The Structure and Dynamical Evolution of Dark Matter Halos

(Shortened) We use N-body simulations to investigate the structure and dynamical evolution of dark matter halos in galaxy clusters. Our sample consists of nine massive halos from an EdS universe with scale free power spectrum and n = -1. Halos are resolved by ~20000 particles each, with a dynamical resolution of 20-25 kpc. Large scale tidal fields are included up to L=150 Mpc using background particles. The halo formation process can be characterized by the alternation of two dynamical configurations: a merging phase and a relaxation phase, defined by their signature on the evolution of the total mass and rms velocity. Halos spend on average one 1/3 of their evolution in the merging phase and 2/3 in the relaxation phase. Using this definition, we study the density profiles and their change during the halo history. The average density profiles are fitted by the NFW analytical model with an rms residual of 17% between the virial radius Rv and 0.01 Rv. The Hernquist (1990) profiles fits the same halos with an rms residual of 26%. The trend with mass of the scale radius of these fits is marginally consistent with that found by Cole & Lacey (1996): in comparison our halos are more centrally concentrated, and the relation between scale radius and halo mass is slightly steeper. We find a moderately large scatter in this relation, due both to dynamical evolution within halos and to fluctuations in the halo population. We analyze the dynamical equilibrium of our halos using the Jeans' equation, and find that on average they are approximately in equilibrium within their virial radius. Finally, we find that the projected mass profiles of our simulated halos are in very good agreement with the profiles of three rich galaxy clusters derived from strong and weak gravitational lensing observations.Comment: 20 pages, Latex, with all figures included. Modified to match the published versio

Modeling the initiation of others into injection drug use, using data from 2,500 injectors surveyed in Scotland during 2008-2009

The prevalence of injection drug use has been of especial interest for assessment of the impact of blood-borne viruses. However, the incidence of injection drug use has been underresearched. Our 2-fold aim in this study was to estimate 1) how many other persons, per annum, an injection drug user (IDU) has the equivalent of full responsibility (EFR) for initiating into injection drug use and 2) the consequences for IDUs' replacement rate. EFR initiation rates are strongly associated with incarceration history, so that our analysis of IDUs' replacement rate must incorporate when, in their injecting career, IDUs were first incarcerated. To do so, we have first to estimate piecewise constant incarceration rates in conjunction with EFR initiation rates, which are then combined with rates of cessation from injecting to model IDUs' replacement rate over their injecting career, analogous to the reproduction number of an epidemic model. We apply our approach to Scotland's IDUs, using over 2,500 anonymous injector participants who were interviewed in Scotland's Needle Exchange Surveillance Initiative during 2008-2009. Our approach was made possible by the inclusion of key questions about initiations. Finally, we extend our model to include an immediate quit rate, as a reasoned compensation for higher-than-expected replacement rates, and we estimate how high initiates' quit rate should be for IDUs' replacement rate to be 1

Biased sampling activity: an investigation to promote discussion.

The statistical concept of sampling is often given little direct attention, typically reduced to the mantra "take a random sample". This low resource and adaptable activity demonstrates sampling and explores issues that arise due to biased sampling

rpsftm: An R Package for Rank Preserving Structural Failure Time Models.

Treatment switching in a randomised controlled trial occurs when participants change from their randomised treatment to the other trial treatment during the study. Failure to account for treatment switching in the analysis (i.e. by performing a standard intention-to-treat analysis) can lead to biased estimates of treatment efficacy. The rank preserving structural failure time model (RPSFTM) is a method used to adjust for treatment switching in trials with survival outcomes. The RPSFTM is due to Robins and Tsiatis (1991) and has been developed by White et al. (1997, 1999). The method is randomisation based and uses only the randomised treatment group, observed event times, and treatment history in order to estimate a causal treatment effect. The treatment effect, ψ, is estimated by balancing counter-factual event times (that would be observed if no treatment were received) between treatment groups. G-estimation is used to find the value of ψ such that a test statistic Z(ψ) = 0. This is usually the test statistic used in the intention-to-treat analysis, for example, the log rank test statistic. We present an R package that implements the method of rpsftm

Masses for the Local Group and the Milky Way

We use the very large Millennium Simulation of the concordance $\Lambda$CDM cosmogony to calibrate the bias and error distribution of Timing Argument estimators of the masses of the Local Group and of the Milky Way. From a large number of isolated spiral-spiral pairs similar to the Milky Way/Andromeda system, we find the interquartile range of the ratio of timing mass to true mass to be a factor of 1.8, while the 5% and 95% points of the distribution of this ratio are separated by a factor of 5.7. Here we define true mass as the sum of the ``virial'' masses $M_{200}$ of the two dominant galaxies. For current best values of the distance and approach velocity of Andromeda this leads to a median likelihood estimate of the true mass of the Local Group of 5.27\times 10^{12}\msun, or $\log M_{LG}/M_\odot = 12.72$, with an interquartile range of $[12.58, 12.83]$ and a 5% to 95% range of $[12.26, 13.01]$. Thus a 95% lower confidence limit on the true mass of the Local Group is 1.81\times 10^{12}\msun. A timing estimate of the Milky Way's mass based on the large recession velocity observed for the distant satellite Leo I works equally well, although with larger systematic uncertainties. It gives an estimated virial mass for the Milky Way of 2.43 \times 10^{12}\msun with a 95% lower confidence limit of 0.80 \times 10^{12}\msun.Comment: 11 pages, 6 figures, MNRAS accepted. Added a new discussion paragraph and a new figure regarding the relative transverse velocity but conclusions unchange

To pray and play: post-postmodern pilgrimage at Lourdes

This research examines the factors that religious pilgrims draw upon when constructing a personal meaning of their visit to Lourdes. Through an ethnographic examination of twenty-five individuals it finds that their experiences may be characterized by the common themes that comprise ‘lived connections’, unexpected ‘encounters’, ‘visual’ and ‘curative’ content. These themes parallel those that feature in the seminal account of Bernadette Soubirous' vision of the Virgin Mary in 1858, which we collectively term ‘Echoes of Bernadette’. Those who successfully navigate the apparently contested spaces and interact in meaningful encounters are partaking of a pilgrimage that is rooted in the religious and the historic. The study provides a contribution to the theory of pilgrimage by declaring that it may be enacted in a post-postmodern duality that accepts the freedom of the individual but recognizes their need for experiences that are grounded in a sociohistorical ‘truth’

Pairing Correlations on t-U-J Ladders

Pairing correlations on generalized t-U-J two-leg ladders are reported. We find that the pairing correlations on the usual t-U Hubbard ladder are significantly enhanced by the addition of a nearest-neighbor exchange interaction J. Likewise, these correlations are also enhanced for the t-J model when the onsite Coulomb interaction is reduced from infinity. Moreover, the pairing correlations are larger on a t-U-J ladder than on a t-Jeff ladder in which Jeff has been adjusted so that the two models have the same spin gap at half-filling. This enhancement of the pairing correlations is associated with an increase in the pair-binding energy and the pair mobility in the t-U-J model and point to the importance of the charge transfer nature of the cuprate systems

Sample size and classification error for Bayesian change-point models with unlabelled sub-groups and incomplete follow-up.

Many medical (and ecological) processes involve the change of shape, whereby one trajectory changes into another trajectory at a specific time point. There has been little investigation into the study design needed to investigate these models. We consider the class of fixed effect change-point models with an underlying shape comprised two joined linear segments, also known as broken-stick models. We extend this model to include two sub-groups with different trajectories at the change-point, a change and no change class, and also include a missingness model to account for individuals with incomplete follow-up. Through a simulation study, we consider the relationship of sample size to the estimates of the underlying shape, the existence of a change-point, and the classification-error of sub-group labels. We use a Bayesian framework to account for the missing labels, and the analysis of each simulation is performed using standard Markov chain Monte Carlo techniques. Our simulation study is inspired by cognitive decline as measured by the Mini-Mental State Examination, where our extended model is appropriate due to the commonly observed mixture of individuals within studies who do or do not exhibit accelerated decline. We find that even for studies of modest size ( n = 500, with 50 individuals observed past the change-point) in the fixed effect setting, a change-point can be detected and reliably estimated across a range of observation-errors.This work was supported by the Medical Research Council (Unit Programme number U105292687)