Upcoming Gigs: New York
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
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
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"
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
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.
Enigmas of Chance
Posted at September 14, 2007 11:15 | permanent link