PHY 28B
Natural Computation and Self-Organization:
The Physics of Information Processing in Complex Systems

Jim Crutchfield
chaos@ucdavis.edu; http://csc.ucdavis.edu/~chaos

Spring
WWW: http://csc.ucdavis.edu/~chaos/courses/ncaso/

Lecture 41: Complexity a la Mode: Spectral Methods for Complex Systems I
Paul Riechers, Physics, UC Davis

Reading: CMR article EC.

Topics:

  1. Visualizing Relaxation Modes and Formalizing those Intuitions
  2. What to Expect
  3. HMMs as Mathematical Objects
  4. Motivating Example: Ion Channel Dynamics
  5. An Operator and Its Spectrum
  6. Eigenvalues and Projection Operators
  7. Functions of Square Matrices
  8. Restrictions on Eigenvalues: Perron-Frobenious Theorem
  9. Autocorrelation Function
  10. Power Spectrum
  11. Examples
  12. What’s Next?