I discuss the relations among four worlds: Reality, mathematical models, computer simulation, and models of computation. Pros and cons of two models of computation, the Turing machine and the real number model, are presented. The the intrinsic difficulty of solving a mathematical model, as...

We study path integration on a quantum computer that performs quantum summation. We assume that the measure of path integration is Gaussian, with the eigenvalues of its covariance operator of order j^{-k} with k1. For the Wiener measure occurring in many applications we have k=2. We want to...

Over the last sixty years there has been a stream of impossibility results from mathematics and theoretical computer science announcing undecidability, non-computability, and intractability. Should these impossibility results be of concern to physics? <p> Two of these impossibility results are...</p>

High-dimensional integrals are usually solved with Monte Carlo algorithms although theory suggests that low-discrepancy algorithms are sometimes superior. We report on numerical testing which compares low-discrepancy and Monte Carlo algorithms on the evaluation of financial derivatives. The...

At its first meeting in 1986 the Computer Science and Technology Board, National Research Council, identified six critical national issues. <p> I discuss these six issues as they appeared in 1986 and how they appear for my 1996 vintage. <p> There was a seventh critical issue which I did not want to...</p></p>

The random graph of Erdos and Renyi is one of the oldest and best studied models of a network, and possesses the considerable advantage of being exactly solvable for many of its average properties. However, as a model of real-world networks such as the Internet, social networks or biological...

We are interested in the strategic implications of asymmetric competition. Previous work (Carpenter, Cooper, Hanssens and Midgley [CCHM] 1988) has estimated the Nash-equilibrium prices and advertising expenditures for asymmetric market-share models in the extreme cases of no competitive reaction...

Experimentally it has been found that any two people in the world, chosen at random, are connected to one another by a short chain of intermediate acquaintances, of typical lenth about six. This phenomenon, colloquially referred to as the "six degrees of separation", has been the subject of a...

During the development of a multicellular organism for a zygote, a large number of epigenetic interactions take place on every level of suborganismal organization. This raises the possibility that the system of epigenetic interactions may compensate or ÒbufferÓ some of the changes that occur...

Previous work on coevolutionary search has demonstrated both successful and unsuccessful applications. As a step in explaining what factors lead to success or failure, we present a comparative study of an evolutionary and a coevolutionary search model. In the latter model, strategies for solving...