Related papers: Measuring the Complexity of Continuous Distributio…
We show one possible dynamical approach to the study of the distribution of prime numbers. Our approach is based on two complexity methods, the Computable Information Content and the Entropy Information Gain, looking for analogies between…
Products between phase-type distributed random variables and any independent, positive and continuous random variable are studied. Their asymptotic properties are established, and an expectation-maximization algorithm for their effective…
The problem of defining and studying complexity of a time series has interested people for years. In the context of dynamical systems, Grassberger has suggested that a slow approach of the entropy to its extensive asymptotic limit is a sign…
We investigate the spread complexity of a generic two-level subsystem of a larger system to analyze the influence of energy level statistics, comparing chaotic and integrable systems. Initially focusing on the nearest-neighbor level…
The entropy is a measure of uncertainty that plays a central role in information theory. When the distribution of the data is unknown, an estimate of the entropy needs be obtained from the data sample itself. We propose a semi-parametric…
This letter reports two moment extensions of the entropy of a distribution. By understanding the traditional entropy as the average of the original distribution up to a random variable transformation, the traditional moments equation become…
We develop information-theoretic measures of spatial structure and pattern in more than one dimension. As is well known, the entropy density of a two-dimensional configuration can be efficiently and accurately estimated via a converging…
In this paper, we present some results on information, complexity and entropy as defined below and we discuss their relations with the Kolmogorov-Sinai entropy which is the most important invariant of a dynamical system. These results have…
The relationship between three probability distributions and their maximizable entropy forms is discussed without postulating entropy property. For this purpose, the entropy I is defined as a measure of uncertainty of the probability…
An axiomatic foundation regarding the entropy for complex systems is established. Missing from decades of research was the requirement that entropy must measure the uncertainty at the informational scale of the maximizing distribution,…
On account of a greater need for understanding the complexity of time series like physiological time series, financial time series, and many more that enter into picture for their inculpation with real-world problems, several complexity…
This paper studies the complexity of estimating Renyi divergences of discrete distributions: $p$ observed from samples and the baseline distribution $q$ known \emph{a priori}. Extending the results of Acharya et al. (SODA'15) on estimating…
We propose a formal expansion of the transfer entropy to put in evidence irreducible sets of variables which provide information for the future state of each assigned target. Multiplets characterized by a large contribution to the expansion…
We consider the number of Bowen sets which are necessary to cover a large measure subset of the phase space. This introduce some complexity indicator characterizing different kind of (weakly) chaotic dynamics. Since in many systems its…
We characterize different cell states, related to cancer and ageing phenotypes, by a measure of entropy of network ensembles, integrating gene expression values and protein interaction networks. The entropy measure estimates the parameter…
We use the $f-divergence$ also called relative entropy as a measure of diversity between probability densities and review its basic properties. In the sequence we define a few objects which capture relevant information from the sample of a…
Within the framework of generalized combinatorial approach, complexity is determined as a disorder measure for hierarchical statistical ensembles related to Cayley trees possessing arbitrary branching and number of levels. With…
A novel, non-trivial, probabilistic upper bound on the entropy of an unknown one-dimensional distribution, given the support of the distribution and a sample from that distribution, is presented. No knowledge beyond the support of the…
We propose utilizing entropy as a diagnostic tool to distinguish between constant and dynamical dark energy models. Entropy, a measure of the system's disorder or information content, captures the complexity and evolution of the universe.…
In its continuous version, the entropy functional measuring the information content of a given probability density may be plagued by a "measure" problem that results from improper weighting of phase space. This issue is addressed…