Computationally efficient numerical methods for time- and space-fractional Fokker–Planck equations

Fractional Fokker–Planck equations have been used to model several physical situations that present anomalous diffusion. In this paper, a class of time- and space-fractional Fokker–Planck equations (TSFFPE), which involve the Riemann–Liouville time-fractional derivative of order 1-α (α(0, 1)) and the Riesz space-fractional derivative (RSFD) of order μ(1, 2), are considered. The solution of TSFFPE is important for describing the competition between subdiffusion and Lévy flights. However, effective numerical methods for solving TSFFPE are still in their infancy. We present three computationally efficient numerical methods to deal with the RSFD, and approximate the Riemann–Liouville time-fractional derivative using the Grünwald method. The TSFFPE is then transformed into a system of ordinary differential equations (ODE), which is solved by the fractional implicit trapezoidal method (FITM). Finally, numerical results are given to demonstrate the effectiveness of these methods. These techniques can also be applied to solve other types of fractional partial differential equations.

Coast control for mass rapid transit railways with searching methods

With daily commercial and social activity in cities, regulation of train service in mass rapid transit railways is necessary to maintain service and passenger flow. Dwell-time adjustment at stations is one commonly used approach to regulation of train service, but its control space is very limited. Coasting control is a viable means of meeting the specific run-time in an inter-station run. The current practice is to start coasting at a fixed distance from the departed station. Hence, it is only optimal with respect to a nominal operational condition of the train schedule, but not the current service demand. The advantage of coasting can only be fully secured when coasting points are determined in real-time. However, identifying the necessary starting point(s) for coasting under the constraints of current service conditions is no simple task as train movement is governed by a large number of factors. The feasibility and performance of classical and heuristic searching measures in locating coasting point(s) is studied with the aid of a single train simulator, according to specified inter-station run times.

Music, Mime & Metamorphosis: Interdisciplinary intersections, interactions and influences between music, mime and corporate communication

This doctoral thesis comprises three distinct yet related projects which investigate interdisciplinary practice across: music collaboration; mime performance; and corporate communication. Both the processes and underpinning research of these projects explore, expose and exploit areas where disparate and apparently conflicting fields of professional practice successfully and effectively; intersect, interact, and inform each other - rather than conflict - thereby enhancing each, both individually and collectively. Informed by three decades of professional practice across: music; stage performance; television; corporate communication; design; and tertiary education, the three projects have produced innovative, creative, and commercial viable outcomes, manifest in a variety of media including: music; written text; digital, audio/visual; and internet. In exploring new practice and creating new knowledge, these project outcomes clearly demonstrate the value and effectiveness of reconciling disparate fields of practice through the application of inter-disciplinary creativity and innovation to professional practice.

New criteria for evaluating methods of identifying hot spots

Identification of hot spots, also known as the sites with promise, black spots, accident-prone locations, or priority investigation locations, is an important and routine activity for improving the overall safety of roadway networks. Extensive literature focuses on methods for hot spot identification (HSID). A subset of this considerable literature is dedicated to conducting performance assessments of various HSID methods. A central issue in comparing HSID methods is the development and selection of quantitative and qualitative performance measures or criteria. The authors contend that currently employed HSID assessment criteria—namely false positives and false negatives—are necessary but not sufficient, and additional criteria are needed to exploit the ordinal nature of site ranking data. With the intent to equip road safety professionals and researchers with more useful tools to compare the performances of various HSID methods and to improve the level of HSID assessments, this paper proposes four quantitative HSID evaluation tests that are, to the authors’ knowledge, new and unique. These tests evaluate different aspects of HSID method performance, including reliability of results, ranking consistency, and false identification consistency and reliability. It is intended that road safety professionals apply these different evaluation tests in addition to existing tests to compare the performances of various HSID methods, and then select the most appropriate HSID method to screen road networks to identify sites that require further analysis. This work demonstrates four new criteria using 3 years of Arizona road section accident data and four commonly applied HSID methods [accident frequency ranking, accident rate ranking, accident reduction potential, and empirical Bayes (EB)]. The EB HSID method reveals itself as the superior method in most of the evaluation tests. In contrast, identifying hot spots using accident rate rankings performs the least well among the tests. The accident frequency and accident reduction potential methods perform similarly, with slight differences explained. The authors believe that the four new evaluation tests offer insight into HSID performance heretofore unavailable to analysts and researchers.

Statistical and Econometric Methods for Transportation Data Analysis, 2nd edition

Now in its second edition, this book describes tools that are commonly used in transportation data analysis. The first part of the text provides statistical fundamentals while the second part presents continuous dependent variable models. With a focus on count and discrete dependent variable models, the third part features new chapters on mixed logit models, logistic regression, and ordered probability models. The last section provides additional coverage of Bayesian statistical modeling, including Bayesian inference and Markov chain Monte Carlo methods. Data sets are available online to use with the modeling techniques discussed.

Experimental evaluation of hotspot identification methods

Identifying crash “hotspots”, “blackspots”, “sites with promise”, or “high risk” locations is standard practice in departments of transportation throughout the US. The literature is replete with the development and discussion of statistical methods for hotspot identification (HSID). Theoretical derivations and empirical studies have been used to weigh the benefits of various HSID methods; however, a small number of studies have used controlled experiments to systematically assess various methods. Using experimentally derived simulated data—which are argued to be superior to empirical data, three hot spot identification methods observed in practice are evaluated: simple ranking, confidence interval, and Empirical Bayes. Using simulated data, sites with promise are known a priori, in contrast to empirical data where high risk sites are not known for certain. To conduct the evaluation, properties of observed crash data are used to generate simulated crash frequency distributions at hypothetical sites. A variety of factors is manipulated to simulate a host of ‘real world’ conditions. Various levels of confidence are explored, and false positives (identifying a safe site as high risk) and false negatives (identifying a high risk site as safe) are compared across methods. Finally, the effects of crash history duration in the three HSID approaches are assessed. The results illustrate that the Empirical Bayes technique significantly outperforms ranking and confidence interval techniques (with certain caveats). As found by others, false positives and negatives are inversely related. Three years of crash history appears, in general, to provide an appropriate crash history duration.

Railway junction traffic control by heuristic methods

Traffic conflicts at railway junctions are very conmon, particularly on congested rail lines. While safe passage through the junction is well maintained by the signalling and interlocking systems, minimising the delays imposed on the trains by assigning the right-of-way sequence sensibly is a bonus to the quality of service. A deterministic method has been adopted to resolve the conflict, with the objective of minimising the total weighted delay. However, the computational demand remains significant. The applications of different heuristic methods to tackle this problem are reviewed and explored, elaborating their feasibility in various aspects and comparing their relative merits for further studies. As most heuristic methods do not guarantee a global optimum, this study focuses on the trade-off between computation time and optimality of the resolution.

Deliberative assessment of surrogate consent in dementia research

Background Research involving incapacitated persons with dementia entails complex scientific, legal, and ethical issues, making traditional surveys of layperson views on the ethics of such research challenging. We therefore assessed the impact of democratic deliberation (DD), involving balanced, detailed education and peer deliberation, on the views of those responsible for persons with dementia. Methods One hundred and seventy-eight community-recruited caregivers or primary decision-makers for persons with dementia were randomly assigned to either an all-day DD session group or a control group. Educational materials used for the DD session were vetted for balance and accuracy by an interdisciplinary advisory panel. We assessed the acceptability of family-surrogate consent for dementia research (“surrogate-based research”) from a societal policy perspective as well as from the more personal perspectives of deciding for a loved one or for oneself (surrogate and self-perspectives), assessed at baseline, immediately post-DD session, and 1 month after DD date, for four research scenarios of varying risk-benefit profiles. Results At baseline, a majority in both the DD and control groups supported a policy of family consent for dementia research in all research scenarios. The support for a policy of family consent for surrogate-based research increased in the DD group, but not in the control group. The change in the DD group was maintained 1 month later. In the DD group, there were transient changes in attitudes from surrogate or self-perspectives. In the control group, there were no changes from baseline in attitude toward surrogate consent from any perspective. Conclusions Intensive, balanced, and accurate education, along with peer deliberation provided by democratic deliberation, led to a sustained increase in support for a societal policy of family consent in dementia research among those responsible for dementia patients.

Wavelet based approaches and high resolution methods for complex process models

Many industrial processes and systems can be modelled mathematically by a set of Partial Differential Equations (PDEs). Finding a solution to such a PDF model is essential for system design, simulation, and process control purpose. However, major difficulties appear when solving PDEs with singularity. Traditional numerical methods, such as finite difference, finite element, and polynomial based orthogonal collocation, not only have limitations to fully capture the process dynamics but also demand enormous computation power due to the large number of elements or mesh points for accommodation of sharp variations. To tackle this challenging problem, wavelet based approaches and high resolution methods have been recently developed with successful applications to a fixedbed adsorption column model. Our investigation has shown that recent advances in wavelet based approaches and high resolution methods have the potential to be adopted for solving more complicated dynamic system models. This chapter will highlight the successful applications of these new methods in solving complex models of simulated-moving-bed (SMB) chromatographic processes. A SMB process is a distributed parameter system and can be mathematically described by a set of partial/ordinary differential equations and algebraic equations. These equations are highly coupled; experience wave propagations with steep front, and require significant numerical effort to solve. To demonstrate the numerical computing power of the wavelet based approaches and high resolution methods, a single column chromatographic process modelled by a Transport-Dispersive-Equilibrium linear model is investigated first. Numerical solutions from the upwind-1 finite difference, wavelet-collocation, and high resolution methods are evaluated by quantitative comparisons with the analytical solution for a range of Peclet numbers. After that, the advantages of the wavelet based approaches and high resolution methods are further demonstrated through applications to a dynamic SMB model for an enantiomers separation process. This research has revealed that for a PDE system with a low Peclet number, all existing numerical methods work well, but the upwind finite difference method consumes the most time for the same degree of accuracy of the numerical solution. The high resolution method provides an accurate numerical solution for a PDE system with a medium Peclet number. The wavelet collocation method is capable of catching up steep changes in the solution, and thus can be used for solving PDE models with high singularity. For the complex SMB system models under consideration, both the wavelet based approaches and high resolution methods are good candidates in terms of computation demand and prediction accuracy on the steep front. The high resolution methods have shown better stability in achieving steady state in the specific case studied in this Chapter.

Tracking employees’ twists and turns : a mixed methods approach to assessing change in the psychological contract

The psychological contract has emerged over the past 60 years as a key analytical device for both academics and practitioners to conceptualise and explain the employment relationship. However, despite the recognised import of this field, some authors suggest it has fallen into a ‘methodological rut’ and is neglecting to empirically assess basic theoretical tenets of the concept – such as the temporal and individualised, subjective nature of the construct. This paper describes the research design of a longitudinal, mixed methods study to explore development and change in the psychological contract and outline how the use of individual growth modelling can be a powerful tool in analysing the type of quantitative data collected. Finally, by briefly outlining the benefits of this approach, the paper seeks to offer an alternative methodology to explore the dynamic and intra-individual processes within the psychological contract domain.

Improving governance : practical methods and an analytic framework for the enhancement of democracy

Seven endemic governance problems are shown to be currently present in governments around the globe and at any level of government as well (for example municipal, federal). These problems have their roots traced back through more than two thousand years of political, specifically ‘democratic’, history. The evidence shows that accountability, transparency, corruption, representation, campaigning methods, constitutionalism and long-term goals were problematic for the ancient Athenians as well as modern international democratisation efforts encompassing every major global region. Why then, given the extended time period humans have had to deal with these problems, are they still present? At least part of the answer to this question is that philosophers, academics and NGOs as well as MNOs have only approached these endemic problems in a piecemeal manner with a skewed perspective on democracy. Their works have also been subject to the ebbs and flows of human history which essentially started and stopped periods of thinking. In order to approach the investigation of endemic problems in relation to democracy (as the overall quest of this thesis was to generate prescriptive results for the improvement of democratic government), it was necessary to delineate what exactly is being written about when using the term ‘democracy’. It is common knowledge that democracy has no one specific definition or practice, even though scholars and philosophers have been attempting to create a definition for generations. What is currently evident, is that scholars are not approaching democracy in an overly simplified manner (that is, it is government for the people, by the people) but, rather, are seeking the commonalities that democracies share, in other words, those items which are common to all things democratic. Following that specific line of investigation, the major practiced and theoretical versions of democracy were thematically analysed. After that, their themes were collapsed into larger categories, at which point the larger categories were comparatively analysed with the practiced and theoretical versions of democracy. Four democratic ‘particles’ (selecting officials, law, equality and communication) were seen to be present in all practiced and theoretical democratic styles. The democratic particles fused with a unique investigative perspective and in-depth political study created a solid conceptualisation of democracy. As such, it is argued that democracy is an ever-present element of any state government, ‘democratic’ or not, and the particles are the bodies which comprise the democratic element. Frequency- and proximity-based analyses showed that democratic particles are related to endemic problems in international democratisation discourse. The linkages between democratic particles and endemic problems were also evident during the thematic analysis as well historical review. This ultimately led to the viewpoint that if endemic problems are mitigated the act may improve democratic particles which might strengthen the element of democracy in the governing apparatus of any state. Such may actively minimise or wholly displace inefficient forms of government, leading to a government specifically tailored to the population it orders. Once the theoretical and empirical goals were attained, this thesis provided some prescriptive measures which government, civil society, academics, professionals and/or active citizens can use to mitigate endemic problems (in any country and at any level of government) so as to improve the human condition via better democratic government.