Searching for γ\gamma-ray signature in WHSP blazars: Fermi-LAT detection of 150 excess signal in the 0.3-500 GeV band

A direct search of $\gamma$-ray emission centered on multi-frequency selected candidates is a valuable complementary approach to the standard search adopted in current $\gamma$-ray Fermi-LAT catalogs. Our candidates are part of the 2WHSP sample, that was assembled with the aim of providing targets for Imaging Atmospheric Cherenkov Telescopes (IACT), and is currently the largest set of high synchrotron peaked (HSP) blazars. We perform a likelihood analysis with the Fermi Science Tools using positions from 400 2WHSP blazars as seeds of tentative $\gamma$-ray sources. This enabled us to detect 150 $\gamma$-ray excess signals that have not yet been reported in previous $\gamma$-ray catalogs (1FGL, 2FGL, and 3FGL). By identifying new sources, we solve a fraction of the extragalactic isotropic $\gamma$-ray background (IGRB) composition, improving the description of the $\gamma$-ray sky. Our analysis considers the 0.3-500 GeV energy band, integrating over 7.2 yrs of Fermi-LAT observation and making use of the Pass 8 data release. Within the 150 2WHSPs that showed excess $\gamma$-ray signature: 85 are high-significance detections with test statistic (TS)$>$25, and 65 are lower-significance detections with TS between 10 to 25. We study the $\gamma$-ray photon spectral index distribution, the likelihood of detection according to the synchrotron peak brightness, and plot the measured $\gamma$-ray LogN-LogS of HSP blazars, also discussing the portion of the IGRB that has been resolved by this work. We report on four cases where we could resolve source confusion and find counterparts for unassociated 3FGL sources with the help of high-energy TS maps together with multi-frequency data. The 150 new $\gamma$-ray sources are named with the acronym 1BIGB for the first version of the Brazil ICRANet Gamma-ray Blazar catalog, in reference to the cooperation agreement supporting this work.Comment: Accepted for publication in A&A: September 01, 201

Achievable Angles Between two Compressed Sparse Vectors Under Norm/Distance Constraints Imposed by the Restricted Isometry Property: A Plane Geometry Approach

The angle between two compressed sparse vectors subject to the norm/distance constraints imposed by the restricted isometry property (RIP) of the sensing matrix plays a crucial role in the studies of many compressive sensing (CS) problems. Assuming that (i) u and v are two sparse vectors separated by an angle thetha, and (ii) the sensing matrix Phi satisfies RIP, this paper is aimed at analytically characterizing the achievable angles between Phi*u and Phi*v. Motivated by geometric interpretations of RIP and with the aid of the well-known law of cosines, we propose a plane geometry based formulation for the study of the considered problem. It is shown that all the RIP-induced norm/distance constraints on Phi*u and Phi*v can be jointly depicted via a simple geometric diagram in the two-dimensional plane. This allows for a joint analysis of all the considered algebraic constraints from a geometric perspective. By conducting plane geometry analyses based on the constructed diagram, closed-form formulae for the maximal and minimal achievable angles are derived. Computer simulations confirm that the proposed solution is tighter than an existing algebraic-based estimate derived using the polarization identity. The obtained results are used to derive a tighter restricted isometry constant of structured sensing matrices of a certain kind, to wit, those in the form of a product of an orthogonal projection matrix and a random sensing matrix. Follow-up applications to three CS problems, namely, compressed-domain interference cancellation, RIP-based analysis of the orthogonal matching pursuit algorithm, and the study of democratic nature of random sensing matrices are investigated.Comment: submitted to IEEE Trans. Information Theor