Madison Chaos and Complex Systems Seminar

Spring 1999 Seminars

All seminars are Tuesday at 12:05 pm in 4274 Chamberlin except as noted

Short List

January 19, 1999

Statistical Learning by Human Infants

Jenny Saffran, UW Department of Psychology

How do human infants learn about their environments? In particular, how do infants learn their native language? Our recent research suggests that infants are surprisingly skilled at detecting statistical cues to structure, such as the transitional probabilities between sounds, in language input. Moreover, infants' abilities to compute sequential statistics are not limited to linguistic input, but may also subserve learning about domains such as music. Implications for the role of statistical learning in theories of language acquisition will be considered.

January 25, 1999 (Note special date and location - noon Monday, 338 Psychology)

There's more to the Hand than Meets the Eye: Links between Gesture, Speech, and Cognition

Jana Iverson, Indiana University

When people talk, they gesture.  With movements of their hands, speakers indicate size, shape, direction, and distance, lend emphasis to particular words, and highlight essential phrases.  In this talk, I address the question of why we gesture.  I begin by presenting data that call into question three commonly held assumptions, that: a) experience with a visual model is necessary in order for gesture to appear; b) the presence of a listener who can appreciate the information contained in gesture is necessary for gesture to occur; and c) gesture is mere motor overflow. By contrast, I suggest that gestures occur because cognition, speech, and gesture are tightly and inextricably linked.  I conclude by describing research assessing the impact on memory of experimental manipulation of gesture production that has yielded preliminary results consistent with this view.

February 2, 1999

Coevolution of Musical Instruments and Scales

William Sethares, UW
Department of Electrical and Computer Engineering

An organizing principle that underlies the creation of musical scales and instruments relates the tuning (the pitches) that instruments use to the timbre (the spectrum) of the sounds. This raises a musical chicken-and-egg paradox. Which came first, the tuning or the instruments? Three examples are given: Western scales are related to the harmonic sounds of string and air-column instruments, Javanese (slendro) scales are related to the sounds of certain metallophones, and Thai (7 tone) scales are related to the sounds of traditional bar instruments.

February 9, 1999

Dynamics of Ocean Circulation around Islands

Zheng-yu Liu, UW Department of Atmospheric and Oceanic Sciences

The dynamics of island circulation is discussed in light of the interaction of Rossby and coastal Kelvin waves. It is found the formation of an island circulation has three stages: 1) the direction of the island circulation is determined by the coastal Kelvin wave adjustment; 2) the strength of the island circulation is determined by the short Rossby waves on the eastern coastal of the island; 3) the spatial pattern of the island circulation is finally determined by the long Rossby waves that radiate from the western coast of the island to the basin.

February 16, 1999

Coping with Chaos:  Seven Simple Tools

Glenda Eoyang, Chaos Limited, Inc.

The science of chaos and complexity provide rich metaphors to describe the systemic and dynamic nature of change in organizations. Characteristic patterns of complex adaptive systems (butterfly effects, turbulent boundaries, transforming feedback loops, fractals, attractors, self-organization, coupling) can be observed and documented in many business environments.  In this talk, I will introduce patterns of behavior that emerge in chaotic systems.  I will demonstrate how those patterns influence understanding and action in complicated human systems and provide advice to help managers and employees cope more effectively with the complex unpredictability of organizational change.

February 23, 1999

The Nonlinear Dynamics of Voice.

David Berry, National Center for Voice and Speech, The University of Iowa

In general, normal sustained voice sounds are nearly periodic. However, rough vocalizations from disordered voices often exhibit more pronounced irregularities, including period-doublings, low-frequency modulations, and aperiodic oscillations.  Only recently have these instabilities been interpreted as the bifurcations of a nonlinear system.  With techniques from nonlinear dynamics (Poincare sections, estimations of attractor dimensions and Lyapunov exponents), it has been shown that the dynamics of newborn infant cries and voice disorders are intimately related to bifurcations and low-dimensional attractors.  Significantly, low-dimensional dynamics facilitates the task of establishing basic mechanisms of irregular vibration in voice. With potential impact for the prevention and treatment of voice disorders, it is the aim of current research to better understand the physiological mechanisms of irregular vocal fold vibrations using high speed video and biomechanical modeling. Recent results and findings will be reported.

February 25, 1999 (Note special date, time - 2:25 pm, and location - B231 Van Vleck)

(under the auspices of the UW MATH PROBABILITY SEMINAR)

A Two-Dimensional Cellular Automaton Crystal with Irrational Density

David Griffeath, UW Mathematics Department

I will present a solution to a problem I posed recently in an Adv. Appl. Math. paper with Janko Gravner: to find a finite seed of 1's for a simple {0,1} - valued cellular automaton (CA) growth model on the two-dimensional lattice such that the occupied crystal spreads with a two-dimensional asymptotic shape and a provably irrational density. The solution, joint with Dean Hickerson and based on two of his patterns from the early 90s, exhibits an initial seed of 2,392 cells for Conway's Game of Life from which the crystal after n updates covers nT with asymptotic density (3 - sqrt(5))/90, where T is a certain triangular region of the plane. This talk and computer demonstration will be accessible to a broad audience, and is intended to illustrate some state-of-the-art constructive methods for the most thoroughly
studied of all CA rules.

March 2, 1999

Congestion and Coordination Failure on the Internet: A Vickrey Toll for El Farol?

Ann M. Bell, Caelum Research, NASA Ames Research Center

El Farol is a bar in Santa Fe. The bar is popular, but becomes overcrowded when more than sixty people attend on any given evening. Everyone enjoys themselves when fewer than sixty people go, but no one has a good time when the bar is overcrowded. How can, or how do, people choose whether to go to El Farol on any given evening?

Brian Arthur's (1) original formulation of the problem utilized a model of "inductive learning" at the level of individual agents. He observed that even when agents use a set of very simplistic or unrealistic rules of thumb to predict bar attendance, the number of people at the bar tends to hover near sixty. Casti uses the El Farol problem to frame his definition of a complex adaptive system as one with "a medium number of intelligent, adaptive agents interacting on the basis of local information" (2, p. 10) and speculates that attendance at the bar is a deterministic random process.

This paper examines El Farol as a simplified model of a class of congestion and coordination problems that arise in modern engineering and economic systems. The El Farol problem emphasizes the difficulty of coordinating the actions of independent agents without a centralized mechanism. Furthermore, because the level of congestion at El Farol depends on the actions of many individual agents, the problem adds the complexity of an endogenously changing environment. These features make it an especially useful tool for analyzing information technology systems which are characterized by decentralized decision making and rapid endogenous changes in the operating environment. For example, despite rapid technological advances and constantly expanding bandwidth, the Internet can become congested when a large number of people independently decide to visit the same web site or to download files at the same time. The level of congestion is endogenously determined by the actions of hundreds or thousands of users.

Standard models of congested public (freely available) resources focus on the marginal costs that an individual user imposes on other potential users. For example, each person who visits a popular web site may increase the download time of other users. Explicitly charging users for these unobserved costs can eliminate the socially inefficient congestion of a scarce resource. (3, 4) However, these models typically analyze equilibrium solutions in which all agents are fully informed about the structure of the problem and the behavior of other agents. Consequently, the relationship between agents' behavior and the congestion they experience is easily discerned. This reliance on information intensive equilibrium solutions limits the applicability of these models to modern information systems such as the Internet.

In contrast, the El Farol problem focuses on the interaction between individual learning strategies and the environment that agents' face. Congestion arises in the El Farol model because agents constantly attempt to predict the aggregate behavior of other agents, which simultaneously depends on all agents' predictions. If agents' could perfectly predict the behavior of all other potential bar goers, El Farol would never experience congestion. Using El Farol to model the Internet environment focuses attention on congestion that arises from coordination failure across agents as well as from absolute constraints on bandwidth.

This paper reviews the El Farol problem and surveys previous treatments, which typically involve complex learning algorithms. The existence and characteristics of deterministic equilibria are explored. In contrast to the frequently repeated claim that "no forecasting rule of deterministic actions can be at the same time correct and available to all agents" (1) we show that agents need not utilize different behavioral rules, nor must they constantly switch between rules, when deciding whether to attend El Farol. We propose a simple adaptive scheme based on habit formation which, if followed by all agents, leads to an outcome close the socially optimal attendance of 60 agents per night. The strategy is investigated via simulation and the algorithm is analyzed in a few simple cases. Finally, the implications for routing Internet traffic when congestion can arise because of coordination failure are discussed.


(1) W. B. Arthur, "Inductive reasoning and bounded rationality: the El Farol problem", American Economic Review: American Economic Association
Papers and Proceedings 1994, Vol. 84, Pp. 406-411, May 1994.

(2) J. L. Casti, "Seeing the light at El Farol," Complexity, Vol. 1, No. 5, Pp. 7-10, 1996.

(3) W. S. Vickrey, "Congestion theory and transport investment", American Economic Review, No. 59, Pp. 251-260, 1969.

(4) J. K. MacKie-Mason and H. R. Varian, "Pricing the Internet", in Public Access to the Internet, Ed. B. Kahin and J. Keller, Prentice-Hall, Englewood Cliffs, New Jersey, 1994.

March 16, 1999

The Galaxy as an Island Universe

Don Cox, UW Department of Physics

No Abstract

March 23, 1999

Evidence for Nonlinearity in the Behaviors of Adolescent Sex Offenders

Keith Warren, UW Department of Social Work

Clinicians working with adolescent sex offenders have suggested that many of them show evidence of an "offense cycle," in which a slow buildup of anger and resentment leads to an outburst of anti-social behavior, which in turn leads to the onset of fear, guilt and shame. This suggests the possibility that sex offender behaviors might conform to a threshold autoregression model, one in which the parameters of the model depend on the behaviors during one or more preceding periods. Threshold autoregression models, in turn, imply the possibility of nonlinear dynamics including limit cycles and deterministic chaos. This presentation will discuss the evidence for nonlinearity in the behaviors of several adolescent sex offenders and the implications for clinicians working with these individuals.

March 30

Is Chaos Good for Learning?

Oguz Yetkin, UW Department of Physics

Neural networks can be made to behave as nonlinear dynamical systems, and have been used to replicate or predict various time series.  A lot of networks that are sufficiently large exhibit chaotic behavior (the sensitivity of the dependence on initial conditions can be quantified by the numerical calculation of the largest Lyapunov Exponent).  This has direct consequences for the quality and the long term behavior of the predicted time series.

We have determined that chaos also has consequences for the performance of the training algorithm -- and that the algorithm (in this case, simulated annealing) can be improved significantly by imposing certain LE constraints. While discarding highly chaotic solutions significantly reduces the time required for training, suppressing all chaos during training leads to a decrease in performance.

April 6, 1999

Neuronal Mechanisms for Sound Localization

Tom Yin, UW Department of Physiology

There are three important acoustical cues for sound localization: interaural time disparities (ITDs), interaural level disparities (ILDs), and spectral cues resulting from the filtering properties of the pinnae, head and shoulders.  Human psychophysical experiments have shown that the threshold for detection of ITDs under optimal conditions is 5-10 microseconds, a remarkable temporal resolution considering that the widths of action potentials used to process these disparities is two orders of magnitude longer.  Anatomical and physiological studies of auditory brainstem nuclei have demonstrated that the major binaural cues, ITD and ILD, are encoded by two different circuits within the superior olivary complex. This talk will focus on the circuitry that encodes ITDs involving cells in the medial superior olive (MSO), as first envisioned by Jeffress (1948). There is evidence supporting all three of Jeffress assumptions (bushy cells from the cochlear nucleus carry temporal information in their discharge pattern about the acoustical waveform to the MSO, they project with lattice-like branching patterns to the MSO, and MSO cells are coincidence detectors, or cross-correlators), as well as the resulting spatial map of ITDs in the MSO.

April 13, 1999

Simplicity in Complexity: Macromechanics of Avalanching and Compaction of Granular Systems

Stefan Linz, University of Augsburg

The dynamics of granular systems such as sand, powder, and beads has recently attracted steadily increasing fascination. Although the micromechanics of these dissipative, classical many particle systems is rather complex, its experimentally observable dynamics is often surprisingly simple. In this talk, we show that at least some aspects of granular dynamics, the surface flow along piles (avalanching) and the densification under tapping, can be successfully modeled by a simple dynamical systems approach that only combines elementary macromechanical mechanisms.

April 16, 1999 (Note special date, time: 4 pm, and place: 1300 Sterling)

The Evolutionary Unfolding of Complexity

James P. Crutchfield
Research Professor
Santa Fe Institute
1399 Hyde Park Road
Santa Fe, New Mexico 87501

This talk presents a new approach to the evolutionary phenomenon of punctuated equilibria---a process introduced by Gould and Eldredge in 1977 to explain the rapid morphological shifts observed in the paleontological record. A wide range of both natural and artificial evolutionary processes exhibit similar behavior in which long periods of stasis in an evolving population are punctuated by sudden bursts of change. The approach---statistical dynamics---combines methods from both statistical mechanics and dynamical systems theory in a way that offers an alternative to current ``landscape'' models of evolutionary optimization and that illustrates how structural complexity becomes  installed in a population through a series of phase transitions.

An introductory paper of the same title is available via

April 20, 1999

Influences of Management and Organizational Factors on Risk

Vicki Bier, UW Department of Industrial Engineering

The effect of management and organizational (M&O) factors on risk has been of significant concern in recent years.  For example, at least for the population of commercial nuclear power plants in the United States (where the current regulatory regime imposes fairly uniform minimum requirements for physical aspects of plant design, such as required safety systems), corporate culture may have if anything a stronger influence on risk than does the design of the plant itself.

Why, given the importance of the issue, are management and organizational influences on risk not yet well understood?  I argue that the study of management and organizational factors is difficult in part because there is no one "correct" management style, corporate culture, or organizational structure.  Rather, these various elements must be consistent both with the demands of the organization's environment and with each other.  Thus, for example, it may be possible to achieve good performance with either a highly democratic and participatory management style or a highly authoritarian and dictatorial approach, as long as the other aspects of the overall organization design are in tune with the management approach.  These views will be supported by a review of the literature on organizational design and management, high reliability organizations, and technological accidents.

The state of the art in the area of organizational performance is well summarized in a report by the National Research Council: "[B]oth the [empirical] research base and organizational theory are in their infancy.  Consequently, neither one is complete enough to derive strategies for change in a rational fashion....Much of the difficulty lies in the accessibility and complexity of the subject matter...."

April 27, 1999

Textual Harassment: Explorations of Chaos and Complexity in Avant-Garde Drama and Performance Art

Mike Vanden Heuvel, UW Department of Theater and Drama

Professor Vanden Heuvel will discuss how early 20th-century theatre artists such as the Italian futurists and the dadaists began exploring the breakdown of textual stability and coherence through eruptive moments of performance. More recent performance art groups, such as the New York collective The Wooster Group, have extended the practice in order to produce performances and audience interactions which mimic the effects of chaos in dynamic systems.

May 3, 1999  (Note special date, time: 2 pm, and place: Genetics/Biotech Auditorium)

Laws for the Dynamics of Regulatory Circuits

Rene Thomas, Universite Libre de Bruxelles

The two types of biological regulation, homeostatic and differentiative (or epigenetic) are revisited in terms of feedback circuits. Homeostasis has been familiar to all physiologists since Claude Bernard (who called it "elasticity"). Not so for epigenetic processes, which are still ill-perceived by most biologists. This is why we begin by a rather detailed description of admirable old experiments by Novick and Weiner and by Cohn and Horibata, to show exactly what "epigenetic differences" are. Delbrick has suggested, and it has since become clear, that differentiation is essentially epigenetic and that it can be understood essentially as the biological facet of a more general process, multistationarity.

We develop the concept of feedback circuit and the meaning of "positive" and "negative" circuits, and show that the presence of positive circuit(s) is a necessary condition for multistationarity (and by inference for cell differentiation) and that negative circuits are required for stable periodicity, an essential element of homeostasis.

These rather abstract notions are illustrated by biological examples coming mostly from bacteriophage genetics. A brief excursion outside biology shows how the concept of circuits can be applied in a much more general way, including such domains as nonlinear dynamics and in particular deterministic chaos (the subject of the second seminar "for the physicists".

May 4, 1999

Nonlinear Dynamics seen in Terms of Feedback Circuits: Generalization of the Rossler Equations, and "Labyrinth Chaos" Generated by a Single Feedback Circuit

Rene Thomas, Universite Libre de Bruxelles

The feedback circuits of a system can be identified in terms of the elements of its matrix of the partial derivatives (the Jacobian matrix). Only those terms of the Jacobian matrix which belong to a circuit are found in the characteristic equation of the system, and consequently only those terms influence the eigenvalues and thus the nature of the steady states. In view of this crucial role of circuits, we call the set of circuits of a system its "logical structure".

We stress that circuits and nonlinearities  are two entirely distinct concepts; as a matter of fact both are necessary for any "nontrivial" behavior such as multistationarity, stable periodicity or deterministic chaos. Circuits are positive or negative depending on the parity of the number of negative interactions. It has been conjectured (Thomas, 1981) and more recently formally proven by others that (1) the presence of a positive circuit is a necessary condition for multistationarity and (2) that a negative circuit (with two or more elements) is a necessary condition for stable periodicity.

Starting from the well-known Rossler equations which generate deterministic chaos in spite of their great simplicity, we analyze the logical ingredients of deterministic chaos. Two observations which may be of interest are (a) that when the proper circuits are present, the precise nature of the nonlinearities has little influence on whether or not the system can display a chaotic dynamics and (b) that a single feedback circuit can  generate chaotic dynamics, but only if the nonlinearity is such that the circuit is positive or negative depending on where we are in phase space (a necessary, not sufficient, condition).