A transversal generated by a system of distinct representatives (SDR) for a collection of sets consists of an element from each set (its representative) such that the representative uniquely identifies the set it belongs to. Theorem 1 gives a necessary and sufficient condition that an arbitrary...

This paper establishes a lower bound on the computational complexity of smooth functions between smooth manifolds. It generalizes one for finite (Boolean) functions obtained (by Arbib and Spira [2]) by counting variables. Instead of a counting procedure, which cannot be used in the infinite...

In this paper we address a long standing gap in economic theory--the gap between claims for the dynamic efficiency of trading in markets, and the findings of formal economic theory, which justify those claims only under restrictive assumptions. We use agent-based methods to study the dynamics of...