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Exactly solvable models of adaptive networks. 2006

Olivier Rivoire, and Julien Barré
Laboratory of Living Matter, The Rockefeller University, 1230 York Ave., New York, New York 10021, USA.

A satisfiability-unsatisfiability (SAT-UNSAT) transition takes place for many optimization problems when the number of constraints, graphically represented by links between variables nodes, is brought above some threshold. If the network of constraints is allowed to adapt by redistributing its links, the SAT-UNSAT transition may be delayed and preceded by an intermediate phase where the structure self-organizes to satisfy the constraints. We present an analytic approach, based on the recently introduced cavity method for large deviations, which exactly describes the two phase transitions delimiting this adaptive intermediate phase. We give explicit results for random bond models subject to the connectivity or rigidity percolation transitions, and compare them with numerical simulations.

UI MeSH Term Description Entries
D008432 Mathematical Computing Computer-assisted interpretation and analysis of various mathematical functions related to a particular problem. Statistical Computing,Computing, Statistical,Mathematic Computing,Statistical Programs, Computer Based,Computing, Mathematic,Computing, Mathematical,Computings, Mathematic,Computings, Mathematical,Computings, Statistical,Mathematic Computings,Mathematical Computings,Statistical Computings
D008962 Models, Theoretical Theoretical representations that simulate the behavior or activity of systems, processes, or phenomena. They include the use of mathematical equations, computers, and other electronic equipment. Experimental Model,Experimental Models,Mathematical Model,Model, Experimental,Models (Theoretical),Models, Experimental,Models, Theoretic,Theoretical Study,Mathematical Models,Model (Theoretical),Model, Mathematical,Model, Theoretical,Models, Mathematical,Studies, Theoretical,Study, Theoretical,Theoretical Model,Theoretical Models,Theoretical Studies

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