Adams-Type Methods for the Numerical Solution of Stochastic Ordinary Differential Equations

Stochastic differential equations (SDEs) arise fi om physical systems where the parameters describing the system can only be estimated or are subject to noise. There has been much work done recently on developing numerical methods for solving SDEs. This paper will focus on stability issues and variable stepsize implementation techniques for numerically solving SDEs effectively. (C) 2000 Elsevier Science B.V. All rights reserved.

Investigating homework as a social practice : a qualitative approach

This thesis examines the social practice of homework. It explores how homework is shaped by the discourses, policies and guidelines in circulation in a society at any given time with particular reference to one school district in the province of Newfoundland and Labrador, Canada. This study investigates how contemporary homework reconstitutes the home as a pedagogical site where the power of the institution of schooling circulates regularly from school to home. It examines how the educational system shapes the organization of family life and how family experiences with homework may be different in different sites depending on the accessibility of various forms of cultural capital. This study employs a qualitative approach, incorporating multiple case studies, and is complemented by insights from institutional ethnography and critical discourse analysis. It draws on the theoretical concepts of Foucault including power and power relations, and governmentality and surveillance, as well as Bourdieu’s concepts of economic, social and cultural capital for analysis. It employs concepts from Bourdieu’s work as they have been expanded on by researchers including Reay (1998), Lareau (2000), and Griffith and Smith (2005). The studies of these researchers allowed for an examination of homework as it related to families and mothers’ work. Smith’s (1987; 1999) concepts of ruling relations, mothers’ unpaid labour, and the engine of inequality were also employed in the analysis. Family interviews with ten volunteer families, teacher focus group sessions with 15 teachers from six schools, homework artefacts, school newsletters, homework brochures, and publicly available assessment and evaluation policy documents from one school district were analyzed. From this analysis key themes emerged and the findings are documented throughout five data analysis chapters. This study shows a change in education in response to a system shaped by standards, accountability and testing. It documents an increased transference of educational responsibility from one educational stakeholder to another. This transference of responsibility shifts downward until it eventually reaches the family in the form of homework and educational activities. Texts in the form of brochures and newsletters, sent home from school, make available to parents specific subject positions that act as instruments of normalization. These subject positions promote a particular ‘ideal’ family that has access to certain types of cultural capital needed to meet the school’s expectations. However, the study shows that these resources are not equally available to all and some families struggle to obtain what is necessary to complete educational activities in the home. The increase in transference of educational work from the school to the home results in greater work for parents, particularly mothers. As well, consideration is given to mother’s role in homework and how, in turn, classroom instructional practices are sometimes dependent on the work completed at home with differential effects for children. This study confirms previous findings that it is mothers who assume the greatest role in the educational trajectory of their children. An important finding in this research is that it is not only middle-class mothers who dedicate extensive time working hard to ensure their children’s educational success; working-class mothers also make substantial contributions of time and resources to their children’s education. The assignments and educational activities distributed as homework require parents’ knowledge of technical school pedagogy to help their children. Much of the homework being sent home from schools is in the area of literacy, particularly reading, but requires parents to do more than read with children. A key finding is that the practices of parents are changing and being reconfigured by the expectations of schools in regard to reading. Parents are now being required to monitor and supervise children’s reading, as well as help children complete reading logs, written reading responses, and follow up questions. The reality of family life as discussed by the participants in this study does not match the ‘ideal’ as portrayed in the educational documents. Homework sessions often create frustrations and tensions between parents and children. Some of the greatest struggles for families were created by mathematical homework, homework for those enrolled in the French Immersion program, and the work required to complete Literature, Heritage and Science Fair projects. Even when institutionalized and objectified capital was readily available, many families still encountered struggles when trying to carry out the assigned educational tasks. This thesis argues that homework and education-related activities play out differently in different homes. Consideration of this significance may assist educators to better understand and appreciate the vast difference in families and the ways in which each family can contribute to their children’s educational trajectory.

System level tests of transformer differential protection using an IEC 61850 process bus

The IEC 61850 family of standards for substation communication systems were released in the early 2000s, and include IEC 61850-8-1 and IEC 61850-9-2 that enable Ethernet to be used for process-level connections between transmission substation switchyards and control rooms. This paper presents an investigation of process bus protection performance, as the in-service behavior of multi-function process buses is largely unknown. An experimental approach was adopted that used a Real Time Digital Simulator and 'live' substation automation devices. The effect of sampling synchronization error and network traffic on transformer differential protection performance was assessed and compared to conventional hard-wired connections. Ethernet was used for all sampled value measurements, circuit breaker tripping, transformer tap-changer position reports and Precision Time Protocol synchronization of sampled value merging unit sampling. Test results showed that the protection relay under investigation operated correctly with process bus network traffic approaching 100% capacity. The protection system was not adversely affected by synchronizing errors significantly larger than the standards permit, suggesting these requirements may be overly conservative. This 'closed loop' approach, using substation automation hardware, validated the operation of protection relays under extreme conditions. Digital connections using a single shared Ethernet network outperformed conventional hard-wired solutions.

Effective punishment experiences : the need for a more comprehensive approach to conceptualising behavioural punishers and reinforcers in a road safety context

Determining what consequences are likely to serve as effective punishment for any given behaviour is a complex task. This chapter focuses specifically on illegal road user behaviours and the mechanisms used to punish and deter them. Traffic law enforcement has traditionally used the threat and/or receipt of legal sanctions and penalties to deter illegal and risky behaviours. This process represents the use of positive punishment, one of the key behaviour modification mechanisms. Behaviour modification principles describe four types of reinforcers: positive and negative punishments and positive and negative reinforcements. The terms ‘positive’ and ‘negative’ are not used in an evaluative sense here. Rather, they represent the presence (positive) or absence (negative) of stimuli to promote behaviour change. Punishments aim to inhibit behaviour and reinforcements aim to encourage it. This chapter describes a variety of punishments and reinforcements that have been and could be used to modify illegal road user behaviours. In doing so, it draws on several theoretical perspectives that have defined behavioural reinforcement and punishment in different ways. Historically, the main theoretical approach used to deter risky road use has been classical deterrence theory which has focussed on the perceived certainty, severity and swiftness of penalties. Stafford and Warr (1993) extended the traditional deterrence principles to include the positive reinforcement concept of punishment avoidance. Evidence of the association between punishment avoidance experiences and behaviour has been established for a number of risky road user behaviours including drink driving, unlicensed driving, and speeding. We chose a novel way of assessing punishment avoidance by specifying two sub-constructs (detection evasion and punishment evasion). Another theorist, Akers, described the idea of competing reinforcers, termed differential reinforcement, within social learning theory (1977). Differential reinforcement describes a balance of reinforcements and punishments as influential on behaviour. This chapter describes comprehensive way of conceptualising a broad range of reinforcement and punishment concepts, consistent with Akers’ differential reinforcement concept, within a behaviour modification framework that incorporates deterrence principles. The efficacy of three theoretical perspectives to explain self-reported speeding among a sample of 833 Australian car drivers was examined. Results demonstrated that a broad range of variables predicted speeding including personal experiences of evading detection and punishment for speeding, intrinsic sensations, practical benefits expected from speeding, and an absence of punishing effects from being caught. Not surprisingly, being younger was also significantly related to more frequent speeding, although in a regression analysis, gender did not retain a significant influence once all punishment and reinforcement variables were entered. The implications for speed management, as well as road user behaviour modification more generally, are discussed in light of these findings. Overall, the findings reported in this chapter suggest that a more comprehensive approach is required to manage the behaviour of road users which does not rely solely on traditional legal penalties and sanctions.

A RBF meshless approach for modeling a fractal mobile/immobile transport model

A fractional differential equation is used to describe a fractal model of mobile/immobile transport with a power law memory function. This equation is the limiting equation that governs continuous time random walks with heavy tailed random waiting times. In this paper, we firstly propose a finite difference method to discretize the time variable and obtain a semi-discrete scheme. Then we discuss its stability and convergence. Secondly we consider a meshless method based on radial basis functions (RBFs) to discretize the space variable. In contrast to conventional FDM and FEM, the meshless method is demonstrated to have distinct advantages: calculations can be performed independent of a mesh, it is more accurate and it can be used to solve complex problems. Finally the convergence order is verified from a numerical example which is presented to describe a fractal model of mobile/immobile transport process with different problem domains. The numerical results indicate that the present meshless approach is very effective for modeling and simulating fractional differential equations, and it has good potential in the development of a robust simulation tool for problems in engineering and science that are governed by various types of fractional differential equations.

The resistance of PRESENT-80 against related-key differential attacks

We examine the security of the 64-bit lightweight block cipher PRESENT-80 against related-key differential attacks. With a computer search we are able to prove that for any related-key differential characteristic on full-round PRESENT-80, the probability of the characteristic only in the 64-bit state is not higher than 2−64. To overcome the exponential (in the state and key sizes) computational complexity of the search we use truncated differences, however as the key schedule is not nibble oriented, we switch to actual differences and apply early abort techniques to prune the tree-based search. With a new method called extended split approach we are able to make the whole search feasible and we implement and run it in real time. Our approach targets the PRESENT-80 cipher however,with small modifications can be reused for other lightweight ciphers as well.

Examples illustrating the use of renormalization techniques for singularly perturbed differential equations

With nine examples, we seek to illustrate the utility of the Renormalization Group approach as a unification of other asymptotic and perturbation methods.

Reduction of amplitude equations by the renormalization group approach

This article elucidates and analyzes the fundamental underlying structure of the renormalization group (RG) approach as it applies to the solution of any differential equation involving multiple scales. The amplitude equation derived through the elimination of secular terms arising from a naive perturbation expansion of the solution to these equations by the RG approach is reduced to an algebraic equation which is expressed in terms of the Thiele semi-invariants or cumulants of the eliminant sequence { Zi } i=1 . Its use is illustrated through the solution of both linear and nonlinear perturbation problems and certain results from the literature are recovered as special cases. The fundamental structure that emerges from the application of the RG approach is not the amplitude equation but the aforementioned algebraic equation. © 2008 The American Physical Society.

Building macroscale models from microscale probabilistic models : a general probabilistic approach for nonlinear diffusion and multispecies phenomena

A discrete agent-based model on a periodic lattice of arbitrary dimension is considered. Agents move to nearest-neighbor sites by a motility mechanism accounting for general interactions, which may include volume exclusion. The partial differential equation describing the average occupancy of the agent population is derived systematically. A diffusion equation arises for all types of interactions and is nonlinear except for the simplest interactions. In addition, multiple species of interacting subpopulations give rise to an advection-diffusion equation for each subpopulation. This work extends and generalizes previous specific results, providing a construction method for determining the transport coefficients in terms of a single conditional transition probability, which depends on the occupancy of sites in an influence region. These coefficients characterize the diffusion of agents in a crowded environment in biological and physical processes.

Victoria's Child FIRST and IFS differential response system : progress and issues

Differential response has long been utilized by statutory child protection systems in Australia. This article describes the advent and history of Victoria's differential response system, with a particular focus on the Child FIRST and IFS programme. This program entails a partnership arrangement between the Department of Human Services child protection services and community-based, not-for-profit agencies to provide a diverse range of early intervention and prevention services. The findings of a recent external service system evaluation, a judicial inquiry, and the large-scale Child and Family Services Outcomes Survey of parents/carers perspectives of their service experiences are used to critically examine the effectiveness of this differential response approach. Service-user perspectives of the health and wellbeing of children and families are identified, as well as the recognized implementation issues posing significant challenges for the goal of an integrated partnership system. The need for ongoing reform agendas is highlighted along with the policy, program and structural tensions that exist in differential response systems, which are reliant upon partnerships and shared responsibilities for protecting children and assisting vulnerable families. Suggestions are made for utilizing robust research and evaluation that gives voice to service users and promotes their rights and interests.

An evaluation of potential candidate genes involved in salinity tolerance in striped catfish (Pangasianodon hypopthalmus) using an RNA-SEQ approach

The project investigated the molecular response of Tra catfish (Pangasianodon hypophthalmus) to elevated salinity conditions. We employed Next generation sequencing platform to evaluate differential gene expression profiles of key genes under two salinity conditions. Results of the current project can form the basis for further studies to confirm the functional roles of specific genes that influence salinity tolerance in the target species and more broadly in other freshwater teleost fishes. Ultimately, the approach can contribute to developing superior culture stocks of the target species.

Evaluation of a skin self examination attitude scale using an item response theory model approach

Introduction The Skin Self-Examination Attitude Scale (SSEAS) is a brief measure that allows for the assessment of attitudes in relation to skin self-examination. This study evaluated the psychometric properties of the SSEAS using Item Response Theory (IRT) methods in a large sample of men ≥ 50 years in Queensland, Australia. Methods A sample of 831 men (420 intervention and 411 control) completed a telephone assessment at the 13-month follow-up of a randomized-controlled trial of a video-based intervention to improve skin self-examination (SSE) behaviour. Descriptive statistics (mean, standard deviation, item–total correlations, and Cronbach’s alpha) were compiled and difficulty parameters were computed with Winsteps using the polytomous Rasch Rating Scale Model (RRSM). An item person (Wright) map of the SSEAS was examined for content coverage and item targeting. Results The SSEAS have good psychometric properties including good internal consistency (Cronbach’s alpha = 0.80), fit with the model and no evidence for differential item functioning (DIF) due to experimental trial grouping was detected. Conclusions The present study confirms the SSEA scale as a brief, useful and reliable tool for assessing attitudes towards skin self-examination in a population of men 50 years or older in Queensland, Australia. The 8-item scale shows unidimensionality, allowing levels of SSE attitude, and the item difficulties, to be ranked on a single continuous scale. In terms of clinical practice, it is very important to assess skin cancer self-examination attitude to identify people who may need a more extensive intervention to allow early detection of skin cancer.

A pseudo-dynamical systems approach to a class of inverse problems in engineering

A pseudo-dynamical approach for a class of inverse problems involving static measurements is proposed and explored. Following linearization of the minimizing functional associated with the underlying optimization problem, the new strategy results in a system of linearized ordinary differential equations (ODEs) whose steady-state solutions yield the desired reconstruction. We consider some explicit and implicit schemes for integrating the ODEs and thus establish a deterministic reconstruction strategy without an explicit use of regularization. A stochastic reconstruction strategy is then developed making use of an ensemble Kalman filter wherein these ODEs serve as the measurement model. Finally, we assess the numerical efficacy of the developed tools against a few linear and nonlinear inverse problems of engineering interest.

Quantum-Ohmic Resistance Fluctuation In Disordered Conductors - An Invariant Imbedding Approach

It is now well known that in extreme quantum limit, dominated by the elastic impurity scattering and the concomitant quantum interference, the zero-temperature d.c. resistance of a strictly one-dimensional disordered system is non-additive and non-self-averaging. While these statistical fluctuations may persist in the case of a physically thin wire, they are implicitly and questionably ignored in higher dimensions. In this work, we have re-examined this question. Following an invariant imbedding formulation, we first derive a stochastic differential equation for the complex amplitude reflection coefficient and hence obtain a Fokker-Planck equation for the full probability distribution of resistance for a one-dimensional continuum with a Gaussian white-noise random potential. We then employ the Migdal-Kadanoff type bond moving procedure and derive the d-dimensional generalization of the above probability distribution, or rather the associated cumulant function –‘the free energy’. For d=3, our analysis shows that the dispersion dominates the mobilitly edge phenomena in that (i) a one-parameter B-function depending on the mean conductance only does not exist, (ii) an approximate treatment gives a diffusion-correction involving the second cumulant. It is, however, not clear whether the fluctuations can render the transition at the mobility edge ‘first-order’. We also report some analytical results for the case of the one dimensional system in the presence of a finite electric fiekl. We find a cross-over from the exponential to the power-low length dependence of resistance as the field increases from zero. Also, the distribution of resistance saturates asymptotically to a poissonian form. Most of our analytical results are supported by the recent numerical simulation work reported by some authors.

Modelling the movement of interacting cell populations: A moment dynamics approach

Mathematical models describing the movement of multiple interacting subpopulations are relevant to many biological and ecological processes. Standard mean-field partial differential equation descriptions of these processes suffer from the limitation that they implicitly neglect to incorporate the impact of spatial correlations and clustering. To overcome this, we derive a moment dynamics description of a discrete stochastic process which describes the spreading of distinct interacting subpopulations. In particular, we motivate our model by mimicking the geometry of two typical cell biology experiments. Comparing the performance of the moment dynamics model with a traditional mean-field model confirms that the moment dynamics approach always outperforms the traditional mean-field approach. To provide more general insight we summarise the performance of the moment dynamics model and the traditional mean-field model over a wide range of parameter regimes. These results help distinguish between those situations where spatial correlation effects are sufficiently strong, such that a moment dynamics model is required, from other situations where spatial correlation effects are sufficiently weak, such that a traditional mean-field model is adequate.