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...

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 consider the situation of an investor facing uncertainty, and whose objective is to survive. First we characterize the probability of survival of a passive agent who does not attempt to influence the evolution of the environment. Secondly, we look at an active agent who chooses...