Long-range Power-law Correlations Research Articles

Cross-correlated fractal components of H-wave amplitude fluctuations in medial gastrocnemius and soleus muscles

The time series of the H-wave amplitude in soleus muscle (SOL) shows fractal (long-range) correlation, which is attributed to input from supraspinal centers. However, whether such long-range power-law correlated input also contributes to the synergistic muscles remains unclear. The purpose of this study was therefore to examine the correlation in the fractal components of H-wave amplitude fluctuations between the synergistic muscles used for plantar flexion, i.e., the medial head of the gastrocnemius muscle (MG) and SOL. In eight young male participants, consecutive H-reflexes were recorded almost simultaneously from the MG and SOL at a stimulation frequency of 0.5 Hz for 30 min. We performed detrending moving-average cross-correlation analysis (DMCA) for each of the H- and M-wave amplitude time series between MG and SOL to assess the existence of a common noise input contributing to these long-range correlations. The cross-correlation coefficient ρDMCA (−1 to 1) was calculated to quantify the strength of the correlation between two different time series. The results indicated a significant long-range power-law correlation between H-wave amplitudes in MG and SOL (ρDMCA: 0.50 (0.22) and 0.22 (0.17), mean (standard deviation) for the original and randomly shuffled surrogate data, respectively, P < 0.05). This was not the case for M-wave amplitudes (ρDMCA: 0.29 (0.23) and 0.20 (0.15), P > 0.05). We conclude that there is a common noise input governing these synergistic muscles, possibly due to supraspinal origin, causing long-range power-law correlations in monosynaptic reflexes.

Long-range temporal correlations in the broadband resting state activity of the human brain revealed by neuronal avalanches

Resting-state brain activity is characterized by the presence of neuronal avalanches showing absence of characteristic size. Such evidence has been interpreted in the context of criticality and associated with the normal functioning of the brain. A distinctive attribute of systems at criticality is the presence of long-range correlations. Thus, to verify the hypothesis that the brain operates close to a critical point and consequently assess deviations from criticality for diagnostic purposes, it is of primary importance to robustly and reliably characterize correlations in resting-state brain activity. Recent works focused on the analysis of narrow-band electroencephalography (EEG) and magnetoencephalography (MEG) signal amplitude envelope, showing evidence of long-range temporal correlations (LRTC) in neural oscillations. However, brain activity is a broadband phenomenon, and a significant piece of information useful to precisely discriminate between normal (critical) and pathological behavior (non-critical), may be encoded in the broadband spatio-temporal cortical dynamics. Here we propose to characterize the temporal correlations in the broadband brain activity through the lens of neuronal avalanches. To this end, we consider resting-state EEG and long-term MEG recordings, extract the corresponding neuronal avalanche sequences, and study their temporal correlations. We demonstrate that the broadband resting-state brain activity consistently exhibits long-range power-law correlations in both EEG and MEG recordings, with similar values of the scaling exponents. Importantly, although we observe that the avalanche size distribution depends on scale parameters, scaling exponents characterizing long-range correlations are quite robust. In particular, they are independent of the temporal binning (scale of analysis), indicating that our analysis captures intrinsic characteristics of the underlying dynamics. Because neuronal avalanches constitute a fundamental feature of neural systems with universal characteristics, the proposed approach may serve as a general, systems- and experiment-independent procedure to infer the existence of underlying long-range correlations in extended neural systems, and identify pathological behaviors in the complex spatio-temporal interplay of cortical rhythms.

Breaking universality in random sequential adsorption on a square lattice with long-range correlated defects.

Jamming and percolation transitions in the standard random sequential adsorption of particles on regular lattices are characterized by a universal set of critical exponents. The universality class is preserved even in the presence of randomly distributed defective sites that are forbidden for particle deposition. However, using large-scale Monte Carlo simulations by depositing dimers on the square lattice and employing finite-size scaling, we provide evidence that the system does not exhibit such well-known universal features when the defects have spatial long-range (power-law) correlations. The critical exponents ν_{j} and ν associated with the jamming and percolation transitions, respectively, are found to be nonuniversal for strong spatial correlations and approach systematically their own universal values as the correlation strength is decreased. More crucially, we have found a difference in the values of the percolation correlation length exponent ν for a small but finite density of defects with strong spatial correlations. Furthermore, for a fixed defect density, it is found that the percolation threshold of the system, at which the largest cluster of absorbed dimers first establishes the global connectivity, gets reduced with increasing the strength of the spatial correlation.

Enhanced multiresolution wavelet analysis of cerebrovascular dynamics

The responses of cerebral circulation to an abrupt increase in blood pressure caused by pharmacologically induced hypertension are compared by means of multiresolution wavelet analysis (MWA), which uses standard deviations of expansion coefficients as diagnostic criteria, and an enhanced approach, combining MWA with analysis of long-range power-law correlations in the wavelet domain. We discuss how applying both of these approaches elicits different types of reactions of large blood vessels in the brain and capillary network and show that the use of simple statistical measures limits the information that can be extracted during data processing. Taking into account the correlation features in addition to the width of the probability density is a possible way to improve the characterization of the effects produced by “jumps” in blood pressure.

Structure of variability in scanning movement predicts braille reading performance in children

Among children learning to read braille, we asked whether the quantitative kinematics of scanning movements of the reading finger would be related to the proficiency of braille reading. Over a period of 12 months, we recorded the position and orientation of the reading fingers of eight congenitally or early blind children. We found that the strength of long-range power-law temporal correlations in the velocity fluctuations increased with performance in braille reading. In addition, we found that the variability of the angular orientation of the reading finger that affects the contact region on the fingerpad was negatively related to braille reading performance. These results confirm that the quantitative kinematics of finger scanning movements were related to functional performance in braille reading. The results add to the growing body of evidence that long-range temporal correlations in exploratory behavior can predict perceptual performance, and that scanning movements that center important tactile information on the small, high resolution area contribute to the pickup of information.

Probability density of fractional Brownian motion and the fractional Langevin equation with absorbing walls

Fractional Brownian motion and the fractional Langevin equation are models of anomalous diffusion processes characterized by long-range power-law correlations in time. We employ large-scale computer simulations to study these models in two geometries, (i) the spreading of particles on a semi-infinite domain with an absorbing wall at one end and (ii) the stationary state on a finite interval with absorbing boundaries at both ends and a source in the center. We demonstrate that the probability density and other properties of the fractional Langevin equation can be mapped onto the corresponding quantities of fractional Brownian motion driven by the same noise if the anomalous diffusion exponent α is replaced by 2 − α. In contrast, the properties of fractional Brownian motion and the fractional Langevin equation with reflecting boundaries were recently shown to differ from each other qualitatively. Specifically, we find that the probability density close to an absorbing wall behaves as P(x) ∼ x κ with the distance x from the wall in the long-time limit. In the case of fractional Brownian motion, κ varies with the anomalous diffusion exponent α as κ = 2/α − 1, as was conjectured previously. We also compare our simulation results to a perturbative analytical approach to fractional Brownian motion.

Detection of crossover points in detrended fluctuation analysis: an application to EEG signals of patients with epilepsy.

The quantification of long-range correlation of electroencephalogram (EEG) signals is an important research direction for its relevance in helping understanding the brain activity. Epileptic seizures have been studied in the past years where different non-linear statistical approaches have been employed to understand the relationship between the EEG signal and the epileptic discharge. One of the most widely used method for to analyse long memory processes is the detrended fluctuation analysis (DFA). However, no objective and pragmatic methods have been developed to detect crossover points and reference channels in DFA. In this article, we propose: (i) two automatic approaches that successfully detect crossover points in DFA related methods on the log-log plot and (ii) a criteria to choose the reference channel for the log-amplitude function. Moreover, the DFA is applied to EEG signals of 10 epileptic patients collected from the CHB-MIT database, being the log-amplitude function used to compare the different brain hemispheres by making use of the methodology proposed in the article. The existence of long-range power-law correlations is demonstrated and indicates that the EEG signals of epileptic patients present three well-defined regions with the first region showing a 1/f noise (pink noise) for seven subjects and a random walk behaviour for three subjects. The second and third regions show anti-persistence behaviour. Moreover, the results of the log-amplitude function were divided in two groups: the first, including seven subjects, where the increase in the scales results in an increase in the fluctuation in the frontal channels and the second, included three subjects, where the fluctuation for large scales are greater for the parietal channels. The functions used in this article are available in the R package DFA (Mesquita et al., 2020). Supplementary data are available at Bioinformatics online.

Random-mass disorder in the critical Gross-Neveu-Yukawa models

An important yet largely unsolved problem in the statistical mechanics of disordered quantum systems is to understand how quenched disorder affects quantum phase transitions in systems of itinerant fermions. In the clean limit, continuous quantum phase transitions of the symmetry-breaking type in Dirac materials such as graphene and the surfaces of topological insulators are described by relativistic (2+1)-dimensional quantum field theories of the Gross-Neveu-Yukawa (GNY) type. We study the universal critical properties of the chiral Ising, XY, and Heisenberg GNY models perturbed by quenched random-mass disorder, both uncorrelated or with long-range power-law correlations. Using the replica method combined with a controlled triple epsilon expansion below four dimensions, we find a variety of new finite-randomness critical and multicritical points with nonzero Yukawa coupling between low-energy Dirac fields and bosonic order parameter fluctuations, and compute their universal critical exponents. Analyzing bifurcations of the renormalization-group flow, we find instances of the fixed-point annihilation scenario—continuously tuned by the power-law exponent of long-range disorder correlations and associated with an exponentially large crossover length—as well as the transcritical bifurcation and the supercritical Hopf bifurcation. The latter is accompanied by the birth of a stable limit cycle on the critical hypersurface, which represents the first instance of fermionic quantum criticality with emergent discrete scale invariance.

Random deposition with surface relaxation model accompanied by long-range correlated noise

The random deposition with surface relaxation model which is accompanied by a long-range power law correlated noise is introduced. The particles are deposited in a selected distance of each other by a power law relation, Δi,j=int[u−12ρ], where u is chosen randomly over the range (0,1) while ρ is called the correlation strength exponent. Each deposited particle diffuses along the surface to find the position with the lowest height. Fractal analysis of the synthetic rough surfaces performed by multifractal detrended fluctuation analysis indicates that the height fluctuations are mono-affine for all values of correlation exponents; while in the random deposition with long-range correlation noise without any short-range correlations, multi-affinity is observed which is due to the diffusion of particles. Furthermore, the growth and roughness exponents increase up to ρc=0.5 which are in agreement with the theoretical relations as β=14+ρ2 and α=2β=12+ρ. For the higher values of correlation exponents (ρ>ρc), the investigated scaling exponents keep a constant value of β=0.5 and α=1 due to the competition of the long-range power law correlation and the short-range correlation raised from the nature of the investigated model.

Extended detrended fluctuation analysis of electroencephalograms signals during sleep and the opening of the blood-brain barrier.

Detrended fluctuation analysis (DFA) is widely used to characterize long-range power-law correlations in complex signals. However, it has restrictions when nonstationarity is not limited only to slow variations in the mean value. To improve the characterization of inhomogeneous datasets, we have proposed the extended DFA (EDFA), which is a modification of the conventional method that evaluates an additional scaling exponent to take into account the features of time-varying nonstationary behavior. Based on EDFA, here, we analyze rat electroencephalograms to identify specific changes in the slow-wave dynamics of brain electrical activity associated with two different conditions, such as the opening of the blood-brain barrier and sleep, which are both characterized by the activation of the brain drainage function. We show that these conditions cause a similar reduction in the scaling exponents of EDFA. Such a similarity may represent an informative marker of fluid homeostasis of the central nervous system.

Extended detrended fluctuation analysis of sound-induced changes in brain electrical activity

Abstract We discuss the problem of revealing structural changes in rat electroencephalograms (EEG) caused by activation of the brain lymphatic drainage function due to a sound-induced stress. For this purpose, we apply the detrended fluctuation analysis (DFA) with its extended version to characterize long-range power-law correlations associated with the slow-wave dynamics of the electrical activity of the brain. The proposed extended DFA (EDFA) provided a stronger separation of groups of rats with different permeability of the blood-brain barrier (BBB) compared to the conventional DFA technique. We argue that such abilities of this tool can be useful in other diagnostic-related studies.

Long-Time Memory in Drought via Detrended Fluctuation Analysis

The persistence of drought events largely determines the severity of socioeconomic and ecological impacts, unfortunately the performance of current weather forecasting models (WFM) to simulate such events is subject to great uncertainties. This study is investigating time-domain characteristics of drought persistence over Turkey by applying the detrended fluctuation analysis (DFA) method to the Palmer drought severity index (PDSI). The existence of long-range power-law correlation in PDSI fluctuations is demonstrated for time scales ranging from monthly to decadal. Understanding of such statistical patterns in PDSI values can definitely be a step forward in drought predictability. From a climatological point of view, it is found that the areas with high level DFA scaling exponent (generalized Hurst) indicate the areas of higher sensitivity to droughts and associated risks. Furthermore, the characteristics of the persistence of the PDSI in climate zones have also been examined by applying the Holdridge Life Zones (HLZ) classification. HLZ classification over Turkey leads to two climate-zones: cool-temperate and warm-temperate. In addition, when topography is taken in account, montane (cool-temperate) and lower-montane (warm-temperate) climate zones can be treated as two different zones. It has been observed that the predictable index (PI) of the PDSI derived from the DFA Hurst exponent is relatively high in the cool-temperate and montane climate zones compared to others. In fact, very different PI values were also obtained in a few HLZ climate classes within the same climate zone and with same vegetation index (i.e. steppe, dry-forest, warm-forest etc.).

Non-equilibrium critical dynamics of bursts in θ and δ rhythms as fundamental characteristic of sleep and wake micro-architecture.

Origin and functions of intermittent transitions among sleep stages, including short awakenings and arousals, constitute a challenge to the current homeostatic framework for sleep regulation, focusing on factors modulating sleep over large time scales. Here we propose that the complex micro-architecture characterizing the sleep-wake cycle results from an underlying non-equilibrium critical dynamics, bridging collective behaviors across spatio-temporal scales. We investigate θ and δ wave dynamics in control rats and in rats with lesions of sleep-promoting neurons in the parafacial zone. We demonstrate that intermittent bursts in θ and δ rhythms exhibit a complex temporal organization, with long-range power-law correlations and a robust duality of power law (θ-bursts, active phase) and exponential-like (δ-bursts, quiescent phase) duration distributions, typical features of non-equilibrium systems self-organizing at criticality. Crucially, such temporal organization relates to anti-correlated coupling between θ- and δ-bursts, and is independent of the dominant physiologic state and lesions, a solid indication of a basic principle in sleep dynamics.

Are cross-correlations between Turkish Stock Exchange and three major country indices multifractal or monofractal?

The analysis of linkages between financial markets has been a promising subject of study after globalization. Main consequence of these linkages is on transmission of the crisis from one country to another. Therefore, identifying and modeling of those linkages are important issues in the analysis of financial markets. According to studies the cross-correlations present nonlinear behavior and in general the well-known methods fail to predict such correlations. In this paper, we aim to show the existence of nonlinear cross-correlations between Turkish Stock Exchange and major developed country indices. For this purpose, we use the Multifractal Detrending Moving-Average Cross-correlation Analysis (MF-X-DMA) which is designed for detecting long-range power-law correlations. In the analysis we use the daily financial return and volatility series of Turkish stock market index BIST100 and developed market indexes which are S&P500, DAX30, FTSE100 for a period of 11 years between 01/01/2007-01/01/2018. The results show the existence of multifractality and long-range power-law cross-correlations.

Scale Analysis and Correlation Study of Wildfire and the Meteorological Factors That Influence It

Wildfire is a large-scale complex system. Insight into the mechanism that drives wildfires can be revealed by the distribution of the wildfire over a large time scale, which is one of the important topics in wildfire research. In this study, the scaling properties of four meteorological factors (relative humidity, daily precipitation, daily average temperature, and maximum wind speed) that can affect wildfires (number of wildfires per day) were investigated by using the detrended fluctuation analysis method. The results showed that the time series for these meteorological factors and wildfires have similar power exponents and turning points for the power exponents curve. The five types of time series have a lasting and steady long-range power law correlation over a certain time scale range, where the corresponding exponents were 0.6484, 0.5724, 0.8647, 0.7344, and 0.6734, respectively. They also have a reversible long-range power law correlation beyond a certain time scale, where the corresponding exponents are 0.3862, 0.2218, 0.1372, 0.2621, and 0.2678. The multifractal detrended fluctuation analysis results showed that the wildfire time series were multifractal. The results of the research based on the detrended cross-correlation analysis and the multifractal detrended cross-correlation analysis showed that relative humidity and daily precipitation have a considerable impact on the wildfire time series, while the impacts of daily average temperature and the maximum wind speed are relatively small. This study showed that identifying the factors causing the inherent volatility in the wildfire time series can improve understanding of the dynamic mechanism controlling wildfires and the meteorological parameters. These results can also be used to quantify the correlation between wildfire and the meteorological factors investigated in this study.

DNA Methylation Landscape Reflects the Spatial Organization of Chromatin in Different Cells

The relationship between DNA methylation and chromatin structure is still largely unknown. By analyzing a large set of published sequencing data, we observed a long-range power law correlation of DNA methylation with cell class-specific scaling exponents in the range of tens of kilobases. We showed that such cell class-specific scaling exponents are caused by different patchiness of DNA methylation in different cells. By modeling the chromatin structure using high-resolution chromosome conformation capture data and mapping the methylation level onto the modeled structure, we demonstrated that the patchiness of DNA methylation is related to chromatin structure. The scaling exponents of the power law correlation are thus a display of the spatial organization of chromatin. Besides the long-range correlation, we also showed that the local correlation of DNA methylation is associated with nucleosome positioning. The local correlation of partially methylated domains is different from that of nonpartially methylated domains, suggesting that their chromatin structures differ at the scale of several hundred base pairs (covering a few nucleosomes). Our study provides a novel, to our knowledge, view of the spatial organization of chromatin structure from a perspective of DNA methylation, in which both long-range and local correlations of DNA methylation along the genome reflect the spatial organization of chromatin.

On the temporal evolution of the tropical stratospheric ozone

According to recent findings the tropospheric-stratospheric temperature in the tropical atmosphere exhibits long range power-law persistence, which becomes stronger as the altitude increases. Because the ozone content is closely associated with the solar radiation and temperature we explore this effect in the vertical ozone distribution. We therefore analyze the tropical monthly mean ozone volume mixing ratios during `1980–2014, which is based on model simulations at heights 30−50km. The results obtained confirm that the modeled ozone data do not exhibit long-range power law correlations and therefore are not biased by a persistent signal.

Many-body localization and transition by density matrix renormalization group and exact diagonalization studies

A many-body localized (MBL) state is a new state of matter emerging in a disordered interacting system at high energy densities through a disorder driven dynamic phase transition. The nature of the phase transition and the evolution of the MBL phase near the transition are the focus of intense theoretical studies with open issues in the field. We develop an entanglement density matrix renormalization group (En-DMRG) algorithm to accurately target the entanglement patterns of highly excited states for MBL systems. By studying the one dimensional Heisenberg spin chain in a random field, we demonstrate the high accuracy of the method in obtaining statistical results of quantum states in the MBL phase. Based on large system simulations by En-DMRG for excited states, we demonstrate some interesting features in the entanglement entropy distribution function, which is characterized by two peaks; one at zero and another one at the quantized entropy $S=ln2$ with an exponential decay tail on the $S>ln2$ side. Combining En-DMRG with exact diagonalization simulations, we demonstrate that the transition from the MBL phase to the delocalized ergodic phase is driven by rare events where the locally entangled spin pairs develop long-range power-law correlations. The corresponding phase diagram contains an intermediate regime, which has power-law spin-z correlations resulting from contributions of the rare events. We discuss the physical picture for the numerical observations in the intermediate regime, where various distribution functions are distinctly different from results deep in the ergodic and MBL phases for finite-size systems. Our results may provide new insights for understanding the phase transition in such systems.

Persistence in eye movement during visual search.

As any cognitive task, visual search involves a number of underlying processes that cannot be directly observed and measured. In this way, the movement of the eyes certainly represents the most explicit and closest connection we can get to the inner mechanisms governing this cognitive activity. Here we show that the process of eye movement during visual search, consisting of sequences of fixations intercalated by saccades, exhibits distinctive persistent behaviors. Initially, by focusing on saccadic directions and intersaccadic angles, we disclose that the probability distributions of these measures show a clear preference of participants towards a reading-like mechanism (geometrical persistence), whose features and potential advantages for searching/foraging are discussed. We then perform a Multifractal Detrended Fluctuation Analysis (MF-DFA) over the time series of jump magnitudes in the eye trajectory and find that it exhibits a typical multifractal behavior arising from the sequential combination of saccades and fixations. By inspecting the time series composed of only fixational movements, our results reveal instead a monofractal behavior with a Hurst exponent , which indicates the presence of long-range power-law positive correlations (statistical persistence). We expect that our methodological approach can be adopted as a way to understand persistence and strategy-planning during visual search.

Multifractal Detrended fluctuation Analysis in Examining Surface Properties of the Gas-Sensing Metal-Containing Polyacrylonitrile

A possibility of applying the multifractal detrended fluctuation analysis (MF-DFA) to the investigation of the gas-sensitivity dependence on the thin-films surface morphology formed using different technological parameters of annealing has been studied. Methods of analyzing the dynamics of complex systems are modified so as to investigate the structure of the metal-containing polyacrylonitrile (PAN) thin films. The long-range power-law correlation in structure of the studied film surface has been studied. The analysis have showed that the time-temperature annealing modes increasing brings to the Hurst parameter value increasing that points to a long-range power-law correlation in structure of the studied film surface.&lt;br /&gt;