Guesswork forms the mathematical framework for quantifying computational security subject to brute-force determination by query. In this paper, we consider guesswork subject to a per-symbol Shannon entropy budget. We introduce inscrutability rate to quantify the asymptotic difficulty of guessing U out of V secret strings drawn from the string-source and prove that the inscrutability rate of any...

We say that two free p.m.p. actions of countable groups are Shannon orbit equivalent if there is an equivalence between them whose associated cocycle partitions have finite entropy. show the acting sofic and each has a w-normal amenable subgroup which neither locally nor virtually cyclic then implies same maximum This extends result Austin beyond finitely generated setting consequence Bernoulli...

Most independent component analysis (ICA) algorithms use mutual information (MI) measures based on Shannon entropy as a cost function, but Shannon entropy is not the only measure in the literature. In this paper, instead of Shannon entropy, Tsallis entropy is used and a novel ICA algorithm, which uses kernel density estimation (KDE) for estimation of source distributions, is proposed. KDE is di...

Abstract This paper deals with the fractional calculus of zeta functions. In particular, study is focused on Hurwitz ? \zeta function. All results are based complex generalization Grünwald-Letnikov derivative. We state and prove functional equation together an integral representation by Bernoulli numbers. Moreover, we ...

In this paper, we derive the exact analytical expressions for the Shannon entropy of generalized orderstatistics from Pareto-type and related distributions.

In this paper, we show that in order to obtain the Tsallis entropy rate for stochastic processes, we can use the limit of conditional entropy, as it was done for the case of Shannon and Renyi entropy rates. Using that we can obtain Tsallis entropy rate for stationary Gaussian processes. Finally, we derive the relation between Renyi, Shannon and Tsallis entropy rates for stationary Gaussian proc...

In this paper, at first we derive a family of maximum Tsallis entropy distributions under optional side conditions on the mean income and the Gini index. Furthermore, corresponding with these distributions a family of Lorenz curves compatible with the optional side conditions is generated. Meanwhile, we show that our results reduce to Shannon entropy as $beta$ tends to one. Finally, by using ac...