477 research outputs found

    How long does it take to compute the eigenvalues of a random symmetric matrix?

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    We present the results of an empirical study of the performance of the QR algorithm (with and without shifts) and the Toda algorithm on random symmetric matrices. The random matrices are chosen from six ensembles, four of which lie in the Wigner class. For all three algorithms, we observe a form of universality for the deflation time statistics for random matrices within the Wigner class. For these ensembles, the empirical distribution of a normalized deflation time is found to collapse onto a curve that depends only on the algorithm, but not on the matrix size or deflation tolerance provided the matrix size is large enough (see Figure 4, Figure 7 and Figure 10). For the QR algorithm with the Wilkinson shift, the observed universality is even stronger and includes certain non-Wigner ensembles. Our experiments also provide a quantitative statistical picture of the accelerated convergence with shifts.Comment: 20 Figures; Revision includes a treatment of the QR algorithm with shift

    Deep Learning Transient Detection with VERITAS

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    Ground-based γ\gamma-ray observatories, such as the VERITAS array of imaging atmospheric Cherenkov telescopes, provide insight into very-high-energy (VHE, E>100 GeV\mathrm{E}>100\,\mathrm{GeV}) astrophysical transient events. Examples include the evaporation of primordial black holes, gamma-ray bursts and flaring blazars. Identifying such events with a serendipitous location and time of occurrence is difficult. Thus, employing a robust search method becomes crucial. An implementation of a transient detection method based on deep-learning techniques for VERITAS will be presented. This data-driven approach significantly reduces the dependency on the characterization of the instrument response and the modelling of the expected transient signal. The response of the instrument is affected by various factors, such as the elevation of the source and the night sky background. The study of these effects allows enhancing the deep learning method with additional parameters to infer their influences on the data. This improves the performance and stability for a wide range of observational conditions. We illustrate our method for an historic flare of the blazar BL Lac that was detected by VERITAS in October 2016. We find a promising performance for the detection of such a flare in timescales of minutes that compares well with the VERITAS standard analysis.Comment: Proceedings of the 37th International Cosmic Ray Conference (ICRC 2021
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