September 7, 1999
Simple Chaotic Systems and Circuits
Clint Sprott, UW Department of Physics
Many new chaotic systems with algebraically simple representations will be described. These systems involve a single third-order autonomous ordinary differential equation (jerk equation) with various nonlinearities. When the nonlinearities are piecewise linear, they can be easily implemented electronically in circuits with diodes and operational amplifiers. Several new simple and robust chaotic electrical circuits will be described and demonstrated.
Slides from talk: http://sprott.physics.wisc.edu/lectures/cktchaos/
September 14, 1999
Instabilities and Nonlinear Dynamics in Flows of Polymeric Liquids
Michael D. Graham, UW Department of Chemical Engineering
Instabilities, time dependence and nonlinear dynamical behavior are ubiquitous, fascinating and technologically important features of fluid dynamical systems. Understanding these behaviors is particularly challenging and rewarding when the flowing material has a complex microstructure, whose evolution is closely coupled with the evolution of the flow. This is the case, for example, for flowing polymer melts or solutions. Upon perturbation, polymer molecules in a fluid may take a macroscopically long time to relax back to their equilibrium configurational distribution. On shorter time scales, the material actually behaves like an elastic solid, while on longer time scales it behaves like a liquid. This property of a material is aptly called viscoelasticity. It makes the fluid mechanics of polymers nonlinear even in the absence of inertia and leads to novel instabilities and dynamics that are only beginning to be understood.
This talk will introduce basic models for the behavior of polymer molecules in flow and the basic mechanisms by which viscoelasticity drives flow instabilities. We will then describe work in our group on methods for using viscoelasticity against itself, to modify flows so that they are less susceptible to instability. Development of such methods is important because many industrial coating processes are limited by the onset of flow instabilities. We will also show how, in the strongly nonlinear regime, very localized "solitary" states develop, which may also affect coating operations even when they are nominally stable.
Finally, we illustrate the connection between the behavior of polymers in flow and the Liapunov exponents that characterize chaotic trajectories in a flow field. This connection may ultimately improve our understanding of the behavior of polymer molecules in flows with complex kinematics, as arise in porous media or turbulence.
September 21, 1999
Nonlinear Dynamics of Motivational Flow
Stephen J. Guastello, Ph.D.
Department of Psychology, Marquette University*
Psychological motivation takes two basic forms: "extrinsic" and "intrinsic." Extrinsic motivation is responsive to rewards delivered by second parties. Intrinsic motivation, on the other hand is inherent in the interest value of the task itself. Motivational flow is the experience of intrinsic motivation, which is in turn the result of the levels of challenge and skill involvement for a particular task. The level of flow is predictive of the amount of time a person will spend in that task, and it is though to form a basis for an individual's time allocation between occupational and leisure activities. In this study, 28 university students, many of whom were employed, completed a 7-day log of their daily activities, their duration, and provided ratings of the level of skills and challenges inherent in the task. The logs provided a time series of several hundred points for each participant, which were each subjected to nonlinear dynamical analysis through nonlinear regression. Principal results were that flow was chaotic for all participants. Nonlinear models fit the data better than linear counterparts. Nonlinear models were stronger for people who spent more time at paying jobs. Evidence for individual differences in dynamical character were uncovered.
*With kudos to my co-authors, Elizabeth Johnson and Mark Rieke.
September 28, 1999
Analysis of a Physiologically Based Mathematical Model of Arterial Pressure Recordings
Christina Kendziorski, UW Department of Biostatistics and Medical Informatics
A stochastic mathematical model of arterial pressure recordings was developed to provide insight into and information about the baroreceptor reflex response. Using the model, the strength of the baroreceptor response can be assessed for an animal given its arterial pressure recording. To interpret the numerical results obtained by fitting this model to a rat population of hypertensive and normotensive rats, the model was analyzed to determine regions of stationarity. In addition, a related deterministic model was analyzed which lead to the identification of period doubling bifurcations. Comparison of these results was used to determine a condition that ensures both stationarity of a stochastic equation and stability of a related deterministic system. The implication of these results in the context of hypertension will be discussed.
October 5, 1999
Chaotic Orbits and Galaxy-Building
Linda Sparke, UW Department of Astronomy
Have you ever wondered why there are no triangular galaxies in the sky? To make one, stars would have to follow orbits that stay mainly within a triangular region. But calculating stellar orbits under the gravitational force of a triangular distribution of mass shows that most of them are chaotic, and they don't stay in the region where the density is high. If you made a triangular galaxy, it would fall apart.
Similar arguments imply that if a galaxy gets too dense at the center, it must become round. This talk will discuss what looking at the possible stellar orbits in a galaxy can tell us about 'ways that galaxies can't be'.
October 12, 1999
Evolving Generative Grammars as Developmental Programs
Thomas Kammeyer, GeneSys Technologies
In this talk, I'll discuss some of my thesis research on the simulated evolution of simple sorting algorithms. The sorting algorithms in question are composed of simple, fixed sequences of operations which sort a list of numbers into ascending order. In the evolutionary algorithm employed, each genotype in the population is a set of rules from which a phenotypic algorithm is derived. The rule sets are simple, phrase-structure grammars. The algorithm evolves developmental programs in the form of rules sets that building sorters. I'll describe the algorithm briefly, emphasizing the developmental aspects and then present some results. Finally, I'll ask some questions about the use of developmental components in evolutionary algorithms, and conditions under which we would expect them to be a good idea.
October 19, 1999
Genetic Algorithms and Stochastic Grammar Induction
Thomas Kammeyer, GeneSys Technologies
Genetic algorithms are machine learning algorithms that operate by engaging in simple simulations of evolution. In this talk, I'll discuss the use of genetic algorithms to discover phrase-structure grammars for some simple formal languages. The genetic algorithm used was kept relatively simple in this work, but the method of representing grammars required concomitantly more effort. I'll introduce the stochastic grammar induction problem and the genetic algorithm briefly, discuss the method for representing grammars, and discuss some results. I'll finish by attempting to relate this work to my talk of the 12th, and mention some future lines of research in which I'm interested.
October 26, 1999
Low-Order Models of Atmospheric Dynamics and Turbulence with Chaotic Behavior
Alexander Gluhovsky, Earth and Atmospheric Sciences, Purdue University
The development of physically sound finite dimensional approximations (low-order models) to the Navier-Stokes equations of fluid motion will be discussed. The models are mathematically devised in the form of simple coupled 3-mode systems known in mechanics as Volterra gyrostats. The simplest Volterra gyrostat in a forced regime is equivalent to the celebrated in chaotic dynamics Lorenz model. The failure for a low-order model to have a gyrostatic structure usually indicates violations of fundamental conservation properties. The exposition will be illustrated with popular fluid dynamical models including a model of turbulence that exhibits the famous Kolmogorov spectral behavior.
November 2, 1999
A General Theory of the Strange Attractors Governing Human Behavior
Jim Gustafson, UW Department of Psychiatry
All of psychopathology can be mapped simply as variations of a two-dimensional field. The two dimensions are the force of the group, and the compensatory force of the individual dream. The prevailing tendency of the group is to make servants of us all, and deplete us. The prevailing tendency of the dream as a searching instrument of individual survival is to subordinate others to its domination. The results are endlessly circular in two dimensions, in which the group is perverse for the individual, the individual perverse for the group: this is a divergent problem, with no solutions, only the same dilemma over and over again. Such circularity can be surmounted only by a third dimension, a fourth, and so forth. A simple metaphor for the two dimensional field is that the group is like the sun, the individual dream like the moon: ordinarily, the sun obscures the moon by day, and the moon takes over by night. These are the two dominant and strange attractors.
Gustafson, James P. (1997). The New Interpretation of Dreams.
Madison, Wisconsin: James P. Gustafson, publisher
Gustafson, James P. (1999). The Common Dynamics of Psychiatry.
Madison, Wisconsin: James P. Gustafson, publisher
November 9, 1999
Visualizing Science: The Scientist, the Artist, and the Public
Jean Trumbo, Assistant Professor, Head, Visual Communication Division, Association for Education in Journalism and Mass Communication (AEJMC)
This presentation will examine some of the aspects of visual literacy that are challenged as the scientist and the computer work to visually represent complex ideas. Science visualization offers tremendous opportunity and tremendous challenges. Visual images have the capacity to bridge gaps in knowledge and to engage a lay audience in the wonder of scientific discovery. Beautiful images of science created through computer media or the artist's hand can be incomprehensible to the audience if questions of visual literacy are not accounted for. Professor Trumbo will suggest some important features of science visualization, visual literacy and visual communication through this illustrated and interactive presentation.
Trained as a graphic designer and writer, Jean Trumbo holds an M.S. in mass communication and an M.F.A. in visual design. She is an assistant professor in Agricultural Journalism at UW where she teaches computer mediated communication, visualizing science and technology, and visual communication. Her research is focused on scientist's use of visual representation in new media.
November 15, 1999 (Note special day: Monday, 12:05 pm in 4274 Chamberlin)
Surfing Through Hyperspace: Understanding Higher Universes in Six Easy Lessons
Clifford A. Pickover, IBM Watson Research Center
I know of no subject in mathematics that has intrigued both children and adults as much as the idea of a fourth dimension -- a spatial direction different from all the directions of our normal three-dimensional space. Philosophers and parapsychologists have meditated upon this dimension that no one can point to but may be all around us. Theologians have speculated that the afterlife, heaven, hell, angels, and our souls could reside in a fourth dimension -- that God and Satan could literally be lumps of hypermatter in a four-dimensional space inches away from our ordinary three-dimensional world. Throughout time, various mystics and prophets have likened our world to a three-dimensional cage and have speculated on how great our perceptions would be if we could break from the confines of our world into higher dimensions. Yet, despite all the philosophical and spiritual implications of the fourth dimension, this extra dimension also has a very practical side. Mathematicians and physicists use the fourth dimension every day in calculations. It's part of important theories that describe the very fabric of our universe.
This fun talk touches on religious, artistic, historical, literary, and scientific aspects of the fourth dimension. Books are available at the University Bookstore and at Border's books.
Clifford A. Pickover is a research staff member at the IBM Watson Research Center in Yorktown Heights, New York. He received his Ph.D. from Yale University and is the author of over twenty highly-acclaimed books on such topics as computers and creativity, art, mathematics, black holes, human behavior and intelligence, time travel, alien life, and science fiction. Pickover is a prolific inventor with dozens of patents, is the associate editor for several journals, and puzzle contributor for magazines like Discover and Odyssey. The Los Angeles Times recently wrote, "Pickover has published nearly a book a year in which he stretches the limits of computers, art and thought." Wired magazine wrote, "Bucky Fuller thought big, Arthur C. Clarke thinks big, but Cliff Pickover outdoes them both." Pickover's computer graphics have been featured on the cover of many popular magazines and on TV shows. His web site, www.pickover.com, has received over 200,000 visits. His latest book is Surfing Through Hyperspace.
November 23, 1999
Testing and Inference in Threshold Autoregressive Models
Bruce Hansen, UW Department of Economics
The talk will review least squares testing and inference in the context of threshold autogressive models (TARs), a particular class of nonlinear time series. The testing problem of interest concerns the presence of a threshold effect, which is non-standard. Simulation methods to calculate asymptotic and bootstrap distributions are presented. Another interesting and tricky issue is construction of confidence intervals for the threshold parameter, since the least-squares estimate has a non-standard asymptotic distribution. We recommend the use of likelihood-based level sets, which are easy to compute and have good statistical properties. The methods are illustrated with three empirical examples: U.S. unemployment rate, U.S. industrial production, and annual sunspot means.
November 30, 1999
The Resilience Network: A Short Tour
William A. Brock, UW Department of Economics
The Resilience Network (Rnet) is a group of ecologists and economists which is run by the Beijer Institute of Sweden and The University of Florida Ecology Group. It has participants from all over the world including our own Steve Carpenter of Limnology as well as myself. The philosophy is to build coupled ecological and economic models with a hierarchy of time scales where the slow time scale acts as a bifurcation parameter where the ecological component is designed to match patterns observed in nature and where the economic component is designed to assist humans in avoiding unpleasant "surprises." This talk will give an overview report and give examples of some of my own research with Rnet members including Carpenter. Mathematical tools include some stochastic difference equations, a little bifurcation theory, and some methods from adaptive agent models. A sample of this research may be viewed at the online journal CONSERVATION ECOLOGY: http://www.consecol.org/Journal/vol3/iss2/art4/, in the article "Ecological and Social Dynamics in Simple Models of Ecosystem Management."
December 7, 1999
A Nonlinear Model of Mental and Behavioral Control Paradoxes
Keith Warren, UW Department of Social Work
In recent years, social psychologists have shown increased interest in issues of mental and behavioral control, and particularly the way in which attempts at mental and behavioral control often backfire -- so-called mental and behavioral control paradoxes. This talk will develop a simple nonlinear model describing attempts at controlling problematic behaviors, and demonstrate that these paradoxes arise naturally out of such a model. The talk will also discuss empirical verification of the model in cases of obsessive-compulsive disorder, substance abuse and antisocial behavior. Nonlinearity in these cases has implications for both clinical research and clinical practice.
December 14, 1999
Signal Processing Using Wavelets and Time-Frequency Representations
Akbar Sayeed, UW Department of Electrical and Computer Engineering
Time-frequency representations are powerful tools for the
processing of signals whose characteristics change over time. They
signals in terms of building blocks that are localized in both
frequency. The wavelet transform is a notable example that figures
in a host of application areas, including signal detection and
image/video compression, and communications. This talk will
basic concepts underlying time-frequency representations and
their utility in a variety of applications.