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Following the theory of information measures based on the cumulative distribution function, we propose the fractional generalized cumulative entropy, and its dynamic version. These entropies are particularly suitable to deal with…

Probability · Mathematics 2021-06-30 Antonio Di Crescenzo , Suchandan Kayal , Alessandra Meoli

Generalised degrees provide a natural bridge between local and global topological properties of networks. We define the generalised degree to be the number of neighbours of a node within one and two steps respectively. Tailored random graph…

Disordered Systems and Neural Networks · Physics 2013-09-17 Ekaterina S. Roberts , Anthonius C. C. Coolen

A strengthened version of the central limit theorem for discrete random variables is established, relying only on information-theoretic tools and elementary arguments. It is shown that the relative entropy between the standardised sum of…

Probability · Mathematics 2021-06-02 Lampros Gavalakis , Ioannis Kontoyiannis

Estimators of information theoretic measures such as entropy and mutual information are a basic workhorse for many downstream applications in modern data science. State of the art approaches have been either geometric (nearest neighbor (NN)…

Information Theory · Computer Science 2016-09-09 Weihao Gao , Sewoong Oh , Pramod Viswanath

This paper introduces "swiveled Renyi entropies" as an alternative to the Renyi entropic quantities put forward in [Berta et al., Phys. Rev. A 91, 022333 (2015)]. What distinguishes the swiveled Renyi entropies from the prior proposal of…

Quantum Physics · Physics 2016-03-22 Frédéric Dupuis , Mark M. Wilde

We define the class of multivariate group entropies as a novel set of information - theoretical measures, which extends significantly the family of group entropies. We propose new examples related to the "super-exponential" universality…

Mathematical Physics · Physics 2020-12-03 Piergiulio Tempesta

Gaussian mixture distributions are commonly employed to represent general probability distributions. Despite the importance of using Gaussian mixtures for uncertainty estimation, the entropy of a Gaussian mixture cannot be calculated…

Machine Learning · Statistics 2025-01-23 Takashi Furuya , Hiroyuki Kusumoto , Koichi Taniguchi , Naoya Kanno , Kazuma Suetake

Transfer entropy provides a general tool for analyzing the magnitudes and directions---but not the \emph{kinds}---of information transfer in a system. We extend transfer entropy in two complementary ways. First, we distinguish…

Data Analysis, Statistics and Probability · Physics 2011-02-09 Paul L. Williams , Randall D. Beer

In [Gallego and Aolita, Physical Review X 5, 041008 (2015)], the authors proposed a definition for the relative entropy of steering and showed that the resulting quantity is a convex steering monotone. Here we advocate for a different…

Quantum Physics · Physics 2017-10-24 Eneet Kaur , Mark M. Wilde

We study the relative entropy density for generalized Gibbs measures. We first show its existence and obtain a familiar expression in terms of entropy and relative energy for a class of ``almost Gibbsian measures'' (almost sure continuity…

Probability · Mathematics 2007-05-23 Christof Kulske , Arnaud Le Ny , Frank Redig

We generalize the topological entanglement entropy to a family of topological Renyi entropies parametrized by a parameter alpha, in an attempt to find new invariants for distinguishing topologically ordered phases. We show that,…

Strongly Correlated Electrons · Physics 2010-01-05 Steven T. Flammia , Alioscia Hamma , Taylor L. Hughes , Xiao-Gang Wen

We consider the one-parameter family of interval maps arising from generalized continued fraction expansions known as alpha-continued fractions. For such maps, we perform a numerical study of the behaviour of metric entropy as a function of…

Dynamical Systems · Mathematics 2015-05-14 Carlo Carminati , Stefano Marmi , Alessandro Profeti , Giulio Tiozzo

For discrete-time stochastic processes, there is a close connection between return/waiting times and entropy. Such a connection cannot be straightforwardly extended to the continuous-time setting. Contrarily to the discrete-time case one…

Probability · Mathematics 2007-05-23 Jean-Rene Chazottes , Cristian Giardina , Frank Redig

This is a review on entropy in various fields of mathematics and science. Its scope is to convey a unified vision of the classical as well as some newer entropy notions to a broad audience with an intermediate background in dynamical…

Dynamical Systems · Mathematics 2022-02-08 José M. Amigó , Karsten Keller , Valentina Unakafova

Entropy and information can be considered dual: entropy is a measure of the subspace defined by the information constraining the given ambient space. Negative entropies, arising in na\"ive extensions of the definition of entropy from…

Probability · Mathematics 2023-03-06 Daniel Lazarev

We study the effect of the choice of embedding geometry on the entropy of random geometric graph ensembles with soft connection functions. First we show that when the connection range is small, the entropy is dependent only on the dimension…

Probability · Mathematics 2026-01-22 Oliver Baker , Carl P. Dettmann

We present a general approach to the study of the local distribution of measures on Euclidean spaces, based on local entropy averages. As concrete applications, we unify, generalize, and simplify a number of recent results on local…

Classical Analysis and ODEs · Mathematics 2015-02-03 Tuomas Sahlsten , Pablo Shmerkin , Ville Suomala

Quantum uncertainty relations are formulated in terms of relative entropy between distributions of measurement outcomes and suitable reference distributions with maximum entropy. This type of entropic uncertainty relation can be applied…

Quantum Physics · Physics 2021-06-07 Stefan Floerchinger , Tobias Haas , Ben Hoeber

We introduce a new class of (not necessarily convex) bodies and show, among other things, that these bodies provide yet another link between convex geometric analysis and information theory. Namely, they give geometric interpretations of…

Functional Analysis · Mathematics 2011-05-17 Justin Jenkinson , Elisabeth Werner

A generalization of metric space is presented which is shown to admit a theory strongly related to that of ordinary metric spaces. To avoid the topological effects related to dropping any of the axioms of metric space, first a new, and…

Metric Geometry · Mathematics 2012-01-20 Ittay Weiss