Related papers: Recurrence Plot Based Measures of Complexity and i…

Chaos and turbulence are complex physical phenomena, yet a precise definition of the complexity measure that quantifies them is still lacking. In this work we consider the relative complexity of chaos and turbulence from the perspective of…

We review possible measures of complexity which might in particular be applicable to situations where the complexity seems to arise spontaneously. We point out that not all of them correspond to the intuitive (or "naive") notion, and that…

In this topical review, we present a brief overview of the different methods and measures to detect the occurrence of critical transitions in complex systems. We start by introducing the mechanisms that trigger critical transitions, and how…

Recurrence analysis is a well settled method allowing to discern chaos from order, and determinism from noise. We apply this tool to study time series representing geodesic and inspiraling motion of a test particle in a deformed Kerr…

Fundamental problems of periodicity and transient process to periodicity of chaotic trajectories in computer realization with finite computation precision is investigated by taking single and coupled Logistic maps as examples. Empirical…

Recurrence quantification analysis (RQA) is a widely used tool for studying complex dynamical systems, but its standard implementation requires computationally expensive calculations of recurrence plots (RPs) and line length histograms.…

We consider a family of singular maps as an example of a simple model of dynamical systems exhibiting the property of robust chaos on a well defined range of parameters. Critical boundaries separating the region of robust chaos from the…

Critical transitions occur in a variety of dynamical systems. Here, we employ quantifiers of chaos to identify changes in the dynamical structure of complex systems preceding critical transitions. As suitable indicator variables for…

Topological data analysis is an emerging area in exploratory data analysis and data mining. Its main tool, persistent homology, has become a popular technique to study the structure of complex, high-dimensional data. In this paper, we…

The complexity of a signal can be measured by the Recurrence period density entropy (RPDE) from the reconstructed phase space. We have chosen a window based RPDE method for the classification of signals, as RPDE is an average entropic…

The effective Hamiltonian formalism is extended to vectorial electromagnetic waves in order to describe statistical properties of the field in reverberation chambers. The latter are commonly used in electromagnetic compatibility tests. As a…

Complexity is an interdisciplinary concept which, first of all, addresses the question of how order emerges out of randomness. For many reasons matrices provide a very practical and powerful tool in approaching and quantifying the related…

We investigate the role of a statistical complexity measure to assign equilibration in isolated quantum systems. While unitary dynamics preserve global purity, expectation values of observables often exhibit equilibration-like behavior,…

Parametric statistical methods play a central role in analyzing risk through its underlying frequency and severity components. Given the wide availability of numerical algorithms and high-speed computers, researchers and practitioners often…

This paper presents an innovative and generic deep learning approach to monitor heart conditions from ECG signals.We focus our attention on both the detection and classification of abnormal heartbeats, known as arrhythmia. We strongly…

Control charts, as had been used traditionally for quality monitoring, were applied alternatively to monitor systems' reliability. In other words, they can be applied to detect changes in the failure behavior of systems. Such purpose…

Entropy measures have become increasingly popular as an evaluation metric for complexity in the analysis of time series data, especially in physiology and medicine. Entropy measures the rate of information gain, or degree of regularity in a…

In this paper we address the problem of uncertainty management for robust design, and verification of large dynamic networks whose performance is affected by an equally large number of uncertain parameters. Many such networks (e.g. power,…

The statistical properties of the quantum chaotic spectra have been studied, so far, only up to the second order correlation effects. The numerical as well as the analytical evidence that random matrix theory can successfully model the…

Cardiac diseases are one of the leading mortality factors in modern, industrialized societies, which cause high expenses in public health systems. Due to high costs, developing analytical methods to improve cardiac diagnostics is essential.…