8,578 research outputs found

    On Multistage Learning a Hidden Hypergraph

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    Learning a hidden hypergraph is a natural generalization of the classical group testing problem that consists in detecting unknown hypergraph Hun=H(V,E)H_{un}=H(V,E) by carrying out edge-detecting tests. In the given paper we focus our attention only on a specific family F(t,s,)F(t,s,\ell) of localized hypergraphs for which the total number of vertices V=t|V| = t, the number of edges Es|E|\le s, sts\ll t, and the cardinality of any edge e|e|\le\ell, t\ell\ll t. Our goal is to identify all edges of HunF(t,s,)H_{un}\in F(t,s,\ell) by using the minimal number of tests. We develop an adaptive algorithm that matches the information theory bound, i.e., the total number of tests of the algorithm in the worst case is at most slog2t(1+o(1))s\ell\log_2 t(1+o(1)). We also discuss a probabilistic generalization of the problem.Comment: 5 pages, IEEE conferenc

    Additional spectroscopic redshift measurements for galaxy clusters from the First Planck Catalogue

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    We present the results of spectroscopic redshift measurements for the galaxy clusters from the first all-sky Planck catalogue of the Sunyaev-Zeldovich sources, that have been mostly identified by means of the optical observations performed previously by our team (Planck Collaboration, 2015a). The data on 13 galaxy clusters at redshifts from z=~0.2 to z=~0.8, including the improved identification and redshift measurement for the cluster PSZ1 G141.73+14.22 at z=0.828, are provided. The measurements were done using the data from Russian-Turkish 1.5-m telescope (RTT-150), 2.2-m Calar Alto Observatory telescope, and 6-m SAO RAS telescope (Bolshoy Teleskop Azimutalnyi, BTA).Comment: published in Astronomy Letter
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