Constraining Dark Energy with X-ray Galaxy Clusters, Supernovae and the Cosmic Microwave Background

We present new constraints on the evolution of dark energy from an analysis of Cosmic Microwave Background, supernova and X-ray galaxy cluster data. Our analysis employs a minimum of priors and exploits the complementary nature of these data sets. We examine a series of dark energy models with up to three free parameters: the current dark energy equation of state w_0, the early time equation of state w_et and the scale factor at transition, a_t. From a combined analysis of all three data sets, assuming a constant equation of state and that the Universe is flat, we measure w_0=-1.05+0.10-0.12. Including w_et as a free parameter and allowing a_t to vary over the range 0.5<a_t<0.95 where the data sets have discriminating power, we measure w_0=-1.27+0.33-0.39 and w_et=-0.66+0.44-0.62. We find no significant evidence for evolution in the dark energy equation of state parameter with redshift. Marginal hints of evolution in the supernovae data become less significant when the cluster constraints are also included in the analysis. The complementary nature of the data sets leads to a tight constraint on the mean matter density, Omega_m and alleviates a number of other parameter degeneracies, including that between the scalar spectral index n_s, the physical baryon density Omega_bh^2 and the optical depth tau. This complementary nature also allows us to examine models in which we drop the prior on the curvature. For non-flat models with a constant equation of state, we measure w_0=-1.09+0.12-0.15 and Omega_de=0.70+-0.03. Our analysis includes spatial perturbations in the dark energy fluid, assuming a sound speed c_s^2 =1. For our most general dark energy model, not including such perturbations would lead to spurious constraints on w_et which would be tighter by approximately a factor two with the current data. (abridged)Comment: 11 pages, 13 figures, 2 tables. Accepted for publication in MNRAS. Two new figures added: Fig.9 shows the effects of including dark energy perturbations and Fig.10 compares X-ray cluster data with 2dF dat

Graduate Recital

The writer, having performed all of Weber\u27s concertos and Johannes Brahms\u27 Sonata in F Minor, found it necessary to adopt a change of style and concept in learning and performing the Mozart concerto. The light, flowing style of the young musical genius is a contrast indeed to the flamboyant flagrancy of Weber. Mozart\u27s conception of the phrase, the musical line, the completeness of each melodic statement varies in large measure from that of Carl von Weber and Johannes Brahms

Area and Length Minimizing Flows for Shape Segmentation

©1997 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or distribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.Presented at the 1997 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, June 17-19, 1997, San Juan, Puerto Rico.DOI: 10.1109/CVPR.1997.609390Several active contour models have been proposed to unify the curve evolution framework with classical energy minimization techniques for segmentation, such as snakes. The essential idea is to evolve a curve (in 20) or a surface (in 30) under constraints from image forces so that it clings to features of interest in an intensity image. Recently the evolution equation has. been derived from first principles as the gradient flow that minimizes a modified length functional, tailored io features such as edges. However, because the flow may be slow to converge in practice, a constant (hyperbolic) term is added to keep the curve/surface moving in the desired direction. In this paper, we provide a justification for this term based on the gradient flow derived from a weighted area functional, with image dependent weighting factor. When combined with the earlier modified length gradient flow we obtain a pde which offers a number of advantages, as illustrated by several examples of shape segmentation on medical images. In many cases the weighted area flow may be used on its own, with significant computational savings

Implicit Priors in Galaxy Cluster Mass and Scaling Relation Determinations

Deriving the total masses of galaxy clusters from observations of the intracluster medium (ICM) generally requires some prior information, in addition to the assumptions of hydrostatic equilibrium and spherical symmetry. Often, this information takes the form of particular parametrized functions used to describe the cluster gas density and temperature profiles. In this paper, we investigate the implicit priors on hydrostatic masses that result from this fully parametric approach, and the implications of such priors for scaling relations formed from those masses. We show that the application of such fully parametric models of the ICM naturally imposes a prior on the slopes of the derived scaling relations, favoring the self-similar model, and argue that this prior may be influential in practice. In contrast, this bias does not exist for techniques which adopt an explicit prior on the form of the mass profile but describe the ICM non-parametrically. Constraints on the slope of the cluster mass--temperature relation in the literature show a separation based the approach employed, with the results from fully parametric ICM modeling clustering nearer the self-similar value. Given that a primary goal of scaling relation analyses is to test the self-similar model, the application of methods subject to strong, implicit priors should be avoided. Alternative methods and best practices are discussed.Comment: 11 pages, 4 figures, 2 tables. Submitted to MNRA