Numerical methods for strong solutions of stochastic differential equations: an overview

This paper gives a review of recent progress in the design of numerical methods for computing the trajectories (sample paths) of solutions to stochastic differential equations. We give a brief survey of the area focusing on a number of application areas where approximations to strong solutions are important, with a particular focus on computational biology applications, and give the necessary analytical tools for understanding some of the important concepts associated with stochastic processes. We present the stochastic Taylor series expansion as the fundamental mechanism for constructing effective numerical methods, give general results that relate local and global order of convergence and mention the Magnus expansion as a mechanism for designing methods that preserve the underlying structure of the problem. We also present various classes of explicit and implicit methods for strong solutions, based on the underlying structure of the problem. Finally, we discuss implementation issues relating to maintaining the Brownian path, efficient simulation of stochastic integrals and variable-step-size implementations based on various types of control.

Performance analysis using equivariant kernel density estimator in nonlinear mixture

This paper investigates the performance analysis of separation of mutually independent sources in nonlinear models. The nonlinear mapping constituted by an unsupervised linear mixture is followed by an unknown and invertible nonlinear distortion, are found in many signal processing cases. Generally, blind separation of sources from their nonlinear mixtures is rather difficult. We propose using a kernel density estimator incorporated with equivariant gradient analysis to separate the sources with nonlinear distortion. The kernel density estimator parameters of which are iteratively updated to minimize the output independence expressed as a mutual information criterion. The equivariant gradient algorithm has the form of nonlinear decorrelation to perform the convergence analysis. Experiments are proposed to illustrate these results.

Numerical simulation of stochastic ordinary differential equations in biomathematical modelling

In this work we discuss the effects of white and coloured noise perturbations on the parameters of a mathematical model of bacteriophage infection introduced by Beretta and Kuang in [Math. Biosc. 149 (1998) 57]. We numerically simulate the strong solutions of the resulting systems of stochastic ordinary differential equations (SDEs), with respect to the global error, by means of numerical methods of both Euler-Taylor expansion and stochastic Runge-Kutta type. (C) 2003 IMACS. Published by Elsevier B.V. All rights reserved.

The application of numerical modelling to the assessment of the potential for, and the detection of, spontaneous combustion in coal mines

Numerical modelling has been used to examine the relationship between the results of two commonly used methods of assessing the propensity of coal to spontaneous combustion, the R70 and Relative Ignition Temperature tests, and the likely behaviour in situ. The criticality of various parameters has been examined and a method of utilising critical self-heating parameters has been developed. This study shows that on their own, the laboratory test results do not provide a reliable guide to in situ behaviour but can be used in combination to considerably increase the ability to predict spontaneous combustion behaviour.

Proceedings of Computational Methods for Coupled Problems in Science and Engineering

Computational Methods for Coupled Problems in Science and Engineering

A comparison of competing methods for the detection of surgical-site infections in patients undergoing total arthroplasty of the knee, partial and total arthroplasty of hip and femoral or similar vascular bypass

Recent research suggests that the retrospective review of the International Classification of Disease (ICD-9-CM) codes assigned to a patient episode will identify a similar number of healthcare-acquired surgical-site infections as compared with prospective surveillance by infection control practitioners (ICP). We tested this finding by replicating the methods for 380 surgical procedures. The sensitivity and specificity of the ICP undertaking prospective surveillance was 80% and 100%, and the sensitivity and specificity of the review of ICD-10-AM codes was 60% and 98.9%. Based on these results we do not support retrospective review of ICD-10-AM codes in preference prospective surveillance for SSI. (C) 2004 The Hospital Infection Society. Published by Elsevier Ltd. All rights reserved.

The Apparitions of the Virgin Mary in Medjugorje: The convergence of Croation nationalism on her apparitions

This article concerns the alleged apparitions of the Virgin Mary in one of the most popular, 'active' apparitional sites in the world: Medjugorje in Bosnia and Herzegovina. The connection between nationalist discourse and apparitions has often been observed and noted in the literature on nationalism; however, the examples of this connection are scattered in the literature and the question why the apparitional phenomenon so easily lends itself to co-option into nationalist discourse has never been addressed. This article explores this question by showing that what binds the two phenomena together is the idea of 'chosenness' and 'specialness', which in turn can be theoretically linked to discussions about national election in the literature on nationalism. This article illustrates the convergence of nationalist and apparitional discourses by drawing on a selected number of examples of how the apparitions in Medjugorje have been appropriated by Croatian nationalist discourse.