783 research outputs found

    Intermittent process analysis with scattering moments

    Full text link
    Scattering moments provide nonparametric models of random processes with stationary increments. They are expected values of random variables computed with a nonexpansive operator, obtained by iteratively applying wavelet transforms and modulus nonlinearities, which preserves the variance. First- and second-order scattering moments are shown to characterize intermittency and self-similarity properties of multiscale processes. Scattering moments of Poisson processes, fractional Brownian motions, L\'{e}vy processes and multifractal random walks are shown to have characteristic decay. The Generalized Method of Simulated Moments is applied to scattering moments to estimate data generating models. Numerical applications are shown on financial time-series and on energy dissipation of turbulent flows.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1276 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

    Exact solutions for the two- and all-terminal reliabilities of the Brecht-Colbourn ladder and the generalized fan

    Full text link
    The two- and all-terminal reliabilities of the Brecht-Colbourn ladder and the generalized fan have been calculated exactly for arbitrary size as well as arbitrary individual edge and node reliabilities, using transfer matrices of dimension four at most. While the all-terminal reliabilities of these graphs are identical, the special case of identical edge (pp) and node (ρ\rho) reliabilities shows that their two-terminal reliabilities are quite distinct, as demonstrated by their generating functions and the locations of the zeros of the reliability polynomials, which undergo structural transitions at ρ=1/2\rho = \displaystyle {1/2}

    Network clustering and community detection using modulus of families of loops

    Get PDF
    Citation: Shakeri, H., Poggi-Corradini, P., Albin, N., & Scoglio, C. (2017). Network clustering and community detection using modulus of families of loops. Physical Review E, 95(1), 7. doi:10.1103/PhysRevE.95.012316We study the structure of loops in networks using the notion of modulus of loop families. We introduce an alternate measure of network clustering by quantifying the richness of families of (simple) loops. Modulus tries to minimize the expected overlap among loops by spreading the expected link usage optimally. We propose weighting networks using these expected link usages to improve classical community detection algorithms. We show that the proposed method enhances the performance of certain algorithms, such as spectral partitioning and modularity maximization heuristics, on standard benchmarks
    corecore