FRIDAY, Nov. 20, Floyd Hanson, Department of Mathematics, Univ. Illinois, Chicago.
Optimal Harvesting with Both Population and Price Stochastic Dynamics
FRIDAY, Nov. 27, Thanksgiving, no talk.
FRIDAY, Dec. 4, Dritan Zela, Department of Mathematics, ASU
"How
to Construct Better High-Dimensional Population Models"
ABSTRACT: Mathematical population
models are constructed based on
plausible explicit and many
implicit biological assumptions. While
it is easy to incorporate
explicit assumptions correctly in the
model, those implicit ones
are often ill treated. Indeed, this
happens to many popular
models in the literature and examples of
such will be mentioned.
For a model to be logically credible, we
must do our best to ensure
that all assumptions are incorporated
consistently. To this end,
a simple set of criteria is proposed by
Arditi and Michalski in
1996. Following this set of criteria and
other well accepted biological
assumptions, we introduce two
interesting three dimensional
ratio-dependent population models.
ATTENTION: TIME CHANGE:
Monday, Sept. 21, PSA 308:
Zhu Jun Jing , Institute of Mathematics, Academic
Sinica, PRC
Local and Global Bifurcations and Applications in Biomath
Abstract: The first part of this talk is to briefly present the
bifurcations of fixed point and periodic solutions, global
bifurcation, some results from bifurcations to chaos, and some
methods of investigating bifurcations. The second part of the
talk is to discuss the applicaions of bifurcation theory in some
AIDS, infection disease and predator-prey's models.
FRIDAY, SEPTEMBER 25, 1998
Irakli Loladze, Department of Mathematics
"Paradox
Of Energy Enrichment: Application of Stoichiometry
to Predator-Prey Models"
ABSTRACT: In 1971 Rosenzweig
proposed Paradox of Enrichment
showing that energy or nutrient
enrichment of the prey population
in stable predator-prey
system results in increase of the predator
biomass leaving prey biomass
at the same level. Further enrichment
results in destabilizing
effect on the system. Recent experiments
by Urabe and Sterner show
that energy (light) enrichment of the
phytoplankton population
(prey) can result in higher prey biomass
and lower growth rates of
zooplankton (predator). This paradoxical
result, which one can call
the Paradox of Energy Enrichment,
contradicts the basic assumption
that more prey is never worse for
the predator and can not
be explained by arguments based solely on
energy flows. Concept of
energy flow through trophic levels is the
main tool in ecosystem modeling
and is present in all modifications
of Lotka-Volterra models.
Adding to this concept the stoichiometric
principles one can explain
the above experiments. The
stoichiometric concepts
will be presented and the two-dimensional
model capturing the negative
effect of energy enrichment on the
consumer (predator) will
be presented.
FRIDAY, Oct. 2 , Hristo Kojouharov, Department of Mathematics,ASU
Accurate Numerical Solution to a Subsurface Biobarrier Formation Model
Abstract: Biofilm forming microbes have complex effect on the flow properties
of natural porous media. Subsurface biofilms have the potential for
biotransformation of organic contaminants, and also to form biobarriers
to
inhibit contaminant migration in groundwater. To describe the population
distribution and movement of bacteria we consider the
numerically challenging convection-dispersion equation with nonlinear
reactions. Nonstandard numerical methods are developed based on the
ideas
of "exact" time-stepping schemes. The new approach leads to significant,
qualitative improvements in the behavior of the numerical solution.
Numerical results for a simple biobarrier formation model are presented
to demonstrate the performance of the proposed new method.
THE CENTER FOR SYSTEMS SCIENCE PRESENTS
Cellular Neural Network Workshop
Date: Friday, October 9, 1998
Place: Goldwater, Room 487
Time: 3:00–5:00
3:00 Introduction: Frank Hoppensteadt, Director of SSERC
3:05–3:45 Leon O. Chua, Professor, Department of Electrical Engineering,
UC-Berkeley
"CNN: A brain-like dynamic array computer on a chip"
Abstract
This talk will present an introduction to the Cellular Neural Network (CNN)
universal chip, which consists of
an array of CMOS circuit cells, where each cell is coupled only to its
nearest neighbors. In addition to
mimicking the salient characteristics of a biological neuron, each cell
is endowed with analog and logic
memory registers, as well as control-communication interfacing circuitry
for executing stored programs, as in
digital computers. However, its working principle is based on nonlinear
dynamics operating at nanosecond
time scales. The CNN universal chip is a universal Turing machine capable
of universal computation. It is a
von Neumann stored program computer, supported by a user-friendly high-level
C-like language, an
operating system, and a compiler. In particular, any cellular automata
can be executed on the CNN universal
chip. It can mimic most vision-related brain functions and is ideally suited
for high-speed image processing and
video applications, such dynamic scene analysis and segmentation, real-time
image fusion, and artificial vision.
3:50–4:30 Tamas Roska Professor, Technical University of Budapest,
Computer and Automation
Institute
"Computing infrastructure and physical implementation of TeraOPS CNN vision
microprocessors"
Abstract
Programmability and efficiency are conflicting goals. In the analogic CNN
array processor architecture, these
conflicts are resolved in a unique way, by exploiting a combination of
spatio-temporal dynamics and logic
(analogic operation). The main themes of the lecture are:
1) from high level language to the extended analogic cell processor
2) from smart sensors to dynamic programmability-circuit aspects
3)keys to make a trillion operation per second vision chip with optical
input-review of the current chip designs
4)10,000 processor chips and beyond - the bottlenecks
5)multi-spectral image fusion - a must for TeraOps chips
FRIDAY, October 16, 1998 NOTE CHANGE
OF ROOM AND TIME!
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COLLOQUIUM & MATHEMATICAL
BIOLOGY SEMINAR PSA 203 3:30 p.m.
(Co-sponsor: Systems Science
and Engineering Research Center)
Marek Kimmel, Statistics
Department, Rice University
"Mathematical Models in Population Genetics, Lyapunov
Differential Equation and Migrations of Early Modern Humans"
ABSTRACT: We derive new
results concerning mathematical description
of genetic composition of
populations under the time-continuous
Fisher-Wright-Moran model
with mutations of the general
Markov-chain form.
Unexpectedly, the matrix R(t) (possibly
infinite) of the joint distributions
of the types of a pair of
alleles sampled from the
population, satisfies a matrix
differential equation of
the Lyapunov type, known in control
theory. Investigation of
behavior of its solutions leads to
consideration of tensor
products of transition (Markov) semigroups.
Semigroup theory
methods allow to prove asymptotic results for
the model, also in the cases
when the population size does not
stay constant. An important
special case of the model arises when
the Markov chain of mutations
has the form of an unrestricted
random walk. stepwise mutation
models with and without allele
size constraints, and with
directional bias of mutations. This
form of mutation process
is used to describe the evolutionary
dynamics of the so-called
repeat-DNA.
An interesting
application involves modeling evolutionary
dynamics of repeat-DNA in
human populations and estimation of
the migrations of early
modern humans (200,000-50,000 ybp).
Refreshments will be served at 3:00 p.m. in PSA 206.
FRIDAY, Oct. 23,
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MATHEMATICAL BIOLOGY SEMINAR
PSA 308 2:40 p.m.
(Co-sponsor: Systems Science
and Engineering Research Center)
Jiping He, Bioengineering,
ASU and Whitaker Center for
Neuromechanical Control
title to be announced
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FRIDAY, Oct. 30, Hal Smith, Department of Mathematics , ASU
Title: Microbial Competition for nutrient and wall sites in plug flow
abstract
A mathematical model of microbial competition for limiting nutrient
and for a limited set of available wall-attachment sites in an
advection-dominated tubular reactor is formulated as a limiting
case of the more general model considered in \cite{ballyk2}. The
model consists of a system of hyperbolic partial differential
equations. The existence and stability properties of its steady
state solutions are investigated, both analytically and
numerically. A surprising finding in the case of two-strain
competition is the existence of a steady state solution
characterized by the segregation of the two bacterial strains to
separate non-overlapping segments along the tubular reactor.
FRIDAY, Nov. 6, Xiao-Qiang Zhao, Department of Mathematics, ASU
``Target Patterns and Spiral Waves in Reaction-Diffusion
Systems with Limit Cycle Kinetics and Weak
Diffusion"
ABSTRACT: Target patterns and spiral waves are commonly observed
in certain models of chemical and biological systems such as the
Belousov-Zhabotinskii reaction and the slime mold Dictyostelium
discoideium. These systems are governed by a chemical or biological
reaction and spatial diffusion, i.e. reaction-diffusion equations.
Generally speaking, a target pattern is a set of concentric rings
of constant concentration each moving outward. Along any radial
line, the pattern behaves asymptotically like a periodic travelling
wave. A spiral wave is a rotating, time periodic, spatial structure
of reactant concentrations where at a fixed time, a snapshot shows
a
typical spiral pattern. There are two important kinds of
reaction-diffusion systems with quite different mechanisms:
one with excitable kinetics and the other with oscillatory kinetics.
In this talk, we will discuss general reaction-diffusion systems with
limit cycle kinetics and weak diffusion. The results are based on
the analysis of a nonlinear partial differential equation which is
derived from singular perturbation techniques. We obtain the first
order approximation expression of the dispersion curve for periodic
wave trains and then show that in the generic case of limit cycle
kinetics there is a one parameter family of target patterns and
rotating spiral waves of Archimedian type exist. Finally, we use
these results to discuss the lambda-omega systems.