Related papers: Permutation extropy: a time series complexity meas…
A new approach is proposed to the quantitative estimation of the complexity of multidimensional discrete sequences in terms of the shapes of their trajectories in the extended space of states. This approach is based on the study of the…
Natural and social multivariate systems are commonly studied through sets of simultaneous and time-spaced measurements of the observables that drive their dynamics, i.e., through sets of time series. Typically, this is done via hypothesis…
Some aspects of the predictability problem in dynamical systems are reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy, Shannon entropy and algorithmic complexity is discussed. In particular, we emphasize how a…
The complexity of computing the Fourier transform is a longstanding open problem. Very recently, Ailon (2013, 2014, 2015) showed in a collection of papers that, roughly speaking, a speedup of the Fourier transform computation implies…
Weighted extropy has recently emerged as a flexible information measure for quantifying uncertainty, with particular relevance to order statistics. In this paper, we introduce and study a weighted cumulative analogue of extropy, extending…
In order to process a potential moment sequence by the entropy optimization method one has to be assured that the original measure is absolutely continuous with respect to Lebesgue measure. We propose a non-linear exponential transform of…
In this paper, we study the stability problem of a stochastic, nonlinear, discrete-time system. We introduce a linear transfer operator-based Lyapunov measure as a new tool for stability verification of stochastic systems. Weaker…
The absence of time-reversal symmetry is a fundamental property of many nonlinear time series. Here, we propose a new set of statistical tests for time series irreversibility based on standard and horizontal visibility graphs. Specifically,…
In this paper we introduce a biparametric family of transformations which can be seen as an extension of the so-called up and down transformations. This new class of transformations allows to us to introduce new informational functionals,…
We introduce a method for quantifying the inherent unpredictability of a continuous-valued time series via an extension of the differential Shannon entropy rate. Our extension, the specific entropy rate, quantifies the amount of predictive…
One of the crucial steps in scientific studies is to specify dependent relationships among factors in a system of interest. Given little knowledge of a system, can we characterize the underlying dependent relationships through observation…
Estimating the entropy rate of discrete time series is a challenging problem with important applications in numerous areas including neuroscience, genomics, image processing and natural language processing. A number of approaches have been…
The concept of multifractality offers a powerful formal tool to filter out multitude of the most relevant characteristics of complex time series. The related studies thus far presented in the scientific literature typically limit themselves…
Deriving the time evolution of a distribution of probability (or a probability density matrix) is a problem encountered frequently in a variety of situations: for physical time, it could be a kinetic reaction study, while identifying time…
The universal concept of complexity by the dynamic redundance paradigm and the ensuing concept of extended dynamic fractality (physics/9806002) are applied here to higher levels of complexity corresponding to living systems. After recalling…
The transfer entropy is a well-established measure of information flow, which quantifies directed influence between two stochastic time series and has been shown to be useful in a variety fields of science. Here we introduce the transfer…
The knowledge of transitions between regular, laminar or chaotic behavior is essential to understand the underlying mechanisms behind complex systems. While several linear approaches are often insufficient to describe such processes, there…
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…
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…
In this paper we examine the concept of complexity as it applies to generative art and design. Complexity has many different, discipline specific definitions, such as complexity in physical systems (entropy), algorithmic measures of…