parameters
from measurements, predictions
are periodic in contrast to
observed chaotic oscillations.
In this talk, I will review the
global topology of some
simple examples of population models,
and show how stochastic
parameters can generate chaotic
behavior. In adition, one
can use these ideas to generate
sustained chaos where there
is no chaotic attrcator.
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Fall, 1997 talks
Spring, 1998 talks,
Fall, 1998
talks
Spring, 1999
Fall, 1999