Narrow Results

This paper describes an approach to support software development process descriptions in the context of the Memphis Environment (a Reuse Based Software Development Environment), allowing the organization of a software development asset, i.e., the process knowledge. The approach uses software patterns to organize the information, and provides a tool that handles the process descriptions as a source of solutions to problems detected by project management. It enhances the environment features in terms of project management support, process modeling capability, and process evolution support.

This paper focuses on the connections between four stochastic and deterministic models for the motion of straight screw dislocations. Starting from a description of screw dislocation motion as interacting random walks on a lattice, we prove explicit estimates of the distance between solutions of this model, an SDE system for the dislocation positions, and two deterministic mean-field models describing the dislocation density. The proof of these estimates uses a collection of various techniques in analysis and probability theory, including a novel approach to establish propagation-of-chaos on a spatially discrete model. The estimates are non-asymptotic and explicit in terms of four parameters: the lattice spacing, the number of dislocations, the dislocation core size, and the temperature. This work is a first step in exploring this parameter space with the ultimate aim to connect and quantify the relationships between the many different dislocation models present in the literature.

It is known that the two-point generator of an SDE determines the law of its flow uniquely. We describe an explicit way to find the coefficients of the SDE from its two-point generator. Indeed, this method of construction produces a sequence of SDEs in a way that the associated sequence of stochastic flows converges to the stochastic flow of the desired SDE.

Forward-backward stochastic differential equation (FBSDE) systems were introduced as a probabilistic description for parabolic type partial differential equations. Although the probabilistic behavior of the FBSDE system makes it a natural mathematical model in many applications, the stochastic integrals contained in the system generate uncertainties in the solutions which makes the solution estimation a challenging task. In this paper, we assume that we could receive partial noisy observations on the solutions and introduce an optimal filtering method to make a data informed solution estimation for FBSDEs.