Related papers: Entropic nonextensivity as a measure of time serie…
Finding interdependency relations between (possibly multivariate) time series provides valuable knowledge about the processes that generate the signals. Information theory sets a natural framework for non-parametric measures of several…
Some bounds on the entropic informational quantities related to a quantum continual measurement are obtained and the time dependencies of these quantities are studied.
Many dynamical phenomena in complex systems concern spreading that plays out on top of networks with changing architecture over time -- commonly known as temporal networks. A complex system's proneness to facilitate spreading phenomena,…
There are numerous characterizations of Shannon entropy and Tsallis entropy as measures of information obeying certain properties. Using work by Faddeev and Furuichi, we derive a very simple characterization. Instead of focusing on the…
A possible mechanism of time is formulated by developing an idea of time replaced by quantum correlations, with the aid of modern quantum information theory. We invent a microscopic model, where correlations of a closed system are steadily…
Informational entropy is often identified as physical entropy. This is surprising because the two quantities are differently defined and furthermore the former is a subjective quantity while the latter is an objective one. We describe the…
We adapt the Kolmogorov-Sinai entropy to the non-extensive perspective recently advocated by Tsallis. The resulting expression is an average on the invariant distribution, which should be used to detect the genuine entropic index Q. We…
The growing study of time series, especially those related to nonlinear systems, has challenged the methodologies to characterize and classify dynamical structures of a signal. Here we conceive a new diagnostic tool for time series based on…
A new method is proposed for analyzing complexity and studying the information in random geometric networks using Tsallis entropy tool. Tsallis entropy of the ensemble of random geometric networks is calculated based on the components of…
The notion of topological entropy can be conceptualized in terms of the number of forward trajectories that are distinguishable at resolution $\varepsilon$ within $T$ time units. It can then be formally defined as a limit of a limit…
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,…
How complex of the complex networks has attracted many researchers to explore it. The entropy is an useful method to describe the degree of the $complex$ of the complex networks. In this paper, a new method which is based on the Tsallis…
The analysis of temporal networks heavily depends on the analysis of time-respecting paths. However, before being able to model and analyze the time-respecting paths, we have to infer the timescales at which the temporal edges influence…
Entropy is a measure of heterogeneity widely used in applied sciences, often when data are collected over space. Recently, a number of approaches has been proposed to include spatial information in entropy. The aim of entropy is to…
We define an entropy based on a chosen governing probability distribution. If a certain kind of measurements follow such a distribution it also gives us a suitable scale to study it with. This scale will appear as a link function that is…
Here, we propose a new tool to estimate the complexity of a time series: the entropy of difference (ED). The method is based solely on the sign of the difference between neighboring values in a time series. This makes it possible to…
Complex systems are found in most branches of science. It is still argued how to best quantify their complexity and to what end. One prominent measure of complexity (the statistical complexity) has an operational meaning in terms of the…
We consider discrete stochastic processes, modeled by classical master equations, on networks. The temporal growth of the lack of information about the system is captured by its non-equilibrium entropy, defined via the transition…
Entropy and information can be considered dual: entropy is a measure of the subspace defined by the information constraining the given ambient space. Negative entropies, arising in na\"ive extensions of the definition of entropy from…
Entropy can signify different things: For instance, heat transfer in thermodynamics or a measure of information in data analysis. Many entropies have been introduced and it can be difficult to ascertain their different importance and…