Madison
Chaos and Complex Systems Seminar

## Spring 1996 Seminars

Dates, speakers, titles and abstracts will be listed as they become
available.
Tentatively, meetings will be noon Tuesdays in 4274 Chamberlin Hall.
#### Short List

- 30 January. Self-organizational
meeting.
- 6 February. Fred Brauer: ``Recruitment
into
a
Core
Group and Its Effect on the Spread of a Sexually Transmitted
Disease.''
- 13 February. Jude W. Shavlik:
``Providing
Advice to
Agents that Learn from Reinforcements''
- 20 February. W. Davis Dechert:
``Spurious
Lyapunov
Exponents in Reconstructed Dynamics.''
- 27 Feburary. Kevin Mirus: ``Effects of
Periodic Perturbations
on Nonlinear Systems.''
- 5 March. Sean B. Carroll: `` Development
and
Evolution
of Butterfly Wing Patterns.''
- 12 March. Spring break --- no seminar
- 19 March. Robert L. Wilson: ``Iterated
Function Systems.''
- 26 March. John Anderson: ``The Solution
of
Signal
Processing Problems Using Genetic Programming Techniques.''
- 2 April. Michael Bleicher: ``A Model for
Interdisciplinary
Programs? --- Symmetry across the Curriculum.''
- 9 April. Clint Sprott: ``Is It Noise, or
Is
It
Chaos?''
- 16 April. David Griffeath:
``Self-Organization
of
Random Cellular Automata''
*in B231 Van Vleck*
- 23 April. Kellie Evans: ``Larger than
Life.''
- 30 April. Cosma Shalizi: ``Is the
Primordial
Soup
Done Yet? Quantifying Self-Organization, Especially in Cellular
Automata.''
- 7 May. Troy Shinbrot: ``Something for
Nothing:
The
Role of Voids in Granular Convection.''

#### 30 January. Self-organizational meeting

Hopefully short. Bring ideas for possible speakers. We will also be
considering
whether to make the seminars less formal and more interactive.

#### 6 February. Fred Brauer, UW Mathematics.
``Recruitment
into a Core Group and Its Effect on the Spread of a Sexually
Transmitted
Disease.''

*Abstract:* In models for the transmission of a sexually
transmitted
disease it is natural to separate the population into groups with
different
levels of sexual activity and to concentrate on a core group of
extremely
active individuals. We begin with an extremely simple model in which
only
the core members are sexually active, but there is a rate of
recruitment
of new members into the core which depends on the prevalence of
infection
among core members. It is possible to have an unstable endemic
equilibrium
with slow oscillations of large amplitude for the infective
population.
If we refine the model by including sexual activity among non-core
members
as well, counter-intuitive behavior is possible. For example, an
increase
in the rate of activity by non-core members may stabilize the system
and
reduce the prevalence of infection. It is not proposed to use this
approach
to control the spread of sexually transmitted diseases.

#### 13 February. Jude W. Shavlik, UW Computer
Sciences.
``Providing Advice to Agents that Learn from Reinforcements.''

*Abstract:* Learning from reinforcements is a promising
approach
for
creating intelligent agents. However, this style of machine learning
usually
requires a large number of training episodes. We present an approach
that
addresses this shortcoming by allowing a reinforcement learner to
accept
advice given, at any time and in a natural manner, by an external
observer.
In our approach, the (human) advice-giver watches the learner and
occasionally
makes suggestions, expressed as instructions in a simple programming
language.
Based on techniques from knowledge-based neural networks, these
programs
are inserted directly into the agent's "utility function." The
advice
need
not be perfectly correct nor complete; subsequent learning further
integrates
and refines the advice. We present empirical evidence that shows our
approach
leads to statistically-significant gains in performance.
Importantly,
the
advice improves the learner regardless of the stage of training at
which
it is given.

#### 20 February. W. Davis Dechert, Department of
Economics,
University of Houston. ``Spurious Lyapunov Exponents in
Reconstructed
Dynamics.''

*Abstract:* One method that has been used to calculate the
Lyapunov
exponents from the data of an unknown dynamical system has been to
fit
a functional form to the data, and then calculate the Lyapunov
exponents
from the fitted function. Because of their universality, neural
networks
are used to represent the dynamical system. In this talk we show
some
of
the problems that can occur with this method, and in particular how
the
largest Lyapunov exponent can be miscalculated in this way.

#### 27 February. Kevin Mirus, UW Physics.
``Effects
of
Periodic Perturbations on Nonlinear Systems.''

*Abstract:* Several methods for controlling chaotic behavior
have
been developed over the last few years. One technique that can be
used
to effect the dynamics of a nonlinear system is to drive
periodically
some
system parameter. This technique has been implemented numerically
over
a wide range of perturbation amplitudes and frequencies on several
chaotic
systems, including the logistic equation, the Lorenz equations, the
Yoshida
equations, and coupled map lattices. Cases have been found in which
the
chaotic behavior can be eliminated at certain perturbation
frequencies
with very small amplitude perturbations, but the overall occurence
of
chaotic
solutions is not greatly diminished.

#### 5 March. Sean B. Carroll, Howard Hughes
Medical
Institute,
UW. ``Development and Evolution of Butterfly Wing Patterns.''

*Abstract:* How do new features evolve? How does natural
selection
act upon animal patterns? Butterfly wings are exceptional in the
complexity
and diversity of their color patterns. I will discuss genetic and
developmental
aspects of wing patterns and the modification of developmental
pathways
in evolution.

#### 12 March. Spring break --- no seminar

#### 19 March. Robert L. Wilson, UW Mathematics.
``Iterated
Function Systems.''

*Abstract*: Iterated Function Systems (IFS) have achieved fame
for
a beautiful picture of a fern, as well as applications in various
areas.
Commercially this technology is being used for image compression. An
IFS
is abstractly a collection of functions which map a space into
itself,
with restrictions on the space and on how the functions move points
around.
Applied repeatedly, in a deterministic or a random way, the
functions
collectively
have a fixed set which acts as an attractor. We will skim lightly
over
the terminology and a minimum of necessary theoretical background,
concentrating
on algorithms to implement an IFS, examples showing how those
algorithms
correspond to pictures, and how an algorithm can be used to encode a
particular
image.

#### 26 March. John Anderson, UW Atmospheric
Science. ``The
Solution of Signal Processing Problems Using Genetic Programming
Techniques.''

*Abstract:* Difficult non-linear optimization problems arise in
several
common signal processing estimation procedures. In many cases the
presence
of large numbers of local minima and the very small convergence
radii
for
the global minimum result in a problem which is essentially
impossible
to solve without resorting to suboptimal approximations of the
original
problem. Koza and others have shown Genetic Programming (GP) methods
to
perform remarkably well on a number of highly non-linear estimation
tasks
including symbolic regression so it is natural to investigate their
performance
in this problem domain. I will present results for two very
different
and
quite difficult problems, ARMA spectral estimation, and the design
of
digital
filters for unequal sample spacings. In each case the GP approach is
shown
to yield usable solutions to problems which are resistant to
conventional
techniques. These problems will also be used to study the effects of
various
selection algorithms on the solution efficiency.

#### 2 April. Michael Bleicher, UW Mathematics.
``A
Model
for Interdisciplinary Programs? --- Symmetry across the
Curriculum.''

*Abstract:* A group of faculty from four different colleges,
representing
over ten departments is working together to create a course on
symmetry
in its various aspects and uses.
This first course currently under construction is for
non-technical
students. It is anticipated it will be a ``Quantitative-B'' course
for
lower division students. It will be modularized, so that given
modules
can be used in other courses in the various departments, as
desired.
There
will be a heavy use of computer visualization in each of the
modules.
It
is hoped that these modules will be prepared for dissemination and
general
use on the World Wide Web.

A panel of the participating faculty will discuss both the nature
of
the content of the course modules and also the computer
visualization
aspects.

This first course is looked at as a first step toward two future
developments.
The first is more advanced and more specialized courses on the
same
topics.
The second is development of a program in computer
visualization.

#### 9 April. Clint Sprott, UW
Physics. ``Is
It Noise, or Is It Chaos?''

*Abstract*: Many quantities in nature fluctuate in time.
Examples
are the stock market, the weather, seismic waves, sunspots,
heartbeats,
and plant and animal populations. New tests are being developed to
determine
whether such fluctuations are random or whether they are examples of
deterministic
chaos, in which case there may be a simple underlying cause. If
evidence
of chaos is found, it may be possible to improve the short-term
predictability.
Methods for distinguishing chaos from noise will be described, and
examples
will be shown.

#### 16 April.David
Griffeath, UW Mathematics. ``Self-Organization of Random
Cellular
Automata.''

*Unusual Place:* Room B231 Van Vleck hall, usual time.
*Abstract:* We will illustrate some contemporary themes in
the
study of cellular automaton (CA) dynamics that form patterns
starting
from
disorder. The presentation will combine colorful real-time
interactive
demos with a tour of CA resources available on the Web.

#### 23 April.Kellie
Evans, UW Mathematics. ``Larger than Life.''

*Abstract:* Larger than Life (LtL) is a four-parameter family
of
cellular
automata that generalizes John Conway's celebrated Game of Life.
Real-time
"movies" will demonstrate the diverse forms of self-organization
exhibited
by the LtL family. Various rigorous and empirical results will be
discussed.

#### 30 April.Cosma
Shalizi, UW Physics. ``Is the Primordial Soup Done Yet?
Quantifying
Self-Organization, Especially in Cellular Automata.''

*Abstract:* Most decisions about whether something is
self-organizing
or not are made at an intuitive, ``I know it when I see it'' level.
The
talk will explain why this is unsatisfactory, describe some possible
quantitative
measures of self-organization from statistical mechanics and from
complexity
theory, and test them on several different cellular automata whose
self-organization,
or lack thereof, is not in dispute.

#### 7 May. Troy Shinbrot, Department of Chemical
Engineering,
Northwestern University. ``Something for Nothing: The Role of
Voids in
Granular Convection.''

*Abstract:* The onset and various aspects of fully developed
granular
convection in vibrated containers can be captured by an analysis of
motion
of voids. Predictions for convective onset as a function of system
parameters
are developed and tested with existing data. Voids --- and how they
are
filled --- provide a stochastic model to mimic fully developed
granular
convection. It is found that the vertical flow field depends on the
hyperbolic
cosine of the horizontal coordinate and on a mixed
linear-exponential
function
of the vertical coordinate. Companion, model-based, numerical
simulations
validate the theoretical predictions. Independent full soft-particle
dynamics
provide an independent check of the predictions of the theory.

Up to the Chaos and Complex Systems Seminar
page.

*(Sun Apr 14 16:35:10 CDT 1996)*

CRS