- 2 January. No Meeting.
- 27 January. George Hrabovsky: ``The Shape of Chaos.''
- 3 February. Blake LeBaron: ``Evolving Neural Network Architectures for Forecasting'' (part 1).
- 10 February. Blake LeBaron: ``Evolving Neural Network Architectures for Forecasting'' (part 2).
- 17 February. Dan Callan: ``A Dynamic Neural Network Model of Speech Production in the Developing Child.''
- 24 February. Craig Berridge: ``The Locus
Coeruleus-Noradrenergic System: Modulation of Behavioral State
and
State-Dependent Processes.''
**Cancelled**due to illness. - 3 March. Olvi Mangasarian: ``Mathematical Programming in Data Mining.''
- 10 March. No seminar --- spring recess.
- 17 March. Julia Evans: ``Nonlinear Dynamic Model of Social Discourse: Implications for the Study of Children with Language Disorders.''
- 24 March. Josh Chover: ``On Modeling Memory.''
- 31 March. Grace Wahba: ````Multivariate Smoothing Methods in Time and Space with Application to Historical Trends and Patterns in the Global Historical Climate Network Data.''
- 7 April. Clarence Clay: ``Fractals and the Ocean Floor.''
- 14 April. John Young: ``El Nino --- An Overview of its Complex Dynamics''
- 21 April. Michael Morgan: ``Using Singular Vectors of Observed Atmospheric Flows to Diagnosis Cyclone Development and Predictability.''
- 22 April.
**Seminar of possible interest:**Steven Strogatz: ``Dynamics of Small-World Networks.'' - 28 April. Amir Assadi: ``Perceptual Simplification of 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 Them?''
- 11 May.
**Seminar of possible interest:**Tomaso Poggio: ``Learning Sparse Representations for Vision.'' - 12 May. Steering Committee Meeting.

*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.

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.

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.

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.

*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.

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.

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.

Up to the Chaos and Complex Systems Seminar page.

Last change worth mentioning Wednesday 6 May 1998

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