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.

In Vitro Proliferation and Osteoblastic Phenotype Expression of Cells Derived From Human Vertebral Lamina and Iliac Crest

Study Design. Osteoblastic cells derived from vertebral lamina and iliac crest were isolated and cultured under the same conditions (osteogenic medium, pH, temperature, and CO(2) levels). Objective. To compare proliferation and expression of osteoblastic phenotype of cells derived from vertebral lamina and iliac grafting. Summary of Background Data. Many factors play a role in the success of bone graft in spinal fusion including osteoblastic cell population. Two common sources of graft are vertebral lamina and iliac crest, however, differences in proliferation and osteoblastic phenotype expression between cells from these sites have not been investigated. Methods. Cells obtained from cancellous bone of both vertebral lamina and iliac crest were cultured and proliferation was evaluated by direct cell counting and viability detected by Trypan blue. Alkaline phosphatase (ALP) activity was evaluated by thymolphthalein release from thymolphthalein monophosphate and matrix mineralization by staining with alizarin red S. Gene expression of ALP, osteocalcin, runt-related transcription factor 2, Msh homeobox 2, bone morphogenetic protein 7, intercellular adhesion molecule 1 precursor, osteoprotegerin, and receptor activator of NF-kB ligand was analyzed by real-time PCR. All comparisons were donor-matched. Results. Proliferation was greater at days 7 and 10 in cells from vertebral lamina compared with ones from iliac crest without difference in cell viability. ALP activity was higher in cells from vertebral lamina compared with cells from iliac crest at days 7 and 10. At 21 days, mineralized matrix was higher in cells derived from vertebral lamina than from iliac crest. At day 7, gene expression of ALP, osteocalcin, runt-related transcription factor 2, Msh homeobox 2, bone morphogenetic protein 7, intercellular adhesion molecule 1 precursor, receptor activator of NF-kB ligand, and osteoprotegerin was higher in cells derived from vertebral lamina compared with iliac crest. Conclusion. Cell proliferation and osteoblastic phenotype development in cells derived from cancellous bone were more exuberant in cultures of vertebral lamina than of iliac crest.

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 longitudinal analysis of cytotoxic T lymphocyte precursor frequencies to the hepatitis B virus in chronically infected patients

Individuals with acute hepatitis B virus (HBV) infection characteristically mount a strong, multispecific cytotoxic T lymphocyte (CTL) response that is effective in eradicating virus. In contrast, this response in chronic carriers is usually weak or undetectable. Since it is generally acknowledged that HBV pathogenesis is immune-mediated, the occurrence of episodes of active liver disease in many carriers suggests that these individuals can mount active CTL responses to HBV. To see whether the detection of circulating CTLs is related to these flare episodes, we have determined the CTL precursor (CTLp) frequencies to HLA-A2-restricted viral peptides in seven patients over a 12-24-month period of their disease. Limiting dilution analyses (LDA) were performed longitudinally to five epitopes comprising the viral capsid (HBc), envelope (HBs) and polymerase (pol) proteins. Assays were performed against a mixture of peptides, or against each individual peptide, to measure overall CTL activity and the multispecificity of the responses, respectively. Since two of the patients were treated with recombinant human interleukin-12 (rHuIL-12) at the time, with one individual achieving complete disease remission a year later after being treated with interferon-alpha, we were also able to examine the effects of these cytokines on HBV cytotoxicity. Our results indicate that weak but detectable CTL responses do occur in chronic carriers which are generally associated with disease flares, although CTLps were also seen occasionally during minimal disease activity. The range of specificities varied between individuals and within each individual during the course of the disease. Finally, we also provide evidence that CTL reactivity is stimulated following treatment with certain cytokines, but is dependent on the time of administration.

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.

The solution structure of C1-T1, a two-domain proteinase inhibitor derived from a circular precursor protein from Nicotiana alata

A two-domain portion of the proteinase inhibitor precursor from Nicotiana alata (NaProPI) has been expressed and its structure determined by NMR spectroscopy. NaProPI contains six almost identical 53 amino acid repeats that fold into six highly similar domains; however, the sequence repeats do nut coincide with the structural domains. Five of the structural domains comprise the C-terminal portion of one repeat and the N-terminal portion of the next. The sixth domain contains the C-terminal portion of the sixth repeat and the N-terminal portion of the first repeat. Disulphide bonds link these C and N-terminal fragments to generate the clasped-bracelet fold of NaProPI. The three-dimensional structure of NaProPI is not known, but it is conceivable that adjacent domains in NaProPI interact to generate the circular bracelet with the N and C termini in close enough proximity to facilitate formation of the disulphide bonds that form the clasp The expressed protein, examined in the current study, comprises residues 25-135 of NaProPI and encompasses the first two contiguous structural domains, namely the chymotrypsin inhibitor C1 and the trypsin inhibitor T1, joined by a five-residue linker, and is referred to as C1-T1. The tertiary structure of each domain in C1-T1 is identical to that found in the isolated inhibitors. However, no nuclear Overhauser effect contacts are observed between the two domains and the five-residue linker adopts an extended conformation. The absence of interactions between the domains indicates that adjacent domains do not specifically interact to drive the circularisation of NaProPI. These results are in agreement with recent data which describe similar PI precursors from other members of the Solanaceae having two, three, or four repeats. The lack of strong interdomain association is likely to be important for the function of individual inhibitors by ensuring that there is no masking of reactive sites upon release from the precursor. (C) 2001 Academic Press.

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.

'Neighbourhood' size, dispersal and density estimates in the prickly forest skink (Gnypetoscincus queenslandiae) using individual genetic and demographic methods

Dispersal, or the amount of dispersion between an individual's birthplace and that of its offspring, is of great importance in population biology, behavioural ecology and conservation, however, obtaining direct estimates from field data on natural populations can be problematic. The prickly forest skink, Gnypetoscincus queenslandiae, is a rainforest endemic skink from the wet tropics of Australia. Because of its log-dwelling habits and lack of definite nesting sites, a demographic estimate of dispersal distance is difficult to obtain. Neighbourhood size, defined as 4 piD sigma (2) (where D is the population density and sigma (2) the mean axial squared parent-offspring dispersal rate), dispersal and density were estimated directly and indirectly for this species using mark-recapture and microsatellite data, respectively, on lizards captured at a local geographical scale of 3 ha. Mark-recapture data gave a dispersal rate of 843 m(2)/generation (assuming a generation time of 6.5 years), a time-scaled density of 13 635 individuals * generation/km(2) and, hence, a neighbourhood size of 144 individuals. A genetic method based on the multilocus (10 loci) microsatellite genotypes of individuals and their geographical location indicated that there is a significant isolation by distance pattern, and gave a neighbourhood size of 69 individuals, with a 95% confidence interval between 48 and 184. This translates into a dispersal rate of 404 m(2)/generation when using the mark-recapture density estimation, or an estimate of time-scaled population density of 6520 individuals * generation/km(2) when using the mark-recapture dispersal rate estimate. The relationship between the two categories of neighbourhood size, dispersal and density estimates and reasons for any disparities are discussed.