On-Site Potential Creates Complexity in Systems with Disordered Coupling

We calculate the average number of critical points N[over ¯] of the energy landscape of a many-body system with disordered two-body interactions and a weak on-site potential. We find that introducing a weak nonlinear on-site potential dramatically increases N[over ¯] to exponential in system size and give a complete picture of the organization of critical points. Our results extend solvable spin-glass models to physically more realistic models and are of relevance to glassy systems, nonlinear oscillator networks, and many-body interacting systems.

Superexponential decay for the GEM process

We show that the GEM process has strong ordering properties: the probability that one of the k largest elements in the GEM sequence is beyond the first ck elements (c > 1) decays superexponentially in k.

A relaxation model for memory with high storage density

We present a relaxation model for memory based on a generalized coulomb potential. The model has arbitrarily large storage capacity and, in addition, well-defined basins of attraction about stored memory states. The model is compared with the Hopfield relaxation model.