DisC Diversity: Result Diversification based on Dissimilarity and Coverage

Recently, result diversification has attracted a lot of attention as a means to improve the quality of results retrieved by user queries. In this paper, we propose a new, intuitive definition of diversity called DisC diversity. A DisC diverse subset of a query result contains objects such that each object in the result is represented by a similar object in the diverse subset and the objects in the diverse subset are dissimilar to each other. We show that locating a minimum DisC diverse subset is an NP-hard problem and provide heuristics for its approximation. We also propose adapting DisC diverse subsets to a different degree of diversification. We call this operation zooming. We present efficient implementations of our algorithms based on the M-tree, a spatial index structure, and experimentally evaluate their performance.Comment: To appear at the 39th International Conference on Very Large Data Bases (VLDB), August 26-31, 2013, Riva del Garda, Trento, Ital

A ratio ergodic theorem for multiparameter non-singular actions

We prove a ratio ergodic theorem for non-singular free $Z^d$ and $R^d$ actions, along balls in an arbitrary norm. Using a Chacon-Ornstein type lemma the proof is reduced to a statement about the amount of mass of a probability measure that can concentrate on (thickened) boundaries of balls in $R^d$. The proof relies on geometric properties of norms, including the Besicovitch covering lemma and the fact that boundaries of balls have lower dimension than the ambient space. We also show that for general group actions, the Besicovitch covering property not only implies the maximal inequality, but is equivalent to it, implying that further generalization may require new methods.Comment: 21 pages, to appear in JEM

Understanding large-scale structure in the SSA22 protocluster region using cosmological simulations

We investigate the nature and evolution of large-scale structure within the SSA22 protocluster region at $z=3.09$ using cosmological simulations. A redshift histogram constructed from current spectroscopic observations of the SSA22 protocluster reveals two separate peaks at $z = 3.065$ (blue) and $z = 3.095$ (red). Based on these data, we report updated overdensity and mass calculations for the SSA22 protocluster. We find $\delta_{b,gal}=4.8 \pm 1.8$, $\delta_{r,gal}=9.5 \pm 2.0$ for the blue and red peaks, respectively, and $\delta_{t,gal}=7.6\pm 1.4$ for the entire region. These overdensities correspond to masses of $M_b = (0.76 \pm 0.17) \times 10^{15} h^{-1} M_{\odot}$, $M_r = (2.15 \pm 0.32) \times 10^{15} h^{-1} M_{\odot}$, and $M_t=(3.19 \pm 0.40) \times 10^{15} h^{-1} M_{\odot}$ for the red, blue, and total peaks, respectively. We use the Small MultiDark Planck (SMDPL) simulation to identify comparably massive $z\sim 3$ protoclusters, and uncover the underlying structure and ultimate fate of the SSA22 protocluster. For this analysis, we construct mock redshift histograms for each simulated $z\sim 3$ protocluster, quantitatively comparing them with the observed SSA22 data. We find that the observed double-peaked structure in the SSA22 redshift histogram corresponds not to a single coalescing cluster, but rather the proximity of a $\sim 10^{15}h^{-1} M_{\odot}$ protocluster and at least one $>10^{14} h^{-1} M_{\odot}$ cluster progenitor. Such associations in the SMDPL simulation are easily understood within the framework of hierarchical clustering of dark matter halos. We finally find that the opportunity to observe such a phenomenon is incredibly rare, with an occurrence rate of 7.4h^3 \mbox{ Gpc}^{-3}.Comment: 13 pages, 8 figures, Accepted to Ap

Structure of the Milky Way stellar halo out to its outer boundary with blue horizontal-branch stars

We present the structure of the Milky Way stellar halo beyond Galactocentric distances of $r = 50$ kpc traced by blue horizontal-branch (BHB) stars, which are extracted from the survey data in the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP). We select BHB candidates based on $(g,r,i,z)$ photometry, where the $z$-band is on the Paschen series and the colors that involve the $z$-band are sensitive to surface gravity. About 450 BHB candidates are identified between $r = 50$ kpc and 300 kpc, most of which are beyond the reach of previous large surveys including the Sloan Digital Sky Survey. We find that the global structure of the stellar halo in this range has substructures, which are especially remarkable in the GAMA15H and XMM-LSS fields in the HSC-SSP. We find that the stellar halo can be fitted to a single power-law density profile with an index of $\alpha \simeq 3.3$ ($3.5$) with (without) these fields and its global axial ratio is $q \simeq 2.2$ ($1.3$). Thus, the stellar halo may be significantly disturbed and be made in a prolate form by halo substructures, perhaps associated with the Sagittarius stream in its extension beyond $r \sim 100$ kpc. For a broken power-law model allowing different power-law indices inside/outside a break radius, we obtain a steep power-law slope of $\alpha \sim 5$ outside a break radius of $\simeq 100$ kpc ($200$ kpc) for the case with (without) GAMA15H and XMM-LSS. This radius of $200$ kpc might be as close as a halo boundary if there is any, although larger BHB sample is required from further HSC-SSP survey to increase its statistical significance.Comment: 12 pages, 8 figures, revised version, accepted for publication in PAS

Ram Selection and Ewe Culling

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