We are interested in stationary “fluid” random evolutions with independent increments. Under some mild assumptions, we show they are solutions of a stochastic differential equation (SDE). There are situations where these evolutions are not described by flows of diffeomorphisms, but by coalescing flows or by flows of probability kernels. In an intermediate phase, for which there exists a coalesc...

We are interested in stationary “fluid” random evolutions with independent increments. Under some mild assumptions, we show they are solutions of a stochastic differential equation (SDE). There are situations where these evolutions are not described by flows of diffeomorphisms, but by coalescing flows or by flows of probability kernels. In an intermediate phase, for which there exists a coalesc...

The dynamics of proteins can be described as the superposition of motions at a continuum of time scales. In the special case of a protein immersed in an implicit solvent, a stochastic differential equation (SDE) can model the dynamics of the solute protein. Traditional model reduction techniques fail because a priori characterization of the slow variables in these SDEs is nearly impossible. We ...

Numerical approximation of the long time behavior of a stochastic differential equation (SDE) is considered. Error estimates for time-averaging estimators are obtained and then used to show that the stationary behavior of the numerical method converges to that of the SDE. The error analysis is based on using an associated Poisson equation for the underlying SDE. The main advantages of this appr...

In this paper, we address the two-stage assembly flowshop scheduling problem with a weighted sum of makespan and mean completion time criteria, known as bicriteria. Since the problem is NP-hard, we propose heuristics to solve the problem. Specifically, we propose three heuristics; simulated annealing (SA), ant colony optimization (ACO), and self-adaptive differential evolution (SDE). We have co...

Starting from the Ashtekar Hamiltonian variables for general relativity, the self-dual Einstein equations (SDE) may be rewritten as evolution equations for three divergence free vector fields given on a three dimensional surface with a fixed volume element. From this general form of the SDE, it is shown how they may be interpreted as the field equations for a two dimensional field theory. It is...

Flows generated by SDEs in Euclidean space is a well-studied topic nowadays. It is well known for example (cf. [1] and ref. therein) that if the coefficients of SDE are Liphitzian then the SDE generates a flow of homeomorphisms, if coefficients are of the class C then SDE generates C-flow of diffeomorphisms, equations for derivatives are obtained by formal differentiation of the SDE etc. Note t...

Differential Evolution (DE) is generally considered as a reliable, accurate, robust and fast optimization technique. DE has been successfully applied to solve a wide range of numerical optimization problems. However, the user is required to set the values of the control parameters of DE for each problem. Such parameter tuning is a time consuming task. Self-adaptive DE (SDE) is a new version of ...

In the past ten years there has been a great deal of interest in the concept of a Software Development Environment (SDE) as a complete, unifying framework of services supporting most (or all) phases of software development and maintenance. We identify three levels at which the issue of integration in a SDE arises as a key concept — at the mechanism level (interoperability of the hardware and ba...

Background Subdural empyema (SDE) in children is a severe intracranial infection. Many pathogens can cause SDE. Case Details In this articlewe present a 15-month old Indonesian boy diagnosed as SDE based on the clinical symptoms and neuroimaging. A complete blood count showed white blood cell count of 13.800/mm3 and the CRP level was 8.3 mg/L. Craniotomy following burr hole drainage procedure...