Madison Chaos and Complex Systems Seminar

Spring 1998 Seminars

Dates, speakers, titles and abstracts will be listed as they become available. Meetings will be noon Tuesdays in 4274 Chamberlin Hall unless otherwise noted.

Short List

27 Jannuary. George E. Hrabovsky, UW Physics: ``The Shape of Chaos.''

Abstract: Chaos is a small part of dynamical systems theory, which treats systems which evolve in time according to specific rules. Such rules are determined by studying the systems in question. There are three broad approaches to this subject; algebraic, analytic, and geometric. Algebraic approaches involve matrices and even more specialized structures to determine the properties of the system in question. An analytic approach involves the solution of a system of very general functions or differential equations. A geometric approach seeks to discover the "shape of the domain of the system." This division is an oversimplification since there is much overlap. In this talk I present some general concepts regarding the shape of the domain of several chaotic systems. Without going into any of the gory mathematics, I will take you on a tour of some of the concepts of modern geometry and topology as they apply to dynamical systems theory.

3 and 10 Februuary. Blake LeBaron, UW Economics: ``Evolving Neural Network Architectures for Forecasting.''

Abstract: These two talks will introduce a procedure combining aspects of evolutionary optimization algorithms along with bootstrap and monte- carlo cross-validation procedures. Evolution is used to search the large space of potential network architectures for lean network structures. These leaner networks reduce overfitting problems and improve numerical maximization properties of the heavily parameterized single hidden layer networks. In sample biases are estimated using several techniques, but estimates using bootstrap based cross- validation are emphasized. The procedure will be applied to two very different examples. The first is the Henon attractor, and the second is a foreign exchange forecasting problem. In both cases this procedure is shown to generate networks which perform well out of sample on several criteria, some of which are motivated by economic objectives.

17 February. Daniel Callan, Waisman Center: ``A Dynamic Neural Network Model of Speech Production in the Developing Child.''

Abstract: Many theories of speech processing propose the existence of motor control systems that utilize invariant vocal tract configurations to specify particular goals of speech production. One problem that challenges these theories is the fact that the associated structures involved with speech production go through a considerable amount of change during development. The same speech goals continue to be achieved during the course of development despite the changes that the vocal tract configuration undergoes. In this paper, characteristics of speech production in the developing child are accounted for by the DIVA model (Guenther, 1995, Guenther, et al., in press), which incorporates auditory perceptual targets to plan articulation. The conversion from articulator configuration to acoustic signal is worked out by a modified version of the Maeda articulation model that utilizes developmental parameters. The performance of the neural network was assessed at different points during development by determining the articulation-acoustic output needed to produce different vowels.

24 February. Craig Berridge, UW Psychology: ``The Locus Coeruleus-Noradrenergic System: Modulation of Behavioral State and State-Dependent Processes.''

Due to illness of the speaker, this seminar was cancelled. It will be rescheduled in the fall.

Abstract: The locus coeruleus-noradrenergic system is one of a number of brainstem-originating ascending systems that display state-dependent activity. During the past 25 years, considerable information has been collected that indicates that this system is well-positioned to exert a widespread and potent modulatory influence throughout the CNS. This talk will review recent observations that indicate that this system enhances acquisition and processing of sensory information, through a series of concerted actions across a variety of disparate brain regions.

3 March. Olvi Mangasarian, UW Computer Sciences: ``Mathematical Programming in Data Mining.''

Abstract: Mathematical programming approaches to two fundamental problems will be described: feature selection and clustering. The feature selection problem considered is that of discriminating between two sets while recognizing irrelevant and redundant features and suppressing them. This creates a lean model that often generalizes better to new unseen data. Computational results on real data confirm improved generalization of leaner models. Clustering is exemplified by the unsupervised learning of patterns and clusters that may exist in a given database and is a useful tool for knowledge discovery in databases (KDD). A mathematical programming formulation of this problem is proposed that is theoretically justifiable and computationally implementable in a finite number of steps. A resulting k-Median Algorithm is utilized to discover very useful survival curves for breast cancer patients from a medical database.

17 March. Julia L. Evans, Waisman Center: ``Nonlinear Dynamic Model of Social Discourse: Implications for the Study of Children with Language Disorders.''

Abstract: Nonlinear dynamic models provide a theoretical framework to study conversations in real-time. In particular, recent models based on the coupling of two complex systems indicate that: 1) speakers have a strong tendency to converge or coordinate their verbal and non-verbal speaking behavior moment-to-moment, 2) changes in the degree to which one speaking partner desires to participate in the conversation affect not only the stability of the dyad as a whole, but the behavior of the second speaker as well. Implications of the model's predictions will be discussed with respect to the nature of verbal interactions for children with language disorders.

24 March. Josh Chover, UW Mathematics: ``On Modeling Memory.''

Abstract: I'll present a model of a neural network which seems to learn sequences of "stimuli" without extensive training, recall them in correct order when prompted, and recognize novelty. The features of the model are conjectured to correspond to basic biological mechanisms. No technical knowledge should be necessary to understand this talk--neither remote nor recent recall.

31 March. Grace Wahba, UW Statistics: ``Multivariate Smoothing Methods in Time and Space with Application to Historical Trends and Patterns in the Global Historical Climate Network Data.''

No abstract yet.

7 April. Clarence Clay, UW Geology and Geophysics: ``Fractals and the Ocean Floor.''

Abstract: We know more about the surface of the moon than the seafloor that covers 70% of planet Earth. The main reason is that the oceans are effectively opaque to electromagnetic and light over distances greater than 10 to 100m. The attenuation of sound waves is small for frequencies less than 12 kHz. Sonars or acoustic echosounders get excellent reflections from the seafloor over most oceans 3 to 5 km depth. The seafloor is mapped by having oceanographic survey ships make many tracks over the survey area. For decades these were single tracks and the "depths" were the shortest time of arrival from a reflection or scattering from features on the bottom. The echo sounder beam widths were in the 10 to 30 degree range. Although the echosounders recorded continuously, the sonar "yard-stick" gives samples of depth at 3.5 km that are are roughly 100 m apart or more. Charts of the seafloor have much simplification, guess work, and artistic imagination. I will show examples of seafloor images for a wide range of scales.

We are interested in knowing the details the seafloor roughness because the geological processes cause it to be rough. We can use acoustic scatter from the seafloor to estimate roughness. Generally, scattering theories use approximate spatial spectra or spatial correlation functions as inputs. If the phases are not random, then a completely different form of acoustic scattering theory is needed.

There are good reasons to believe that the seafloor has a fractal structure. Measurements of the spatial power spectra give exponents of the wave numbers that are in the range of -2 to -5. The conventional wisdom is that the spectral components have random phases. The task for the marine geophysicist is to interpolate the seafloor roughness between sonar yard-stick measurements of depth. I analyzed a published profile and got a wavenumber slope of -3.2. However, the unwrapped phases have linear dependencies on wavenumber over decent ranges of the wavenumbers. I believe that fractal interpolation methods are a good replacement for the artist's imagination. With luck, I will show fractal interpolations for the echosounding profile that I used.

14 April. John Young, UW Atmospheric and Oceanic Sciences: ``El Nino --- An Overview of its Complex Dynamics.''

Abstract: The phenomenon of ``El Nino'' is an irregular, inter-annual disruption of the dynamical climate of the tropical ocean and atmosphere. This anomalous state is believed to depend strongly upon air-sea coupling and probably inherent dynamical nonlinearities in the dynamics of each fluid system. The resulting behavior is complex, but it seems to be partly predictable several months in advance.

In this talk, I will begin by briefly showing the structures of the physical components of this year's event, and historical time series indicating coupled but irregular behavior over the past decades. I will schematically review the governing mathematical equations, focusing on the crucial elements of air-sea coupling, Kelvin and Rossby waves, and nonlinearities.

In simple models, increased coupling suggests that unstable wave growth can exist, which can lead to chaotic behavior which probably dooms predictions beyond a year into the future. However, some models with more degrees of freedom suggest that the chaotic tendencies are less strong, and that prediction error growth is influenced more by stochastic influences. Resolution of these issues will be of practical societal as well as scientific benefit.

21 April. Michael Morgan, UW Atmospheric and Oceanic Sciences: ``Using Singular Vectors of Observed Atmospheric Flows to Diagnosis Cyclone Development and Predictability.''

Abstract: Quasi-geostrophic (QG) models of baroclinic instability successfully capture many of the salient characteristics of observed cyclones including the westward tilt with height of the geopotential field, growth rates, and the horizontal length scales of the disturbance. A more recent description of surface cyclogenesis views it as an initial value problem. Rather than disturbances being of normal mode form, the structure of the growing disturbance changes from being initially tilted against the flow to being tilted downshear at a later time. For a given flow, one may identify those disturbances which amplify most rapidly over a fixed time interval, for a given norm. These "optimal" disturbances are the singular vectors of the linear operator which describes the dynamical evolution of the fluid system.

In this presentation, calculations of singular vectors from simple QG models are presented and interpreted from a potential vorticity perspective. The salient features of the transient development of these singular vectors are identified and related to structures seen in cyclogenesis events. The relationship of singular vectors to predictability and the deployment of adaptive observing systems is also discussed.

22 April. Seminar of Possible Interest: Steven Strogatz, Dept. of Theoretical and Applied Mechanics, Cornell: ``Dynamics of Small World Networks.''

Unusual time and place: Wednesday, 2:25pm in room 901 Van Vleck.

Abstract: According to folklore, everyone on the planet is connected to everyone else through a short chain of acquaintances. This idea is often called ``six degrees of separation'' (after the play, and later Hollywood film, of the same name). The Kevin Bacon game, Erdös numbers, and the small-world phenomenon are all variations on the same theme. In this talk, I'll explore the mathematics underlying the small-world phenomenon, and argue that it is not merely a curiosity --- it is probably a common feature of large, sparse networks that are neither completely regular nor completely random. Networks in this middle ground have not been studied much, but they are ubiquitous and scientifically important; examples include neural networks and the electrical power grid of the western United States. Simple models of dynamical systems with small-world coupling appear to display enhanced propagation speed and computational power, compared to their locally-connected counterparts. This is joint work with Duncan Watts.

28 April. Amir Assadi, UW Mathematics: ``Perceptual Simplification of Geometry of Natural Surfaces in Human Vision.''

Abstract: Obect recognition in human vision begins with rays of photons that are emitted from the object reaching the eyes. A sequence of elaborate information processing tasks takes place in the brain, and leads to complex products such as object recognition and visual attention. The complexity of visual perception stems from many factors. Among them, there are billions of neurons, their circuits and networks mainly dedicated to vision. Nonetheless, every-day visual tasks are performed with great ease.

How does the visual system solve the numerous geometric problems, such as estimating the shape and spatial position of objects in a scene? Traditionally, two levels of information processing are distinguished: the bottom-up processes in Early (or Low Level) Vision, and the top-down processes in High Level Vision. Vision employs a combination of sequences of such processes in addition to other cognitive processes. While Low Level Vision is primarily concerned with local information, High Level Vision focuses on global phenomena. Where and how does the local-to-global transition in information processing occur?

We propose a hypothesis that there is a processing stage intermediate to these two levels. In this intermediate level, the visual system associates the simplest global geometric structures to the complex array of Early visual processes of local nature, taking into account the statistical nature of perception and the observer's ability to estimate global shapes of objects. Based on this model, we provide numerical estimates for some common geometric attributes of textured surfaces that the visual system might qualitatively perceive.

5 May. David Newman, Fusion Energy Division, Oak Ridge National Laboratory: ``If Self Organized Critical Systems Are All Around Us, Can We Identify and Control Them?''

Abstract: In nature there are many systems which appear to exhibit some form of self-organization. Among these are forest fires, earthquakes, sandpiles, turbulent transport and even many aspects of society itself. Investigations into the similarity of the dynamics of such systems have been undertaken by using simple cellular automata models. These models have produced a remarkable amount of insight into the dynamics of such systems. Some basic features of SOC systems, from forest fires to earthquakes and sandpiles will be discussed.

Recently a Self-Organized Criticality (SOC) model for turbulent transport in magnetically confined plasmas was proposed in order to explain some of the observed features of the transport dynamics in these plasmas. Because of this there has been an increased interest in methods for identifying and controlling such systems. A perturbed extension to a sandpile model of turbulent transport and data from various systems are used to investigate methods for possible control of SOC systems and methods for identifying whether these systems are SOC. Time permitting, some speculation on the implications to society of attempting to control certain behavior (for example, risk avoidance) in the context of controlling a SOC system will be discussed.

11 May. Tomaso Poggio, Brain Science Department and A. I. Lab, MIT: ``Learning Sparse Representations for Vision.''

Unusual Time and Place: Monday, 11 May, 3:30-4:30pm in room 1221 Computer Sciences and Statistics
Abstract: Learning is becoming the central problem in trying to understand intelligence and in trying to develop intelligent machines. I will outline some of our recent efforts in the domain of vision to develop machines that learn and to understand brain mechanisms of learning. I will begin with some recent theoretical results on the problem of function approximation and sparse representations that connect regularization theory, Support Vector Machine Regression, Basis Pursuit Denoising and PCA techniques. I will then motivate the appeal of learning sparse representations from an overcomplete dictionary of basis functions in terms of recent results in two different fields: computer vision and neuroscience. In particular, we have developed a trainable object detection architecture that succeeds in learning a sparse representation from an overcomplete set of Haar wavelets to perform difficult object detection tasks. In neuroscience, physiological data from IT cortex suggest that individual neurons encode a large vocabulary of elementary shapes before converging on cells tuned to specific views of specific 3D objects.

12 May. Steering Committee Meeting

Open meeting of the seminar steering committee; all are welcome to attend.
Up to the Chaos and Complex Systems Seminar page.
Last change worth mentioning Wednesday 6 May 1998
CRS