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
- 2 January. No Meeting.
- 27 January. George Hrabovsky: ``The Shape
- 3 February. Blake LeBaron:
Network Architectures for Forecasting'' (part 1).
- 10 February. Blake LeBaron:
Network Architectures for Forecasting'' (part 2).
- 17 February. Dan Callan: ``A Dynamic
Model of Speech Production in the Developing Child.''
- 24 February. Craig Berridge: ``The Locus
Coeruleus-Noradrenergic System: Modulation of Behavioral State
State-Dependent Processes.'' Cancelled due to
- 3 March. Olvi Mangasarian: ``Mathematical
in Data Mining.''
- 10 March. No seminar --- spring recess.
- 17 March. Julia Evans: ``Nonlinear
Social Discourse: Implications for the Study of Children with
- 24 March. Josh Chover: ``On Modeling
- 31 March. Grace Wahba: ````Multivariate
Methods in Time and Space with Application to Historical Trends
the Global Historical Climate Network Data.''
- 7 April. Clarence Clay: ``Fractals and the
- 14 April. John Young: ``El Nino --- An
its Complex Dynamics''
- 21 April. Michael Morgan: ``Using
Observed Atmospheric Flows to Diagnosis Cyclone Development and
- 22 April. Seminar of possible
interest: Steven Strogatz: ``Dynamics of Small-World
- 28 April. Amir Assadi: ``Perceptual
Geometry of Natural Surfaces in Human Vision.''
- 5 May. David Newman: ``If Self Organized
Critical Systems Are All Around Us, Can We Identify and Control
- 11 May. Seminar of possible
Tomaso Poggio: ``Learning Sparse Representations for Vision.''
- 12 May. Steering Committee Meeting.
27 Jannuary. George E. Hrabovsky, UW
Shape of Chaos.''
Abstract: Chaos is a small part of dynamical systems
which treats systems which
evolve in time according to specific rules. Such rules are
studying the systems in question. There are three broad approaches
subject; algebraic, analytic, and geometric. Algebraic approaches
matrices and even more specialized structures to determine the
the system in question. An analytic approach involves the solution
of very general functions or differential equations. A geometric
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
general concepts regarding the shape of the domain of several
Without going into any of the gory mathematics, I will take you on a
some of the concepts of modern geometry and topology as they apply
3 and 10 Februuary. Blake LeBaron, UW
Economics: ``Evolving Neural Network Architectures for
These two talks will introduce a procedure combining aspects of
optimization algorithms along with bootstrap and monte- carlo
procedures. Evolution is used to search the large space of potential
architectures for lean network structures. These leaner networks
overfitting problems and improve numerical maximization properties
heavily parameterized single hidden layer networks. In sample biases
estimated using several techniques, but estimates using bootstrap
validation are emphasized. The procedure will be applied to two very
examples. The first is the Henon attractor, and the second is a
exchange forecasting problem. In both cases this procedure is shown
networks which perform well out of sample on several criteria, some
are motivated by economic objectives.
17 February. Daniel Callan, Waisman Center:
Dynamic Neural Network Model of Speech Production in the
Many theories of speech processing propose the existence of motor
systems that utilize invariant vocal tract configurations to specify
goals of speech production. One problem that challenges these
fact that the associated structures involved with speech production
a considerable amount of change during development. The same speech
continue to be achieved during the course of development despite the
that the vocal tract configuration undergoes. In this paper,
of speech production in the developing child are accounted for by
model (Guenther, 1995, Guenther, et al., in press), which
perceptual targets to plan articulation. The conversion from
configuration to acoustic signal is worked out by a modified version
Maeda articulation model that utilizes developmental parameters. The
performance of the neural network was assessed at different points
development by determining the articulation-acoustic output needed
24 February. Craig Berridge, UW Psychology:
Locus Coeruleus-Noradrenergic System: Modulation of Behavioral
Due to illness of the speaker, this seminar was cancelled.
will be rescheduled in the fall.
The locus coeruleus-noradrenergic system is one of a number of
brainstem-originating ascending systems that display
During the past 25 years, considerable information has been
indicates that this system is well-positioned to exert a
modulatory influence throughout the CNS. This talk will review
observations that indicate that this system enhances acquisition
of sensory information, through a series of concerted actions
of disparate brain regions.
3 March. Olvi Mangasarian, UW Computer
``Mathematical Programming in Data Mining.''
Mathematical programming approaches to two fundamental problems will
described: feature selection and clustering. The feature selection
considered is that of discriminating between two sets while
irrelevant and redundant features and suppressing them. This creates
model that often generalizes better to new unseen data.
on real data confirm improved generalization of leaner models.
exemplified by the unsupervised learning of patterns and clusters
exist in a given database and is a useful tool for knowledge
databases (KDD). A mathematical programming formulation of this
proposed that is theoretically justifiable and computationally
a finite number of steps. A resulting k-Median Algorithm is utilized
discover very useful survival curves for breast cancer patients from
17 March. Julia L. Evans, Waisman Center:
Dynamic Model of Social Discourse: Implications for the Study of
Nonlinear dynamic models provide a theoretical framework to study
in real-time. In particular, recent models based on the coupling of
systems indicate that: 1) speakers have a strong tendency to
coordinate their verbal and non-verbal speaking behavior
changes in the degree to which one speaking partner desires to
the conversation affect not only the stability of the dyad as a
behavior of the second speaker as well. Implications of the model's
will be discussed with respect to the nature of verbal interactions
children with language disorders.
24 March. Josh Chover, UW Mathematics: ``On
I'll present a model of a neural network which seems to learn
of "stimuli" without extensive training, recall them in correct
when prompted, and recognize novelty. The features of the model are
conjectured to correspond to basic biological mechanisms. No
knowledge should be necessary to understand this talk--neither
nor recent recall.
Grace Wahba, UW
``Multivariate Smoothing Methods in Time and Space with
Historical Trends and Patterns in the Global Historical Climate
No abstract yet.
7 April. Clarence Clay, UW Geology and
``Fractals and the Ocean Floor.''
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
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
many tracks over the survey area. For decades these were single
and the "depths" were the shortest time of arrival from a reflection
scattering from features on the bottom. The echo sounder beam widths
were in the 10 to 30 degree range. Although the echosounders
continuously, the sonar "yard-stick" gives samples of depth at 3.5
that are are roughly 100 m apart or more. Charts of the seafloor
much simplification, guess work, and artistic imagination. I will
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.
scattering theories use approximate spatial spectra or spatial
correlation functions as inputs. If the phases are not random,
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
the wave numbers that are in the range of -2 to -5. The
wisdom is that the spectral components have random phases. The
the marine geophysicist is to interpolate the seafloor roughness
between sonar yard-stick measurements of depth. I analyzed a
profile and got a wavenumber slope of -3.2. However, the unwrapped
phases have linear dependencies on wavenumber over decent ranges
wavenumbers. I believe that fractal interpolation methods are a
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
Sciences: ``El Nino --- An Overview of its Complex Dynamics.''
The phenomenon of ``El Nino'' is an irregular, inter-annual
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
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
physical components of this year's event, and historical time
indicating coupled but irregular behavior over the past decades. I
schematically review the governing mathematical equations,
the crucial elements of air-sea coupling, Kelvin and Rossby waves,
In simple models, increased coupling suggests that unstable wave
growth can exist, which can lead to chaotic behavior which
dooms predictions beyond a year into the future. However, some
with more degrees of freedom suggest that the chaotic tendencies
less strong, and that prediction error growth is influenced more
stochastic influences. Resolution of these issues will be of
societal as well as scientific benefit.
21 April. Michael Morgan, UW Atmospheric and
Sciences: ``Using Singular Vectors of Observed Atmospheric Flows
Diagnosis Cyclone Development and Predictability.''
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
value problem. Rather than disturbances being of normal mode form,
structure of the growing disturbance changes from being initially
tilted against the flow to being tilted downshear at a later time.
a given flow, one may identify those disturbances which amplify most
rapidly over a fixed time interval, for a given norm. These
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
QG models are presented and interpreted from a potential vorticity
perspective. The salient features of the transient development of
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
22 April. Seminar of Possible Interest:
Strogatz, Dept. of Theoretical and Applied Mechanics, Cornell:
Small World Networks.''
Unusual time and place: Wednesday, 2:25pm in room 901 Van
Abstract: According to folklore, everyone on the planet
connected to everyone else through a short chain of acquaintances.
is often called ``six degrees of separation'' (after the play, and
Hollywood film, of the same name). The Kevin Bacon game,
and the small-world phenomenon are all variations on the same
talk, I'll explore the mathematics underlying the small-world
argue that it is not merely a curiosity --- it is probably a
large, sparse networks that are neither completely regular nor
random. Networks in this middle ground have not been studied much,
are ubiquitous and scientifically important; examples include
and the electrical power grid of the western United States. Simple
dynamical systems with small-world coupling appear to display
propagation speed and computational power, compared to their
counterparts. This is joint work with Duncan Watts.
28 April. Amir Assadi, UW Mathematics:
Simplification of Geometry of Natural Surfaces in Human
Obect recognition in human vision begins with rays of photons that
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.
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
with great ease.
How does the visual system solve the numerous geometric problems,
estimating the shape and spatial position of objects in a scene?
Traditionally, two levels of information processing are
bottom-up processes in Early (or Low Level) Vision, and the
in High Level Vision. Vision employs a combination of sequences of
processes in addition to other cognitive processes. While Low
primarily concerned with local information, High Level Vision
phenomena. Where and how does the local-to-global transition in
We propose a hypothesis that there is a processing stage
these two levels. In this intermediate level, the visual system
simplest global geometric structures to the complex array of Early
processes of local nature, taking into account the statistical
perception and the observer's ability to estimate global shapes of
Based on this model, we provide numerical estimates for some
attributes of textured surfaces that the visual system might
5 May. David Newman, Fusion Energy Division,
Ridge National Laboratory: ``If Self Organized Critical Systems
Around Us, Can We Identify and Control Them?''
In nature there are many systems which appear to exhibit some form
self-organization. Among these are forest fires, earthquakes,
turbulent transport and even many aspects of society itself.
into the similarity of the dynamics of such systems have been
using simple cellular automata models. These models have produced a
amount of insight into the dynamics of such systems. Some basic
SOC systems, from forest fires to earthquakes and sandpiles will be
Recently a Self-Organized Criticality (SOC) model for turbulent
magnetically confined plasmas was proposed in order to explain
observed features of the transport dynamics in these plasmas.
there has been an increased interest in methods for identifying
such systems. A perturbed extension to a sandpile model of
and data from various systems are used to investigate methods for
control of SOC systems and methods for identifying whether these
SOC. Time permitting, some speculation on the implications to
attempting to control certain behavior (for example, risk
context of controlling a SOC system will be discussed.
11 May. Tomaso Poggio,
Department and A. I. Lab, MIT: ``Learning Sparse Representations
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
understand intelligence and in trying to develop intelligent
outline some of our recent efforts in the domain of vision to
that learn and to understand brain mechanisms of learning. I will
some recent theoretical results on the problem of function
sparse representations that connect regularization theory, Support
Machine Regression, Basis Pursuit Denoising and PCA techniques. I
motivate the appeal of learning sparse representations from an
dictionary of basis functions in terms of recent results in two
fields: computer vision and neuroscience. In particular, we have
trainable object detection architecture that succeeds in learning a
representation from an overcomplete set of Haar wavelets to perform
object detection tasks. In neuroscience, physiological data from IT
suggest that individual neurons encode a large vocabulary of
before converging on cells tuned to specific views of specific 3D
12 May. Steering Committee Meeting
Open meeting of the seminar steering committee; all are welcome to
Up to the Chaos and Complex Systems Seminar
Last change worth mentioning Wednesday 6 May 1998