Stable strong order 1.0 schemes for solving stochastic ordinary differential equations

The Balanced method was introduced as a class of quasi-implicit methods, based upon the Euler-Maruyama scheme, for solving stiff stochastic differential equations. We extend the Balanced method to introduce a class of stable strong order 1. 0 numerical schemes for solving stochastic ordinary differential equations. We derive convergence results for this class of numerical schemes. We illustrate the asymptotic stability of this class of schemes is illustrated and is compared with contemporary schemes of strong order 1. 0. We present some evidence on parametric selection with respect to minimising the error convergence terms. Furthermore we provide a convergence result for general Balanced style schemes of higher orders.

Evaluation of methods for cultivating limbal mesenchymal stromal cells

Background: Mesenchymal stromal cells (MSC) with similar properties to bone marrow derived mesenchymal stromal cells (BM-MSC) have recently been grown from the limbus of the human cornea. We presently contribute to this novel area of research by evaluating methods for culturing human limbal MSC (L-MSC). Methods: Four basic strategies are compared: serum-supplemented medium (10% foetal bovine serum; FBS), standard serum-free medium supplemented with B-27, epidermal growth factor, and fibroblast growth factor 2, or one of two commercial serum-free media including Defined Keratinocyte Serum Free Medium (Invitrogen), and MesenCult-XF (Stem Cell Technologies). The phenotype of resulting cultures was examined using photography, flow cytometry (for CD34, CD45, CD73, CD90, CD105, CD141, CD271), immunocytochemistry (α-sma), differentiation assays (osteogenesis, adipogenesis, chrondrogenesis), and co-culture experiments with human limbal epithelial (HLE) cells. Results: While all techniques supported to varying degrees establishment of cultures, sustained growth and serial propagation was only achieved in 10% FBS medium or MesenCult-XF medium. Cultures established in 10% FBS medium were 70-80% CD34-/CD45-/CD90+/CD73+/CD105+, approximately 25% α-sma+, and displayed multi-potency. Cultures established in MesenCult-XF were >95% CD34-/CD45-/CD90+/CD73+/CD105+, 40% CD141+, rarely expressed α-sma, and displayed multi-potency. L-MSC supported growth of HLE cells, with the largest epithelial islands being observed in the presence of MesenCult-XF-grown L-MSC. All HLE cultures supported by L-MSC widely expressed the progenitor cell marker ∆Np63, along with the corneal differentiation marker cytokeratin 3. Conclusions: We conclude that MesenCult-XF® is a superior culture system for L-MSC, but further studies are required to explore the significance of CD141 expression in these cells.

A dual-scale modelling approach for drying hygroscopic porous media

A new dualscale modelling approach is presented for simulating the drying of a wet hygroscopic porous material that couples the porous medium (macroscale) with the underlying pore structure (microscale). The proposed model is applied to the convective drying of wood at low temperatures and is valid in the so-called hygroscopic range, where hygroscopically held liquid water is present in the solid phase and water exits only as vapour in the pores. Coupling between scales is achieved by imposing the macroscopic gradients of moisture content and temperature on the microscopic field using suitably-defined periodic boundary conditions, which allows the macroscopic mass and thermal fluxes to be defined as averages of the microscopic fluxes over the unit cell. This novel formulation accounts for the intricate coupling of heat and mass transfer at the microscopic scale but reduces to a classical homogenisation approach if a linear relationship is assumed between the microscopic gradient and flux. Simulation results for a sample of spruce wood highlight the potential and flexibility of the new dual-scale approach. In particular, for a given unit cell configuration it is not necessary to propose the form of the macroscopic fluxes prior to the simulations because these are determined as a direct result of the dual-scale formulation.

A variable-stepsize Jacobian-free exponential integrator for simulating transport in heterogeneous porous media : application to wood drying

A Jacobian-free variable-stepsize method is developed for the numerical integration of the large, stiff systems of differential equations encountered when simulating transport in heterogeneous porous media. Our method utilises the exponential Rosenbrock-Euler method, which is explicit in nature and requires a matrix-vector product involving the exponential of the Jacobian matrix at each step of the integration process. These products can be approximated using Krylov subspace methods, which permit a large integration stepsize to be utilised without having to precondition the iterations. This means that our method is truly "Jacobian-free" - the Jacobian need never be formed or factored during the simulation. We assess the performance of the new algorithm for simulating the drying of softwood. Numerical experiments conducted for both low and high temperature drying demonstrates that the new approach outperforms (in terms of accuracy and efficiency) existing simulation codes that utilise the backward Euler method via a preconditioned Newton-Krylov strategy.

Greek or not : the use of symbols and abbreviations in mathematics

The use of symbols and abbreviations adds uniqueness and complexity to the mathematical language register. In this article, the reader’s attention is drawn to the multitude of symbols and abbreviations which are used in mathematics. The conventions which underpin the use of the symbols and abbreviations and the linguistic difficulties which learners of mathematics may encounter due to the inclusion of the symbolic language are discussed. 2010 NAPLAN numeracy tests are used to illustrate examples of the complexities of the symbolic language of mathematics.

Jabberwocky : the complexities of mathematical English

Mathematical English is a unique language based on ordinary English, with the addition of highly stylised formal symbol systems. Some words have a redefined status. Mathematical English has its own lexicon, syntax, semantics and literature. It is more difficult to understand than ordinary English. Ability in basic interpersonal communication does not necessarily result in proficiency in the use of mathematical English. The complex nature of mathematical English may impact upon the ability of students to succeed in mathematical and numeracy assessment. This article presents a review of the literature about the complexities of mathematical English. It includes examples of more than fifty language features that have been shown to add to the challenge of interpreting mathematical texts. Awareness of the complexities of mathematical English is an essential skill needed by mathematics teachers when teaching and when designing assessment tasks.

Observational research and verbal protocol methods

This paper describes observational research and verbal protocols methods, how these methods are applied and integrated within different contexts, and how they complement each other. The first case study focuses on nurses’ interaction during bandaging of patients’ lower legs. To maintain research rigor a triangulation approach was applied that links observations of current procedures, ‘talk-aloud’ protocol during interaction and retrospective protocol. Maps of interactions demonstrated that some nurses bandage more intuitively than others. Nurses who bandage intuitively assemble long sequences of bandaging actions while nurses who bandage less intuitively ‘focus-shift’ in between bandaging actions. Thus different levels of expertise have been identified. The second case study consists of two laboratory experiments. It focuses on analysing and comparing software and product design teams and how they approached a design problem. It is based on the observational and verbal data analysis. The coding scheme applied evolved during the analysis of the activity of each team and is identical for all teams. The structure of knowledge captured from the analysis of the design team maps of interaction is identified. The significance of this work is within its methodological approach. The maps of interaction are instrumental for understanding the activities and interactions of the people observed. By examining the maps of interaction, it is possible to draw conclusions about interactions, structure of knowledge captured and level of expertise. This research approach is transferable to other design domains. Designers will be able to transfer the interaction maps outcomes to systems and services they design.

‘Wide Atlantic Ocean’ : acting methods and cultural translation in mainstream theatre

A recent production of Nicholson’s Shadowlands at the Brisbane Powerhouse could have included two advertising lines: “Outspoken American-Jewish poet meets conservative British Oxford scholar” and “Emotive American Method trained actor meets contained British trained actor.” While the fusion of acting methodologies in intercultural acting has been discussed at length, little discussion has focussed on the juxtaposition of diverse acting styles in production in mainstream theatre. This paper explores how the permutation of American Method acting and a more traditional British conservatory acting in Crossbow’s August 2010 production of Shadowlands worked to add extra layers of meaning to the performance text. This sometimes inimical relationship between two acting styles had its beginnings in the rehearsal room and continued onstage. Audience reception to the play in post-performance discussions revealed the audience’s acute awareness of the transatlantic cultural tensions on stage. On one occasion, this resulted in a heated debate on cultural expression, continuing well after the event, during which audience members became co-performers in the cultural discourses of the play.

Experiences with implementing common mathematical operations using field programmable gate arrays

Many computationally intensive scientific applications involve repetitive floating point operations other than addition and multiplication which may present a significant performance bottleneck due to the relatively large latency or low throughput involved in executing such arithmetic primitives on commod- ity processors. A promising alternative is to execute such primitives on Field Programmable Gate Array (FPGA) hardware acting as an application-specific custom co-processor in a high performance reconfig- urable computing platform. The use of FPGAs can provide advantages such as fine-grain parallelism but issues relating to code development in a hardware description language and efficient data transfer to and from the FPGA chip can present significant application development challenges. In this paper, we discuss our practical experiences in developing a selection of floating point hardware designs to be implemented using FPGAs. Our designs include some basic mathemati cal library functions which can be implemented for user defined precisions suitable for novel applications requiring non-standard floating point represen- tation. We discuss the details of our designs along with results from performance and accuracy analysis tests.

Performance assessment of exponential Rosenbrock method for large systems of ODE

This paper studies time integration methods for large stiff systems of ordinary differential equations (ODEs) of the form u'(t) = g(u(t)). For such problems, implicit methods generally outperform explicit methods, since the time step is usually less restricted by stability constraints. Recently, however, explicit so-called exponential integrators have become popular for stiff problems due to their favourable stability properties. These methods use matrix-vector products involving exponential-like functions of the Jacobian matrix, which can be approximated using Krylov subspace methods that require only matrix-vector products with the Jacobian. In this paper, we implement exponential integrators of second, third and fourth order and demonstrate that they are competitive with well-established approaches based on the backward differentiation formulas and a preconditioned Newton-Krylov solution strategy.

Evaluation of the quality of diverse teaching practice in higher education research methods

The purpose of this paper is to report on a methods research project investigating the evaluation of diverse teaching practice in Higher Education. The research method is a single site case study of an Australian university with data collected through published documents, surveys, interviews and focus groups. This project provides evidence of the wide variety of evaluation practice and diverse teaching practice across the university. This breadth identifies the need for greater flexibility of evaluation processes, tools and support to assist teaching staff to evaluate their diverse teaching practice. The employment opportunities for academics benchmark the university nationally and position the case study in the field. Finally this reaffirms the institutional responsibility for services to support teaching staff in an ongoing manner.

The Donald Mackay Churchill Fellowship to study methods of preventing and supporting victims of online fraud

Every day inboxes are being flooded with invitations to invest money in overseas schemes, notifications of overseas lottery wins and inheritances, as well as emails from banks and other institutions asking for customers to confirm information about their identity and account details. While these requests may seem outrageous, many believe the request to be true and respond, through the sending of money or personal details. This can have devastating consequences, financially, emotionally and physically. While enforcement action is important, greater success is likely to come in the area of prevention, which avoids victim losses in the first place. Considerable victim support is also required by victims who have suffered significant losses, in trying to get their lives back on track. This project examined fraud prevention strategies and support services for victims of online fraud across the United Kingdom, United States of America and Canada. While much work has already been undertaken in Queensland, there is considerable room for improvement and a great deal can be learnt from these overseas jurisdictions. There are several examples of innovative and effective responses, particularly in the area of victim support, that are highlighted throughout this report. It is advocated that Australia can continue to improve its position regarding the prevention and support of online fraud victims, by applying the knowledge and expertise learnt overseas to a local context.

Refraction in children : a comparison of two methods of accommodation control

Purpose: The prevalence of refractive errors in children has been extensively researched. Comparisons between studies can, however, be compromised because of differences between accommodation control methods and techniques used for measuring refractive error. The aim of this study was to compare spherical refractive error results obtained at baseline and using two different accommodation control methods – extended optical fogging and cycloplegia, for two measurement techniques – autorefraction and retinoscopy. Methods: Participants comprised twenty-five school children aged between 6 and 13 years (mean age: 9.52 ± 2.06 years). The refractive error of one eye was measured at baseline and again under two different accommodation control conditions: extended optical fogging (+2.00DS for 20 minutes) and cycloplegia (1% cyclopentolate). Autorefraction and retinoscopy were both used to measure most plus spherical power for each condition. Results: A significant interaction was demonstrated between measurement technique and accommodation control method (p = 0.036), with significant differences in spherical power evident between accommodation control methods for each of the measurement techniques (p < 0.005). For retinoscopy, refractive errors were significantly more positive for cycloplegia compared to optical fogging, which were in turn significantly more positive than baseline, while for autorefraction, there were significant differences between cycloplegia and extended optical fogging and between cycloplegia and baseline only. Conclusions: Determination of refractive error under cycloplegia elicits more plus than using extended optical fogging as a method to relax accommodation. These findings support the use of cycloplegic refraction compared with extended optical fogging as a means of controlling accommodation for population based refractive error studies in children.

An introduction to mixed methods research for nephrology nurses

Mixed methods research is the use of qualitative and quantitative methods in the same study to gain a more rounded and holistic understanding of the phenomena under investigation. This type of research approach is gaining popularity in the nursing literature as a way to understand the complexity of nursing care and as a means to enhance evidenced-based practice. This paper introduces nephrology nurses to mixed methods research, its terminology and application to nephrology nursing. Five common mixed methods designs will be described highlighting the purposes, strengths and weaknesses of each design. Examples of mixed methods research will be given to illustrate the wide application of mixed methods research to nursing and its usefulness in nephrology nursing research.

Quantitative evaluation of matching methods and validity measures for stereo vision

The authors present a qualitative and quantitative comparison of various similarity measures that form the kernel of common area-based stereo-matching systems. The authors compare classical difference and correlation measures as well as nonparametric measures based on the rank and census transforms for a number of outdoor images. For robotic applications, important considerations include robustness to image defects such as intensity variation and noise, the number of false matches, and computational complexity. In the absence of ground truth data, the authors compare the matching techniques based on the percentage of matches that pass the left-right consistency test. The authors also evaluate the discriminatory power of several match validity measures that are reported in the literature for eliminating false matches and for estimating match confidence. For guidance applications, it is essential to have and estimate of confidence in the three-dimensional points generated by stereo vision. Finally, a new validity measure, the rank constraint, is introduced that is capable of resolving ambiguous matches for rank transform-based matching.