Course Proposal : Studying Optimization of Complex Systems By Modeling Them as Spin Glasses

Reproduction from C. Speranza's Master's Thesis show at Ohio State University, Columbus, OH, May 1989.

A course to be offered at San Francisco State.

There are many branches of science where the olde methods of 19th century mathematics and physics have yielded their last fruits. These methods rely primarily on linear differential equations and on approximating solutions of complex, coupled systems - usually described by non-linear differential equations - by small perturbations about non-interacting, free solutions. There are many branches of Science, like Electrical Engineering, Computer Science, BioPhysics, Physics, Economics, Psychology, and others, where these perturbative solutions are not sufficient anymore. There is a need to develop new methods to study these non-linear, non-perturbative solutions. In this Course I am proposing to study one such method, which arose in the study of Condensed Matter Physics, namely Spin Glasses, and look at its applications to some of the branches of Science mentioned above.

Course of Study
This is a proposal for a Master's level or undergraduate level course. This course would cover several topics

• Magnetic Systems and their Phase Transitions.
• The Replica Approach.
• The TAP Approach.
• Breaking the Replica Symmetry.
• The Nature of the Spin Glass Phase.
• Combinatorial Optimization Problems.
• Simulated Annealing.
• Analytic Results.
  Then there will be several topics in applications of Spin Glasses to (non-linear) optimization:
• Applications to Computer Science , like the Traveling Salesman Problem, the Matching Problem, The Assignment Problem;
• Applications to Electrical Engineering, like Error Correcting;
• Biological Applications, like brain modeling.
• Hopfield Model and its Variations.
• Protein Folding ;
• Particle Physics Applications, like Jet Analysis;

Reproduction from J. Campbell's Occidental Mythologies.

(To Physics Research)

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