The Reduction of the Electron Abundance during the Pre-explosion Simmering in White Dwarf Supernovae

Prior to the explosion of a carbon-oxygen white dwarf in a Type Ia supernova there is a long "simmering," during which the 12C + 12C reaction gradually heats the white dwarf on a long (~ 1000 yr) timescale. Piro & Bildsten showed that weak reactions during this simmering set a maximum electron abundance Ye at the time of the explosion. We investigate the nuclear reactions during this simmering with a series of self-heating, at constant pressure, reaction network calculations. Unlike in AGB stars, proton captures onto 22Ne and heavier trace nuclei do not play a significant role. The 12C abundance is sufficiently high that the neutrons preferentially capture onto 12C, rather than iron group nuclei. As an aid to hydrodynamical simulations of the simmering phase, we present fits to the rates of heating, electron capture, change in mean atomic mass, and consumption of 12C in terms of the screened thermally averaged cross section for 12C + 12C. Our evaluation of the net heating rate includes contributions from electron captures into the 3.68 MeV excited state of 13C. This results in a slightly larger energy release, per 12C consumed, than that found by Piro & Bildsten, but less than that released for a burn to only 20Ne and 23Na. We compare our one-zone results to more accurate integrations over the white dwarf structure to estimate the amount of 12C that must be consumed to raise the white dwarf temperature, and hence to determine the net reduction of Ye during simmering.Comment: Accepted for publication in The Astrophysical Journal, 9 pages, 6 figure

Logistic random effects regression models: a comparison of statistical packages for binary and ordinal outcomes

<p>Abstract</p> <p>Background</p> <p>Logistic random effects models are a popular tool to analyze multilevel also called hierarchical data with a binary or ordinal outcome. Here, we aim to compare different statistical software implementations of these models.</p> <p>Methods</p> <p>We used individual patient data from 8509 patients in 231 centers with moderate and severe Traumatic Brain Injury (TBI) enrolled in eight Randomized Controlled Trials (RCTs) and three observational studies. We fitted logistic random effects regression models with the 5-point Glasgow Outcome Scale (GOS) as outcome, both dichotomized as well as ordinal, with center and/or trial as random effects, and as covariates age, motor score, pupil reactivity or trial. We then compared the implementations of frequentist and Bayesian methods to estimate the fixed and random effects. Frequentist approaches included R (lme4), Stata (GLLAMM), SAS (GLIMMIX and NLMIXED), MLwiN ([R]IGLS) and MIXOR, Bayesian approaches included WinBUGS, MLwiN (MCMC), R package MCMCglmm and SAS experimental procedure MCMC.</p> <p>Three data sets (the full data set and two sub-datasets) were analysed using basically two logistic random effects models with either one random effect for the center or two random effects for center and trial. For the ordinal outcome in the full data set also a proportional odds model with a random center effect was fitted.</p> <p>Results</p> <p>The packages gave similar parameter estimates for both the fixed and random effects and for the binary (and ordinal) models for the main study and when based on a relatively large number of level-1 (patient level) data compared to the number of level-2 (hospital level) data. However, when based on relatively sparse data set, i.e. when the numbers of level-1 and level-2 data units were about the same, the frequentist and Bayesian approaches showed somewhat different results. The software implementations differ considerably in flexibility, computation time, and usability. There are also differences in the availability of additional tools for model evaluation, such as diagnostic plots. The experimental SAS (version 9.2) procedure MCMC appeared to be inefficient.</p> <p>Conclusions</p> <p>On relatively large data sets, the different software implementations of logistic random effects regression models produced similar results. Thus, for a large data set there seems to be no explicit preference (of course if there is no preference from a philosophical point of view) for either a frequentist or Bayesian approach (if based on vague priors). The choice for a particular implementation may largely depend on the desired flexibility, and the usability of the package. For small data sets the random effects variances are difficult to estimate. In the frequentist approaches the MLE of this variance was often estimated zero with a standard error that is either zero or could not be determined, while for Bayesian methods the estimates could depend on the chosen "non-informative" prior of the variance parameter. The starting value for the variance parameter may be also critical for the convergence of the Markov chain.</p

The correlation between C/O ratio, metallicity and the initial WD mass for SNe Ia

In this paper, we want to check whether or not the carbon abundance can be affected by initial metallicity. We calculated a series of stellar evolution. We found that when $Z\leq0.02$, the carbon abundance is almost independent of metallicity if it is plotted against the initial WD mass. However, when $Z>0.02$, the carbon abundance is not only a function of the initial WD mass, but also metallicity, i.e. for a given initial WD mass, the higher the metallicity, the lower the carbon abundance. Based on some previous studies, i.e. both a high metallicity and a low carbon abundance lead to a lower production of $^{\rm 56}$Ni formed during SN Ia explosion, the effects of the carbon abundance and the metallicity on the amount of $^{\rm 56}$Ni are enhanced by each other, which may account for the variation of maximum luminosity of SNe Ia, at least qualitatively. Considering that the central density of WD before supernova explosion may also play a role on the production of $^{\rm 56}$Ni and the carbon abundance, the metallicity and the central density are all determined by the initial parameters of progenitor system, i.e. the initial WD mass, metallicity, orbital period and secondary mass, the amount of $^{\rm 56}$Ni might be a function of the initial parameters. Then, our results might construct a bridge linking the progenitor model and the explosion model of SNe Ia.Comment: 7pages, 4 figures, accepted for publication in A&

On Simulating Type Ia Supernovae

Type Ia supernovae are bright stellar explosions distinguished by standardizable light curves that allow for their use as distance indicators for cosmological studies. Despite their highly successful use in this capacity, the progenitors of these events are incompletely understood. We describe simulating type Ia supernovae in the paradigm of a thermonuclear runaway occurring in a massive white dwarf star. We describe the multi-scale physical processes that realistic models must incorporate and the numerical models for these that we employ. In particular, we describe a flame-capturing scheme that addresses the problem of turbulent thermonuclear combustion on unresolved scales. We present the results of our study of the systematics of type Ia supernovae including trends in brightness following from properties of the host galaxy that agree with observations. We also present performance results from simulations on leadership-class architectures.Comment: 13 pages, 3 figures, accepted to proceedings of the Conference on Computational Physics, Oct. 30 - Nov. 3, 201

Sample size considerations for trials using cerebral white matter hyperintensity progression as an intermediate outcome at 1 year after mild stroke: Results of a prospective cohort study

Background: White matter hyperintensities (WMHs) are commonly seen on in brain imaging and are associated with stroke and cognitive decline. Therefore, they may provide a relevant intermediate outcome in clinical trials. WMH can be measured as a volume or visually on the Fazekas scale. We investigated predictors of WMH progression and design of efficient studies using WMH volume and Fazekas score as an intermediate outcome. Methods: We prospectively recruited 264 patients with mild ischaemic stroke and measured WMH volume, Fazekas score, age and cardiovascular risk factors at baseline and 1 year. We modelled predictors of WMH burden at 1 year and used the results in sample size calculations for hypothetical randomised controlled trials with different analysis plans and lengths of follow-up. Results: Follow-up WMH volume was predicted by baseline WMH: a 0.73-ml (95% CI 0.65-0.80, p < 0.0001) increase per 1-ml baseline volume increment, and a 2.93-ml increase (95% CI 1.76-4.10, p < 0.0001) per point on the Fazekas scale. Using a mean difference of 1 ml in WMH volume between treatment groups, 80% power and 5% alpha, adjusting for all predictors and 2-year follow-up produced the smallest sample size (n = 642). Other study designs produced samples sizes from 2054 to 21,270. Sample size calculations using Fazekas score as an outcome with the same power and alpha, as well as an OR corresponding to a 1-ml difference, were sensitive to assumptions and ranged from 2504 to 18,886. Conclusions: Baseline WMH volume and Fazekas score predicted follow-up WMH volume. Study size was smallest using volumes and longer-term follow-up, but this must be balanced against resources required to measure volumes versus Fazekas scores, bias due to dropout and scanner drift. Samples sizes based on Fazekas scores may be best estimated with simulation studies

Methodological issues in epidemiological studies of periodontitis - how can it be improved?

Background: This position paper was commissioned by the European Association of Dental Public Health, which has established six working groups to investigate the current status of six topics related to oral public health. One of these areas is epidemiology of periodontal diseases. Methods: Two theses "A systematic review of definitions of periodontitis and the methods that have been used to identify periodontitis" [1] and "Factors affecting community oral health care needs and provision" [2] formed the starting point for this position paper. Additional relevant and more recent publications were retrieved through a MEDLINE search. Results: The literature reveals a distinct lack of consensus and uniformity in the definition of periodontitis within epidemiological studies. There are also numerous differences in the methods used. The consequence is that data from studies using differing case definitions and differing survey methods are not easily interpretable or comparable. The limitations of the widely used Community Periodontal Index of Treatment Need (CPITN) and its more recent derivatives are widely recognized. Against this background, this position paper reviews the current evidence base, outlines existing problems and suggests how epidemiology of periodontal diseases may be improved. Conclusions: The remit of this working group was to review and discuss the existing evidence base of epidemiology of periodontal diseases and to identify future areas of work to further enhance it

Astronomical Distance Determination in the Space Age: Secondary Distance Indicators

The formal division of the distance indicators into primary and secondary leads to difficulties in description of methods which can actually be used in two ways: with, and without the support of the other methods for scaling. Thus instead of concentrating on the scaling requirement we concentrate on all methods of distance determination to extragalactic sources which are designated, at least formally, to use for individual sources. Among those, the Supernovae Ia is clearly the leader due to its enormous success in determination of the expansion rate of the Universe. However, new methods are rapidly developing, and there is also a progress in more traditional methods. We give a general overview of the methods but we mostly concentrate on the most recent developments in each field, and future expectations. © 2018, The Author(s)

Random non-autonomous second order linear differential equations: mean square analytic solutions and their statistical properties

[EN] In this paper we study random non-autonomous second order linear differential equations by taking advantage of the powerful theory of random difference equations. The coefficients are assumed to be stochastic processes, and the initial conditions are random variables both defined in a common underlying complete probability space. Under appropriate assumptions established on the data stochastic processes and on the random initial conditions, and using key results on difference equations, we prove the existence of an analytic stochastic process solution in the random mean square sense. Truncating the random series that defines the solution process, we are able to approximate the main statistical properties of the solution, such as the expectation and the variance. We also obtain error a priori bounds to construct reliable approximations of both statistical moments. We include a set of numerical examples to illustrate the main theoretical results established throughout the paper. 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Determinants of director compensation in two-tier systems: evidence from German panel data

Building on a unique panel data set of German Prime Standard companies for the period 2005-2008, this paper investigates the influencing factors of both director compensation levels and structure, i.e. the probability of performance-based compensation. Drawing on agency theory arguments and previous literature, we analyze a comprehensive group of determinants, including detailed corporate performance, ownership and board characteristics. While controlling for unobserved heterogeneity, we find director compensation to be set in ways consistent with optimal contracting theory. I.e. compensation is systematically structured to mitigate agency conflicts and to encourage effective monitoring. Thus, our results indicate that similar types of agency conflicts exist in the German two-tier setting