Related papers: Studies of entropy measures concerning the gaps of…
Ever since Claude Shannon used entropy for his "Mathematical Theory of Communication", entropy has become a buzzword in research circles with scientists applying entropy to describe any phenomena that are reminiscent of disorder. In this…
Entropy is a measure of self-information which is used to quantify losses. Entropy was developed in thermodynamics, but is also used to compare probabilities based on their deviating information content. Corresponding model uncertainty is…
In the present work we investigate phase correlations by recourse to the Shannon entropy. Using theoretical arguments we show that the entropy provides an accurate measure of phase correlations in any dynamical system, in particular when…
The weak law of large numbers implies that, under mild assumptions on the source, the Renyi entropy per produced symbol converges (in probability) towards the Shannon entropy rate. This paper quantifies the speed of this convergence for…
Under the scenario of generalized measurements, it can be questioned how much of quantum uncertainty can be attributed to measuring device, independent of the uncertainty in the measured system. On the course to answer the question, we…
We propose a definition for the entropy of capacities defined on lattices. Classical capacities are monotone set functions and can be seen as a generalization of probability measures. Capacities on lattices address the general case where…
Relations between Shannon entropy and Renyi entropies of integer order are discussed. For any N-point discrete probability distribution for which the Renyi entropies of order two and three are known, we provide an lower and an upper bound…
The classical Maximum-Entropy Principle (MEP) based on Shannon entropy is widely used to construct least-biased probability distributions from partial information. However, the Shore-Johnson axioms that single out the Shannon functional…
In estimating the complexity of objects, in particular of graphs, it is common practice to rely on graph- and information-theoretic measures. Here, using integer sequences with properties such as Borel normality, we explain how these…
A measure called Physical Complexity is established and calculated for a population of sequences, based on statistical physics, automata theory, and information theory. It is a measure of the quantity of information in an organism's genome.…
We prove a sharp bound between sampling numbers and entropy numbers in the uniform norm for bounded convex sets of bounded functions.
The aim of this paper is to introduce the Lempel-Ziv permutation complexity vs permutation entropy plane as a tool to analyze time series of different nature. This two quantities make use of the Bandt and Pompe representation to quantify…
Recently, a new type of set, named as random permutation set (RPS), is proposed by considering all the permutations of elements in a certain set. For measuring the uncertainty of RPS, the entropy of RPS is presented. However, the maximum…
Shannon entropy is the most crucial foundation of Information Theory, which has been proven to be effective in many fields such as communications. Renyi entropy and Chernoff information are other two popular measures of information with…
This paper addresses the problem of determining the distance between two regular languages. It will show how to expand Jaccard distance, which works on finite sets, to potentially-infinite regular languages. The entropy of a regular…
Gamma distributions, which contain the exponential as a special case, have a distinguished place in the representation of near-Poisson randomness for statistical processes; typically, they represent distributions of spacings between events…
The statistical analysis of data stemming from dynamical systems, including, but not limited to, time series, routinely relies on the estimation of information theoretical quantities, most notably Shannon entropy. To this purpose, possibly…
We propose a new interpretation of measures of information and disorder by connecting these concepts to group theory in a new way. Entropy and group theory are connected here by their common relation to sets of permutations. A combinatorial…
We show how the Shannon entropy function can be used as a basis to set up complexity measures weighting the economic efficiency of countries and the specialization of products beyond bare diversification. This entropy function guarantees…
We address the generalized uncertainty principle in scenarios of successive measurements. Uncertainties are characterized by means of generalized entropies of both the R\'{e}nyi and Tsallis types. Here, specific features of measurements of…