Modelling road traffic accidents using macroscopic second-order models of traffic flow

In this paper, we introduce a macroscopic model for road traffic accidents along highway sections. We discuss the motivation and the derivation of such a model, and we present its mathematical properties. The results are presented by means of examples where a section of a crowded one-way highway contains in the middle a cluster of drivers whose dynamics are prone to road traffic accidents. We discuss the coupling conditions and present some existence results of weak solutions to the associated Riemann Problems. Furthermore, we illustrate some features of the proposed model through some numerical simulations. © The authors 2012.

Investigating the efficiency of fitting Coxian phase-type distributions to health care data

Coxian phase-type distributions are becoming a popular means of representing survival times within a health care environment. They are favoured as they show a distribution as a system of phases and can allow for an easy visual representation of the rate of flow of patients through a system. Difficulties arise, however, in determining the parameter estimates of the Coxian phase-type distribution. This paper examines ways of making the fitting of the Coxian phase-type distribution less cumbersome by outlining different software packages and algorithms available to perform the fit and assessing their capabilities through a number of performance measures. The performance measures rate each of the methods and help in identifying the more efficient. Conclusions drawn from these performance measures suggest SAS to be the most robust package. It has a high rate of convergence in each of the four example model fits considered, short computational times, detailed output, convergence criteria options, along with a succinct ability to switch between different algorithms.

Cosmological Constraints from Measurements of Type Ia Supernovae Discovered During the First 1.5 Yr of the Pan-STARRS1 Survey

We present griz_P1 light curves of 146 spectroscopically confirmed Type Ia supernovae (SNe Ia; 0.03 < z < 0.65) discovered during the first 1.5 yr of the Pan-STARRS1 Medium Deep Survey. The Pan-STARRS1 natural photometric system is determined by a combination of on-site measurements of the instrument response function and observations of spectrophotometric standard stars. We find that the systematic uncertainties in the photometric system are currently 1.2% without accounting for the uncertainty in the Hubble Space Telescope Calspec definition of the AB system. A Hubble diagram is constructed with a subset of 113 out of 146 SNe Ia that pass our light curve quality cuts. The cosmological fit to 310 SNe Ia (113 PS1 SNe Ia + 222 light curves from 197 low-z SNe Ia), using only supernovae (SNe) and assuming a constant dark energy equation of state and flatness, yields w = -1.120^+0.360_-0.206(Stat)^+0.269_0.291(Sys). When combined with BAO+CMB(Planck)+H₀, the analysis yields Ω_M = 0.280^+0.013_0.012 and w = -1.166^+0.072_-0.069 including all identified systematics. The value of w is inconsistent with the cosmological constant value of -1 at the 2.3σ level. Tension endures after removing either the baryon acoustic oscillation (BAO) or the H₀ constraint, though it is strongest when including the H₀ constraint. If we include WMAP9 cosmic microwave background (CMB) constraints instead of those from Planck, we find w = -1.124^+0.083_-0.065, which diminishes the discord to <2σ. We cannot conclude whether the tension with flat ΛCDM is a feature of dark energy, new physics, or a combination of chance and systematic errors. The full Pan-STARRS1 SN sample with ∼three times as many SNe should provide more conclusive results.

A Pilot Study of Reciprocal Peer Tutoring in Irish Medium Schools

A pilot study to investigate the effects of mathematics peer tutoring in Irish medium primary schools was undertaken. Five schools and 90 students took part in the pilot. Materials and resources that had previously been shown to work in English medium Scottish schools were translated into Irish by CCEA. Irish medium teachers attended three professional development days. Teachers implemented the peer tutoring techniques during mathematics lessons during a period of 16 weeks. Changes in attainment were measures with an Irish translation of the Scottish Survey of Achievement Mathematics Test. Results were positive. Student attainment was significantly raised during the 16-week implementation period by over one standard deviation. This equated to one-year’s worth of mathematics development during this time period. Results must be treated with caution. No control group was used in the pilot study. However, results are very promising and indicate that reciprocal role peer tutoring may be a useful pedagogy in Irish medium education. Further work would be required to establish this definitively.

Mathematics Learning Support in Ireland in 2015

The provision of mathematics learning support in higher-level institutions on the island of Ireland has developed rapidly in recent times with the number of institutions providing some form of support doubling in the past seven years. The Irish Mathematics Learning Support Network aims to inform all mathematics support practitioners in Ireland on relevant issues. Consequently it was decided that a detailed picture of current provision was necessary. A comprehensive online survey was conducted to amass the necessary data. The ultimate aim of the survey is to benefit all mathematics support practitioners in Ireland, in particular those in third-level institutions who require further support to enhance the mathematical learning experience of their students. The survey reveals that the majority of Irish higher-level institutions provide mathematics learning support to some extent, with 65% doing so through a support centre. Learners of service mathematics are the primary users: first-year science, engineering and business undergraduates, with non-traditional students being a sizeable element. Despite the growing recognition for the need to offer mathematics learning support almost half of the centres are subject to annual review. Further, less than half the support offerings have a dedicated full-time manager, while 60% operate with a staff of five or fewer. The elevation of mathematics support as a viable and worthwhile career in order to attract and retain high quality staff is seen by many respondents as the crucial next phase of development.

Curriculum and beyond: Mathematics support for first year life science students

The move into higher education is a real challenge for students from all educational backgrounds, with the adaptation to a new curriculum and style of learning and teaching posing a daunting task. A series of exercises were planned to boost the impact of the mathematics support for level four students and was focussed around a core module for all students. The intention was to develop greater confidence in tackling mathematical problems in all levels of ability and to provide more structured transition period in the first semester of level 4. Over a two-year period the teaching team for Biochemistry and Molecular Biology provided a series of structured formative tutorials and “interactive” online problems. Video solutions to all formative problems were made available, in order that students were able to engage with the problems at any time and were not disadvantaged if they could not attend. The formative problems were specifically set to dovetail into a practical report in which the mathematical skills developed were specifically assessed. Students overwhelmingly agreed that the structured formative activities had broadened their understanding of the subject and that more such activities would help. Furthermore, it is interesting to note that the package of changes undertaken resulted in a significant increase in the overall module mark over the two years of development.

Self-adaptive combination of global tabu search and local search for nonlinear equations

Solving systems of nonlinear equations is a very important task since the problems emerge mostly through the mathematical modelling of real problems that arise naturally in many branches of engineering and in the physical sciences. The problem can be naturally reformulated as a global optimization problem. In this paper, we show that a self-adaptive combination of a metaheuristic with a classical local search method is able to converge to some difficult problems that are not solved by Newton-type methods.

Nietzsche's eternal recurrence of the same : the effect of logic abridgement, contradictions and inconsistencies

I will argue that the doctrine of eternal recurrence of the same no better interprets cosmology than pink elephants interpret zoology. I will also argue that the eternal-reiurn-of-the-same doctrine as what Magnus calls "existential imperative" is without possibility of application and thus futile. To facilitate those arguments, the validity of the doctrine of the eternal recurrence of the same will be tested under distinct rubrics. Although each rubric will stand alone, one per chapter, as an evaluation of some specific aspect of eternal recurrence, the rubric sequence has been selected to accommodate the identification of what I shall be calling logic abridgments. The conclusions to be extracted from each rubric are grouped under the heading CONCLUSION and appear immediately following rubric ten. Then, or if, at the end of a rubric a reader is inclined to wonder which rubric or topic is next, and why, the answer can be found at the top of the following page. The question is usually answered in the very first sentence, but always answered in the first paragraph. The first rubric has been placed in order by chronological entitlement in that it deals with the evolution of the idea of eternal recurrence from the time of the ancient Greeks to Nietzsche's August, 1881 inspiration. This much-recommended technique is also known as starting at the beginning. Rubric 1 also deals with 20th. Century philosophers' assessments of the relationship between Nietzsche and ancient Greek thought. The only experience of E-R, Zarathustra's mountain vision, is second only because it sets the scene alluded to in following rubrics. The third rubric explores .ii?.ih T jc,i -I'w Nietzsche's evaluation of rationality so that his thought processes will be understood appropriately. The actual mechanism of E-R is tested in rubric four...The scientific proof Nietzsche assembled in support of E-R is assessed by contemporary philosophers in rubric five. E-R's function as an ethical imperative is debated in rubrics six and seven.. .The extent to which E-R fulfills its purpose in overcoming nihilism is measured against the comfort assured by major world religions in rubric eight. Whether E-R also serves as a redemption for revenge is questioned in rubric nine. Rubric ten assures that E-R refers to return of the identically same and not merely the similar. In addition to assemblage and evaluation of all ten rubrics, at the end of each rubric a brief recapitulation of its principal points concludes the chapter. In this essay I will assess the theoretical conditions under which the doctrine cannot be applicable and will show what contradictions and inconsistencies follow if the doctrine is taken to be operable. Harold Alderman in his book Nietzsche's Gift wrote, the "doctrine of eternal recurrence gives us a problem not in Platonic cosmology, but in Socratic selfreflection." ^ I will illustrate that the recurrence doctrine's cosmogony is unworkable and that if it were workable, it would negate self-reflection on the grounds that selfreflection cannot find its cause in eternal recurrence of the same. Thus, when the cosmology is shown to be impossible, any expected ensuing results or benefits will be rendered also impossible. The so-called "heaviest burden" will be exposed as complex, engrossing "what if speculations deserving no linkings to reality. To identify ^Alderman p. 84 abridgments of logic, contradictions and inconsistencies in Nietzsche's doctrine of eternal recurrence of the same, I. will examine the subject under the following schedule. In Chapter 1 the ancient origins of recurrence theories will be introduced. ..This chapter is intended to establish the boundaries within which the subsequent chapters, except Chapter 10, will be confined. Chapter 2, Zarathustra's vision of E-R, assesses the sections of Thus Spoke Zarathustra in which the phenomenon of recurrence of the same is reported. ..Nihilism as a psychological difficulty is introduced in this rubric, but that subject will be studied in detail in Chapter 8. In Chapter 2 the symbols of eternal recurrence of the same will be considered. Whether the recurrence image should be of a closed ring or as a coil will be of significance in many sections of my essay. I will argue that neither symbolic configuration can accommodate Nietzsche's supposed intention. Chapter 3 defends the description of E-R given by Zarathustra. Chapter 4, the cosmological mechanics of E-R, speculates on the seriousness with which Nietzsche might have intended the doctrine of eternal recurrence to be taken. My essay reports, and then assesses, the argument of those who suppose the doctrine to have been merely exploratory musings by Nietzsche on cosmological hypotheses...The cosmogony of E-R is examined. In Chapter 5, cosmological proofs tested, the proofs for Nietzsche's doctrine of return of the same are evaluated. This chapter features the position taken by Martin ' Heidegger. My essay suggests that while Heidegger's argument that recurrence of the same is a genuine cosmic agenda is admirable, it is not at all persuasive. Chapter 6, E-R is an ethical imperative, is in essence the reporting of a debate between two scholars regarding the possibility of an imperative in the doctrine of recurrence. Their debate polarizes the arguments I intend to develop. Chapter 7, does E-R of the same preclude alteration of attitudes, is a continuation of the debate presented in Chapter 6 with the focus shifted to the psychological from the cosmological aspects of eternal recurrence of the same. Chapter 8, Can E-R Overcome Nihilism?, is divided into two parts. In the first, nihilism as it applies to Nietzsche's theory is discussed. ..In part 2, the broader consequences, sources and definitions of nihilism are outlined. My essay argues that Nietzsche's doctrine is more nihilistic than are the world's major religions. Chapter 9, Is E-R a redemption for revenge?, examines the suggestion extracted from Thus Spoke Zarathustra that the doctrine of eternal recurrence is intended, among other purposes, as a redemption for mankind from the destructiveness of revenge. Chapter 10, E-R of the similar refuted, analyses a position that an element of chance can influence the doctrine of recurrence. This view appears to allow, not for recurrence of the same, but recurrence of the similar. A summary will recount briefly the various significant logic abridgments, contradictions, and inconsistencies associated with Nietzsche's doctrine of eternal recurrence of the same. In the 'conclusion' section of my essay my own opinions and observations will be assembled from the body of the essay.

Education, sport and myth in the community of Glengarry, Ontario : the athletic career of Roderick R. McLennan. 260 St. Catharines, Ont. : Faculty of Education, Brock University ;

This study examined how the athletic career of Roderick R. McLennan contributed to the popularization and subsequent development of Caledonian games in Ontario during the latter nineteenth century. Initially, the development of Caledonian games during the 1800s was examined to provide a contextual framework for McLennan's career. This investigation revealed that the games emerged from rural athletic events at pioneer working bees in the first quarter of the nineteenth century to regional sporting events by the mid-1800s, and finally into annual federated Caledonian games in 1870. Noteworthy primary source material for this chapter included the John MacGillivray Papers at the National Archives of Canada, the Scottish American Journal (NY) and the files retained by the Glengarry Sport Hall of Fame in Maxville, Ontario. Following the investigation of Caledonian games, McLennan's early athletic career was studied. Analysis of the Roderick and Farquhar McLennan Papers at the Archives of Ontario and the newspapers from the period revealed that McLennan rose to popularity in 1865 through a "Championship of the World" hammer throwing match in Cornwall and two "Starring Tours". The next chapter examined the height of McLennan's career through an investigation of the Roderick McLennan versus Donald Dinnie rivalry of the early .. n 1870s. It was detennined that the rivalry between McLennan and Dinnie, the champion athlete of Highland games in Scotland, was a popular attraction and had an impact on the Toronto and Montreal games of 1870 and the Toronto games of 1872. Finally, the athletic records established by McLennan during the 1860s and 1870s were investigated. These records were examined through the context of a media controversy over McLennan's feats that developed in the early 1880s between two newspapers. This controversy erupted between the Toronto Mail and the Spirit of the Times. Caledonian games in Canada have only been briefly examined and a thorough examination of prominent Canadian figures in this context has yet to be undertaken. This study unearths a prominent Canadian athlete of Scottish decent and details his involvement in the Caledonian games of nineteenth century Ontario.

The effects of computer assisted interactive fiction on the development of reading comprehension in grade five students

This study was undertaken in order to determine the effects of playing computer based text adventure games on the reading comprehension gains of students. Forty-five grade five students from one elementary school were randomly assigned to experimental and control groups, and were tested with regard to ability, achievement and reading skills. An experimental treatment, consisting of playing computer based interactive fiction games of the student's choice for fifteen minutes each day over an eight-week period, was administered. A comparison treatment engaged the control group in sustained silent reading of materials of the student's choice for an equal period of time. Following the experimental period all students were post-tested with an alternate form of the pre-test in reading skills, and gain scores were analysed. It was found that there were no significant differences in the gain scores of the experimental and control groups for overall reading comprehenSion, but the experimental group showed greater gains than the control group in the structural analysis reading sub-skill. Extreme variance in the data made generalization very difficult, but the findings indicated a potential for computer based interactive fiction as a useful tool for developing reading sl

On the design of customized risk measures in insurance, the problem of capital allocation and the theory of fluctuations for Lévy processes

Dans cette thèse, nous étudions quelques problèmes fondamentaux en mathématiques financières et actuarielles, ainsi que leurs applications. Cette thèse est constituée de trois contributions portant principalement sur la théorie de la mesure de risques, le problème de l’allocation du capital et la théorie des fluctuations. Dans le chapitre 2, nous construisons de nouvelles mesures de risque cohérentes et étudions l’allocation de capital dans le cadre de la théorie des risques collectifs. Pour ce faire, nous introduisons la famille des "mesures de risque entropique cumulatifs" (Cumulative Entropic Risk Measures). Le chapitre 3 étudie le problème du portefeuille optimal pour le Entropic Value at Risk dans le cas où les rendements sont modélisés par un processus de diffusion à sauts (Jump-Diffusion). Dans le chapitre 4, nous généralisons la notion de "statistiques naturelles de risque" (natural risk statistics) au cadre multivarié. Cette extension non-triviale produit des mesures de risque multivariées construites à partir des données financiéres et de données d’assurance. Le chapitre 5 introduit les concepts de "drawdown" et de la "vitesse d’épuisement" (speed of depletion) dans la théorie de la ruine. Nous étudions ces concepts pour des modeles de risque décrits par une famille de processus de Lévy spectrallement négatifs.

WAIS seminar:Mathematics for Web Science Part3-1

ABSTRACT In the first two seminars we looked at the evolution of Ontologies from the current OWL level towards more powerful/expressive models and the corresponding hierarchy of Logics that underpin every stage of this evolution. We examined this in the more general context of the general evolution of the Web as a mathematical (directed and weighed) graph and the archetypical “living network” In the third seminar we will analyze further some of the startling properties that the Web has as a graph/network and which it shares with an array of “real-life” networks as well as some key elements of the mathematics (probability, statistics and graph theory) that underpin all this. No mathematical prerequisites are assumed or required. We will outline some directions that current (2005-now) research is taking and conclude with some illustrations/examples from ongoing research and applications that show great promise.