Related papers: Generalized informational functionals and new mono…
In this study an attempt has been made to propose a way to develop new distribution. For this purpose, we need only idea about distribution function. Some important statistical properties of the new distribution like moments, cumulants,…
We introduce an information theoretic measure of statistical structure, called 'binding information', for sets of random variables, and compare it with several previously proposed measures including excess entropy, Bialek et al.'s…
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,…
Measuring the complexity of high-dimensional data in physical systems becomes a critical factor in determining the information and quality of the systems. However, traditional metrics, such as Lyapunov exponent, fractal dimension, and…
Shannon information entropy is a natural measure of probability (de)localization and thus (un)predictability in various procedures of data analysis for model systems. We pay particular attention to links between the Shannon entropy and the…
A new summation method is introduced to convert a relatively wide family of infinite sums and local expansions into integrals. The integral representations yield global information such as analytic continuability, position of singularities,…
In this chapter, a statistical measure of complexity and the Fisher-Shannon information product are introduced and their properties are discussed. These measures are based on the interplay between the Shannon information, or a function of…
In classical density (or density-functional) estimation, it is standard to assume that the underlying distribution has a density with respect to the Lebesgue measure. However, when the data distribution is a mixture of continuous and…
Understanding how network structure constrains and enables information processing is a central problem in the statistical mechanics of interacting systems. Here we study random networks across the structural percolation transition and…
This article presents a new class of generalized transmuted lifetime distributions which includes a large number of lifetime distributions as sub-family. Several important mathematical quantities such as density function, distribution…
A consistent generalization of statistical mechanics is obtained by applying the maximum entropy principle to a trace-form entropy and by requiring that physically motivated mathematical properties are preserved. The emerging…
Algebraic tools in statistics have recently been receiving special attention and a number of interactions between algebraic geometry and computational statistics have been rapidly developing. This paper presents another such connection,…
We study geometric properties of trace functionals that generalize those in [Zhang, Adv. Math. 365:107053 (2020)], arising from a novel family of conditional entropies with applications in quantum information. Building on new convexity…
There is no single universally accepted definition of "Complexity". There are several perspectives on complexity and what constitutes complex behaviour or complex systems, as opposed to regular, predictable behaviour and simple systems. In…
A novel heuristic approach is proposed here for time series data analysis, dubbed Generalized weighted permutation entropy, which amalgamates and generalizes beyond their original scope two well established data analysis methods:…
The electrical activity of external anal sphincter can be registered with surface electromyography. This signals are known to be highly complex and nonlinear. This work aims in characterisation of the information carried in the signals by…
This paper introduces "swiveled Renyi entropies" as an alternative to the Renyi entropic quantities put forward in [Berta et al., Phys. Rev. A 91, 022333 (2015)]. What distinguishes the swiveled Renyi entropies from the prior proposal of…
The meromorphic functional calculus developed in Part I overcomes the nondiagonalizability of linear operators that arises often in the temporal evolution of complex systems and is generic to the metadynamics of predicting their behavior.…
The entropy of a graph is an information-theoretic quantity which expresses the complexity of a graph \cite{DM1,M}. After Shannon introduced the definition of entropy to information and communication, many generalizations of the entropy…
We study the $n^{\rm th}$ centered moments of the $1$-level density for the low-lying zeros of $L$-functions attached to holomorphic cuspidal newforms of large prime level and fixed weight. Assuming the Generalized Riemann Hypotheses, we…