Revisiting the Characterization of Resting Brain Dynamics with the Permutation Jensen-Shannon Distance.

Taking into account the complexity of the human brain dynamics, the appropriate characterization of any brain state is a challenge not easily met. Actually, even the discrimination of simple behavioral tasks, such as resting with eyes closed or eyes open, represents an intricate problem and many efforts have been and are being made to overcome it. In this work, the aforementioned issue is carefully addressed by performing multiscale analyses of electroencephalogram records with the permutation Jensen-Shannon distance.

Characterizing unstructured data with the nearest neighbor permutation entropy.

Permutation entropy and its associated frameworks are remarkable examples of physics-inspired techniques adept at processing complex and extensive datasets. Despite substantial progress in developing and applying these tools, their use has been predominantly limited to structured datasets such as time series or images. Here, we introduce the k-nearest neighbor permutation entropy, an innovative extension of the permutation entropy tailored for unstructured data, irrespective of their spatial or temporal configuration and dimensionality.

Quantifying the diversity of multiple time series with an ordinal symbolic approach.

The main motivation of this paper is to introduce the ordinal diversity, a symbolic tool able to quantify the degree of diversity of multiple time series. Analytical, numerical, and experimental analyses illustrate the utility of this measure to quantify how diverse, from an ordinal perspective, a set of many time series is. We have shown that ordinal diversity is able to characterize dynamical richness and dynamical transitions in stochastic processes and deterministic systems, including chaotic regimes.

Ordinal analysis of lexical patterns.

Words are fundamental linguistic units that connect thoughts and things through meaning. However, words do not appear independently in a text sequence. The existence of syntactic rules induces correlations among neighboring words.

Permutation Jensen-Shannon distance: A versatile and fast symbolic tool for complex time-series analysis.

The main motivation of this paper is to introduce the permutation Jensen-Shannon distance, a symbolic tool able to quantify the degree of similarity between two arbitrary time series. This quantifier results from the fusion of two concepts, the Jensen-Shannon divergence and the encoding scheme based on the sequential ordering of the elements in the data series. The versatility and robustness of this ordinal symbolic distance for characterizing and discriminating different dynamics are illustrated through several numerical and experimental applications.

Time-Delay Identification Using Multiscale Ordinal Quantifiers.

Time-delayed interactions naturally appear in a multitude of real-world systems due to the finite propagation speed of physical quantities. Often, the time scales of the interactions are unknown to an external observer and need to be inferred from time series of observed data. We explore, in this work, the properties of several ordinal-based quantifiers for the identification of time-delays from time series.

Unraveling the decay of the number of unobserved ordinal patterns in noisy chaotic dynamics.

In this paper, we introduce a model to describe the decay of the number of unobserved ordinal patterns as a function of the time series length in noisy chaotic dynamics. More precisely, we show that a stretched exponential model fits the decay of the number of unobserved ordinal patterns for both discrete and continuous chaotic systems contaminated with observational noise, independently of the noise level and the sampling time. Numerical simulations, obtained from the logistic map and the x coordinate of the Lorenz system, both operating in a totally chaotic dynamics were used as test beds.

Multi-Lag Analysis of Symbolic Entropies on EEG Recordings for Distress Recognition.

Distress is a critical problem in developed societies given its long-term negative effects on physical and mental health. The interest in studying this emotion has notably increased during last years, being electroencephalography (EEG) signals preferred over other physiological variables in this research field. In addition, the non-stationary nature of brain dynamics has impulsed the use of non-linear metrics, such as symbolic entropies in brain signal analysis.

An analysis of high-frequency cryptocurrencies prices dynamics using permutation-information-theory quantifiers.

This paper discusses the dynamics of intraday prices of 12 cryptocurrencies during the past months' boom and bust. The importance of this study lies in the extended coverage of the cryptoworld, accounting for more than 90% of the total daily turnover. By using the complexity-entropy causality plane, we could discriminate three different dynamics in the data set.

Application of Permutation Entropy and Permutation Min-Entropy in Multiple Emotional States Analysis of RRI Time Series.

This study's aim was to apply permutation entropy (PE) and permutation min-entropy (PME) over an RR interval time series to quantify the changes in cardiac activity among multiple emotional states. Electrocardiogram (ECG) signals were recorded under six emotional states (neutral, happiness, sadness, anger, fear, and disgust) in 60 healthy subjects at a rate of 1000 Hz. For each emotional state, ECGs were recorded for 5 min and the RR interval time series was extracted from these ECGs.

Multiscale permutation entropy analysis of laser beam wandering in isotropic turbulence.

We have experimentally quantified the temporal structural diversity from the coordinate fluctuations of a laser beam propagating through isotropic optical turbulence. The main focus here is on the characterization of the long-range correlations in the wandering of a thin Gaussian laser beam over a screen after propagating through a turbulent medium. To fulfill this goal, a laboratory-controlled experiment was conducted in which coordinate fluctuations of the laser beam were recorded at a sufficiently high sampling rate for a wide range of turbulent conditions.

Using missing ordinal patterns to detect nonlinearity in time series data.

The number of missing ordinal patterns (NMP) is the number of ordinal patterns that do not appear in a series after it has been symbolized using the Bandt and Pompe methodology. In this paper, the NMP is demonstrated as a test for nonlinearity using a surrogate framework in order to see if the NMP for a series is statistically different from the NMP of iterative amplitude adjusted Fourier transform (IAAFT) surrogates. It is found that the NMP works well as a test statistic for nonlinearity, even in the cases of very short time series.

Characterizing time series via complexity-entropy curves.

The search for patterns in time series is a very common task when dealing with complex systems. This is usually accomplished by employing a complexity measure such as entropies and fractal dimensions. However, such measures usually only capture a single aspect of the system dynamics.

Estimation of Cn² based on scintillation of fixed targets imaged through atmospheric turbulence.

We define a pixel-based scintillation index for dynamic incoherent imaging of fixed high-contrast targets through atmospheric turbulence. We propose a simple setup to study this parameter varying the Cn(2) constant in controlled laboratory conditions (weak fluctuation regime). We find the semi-empirical relationship between the pixel-based scintillation index and the index of refraction structure constant, which we then employ to estimate Cn(2) successfully in an independent case in which this value was not known beforehand.

Turbulence-induced persistence in laser beam wandering.

We have experimentally confirmed the presence of long-memory correlations in the wandering of a thin Gaussian laser beam over a screen after propagating through a turbulent medium. A laboratory-controlled experiment was conducted in which coordinate fluctuations of the laser beam were recorded at a sufficiently high sampling rate for a wide range of turbulent conditions. Horizontal and vertical displacements of the laser beam centroid were subsequently analyzed by implementing detrended fluctuation analysis.

Experimental confirmation of long-memory correlations in star-wander data.

In this Letter we have analyzed the temporal correlations of the angle-of-arrival fluctuations of stellar images. Experimentally measured data were carefully examined by implementing multifractal detrended fluctuation analysis. This algorithm is able to discriminate the presence of fractal and multifractal structures in recorded time sequences.

Estimating the optimal sampling rate using wavelet transform: an application to optical turbulence.

Sampling rate and frequency content determination for optical quantities related to light propagation through turbulence are paramount experimental topics. Some papers about estimating properties of the optical turbulence seem to use ad hoc assumptions to set the sampling frequency used; this chosen sampling rate is assumed good enough to perform a proper measurement. On the other hand, other authors estimate the optimal sampling rate via fast Fourier transform of data series associated to the experiment.

Complexity-entropy causality plane as a complexity measure for two-dimensional patterns.

Complexity measures are essential to understand complex systems and there are numerous definitions to analyze one-dimensional data. However, extensions of these approaches to two or higher-dimensional data, such as images, are much less common. Here, we reduce this gap by applying the ideas of the permutation entropy combined with a relative entropic index.

Distinguishing fingerprints of hyperchaotic and stochastic dynamics in optical chaos from a delayed opto-electronic oscillator.

In the dynamics of optical systems, one commonly needs to cope with the problem of coexisting deterministic and stochastic components. The separation of these components is an important, although difficult, task. Often the time scales at which determinism and noise dominate the system's dynamics differ.

Generalized wavefront phase for non-Kolmogorov turbulence.

We introduce the Lévy fractional Brownian field family to model the turbulent wavefront phase. This generalized model allows us to overcome the limitations found in a previous approach [Perez et al., J.

The inhibition of paw oedema formation caused by the oil of Copaifera multijuga Hayne and its fractions.

Two oils exuded from a Copaifera multijuga Hayne tree (Leguminosae-Caesalpinoideae), collected from the same plant, but in different periods of the year, and the hexanic, dichloromethanic and methanolic fractions of one of these oils were analysed by high-resolution gas chromatography (HRGC) and HRGC coupled with mass spectrometry (HRGC-MS). In addition, the in-vivo preliminary anti-oedematogenic actions of the oil and some fractions of it were assessed against carrageenan- and bradykinin-induced oedema formation in the rat paw. Twenty-seven sesquiterpenes and six diterpenes were identified, beta-caryophyllene, alpha-copaene and copalic acid being the main components.

Modeling turbulent wave-front phase as a fractional Brownian motion: a new approach.

We introduce a new, general formalism to model the turbulent wave-front phase by using fractional Brownian motion processes. Moreover, it extends results to non-Kolmogorov turbulence. In particular, generalized expressions for the Strehl ratio and the angle-of-arrival variance are obtained.