Physics of Computation

Physics 2^{8}B

Syllabus (Spring)

Instructor: Prof. Jim Crutchfield (chaos@ucdavis.edu; http://csc.ucdavis.edu/~chaos)

WWW: http://csc.ucdavis.edu/~chaos/courses/poci/

1 Natural Computation

1.1 Lecture 21: Overview

1.2 Lecture 22: The Learning Channel

1.3 Lecture 23: ϵ-Machine Reconstruction

1.4 Lecture 24: ϵ-Machine Optimalities

1.5 Lecture 25: Measures of Structural Complexity I

1.6 Lecture 25: Measures of Structural Complexity II

1.7 Lecture 27: Information Diagrams for Processes

1.8 Lectures 29 and 30: Directional Computational Mechanics

1.9 Lecture 31: Complex Materials I (Dowman Varn)

1.10 Lecture 32: Complex Materials II (Dowman Varn)

1.11 Lecture 26: Mixed States (Chris Ellison)

1.12 Lecture 28: The Reverse ϵ-Machine (Chris Ellison)

1.13 Lecture 30: Hierarchical ϵ-Machines

1.14 Lecture 36: Information Thermodynamics

1.15 Lecture 37: Intrinsic Semantics of Information I (Ryan James)

1.16 Lecture 39: Intrinsic Semantics of Information II (Ryan James)

2 Project Presentations

2.1 Lecture 39: Project Presentations

2.2 Lecture 40: Project Presentations

1.1 Lecture 21: Overview

1.2 Lecture 22: The Learning Channel

1.3 Lecture 23: ϵ-Machine Reconstruction

1.4 Lecture 24: ϵ-Machine Optimalities

1.5 Lecture 25: Measures of Structural Complexity I

1.6 Lecture 25: Measures of Structural Complexity II

1.7 Lecture 27: Information Diagrams for Processes

1.8 Lectures 29 and 30: Directional Computational Mechanics

1.9 Lecture 31: Complex Materials I (Dowman Varn)

1.10 Lecture 32: Complex Materials II (Dowman Varn)

1.11 Lecture 26: Mixed States (Chris Ellison)

1.12 Lecture 28: The Reverse ϵ-Machine (Chris Ellison)

1.13 Lecture 30: Hierarchical ϵ-Machines

1.14 Lecture 36: Information Thermodynamics

1.15 Lecture 37: Intrinsic Semantics of Information I (Ryan James)

1.16 Lecture 39: Intrinsic Semantics of Information II (Ryan James)

2 Project Presentations

2.1 Lecture 39: Project Presentations

2.2 Lecture 40: Project Presentations

Theme: Causal Architecture of Dynamical Systems and Stochastic Processes

- Prediction and Learning
- ϵ-Machines and Causal Architecture
- Measures of Structural Complexity
- How to Calculate
- Complex Materials
- Intrinsic Semantics in Information

Readings (available via course website):

- CMR article Chance and Order, Stanislaw Lem, New Yorker 59 (1984) 88–98.
- CMR article Revealing Order in the Chaos, Mark Buchanan, New Scientist, 26 February 2005; available at http://csc.ucdavis.edu/~chaos/news/.

Topics:

- Recall Physics 2
^{8}A - Introduction and motivations
- Inadequacy of Information Theory
- Structure and Learning
- Survey interests, background, and abilities
- Course logistics
- CMPy Labs
- Projects
- Software and program development

Homework: Assign Week 10’s today.

Reading:

- CMR article RURO (Intro) and Lecture Notes.

Topics:

- The Learning Channel
- The Prediction Game
- Space of histories
- Predictive equivalence relation
- Causal states
- ϵ-Machines

Reading: CMR article CMPPSS and Lecture Notes.

Topics:

- Review last lecture
- Causal states
- ϵ-Machine reconstruction
- Simple Processes: Predictable (Period-1), Fair Coin, and Biased Coin
- Complex Processes: Period-2, Golden Mean, and Even Processes

Homework: Collect Week 10’s and assign Week 11’s today.

Reading: CMR article CMPPSS.

Topics:

- Optimal Prediction
- Minimality
- Uniqueness
- Minimal Sufficient Statistic
- Minimal Stochasticity

Reading: CMR article CMPPSS.

Topics:

- Entropy rate
- Statistical complexity
- Excess entropy
- Statistical complexity bounds excess entropy

Homework: Collect Week 11’s and assign Week 12’s today.

Reading: CMR article CMPPSS.

Topics:

- Cryptographic Limit
- Stored versus transmitted information
- Pattern: Groups versus semi-groups, exact and statistical symmetries
- Measurement Semantics
- Excess Entropy Bound
- Forward and Reverse Processes and their ϵ-Machines
- Causal Irreversibility

Reading: CMR articles TBA and Yeung.

Topics:

- Information diagrams
- Markov chain information diagrams
- Shannon information measures
- Process information diagrams

Homework: Collect Week 12’s and assign Week 13’s today.

Projects: Project topic should be selected by now.

Reading: CMR articles TBA, PRATISP, and IACP.

Topics:

- Forward and reverse processes
- Causal irreversibility
- The process lattice
- Calculating reverse ϵ-machine from the forward ϵ-machine

Homework: Collect Week 13’s due; assign Week 14’s.

Reading: CMR articles BTFM1 and BTFM2.

Topics:

- One-Dimensional materials: Physics of polytypes
- Experimental studies
- Fault model

Homework: Collect Week 14’s and assign Week 15’s today.

Reading: CMR articles BTFM1 and BTFM2.

Topics:

- ϵ-Machine spectral reconstruction
- Structure in disorder: Beyond the fault model
- Zinc-Sulfide

Reading: CMR articles SON and OCI.

Topics:

- Mixed states and their presentations
- Synchronization-Control Decomposition
- Changing presentations

Homework: No more homework. Work on your projects!

Reading: CMR articles SON and OCI.

Topics:

- Reversibility
- Reverse ϵ-machine
- The bimachine
- Excess entropy, revisited and exactly calculated

Reading: CMR article CMPPSS.

Topics:

- Review Causal State Equivalence Relation
- Hierarchical ϵ-Machine Reconstruction
- Infinite Processes: Onset of Chaos

Reading: CMR article TBD.

Topics:

- Thermodynamics of Information Processing
- The Szilard Demon
- The Chaotic Szilard Map

Reading: Anatomy of a Bit article.

Topics:

- Information Diagrams, revisited
- Anatomy of a Bit
- Semantics

Reading: Many Roads to Synchrony article.

Topics:

- Cryptic and Markov Orders
- Synchronization

- Presentations will be organized according to class size.
- If the class is large, most likely they will be given at a mini-workshop, some evening.