Statistical and Computational Physics for Complex Systems
I am trying to clarify the problems in the socalled "complex systems" like ecological systems, proteins, neural networks and their learning processes, and combinatorial optimization problems in terms of nonlinear mechanics, statistical physics and computational physics. Although the subjects are quite different each other at first glance, they share the key concepts: their complex behaviors are emerged by large number of relatively simple elements with complex interactions. Studying them in the uniform view point, we can make each particular case clear all the more.
 Largescale Ecological systems
 Random interspecies interactions and the extinction threshold
 The Extinction dynamics (KT&AY, 99; 00)
 Origin of the biodiversity of ecosystems
 Biotic fusion, extinction, invasion, neutral mutation...(KT&AY, 03)
 Game dynamical equation w/antisymmetric random interactions
 A mechanism of mainteining biodiversity
(TC&KT, 02)
 LotkaVolterra equation w/hierarchically ordered random interactions
(KT&TC, in prep.)
 Species abundance patterns in replicator dynamics w/random interactions
(KT, 04; 06; YY,TG&KT 07;08)
 Species abundance distributions and the species area relationships (HI&KT 12)
 Neutral models of ecology (TO&KT 13)
 Protein foldings and inverse foldings
 Fast algorithm for
the inverse folding problem = The Design equation
(YI,KT&MK, 98; KT,MK&YI, 00)
 Neural networks and learning theories
 Multivalley free energy landscape in the Hopfield model (KT, 93; 94)
 Full replicasymmetrybreaking(RSB) formulation of the Hopfield model (KT, 94)
 Miscellaneous
 Statistical mechanics of combinatorial optimization problems
 Nonequiliburium dynamics for economical systems, game, cell, viruses and immune systems, etc.
