Stiffly accurate Runge-Kutta methods for stiff stochastic differential equations

In this paper we discuss implicit methods based on stiffly accurate Runge-Kutta methods and splitting techniques for solving Stratonovich stochastic differential equations (SDEs). Two splitting techniques: the balanced splitting technique and the deterministic splitting technique, are used in this paper. We construct a two-stage implicit Runge-Kutta method with strong order 1.0 which is corrected twice and no update is needed. The stability properties and numerical results show that this approach is suitable for solving stiff SDEs. (C) 2001 Elsevier Science B.V. All rights reserved.

A retrospective analysis of mycophenolic acid and cyclosporin concentrations with acute rejection in renal transplant recipients

Objectives: Although monitoring of cyclosporin (CsA) is standard clinical practice postrenal transplantation. mycophenolic acid (MPA) concentrations are not routinely measured. There is evidence that a relationship exists between MPA area under the concentration-time curve (AUC) and rejection. In this study, a retrospective analysis was undertaken of 27 adult renal transplant recipients. Methods: Patients received CsA and MPA therapy and had a four-point MPA AUC investigation. The relationship between MPA AUC performed in the first week after transplantation, as well as median trough cyclosporin concentrations, and clinical outcomes in the first month posttransplant were evaluated. Results: A total of 12 patients experienced biopsy proven rejection (44.4%) and 4 patients had gastrointestinal adverse events (14.8%). A statistically significant relationship was observed between the incidence of biopsy proven rejection and both MPA AUC (p = 0.02) and median trough CsA concentration (p = 0.008). No relationship between trough MPA concentration and rejection was observed (p = 0.21). Only 3 of 11 (27%) patients with an MPA AUC > 30 mg.h/L and a median trough CsA > 175 mug/L experienced acute rejection, compared with a 56% incidence of rejection for the remaining 16 patients. Patients who experienced adverse gastrointestinal events had significantly lower MPA AUC (p = 0.04), but median trough CsA concentrations were not significantly different (p = 0.24). Further, 3 of these 4 patients had rejection episodes. Conclusions: in addition to standard CsA monitoring, we propose further investigation of the use of a 4-point sampling strategy to predict MPA AUC in the first week posttransplant, which may facilitate optimization of mycophenolate mofetil dose at a rime when patients are most vulnerable to acute rejection. (C) 2001 The Canadian Society of Clinical Chemists. All rights reserved.

Development of ligase-assisted spacer addition for the measurement of microsatellites

Conventional methods for detecting differences in microsatellite repeat lengths rely on electrophoretic fractionation on long denaturing polyacrylamide gels, a time-consuming and labor-intensive method. Therefore, there is a need for the development of new and rapid approaches to routinely detect such length polymorphisms. The advent of techniques allowing the coupling of DNA molecules to solid surfaces has provided new prospects in the area of mutation. We describe here the development and optimization of the ligase-assisted spacer addition (LASA) method, a novel and rapid procedure based on an ELISA format to measure microsatellite repeat lengths. The LASA assay was successfully applied to a set of 11 bird samples to assess its capability as a genotyping method.

Development and implementation of the population Fisher information matrix for the evaluation of population pharmacokinetic designs.

In population pharmacokinetic studies, the precision of parameter estimates is dependent on the population design. Methods based on the Fisher information matrix have been developed and extended to population studies to evaluate and optimize designs. In this paper we propose simple programming tools to evaluate population pharmacokinetic designs. This involved the development of an expression for the Fisher information matrix for nonlinear mixed-effects models, including estimation of the variance of the residual error. We implemented this expression as a generic function for two software applications: S-PLUS and MATLAB. The evaluation of population designs based on two pharmacokinetic examples from the literature is shown to illustrate the efficiency and the simplicity of this theoretic approach. Although no optimization method of the design is provided, these functions can be used to select and compare population designs among a large set of possible designs, avoiding a lot of simulations.

Time evolution in the unimolecular master equation at low temperatures: full spectral solution with scalable iterative methods and high precision

A new method is presented to determine an accurate eigendecomposition of difficult low temperature unimolecular master equation problems. Based on a generalisation of the Nesbet method, the new method is capable of achieving complete spectral resolution of the master equation matrix with relative accuracy in the eigenvectors. The method is applied to a test case of the decomposition of ethane at 300 K from a microcanonical initial population with energy transfer modelled by both Ergodic Collision Theory and the exponential-down model. The fact that quadruple precision (16-byte) arithmetic is required irrespective of the eigensolution method used is demonstrated. (C) 2001 Elsevier Science B.V. All rights reserved.

Application of Petrov-Galerkin methods to transient boundary value problems in chemical engineering: adsorption with steep gradients in bidisperse solids

Petrov-Galerkin methods are known to be versatile techniques for the solution of a wide variety of convection-dispersion transport problems, including those involving steep gradients. but have hitherto received little attention by chemical engineers. We illustrate the technique by means of the well-known problem of simultaneous diffusion and adsorption in a spherical sorbent pellet comprised of spherical, non-overlapping microparticles of uniform size and investigate the uptake dynamics. Solutions to adsorption problems exhibit steep gradients when macropore diffusion controls or micropore diffusion controls, and the application of classical numerical methods to such problems can present difficulties. In this paper, a semi-discrete Petrov-Galerkin finite element method for numerically solving adsorption problems with steep gradients in bidisperse solids is presented. The numerical solution was found to match the analytical solution when the adsorption isotherm is linear and the diffusivities are constant. Computed results for the Langmuir isotherm and non-constant diffusivity in microparticle are numerically evaluated for comparison with results of a fitted-mesh collocation method, which was proposed by Liu and Bhatia (Comput. Chem. Engng. 23 (1999) 933-943). The new method is simple, highly efficient, and well-suited to a variety of adsorption and desorption problems involving steep gradients. (C) 2001 Elsevier Science Ltd. All rights reserved.

On surrogate methods for detecting lateral gene transfer

Surrogate methods for detecting lateral gene transfer are those that do not require inference of phylogenetic trees. Herein I apply four such methods to identify open reading frames (ORFs) in the genome of Escherichia coli K12 that may have arisen by lateral gene transfer. Only two of these methods detect the same ORFs more frequently than expected by chance, whereas several intersections contain many fewer ORFs than expected. Each of the four methods detects a different non-random set of ORFs. The methods may detect lateral ORFs of different relative ages; testing this hypothesis will require rigorous inference of trees. (C) 2001 Federation of European Microbiological Societies. Published by Elsevier Science BN. All rights reserved.