The mathematics associated with the analysis of these complex systems is directly applicable to problems in neural networks, artificial life, and genetic algorithms. My research investigates the effects of different types of competing interactions. These investigations employ computer simulations to study nonlinearities that arise in systems that can be characterized with certain degrees of randomness and frustration.
Frustration refers to the inability of a system to simultaneously satisfy all constraints present.
Analytical techniques, developed using modern theories from statistical mechanics, have allowed us to better understand the nonequilibrium and equilibrium phenomenon observed in these systems.