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 42: Complexity a la Mode: Spectral Methods for Complex Systems II
Paul Riechers, Physics, UC Davis

Reading: CMR article EC.

Topics:

  1. Review:
    1. Processes
    2. Models
    3. Mixed State Presentations
  2. Information Measures From MSPs
    1. Word Distributions
    2. Entropy Rates
    3. Statistical Complexity
    4. Synchronization Information
  3. Spectral Decomposition of Functions of Nondiagonalizable Dynamics
  4. Projection Operators
  5. Exact Complexities
    1. Autocorrelation Function and Power Spectra
    2. Finite-Length and Asymptotic Entropy Rates
    3. Excess Entropy
    4. Synchronization Information
    5. Transient Information
  6. Diagonalizable and Almost Diagonalizable Dynamics
  7. Examples