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.

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.

Combined effect of cyclosporine and sirolimus on improving the longevity of recombinant adenovirus-mediated transgene expression in the retina

Objectives: To reevaluate the longevity and intraocular safety of recombinant adenovirus (rAd)-mediated gene delivery after subretinal injection, and to prolong transgene expression through the combination of 2 synergistic immunosuppressants. Methods: An rAd vector carrying green fluorescent protein (GFP) gene was delivered subretinally in the rat eye. The GFP expression was monitored in real time by fundus fluorescent photography. Intraocular safety was examined by observation of changes of retinal pigmentation, cell infiltration in virus-contacted area, immunophenotyping for CD4(+) and CD8(+) cytotoxic T lymphocytes, and CD68(+) macrophages, histologic findings, and dark-adapted electroretinography. Two synergistic immunosuppressants, cyclosporine and sirolimus, were used alone or in combination to prolong transgene expression by temporary immunosuppression. Results: The GFP expression peaked on day 4, dramatically decreased on day 10, and was not detectable on day 14. The decreased GFP expression was coincident with cell infiltration in virus-contacted area. Immunostaining showed that the infiltrating cells were CD4(+) and CD8(+) cytotoxic T lymphocytes and CD68(+) macrophages. Clumped retinal pigmentation and decreased b wave of dark-adapted electroretinogram were observed at 3 to 4 weeks after injection. Histologic examination confirmed rAd-induced retinal degeneration. Transient immunosuppression by cyclosporine and sirolimus, either alone or in combination, improved transgene expression, with the combination being the most efficient. The combined immunosuppression attenuated but did not retard the rAd-induced retinal damage. Conclusions: Transgene expression mediated by rAd after subretinal delivery is short-term and toxic to the retina. Combination of cyclosporine and sirolimus may act as an immunosuppressive adjunct to prolong rAd-mediated gene transfer. Clinical Relevance: The intraocular safety of rAd should be carefully considered before clinical trials are performed.

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.

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.

The investigation of optimal bombardment parameters for transient and stable transgene expression in sorghum

This report outlines the development of optimized particle inflow gun (PIG) parameters for producing transgenic sorghum (Sorghum bicolor (L.) Moench). Both transient and stable expression were examined when determining these parameters. The uidA reporter gene (GUS) encoding beta -glucuronidase was used in transient experiments and the green fluorescent protein (GFP) used to monitor stable expression. Initially, optimization was conducted using leaf segments, as the generation of sorghum callus in sufficiently large quantities is time-consuming. Following leaf optimization, experiments were conducted using callus, identifying a high similarity between the two tissue types (r(s) = 0.83). High levels of GUS expression were observed in both leaf and callus material when most distant from the DNA expulsion point, and using a pressure greater than 1800 kPa. A higher level of expression was also observed when the aperture of the helium inlet valve was constricted. Using the optimized conditions (pressure of 2200 kPa, distance to target tissue of 15 cm from the expulsion point, and the aperture of the helium inlet valve at one full turn), three promoters (Ubiquitin, Actin1 and CaMV 35S) were evaluated over a 72-h period using GUS as the reporter gene. A significantly higher number of GUS foci were counted with the Ubiquitin construct over this period, compared to the Actin1 and CaMV 35S constructs. Stable callus sectors (on 2 mg l(-1) bialaphos) with GFP expression were visualized for as long as 6 wk post-bombardment. Using this optimized protocol, several plants were regenerated after having been bombarded with the pAHC20 construct (containing the bar gene), with molecular evidence confirming integration.

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.