A reciprocity for symmetric algebras

The aim of this note is to show, that the reciprocity property of group algebras in [5, (11.5)] can be deduced from formal properties of symmetric algebras, as exposed in [1], for instance

Investigating the Relation between Galaxy Properties and the Gaussianity of the Velocity Distribution of Groups and Clusters

We investigate the dependence of stellar population properties of galaxies on group dynamical stage for a subsample of Yang catalog. We classify groups according to their galaxy velocity distribution into Gaussian (G) and Non-Gaussian (NG). Using two totally independent approaches we have shown that our measurement of Gaussianity is robust and reliable. Our sample covers Yang's groups in the redshift range 0.03 $\leq$ z $\leq$ 0.1 having mass $\geq$ 10$^{14} \rm M_{\odot}$. The new method, Hellinger Distance (HD), to determine whether a group has a velocity distribution Gaussian or Non-Gaussian is very effective in distinguishing between the two families. NG groups present halo masses higher than the G ones, confirming previous findings. Examining the Skewness and Kurtosis of the velocity distribution of G and NG groups, we find that faint galaxies in NG groups are mainly infalling for the first time into the groups. We show that considering only faint galaxies in the outskirts, those in NG groups are older and more metal rich than the ones in G groups. Also, examining the Projected Phase Space of cluster galaxies we see that bright and faint galactic systems in G groups are in dynamical equilibrium which does not seem to be the case in NG groups. These findings suggest that NG systems have a higher infall rate, assembling more galaxies which experienced preprocessing before entering the group.Comment: 55 pages, 5 Tables and 12 Figures. Accepted for publication in Astronomical Journa

Localization Recall Precision (LRP): A New Performance Metric for Object Detection

Average precision (AP), the area under the recall-precision (RP) curve, is the standard performance measure for object detection. Despite its wide acceptance, it has a number of shortcomings, the most important of which are (i) the inability to distinguish very different RP curves, and (ii) the lack of directly measuring bounding box localization accuracy. In this paper, we propose 'Localization Recall Precision (LRP) Error', a new metric which we specifically designed for object detection. LRP Error is composed of three components related to localization, false negative (FN) rate and false positive (FP) rate. Based on LRP, we introduce the 'Optimal LRP', the minimum achievable LRP error representing the best achievable configuration of the detector in terms of recall-precision and the tightness of the boxes. In contrast to AP, which considers precisions over the entire recall domain, Optimal LRP determines the 'best' confidence score threshold for a class, which balances the trade-off between localization and recall-precision. In our experiments, we show that, for state-of-the-art object (SOTA) detectors, Optimal LRP provides richer and more discriminative information than AP. We also demonstrate that the best confidence score thresholds vary significantly among classes and detectors. Moreover, we present LRP results of a simple online video object detector which uses a SOTA still image object detector and show that the class-specific optimized thresholds increase the accuracy against the common approach of using a general threshold for all classes. At https://github.com/cancam/LRP we provide the source code that can compute LRP for the PASCAL VOC and MSCOCO datasets. Our source code can easily be adapted to other datasets as well.Comment: to appear in ECCV 201

The Evolution of the Intracluster Medium Metallicity in Sunyaev-Zel'dovich-Selected Galaxy Clusters at 0 < z < 1.5

We present the results of an X-ray spectral analysis of 153 galaxy clusters observed with the Chandra, XMM-Newton, and Suzaku space telescopes. These clusters, which span 0 < z < 1.5, were drawn from a larger, mass-selected sample of galaxy clusters discovered in the 2500 square degree South Pole Telescope Sunyaev Zel'dovich (SPT-SZ) survey. With a total combined exposure time of 9.1 Ms, these data yield the strongest constraints to date on the evolution of the metal content of the intracluster medium (ICM). We find no evidence for strong evolution in the global (r<R500) ICM metallicity (dZ/dz = -0.06 +/- 0.04 Zsun), with a mean value at z=0.6 of = 0.23 +/- 0.01 Zsun and a scatter of 0.08 +/- 0.01 Zsun. These results imply that >60% of the metals in the ICM were already in place at z=1 (at 95% confidence), consistent with the picture of an early (z>1) enrichment. We find, in agreement with previous works, a significantly higher mean value for the metallicity in the centers of cool core clusters versus non-cool core clusters. We find weak evidence for evolution in the central metallicity of cool core clusters (dZ/dz = -0.21 +/- 0.11 Zsun), which is sufficient to account for this enhanced central metallicity over the past ~10 Gyr. We find no evidence for metallicity evolution outside of the core (dZ/dz = -0.03 +/- 0.06 Zsun), and no significant difference in the core-excised metallicity between cool core and non-cool core clusters. This suggests that strong radio-mode AGN feedback does not significantly alter the distribution of metals at r>0.15R500. Given the limitations of current-generation X-ray telescopes in constraining the ICM metallicity at z>1, significant improvements on this work will likely require next-generation X-ray missions.Comment: 11 pages, 8 figures, 2 tables. Submitted to ApJ. Comments welcome

Star-Forming Brightest Cluster Galaxies at 0.25 < z < 1.25: A Transitioning Fuel Supply

We present a multi-wavelength study of 90 brightest cluster galaxies (BCGs) in a sample of galaxy clusters selected via the Sunyaev Zel'dovich effect by the South Pole Telescope, utilizing data from various ground- and space-based facilities. We infer the star formation rate (SFR) for the BCG in each cluster, based on the UV and IR continuum luminosity, as well as the [O II] emission line luminosity in cases where spectroscopy is available, finding 7 systems with SFR > 100 Msun/yr. We find that the BCG SFR exceeds 10 Msun/yr in 31 of 90 (34%) cases at 0.25 < z < 1.25, compared to ~1-5% at z ~ 0 from the literature. At z > 1, this fraction increases to 92(+6)(-31)%, implying a steady decrease in the BCG SFR over the past ~9 Gyr. At low-z, we find that the specific star formation rate in BCGs is declining more slowly with time than for field or cluster galaxies, most likely due to the replenishing fuel from the cooling ICM in relaxed, cool core clusters. At z > 0.6, the correlation between cluster central entropy and BCG star formation - which is well established at z ~ 0 - is not present. Instead, we find that the most star-forming BCGs at high-z are found in the cores of dynamically unrelaxed clusters. We investigate the rest-frame near-UV morphology of a subsample of the most star-forming BCGs using data from the Hubble Space Telescope, finding complex, highly asymmetric UV morphologies on scales as large as ~50-60 kpc. The high fraction of star-forming BCGs hosted in unrelaxed, non-cool core clusters at early times suggests that the dominant mode of fueling star formation in BCGs may have recently transitioned from galaxy-galaxy interactions to ICM cooling.Comment: 20 pages, 10 figures. Submitted for publication in ApJ. Comments welcom

Optical followup of galaxy clusters detected by the South Pole Telescope

The South Pole Telescope (SPT) is a 10 meter telescope operating at mm wavelengths. It has recently completed a three-band survey covering 2500 sq. degrees. One of the survey's main goals is to detect galaxy clusters using Sunyaev-Zeldovich effect and use these clusters for a variety of cosmological and astrophysical studies such as the dark energy equation of state, the primordial non-gaussianity and the evolution of galaxy populations. Since 2005, we have been engaged in a comprehensive optical and near-infrared followup program (at wavelengths between 0.4 and 5 {\mu}m) to image high-significance SPT clusters, to measure their photometric redshifts, and to estimate the contamination rate of the candidate lists. These clusters are then used for various cosmological and astrophysical studies.Comment: For TAUP 2011 proceeding