相关论文: A note on bounded entropies

We consider the entropy of sums of independent discrete random variables, in analogy with Shannon's Entropy Power Inequality, where equality holds for normals. In our case, infinite divisibility suggests that equality should hold for…

Estimating entropies from limited data series is known to be a non-trivial task. Naive estimations are plagued with both systematic (bias) and statistical errors. Here, we present a new 'balanced estimator' for entropy functionals Shannon,…

We conclude a sequence of work by giving near-optimal sketching and streaming algorithms for estimating Shannon entropy in the most general streaming model, with arbitrary insertions and deletions. This improves on prior results that obtain…

We study how the Shannon entropy of sequences produced by an information source converges to the source's entropy rate. We synthesize several phenomenological approaches to applying information theoretic measures of randomness and memory to…

We present a unifying approach to the study of entropies in Mathematics, such as measure entropy, topological entropy, algebraic entropy, set-theoretic entropy. We take into account discrete dynamical systems, that is, pairs $(X,T)$, where…

For any Bell locality scenario (or Kochen-Specker noncontextuality scenario), the joint Shannon entropies of local (or noncontextual) models define a convex cone for which the non-trivial facets are tight entropic Bell (or contextuality)…

Entanglement entropy appears as a central property of quantum systems in broad areas of physics. However, its precise value is often sensitive to unknown microphysics, rendering it incalculable. By considering parametric dependence on…

Maximum entropy estimation is of broad interest for inferring properties of systems across many different disciplines. In this work, we significantly extend a technique we previously introduced for estimating the maximum entropy of a set of…

In the past over two decades, very fruitful results have been obtained in information theory in the study of the Shannon entropy. This study has led to the discovery of a new class of constraints on the Shannon entropy called…

Recently in [Physica A 411 (2014) 138] Ili\'{c} and Stankovi\'{c} have suggested that there may be problem for the class of hybrid entropies introduced in [P.~Jizba and T.~Arimitsu, Physica A 340 (2004) 110]. In this Comment we point out…

We propose an additional category of dimensionless groups based on the principle of {\it entropic similarity}, defined by ratios of (i) entropy production terms; (ii) entropy flow rates or fluxes; or (iii) information flow rates or fluxes.…

We generalize the Shannon's information theory in a nonadditive way by focusing on the source coding theorem. The nonadditive information content we adopted is consistent with the concept of the form invariance structure of the nonextensive…

Shannon's entropy and other entropy-based concepts are derived from the new, more general concept of relative divergence of one "grading' function on a linearly ordered set from another such function. The definition of relative divergence…

The asymptotic correspondence between the probability mass function of the $q$-deformed multinomial distribution and the $q$-generalised Kullback-Leibler divergence, also known as Tsallis relative entropy, is established. The probability…

In information theory, one major goal is to find useful functions that summarize the amount of information contained in the interaction of several random variables. Specifically, one can ask how the classical Shannon entropy, mutual…

The new estimates of the conditional Shannon entropy are introduced in the framework of the model describing a discrete response variable depending on a vector of d factors having a density w.r.t. the Lebesgue measure in R^d. Namely, the…

The Shannon entropy of a random variable has much behaviour analogous to a signed measure. Previous work has explored this connection by defining a signed measure on abstract sets, which are taken to represent the information that different…

The structure entropy is one of the most important parameters to describe the structure property of the complex networks. Most of the existing struc- ture entropies are based on the degree or the betweenness centrality. In order to describe…

In this paper, we consider the information content of maximum ranked set sampling procedure with unequal samples (MRSSU) in terms of Tsallis entropy which is a nonadditive generalization of Shannon entropy. We obtain several results of…

The paper examines relationships between the Shannon entropy and the $\ell_{\alpha}$-norm for $n$-ary probability vectors, $n \ge 2$. More precisely, we investigate the tight bounds of the $\ell_{\alpha}$-norm with a fixed Shannon entropy,…