Prior elicitation in Bayesian quantile regression for longitudinal data

© 2011 Alhamzawi R, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original auhor and source are credited.This article has been made available through the Brunel Open Access Publishing Fund.In this paper, we introduce Bayesian quantile regression for longitudinal data in terms of informative priors and Gibbs sampling. We develop methods for eliciting prior distribution to incorporate historical data gathered from similar previous studies. The methods can be used either with no prior data or with complete prior data. The advantage of the methods is that the prior distribution is changing automatically when we change the quantile. We propose Gibbs sampling methods which are computationally efficient and easy to implement. The methods are illustrated with both simulation and real data.This article is made available through the Brunel Open Access Publishing Fund

Apocenter glow in eccentric debris disks: implications for Fomalhaut and epsilon Eridani

Debris disks often take the form of eccentric rings with azimuthal asymmetries in surface brightness. Such disks are often described as showing "pericenter glow", an enhancement of the disk brightness in regions nearest the central star. At long wavelengths, however, the disk apocenters should appear brighter than their pericenters: in the long wavelength limit, we find the apocenter/pericenter flux ratio scales as 1+e for disk eccentricity e. We produce new models of this "apocenter glow" to explore its causes and wavelength dependence and study its potential as a probe of dust grain properties. Based on our models, we argue that several far-infrared and (sub)millimeter images of the Fomalhaut and epsilon Eridani debris rings obtained with Herschel, JCMT, SHARC II, ALMA, and ATCA should be reinterpreted as suggestions or examples of apocenter glow. This reinterpretation yields new constraints on the disks' dust grain properties and size distributions.Comment: 20 pages, 7 figures; accepted to Ap

Layers of powers: societies and institutions in Europe

Historians and social scientists have offered many and varied definitions of the term “community”. This chapter focuses on specific examples of face-to-face or local communities in order to test the possibilities and limits of the two major analytical approaches to communities: an anthropological approach which identifies ‘community’ as an organic entity, and a symbolic one which considers feelings of belonging and self-identification as constitutive aspects of a community. In this quest, close attention is paid to the question of the stabilization of community’s structures through legislation and institutions, a process that integrates such micro-societies into broader networks of power, and renders them visible to historians. In the first section we examine what we have called a “world of communities”, from periods when communities constituted the dominant element of social structure. Examining ancient Jewish and medieval Icelandic communities, and then early modern Irish and Scottish clans, we try to identify their basic characteristics and to reconstruct the way they related to the rest of the social structure. The second section analyzes the emergence of new loyalties and models of social membership from the 19th century onwards, emphasizing how the discourse on communities played a crucial role in the construction of these diverse patterns of identification and differentiation. Finally, we explore the permanence of the communitarian world supposedly replaced by nationalism and other major modern ideologies along with the new meanings and uses of communities in the 20th and 21st centuries. In sum, this broad overview provides a preliminary narrative of the changes in the structures of communities and their shifting position within wider patterns of social organizations while drawing attention to parallel transformations in theoretical reflection on communities

Temperature determination from the lattice gas model

Determination of temperature from experimental data has become important in searches for critical phenomena in heavy ion collisions. Widely used methods are ratios of isotopes (which rely on chemical and thermal equilibrium), population ratios of excited states etc. Using the lattice gas model we propose a new observable: $n_{ch}/Z$ where $n_{ch}$ is the charge multiplicity and $Z$ is the charge of the fragmenting system. We show that the reduced multiplicity is a good measure of the average temperature of the fragmenting system.Comment: 11 pages, 2 ps file

Density Variations over Subparsec Scales in Diffuse Molecular Gas

We present high-resolution observations of interstellar CN, CH, CH^{+}, \ion{Ca}{1}, and \ion{Ca}{2} absorption lines toward the multiple star systems HD206267 and HD217035. Substantial variations in CN absorption are observed among three sight lines of HD206267, which are separated by distances of order 10,000 AU; smaller differences are seen for CH, CH^{+}, and \ion{Ca}{1}. Gas densities for individual velocity components are inferred from a chemical model, independent of assumptions about cloud shape. While the component densities can differ by factors of 5.0 between adjacent sightlines, the densities are always less than 5000 cm^{-3}. Calculations show that the derived density contrasts are not sensitive to the temperature or reaction rates used in the chemical model. A large difference in the CH^{+} profiles (a factor of 2 in column density) is seen in the lower density gas toward HD217035.Comment: 9 pages, 2 figures. Accepted for publication in ApJ

New mechanism for the enhancement of sdsd dominance in interacting boson models

We introduce an exactly solvable model for interacting bosons that extend up to high spin and interact through a repulsive pairing force. The model exhibits a phase transition to a state with almost complete $sd$ dominance. The repulsive pairing interaction that underlies the model has a natural microscopic origin in the Pauli exclusion principle between contituent nucleons. As such, repulsive pairing between bosons seems to provide a new mechanism for the enhancement of $sd$ dominance, giving further support for the validity of the $sd$ Interacting Boson Model.Comment: 4 pages, 2 figure

The induced representations of Brauer algebra and the Clebsch-Gordan coefficients of SO(n)

Induced representations of Brauer algebra $D_{f}(n)$ from $S_{f_{1}}\times S_{f_{2}}$ with $f_{1}+f_{2}=f$ are discussed. The induction coefficients (IDCs) or the outer-product reduction coefficients (ORCs) of $S_{f_{1}}\times S_{f_{2}}\uparrow D_{f}(n)$ with $f\leq 4$ up to a normalization factor are derived by using the linear equation method. Weyl tableaus for the corresponding Gel'fand basis of SO(n) are defined. The assimilation method for obtaining CG coefficients of SO(n) in the Gel'fand basis for no modification rule involved couplings from IDCs of Brauer algebra are proposed. Some isoscalar factors of $SO(n)\supset SO(n-1)$ for the resulting irrep $[\lambda_{1},~\lambda_{2},~ \lambda_{3},~\lambda_{4},\dot{0}]$ with $\sum\limits_{i=1}^{4}\lambda_{i}\leq .Comment: 48 pages latex, submitted to Journal of Phys.

Lattice gas model for fragmentation: From Argon on Scandium to Gold on Gold

The recent fragmentation data for central collisions of Gold on Gold are even qualitatively different from those for central collisions of Argon on Scandium. The latter can be fitted with a lattice gas model calculation. Effort is made to understand why the model fails for Gold on Gold. The calculation suggests that the large Coulomb interaction which is operative for the larger system is responsible for this discrepancy. This is demonstrated by mapping the lattice gas model to a molecular dynamics calculation for disassembly. This mapping is quite faithful for Argon on Scandium but deviates strongly for Gold on Gold. The molecular dynamics calculation for disassembly reproduces the characteristics of the fragmentation data for both Gold on Gold and Argon on Scandium.Comment: 13 pages, Revtex, 8 figures in ps files, submitted to Phys. Rev.

A New Young Diagrammatic Method For Kronecker Products of O(n) and Sp(2m)

A new simple Young diagrammatic method for Kronecker products of O(n) and Sp(2m) is proposed based on representation theory of Brauer algebras. A general procedure for the decomposition of tensor products of representations for O(n) and Sp(2m) is outlined, which is similar to that for U(n) known as the Littlewood rules together with trace contractions from a Brauer algebra and some modification rules given by King.Comment: Latex, 11 pages, no figure