Reappraisal of disparities between osmolality estimates by freezing point depression and vapor pressure deficit methods

As a response to recent expression of concern about possible unreliability of vapor pressure deficit measurements K Kiyosawa, Biophys. Chem. 104 (2003) 171-188), the results of published studies on the temperature dependence of the osmotic pressure of aqueous polyethylene glycol solutions are shown to account for the observed discrepancies between osmolality estimates obtained by freezing point depression and vapor pressure deficit osmometry - the cause of the concern. (C) 2003 Elsevier B.V. All rights reserved.

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.