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The effect of electrostatic microturbulence on fast particles rapidly decreases at high energy, but can be significant at moderate energy. Previous studies found that, in addition to changes in the energetic particle density, this results in non-trivial changes to the equilibrium velocity distribution. These effects have implications for plasma heating and the stability of Alfvén eigenmodes, but make multiscale simulations much more difficult without further approximations. Here, several related analytic model distribution functions are derived from first principles. A single dimensionless parameter characterizes the relative strength of turbulence relative to collisions, and this parameter appears as an exponent in the model distribution functions. Even the most simple of these models reproduces key features of the numerical phase-space transport solution and provides a useful a priori heuristic for determining how strong the effect of turbulence is on the redistribution of energetic particles in toroidal plasmas.
In July 2013 an LMS-EPSRC Short Instructional Course on ‘O-minimality and diophantine geometry’ was held in the School of Mathematics at the University of Manchester. This volume consists of lecture notes from the courses together with several other surveys. The motivation behind the short course was to introduce participants to some of the ideas behind Pila's recent proof of the André-Oort conjecture for products of modular curves. The underlying ideas are similar to an earlier proof by Pila and Zannier of the Manin-Mumford conjecture (which has in fact long been a theorem, originally due to Raynaud) and combining the results of the various contributions here leads to a proof of this conjecture in certain cases. The basic strategy has three main ingredients: the Pila-Wilkie theorem, bounds on Galois orbits, and functional transcendence results. Each of the topics was the focus of a course. Wilkie discussed o-minimality and the Pila-Wilkie theorem without assuming any background in mathematical logic. (The argument given here is, in fact, slightly different from that given in the original paper, at least in the one-dimensional case.) Habegger's course focused on the Galois bounds and on the completion of the proof (of certain cases of Manin-Mumford) from the various ingredients. And Pila's lectures covered functional transcendence, also touching on various recent related work by Zilber.We have also included some further lecture notes by Wilkie containing a proof of the o-minimality of the expansion of the real field by restricted analytic functions, which is sufficient for the application of Pila-Wilkie to Manin-Mumford. At the short course there were also three guest lectures. Yafaev spoke on very recent breakthroughs on the functional transcendence side in the setting of general Shimura varieties. Masser spoke on some other results (‘relative Manin-Mumford’) that can be obtained by a similar strategy. Jones discussed improvements to the Pila-Wilkie theorem. Unfortunately, Yafaev was unable to contribute to this volume. During the week of the course, tutorials were given by Daw and Orr. For this volume, Orr has written a survey of abelian varieties which contains a proof of the functional transcendence result necessary for the application in Habegger's course.
Most of the papers in this volume depend on what has become known as the o-minimal point counting theorem. The aim of this article is to provide enough background in both model theory and number theory for a graduate student in one, but not necessarily both, of these disciplines to be able to understand the statement and the proof of the theorem.
The one dimensional case of the theorem is treated here in full and differs from the original paper ([PW]) in both its number theoretic side (I use the Thue-Siegel Lemma rather than the Bombieri-Pila determinant method) and in its model theoretic side (where the reparametrization of definable functions is made very explicit). The Thue-Siegel method extends easily to the higher dimensional case but, just as in [PW], one has to revert to Yomdin's original inductive argument to extend the reparametrization, and this is only sketched here.
I am extremely grateful to Adam Gutter for typing up my handwritten notes of the Manchester LMS course on which this paper is based. Also, my deepest thanks to Margaret Thomas for so carefully reading the original manuscript. Her numerous suggestions have greatly improved the presentation.
So, the aim of these notes is to prove the following:
1.1 Theorem (Pila-Wilkie [PW])
Let S ⊆ Rn be a set definable in some o-minimal expansion of the ordered field of real numbers. Assume that S contains no infinite, semi-algebraic subset. Let ∊ > 0 be given. Then for all sufficiently large H, the set S contains at most H∊ rational points of height at most H.
This collection of articles, originating from a short course held at the University of Manchester, explores the ideas behind Pila's proof of the Andre–Oort conjecture for products of modular curves. The basic strategy has three main ingredients: the Pila–Wilkie theorem, bounds on Galois orbits, and functional transcendence results. All of these topics are covered in this volume, making it ideal for researchers wishing to keep up to date with the latest developments in the field. Original papers are combined with background articles in both the number theoretic and model theoretic aspects of the subject. These include Martin Orr's survey of abelian varieties, Christopher Daw's introduction to Shimura varieties, and Jacob Tsimerman's proof via o-minimality of Ax's theorem on the functional case of Schanuel's conjecture.
Electronic health records (EHRs) may contain infomarkers that identify patients near the end of life for whom it would be appropriate to shift care goals to palliative care. Discovery and use of such infomarkers could be used to conduct effectiveness research that ultimately could help to reduce the monumental cost of caring for the dying. The aim of our study was to identify changes in the plans of care that represent infomarkers, which signal a transition of care goals from nonpalliative care ones to those consistent with palliative care.
Using an existing electronic health record database generated during a two-year longitudinal study of nine diverse medical–surgical units from four Midwest hospitals and a known group approach, we evaluated patient care episodes for 901 patients who died (mean age = 74.5 ± 14.6 years). We used ANOVA and Tukey's post-hoc tests to compare patient groups.
We identified 11 diagnoses, including Death Anxiety and Anticipatory Grieving, whose addition to the care plan, some of which also occurred with removal of nonpalliative care diagnoses, represent infomarkers of transition to palliative care goals. There were four categories of patients, those who had: no infomarkers on plans (n = 507), infomarkers added on the admission plan (n = 194), infomarkers added on a post-admission plan (minor transitions, n = 109), and infomarkers added and nonpalliative care diagnoses removed on a post-admission plan (major transition, n = 91). Age, length of stay, and pain outcomes differed significantly for these four categories of patients.
Significance of Results:
EHRs contain pertinent infomarkers that if confirmed in future studies could be used for timely referral to palliative care for improved focus on comfort outcomes and to identify palliative care subjects from data repositories in order to conduct big-data research, comparative effectiveness studies, and health-services research.
To rigorously model fast ions in fusion plasmas, a non-Maxwellian equilibrium distribution must be used. In this work, the response of high-energy alpha particles to electrostatic turbulence has been analyzed for several different tokamak parameters. Our results are consistent with known scalings and experimental evidence that alpha particles are generally well confined: on the order of several seconds. It is also confirmed that the effect of alphas on the turbulence is negligible at realistically low concentrations, consistent with linear theory. It is demonstrated that the usual practice of using a high-temperature Maxwellian, while previously shown to give an adequate order-of-magnitude estimate of the diffusion coefficient, gives incorrect estimates for the radial alpha particle flux, and a method of correcting it in general is provided. Furthermore, we see that the timescales associated with collisions and transport compete at moderate energies, calling into question the assumption that alpha particles remain confined to a flux surface that is used in the derivation of the slowing-down distribution.
In the course of work undertaken as members of the Executive Committee of the Continuous Mortality Investigation Bureau in the preparation of graduated tables of mortality for the experiences of 1979–82, we have had occasion to make use of and develop a number of statistical techniques with which actuaries may not be familiar, and which are not fully discussed in the current textbook by Benjamin & Pollard (1980), though some of them have been referred to in previous papers by the CMI Committee (1974, 1976). We therefore felt that it would be useful to the profession if we were to present these methods comprehensively in one paper. We do this with the permission of the other members of the CMI Committee, who do not, however, take responsibility for what follows, whether good or bad.
The following notes are intended as an introduction to the Faculty discussion on actuarial education. They are presented by the authors separately and personally, but solely as introductory notes, rather than as actuarial papers which might represent their considered judgement about the nature and purpose of what actuarial education should be. Instead it is hoped that they will stimulate a wide-ranging discussion about all aspects of actuarial education, particularly of course in the context of what the Faculty does or might do in this respect.
Increasing numbers of young people experience disruption to their schooling owing to chronic illness. Absence from the day-to-day life of their school for prolonged or accumulative periods of time can erode their sense of belonging and create anxiety about falling behind academically. Maintaining positive connections to school can meet their desire for normalcy and realisable educational goals. Part of a project called Link ‘n’ Learn, funded by an Australian Research Council Linkage grant (2008–2010), this in-depth qualitative case study of 22 participants — senior secondary students and their mathematics teachers — investigated academic continuity: students’ access to and utilisation of opportunities to learn effectively so that academic progress is made despite disruption to full-time schooling. The students experienced diverse types of chronic illness, medical interventions, and patterns of absence from school. They all sought to continue their school studies. Their teachers highlighted surprise, concern and discomfort related to students studying during serious illness, and school workload issues. Ambiguities about educational responsibility for students during absence were widespread. Teachers demonstrated hesitance to initiate contact with students, but students nevertheless expressed their desire for teachers to remain involved with them. Implications for the educational support of young people with chronic illness are presented.
The term “nanocomposite” is widely used to describe a very broad range of materials, where one of the phases has a submicrometer dimension . In the case of polymer-based nanocomposites, this typically involves the incorporation of “nano” fillers with one (platelets), two (fibers, tubes), or all three dimensions at the submicrometer scale. However, strictly speaking, simply using nanometer-scaled fillers is not sufficient for obtaining genuine/true nanocomposites: these fillers must also be well dispersed down to individual particles and give rise to intrinsically new properties, which are not present in the respective macroscopic composites or the pure components. In this chapter, we shall use a broader definition, encompassing also “nanofilled polymer composites”, where – even without complete dispersion or in the absence of any new/novel functionalities – there exist substantial concurrent enhancements of multiple properties (for example, mechanical, thermal, thermomechanical, barrier, and flammability). Further, we shall limit our discussion to one example, focusing on poly(ethylene terephthalate) (PET) with mica-type layered aluminosilicates.
In this paper we review the Wilkie asset model for a variety of UK economic indices, including the Retail Prices Index, both without and with an ARCH model, the wages index, share dividend yields, share dividends and share prices, long term bond yields, short term bond yields and index-linked bond yields, in each case by updating the parameters to June 2009. We discuss how the model has performed from 1994 to 2009 and estimate the values of the parameters and their confidence intervals over various sub-periods to study their stability. Our analysis shows that the residuals of many of the series are much fatter-tailed than in a normal distribution. We observe also that besides the stochastic uncertainty built into the model by the random innovations there is also parameter uncertainty arising from the estimated values of the parameters.
The interfacial reactions and microstructures of metal-GaAs contacts are, in general, much more complicated and difficult to control than the corresponding metal-Si contacts. They are very sensitive to reaction temperature, ambient, metal layer thickness, and the GaAs surface cleaning procedure. Many of the ohmic and gate contacts to GaAs currently in use or under development for GaAs FET devices are comprised of more than one metal species and in some cases a doping element as well. In dealing with these complexities, information about the microstructure at the contact interface is critically needed: for the evaluation of a specific contact metallurgy, for the definition of an optimum fabrication process, and, most important of all, for generating new ideas for better contact schemes. In this paper, our TEM and STEM studies of several ohmic and gate contacts that are of technological interest will be described. Attention will be drawn to the link between the interfacial microstructures and their electrical behavior, the kinetics of interfacial reactions, and thermal stability. The current constraints on obtaining ideal, reliable and controllable metal-GaAs contacts will also be discussed.
Let be an o-minimal expansion of the ordered field of real numbers , and let S be an -definable subset (parameters allowed unless otherwise stated) of ℝn. In this note I investigate questions concerning the distribution of points on S with integer coordinates. My main theorem gives an estimate which, though probably far from best possible, at least shows that the o-minimal assumption does have diophantine consequences. This is, perhaps, surprising in view of the flexibility that we now seem to have in constructing o-minimal expansions of (see, e. g. , , ).
This report, which was sponsored by the Life Board of the Faculty and Institute of Actuaries, was originally published in November 1997.
Because it is referred to several times in the paper ‘Reserving, Pricing and Hedging for Policies with Guaranteed Annuity Options’, and in the discussions of the paper, and because it is not easily accessible elsewhere, it is printed here as a background paper for reference.