Madison Chaos and Complex Systems Seminar

Fall 2003 Seminars

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

Short List


Abstracts

September 2, 2003

Space-time dynamics observed in primary auditory cortex

Rick Jenison, UW Department of Psychology

Numerous studies have investigated the spatial sensitivity of cat auditory cortical neurons, but possible dynamic properties of the spatial receptive fields have been largely ignored. Given the considerable amount of evidence that implicates AI in the neural pathways responsible for the perception of sound source location, a logical extension to earlier observations of spectro-temporal receptive fields, which characterize the dynamics of frequency tuning, is a description that uses sound source direction, rather than sound frequency, to examine the evolution of spatial tuning over time. In this talk, auditory space-time receptive field dynamics will be described using a new method based on cross-correlational techniques and white-noise analysis in spherical auditory space.  Auditory receptive fields are characterized in 2 spherical dimensions of space (azimuth and elevation) plus a third dimension of time. Analysis has revealed that spatial receptive fields of neurons in auditory cortex, like those in the visual system, are not static, but can exhibit marked temporal dynamics. This might result, for example, in a neuron becoming selective for the direction and speed of moving auditory sound sources. A first-order system kernel models the neuron's "memory" for the stimulus history in terms of a linear filter, however this kernel represents only a linear approximation to the true transfer function. Further evidence for motion selectivity can be observed in the second-order kernel, which characterizes the higher-order covariances between sound sources in space and time.


September 9, 2003

Images of a complex world: the art and poetry of chaos

Robin Chapman, UW Department of Communicative Disorders

A multi-media extravaganza of plain-English and poetic definitions of chaos concepts and computer-generated art. Sprott's artwork depicts strange attractors, fractals, attractor icons, cellular automata, iterated function systems, and Julia sets, drawn from millions of equations and sorted by artist-tutored criteria. Chapman's poetry reflects both basic concepts of complex systems, in example and metaphor; and the content of Chaos seminar presentations. Participants are invited to help us make the English even plainer: simple vs. complex systems, linear vs. nonlinear-- and the examples more extended in this collaboration on a coffee-table book for the curious.


September 16, 2003

Regime shifts in the climate and environment of the Sahel region of Africa:  Complex interactions among atmosphere,
ecosystems, oceans and people

Jon Foley, UW Department of Atomospheric and Oceanic Sciences

The Sahara and Sahel regions of northern Africa have complex environmental histories, punctuated by sudden and dramatic “regime shifts” in climate >and ecological conditions. Here we review the current understanding of the causes and consequences of two environmental regime shifts in the Sahara and Sahel.

The first regime shift we consider is the sudden transition from vegetated to desert conditions in the Sahara about 5,500 years ago. Geologic data show that wet environmental conditions in this region – including extensive vegetation, lakes and wetlands – came to an abrupt end ~5,500 years ago.  Explanations for climatic changes in northern Africa during the Holocene have suggested that millennial-scale changes in Earth’s orbit could have caused wet conditions in the early Holocene, and dry conditions today.  But the orbital hypothesis, by itself, does not explain the sudden regime shift 5,500 years ago. Several modeling studies have proposed that strong, non-linear feedbacks between vegetation and the atmosphere could amplify the effects of orbital variations, and create two alternative stable states (or “regimes”) in the climate and ecosystems of the Sahara:  a “green Sahara” or a “desert Sahara”.  A recent coupled atmosphere-ocean-land modeling result indicated that there was a sudden shift from the “green Sahara” to the “desert Sahara” regime approximately 5,500 years ago.

The second regime shift we analyze is the onset of a major 30-year drought over the Sahel around 1969.  Several lines of evidence have suggested that the interactions between atmosphere and vegetation act to reinforce either a “wet Sahel” or a “dry Sahel” climatic regime, which may persist for decades at a time.  Recent modeling studies have indicated that the shift from a “wet Sahel” to a “dry Sahel” regime are caused by strong feedbacks between climate and vegetation cover, and may have been triggered by slow changes in either land degradation or sea surface temperatures.

Taken together, we find that the existence of alternative stable states (or regimes) in the climate and ecosystems of the Sahara and Sahel may be the result of strong, non-linear interactions between vegetation and the atmosphere.  We find that shifts between these regimes occur rapidly, although they are made possible by slow, subtle changes in underlying environmental conditions – including slow changes in incoming solar radiation, sea surface temperatures, or the degree of land degradation.


September 23, 2003

Competition with evolution in ecology and finance

Clint Sprott, UW Department of Physics

The Lotka-Volterra (predator-prey) model has been used extensively to understand competition in ecological and other similar systems. However, when applied to situations where there are many species, only a few of the dominant species are observed to survive (the "principle of competitive exclusion" or "survival of the fittest"). This talk will describe a variant of the Lotka-Volterra model in which species that die are replaced by new species chosen randomly, as a crude model of biological evolution. The result is that a few species still dominate, but they are eventually replaced by new ones. The behavior resembles the "punctuated equilibrium" discussed by Stephen J. Gould. Total biomass and biodiversity have periods of relative stationarity punctuated with intervals of rapid change and sensitive dependence on initial conditions (chaos). The behavior is similar to that observed in stock prices and foreign exchange rates, which are characterized by traders competing for finite resources just as in an ecological system. Such a model reproduces the variations in volatility and positive kurtosis that are characteristic of ecology and finance without resorting to external (exogenous) events. It may also have application to eye movements and fluctuations in magnetized plasmas.

Ref: http://sprott.physics.wisc.edu/lectures/darwin.ppt


September 30, 2003

Children's language learning: A solution to the poverty of the stimulus problem

Mark Seidenberg, UW Department of Psychology

One of the key ideas in the modern study of language is that language learning is possible only because children are born with knowledge of linguistic universals ("universal grammar"). This conclusion follows from the "poverty of the stimulus" argument, Chomsky's famous statement of the problem of language acquisition and why it cannot in principle be learned without such innate, domain-specific knowledge.  The idea of an innate language organ is increasingly at odds with evidence about how brains actually develop: there is little evidence that they are hard-wired at birth with specific types of knowledge. Moreover, the innate universal grammar assumption left it unclear how the child could actually succeed in acquiring a language. More recent research emphasizes statistical and probabilistic aspects of language that traditional approaches ignored. This research involves a different formulation of the language acquisition problem and suggests how it is solved despite the putative poverty of the stimulus.


October 7, 2003

A clear alternative to the Indo-European theory of language origins

Edo Nyland, Independent Scholar, Vancouver, BC

References:

1. Nyland, Edo: Linguistic Archeology: An Introduction. Victoria, BC, Canada: Trafford, 2001.
2. Nyland, Edo: Odysseus and The Sea Peoples: A Bronze Age History of Scotland. Victoria, BC, Canada: Trafford, 2001.
Available via http://www.trafford.com/robots/01-0069.html -- or alternatively from email: sales@trafford.com
Or Suite 6E, 2333 Government St., Victoria, B.C. V8T 4P4, CANADA
Nyland Website: http://www.islandnet.com/~edonon/


October 14, 2003

Understanding language comprehension by studying language production

Maryellen MacDonald, UW Department of Psychology

Research seeking to understand the cognitive processes underlying language comprehension is typically conducted independently from research investigating processes of language production.  The underlying assumption is that these two tasks are too different to be investigated conjointly.  This talk offers an alternative view, that key insights into comprehension processes can be gained through an understanding of production processes.  In particular, in order to maintain fluency in the face of the difficult task of language production, speakers make particular choices of sentence structure and word order so as to put easily planned and articulated material early in an utterance, giving them more time to plan more difficult material.  These choices lead to particular distributional patterns of word order and sentence structure in speakers' utterances.  Comprehenders are extremely sensitive to such distributional patterns and find higher frequency patterns easier to comprehend than lower frequency patterns. Whereas traditional theories of comprehension processes posit comprehension-specific mechanisms to account for the comprehension difficulty of some sentence types, this account points instead to sensitivity to the production-based statistics in the language, obviating the need for additional hypotheses concerning the architecture of the comprehension system.


October 21, 2003

Health care dynamics and the goldilocks economy: Too hot or too cold?

George Pasdirtz, UW Division of Information Technology

During the mid- to late-1990's the US economy was neither too hot (inflation) nor too cold (unemployment). At the same time, the Clinton administration was proposing a major overhaul of the health care system. Did health care participate in the Goldilocks economy? If not, why not. If so, what was the Clinton administration thinking about proposing regulatory overhaul? Even though the Clinton program failed to pass Congress, we will continue to see policy proposals to change the health care system. It would be useful to have a better understanding of how the health care sector is or is not integrated with the overall economy to help evaluate alternative recommendations. During the seminar we will explore the dynamics of the health care sector with a macro simulation model designed to handle the inherent complexity of the problem.


October 28, 2003

Cascading failure, the risk of large blackouts, criticality and self-organization

Ian Dobson, UW Department of Electrical and Computer Engineering

What is the risk of large blackouts such as the spectacular cascading blackout in August that cut power to 50 million North Americans? Data on North American blackouts suggest that large blackouts, although rare, occur more frequently than expected. Indeed the empirical probability distribution of blackout sizes shows a power tail similar to that observed in other complex systems near criticality. Since component failures in power systems tend to be dependent on component  loading and can cause further failures in a cascading fashion, we examine a probabilistic model that represents these general characteristics. The model shows power tails in the distribution of the number of failed components at a critical loading. Why would a power system be operated at a critical loading? We propose that economic and engineering forces could self-organize the power system to be operated near criticality. This research is joint work with Ben Carreras at Oak Ridge National Laboratory, Tennessee and David Newman at the University of Alaska.


November 4, 2003

What the heck is a pughshub?

Dave Albers, UW Department of Physics

Micheal Shub and Charles Pugh are two central members of the dynamics community that formed around Steven Smale (amoung others) in the late 1960's. This group drove much of the early work in dynamics in the US that was later termed "chaos theory." In recent years, Pugh and Shub have revived some of the dynamics community with a very general stability conjecture and a wonderful theorem. Since these claims are based heavily on geometry, they are, in a sense, accessible to a non-technical audience. Further, these results could have wide-ranging implications to practical scientists. I will explain both what the Pugh-Shub theorem means with pictures and ordinary words, and what its implications might be for applied fields of science. The goal will be a basic geometric picture geared for those with little mathematical expertise.

For a PDF version of the talk, see http://www.santafe.edu/~albers/sciencetalks.html


November 11, 2003

The beast within
Or, human animals, human selves

Deric Bownds, UW Departments of Molecular Biology and Zoology

This lecture tries to think about those components of our human actions, feelings, and mental lives that might be similar to those of other animals. Because most of us live mainly in our verbal linguistic minds it is quite easy for us to lose touch with the elemental and basic ways that our human selves are built on an animal substrate. A growing literature suggests correlations between different levels and varieties of our subjective experience, the evolutionary functional structure of the brain, and modern brain imaging measurements. For every level of our self consciousness - from basic bodily regulation, to emotional valence, to higher cognition - there is a time in the evolutionary history of this planet when it was exemplified for the first time. I review the kind of 'selves' we can attribute to other animals, and then try to make a case that our introspective capabilities permit us to distinguish sensations and feelings that correspond to regulatory levels of our brain and nervous system, from basic homeostasis through innate drives and reflexes to learned emotional behaviors and social rituals. We can distinguish in ourselves the behavioral repertories that appear to have been permitted at various stages of vertebrate evolution. We appear to be able to know the animal within us in a way that is closed to other animals lacking an "I". We are able to introspectively note how and when these experiences occur, to appreciate a 'natural history' of the brain actions that compose us, and thus gain a degree of freedom in the expression of our behaviors that is completely closed to other animals.


November 18, 2003

Randomness, roundness, and rules

Jim Propp, UW Department of Mathematics

The theory of cellular automata gives so many examples of complex behavior emerging from simple deterministic rules that some theorists have proposed that reality is a cellular automaton.  Leaving aside the empirical question of whether this is true, an interesting mathematical question is, Could it be true?  One major contrast between the world we see and the toy worlds of grid-based cellular automata is that our world is isotropic (no directions or axes are preferred or singled out by the laws of physics) whereas cellular automaton universes are built on Cartesian grids.  One can wave one's hands at this contrast and assert that reality could have preferred directions on inaccessible microscopic scales but be isotropic at larger scales.  What sort of mechanisms could allow for this?

I will describe a very simple scheme (the "rotor-router mechanism") that mediates between grid-geometry at microscopic scales and Euclidean geometry at macroscopic scales.  In particular, I will describe what I believe to be the first deterministic, purely local scheme for growing ever-larger blobs in the infinite grid that, as ever more particles are added, approach the ideal of Euclidean circularity ever more closely.

If there is interest (and time), I also hope to talk about how some of the relevant ideas can be traced back to work by physicists studying self-organizing criticality in the 1980s, and work done by a computer scientist back in the 1970s who wanted to find new ways to teach probability theory to elementary school students.


November 25, 2003

Multiple agent dynamical systems

John Albers, UW Department of Atmospheric and Oceanic Sciences

Learning theory is an area which manifests itself in a broad range of scientific fields from biology to robotics.  The research presented will attempt to present how dynamical systems can be used to approach problems within a specific area of learning theory, multiple agent reinforcement learning.  Topics such as the single and mulitple agent learning environment and the dynamics of the collective state space will be presented within a basic mathematical and learning theoretic framework in the hopes of providing a informative introduction to the Dynamics of Learning Project at the Santa Fe Institute.


December 2, 2003

A clear alternative to the Indo-European theory of language origins

Russ Gardner, Jr., UW Department of Psychiatry

The Indo-European (IE) hypothesis for the natural evolution of language forms originated well over two centuries old, but remains as yet no closer to confirmation than at its onset. No primordial land has been identified where the original tongue from which Sanskrit and modern European languages naturally evolved. However, the hypothesis would gain plausibility if a clear-cut alternative hypothesis were disproved. The two books listed below provide such an alternative. The author, Edo Nyland, provides data that the so-called IE languages in fact were invented, likely, he suggests, by priest-missionaries who used an ancient decoding formula to change an original widely disseminated language to multiple new languages. They used these to more readily convert to new religions the children – and through them the populace – of those practicing ancient forms of worship. Nyland suggests that many languages represent coded versions of Basque, not tongues independent of it as currently assumed. He provides a back-decoding formula that he has successfully and extensively applied and that can be used easily by others. It represents a falsifiable hypothesis. Additionally, in support of his conclusions on a widespread mother tongue, he shows word meaning similarities amongst Basque, Ainu and Dravidian languages. This reviewer suggests that Nyland’s work shows sufficient plausibility that other investigators should pursue it. Since he postulates a giant conspiracy theory, I visited him and found him eminently sensible and normal (not at all paranoid). While the ideas may initially seem improbable, they should be dismissed only after careful effort to understand the propositions – with skepticism suspended until the argument is absorbed and attempts at data replication completed. To summarize, Nyland’s suggestions provide an alternative approach to the IE hypothesis. If others replicate his findings, the “natural” evolution of modern languages from a common source will be less likely. If his conclusions are disproved, then the venerable IE hypothesis may gain strength.

Books under review:
1. Nyland, Edo: Linguistic Archeology: An Introduction. Victoria, BC, Canada: Trafford, 2001.
2. Nyland, Edo: Odysseus and The Sea Peoples: A Bronze Age History of Scotland. Victoria, BC, Canada: Trafford, 2001.
Available via http://www.trafford.com/robots/01-0069.html -- or alternatively from email: sales@trafford.com
Or Suite 6E, 2333 Government St., Victoria, B.C. V8T 4P4, CANADA
Nyland Website: http://www.islandnet.com/~edonon/

I have written a more extensive review approximately 4000 words long entitled “Believing Six Impossible Things Before Breakfast: Review of Edo Nyland books” that can be provided should someone wish.


December 9, 2003

The stability of slinkies, slide guitars and the Solar System.
(Technical title: A KAM theorem for torus mappings arising in the study of resonating cavities)

John Vano, UW Department of Mathematics

The KAM theorem (named after A. N. Kolmogorov, V. I. Arnold, and J. K. Moser) is a stability theory for perturbations of certain classes of dynamical systems, the most famous being the stability of the solar system.

This theory can also be applied to study a model for a laser oscillating in an optically active media, compression waves in elastic media (a slinky) or the transverse displacement of a guitar (or violin) string.  The consequences of this stability theory give an understanding of the long term behavior of these systems and can also be viewed as answering an infinite dimensional control problem.