High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations

The pioneering work of Runge and Kutta a hundred years ago has ultimately led to suites of sophisticated numerical methods suitable for solving complex systems of deterministic ordinary differential equations. However, in many modelling situations, the appropriate representation is a stochastic differential equation and here numerical methods are much less sophisticated. In this paper a very general class of stochastic Runge-Kutta methods is presented and much more efficient classes of explicit methods than previous extant methods are constructed. In particular, a method of strong order 2 with a deterministic component based on the classical Runge-Kutta method is constructed and some numerical results are presented to demonstrate the efficacy of this approach.

Synthesis and characterisation of organo-beidellite

Today, there are growing concerns about the presence of environmental pollutants in many parts of the world. In particular, a lot of attention has been drawn to the levels of water and soil contaminants (de Paiva et al., 2008). The majority of these contaminants consist of NOCs (non-ionic organic compounds) and can enter our waterways through industrial activities, mining operations, crop and animal production, waste disposal and accidental leakage (de Paiva et al., 2008; Park et al., 2011). Therefore, there is an increased interest in the synthesis of new materials that can be used to remove potentially carcinogenic and toxic water contaminants. Smectite type organoclays are widely used in numerous applications, such as sorbent agents for environmental remediation, due to their unique properties (Jiunn-Fwu et al., 1990; Sheng et al., 1996; Zhou et al., 2007; Bektas et al., 2011; Park et al., 2011). This investigation focuses on beidellite (SBId-1), which belongs to the smectite clay family. Their properties include high cation exchange capacity (CEC), swelling properties, porous, high surface area and consequential strong adsorption/absorption capacity (Xi et al., 2007). However, swelling clays in general are not an effective sorbent agent in nature due to their hydrophilic properties. The hydrophilic properties of the clay can be changed to organophilic by intercalating a cationic surfactant. Many applications of organoclays are strongly dependent on their structural properties and hence, a better understanding of the configuration and structural change of organoclay is crucial. Organoclays were synthesised through ion exchange of 21CODTMA (MW: 392.5 g mol-1) and characterised using XRD and FTIR spectroscopy. This study investigates the structural and conformational changes of beidellite intercalated with octadecyltrimethylammonium bromide.

High strong order methods for non-commutative stochastic ordinary differential equation systems and the Magnus formula

In recent years considerable attention has been paid to the numerical solution of stochastic ordinary differential equations (SODEs), as SODEs are often more appropriate than their deterministic counterparts in many modelling situations. However, unlike the deterministic case numerical methods for SODEs are considerably less sophisticated due to the difficulty in representing the (possibly large number of) random variable approximations to the stochastic integrals. Although Burrage and Burrage [High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations, Applied Numerical Mathematics 22 (1996) 81-101] were able to construct strong local order 1.5 stochastic Runge-Kutta methods for certain cases, it is known that all extant stochastic Runge-Kutta methods suffer an order reduction down to strong order 0.5 if there is non-commutativity between the functions associated with the multiple Wiener processes. This order reduction down to that of the Euler-Maruyama method imposes severe difficulties in obtaining meaningful solutions in a reasonable time frame and this paper attempts to circumvent these difficulties by some new techniques. An additional difficulty in solving SODEs arises even in the Linear case since it is not possible to write the solution analytically in terms of matrix exponentials unless there is a commutativity property between the functions associated with the multiple Wiener processes. Thus in this present paper first the work of Magnus [On the exponential solution of differential equations for a linear operator, Communications on Pure and Applied Mathematics 7 (1954) 649-673] (applied to deterministic non-commutative Linear problems) will be applied to non-commutative linear SODEs and methods of strong order 1.5 for arbitrary, linear, non-commutative SODE systems will be constructed - hence giving an accurate approximation to the general linear problem. Secondly, for general nonlinear non-commutative systems with an arbitrary number (d) of Wiener processes it is shown that strong local order I Runge-Kutta methods with d + 1 stages can be constructed by evaluated a set of Lie brackets as well as the standard function evaluations. A method is then constructed which can be efficiently implemented in a parallel environment for this arbitrary number of Wiener processes. Finally some numerical results are presented which illustrate the efficacy of these approaches. (C) 1999 Elsevier Science B.V. 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.

Preceptorship : making a difference

A preceptor project at the Royal Brisbane and Women's Hospital in Queensland, Australia, explored existing levels of preceptorship support during the transition processes of newly employed or transferred nurses and midwives. Initiatives adopted have enhanced the implementation and maintenance of preceptorship principles and communication processes and defined accountability and responsibilities. Outcomes have contributed to enhanced role clarity, improved communication, increased support for teaching and learning, and infrastructure processes to facilitate the preceptor-preceptee relationship and increased retention.

A strong quantitative trait locus for wing length on chromosome 2 in a wild population of great reed warblers

Wing length is a key character for essential behaviours related to bird flight such as migration and foraging. In the present study, we initiate the search for the genes underlying wing length in birds by studying a long-distance migrant, the great reed warbler (Acrocephalus arundinaceus). In this species wing length is an evolutionary interesting trait with pronounced latitudinal gradient and sex-specific selection regimes in local populations. We performed a quantitative trait locus (QTL) scan for wing length in great reed warblers using phenotypic, genotypic, pedigree and linkage map data from our long-term study population in Sweden. We applied the linkage analysis mapping method implemented in GRIDQTL (a new web-based software) and detected a genome-wide significant QTL for wing length on chromosome 2, to our knowledge, the first detected QTL in wild birds. The QTL extended over 25 cM and accounted for a substantial part (37%) of the phenotypic variance of the trait. A genome scan for tarsus length (a bodysize-related trait) did not show any signal, implying that the wing-length QTL on chromosome 2 was not associated with body size. Our results provide a first important step into understanding the genetic architecture of avian wing length, and give opportunities to study the evolutionary dynamics of wing length at the locus level. This journal is© 2010 The Royal Society.

Ion transport in small-molecule electrolytes based on LiI/3-hydroxypropionitrile with high salt contents

Abnormal “polymer-in-salt” conduction behavior is observed in a solid electrolyte composed of lithium iodide (LiI) and 3-hydroxypropionitrile (HPN). Based on comprehensive investigations by X-ray diffraction (XRD) and Raman and infrared spectroscopy, this abnormal conduction behavior is attributed to the formation of new ionic associates [Lim +In−]· · ·N C (m> n) and the reinforced hydrogen bonding of I· · ·HO in the electrolyte at high LiI concentrations.

A model for enhancing assessment and teaching practice at the coalface : Insights from a Fellow-In-Residence engagement program

Australian universities are currently engaging with new governmental policies and regulations that require them to demonstrate enhanced quality and accountability in teaching and research. The development of national academic standards for learning outcomes in higher education is one such instance of this drive for excellence. These discipline-specific standards articulate the minimum, or Threshold Learning Outcomes, to be addressed by higher education institutions so that graduating students can demonstrate their achievement to their institutions, accreditation agencies, and industry recruiters. This impacts not only on the design of Engineering courses (with particular emphasis on pedagogy and assessment), but also on the preparation of academics to engage with these standards and implement them in their day-to-day teaching practice on a micro level. This imperative for enhanced quality and accountability in teaching is also significant at a meso level, for according to the Australian Bureau of Statistics, about 25 per cent of teachers in Australian universities are aged 55 and above and more than 54 per cent are aged 45 and above (ABS, 2006). A number of institutions have undertaken recruitment drives to regenerate and enrich their academic workforce by appointing capacity-building research professors and increasing the numbers of early- and mid-career academics. This nationally driven agenda for quality and accountability in teaching permeates also the micro level of engineering education, since the demand for enhanced academic standards and learning outcomes requires both a strong advocacy for a shift to an authentic, collaborative, outcomes-focused education and the mechanisms to support academics in transforming their professional thinking and practice. Outcomes-focused education means giving greater attention to the ways in which the curriculum design, pedagogy, assessment approaches and teaching activities can most effectively make a positive, verifiable difference to students’ learning. Such education is authentic when it is couched firmly in the realities of learning environments, student and academic staff characteristics, and trustworthy educational research. That education will be richer and more efficient when staff works collaboratively, contributing their knowledge, experience and skills to achieve learning outcomes based on agreed objectives. We know that the school or departmental levels of universities are the most effective loci of changes in approaches to teaching and learning practices in higher education (Knight & Trowler, 2000). Heads of Schools are being increasingly entrusted with more responsibilities - in addition to setting strategic directions and managing the operational and sometimes financial aspects of their school, they are also expected to lead the development and delivery of the teaching, research and other academic activities. Guiding and mentoring individuals and groups of academics is one critical aspect of the Head of School’s role. Yet they do not always have the resources or support to help them mentor staff, especially the more junior academics. In summary, the international trend in undergraduate engineering course accreditation towards the demonstration of attainment of graduate attributes poses new challenges in addressing academic staff development needs and the assessment of learning. This paper will give some insights into the conceptual design, implementation and empirical effectiveness to date, of a Fellow-In-Residence Engagement (FIRE) program. The program is proposed as a model for achieving better engagement of academics with contemporary issues and effectively enhancing their teaching and assessment practices. It will also report on the program’s collaborative approach to working with Heads of Schools to better support academics, especially early-career ones, by utilizing formal and informal mentoring. Further, the paper will discuss possible factors that may assist the achievement of the intended outcomes of such a model, and will examine its contributions to engendering an outcomes-focussed thinking in engineering education.

Tsunami alert : the mobile phone difference

Substantial growth has occurred in the telecommunication sector in Papua New Guinea (PNG) since 2007. Mobile telephony has spread to rural and remote localities, following decades of inadequate telephone services. This paper examines the introduction of mobile telephones into a rural village in PNG, and focuses on information access during emergency situations. It considers three tsunami alerts: one immediately prior to the introduction of mobile phone services in the area, and two which occurred after mobile phone reception became available. The research shows that for people with limited access to information, responses to threats such as tsunamis can be inappropriate and driven by fear and panic. By contrast, when there is reliable, timely information available, measured responses can be adopted. This research demonstrates how the use of newly-introduced communication technologies for handling emergencies may work in practice, benefitting people in poorer, rural communities.

Planar difference functions

In 1980 Alltop produced a family of cubic phase sequences that nearly meet the Welch bound for maximum non-peak correlation magnitude. This family of sequences were shown by Wooters and Fields to be useful for quantum state tomography. Alltop’s construction used a function that is not planar, but whose difference function is planar. In this paper we show that Alltop type functions cannot exist in fields of characteristic 3 and that for a known class of planar functions, x^3 is the only Alltop type function.

ACE research vignette 023 : Does firm location make a difference to the export performance of SME's?

This series of research vignettes is aimed at sharing current and interesting research findings from our team of international Entrepreneurship researchers. This vignette, written by Mr. Darren Kavenagh and Professor Per Davidsson, deals with export capacity of Australian SMEs.

Candidate gene analysis for quantitative traits using the transmission disequilibrium test : the example of the melanocortin 4-receptor in pigs

Population-wide associations between loci due to linkage disequilibrium can be used to map quantitative trait loci (QTL) with high resolution. However, spurious associations between markers and QTL can also arise as a consequence of population stratification. Statistical methods that cannot differentiate between loci associations due to linkage disequilibria from those caused in other ways can render false-positive results. The transmission-disequilibrium test (TDT) is a robust test for detecting QTL. The TDT exploits within-family associations that are not affected by population stratification. However, some TDTs are formulated in a rigid-form, with reduced potential applications. In this study we generalize TDT using mixed linear models to allow greater statistical flexibility. Allelic effects are estimated with two independent parameters: one exploiting the robust within-family information and the other the potentially biased between-family information. A significant difference between these two parameters can be used as evidence for spurious association. This methodology was then used to test the effects of the fourth melanocortin receptor (MC4R) on production traits in the pig. The new analyses supported the previously reported results; i.e., the studied polymorphism is either causal of in very strong linkage disequilibrium with the causal mutation, and provided no evidence for spurious association.

Stealing and “Dishonest Application” : defining the difference in Queensland

The 1st July 1997 heralded the implementation of a number of amendments to the Queensland Criminal Code including some intriguing changes affecting the principal property offences of stealing (section 398) and dishonest application (section 408C). This article discusses the impact of the changes. It examines the extent of the amendments and then aims to delineate the ambit of each offence drawing on some of the more recent judgments in the area. It concludes that the offences are moving closer together while retaining many of the complexities of proof experienced in the past.