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

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