Related papers: Studies of entropy measures concerning the gaps of…
The analysis of execution paths (also known as software traces) collected from a given software product can help in a number of areas including software testing, software maintenance and program comprehension. The lack of a scalable…
A few years ago we identified a recursion that works directly with the gaps among the generators in each stage of Eratosthenes sieve. This recursion provides explicit enumerations of sequences of gaps among the generators, which are known…
We study entropic uncertainty relations by using stepwise linear functions and quadratic functions. Two kinds of improved uncertainty lower bounds are constructed: the state-independent one based on the lower bound of Shannon entropy and…
Entropic uncertainty relations are interesting in their own rights as well as for a lot of applications. Keeping this in mind, we try to make the corresponding inequalities as tight as possible. The use of parametrized entropies also allows…
Shannon's Entropy Power Inequality can be viewed as characterizing the minimum differential entropy achievable by the sum of two independent random variables with fixed differential entropies. The entropy power inequality has played a key…
High-order phenomena play crucial roles in many systems of interest, but their analysis is often highly nontrivial. There is a rich literature providing a number of alternative information-theoretic quantities capturing high-order…
It is often stated that if one is presented with a snapshot of the positions of the molecules of a glass and one of a liquid, one is unable to tell the difference. Here we argue instead that given several such snapshots taken over a…
We present a new class of estimators of Shannon entropy for severely undersampled discrete distributions. It is based on a generalization of an estimator proposed by T. Schuermann, which itself is a generalization of an estimator proposed…
We give an effective method to compute the entropy for polynomials orthogonal on a segment of the real axis that uses as input data only the coefficients of the recurrence relation satisfied by these polynomials. This algorithm is based on…
Numerical experiments support the interesting conjecture that statistical methods be applicable not only to fully-chaotic systems, but also at the edge of chaos by using Tsallis' generalizations of the standard exponential and entropy. In…
For statistical systems that violate one of the four Shannon-Khinchin axioms, entropy takes a more general form than the Boltzmann-Gibbs entropy. The framework of superstatistics allows one to formulate a maximum entropy principle with…
This paper is prepared as a contribution to the proceedings after the 12th ICSSUR/Feynfest Conference held in Foz do Iguacu (Brazil) from 2 to 6 May 2011. In the first part I briefy report the topic of entropic uncertainty relations for…
Convergence properties of Shannon Entropy are studied. In the differential setting, it is shown that weak convergence of probability measures, or convergence in distribution, is not enough for convergence of the associated differential…
The notion of entropy penetrates much of science. A key feature of the all-important notion of Boltzmann-Gibbs-Shannon entropy is its extensivity (additivity over independent subsystems). However, there is a need for other quantities. In…
We show that the way in which the Shannon entropy of sequences produced by an information source converges to the source's entropy rate can be used to monitor how an intelligent agent builds and effectively uses a predictive model of its…
Estimation of Shannon and R\'enyi entropies of unknown discrete distributions is a fundamental problem in statistical property testing and an active research topic in both theoretical computer science and information theory. Tight bounds on…
We develop entropy and variance results for the product of independent identically distributed random variables on Lie groups. Our results apply to the study of stationary measures in various contexts.
Building on work of Kontsevich, we introduce a definition of the entropy of a finite probability distribution in which the "probabilities" are integers modulo a prime p. The entropy, too, is an integer mod p. Entropy mod p is shown to be…
The R\'enyi entropy is a generalization of the Shannon entropy and is widely used in mathematical statistics and applied sciences for quantifying the uncertainty in a probability distribution. We consider estimation of the quadratic R\'enyi…
Aim of this short note is to study Shannon's entropy power along entropic interpolations, thus generalizing Costa's concavity theorem. We shall provide two proofs of independent interest: the former by $\Gamma$-calculus, hence applicable to…