My current focus is on the analysis of time-series data from
complex adaptive nonlinear systems. I use a variety of
approaches, ranging from the traditional ones from nonlinear dynamics
(delay reconstruction, Lyapunov exponents, etc.) to information theory
and topological data analysis.
In the past, I have done some work in the area of artificial
intelligence: in particular, computer tools that autonomously analyze
and/or design things. My focus has largely shifted away from this
area. Note: I do not work on machine learning. Please do not
contact me about projects in that area.
- Human movement dynamics: this area has two distinct foci:
Riffing on that, students in my group (and
in my class) have used chaos to
generate variations on different kinds of sequences,
rock climbing, and many other movement genres - as well as music
genres ranging from jazz guitar to tabla.
- Flow control: intentionally inducing,
suppressing, and "guiding" chaotic flows in a fluid using
micromachined flaps in the boundary layer of a jet.
- The nonlinear dynamics of
computer performance: frameworks for modeling computers as
deterministic nonlinear dynamical systems, and using those models to
forecast their performance.
- Control of internet attacks using
nonlinear dynamics, stochastic models, and control theory.
- Recurrence plots: a visualization tool
that brings out correlations in time-series data.
- Phase-locked loop: using chaos to improve
the capture range of a common and useful electronic circuit.
- CScience: an integrated software
system that helps geoscientists construct age models (which
relate depth to calendar age) for an ice or ocean-sediment core.
- ACE: an argumentation
system that helps geologists deduce the age of a landform, given
samples of rocks from that landform. As a successful, deployed
workflow-based system for doing earth science, ACE has been featured
EarthCube Workflow Community Group's "workflow vignettes" website
and in the
EarthCube Workflows Roadmap for the Geosciences
document (see pp33-36).
- Intelligent computation of
reachability sets: automatically exploring the evolving geometry
of the set of allowed paths of a spacecraft.
- PRET, a computer program that
deduces the internal dynamics of a nonlinear black-box system solely
from observations of its outputs, automating the process known to
control theorists as system identification.
- Feature recognition in scientific data
sets: computer tools for recognizing when a numerical simulation
is going bad, when an atmospheric data set contains a hurricane, when
two photos of the sky show the emergence of a supernova, etc.
Many of the links in the "Current Projects" section above point to
documents that describe current research opportunities. These range
from one-semester undergraduate research projects through M.S. and
Ph.D. theses to postdoctoral appointments. Please shoot me an email
message if you're interested in any of these opportunities. And I'm
happy to work with smart, independent students on projects of their
own choosing, even if I don't know much about the associated area.
Here are some examples: