Basic research is no longer confined just to ivory towers and is no longer confined to just a few interested people. The money which is spent for basic research is tremendous. The annual budget of the German National Science Foundation (DFG) is larger than 1.5 Billion DM (1 Billion US Dollar)....

We propose some simple models of the growth of social networks, based on three general principles: (1) meetings take place between pairs of individuals at a rate which is high if a pair has one or more mutual friends and low otherwise; (2) acquaintances between pairs of individuals who rarely...

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...

The critical boundaries separating ordered from chaotic behavior in randomly wired S-state networks are calculated. These networks are a natural generalization of random Boolean net and are proposed as an extended approach to genetic regulatory systems, sets of cells in different states or...

In this paper we study the relationship between the stability of a competitive equilibrium (CE) and the price adjustment mechanism used to attain that equilibrium point. Using two specific examples, a three- commodity exchange economy with a unique competitive equilibrium (Scarf's global...

A method for estimation of coarse-grained entropy rates (CER's) from time series is presented, based on information-theoretic functionals---redundancies. The CER's are relative measures of regularity and predictability, and for data generated by dynamical systems they are related to...

In the final paragraph of her recent book Uncommon Understanding, Bishop (1997), concludes her comprehensive review of the research literature on etiology, assessment and treatment of children with receptive language impairments with the following quote: <p> "The ultimate test of a hypothesis is...</p>

We introduce a simple spin model which shows glassy behavior at low temperatures, despite a Hamiltonian which is completely homogeneous and possesses no randomness; ergodicity breaking in this model is due entirely to the model's dynamics. We solve exactly for the model's equilibrium partition...

It is well-known that the question of whether a given finite region can be tiled with a given set of tiles is NP-complete. We show that the same is true for the right tromino and square tetromino on the square lattice, or for the right tromino alone. In the process, we show tthat Monotone 1-in-3...

We develop a system of recursive functions on the reals analogous to classical recursion theory on the natural numbers. This system turns out to include many sets and functions that are uncomputable in the traditional sense. <p> These functions can be computed by an idealized computer that runs on...</p>