I'm giving two talks in New York state in the first week of October.

- Tuesday, 2 October, Columbia University: "Reconstructing Stochastic State Spaces from Discrete Time Series"
- Applied Mathematics Colloquium, 2:45 pm in 214 Mudd; hosted by Chris Wiggins
*Abstract:*State-space reconstruction --- inferring a latent dynamical system directly from time series --- has become a fundamental tool of experimental nonlinear dynamics. Unfortunately, its mathematical basis, the Takens embedding theorem, only applies, strictly speaking, to smooth, deterministic dynamics, measured without noise. Attempts to apply it to stochastic dynamical systems often end in tears. In this talk, I will discuss theoretical reasons for hoping that we can reconstruct stochastic state spaces, based on ideas about Markovian representations and information-theoretic prediction, and some recent progress on consistent algorithms for discrete-valued, discrete-time data. An equivalent, if more statistical-sounding, way to think about all this is "adaptive nonparametric modeling of categorical time series". I'll close with some examples of applications to real data.- Friday, 5 October, University at Albany: "Quantifying self-organization and coherent structures"
- Physics Department seminar, place and time when I know them; hosted by Kevin Knuth and Adom Giffin
*Abstract:*Despite broad interest in self-organizing systems, there are few quantitative criteria for self-organization which can be applied to dynamical models, let alone experimental data. All existing criteria give counter-intuitive results in important cases. A solution is offered by a new criterion, namely an internally-generated increase in the statistical complexity, the amount of information required for optimal prediction of the system's dynamics. This complexity can be precisely defined, using the probabilistic ideas of mutual information and minimal sufficient statistics. The definition also leads to a general method for predicting such systems. Examining the variation in the statistical complexity over space and time provides a way of automatically identifying the coherent structures generated by the system. Illustrations come from cellular automaton models of excitable media and sand-piles, and from computational fluid dynamics.

I'll also give a "how to get a job like mine" talk to Chris's class for advanced undegraduate applied math majors. I will try to limit the amount of wrongthink I dispense, but I doubt I'll be able to resist the temptation to show them questionable pictures.

I have, to my embarrassment, gone this far in life without ever having been to New York City. Drop me a line if you'd like to get in touch, or have some suggestions on what a traveler from the provinces should do on his first visit to the world capital.

Posted at September 14, 2007 11:15 | permanent link