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.

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.

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.

Small business entity tax concessions : through the eyes of the practitioner

Australia’s small business sector has pursued often-competing imperatives of simplicity, equity and efficiency in the income tax regime (particularly focusing on the notion of simplicity) over the last decade. In 2001, there was an attempt to provide such simplification and reduce the compliance burden faced by Australian small businesses through the ‘simplified tax system’ (‘STS’). However, despite amendments over the years, the regime is much criticised. This article explores how the STS (now known as the ‘small business entity’ regime or ‘SBE’) is utilised from the perspective of tax practitioners, by analysing their recommendations to small business clients in respect of the regime. The results indicate that practitioners believe the regime did nothing to simplify the tax system for small businesses or reduce tax compliance costs. Indeed, the practitioners believed that the introduction of small business concessions had actually achieved the opposite result — it had increased tax compliance costs for their small business clients. However, tax practitioners still recommend the regime highly because it minimises their client’s tax liability.

Which procurement system? Towards a universal procurement selection technique

Two approaches are described, which aid the selection of the most appropriate procurement arrangements for a building project. The first is a multi-attribute technique based on the National Economic Development Office procurement path decision chart. A small study is described in which the utility factors involved were weighted by averaging the scores of five 'experts' for three hypothetical building projects. A concordance analysis is used to provide some evidence of any abnormal data sources. When applied to the study data, one of the experts was seen to be atypical. The second approach is by means of discriminant analysis. This was found to provide reasonably consistent predictions through three discriminant functions. The analysis also showed the quality criteria to have no significant impact on the decision process. Both approaches provided identical and intuitively correct answers in the study described. Some concluding remarks are made on the potential of discriminant analysis for future research and development in procurement selection techniques.

Reproductive behavioural differences between wild-caught and pond-reared Penaeus monodon prawn broodstock

Ongoing problems exist with the commercial scale domestication of Penaeus monodon. One of the major issues, in terms of reproductive performance, is the low egg hatch rate of eggs from these captive bred prawns. The current study investigated the related issue of mating success. Time lapse video observations were conducted to compare the mating behaviour of pond-reared (domesticated) and wild-caught prawn P. monodon broodstock. Mating success of the pond-reared prawns was found to be low relative to wild-caught. It was determined that both male and female prawns contributed to this low mating rate suggesting both genders were impacted negatively by the domestication process. The causative factors for the low mating success are yet to be determined, however external physical abnormalities and lack of sexual maturity did not appear to play a role. The most notable behavioural difference between wild-caught and domesticated prawns was a reduced level of pursuit behaviour by domesticated males. This and other behavioural differences are discussed in relation to an increasing body of evidence that male prawns respond to sex pheromones produced by receptive females and that males detect these chemical signals in part, via their second antennal flagella. Accordingly we hypothesise that pond-reared (domesticated) females may have a reduced ability to produce or release sex pheromones and males, a reduced ability to detect them when compared to their wild-caught counterparts.

Book review : Reply to Holmes’s review of the "Social Construction of Anorexia Nervosa"

It is always difficult to know what reviewers such as Colin Holmes (2001) want from a book. While he knows something of the claims that Gull was thought by some to be Jack the Ripper – an historical digression deliberately omitted from the book – Holmes has, it would seem, little understanding of the practice implications of Foucauldian analysis...

Phylodynamic analysis of the emergence and epidemiological impact of transmissible defective dengue viruses

Intra-host sequence data from RNA viruses have revealed the ubiquity of defective viruses in natural viral populations, sometimes at surprisingly high frequency. Although defective viruses have long been known to laboratory virologists, their relevance in clinical and epidemiological settings has not been established. The discovery of long-term transmission of a defective lineage of dengue virus type 1 (DENV-1) in Myanmar, first seen in 2001, raised important questions about the emergence of transmissible defective viruses and their role in viral epidemiology. By combining phylogenetic analyses and dynamical modelling, we investigate how evolutionary and ecological processes at the intra-host and inter-host scales shaped the emergence and spread of the defective DENV-1 lineage. We show that this lineage of defective viruses emerged between June 1998 and February 2001, and that the defective virus was transmitted primarily through co-transmission with the functional virus to uninfected individuals. We provide evidence that, surprisingly, this co-transmission route has a higher transmission potential than transmission of functional dengue viruses alone. Consequently, we predict that the defective lineage should increase overall incidence of dengue infection, which could account for the historically high dengue incidence reported in Myanmar in 2001-2002. Our results show the unappreciated potential for defective viruses to impact the epidemiology of human pathogens, possibly by modifying the virulence-transmissibility trade-off, or to emerge as circulating infections in their own right. They also demonstrate that interactions between viral variants, such as complementation, can open new pathways to viral emergence.

The use of electronic portal imaging to verify patient position during intensity-modulated radiotherapy delivered by the dynamic MLC technique

Purpose: The precise shape of the three-dimensional dose distributions created by intensity-modulated radiotherapy means that the verification of patient position and setup is crucial to the outcome of the treatment. In this paper, we investigate and compare the use of two different image calibration procedures that allow extraction of patient anatomy from measured electronic portal images of intensity-modulated treatment beams. Methods and Materials: Electronic portal images of the intensity-modulated treatment beam delivered using the dynamic multileaf collimator technique were acquired. The images were formed by measuring a series of frames or segments throughout the delivery of the beams. The frames were then summed to produce an integrated portal image of the delivered beam. Two different methods for calibrating the integrated image were investigated with the aim of removing the intensity modulations of the beam. The first involved a simple point-by-point division of the integrated image by a single calibration image of the intensity-modulated beam delivered to a homogeneous polymethyl methacrylate (PMMA) phantom. The second calibration method is known as the quadratic calibration method and required a series of calibration images of the intensity-modulated beam delivered to different thicknesses of homogeneous PMMA blocks. Measurements were made using two different detector systems: a Varian amorphous silicon flat-panel imager and a Theraview camera-based system. The methods were tested first using a contrast phantom before images were acquired of intensity-modulated radiotherapy treatment delivered to the prostate and pelvic nodes of cancer patients at the Royal Marsden Hospital. Results: The results indicate that the calibration methods can be used to remove the intensity modulations of the beam, making it possible to see the outlines of bony anatomy that could be used for patient position verification. This was shown for both posterior and lateral delivered fields. Conclusions: Very little difference between the two calibration methods was observed, so the simpler division method, requiring only the single extra calibration measurement and much simpler computation, was the favored method. This new method could provide a complementary tool to existing position verification methods, and it has the advantage that it is completely passive, requiring no further dose to the patient and using only the treatment fields.

Proteomics science and society :the role of knowledge translation in moving towards clinical applications

Gaining support for proteomics science requires effective knowledge translation. Knowledge translation (KT) processes turn the evidence generated by scientific discovery into recommendations for clinical applications, funding priorities, and policy/regulatory reforms. Clinicians, regulators, and funders need to understand why emerging proteomics knowledge is relevant, and what are the potential applications of that knowledge. A lack of clarity remains about what KT means.

Post-genomic science & society : Getting our fangs into omics science and its implications

Genomics and genetic findings have been hailed with promises of unlocked codes and new frontiers of personalized medicine. Despite cautions about gene hype, the strong cultural pull of genes and genomics has allowed consideration of genomic personhood. Populated by the complicated records of mass spectrometer, proteomics, which studies the human protein, has not achieved either the funding or the popular cultural appeal proteomics scientists had hoped it would. While proteomics, being focused on the proteins that actually indicate and create disease states, has a more direct potential for clinical applications than genomic risk predictions, culturally, it has not provided the material for identity creation. In our ethnographic research, we explore how proteomic scientists attempting to shape an appeal to personhood through which legitimacy may be defined.

The CGT small business concessions : recent evidence from the perspective of the tax practitioner

On 21 September 1999 Division 152 was inserted into the Income Tax Assessment Act (1997) (ITAA 1997). It was subsequently subject to amendments in 2006. Division 152 contains the small business CGT concessions, which enables eligible small business taxpayers to reduce the amount of tax payable on capital gains arising from certain CGT events (including the sale of the small business itself) that occur after 11:45 am on 21 September 1999. One of the stated principal objectives of the legislation was to provide a concessionary regime for small business owners who did not have the same ability to access the concessionary superannuation regime (particularly the superannuation guarantee charge) generally available to employees. The then Federal Treasurer, Mr Peter Costello, when announcing the introduction of the concessions, specifically stated that the object of Div 152 was to provide “small business people with access to funds for retirement or expansion”. The purpose of this project is to: one, assess the extent to which small business taxpayers understand the CGT small business concessions, particularly when considering sale of their business; two, determine which of the four small business CGT concessions are being adopted and/or recommended by tax advisors to clients; and three, determine whether the recent superannuation changes announced by the Federal Government in relation to the capping of the concessional superannuation thresholds have had an impact on the use of the small business retirement concession. It is anticipated that the results of this study will reveal that that small business owners are reliant on their tax advisors to explain the operation of Division 152. It is plausible that give the complexity of the CGT concessions, most small business owners are completely unaware of the four small business CGT concessions contained in Division 152 and do not understand how these concessions apply. Our study will also reveal the extent to which each CGT small business concession has been adopted (and reasons why). In particular, emphasis will be placed on the adoption of the small business retirement concession contained in Subdivision 152-D (and specific reasons for its adoption). This study also seeks to understand whether the recent (and impending) changes to the concessional superannuation cap has resulted in the retirement concession being more widely adopted (or recommended) by tax advisors. We would expect that the results of our study to confirm this to be the case, particularly coupled with the recent economic downturn, which has led to lower superannuation fund balances. By providing accounting firms with this information, small business owners will benefit from the information, becoming better placed to be long-term self funded retirees, providing not only financial benefits to the individuals and the country, but a significant increase in social self-assurance by these members of the community.

Creative entrepreneurship education for graduate employability in the creative arts

The higher education sector in Australia is under increasing pressure to prove quality and efficacy of education provision, including graduate outcomes. One of the central tasks of higher education has become to prepare nascent professionals as far as possible for initial employment and future working lives beyond this (Boden & Nedeva, 2010). Tertiary educators in the creative arts face significant and distinctive challenges in demonstrating graduate employability, and creative graduates consistently have the poorest outcomes of any subject grouping. In part, this is because the national graduate destinations survey (Graduate Careers Council of Australia, 2012) does not cater to the distinctive ‘portfolio’ nature of creative careers, or take account of the fact that creative careers can take concerted effort over several years to establish (e.g., McCowan & Wyganowska, 2010). However, it is worth asking whether we as tertiary arts educators are doing enough to prepare creative arts students for the world of work, particularly given that the majority of them will be self-employed to some degree (Bureau of Labour Statistics, 2011, Throsby & Zednik, 2010), and will be challenged to build their own careers without recourse to the support of HR departments or intra-firm promotion schemes. It has been demonstrated empirically that career management and creative enterprise skills are among the most important graduate capabilities in determining early creative career success (Bridgstock, 2011), although these skills do not appear in the Learning and Teaching Academic Standards for the Creative and Performing Arts (2010). This paper explores the nature and development of enterprise capabilities for creative arts students (as distinct from students of the business school), examines best practice in the field internationally, and proposes a theoretically-driven creative arts-specific enterprise curriculum model which commences in first year, for demonstrable impact on student enterprise behaviours (such as grant seeking, professional networking and intention to start an enterprise) and employability.