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Complex Systems Summer School 2011 Modules

Organized by Jim Crutchfield


  • T. Cover and J.Thomas, Elements of Information Theory, Wiley, Second Edition (2006) Chapters 1 - 7.
  • M. Li and P.M.B.Vitanyi, An Introduction to Kolmogorov Complexity and its Applications , Springer, New York (1993).
  • J. P. Crutchfield and D. P. Feldman, “Regularities Unseen, Randomness Observed: Levels of Entropy Convergence”,CHAOS 13:1 (2003) 25-54.

Lecture Notes

Ryan's talks

  1. Anatomy of an Observation
  2. Length Scales in Complex Time Series


James P. Crutchfield: The Calculi of Emergence

Mikhail Prokopenko, Fabio Boschetti, and Alex J. Ryan: An Information-Theoretic Primer on Complexity, Self-Organisation and Emergence

Cosma Rohilla Shalizi, James P. Crutchfield: Pattern Discovery and Computational Mechanics

Ryan G. James, John R. Mahoney, Christopher J. Ellison, James P. Crutchfield: Many Roads to Synchrony: Natural Time Scales and Their Algorithms

James P. Crutchfield, Christopher J. Ellison, Ryan G. James, John R. Mahoney: Synchronization and Control in Intrinsic and Designed Computation: An Information-Theoretic Analysis of Competing Models of Stochastic Computation

John R. Mahoney, Christopher J. Ellison, James P. Crutchfield: Information Accessibility and Cryptic Processes

Christopher J. Ellison, John R. Mahoney, James P. Crutchfield: Prediction, Retrodiction, and The Amount of Information Stored in the Present

David P. Feldman, Carl S. McTague, James P. Crutchfield: The Organization of Intrinsic Computation: Complexity-Entropy Diagrams and the Diversity of Natural Information Processing

Ryan G. James, Christopher J. Ellison, James P. Crutchfield: Anatomy of a Bit: Information in a Time Series Observation

Joseph T. Lizier, Mikhail Prokopenko, and Albert Y. Zomaya: Information modification and particle collisions in distributed computation

Nicolas Brodu: Reconstruction of Epsilon-Machines in Predictive Frameworks and Decisional States

Samer A. Abdallah, Mark D. Plumbley: A measure of statistical complexity based on predictive information

Łukasz Dęowski: Excess entropy in natural language: present state and perspectives

Online Labs

CMPy Notebook

Complexity Lab 1

Complexity Lab 2

Complexity Lab 3

Complexity Lab 4