Stochastic di erential games are considered in a non-Markovian setting. Typically, in stochastic di erential games the modulating process of the di usion equation describing the state ow is taken to be Markovian. Then Nash equilibria or other types of solution such as Pareto equilibria are constructed using Hamilton-Jacobi-Bellman (HJB) equations. But in a non-Markovian setting the HJB method i...

Data-dependent rotations have been found to be a useful component for designing block cipher including MARS and RC6, two candidates for AES. Existing analysis indicates that data-dependent rotations play an important role in thwarting di erential and linear attacks. In this paper, we study di erential properties of data-dependent rotations, and derive a complete characterization of all possible...

This paper describes the design philosophy behind the recent replacement of the NAG Ordinary Di erential Equation (ODE) sti integrators. This replacement was is intended to update the ODE chapter algorithmically but, more importantly in the context of this paper, it provides a more exible interface than has been available in the past. This interface is designed to permit a wide variety of probl...

After a series of application papers have proven the approach to be numerically e ective, this paper gives the rst theoretical foundation for methods solving partial di erential equations by collocation with (possibly radial) basis functions.

We propose a di erential equation model for gene expression and provide two methods to construct the model from a set of temporal data. We model both transcription and translation by kinetic equations with feedback loops from translation products to transcription. Degradation of proteins and mRNAs is also incorporated. We study two methods to construct the model from experimental data: MinimumW...

This paper studies the rst order necessary conditions for the optimal controls of semilinear and quasilinear parabolic partial di erential equations with pointwise state constraints. Pontryagin type maximum principle is obtained.

We prove an existence and uniqueness theorem for backward stochastic di erential equations driven by a Brownian motion, where the uniform Lipschitz continuity is replaced by a stochastic one.

An exact solution of a system of coupled di erential equations describing the dynamics of a special class of winner-take-all networks is given. From the solution two properties of the short-termmemory traces are derived: (1) information preservation and (2) a discrimination measure. These properties justify a biologically inspired fault tolerant extension of the network using di erentiating neu...

On q-Di®erence Equations Moemen H. Abu-Risha Department of Mathematics Cairo University, Eygpt E-mail: [email protected] We give an investigation of some properties of solutions of linear q¡di®erence equations de ̄ned on an interval [a;1): The cases a = 0 and a > 0 are essentially di®erent. The study of the latter case is necessary for the derivation of asymptotic formulae and oscil...

Overlapping Schwarz is a family of preconditioners for solving large sparse linear systems arising from the discretization of partial di erential equations see e g CS DW SBG Here we report on our preliminary experiences on using it in the implicit solution of unsteady Navier Stokes N S equations discretized on two dimensional unstructured meshes One of the advantages of implicit methods is that...