Adams-Type Methods for the Numerical Solution of Stochastic Ordinary Differential Equations

Stochastic differential equations (SDEs) arise fi om physical systems where the parameters describing the system can only be estimated or are subject to noise. There has been much work done recently on developing numerical methods for solving SDEs. This paper will focus on stability issues and variable stepsize implementation techniques for numerically solving SDEs effectively. (C) 2000 Elsevier Science B.V. All rights reserved.

General order conditions for stochastic Runge-Kutta methods for both commuting and non-commuting stochastic ordinary differential equation systems

In many modeling situations in which parameter values can only be estimated or are subject to noise, the appropriate mathematical representation is a stochastic ordinary differential equation (SODE). However, unlike the deterministic case in which there are suites of sophisticated numerical methods, numerical methods for SODEs are much less sophisticated. Until a recent paper by K. Burrage and P.M. Burrage (1996), the highest strong order of a stochastic Runge-Kutta method was one. But K. Burrage and P.M. Burrage (1996) showed that by including additional random variable terms representing approximations to the higher order Stratonovich (or Ito) integrals, higher order methods could be constructed. However, this analysis applied only to the one Wiener process case. In this paper, it will be shown that in the multiple Wiener process case all known stochastic Runge-Kutta methods can suffer a severe order reduction if there is non-commutativity between the functions associated with the Wiener processes. Importantly, however, it is also suggested how this order can be repaired if certain commutator operators are included in the Runge-Kutta formulation. (C) 1998 Elsevier Science B.V. and IMACS. All rights reserved.

A bound on the maximum strong order of stochastic Runge-Kutta methods for stochastic ordinary differential equations

In Burrage and Burrage [1] it was shown that by introducing a very general formulation for stochastic Runge-Kutta methods, the previous strong order barrier of order one could be broken without having to use higher derivative terms. In particular, methods of strong order 1.5 were developed in which a Stratonovich integral of order one and one of order two were present in the formulation. In this present paper, general order results are proven about the maximum attainable strong order of these stochastic Runge-Kutta methods (SRKs) in terms of the order of the Stratonovich integrals appearing in the Runge-Kutta formulation. In particular, it will be shown that if an s-stage SRK contains Stratonovich integrals up to order p then the strong order of the SRK cannot exceed min{(p + 1)/2, (s - 1)/2), p greater than or equal to 2, s greater than or equal to 3 or 1 if p = 1.

Using patterns co-occurrence matrix for cleaning closed sequential patterns for text mining

With the overwhelming increase in the amount of texts on the web, it is almost impossible for people to keep abreast of up-to-date information. Text mining is a process by which interesting information is derived from text through the discovery of patterns and trends. Text mining algorithms are used to guarantee the quality of extracted knowledge. However, the extracted patterns using text or data mining algorithms or methods leads to noisy patterns and inconsistency. Thus, different challenges arise, such as the question of how to understand these patterns, whether the model that has been used is suitable, and if all the patterns that have been extracted are relevant. Furthermore, the research raises the question of how to give a correct weight to the extracted knowledge. To address these issues, this paper presents a text post-processing method, which uses a pattern co-occurrence matrix to find the relation between extracted patterns in order to reduce noisy patterns. The main objective of this paper is not only reducing the number of closed sequential patterns, but also improving the performance of pattern mining as well. The experimental results on Reuters Corpus Volume 1 data collection and TREC filtering topics show that the proposed method is promising.

Managing memory and reducing I/O cost for correlation matrix calculation in bioinformatics

The generation of a correlation matrix from a large set of long gene sequences is a common requirement in many bioinformatics problems such as phylogenetic analysis. The generation is not only computationally intensive but also requires significant memory resources as, typically, few gene sequences can be simultaneously stored in primary memory. The standard practice in such computation is to use frequent input/output (I/O) operations. Therefore, minimizing the number of these operations will yield much faster run-times. This paper develops an approach for the faster and scalable computing of large-size correlation matrices through the full use of available memory and a reduced number of I/O operations. The approach is scalable in the sense that the same algorithms can be executed on different computing platforms with different amounts of memory and can be applied to different problems with different correlation matrix sizes. The significant performance improvement of the approach over the existing approaches is demonstrated through benchmark examples.

Improved estimates of percolation and anisotropic permeability from 3-D X-ray microtomography using stochastic analyses and visualization

X-ray microtomography (micro-CT) with micron resolution enables new ways of characterizing microstructures and opens pathways for forward calculations of multiscale rock properties. A quantitative characterization of the microstructure is the first step in this challenge. We developed a new approach to extract scale-dependent characteristics of porosity, percolation, and anisotropic permeability from 3-D microstructural models of rocks. The Hoshen-Kopelman algorithm of percolation theory is employed for a standard percolation analysis. The anisotropy of permeability is calculated by means of the star volume distribution approach. The local porosity distribution and local percolation probability are obtained by using the local porosity theory. Additionally, the local anisotropy distribution is defined and analyzed through two empirical probability density functions, the isotropy index and the elongation index. For such a high-resolution data set, the typical data sizes of the CT images are on the order of gigabytes to tens of gigabytes; thus an extremely large number of calculations are required. To resolve this large memory problem parallelization in OpenMP was used to optimally harness the shared memory infrastructure on cache coherent Non-Uniform Memory Access architecture machines such as the iVEC SGI Altix 3700Bx2 Supercomputer. We see adequate visualization of the results as an important element in this first pioneering study.

Sample size considerations and augmentation of computer experiments

Computer Experiments, consisting of a number of runs of a computer model with different inputs, are now common-place in scientific research. Using a simple fire model for illustration some guidelines are given for the size of a computer experiment. A graph is provided relating the error of prediction to the sample size which should be of use when designing computer experiments. Methods for augmenting computer experiments with extra runs are also described and illustrated. The simplest method involves adding one point at a time choosing that point with the maximum prediction variance. Another method that appears to work well is to choose points from a candidate set with maximum determinant of the variance covariance matrix of predictions.

Quality Assessment Matrix : A Collaborative Evaluation Using Multiple Lines of Evidence

Welcome to the Quality assessment matrix. This matrix is designed for highly qualified discipline experts to evaluate their course, major or unit in a systematic manner. The primary purpose of the Quality assessment matrix is to provide a tool that a group of academic staff at universities can collaboratively review the assessment within a course, major or unit annually. The annual review will result in you being read for an external curricula review at any point in time. This tool is designed for use in a workshop format with one, two or more academic staff, and will lead to an action plan for implementation.

Ruptures in the heterosexual matrix through teenage flows and multiplicities

This article analyzes a series of stories and artworks that were produced in a collective biography workshop. It explores Judith Butler’s concept of the heterosexual matrix combined with a Deleuzian theoretical framework. The article begins with an overview of Butler’s concept of the heterosexual matrix and her theorizations on how it might be disrupted. It then suggests how a Deleuzian framework offers other tools for analyzing these ruptures at the micro level of girls’ everyday interactions.

Matrix metalloproteinase biosensor based on a porous silicon reflector

Matrix metalloproteinases (MMPs) are proteolytic enzymes important to wound healing. In non-healing wounds, it has been suggested that MMP levels become dysfunctional, hence it is of great interest to develop sensors to detect MMP biomarkers. This study presents the development of a label-free optical MMP biosensor based on a functionalised porous silicon (pSi) thin film. The biosensor is fabricated by immobilising a peptidomimetic MMP inhibitor in the porous layer using hydrosilylation followed by amide coupling. The binding of MMP to the immobilised inhibitor translates into a change of effective optical thickness (EOT) over the time. We investigate the effect of surface functionalisation on the stability of pSi surface and evaluate the sensing performance. We successfully demonstrate MMP detection in buffer solution and human wound fluid at physiologically relevant concentrations. This biosensor may find application as a point-of-care device that is prognostic of the healing trajectory of chronic wounds.

Development of a large scale flexible LED display matrix for the screen industry

This project addresses the viability of lightweight, low power consumption, flexible, large format LED screens. The investigation encompasses all aspects of the electrical and mechanical design, individually and as a system, and achieves a successful full scale prototype. The prototype implements novel techniques to achieve large displacement colour aliasing, a purely passive thermal management solution, a rapid deployment system, individual seven bit LED current control with two way display communication, auto-configuration and complete signal redundancy, all of which are in direct response to industry needs.

Matrix metalloproteinase localisation by in situ-RT-PCR in archival human breast biopsy material

Utilising archival human breast cancer biopsy material we examined the stromal/epithelial interactions of several matrix metalloproteinases (MMPs) using in situ-RT-PCR (IS-RT-PCR). In breast cancer, the stromal/epithelial interactions that occur, and the site of production of these proteases, are central to understanding their role in invasive and metastatic processes. We examined MT1-MMP (MMP-14, membrane type-1-MMP), MMP-1 (interstitial collagenase) and MMP-3 (stromelysin-1) for their localisation profile in progressive breast cancer biopsy material (poorly differentiated invasive breast carcinoma (PDIBC), invasive breast carcinomas (IBC) and lymph node metastases (LNM)). Expression of MT1-MMP, MMP-1 and MMP-3 was observed in both the tumour epithelial and surrounding stromal cells in most tissue sections examined. MT1-MMP expression was predominantly localised to the tumour component in the pre-invasive lesions. MMP-1 gene expression was relatively well distributed between both tissue compartments, while MMP-3 demonstrated highest expression levels in the stromal tissue surrounding the epithelial tumour cells. The results demonstrate the ability to distinguish compartmental gene expression profiles using IS-RT-PCR. Further, we suggest a role for MT1-MMP in early tumour progression, expression of MMP-1 during metastasis and focal expression pattern of MMP-3 in areas of expansion. These expression profiles may provide markers for early breast cancer diagnoses and present potential therapeutic targets.

Distinguishing between mean-field, moment dynamics and stochastic descriptions of birth-death-movement processes

Mathematical descriptions of birth–death–movement processes are often calibrated to measurements from cell biology experiments to quantify tissue growth rates. Here we describe and analyze a discrete model of a birth–death-movement process applied to a typical two–dimensional cell biology experiment. We present three different descriptions of the system: (i) a standard mean–field description which neglects correlation effects and clustering; (ii) a moment dynamics description which approximately incorporates correlation and clustering effects, and; (iii) averaged data from repeated discrete simulations which directly incorporates correlation and clustering effects. Comparing these three descriptions indicates that the mean–field and moment dynamics approaches are valid only for certain parameter regimes, and that both these descriptions fail to make accurate predictions of the system for sufficiently fast birth and death rates where the effects of spatial correlations and clustering are sufficiently strong. Without any method to distinguish between the parameter regimes where these three descriptions are valid, it is possible that either the mean–field or moment dynamics model could be calibrated to experimental data under inappropriate conditions, leading to errors in parameter estimation. In this work we demonstrate that a simple measurement of agent clustering and correlation, based on coordination number data, provides an indirect measure of agent correlation and clustering effects, and can therefore be used to make a distinction between the validity of the different descriptions of the birth–death–movement process.

Heat-producing crust regulation of subsurface temperatures : a stochastic model re-evaluation of the geothermal potential in western Queensland, Australia

A large subsurface, elevated temperature anomaly is well documented in Central Australia. High Heat Producing Granites (HHPGs) intersected by drilling at Innamincka are often assumed to be the dominant cause of the elevated subsurface temperatures, although their presence in other parts of the temperature anomaly has not been confirmed. Geological controls on the temperature anomaly remain poorly understood. Additionally, methods previously used to predict temperature at 5 km depth in this area are simplistic and possibly do not give an accurate representation of the true distribution and magnitude of the temperature anomaly. Here we re-evaluate the geological controls on geothermal potential in the Queensland part of the temperature anomaly using a stochastic thermal model. The results illustrate that the temperature distribution is most sensitive to the thermal conductivity structure of the top 5 km. Furthermore, the results indicate the presence of silicic crust enriched in heat producing elements between and 40 km.

A matrix for appropriate assessment of workplace learning in stem disciplines

With increasing interest shown by Universities in workplace learning, especially in STEM disciplines, an issue has arisen amongst educators and industry partners regarding authentic assessment tasks for work integrated learning (WIL) subjects. This paper describes the use of a matrix, which is also available as a decision-tree, based on the features of the WIL experience, in order to facilitate the selection of appropriate assessment strategies. The matrix divides the WIL experiences into seven categories, based on such factors as: the extent to which the experience is compulsory, required for membership of a professional body or elective; whether the student is undertaking a project, or embedding in a professional culture; and other key aspects of the WIL experience. One important variable is linked to the fundamental purpose of the assessment. This question revolves around the focus of the assessment: whether on the person (student development); the process (professional conduct/language); or the product (project, assignment, literature review, report, software). The matrix has been trialed at QUT in the Faculty of Science and Technology, and also at the University of Surrey, UK, and has proven to have good applicability in both universities.