Asymptotics of lattice walks via analytic combinatorics in several variables

We consider the enumeration of walks on the two dimensional non-negative integer lattice with short steps. Up to isomorphism there are 79 unique two dimensional models to consider, and previous work in this area has used the kernel method, along with a rigorous computer algebra approach, to show that 23 of the 79 models admit D-finite generating functions. In 2009, Bostan and Kauers used Pad\'e-Hermite approximants to guess differential equations which these 23 generating functions satisfy, in the process guessing asymptotics of their coefficient sequences. In this article we provide, for the first time, a complete rigorous verification of these guesses. Our technique is to use the kernel method to express 19 of the 23 generating functions as diagonals of tri-variate rational functions and apply the methods of analytic combinatorics in several variables (the remaining 4 models have algebraic generating functions and can thus be handled by univariate techniques). This approach also shows the link between combinatorial properties of the models and features of its asymptotics such as asymptotic and polynomial growth factors. In addition, we give expressions for the number of walks returning to the x-axis, the y-axis, and the origin, proving recently conjectured asymptotics of Bostan, Chyzak, van Hoeij, Kauers, and Pech.Comment: 10 pages, 3 tables, as accepted to proceedings of FPSAC 2016 (without conference formatting

Young children learning in Gaelic: Investigating children's learning experiences in Gaelic-medium pre-school. Research Briefing 6E. Stirling

Gaelic-medium (GM) education is an important part of current efforts to re-vitalise the language in Scotland. Beginning Gaelic-medium education in preschool is seen as a crucial entry point, enhancing the numbers entering GM primary education and facilitating transition to the school learning environment. However, it is essential that GM preschool is of high quality. Government-funded provision is expected to offer children the same learning opportunities as their peers who attend English-medium settings. Meeting these expectations is challenging because most children enter Gaelic-medium preschool from English-speaking homes so that the nursery or playgroup is their only exposure to Gaelic. Our earlier study mapped the range and extent of Gaelic-medium early education and childcare provision but in the research reported here our focus was on what happens within settings, the children’s activities in the playroom and the ways in which practitioners help them to learn Gaelic, as well as ensuring that national expectations about curriculum and learning outcomes are met

Primary care-led commissioning and public involvement in the English National Health Service. Lessons from the past.

Background: Patient and Public involvement (PPI) in health care occupies a central place in Western democracies. In England, this theme has been continuously prominent since the introduction of market reforms in the early 1990s. The health care reforms implemented by the current Coalition Government are making primary care practitioners the main commissioners of health care services in the National Health Service, and a duty is placed on them to involve the public in commissioning decisions and strategies. Since implementation of PPI initiatives in primary care commissioning is not new, we asked how likely it is that the new reforms will make a difference. We scanned the main literature related to primary care-led commissioning and found little evidence of effective PPI thus far. We suggest that unless the scope and intended objectives of PPI are clarified and appropriate resources are devoted to it, PPI will continue to remain empty rhetoric and box ticking. Aim: To examine the effect of previous PPI initiatives on health care commissioning and draw lessons for future development. Method: We scanned the literature reporting on previous PPI initiatives in primary careled commissioning since the introduction of the internal market in 1991. In particular, we looked for specific contexts, methods and outcomes of such initiatives. Findings: 1. PPI in commissioning has been constantly encouraged by policy makers in England. 2. Research shows limited evidence of effective methods and outcomes so far. 3. Constant reconfi- guration of health care structures has had a negative impact on PPI. 4. The new structures look hardly better poised to bring about effective public and patient involvement

The happiness - suicide paradox

Suicide is an important scientific phenomenon. Yet its causes remain poorly understood. This study documents a paradox: the happiest places have the highest suicide rates. The study combines findings from two large and rich individual-level data sets—one on life satisfaction and another on suicide deaths—to establish the paradox in a consistent way across U.S. states. It replicates the finding in data on Western industrialized nations and checks that the paradox is not an artifact of population composition or confounding factors. The study concludes with the conjecture that people may find it particularly painful to be unhappy in a happy place, so that the decision to commit suicide is influenced by relative comparisons.Happiness ; Suicide

Development of a New, Precise Near-infrared Doppler Wavelength Reference: A Fiber Fabry-Perot Interferometer

We present the ongoing development of a commercially available Micron Optics fiber-Fabry Perot Interferometer as a precise, stable, easy to use, and economic spectrograph reference with the goal of achieving <1 m/s long term stability. Fiber Fabry-Perot interferometers (FFP) create interference patterns by combining light traversing different delay paths. The interference creates a rich spectrum of narrow emission lines, ideal for use as a precise Doppler reference. This fully photonic reference could easily be installed in existing NIR spectrographs, turning high resolution fiber-fed spectrographs into precise Doppler velocimeters. First light results on the Sloan Digital Sky Survey III (SDSS-III) Apache Point Observatory Galactic Evolution Experiment (APOGEE) spectrograph and several tests of major support instruments are also presented. These instruments include a SuperK Photonics fiber supercontinuum laser source and precise temperature controller. A high resolution spectrum obtained using the NIST 2-m Fourier transform spectrometer (FTS) is also presented. We find our current temperature control precision of the FFP to be 0.15 mK, corresponding to a theoretical velocity stability of 35 cm/s due to temperature variations of the interferometer cavity.Comment: 16 pages, 11 figures. To appear in the proceedings of the SPIE 2012 Astronomical Instrumentation and Telescopes conferenc

The Fate of Local Food Systems in the Global Industrialization Market: Food and Social Justice in the Rural South

This paper investigates the connection between local food systems, health disparities, and social justice in the rural South. It begins with the relationship between food insecurity and health disparities that disproportionately affect racial and ethnic minority populations, and non-minority women and children. First, we discuss the concept of health disparities within the context of bioethics and public health ethics in order to explore the link between the food system and health as a social justice issue. Second, we define health disparities and discuss how they have historically plagued and disadvantaged racial minority populations. Third, we examine these disparities within the context of the structure of the food system and the related social justice issues. We conclude that food insecurity in the rural south is ethically unacceptable because it harms the disadvantaged populations living in these areas. It worsens their vulnerability, truncates their flourishing, and makes their optimal health a mirage

An evaluation of the impact upon productivity of ending resale price maintenance on books

Report prepared for the OFT by the Centre for Competition Policy at University of East Anglia. An examination of the ending of RPM aims to improve understanding of how competition interventions affect productivity, provide a methodological framework that could inform future evaluations and provide inputs to the ongoing debate about the effects of RPM

Universal magnetic and structural behaviors in the iron arsenides

Commonalities among the order parameters of the ubiquitous antiferromagnetism present in the parent compounds of the iron arsenide high temperature superconductors are explored. Additionally, comparison is made between the well established two-dimensional Heisenberg-Ising magnet, K$_2$NiF$_4$ and iron arsenide systems residing at a critical point whose structural and magnetic phase transitions coincide. In particular, analysis is presented regarding two distinct classes of phase transition behavior reflected in the development of antiferromagnetic and structural order in the three main classes of iron arsenide superconductors. Two distinct universality classes are mirrored in their magnetic phase transitions which empirically are determined by the proximity of the coupled structural and magnetic phase transitions in these materials.Comment: 6 pages, 4 figure

The connective Morava K-theory of the second mod p Eilenberg-MacLane space

We develop tools for computing the connective n-th Morava K-theory of spaces. Starting with a Universal Coefficient Theorem that computes the cohomology version from the homology version, we show that every step in the process of computing one is mirrored in the other and that this can be used to make computations. As our example, we compute the connective n-th Morava K-theory of the second mod p Eilenberg-MacLane space.Comment: minor change of title and one sentence adde