RESEARCH

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Research Interests:

	Artificial Intelligence: computer tools that autonomously analyze and/or design things.
	Nonlinear Dynamics: techniques for characterizing and exploiting the unique properties of chaos.

Some artificial intelligence projects:

• 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.
• Chaography: two AI tools that use mathematics to generate human motion sequences.
• 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 a supernova, etc.
• A program that parses a complex electronic schematic into functional blocks (this project is not yet underway).

Some nonlinear dynamics projects:

• Analysis:
  • recurrence plots: a visualization tool that brings out correlations in time-series data.
  • computational topology: a technique for describing the connectedness properties of an object, using only discrete data about that object.
  • Applications: analysis tools like these are useful in applications ranging from microwave circuits and Greenland ice-core data to the control of fluid flows and internet attacks.
• Synthesis:
  • phase-locked loop: using chaos to improve the capture range of a common and useful electronic circuit.
  • flow control: intentionally inducing, suppressing, and "guiding" chaotic flows in a fluid using micromachined flaps in the boundary layer of a jet.
  • dance using chaos to generate variations on human movement sequences. This project straddles the areas of artificial intelligence and nonlinear dynamics, so it is listed under both areas.)
  • control of internet attacks using nonlinear dynamics, stochastic models, and control theory.
• Here's a webcast of a talk that hits some of the high points of this stuff.

Many of the links on this page point to documents that describe current research opportunities, ranging from one-semester undergraduate research projects, through M.S. and Ph.D. theses, to postdoctoral appointments. Please contact me if you're interested!