The brain is a vastly complex dynamical system. Cognitive functions such as memory, learning, volition, and consciousness seem to emerge as high level properties from the activity of billions of neurons sparsely connected into complex networks. What is it about networks that allows such...

Simulating a cellular automata (CA) for t time-steps into the future requires t[super 2] serial computation steps or t parallel ones. However, certain CAs based on an Abelian group, such as addition mod 2, are termed linear because they obey a principle of superposition. This allows them to be...

We investigate the structure of scientific collaboration networks. We consider two scientists to be connected if they have authored a paper together, and construct explicit networks of such connections using data drawn from a number of databases, including MEDLINE (biomedical research), the Los...

The Bayesian ``evidence'' approximation, which is closely related to generalized maximum likelihood, has recently been employed to determine the noise and weight-penalty terms for training neural nets. This paper shows that it is far simpler to perform the exact calculation than it is to set up...

Spatially extended excitable systems exhibit a variety of spatiotemporal dynamics--from stable to chaotic. These dynamics can change under pathological conditions and impair normal functions. Thus being able to control the altered dynamics for improved functioning has potential for wide ranging...

Epochal dynamics, in which long periods of stasis in population fitness are punctuated by sudden innovations, is a common behavior in both natural and artificial evolutionary processes. We use a recent quantitative mathematical analysis of epochal evolution to estimate, as a function of...

A simple response threshold model is used to explain a pattern of division of labour observed in the ponerine ant Ectatomma ruidum, where it was found that prey-foraging behaviour could be subdivided into two categories: stinging and transporting. Stingers kill live prey and transporters carry...

Numerical estimates for the number of local optima of p-spin Hamiltonians with p=3,4,5, and 6 are reported. The data can be explained by means of a simple estimate in terms of the "correlation length" of the Hamiltonian.

The notion that complexity increases in evolution is widely accepted, but the best-known evidence is highly impressionistic. In this paper, I propose a scheme for understanding complexity which provides a conceptual basis for objective measurement. The Scheme also shows complexity to be a...

A prominent feature of comparative life histories in the well documented negative correlation between growth rate and life span [1,2]. Patterns of resource allocation during growth reflect life-history differences between species [1,2]. This is particularly striking in tropical forests, where...