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>

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...

I raise questions regarding the unknown and the unknowable in science. I also briefly address two topics which have been much in the news in 1996, and which might erroneously be confused with my topic. These are, first, the book by John Horgan, called The End of Science, and second, the great...

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...

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...

In an electoral framework of unidimensional two-candidate spatial competition with probabilistic voting, special interest groups present candidates with schedules that give the level of campaign contribution they will make for each feasible candidate policy location. Candidates, motivated by the...

A large body of literature documents that returns from currency speculation are highly volatile and possess a predictable component, which is itself highly volatile and serially correlated. Explaining the returns from currency speculation through the presence of a risk premium has proven...

Self-organizing maps (SOM) are unsupervised, competitive neural networks used to project high-dimensional data onto a low-dimensial space. In this article we show how SOM can be sued to draw graphs in the plane. The SOM-based approach to graph drawing, which belongs to the general class of...