Many problems arising in applications result in the need to probe a probability distribution for functions. Examples include Bayesian nonparametric statistics and conditioned diffusion processes. Standard MCMC algorithms typically become arbitrarily slow under the mesh refinement dictated by nonparametric description of the unknown function. We describe an approach to modifying a whole range of MCMC methods, applicable whenever the target measure has density with respect to a Gaussian process or Gaussian random field reference measure, which ensures that their speed of convergence is robust under mesh refinement. Gaussian processes or random fields are fields whose marginal distributions, when evaluated at any finite set of $N$ points, are $\mathbb{R}^N$-valued Gaussians. The algorithmic approach that we describe is applicable not only when the desired probability measure has density with respect to a Gaussian process or Gaussian random field reference measure, but also to some useful non-Gaussian reference measures constructed through random truncation. In the applications of interest the data is often sparse and the prior specification is an essential part of the overall modelling strategy. These Gaussian-based reference measures are a very flexible modelling tool, finding wide-ranging application. Examples are shown in density estimation, data assimilation in fluid mechanics, subsurface geophysics and image registration. The key design principle is to formulate the MCMC method so that it is, in principle, applicable for functions; this may be achieved by use of proposals based on carefully chosen time-discretizations of stochastic dynamical systems which exactly preserve the Gaussian reference measure. Taking this approach leads to many new algorithms which can be implemented via minor modification of existing algorithms, yet which show enormous speed-up on a wide range of applied problems.Comment: Published in at http://dx.doi.org/10.1214/13-STS421 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

In this paper we present an X-ray image deprojection analysis of EINSTEIN OBSERVATORY imaging data on 207 clusters of galaxies. The resulting radial profiles for luminosity, temperature, and electron density variations are determined from the cluster surface-brightness profiles according to gravitational potential constraints from average X-ray temperatures and optical velocity dispersions. This enables us to determine cooling-flow and other cluster properties, such as baryon fractions, Sunyaev-Zeldovich microwave decrements, and Thomson depths. From the results, we have compiled a catalogue of the detected cooling flows, and investigated their effects on general cluster properties. To assist in the analysis, we have constructed self-consistent correlations between the cluster X-ray luminosity, temperature, and optical velocity-dispersion, using 'orthogonal distance' regression to account for errors in both dimensions of the data. These fits indicate that, in general, the temperatures of clusters are isothermal and that they have spectral β-values consistent with unity.We find that the X-ray luminosity, temperature, and optical velocity dispersion relations depend significantly on the cooling flow mass-deposition rate, through characteristic differences in the density profiles. Clusters of similar cooling flow mass-deposition rate exhibit self-similar density profiles, with larger cooling flows showing higher central densities. This leads to scatter in the luminosity related correlations within the X-ray luminosity, temperature and optical velocity dispersion plane. The segregation in density also leads to dispersion in other related properties such as 'half-light radii' and baryon fractions. The baryon fraction in the cores of cooling flow clusters appears to be higher, but as the density profiles tend to a similar value at larger radii, irrespective of cooling flow property, so too do the baryon fraction profiles appear to rise to a concordant value of greater than 10 percent at 1 Mpc. Thus, this sample indicates that clusters, as a whole, are inconsistent with primordial nucleosynthesis baryon fraction prediction, for a flat Universe, of 6 percent.

A B S T R A C TIn Paper I we presented a methodology to recover the spatial variations of properties of the intracluster gas from ASCA X-ray satellite observations of galaxy clusters. We verified the correctness of this procedure by applying it to simulated cluster data sets that we had subjected to the various contaminants common in ASCA data. In this paper we present the results that we obtain when we apply this method to real galaxy cluster observations. We determine broad-band temperature and cooling-flow mass-deposition rates for the 106 clusters in our sample, and obtain temperature, abundance and emissivity profiles (i.e., at least two annular bins) for 98 of these clusters. We find that 90 per cent of these temperature profiles are consistent with isothermality at the 3s confidence level. This conflicts with the prevalence of steeply declining cluster temperature profiles found by Markevitch et al. from a sample of 30 clusters.

Lee S, Deldin AR, White D, Kim Y, Libman I, Rivera-Vega M, Kuk JL, Sandoval S, Boesch C, Arslanian S. Aerobic exercise but not resistance exercise reduces intrahepatic lipid content and visceral fat and improves insulin sensitivity in obese adolescent girls: a randomized controlled trial. Am J Physiol Endocrinol Metab 305: E1222-E1229, 2013. First published September 17, 2013; doi:10.1152/ajpendo.00285.2013.-It is unclear whether regular exercise alone (no caloric restriction) is a useful strategy to reduce adiposity and obesity-related metabolic risk factors in obese girls. We examined the effects of aerobic (AE) vs. resistance exercise (RE) alone on visceral adipose tissue (VAT), intrahepatic lipid, and insulin sensitivity in obese girls. Forty-four obese adolescent girls (BMI Ն95th percentile, 12-18 yr) with abdominal obesity (waist circumference 106.5 Ϯ 11.1 cm) were randomized to 3 mo of 180 min/wk AE (n ϭ 16) or RE (n ϭ 16) or a nonexercising control group (n ϭ 12). Total fat and VAT were assessed by MRI and intrahepatic lipid by proton magnetic resonance spectroscopy. Intermuscular AT (IMAT) was measured by CT. Insulin sensitivity was evaluated by a 3-h hyperinsulinemic (80 mU·m 2 ·min Ϫ1 ) euglycemic clamp. Compared with controls (0.13 Ϯ 1.10 kg), body weight did not change (P Ͼ 0.1) in the AE (Ϫ1.31 Ϯ 1.43 kg) and RE (Ϫ0.31 Ϯ 1.38 kg) groups. Despite the absence of weight loss, total body fat (%) and IMAT decreased (P Ͻ 0.05) in both exercise groups compared with control. Compared with control, significant (P Ͻ 0.05) reductions in VAT (⌬Ϫ15.68 Ϯ 7.64 cm 2 ) and intrahepatic lipid (⌬Ϫ1.70 Ϯ 0.74%) and improvement in insulin sensitivity (⌬0.92 Ϯ 0.27 mg·kg Ϫ1 ·min Ϫ1 per U/ml) were observed in the AE group but not the RE group. Improvements in insulin sensitivity in the AE group were associated with the reductions in total AT mass (r ϭ Ϫ0.65, P ϭ 0.02). In obese adolescent girls, AE but not RE is effective in reducing liver fat and visceral adiposity and improving insulin sensitivity independent of weight loss or calorie restriction. insulin sensitivity; intrahepatic lipid; visceral fat; exercise; adolescents THE EPIDEMIC RATE OF CHILDHOOD OBESITY is a major health concern in the US, as overweight and obese youth are at increased risk of developing comorbidities such as nonalcoholic fatty liver disease (35), type 2 diabetes (33), and metabolic syndrome (21, 41), once considered diseases of adulthood. Although both diet and physical activity are considered to be the first lines of approach to treat obese youth (9), we recently reported that, in obese adolescent boys, increasing physical activity alone, independent of calorie restriction, is beneficial to reduce total fat, visceral adiposity, and intrahepatic lipid and improves cardiorespiratory fitness (CRF) (22). In obese adolescent girls, the utility of exercise alone as a strategy for reducing obesity-related metabolic risk factors is currently unclear. Given the lower physical activity levels in girls than in boys (14) and the fact that physical activi...

We analyse the X-ray surface brightness profiles of 19 moderately distant and luminous clusters of galaxies observed with the Einstein Observatory . Our aim is to determine cluster gas masses out to radii between 1 and 3 Mpc, and to confirm the apparent conflict, if Ω 0 = 1, between the current calculations of the mean baryon fraction of the Universe expected from standard primordial nucleosynthesis, and the fraction of the mass in clusters which is in gas. Our analysis shows that baryon overdensities in clusters are much more widespread than only the Coma cluster with which S. White & Frenk originally highlighted this problem. The uncertainties involved in our analysis and some cosmological implications from our results are briefly discussed. For a refined sample of 13 clusters we find that the baryon fraction for the gas within 1 Mpc lies between 10 and 22 per cent.