Implicit Taylor methods for stiff stochastic differential equations

In this paper we discuss implicit Taylor methods for stiff Ito stochastic differential equations. Based on the relationship between Ito stochastic integrals and backward stochastic integrals, we introduce three implicit Taylor methods: the implicit Euler-Taylor method with strong order 0.5, the implicit Milstein-Taylor method with strong order 1.0 and the implicit Taylor method with strong order 1.5. The mean-square stability properties of the implicit Euler-Taylor and Milstein-Taylor methods are much better than those of the corresponding semi-implicit Euler and Milstein methods and these two implicit methods can be used to solve stochastic differential equations which are stiff in both the deterministic and the stochastic components. Numerical results are reported to show the convergence properties and the stability properties of these three implicit Taylor methods. The stability analysis and numerical results show that the implicit Euler-Taylor and Milstein-Taylor methods are very promising methods for stiff stochastic differential equations.

Topological methods for some boundary value problems

We establish existence of solutions for a finite difference approximation to y = f(x, y, y ') on [0, 1], subject to nonlinear two-point Sturm-Liouville boundary conditions of the form g(i)(y(i),y ' (i)) = 0, i = 0, 1, assuming S satisfies one-sided growth bounds with respect to y '. (C) 2001 Elsevier Science Ltd. All rights reserved.

Estimates of the real structured radius of stability of linear dynamic systems

A question is examined as to estimates of the norms of perturbations of a linear stable dynamic system, under which the perturbed system remains stable in a situation R:here a perturbation has a fixed structure.

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.

Diagnostic performance of Antineutrophil Cytoplasmic Antibody tests for Idiopathic Vasculitides: Metaanalysis with a focus on antimyeloperoxidase antibodies

Objective. The diagnostic value of tests for antimyeloperoxidase antibodies (anti-MPO) for systemic vasculitis is less established than that for cytoplasmic antineutrophil cytoplasmic antibody (cANCA)/antiproteinase 3 antibodies (anti-PR3). Controversy exists regarding the optimal utilization of indirect immunofluorescence (IIF) ANCA testing versus antigen-specific ANCA testing. To summarize the pertinent data, we conducted a metaanalysis examining the diagnostic value of ANCA testing systems that include assays for anti-MPO. Methods. We performed a structured Medline search and reference list review. Target articles in the search strategy were those reporting the diagnostic value of immunoassays for anti-MPO for the spectrum of systemic necrotizing vasculitides that includes Wegener's granulomatosis, microscopic polyangiitis, the Churg-Strauss syndrome, and isolated pauci-immune necrotizing or crescentic glomerulonephritis, regardless of other types of ANCA tests. Inclusion criteria required specification of a consecutive or random patient selection method and the use of acceptable criteria for the diagnosis of vasculitis exclusive of ANCA test results. Weighted pooled summary estimates of sensitivity and specificity were calculated for anti-MPO alone, anti-MPO + perinuclear ANCA (pANCA), and anti-MPO/pANCA + anti-PR3/cANCA. Results. Of 457 articles reviewed, only 7 met the selection criteria. Summary estimates of sensitivity and specificity (against disease controls only) of assays for anti-MPO for the diagnosis of systemic necrotizing vasculitides were 37.1% (confidence interval 26.6% to 47.6%) and 96.3% (CI 94.1% to 98.5%), respectively. When the pANCA pattern by IIF was combined with anti-MPO testing, the specificity improved to 99.4%, with a lower sensitivity, 31.5%. The combined ANCA testing system (anti-PR3/cANCA + anti-MPO/pANCA) increased the sensitivity to 85.5% with a specificity of 98.6%. Conclusion. These results suggest that while anti-MPO is relatively specific for the diagnosis of systemic vasculitis, the combination system of immunoassays for anti-MPO and IIF for pANCA is highly specific and both tests should be used together given the high diagnostic precision required for these conditions. Because patients with ANCA associated vasculitis have either anti-MPO with pANCA or anti-PR3 with cANCA, and rarely both, a combined ANCA testing system including anti-PR3/cANCA and anti-MPO/pANCA is recommended to optimize the diagnostic performance of ANCA testing. (J Rheumatol 2001;28:1584-90)

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.

Stickiness in foods: A review of mechanisms and test methods

Problems associated with the stickiness of food in processing and storage practices along with its causative factors are outlined. Fundamental mechanisms that explain why and how food products become sticky are discussed. Methods currently in use for characterizing and overcoming stickiness problems in food processing and storage operations are described. The use of glass transition temperature-based model, which provides a rational basis for understanding and characterizing the stickiness of many food products, is highlighted.