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.

Supplement : Efficient weak second-order stochastic Runge-Kutta methods for non-commutative Stratonvich stochastic differential equations

This paper gives a modification of a class of stochastic Runge–Kutta methods proposed in a paper by Komori (2007). The slight modification can reduce the computational costs of the methods significantly.

Modelling and solving train scheduling problems under capacity constraints

Many large coal mining operations in Australia rely heavily on the rail network to transport coal from mines to coal terminals at ports for shipment. Over the last few years, due to the fast growing demand, the coal rail network is becoming one of the worst industrial bottlenecks in Australia. As a result, this provides great incentives for pursuing better optimisation and control strategies for the operation of the whole rail transportation system under network and terminal capacity constraints. This PhD research aims to achieve a significant efficiency improvement in a coal rail network on the basis of the development of standard modelling approaches and generic solution techniques. Generally, the train scheduling problem can be modelled as a Blocking Parallel- Machine Job-Shop Scheduling (BPMJSS) problem. In a BPMJSS model for train scheduling, trains and sections respectively are synonymous with jobs and machines and an operation is regarded as the movement/traversal of a train across a section. To begin, an improved shifting bottleneck procedure algorithm combined with metaheuristics has been developed to efficiently solve the Parallel-Machine Job- Shop Scheduling (PMJSS) problems without the blocking conditions. Due to the lack of buffer space, the real-life train scheduling should consider blocking or hold-while-wait constraints, which means that a track section cannot release and must hold a train until the next section on the routing becomes available. As a consequence, the problem has been considered as BPMJSS with the blocking conditions. To develop efficient solution techniques for BPMJSS, extensive studies on the nonclassical scheduling problems regarding the various buffer conditions (i.e. blocking, no-wait, limited-buffer, unlimited-buffer and combined-buffer) have been done. In this procedure, an alternative graph as an extension of the classical disjunctive graph is developed and specially designed for the non-classical scheduling problems such as the blocking flow-shop scheduling (BFSS), no-wait flow-shop scheduling (NWFSS), and blocking job-shop scheduling (BJSS) problems. By exploring the blocking characteristics based on the alternative graph, a new algorithm called the topological-sequence algorithm is developed for solving the non-classical scheduling problems. To indicate the preeminence of the proposed algorithm, we compare it with two known algorithms (i.e. Recursive Procedure and Directed Graph) in the literature. Moreover, we define a new type of non-classical scheduling problem, called combined-buffer flow-shop scheduling (CBFSS), which covers four extreme cases: the classical FSS (FSS) with infinite buffer, the blocking FSS (BFSS) with no buffer, the no-wait FSS (NWFSS) and the limited-buffer FSS (LBFSS). After exploring the structural properties of CBFSS, we propose an innovative constructive algorithm named the LK algorithm to construct the feasible CBFSS schedule. Detailed numerical illustrations for the various cases are presented and analysed. By adjusting only the attributes in the data input, the proposed LK algorithm is generic and enables the construction of the feasible schedules for many types of non-classical scheduling problems with different buffer constraints. Inspired by the shifting bottleneck procedure algorithm for PMJSS and characteristic analysis based on the alternative graph for non-classical scheduling problems, a new constructive algorithm called the Feasibility Satisfaction Procedure (FSP) is proposed to obtain the feasible BPMJSS solution. A real-world train scheduling case is used for illustrating and comparing the PMJSS and BPMJSS models. Some real-life applications including considering the train length, upgrading the track sections, accelerating a tardy train and changing the bottleneck sections are discussed. Furthermore, the BPMJSS model is generalised to be a No-Wait Blocking Parallel- Machine Job-Shop Scheduling (NWBPMJSS) problem for scheduling the trains with priorities, in which prioritised trains such as express passenger trains are considered simultaneously with non-prioritised trains such as freight trains. In this case, no-wait conditions, which are more restrictive constraints than blocking constraints, arise when considering the prioritised trains that should traverse continuously without any interruption or any unplanned pauses because of the high cost of waiting during travel. In comparison, non-prioritised trains are allowed to enter the next section immediately if possible or to remain in a section until the next section on the routing becomes available. Based on the FSP algorithm, a more generic algorithm called the SE algorithm is developed to solve a class of train scheduling problems in terms of different conditions in train scheduling environments. To construct the feasible train schedule, the proposed SE algorithm consists of many individual modules including the feasibility-satisfaction procedure, time-determination procedure, tune-up procedure and conflict-resolve procedure algorithms. To find a good train schedule, a two-stage hybrid heuristic algorithm called the SE-BIH algorithm is developed by combining the constructive heuristic (i.e. the SE algorithm) and the local-search heuristic (i.e. the Best-Insertion- Heuristic algorithm). To optimise the train schedule, a three-stage algorithm called the SE-BIH-TS algorithm is developed by combining the tabu search (TS) metaheuristic with the SE-BIH algorithm. Finally, a case study is performed for a complex real-world coal rail network under network and terminal capacity constraints. The computational results validate that the proposed methodology would be very promising because it can be applied as a fundamental tool for modelling and solving many real-world scheduling problems.

Three primary school students’ cognition about 3D rotation in a virtual reality learning environment

This paper reports on three primary school students’ explorations of 3D rotation in a virtual reality learning environment (VRLE) named VRMath. When asked to investigate if you would face the same direction when you turn right 45 degrees first then roll up 45 degrees, or when you roll up 45 degrees first then turn right 45 degrees, the students found that the different order of the two turns ended up with different directions in the VRLE. This was contrary to the students’ prior predictions based on using pen, paper and body movements. The findings of this study showed the difficulty young children have in perceiving and understanding the non-commutative nature of 3D rotation and the power of the computational VRLE in giving students experiences that they rarely have in real life with 3D manipulations and 3D mental movements.

A stochastic exponential Euler scheme for simulation of stiff biochemical reaction systems

In order to simulate stiff biochemical reaction systems, an explicit exponential Euler scheme is derived for multidimensional, non-commutative stochastic differential equations with a semilinear drift term. The scheme is of strong order one half and A-stable in mean square. The combination with this and the projection method shows good performance in numerical experiments dealing with an alternative formulation of the chemical Langevin equation for a human ether a-go-go related gene ion channel mode

Exploring non-cancer pain conditions in a community sample : critiquing a current conceptual model of the acute to chronic pain transition and examining predictors of chronicity

This program of research examines the experience of chronic pain in a community sample. While, it is clear that like patient samples, chronic pain in non-patient samples is also associated with psychological distress and physical disability, the experience of pain across the total spectrum of pain conditions (including acute and episodic pain conditions) and during the early course of chronic pain is less clear. Information about these aspects of the pain experience is important because effective early intervention for chronic pain relies on identification of people who are likely to progress to chronicity post-injury. A conceptual model of the transition from acute to chronic pain was proposed by Gatchel (1991a). In brief, Gatchel’s model describes three stages that individuals who have a serious pain experience move through, each with worsening psychological dysfunction and physical disability. The aims of this program of research were to describe the experience of pain in a community sample in order to obtain pain-specific data on the problem of pain in Queensland, and to explore the usefulness of Gatchel’s Model in a non-clinical sample. Additionally, five risk factors and six protective factors were proposed as possible extensions to Gatchel’s Model. To address these aims, a prospective longitudinal mixed-method research design was used. Quantitative data was collected in Phase 1 via a comprehensive postal questionnaire. Phase 2 consisted of a follow-up questionnaire 3 months post-baseline. Phase 3 consisted of semi-structured interviews with a subset of the original sample 12 months post follow-up, which used qualitative data to provide a further in-depth examination of the experience and process of chronic pain from respondents’ point of view. The results indicate chronic pain is associated with high levels of anxiety and depressive symptoms. However, the levels of disability reported by this Queensland sample were generally lower than those reported by clinical samples and consistent with disability data reported in a New South Wales population-based study. With regard to the second aim of this program of research, while some elements of the pain experience of this sample were consistent with that described by Gatchel’s Model, overall the model was not a good fit with the experience of this non-clinical sample. The findings indicate that passive coping strategies (minimising activity), catastrophising, self efficacy, optimism, social support, active strategies (use of distraction) and the belief that emotions affect pain may be important to consider in understanding the processes that underlie the transition to and continuation of chronic pain.

Is there a future for non-motorized public transport in Asia?

Non-motorized public transport (NMPT), especially three-wheeler cycle rickshaws, has a long history in East Asia; and has long been a major transport planning issue. Policy measures to restrict or eliminate NMPT have already been implemented in many developing cities with mixed success. However given the economic, social and cultural significance of NMPT, its environmental benefits, and the magnitude of its role in sustaining the mobility needs of citizens, it is timely to reconsider the future role of NMPT. Rather than pursuing policies to eliminate NMPT, a better approach may be to integrate motorized and non-motorized vehicles as complementary rather than competitive forces. With this backdrop and given the international significance of the problem, this paper examines the current role and significance of NMPT using Dhaka as a case study, and sets a research agenda for the future of NMPT in a sustainable transport system.

A problem-posing intervention in the development of problem-solving competence of underachieving, middle-year students

This study reported on the issues surrounding the acquisition of problem-solving competence of middle-year students who had been ascertained as above average in intelligence, but underachieving in problem-solving competence. In particular, it looked at the possible links between problem-posing skills development and improvements in problem-solving competence. A cohort of Year 7 students at a private, non-denominational, co-educational school was chosen as participants for the study, as they undertook a series of problem-posing sessions each week throughout a school term. The lessons were facilitated by the researcher in the students’ school setting. Two criteria were chosen to identify participants for this study. Firstly, each participant scored above the 60th percentile in the standardized Middle Years Ability Test (MYAT) (Australian Council for Educational Research, 2005) and secondly, the participants all scored below the cohort average for Criterion B (Problem-solving Criterion) in their school mathematics tests during the first semester of Year 7. Two mutually exclusive groups of participants were investigated with one constituting the Comparison Group and the other constituting the Intervention Group. The Comparison Group was chosen from a Year 7 cohort for whom no problem-posing intervention had occurred, while the Intervention Group was chosen from the Year 7 cohort of the following year. This second group received the problem-posing intervention in the form of a teaching experiment. That is, the Comparison Group were only pre-tested and post-tested, while the Intervention Group was involved in the teaching experiment and received the pre-testing and post-testing at the same time of the year, but in the following year, when the Comparison Group have moved on to the secondary part of the school. The groups were chosen from consecutive Year 7 cohorts to avoid cross-contamination of the data. A constructionist framework was adopted for this study that allowed the researcher to gain an “authentic understanding” of the changes that occurred in the development of problem-solving competence of the participants in the context of a classroom setting (Richardson, 1999). Qualitative and quantitative data were collected through a combination of methods including researcher observation and journal writing, video taping, student workbooks, informal student interviews, student surveys, and pre-testing and post-testing. This combination of methods was required to increase the validity of the study’s findings through triangulation of the data. The study findings showed that participation in problem-posing activities can facilitate the re-engagement of disengaged, middle-year mathematics students. In addition, participation in these activities can result in improved problem-solving competence and associated developmental learning changes. Some of the changes that were evident as a result of this study included improvements in self-regulation, increased integration of prior knowledge with new knowledge and increased and contextualised socialisation.

An advanced implicit meshless approach for the non-linear anomalous subdiffusion equation

Recently, the numerical modelling and simulation for anomalous subdiffusion equation (ASDE), which is a type of fractional partial differential equation( FPDE) and has been found with widely applications in modern engineering and sciences, are attracting more and more attentions. The current dominant numerical method for modelling ASDE is Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings. This paper aims to develop an implicit meshless approach based on the radial basis functions (RBF) for numerical simulation of the non-linear ASDE. The discrete system of equations is obtained by using the meshless shape functions and the strong-forms. The stability and convergence of this meshless approach are then discussed and theoretically proven. Several numerical examples with different problem domains are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. The results obtained by the meshless formulations are also compared with those obtained by FDM in terms of their accuracy and efficiency. It is concluded that the present meshless formulation is very effective for the modeling and simulation of the ASDE. Therefore, the meshless technique should have good potential in development of a robust simulation tool for problems in engineering and science which are governed by the various types of fractional differential equations.

Defending the patch : a labour geography analysis of unions’ construction of and responses to the problem of declining union membership amongst youth

If the trade union movement is to remain an influential force in the industrial, economic and socio/political arenas of industrialised nations it is vital that its recruitment of young members improve dramatically. Australian union membership levels have declined markedly over the last three decades and youth union membership levels have decreased more than any age group. Currently around 10% of young workers aged between 16-24 years are members of unions in Australia compared to 26% of workers aged 45-58 (Oliver, 2008). This decline has occurred throughout the union movement, in all states and in almost all industries and occupations. This research, which consists of interviews with union organisers and union officials, draws on perspectives from the labour geography literature to explore how union personnel located in various places, spaces and scales construct the issue of declining youth union membership. It explores the scale of connections within the labour movement and the extent to which these connections are leveraged to address the problem of youth union membership decline. To offer the reader a sense of context and perspective, the thesis firstly outlines the historical development of the union movement. It also reviews the literature on youth membership decline. Labour geography offers a rich and apposite analytical tool for investigation of this area. The notion of ‘scale’ as a dynamic, interactive, constructed and reconstructed entity (Ellem, 2006) is an appropriate lens for viewing youth-union membership issues. In this non-linear view, scale is a relational element which interplays with space, place and the environment (Howett, in Marston, 2000) rather than being ‘sequential’ and hierarchical. Importantly, the thesis investigates the notion of unions as ‘spaces of dependence’ (Cox, 1998a, p.2), organisations whose space is centred upon realising essential interests. It also considers the quality of unions’ interactions with others – their ‘spaces of engagement‘(Cox, 1998a, p.2), and the impact that this has upon their ability to recruit youth. The findings reveal that most respondents across the spectrum of the union movement attribute the decline in youth membership levels to factors external to the movement itself, such as changes to industrial relations legislation and the impact of globalisation on employment markets. However, participants also attribute responsibility for declining membership levels to the union movement itself, citing factors such as a lack of resourcing and a need to change unions’ perceived identity and methods of operation. The research further determined that networks of connections across the union movement are tenuous and, to date, are not being fully utilised to assist unions to overcome the youth recruitment dilemma. The study concludes that potential connections between unions are hampered by poor resourcing, workload issues and some deeply entrenched attitudes related to unions ‘defending (and maintaining) their patch’.

Using Association Rules to Solve the Cold-Start Problem in Recommender Systems

Recommender systems are widely used online to help users find other products, items etc that they may be interested in based on what is known about that user in their profile. Often however user profiles may be short on information and thus it is difficult for a recommender system to make quality recommendations. This problem is known as the cold-start problem. Here we investigate using association rules as a source of information to expand a user profile and thus avoid this problem. Our experiments show that it is possible to use association rules to noticeably improve the performance of a recommender system under the cold-start situation. Furthermore, we also show that the improvement in performance obtained can be achieved while using non-redundant rule sets. This shows that non-redundant rules do not cause a loss of information and are just as informative as a set of association rules that contain redundancy.

Reliability analysis and economic equipment replacement appraisal for substation and sub-transmission systems with explicit inclusion of non-repairable failures

The modern society has come to expect the electrical energy on demand, while many of the facilities in power systems are aging beyond repair and maintenance. The risk of failure is increasing with the aging equipments and can pose serious consequences for continuity of electricity supply. As the equipments used in high voltage power networks are very expensive, economically it may not be feasible to purchase and store spares in a warehouse for extended periods of time. On the other hand, there is normally a significant time before receiving equipment once it is ordered. This situation has created a considerable interest in the evaluation and application of probability methods for aging plant and provisions of spares in bulk supply networks, and can be of particular importance for substations. Quantitative adequacy assessment of substation and sub-transmission power systems is generally done using a contingency enumeration approach which includes the evaluation of contingencies, classification of the contingencies based on selected failure criteria. The problem is very complex because of the need to include detailed modelling and operation of substation and sub-transmission equipment using network flow evaluation and to consider multiple levels of component failures. In this thesis a new model associated with aging equipment is developed to combine the standard tools of random failures, as well as specific model for aging failures. This technique is applied in this thesis to include and examine the impact of aging equipments on system reliability of bulk supply loads and consumers in distribution network for defined range of planning years. The power system risk indices depend on many factors such as the actual physical network configuration and operation, aging conditions of the equipment, and the relevant constraints. The impact and importance of equipment reliability on power system risk indices in a network with aging facilities contains valuable information for utilities to better understand network performance and the weak links in the system. In this thesis, algorithms are developed to measure the contribution of individual equipment to the power system risk indices, as part of the novel risk analysis tool. A new cost worth approach was developed in this thesis that can make an early decision in planning for replacement activities concerning non-repairable aging components, in order to maintain a system reliability performance which economically is acceptable. The concepts, techniques and procedures developed in this thesis are illustrated numerically using published test systems. It is believed that the methods and approaches presented, substantially improve the accuracy of risk predictions by explicit consideration of the effect of equipment entering a period of increased risk of a non-repairable failure.

Punitiveness and the criminalisation of the other : State wards, unlawful non-citizens and Indigenous youth

This paper explores the genealogies of bio-power that cut across punitive state interventions aimed at regulating or normalising several distinctive ‘problem’ or ‘suspect’ deviant populations, such as state wards, non-lawful citizens and Indigenous youth. It begins by making some general comments about the theoretical approach to bio-power taken in this paper. It then outlines the distinctive features of bio-power in Australia and how these intersected with the emergence of penal welfarism to govern the unruly, unchaste, unlawful, and the primitive. The paper draws on three examples to illustrate the argument – the gargantuan criminalisation rates of Aboriginal youth, the history of incarcerating state wards in state institutions, and the mandatory detention of unlawful non-citizens and their children. The construction of Indigenous people as a dangerous presence, alongside the construction of the unruly neglected children of the colony — the larrikin descendants of convicts as necessitating special regimes of internal controls and institutions, found a counterpart in the racial and other exclusionary criteria operating through immigration controls for much of the twentieth century. In each case the problem child or population was expelled from the social body through forms of bio-power, rationalised as strengthening, protecting or purifying the Australian population.