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.

Miscibility and phase separation in blends of phenolphthalein poly(aryl ether ketone) and poly(ethylene oxide): a differential scanning calorimetric study

Miscibility and phase separation in the blends of phenolphthalein poly(aryl ether ketone) (PPAEK) and poly(ethylene oxide) (PEO) were investigated by means of differential scanning calorimetry (DSC). The PPAEK/PEO blends prepared by solution casting from N,N-dimethylformamide (DMF) displayed single composition-dependent glass transition temperatures (T-g), intermediate between those of the pure components, suggesting that the blend system is miscible in the amorphous state at all compositions. All the blends underwent phase separation at higher temperatures and the system exhibited a lower critical solution temperature (LCST) behavior. A step-heating thermal analysis was designed to determine the phase boundaries with DSC. The significant changes in the thermal properties of blends were utilized to judge the mixing status for the blends and the phase diagram was thus established. (C) 2004 Elsevier B.V. All rights reserved.

A genetic estimation algorithm for parameters of stochastic ordinary differential equations

A generic method for the estimation of parameters for Stochastic Ordinary Differential Equations (SODEs) is introduced and developed. This algorithm, called the GePERs method, utilises a genetic optimisation algorithm to minimise a stochastic objective function based on the Kolmogorov-Smirnov statistic. Numerical simulations are utilised to form the KS statistic. Further, the examination of some of the factors that improve the precision of the estimates is conducted. This method is used to estimate parameters of diffusion equations and jump-diffusion equations. It is also applied to the problem of model selection for the Queensland electricity market. (C) 2003 Elsevier B.V. All rights reserved.

Wheat grain cooking process as investigated by modulated temperature differential scanning calorimetry

The thermal properties of soft and hard wheat grains, cooked in a steam pressure cooker, as a function of cooking temperature and time were investigated by modulated temperature differential scanning calorimetry (MTDSC). Four cooking temperatures (110, 120, 130 and 140 degrees C) and six cooking times (20, 40, 60, 80, 100 and 120 min) for each temperature were studied. It was found that typical non-reversible heat flow thermograms of cooked and uncooked wheat grains consisted of two endothermic baseline shifts localised around 40-50 degrees C and then 60-70 degrees C. The second peaks of non-reversible heat flow thermograms (60-70 degrees C) were associated with starch gelatinisation. The degree of gelatinisation was quantified based on these peaks. In this study, starch was completely gelatinised within 60-80 min for cooking temperatures at 110-120 degrees C and within 20 min for cooking temperatures at 130-140 degrees C. MTDSC detected reversible endothermic baseline shifts in most samples, localised broadly around 48-67 degrees C with changes in heat capacity ranging from 0.02 to 0.06 J/g per degrees C. These reversible endothermic baseline shifts are related to the glass transition, which occurs during starch gelatinisation. Data on the specific heat capacity of the cooked wheat samples are provided. (C) 2005 Elsevier Ltd. All rights reserved.

An experimental and finite element poroelastic creep response analysis of an intervertebral hydrogel disc model in axial compression

A hydrogel intervertebral disc (lVD) model consisting of an inner nucleus core and an outer anulus ring was manufactured from 30 and 35% by weight Poly(vinyl alcohol) hydrogel (PVA-H) concentrations and subjected to axial compression in between saturated porous endplates at 200 N for 11 h, 30 min. Repeat experiments (n = 4) on different samples (N = 2) show good reproducibility of fluid loss and axial deformation. An axisymmetric nonlinear poroelastic finite element model with variable permeability was developed using commercial finite element software to compare axial deformation and predicted fluid loss with experimental data. The FE predictions indicate differential fluid loss similar to that of biological IVDs, with the nucleus losing more water than the anulus, and there is overall good agreement between experimental and finite element predicted fluid loss. The stress distribution pattern indicates important similarities with the biological lVD that includes stress transference from the nucleus to the anulus upon sustained loading and renders it suitable as a model that can be used in future studies to better understand the role of fluid and stress in biological IVDs. (C) 2005 Springer Science + Business Media, Inc.

Drinking refusal self-efficacy questionnaire-revised (DRSEQ-R): a new factor structure with confirmatory factor analysis

The drinking refusal self-efficacy questionnaire (DRSEQ: Young, R.M., Oei, T.P.S., 1996. Drinking expectancy profile: test manual. Behaviour Research and Therapy Centre, University of Queensland, Australia Young, R.M., Oei, T.P.S., Crook, G.M., 1991. Development of a drinking refusal self-efficacy questionnaire. J. Psychopathol. Behav. Assess., 13, 1-15) assesses a person's belief in their ability to resist alcohol. The DRSEQ is a sound psychometric instrument based on exploratory factor analyses, but has not been subjected to confirmatory factor analysis. In total 2773 participants were used to confirm the factor structure of the DRSEQ. Initial analyses revealed that the original structure was not confirmed in the current study. Subsequent analyses resulted in a revised factor structure (DRSEQ-R) being confirmed in community, student and clinical samples. The DRSEQ-R was also found to have good construct and concurrent validity. The factor structure of the DRSEQ-R is more stable than the original structure of the DRSEQ and the revised scale has considerable potential in future alcohol-related research. (c) 2004 Elsevier Ireland Ltd. All rights reserved.

An examination of the dynamic relationship between self-efficacy and performance across levels of analysis and levels of specificity

This research used resource allocation theory to generate predictions regarding dynamic relationships between self-efficacy and task performance from 2 levels of analysis and specificity. Participants were given multiple trials of practice on an air traffic control task. Measures of task-specific self-efficacy and performance were taken at repeated intervals. The authors used multilevel analysis to demonstrate differential and dynamic effects. As predicted, task-specific self-efficacy was negatively associated with task performance at the within-person level. On the other hand, average levels of task-specific self-efficacy were positively related to performance at the between-persons level and mediated the effect of general self-efficacy. The key findings from this research relate to dynamic effects - these results show that self-efficacy effects can change over time, but it depends on the level of analysis and specificity at which self-efficacy is conceptualized. These novel findings emphasize the importance of conceptualizing self-efficacy within a multilevel and multispecificity framework and make a significant contribution to understanding the way this construct relates to task performance.

Applying network analysis to the conservation of habitat trees in urban environments: a case study from Brisbane, Australia

In Australia more than 300 vertebrates, including 43 insectivorous bat species, depend on hollows in habitat trees for shelter, with many species using a network of multiple trees as roosts, We used roost-switching data on white-striped freetail bats (Tadarida australis; Microchiroptera: Molossidae) to construct a network representation of day roosts in suburban Brisbane, Australia. Bats were caught from a communal roost tree with a roosting group of several hundred individuals and released with transmitters. Each roost used by the bats represented a node in the network, and the movements of bats between roosts formed the links between nodes. Despite differences in gender and reproductive stages, the bats exhibited the same behavior throughout three radiotelemetry periods and over 500 bat days of radio tracking: each roosted in separate roosts, switched roosts very infrequently, and associated with other bats only at the communal roost This network resembled a scale-free network in which the distribution of the number of links from each roost followed a power law. Despite being spread over a large geographic area (> 200 km(2)), each roost was connected to others by less than three links. One roost (the hub or communal roost) defined the architecture of the network because it had the most links. That the network showed scale-free properties has profound implications for the management of the habitat trees of this roosting group. Scale-free networks provide high tolerance against stochastic events such as random roost removals but are susceptible to the selective removal of hub nodes. Network analysis is a useful tool for understanding the structural organization of habitat tree usage and allows the informed judgment of the relative importance of individual trees and hence the derivation of appropriate management decisions, Conservation planners and managers should emphasize the differential importance of habitat trees and think of them as being analogous to vital service centers in human societies.

Stochastic delay differential equations for genetic regulatory networks

Time delay is an important aspect in the modelling of genetic regulation due to slow biochemical reactions such as gene transcription and translation, and protein diffusion between the cytosol and nucleus. In this paper we introduce a general mathematical formalism via stochastic delay differential equations for describing time delays in genetic regulatory networks. Based on recent developments with the delay stochastic simulation algorithm, the delay chemical masterequation and the delay reaction rate equation are developed for describing biological reactions with time delay, which leads to stochastic delay differential equations derived from the Langevin approach. Two simple genetic regulatory networks are used to study the impact of' intrinsic noise on the system dynamics where there are delays. (c) 2006 Elsevier B.V. All rights reserved.

Microarray and proteomic analysis of the human alcoholic brain

The superior frontal cortex (SFC) is selectively damaged in chronic alcohol abuse, with localized neuronal loss and tissue atrophy. Regions such as motor cortex show little neuronal loss except in severe co-morbidity (liver cirrhosis or WKS). Altered gene expression was found in microarray comparisons of alcoholic and control SFC samples [1]. We used Western blots and proteomic analysis to identify the proteins that also show differential expression. Tissue was obtained at autopsy under informed, written consent from uncomplicated alcoholics and age- and sex-matched controls. Alcoholics had consumed 80 g ethanol/day chronically (often, 200 g/day for 20 y). Controls either abstained or were social drinkers ( 20 g/day). All subjects had pathological confirmation of liver and brain diagnosis; none had been polydrug abusers. Samples were homogenized in water and clarified by brief centrifugation (1000g, 3 min) before storage at –80°C. For proteomics the thawed suspensions were centrifuged (15000g, 50 min) to prepare soluble fractions. Aliquots were pooled from SFC samples from the 5 chronic alcoholics and 5 matched controls used in the previous microarray study [1]. 2-Dimensional electrophoresis was performed in triplicate using 18 cm format pH 4–7 and pH 6–11 immobilized pH gradients for firstdimension isoelectric focusing. Following second-dimension SDS-PAGE the proteins were fluorescently stained and the images collected by densitometry. 182 proteins differed by 2-fold between cases and controls. 141 showed lower expression in alcoholics, 33 higher, and 8 were new or had disappeared. To date 63 proteins have been identified using MALDI-MS and MS-MS. Western blots were performed on uncentrifuged individual samples from 76 subjects (controls, uncomplicated alcoholics and cirrhotic alcoholics). A common standard was run on every gel. After transfer, immunolabeling, and densitometry, the intensities of the unknown bands were compared to those of the standards. We focused on proteins from transcripts that showed clear differences in a series of microarray studies, classified into common sets including Regulators of G-protein Signaling and Myelin-associated proteins. The preponderantly lower level of differentially expressed proteins in alcoholics parallels the microarray mRNA analysis in the same samples. We found that mRNA and protein expression do not frequently correspond; this may help identify pathogenic processes acting at the level of transcription, translation, or post-translationally.

Genomic and proteomic analysis of synaptic protein expression in the brains of human alcoholics

Alcoholism results in changes in the human brain which reinforce the cycle of craving and dependency, and these changes are manifest in the pattern of expression of mRNA and proteins in key cells and brain areas. Long-term alcohol abuse also results in damage to selected regions of the cortex. We have used cDNA microarrays to show that less than 1% of mRNA transcripts differ signifi cantly between cases and controls in the susceptible area and that the expression profi le of a subset of these transcripts is suffi cient to distinguish alcohol abusers from controls. In addition, we have utilized a 2D gel proteomics based approach to determine the identity of proteins in the superior frontal cortex (SFC) of the human brain that show differential expression in controls and long term alcohol abusers. Overall, 182 proteins differed by the criterion of > 2-fold between case and control samples. Of these, 139 showed signifi cantly lower expression in alcoholics, 35 showed signifi cantly higher expression, and 8 were new or had disappeared. To date 63 proteins have been identifi ed. The expression of one family of proteins, the synucleins, has been further characterized using Real Time PCR and Western Blotting. The expression of alpha-synuclein mRNA was signifi cantly lower in the SFC of alcoholics compared with the same area in controls (P = 0.01) whereas no such difference in expression was found in the motor cortex. The expression of beta- and gamma- synuclein were not signifi cantly different between alcoholics and controls. In contrast, the pattern of alphasynuclein protein expression differs from that of the corresponding RNA transcript. Because of the key role of synaptic proteins in the pathogenesis of alcoholism, we are developing 2-D DIGE based techniques to quantify expression changes in synaptosomes prepared from the SFC of controls and alcoholics.