NUMERICS

We show that human consciousness can be modeled as a classical (not quantum) probabilistic computer. A quantum computer representation does not appear to be indicated because no known feature of consciousness depends on Planck's constant h, the telltale sign of quantum phenomena. It is argued that the facets of consciousness are describable by an object-oriented design with dynamically defined classes and objects. A comparison to economic theory is also made. We argue consciousness may also have redundant, protective mechanisms.

Extremal optimization, a recently introduced meta-heuristic for hard optimization problems, is analysed on a simple model of jamming. The model is motivated first by the problem of finding lowest energy configurations for a disordered spin system on a fixed-valence graph. The numerical results for the spin system exhibit the same phenomenology found in all earlier studies of extremal optimization, and our analytical results for the model reproduce many of these features.

Numerical simulations of strongly correlated electron systems suffer from the notorious fermion sign problem which has prevented progress in understanding if systems like the Hubbard model display high-temperature superconductivity. Here we show how the fermion sign problem can be solved completely with meron-cluster methods in a large class of models of strongly correlated electron systems, some of which are in the extended Hubbard model family and show s-wave superconductivity. In these models we also find that on-site repulsion can even coexist with a weak chemical potential without introducing sign problems. We argue that since these models can be simulated efficiently using cluster algorithms they are ideal for studying many of the interesting phenomena in strongly correlated electron systems.