In order to develop fast and robust methods for extracting qualitative information from non-linear time series, Bandt and Pompe have proposed to consider time series from the pure ordinal viewpoint. On the base of counting ordinal patterns, which describe the up-and-down in a time series, they have introduced the concept of permutation entropy for quantifying the complexity of a system behind a...

The maximum entropy spectral estimator is widely used because of its high spectral resolution, but it lacks an easy procedure for evaluating the statistical significance of the spectral estimates. We implemented the non-parametric computer intensive permutation test in order to evaluate the statistical significance of the maximum entropy spectral estimates. There is the possibility of choosing ...

Permutation entropy, introduced by Bandt and Pompe, is a conceptually simple and well-interpretable measure of time series complexity. In this paper, we propose efficient methods for computing it and related ordinal-patterns-based characteristics. The methods are based on precomputing values of successive ordinal patterns of order d, considering the fact that they are “overlapped” in d points, ...

HIGHLIGHTS ► Twelve entropy indices were systematically compared in monitoring depth of anesthesia and detecting burst suppression.► Renyi permutation entropy performed best in tracking EEG changes associated with different anesthesia states.► Approximate Entropy and Sample Entropy performed best in detecting burst suppression. OBJECTIVE Entropy algorithms have been widely used in analyzing E...

The aim of this paper is to introduce the Lempel–Ziv permutation complexity vs permutation entropy plane as a tool to analyze time series of different nature. This two quantities make use of the Bandt and Pompe representation to quantify continuous-state time series. The strength of this plane is to combine two different perspectives to analyze a signal, one being statistic (the permutation ent...

The Bandt-Pompe permutation entropy and the Jensen-Shannon statistical complexity are used to analyze fluctuating time series of three different turbulent plasmas: the magnetohydrodynamic (MHD) turbulence in the plasma wind tunnel of the Swarthmore Spheromak Experiment (SSX), drift-wave turbulence of ion saturation current fluctuations in the edge of the Large Plasma Device (LAPD), and fully de...

Brain electrical activity as reflected in Electroencephalography (EEG) have been analyzed and diagnosed using various techniques. Among them complexity measure, nonlinearity, disorder and unpredictability play vital role due to nonlinear interconnection between functional and anatomical subsystem emerged in brain in healthy state and during various diseases. There are many social and economical...

In combinatorics on words, a word w over an alphabet Σ is said to avoid a pattern p over an alphabet ∆ if there is no factor f of w such that f = h(p) where h : ∆∗ → Σ∗ is a non-erasing morphism. A pattern p is said to be k-avoidable if there exists an infinite word over a k-letter alphabet that avoids p. We give a positive answer to Problem 3.3.2 in Lothaire’s book “Algebraic combinatorics on ...

Kinetics Monte Carlo simulation has been done for solving Master equation about dynamics of intracellular viral reaction kinetics. Scaling relationship between equilibrium time and initial population of template has been founded as power low, ( ) b eq time f N aN  , where N , ( ) eq time f N are the number of initial population of template species , equilibrium time, a = 274.2, b = 0.1378 resp...

Understanding the transition of brain activities towards an absence seizure, called pre-epileptic seizure, is a challenge. In this study, multiscale permutation entropy (MPE) is proposed to describe dynamical characteristics of electroencephalograph (EEG) recordings on different absence seizure states. The classification ability of the MPE measures using linear discriminant analysis is evaluate...