This paper presents a multifractal analysis of EcoSim, a large evolving ecosystem simulation. Multifractal analysis of ecosystem time series using the Rényi fractal dimension spectrum demonstrates a self-similarity characteristic for a complex ecosystem. Results suggest the applicability of Rényi dimensions spectra to individuals' spatial distribution characterization for modeling empirical dat...

We study matchings on sparse random graphs by means of the cavity method. We first show how the method reproduces several known results about maximum and perfect matchings in regular and Erdös-Rényi random graphs. Our main new result is the computation of the entropy, i.e. the leading order of the logarithm of the number of solutions, of matchings with a given size. We derive both an algorithm ...

In this paper we obtain new bounds for the minimum output entropies of random quantum channels. These bounds rely on random matrix techniques arising from free probability theory. We then revisit the counterexamples developed by Hayden and Winter to get violations of the additivity equalities for minimum output Rényi entropies. We show that random channels obtained by randomly coupling the inpu...

Supersymmetric Rényi entropies are defined for three-dimensional N = 2 superconformal field theories on a branched covering of a three-sphere by using the localized partition functions. Under a conformal transformation, the branched covering is mapped to S1 × H2, whose gravity dual is the charged topological AdS4 black hole. The black hole can be embedded into four-dimensional N = 2 gauged supe...

It is known that the security evaluation can be done by smoothing of Rényi entropy of order 2 in the classical and quantum settings when we apply universal2 hash functions. Using the smoothing of Rényi entropy of order 2, we derive security bounds for L1 distinguishability and modified mutual information criterion under the classical and quantum setting, and have derived these exponential decre...