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.

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.

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.

The ghrelin receptor isoforms (GHS-R1a and GHS-R1b) and GPR39 : an investigation into receptor dimerisation

Prostate cancer is the second most common cause of cancer-related deaths in Western males. Current diagnostic, prognostic and treatment approaches are not ideal and advanced metastatic prostate cancer is incurable. There is an urgent need for improved adjunctive therapies and markers for this disease. GPCRs are likely to play a significant role in the initiation and progression of prostate cancer. Over the last decade, it has emerged that G protein coupled receptors (GPCRs) are likely to function as homodimers and heterodimers. Heterodimerisation between GPCRs can result in the formation of novel pharmacological receptors with altered functional outcomes, and a number of GPCR heterodimers have been implicated in the pathogenesis of human disease. Importantly, novel GPCR heterodimers represent potential new targets for the development of more specific therapeutic drugs. Ghrelin is a 28 amino acid peptide hormone which has a unique n-octanoic acid post-translational modification. Ghrelin has a number of important physiological roles, including roles in appetite regulation and the stimulation of growth hormone release. The ghrelin receptor is the growth hormone secretagogue receptor type 1a, GHS-R1a, a seven transmembrane domain GPCR, and GHS-R1b is a C-terminally truncated isoform of the ghrelin receptor, consisting of five transmembrane domains. Growing evidence suggests that ghrelin and the ghrelin receptor isoforms, GHS-R1a and GHS-R1b, may have a role in the progression of a number of cancers, including prostate cancer. Previous studies by our research group have shown that the truncated ghrelin receptor isoform, GHS-R1b, is not expressed in normal prostate, however, it is expressed in prostate cancer. The altered expression of this truncated isoform may reflect a difference between a normal and cancerous state. A number of mutant GPCRs have been shown to regulate the function of their corresponding wild-type receptors. Therefore, we investigated the potential role of interactions between GHS-R1a and GHS-R1b, which are co-expressed in prostate cancer and aimed to investigate the function of this potentially new pharmacological receptor. In 2005, obestatin, a 23 amino acid C-terminally amidated peptide derived from preproghrelin was identified and was described as opposing the stimulating effects of ghrelin on appetite and food intake. GPR39, an orphan GPCR which is closely related to the ghrelin receptor, was identified as the endogenous receptor for obestatin. Recently, however, the ability of obestatin to oppose the effects of ghrelin on appetite and food intake has been questioned, and furthermore, it appears that GPR39 may in fact not be the obestatin receptor. The role of GPR39 in the prostate is of interest, however, as it is a zinc receptor. Zinc has a unique role in the biology of the prostate, where it is normally accumulated at high levels, and zinc accumulation is altered in the development of prostate malignancy. Ghrelin and zinc have important roles in prostate cancer and dimerisation of their receptors may have novel roles in malignant prostate cells. The aim of the current study, therefore, was to demonstrate the formation of GHS-R1a/GHS-R1b and GHS-R1a/GPR39 heterodimers and to investigate potential functions of these heterodimers in prostate cancer cell lines. To demonstrate dimerisation we first employed a classical co-immunoprecipitation technique. Using cells co-overexpressing FLAG- and Myc- tagged GHS-R1a, GHS-R1b and GPR39, we were able to co-immunoprecipitate these receptors. Significantly, however, the receptors formed high molecular weight aggregates. A number of questions have been raised over the propensity of GPCRs to aggregate during co-immunoprecipitation as a result of their hydrophobic nature and this may be misinterpreted as receptor dimerisation. As we observed significant receptor aggregation in this study, we used additional methods to confirm the specificity of these putative GPCR interactions. We used two different resonance energy transfer (RET) methods; bioluminescence resonance energy transfer (BRET) and fluorescence resonance energy transfer (FRET), to investigate interactions between the ghrelin receptor isoforms and GPR39. RET is the transfer of energy from a donor fluorophore to an acceptor fluorophore when they are in close proximity, and RET methods are, therefore, applicable to the observation of specific protein-protein interactions. Extensive studies using the second generation bioluminescence resonance energy transfer (BRET2) technology were performed, however, a number of technical limitations were observed. The substrate used during BRET2 studies, coelenterazine 400a, has a low quantum yield and rapid signal decay. This study highlighted the requirement for the expression of donor and acceptor tagged receptors at high levels so that a BRET ratio can be determined. After performing a number of BRET2 experimental controls, our BRET2 data did not fit the predicted results for a specific interaction between these receptors. The interactions that we observed may in fact represent ‘bystander BRET’ resulting from high levels of expression, forcing the donor and acceptor into close proximity. Our FRET studies employed two different FRET techniques, acceptor photobleaching FRET and sensitised emission FRET measured by flow cytometry. We were unable to observe any significant FRET, or FRET values that were likely to result from specific receptor dimerisation between GHS-R1a, GHS-R1b and GPR39. While we were unable to conclusively demonstrate direct dimerisation between GHS-R1a, GHS-R1b and GPR39 using several methods, our findings do not exclude the possibility that these receptors interact. We aimed to investigate if co-expression of combinations of these receptors had functional effects in prostate cancers cells. It has previously been demonstrated that ghrelin stimulates cell proliferation in prostate cancer cell lines, through ERK1/2 activation, and GPR39 can stimulate ERK1/2 signalling in response to zinc treatments. Additionally, both GHS-R1a and GPR39 display a high level of constitutive signalling and these constitutively active receptors can attenuate apoptosis when overexpressed individually in some cell types. We, therefore, investigated ERK1/2 and AKT signalling and cell survival in prostate cancer the potential modulation of these functions by dimerisation between GHS-R1a, GHS-R1b and GPR39. Expression of these receptors in the PC-3 prostate cancer cell line, either alone or in combination, did not alter constitutive ERK1/2 or AKT signalling, basal apoptosis or tunicamycin-stimulated apoptosis, compared to controls. In summary, the potential interactions between the ghrelin receptor isoforms, GHS-R1a and GHS-R1b, and the related zinc receptor, GPR39, and the potential for functional outcomes in prostate cancer were investigated using a number of independent methods. We did not definitively demonstrate the formation of these dimers using a number of state of the art methods to directly demonstrate receptor-receptor interactions. We investigated a number of potential functions of GPR39 and GHS-R1a in the prostate and did not observe altered function in response to co-expression of these receptors. The technical questions raised by this study highlight the requirement for the application of extensive controls when using current methods for the demonstration of GPCR dimerisation. Similar findings in this field reflect the current controversy surrounding the investigation of GPCR dimerisation. Although GHS-R1a/GHS-R1b or GHS-R1a/GPR39 heterodimerisation was not clearly demonstrated, this study provides a basis for future investigations of these receptors in prostate cancer. Additionally, the results presented in this study and growing evidence in the literature highlight the requirement for an extensive understanding of the experimental method and the performance of a range of controls to avoid the spurious interpretation of data gained from artificial expression systems. The future development of more robust techniques for investigating GPCR dimerisation is clearly required and will enable us to elucidate whether GHS-R1a, GHS-R1b and GPR39 form physiologically relevant dimers.