We give improved hitting sets for two special cases of Read-once Oblivious Arithmetic Branching Programs (ROABP). First is the case of an ROABP with known order of the variables. The best previously known hitting set for this case had size (nw)O(logn) where n is the number of variables and w is the width of the ROABP. Even for a constantwidth ROABP, nothing better than a quasi-polynomial bound ...

We use methods from Markov chain theory to analyze the performance of some simple GA models on a class of deceptive objective functions. We consider the invariant distribution, the average expected hitting time, the mixing rate, and limits of these quantities as the objective function becomes more and more highly skewed.

We propose a mathematical model for one pattern of charts studied in technical analysis: in a phase of consolidation, the price of a risky asset goes down ξ times after hitting a resistance level. We construct a mathematical strategy and we calculate the expectation of the wealth for the logaritmic utility function. Via simulations, we compare the strategy with the standard one.

The hitting time Hxy between two vertices x and y of a graph is the average time that the standard simple random walk takes to get from x to y. In this paper, we study the distribution of the hitting time between two randomly chosen vertices of a random tree. We consider both uniformly random labelled trees and a more general model with vertex weights akin to simply generated trees. We show tha...

The first passage time problem for Brownian motions hitting a barrier has been extensively studied in the literature. In particular, many incarnations of integral equations which link the density of the hitting time to the equation for the barrier itself have appeared. Most interestingly, Peskir (2002b) demonstrates that a master integral equation can be used to generate a countable number of n...

The use of Lyapunov conditions for proving functional inequalities was initiated in [5]. It was shown in [4, 30] that there is an equivalence between a Poincaré inequality, the existence of some Lyapunov function and the exponential integrability of hitting times. In the present paper, we close the scheme of the interplay between Lyapunov conditions and functional inequalities by • showing that...