Ariel - Volume 2 Number 5

Editors Delvyn C. Case, Jr. Paul M. Fernhoff News Editors Richard Bonanno Robin A. Edwards Features Editors Stephen P. Flynn Steven A. Ager Lay-Out Editor Carol Dolinskas Contributing Editors Michael J. Blecker W. Cherry Light Eugenia Miller Lin Sey Edwards Jack Guralnik Tom Williams James Noco

Finite to infinite steady state solutions, bifurcations of an integro-differential equation

We consider a bistable integral equation which governs the stationary solutions of a convolution model of solid--solid phase transitions on a circle. We study the bifurcations of the set of the stationary solutions as the diffusion coefficient is varied to examine the transition from an infinite number of steady states to three for the continuum limit of the semi--discretised system. We show how the symmetry of the problem is responsible for the generation and stabilisation of equilibria and comment on the puzzling connection between continuity and stability that exists in this problem

Genomic Prediction Accounting for Residual Heteroskedasticity

Citation: Ou, Z. N., Tempelman, R. J., Steibel, J. P., Ernst, C. W., Bates, R. O., & Bello, N. M. (2016). Genomic Prediction Accounting for Residual Heteroskedasticity. G3-Genes Genomes Genetics, 6(1), 1-13. doi:10.1534/g3.115.022897Whole-genome prediction (WGP) models that use single-nucleotide polymorphism marker information to predict genetic merit of animals and plants typically assume homogeneous residual variance. However, variability is often heterogeneous across agricultural production systems and may subsequently bias WGP-based inferences. This study extends classical WGP models based on normality, heavy-tailed specifications and variable selection to explicitly account for environmentally-driven residual heteroske-dasticity under a hierarchical Bayesian mixed-models framework. WGP models assuming homogeneous or heterogeneous residual variances were fitted to training data generated under simulation scenarios reflecting a gradient of increasing heteroskedasticity. Model fit was based on pseudo-Bayes factors and also on prediction accuracy of genomic breeding values computed on a validation data subset one generation removed from the simulated training dataset. Homogeneous vs. heterogeneous residual variance WGP models were also fitted to two quantitative traits, namely 45-min postmortem carcass temperature and loin muscle pH, recorded in a swine resource population dataset prescreened for high and mild residual heteroskedasticity, respectively. Fit of competing WGP models was compared using pseudo-Bayes factors. Predictive ability, defined as the correlation between predicted and observed phenotypes in validation sets of a five-fold cross-validation was also computed. Heteroskedastic error WGP models showed improved model fit and enhanced prediction accuracy compared to homoskedastic error WGP models although the magnitude of the improvement was small (less than two percentage points net gain in prediction accuracy). Nevertheless, accounting for residual heteroskedasticity did improve accuracy of selection, especially on individuals of extreme genetic merit

Evaluation of Lancashire and South Cumbria's suicide prevention training programmes and community-based projects

Suicide is a serious public health problem, accounting for half of all violence-related deaths globally. Across England, Lancashire and South Cumbria had the second highest suicide rate in 2012-14 (12.6 per 100,000 population). The high level of suicide in Lancashire and South Cumbria has been recognised as a key priority and a suicide prevention strategy has been developed with the aim of reducing the number of people taking their own life by 10% by 2021 compared to 2016/17 rates. This study evaluated two of the key activities implemented as part of the broader piece of work: a suite of training programmes on suicide prevention, self-harm intervention and, mental health and resilience; and, an Innovation Fund to support community-based projects. Key findings from the study suggested that the training programmes were associated with significant improvements in trainees’: attitudes to intervention work; confidence to intervene with at risk individuals; knowledge on suicide/self-harm; and, skills in appropriate clinical responses to disclosures from pre to post-training measurement. Reported outcomes from the Innovation Fund community projects suggested increased awareness of suicide risk and support services amongst project participants and their wider communities, and improved mental wellbeing. Such outcomes represent a vital step in achieving the long-term aim of a reduction in suicide rates across Lancashire and South Cumbria by 2021

Directed motion emerging from two coupled random processes: Translocation of a chain through a membrane nanopore driven by binding proteins

We investigate the translocation of a stiff polymer consisting of M monomers through a nanopore in a membrane, in the presence of binding particles (chaperones) that bind onto the polymer, and partially prevent backsliding of the polymer through the pore. The process is characterized by the rates: k for the polymer to make a diffusive jump through the pore, q for unbinding of a chaperone, and the rate q kappa for binding (with a binding strength kappa); except for the case of no binding kappa=0 the presence of the chaperones give rise to an effective force that drives the translocation process. Based on a (2+1) variate master equation, we study in detail the coupled dynamics of diffusive translocation and (partial) rectification by the binding proteins. In particular, we calculate the mean translocation time as a function of the various physical parameters.Comment: 22 pages, 5 figures, IOP styl

Strong-Segregation Theory of Bicontinuous Phases in Block Copolymers

We compute phase diagrams for $A_nB_m$ starblock copolymers in the strong-segregation regime as a function of volume fraction $\phi$, including bicontinuous phases related to minimal surfaces (G, D, and P surfaces) as candidate structures. We present the details of a general method to compute free energies in the strong segregation limit, and demonstrate that the gyroid G phase is the most nearly stable among the bicontinuous phases considered. We explore some effects of conformational asymmetry on the topology of the phase diagram.Comment: 14 pages, latex, 21 figures, to appear in Macromolecule

Symbiotic Bright Solitary Wave Solutions of Coupled Nonlinear Schrodinger Equations

Conventionally, bright solitary wave solutions can be obtained in self-focusing nonlinear Schrodinger equations with attractive self-interaction. However, when self-interaction becomes repulsive, it seems impossible to have bright solitary wave solution. Here we show that there exists symbiotic bright solitary wave solution of coupled nonlinear Schrodinger equations with repulsive self-interaction but strongly attractive interspecies interaction. For such coupled nonlinear Schrodinger equations in two and three dimensional domains, we prove the existence of least energy solutions and study the location and configuration of symbiotic bright solitons. We use Nehari's manifold to construct least energy solutions and derive their asymptotic behaviors by some techniques of singular perturbation problems.Comment: to appear in Nonlinearit

Diagnosis-based risk adjustment for Medicare capitation payments

Using 1991-92 data for a 5-percent Medicare sample, we develop, estimate, and evaluate risk-adjustment models that utilize diagnostic information from both inpatient and ambulatory claims to adjust payments for aged and disabled Medicare enrollees. Hierarchical coexisting conditions (HCC) models achieve greater explanatory power than diagnostic cost group (DCG) models by taking account of multiple coexisting medical conditions. Prospective models predict average costs of individuals with chronic conditions nearly as well as concurrent models. All models predict medical costs far more accurately than the current health maintenance organization (HMO) payment formula

Knotting probabilities after a local strand passage in unknotted self-avoiding polygons

We investigate the knotting probability after a local strand passage is performed in an unknotted self-avoiding polygon on the simple cubic lattice. We assume that two polygon segments have already been brought close together for the purpose of performing a strand passage, and model this using Theta-SAPs, polygons that contain the pattern Theta at a fixed location. It is proved that the number of n-edge Theta-SAPs grows exponentially (with n) at the same rate as the total number of n-edge unknotted self-avoiding polygons, and that the same holds for subsets of n-edge Theta-SAPs that yield a specific after-strand-passage knot-type. Thus the probability of a given after-strand-passage knot-type does not grow (or decay) exponentially with n, and we conjecture that instead it approaches a knot-type dependent amplitude ratio lying strictly between 0 and 1. This is supported by critical exponent estimates obtained from a new maximum likelihood method for Theta-SAPs that are generated by a composite (aka multiple) Markov Chain Monte Carlo BFACF algorithm. We also give strong numerical evidence that the after-strand-passage knotting probability depends on the local structure around the strand passage site. Considering both the local structure and the crossing-sign at the strand passage site, we observe that the more "compact" the local structure, the less likely the after-strand-passage polygon is to be knotted. This trend is consistent with results from other strand-passage models, however, we are the first to note the influence of the crossing-sign information. Two measures of "compactness" are used: the size of a smallest polygon that contains the structure and the structure's "opening" angle. The opening angle definition is consistent with one that is measurable from single molecule DNA experiments.Comment: 31 pages, 12 figures, submitted to Journal of Physics