PHY 2⁸ A (Winter) & B (Spring)
Natural Computation and Self-Organization:

The Physics of Information Processing in Complex Systems

Announcements:

• Mark your calendar: NCASO Fest 2013, Saturday 1 June (afternoon, evening), Martinez (easy train access from Davis and Berkeley). Project presentations and BBQ!
• Upcoming lectures: Complex Materials (21, 23 May) and Information Thermodynamics (28 May).
• Work on your projects! No additional homework assignments after HW 15.
• However, there are two SAGE/CMPy labs on Bayesian Inference of ε-Machines. You may find these useful for your projects, especially if you're analyzing data.
• And, there is an optional homework on analyzing complex materials for those who'd like to see computational mechanics in experimental action.
• Online Resources and Webcasting News.

Instructor: Professor Jim Crutchfield (Physics and CSC)
Assistants: Dr. Korana Burke and Ryan James (Physics and CSC).
WWW: csc.ucdavis.edu/~chaos/courses/ncaso/

Catalog number:

• Winter, Physics 256 Section 1 (CRN 66729)
• Spring, Physics 250 Section 3 (CRN 63468)

• Live: 185 Physics, UC Davis
• Webcast: 560 Evans Hall, UC Berkeley

The course explores how nature's structure reflects how nature computes. It introduces intrinsic unpredictability (deterministic chaos) and the emergence of structure (self-organization) in natural complex systems. Using statistical mechanics, information theory, and computation theory, the course develops a systematic framework for analyzing processes in terms of their causal architecture. This is determined by answering three questions: (i) How much historical information does a process store? (ii) How is that information stored? And (iii) how is the stored information used to produce future behavior? The answers to these questions tell one how a system intrinsically computes.

The course introduces tools to describe and quantify randomness and structure. It shows how they are necessarily complementary and how they are intimately related to concepts from the theory of computation. A number of example complex systems—taken from physics, chemistry, and biology—are used to illustrate the phenomena and methods. The course also takes time to reflect on the intellectual history of these topics, which is quite rich and touches on many basic questions in fundamental physics and the sciences and technology generally. New topics this year include complex materials and computation in quantum systems. The course will bring students to the research frontier in nonlinear physics and complex systems.

Outline:
PHY 256 (Winter 2013) (aka 256A): (Course Syllabus [PDF] [HTML] )

• Weeks 1-4: Self-Organization (Nonlinear dynamics and pattern formation)
• Weeks 5-6: Measurement Theory (Symbolic dynamics and stochastic processes)
• Weeks 7-10: Information Processing (Introduction to information theory)

• Weeks 1-4: Natural Computation (Computational mechanics)
• Weeks 6-8: Example Complex Systems
• Weeks 9-10: Projects.

Complex systems to be analyzed:

• Low-dimensional chaos and routes to chaos
• Hidden Markov models
• Cellular automata
• 1D/2D spin systems
• One-dimensional materials
• Quantum dynamical systems

Audience: Graduate students in physics, mathematics, computer science, engineering, mathematical biology, and theoretical neuroscience. Others also welcome.

Reference materials:

1. Books:
   • Elements of Information Theory, T. M. Cover and J. A. Thomas, Second Edition, Wiley-Interscience, New York (2006).
   • Nonlinear Dynamics and Chaos: with applications to physics, biology, chemistry, and engineering, S. H. Strogatz, Second Edition, Addison-Wesley, Reading, Massachusetts (December 2000 or later printing).
2. Computational Mechanics Reader.
3. Lecture notes.
4. Software tools.
5. Supplemental Readings for historical background, projects, programming, and amusement.

Course Work:

1. Assigned Readings.
2. Weekly Problem Sets (Both Winter and Spring 2013, 40%).
3. Mid-term Exam (PHY 256 Winter 2013, 30%): Take home.
4. Final Exam (PHY 256 Winter 2013, 30%): Take home.
5. Research Project (PHY 250 Spring 2013, 60%):
   • Project report:
     • Orally presented as final exam during last class meetings.
     • Written report: Due electronically NN June.
   • Project Presentation Schedule.
   • Report Organization.
   • Example projects can be found here.