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.

Assessing eco-environmental performance of agricultural production in OECD countries : combination of soil surface, soil system and farm gate methods of nutrient auditing

Nitrogen balance is increasingly used as an indicator of the environmental performance of agricultural sector in national, international, and global contexts. There are three main methods of accounting the national nitrogen balance: farm gate, soil surface, and soil system. OECD (2008) recently reported the nitrogen and phosphorus balances for member countries for the 1985 - 2004 period using the soil surface method. The farm gate and soil system methods were also used in some international projects. Some studies have provided the comparison among these methods and the conclusion is mixed. The motivation of this present paper was to combine these three methods to provide a more detailed auditing of the nitrogen balance and flows for national agricultural production. In addition, the present paper also provided a new strategy of using reliable international and national data sources to calculate nitrogen balance using the farm gate method. The empirical study focused on the nitrogen balance of OECD countries for the period from 1985 to 2003. The N surplus sent to the total environment of OECD surged dramatically in early 1980s, gradually decreased during 1990s but exhibited an increasing trends in early 2000s. The overall N efficiency however fluctuated without a clear increasing trend. The eco-environmental ranking shows that Australia and Ireland were the worst while Korea and Greece were the best.

Free-surface flow past arbitrary topography and an inverse approach for wave-free solutions

An efficient numerical method to compute nonlinear solutions for two-dimensional steady free-surface flow over an arbitrary channel bottom topography is presented. The approach is based on a boundary integral equation technique which is similar to that of Vanden-Broeck's (1996, J. Fluid Mech., 330, 339-347). The typical approach for this problem is to prescribe the shape of the channel bottom topography, with the free-surface being provided as part of the solution. Here we take an inverse approach and prescribe the shape of the free-surface a priori while solving for the corresponding bottom topography. We show how this inverse approach is particularly useful when studying topographies that give rise to wave-free solutions, allowing us to easily classify eleven basic flow types. Finally, the inverse approach is also adapted to calculate a distribution of pressure on the free-surface, given the free-surface shape itself.

Application of multi-criteria decision making methods to compression ignition engine efficiency and gaseous, particulate and greenhouse gas emissions

Compression ignition (CI) engine design is subject to many constraints which presents a multi-criteria optimisation problem that the engine researcher must solve. In particular, the modern CI engine must not only be efficient, but must also deliver low gaseous, particulate and life cycle greenhouse gas emissions so that its impact on urban air quality, human health, and global warming are minimised. Consequently, this study undertakes a multi-criteria analysis which seeks to identify alternative fuels, injection technologies and combustion strategies that could potentially satisfy these CI engine design constraints. Three datasets are analysed with the Preference Ranking Organization Method for Enrichment Evaluations and Geometrical Analysis for Interactive Aid (PROMETHEE-GAIA) algorithm to explore the impact of 1): an ethanol fumigation system, 2): alternative fuels (20 % biodiesel and synthetic diesel) and alternative injection technologies (mechanical direct injection and common rail injection), and 3): various biodiesel fuels made from 3 feedstocks (i.e. soy, tallow, and canola) tested at several blend percentages (20-100 %) on the resulting emissions and efficiency profile of the various test engines. The results show that moderate ethanol substitutions (~20 % by energy) at moderate load, high percentage soy blends (60-100 %), and alternative fuels (biodiesel and synthetic diesel) provide an efficiency and emissions profile that yields the most “preferred” solutions to this multi-criteria engine design problem. Further research is, however, required to reduce Reactive Oxygen Species (ROS) emissions with alternative fuels, and to deliver technologies that do not significantly reduce the median diameter of particle emissions.

The adoption of e-learning 2.0 in higher education by teachers and students : an investigation using mixed methods approach

This paper describes an approach to investigate the adoption of Web 2.0 in the classroom using a mixed methods study. By using a combination of qualitative or quantitative data collection and analysis techniques, we attempt to synergize the results and provide a more valid understanding of Web 2.0 adoption for learning by both teachers and students. This approach is expected to yield a better holistic view on the adoption issues associated with the e-learning 2.0 concept in current higher education as opposed to single method studies done previously. This paper also presents some early findings of e-learning 2.0 adoption using this research method

Methods to estimate the size and shape of the unaccommodated crystalline lens in vivo

Purpose. The purpose of this article was to present methods capable of estimating the size and shape of the human eye lens without resorting to phakometry or magnetic resonance imaging (MRI). Methods. Previously published biometry and phakometry data of 66 emmetropic eyes of 66 subjects (age range [18, 63] years, spherical equivalent range [−0.75, +0.75] D) were used to define multiple linear regressions for the radii of curvature and thickness of the lens, from which the lens refractive index could be derived. MRI biometry was also available for a subset of 30 subjects, from which regressions could be determined for the vertex radii of curvature, conic constants, equatorial diameter, volume, and surface area. All regressions were compared with the phakometry and MRI data; the radii of curvature regressions were also compared with a method proposed by Bennett and Royston et al. Results. The regressions were in good agreement with the original measurements. This was especially the case for the regressions of lens thickness, volume, and surface area, which each had an R2 > 0.6. The regression for the posterior radius of curvature had an R2 < 0.2, making this regression unreliable. For all other regressions we found 0.25 < R2 < 0.6. The Bennett-Royston method also produced a good estimation of the radii of curvature, provided its parameters were adjusted appropriately. Conclusions. The regressions presented in this article offer a valuable alternative in case no measured lens biometry values are available; however care must be taken for possible outliers.

Riding a mile in their shoes : understanding Australian metropolitan rail passenger perceptions and experiences of crowdedness using mixed-methods research

Metrics such as passengers per square metre have been developed to define optimum or crowded rail passenger density. Whilst such metrics are important to operational procedures, service evaluation and reporting, they fail to fully capture and convey the ways in which passengers experience crowded situations. This paper reports findings from a two year study of rail passenger crowding in five Australian capital cities which involved a novel mixed-methodology including ethnography, focus groups and an online stated preference choice experiment. The resulting data address the following four fundamental research questions: 1) to what extent are Australian rail passengers concerned by crowding, 2) what conditions exacerbate feelings of crowdedness, 3) what conditions mitigate feelings of crowdedness, and 4) how can we usefully understand passengers’ experiences of crowdedness? It concludes with some observations on the significance and implications of these findings for customer service provision. The findings outlined in this paper demonstrate that the experience of crowdedness (including its tolerance) cannot be understood in isolation from other customer services issues such as interior design, quality of environment, safety and public health concerns. It is hypothesised that tolerance of crowding will increase alongside improvements to overall customer service. This was the first comprehensive study of crowding in the Australian rail industry.

Permeability estimation conditioned to geophysical downhole log data in sandstones of the northern Galilee Basin, Queensland : methods and application

This study uses borehole geophysical log data of sonic velocity and electrical resistivity to estimate permeability in sandstones in the northern Galilee Basin, Queensland. The prior estimates of permeability are calculated according to the deterministic log–log linear empirical correlations between electrical resistivity and measured permeability. Both negative and positive relationships are influenced by the clay content. The prior estimates of permeability are updated in a Bayesian framework for three boreholes using both the cokriging (CK) method and a normal linear regression (NLR) approach to infer the likelihood function. The results show that the mean permeability estimated from the CK-based Bayesian method is in better agreement with the measured permeability when a fairly apparent linear relationship exists between the logarithm of permeability and sonic velocity. In contrast, the NLR-based Bayesian approach gives better estimates of permeability for boreholes where no linear relationship exists between logarithm permeability and sonic velocity.

I know, but I don’t care : how awareness of Queensland’s drug driving testing methods impact upon perceptions of deterrence and offending behaviours

An increasing body of research is highlighting the involvement of illicit drugs in many road fatalities. Deterrence theory has been a core conceptual framework underpinning traffic enforcement as well as interventions designed to reduce road fatalities. Essentially the effectiveness of deterrence-based approaches is predicated on perceptions of certainty, severity, and swiftness of apprehension. However, much less is known about how the awareness of legal sanctions can impact upon the effectiveness of deterrence mechanisms and whether promoting such detection methods can increase the deterrent effect. Nevertheless, the implicit assumption is that individuals aware of the legal sanctions will be more deterred. This study seeks to explore how awareness of the testing method impacts upon the effectiveness of deterrence-based interventions and intentions to drug drive again in the future. In total, 161 participants who reported drug driving in the previous six months took part in the current study. The results show that awareness of testing had a small effect upon increasing perceptions of the certainty of apprehension and severity of punishment. However, awareness was not a significant predictor of intentions to drug drive again in the future. Importantly, higher levels of drug use were a significant predictor of intentions to drug drive in the future. Whilst awareness does have a small effect on deterrence variables, the influence of levels of drug use seems to reduce any deterrent effect.

Qualitative methods in information systems research

Qualitative research methods are widely accepted in Information Systems and multiple approaches have been successfully used in IS qualitative studies over the years. These approaches include narrative analysis, discourse analysis, grounded theory, case study, ethnography and phenomenological analysis. Guided by critical, interpretive and positivist epistemologies (Myers 1997), qualitative methods are continuously growing in importance in our research community. In this special issue, we adopt Van Maanen's (1979: 520) definition of qualitative research as an umbrella term to cover an “array of interpretive techniques that can describe, decode, translate, and otherwise come to terms with the meaning, not the frequency, of certain more or less naturally occurring phenomena in the social world”. In the call for papers, we stated that the aim of the special issue was to provide a forum within which we can present and debate the significant number of issues, results and questions arising from the pluralistic approach to qualitative research in Information Systems. We recognise both the potential and the challenges that qualitative approaches offers for accessing the different layers and dimensions of a complex and constructed social reality (Orlikowski, 1993). The special issue is also a response to the need to showcase the current state of the art in IS qualitative research and highlight advances and issues encountered in the process of continuous learning that includes questions about its ontology, epistemological tenets, theoretical contributions and practical applications.

A case for optimising fracture healing through inverse dynamization

The mechanical conditions in the repair tissues are known to influence the outcome of fracture healing. These mechanical conditions are determined by the stiffness of fixation and limb loading. Experimental studies have shown that there is a range of beneficial fixation stiffness for timely healing and that fixation stiffness that is either too flexible or too stiff impairs callus healing. However, much less is known about how mechanical conditions influence the biological processes that make up the sequence of bone repair and if indeed mechanical stimulation is required at all stages of repair. Secondary bone healing occurs through a sequence of events broadly characterised by inflammation, proliferation, consolidation and remodelling. It is our hypothesis that a change in fixation stiffness from very flexible to stiff can shorten the time to healing relative to constant fixation stiffness. Flexible fixation has the benefit of promoting greater callus formation and needs to be applied during the proliferative stage of repair. The greater callus size helps to stabilize the fragments earlier allowing mineralization to occur faster. Together with stable/rigid fixation applied during the latter stage of repair to ensure mineralization of the callus. The predicted benefits of inverse dynamization are shortened healing in comparison to very flexible fixation and healing time comparable or faster than stable fixation with greater callus stiffness.