Presence Of Long-range Temporal Correlations Research Articles

Comparative multifractal analysis of methane gas concentration time series in India and regions within India

In the present study GOSAT CH4 has been used to analyze the methane gas concentration in India over the eight years from 2010 to 2017. The data have been analyzed using the multifractal detrended fluctuation analysis technique. Two different geographical regions within India have been selected and CH4 data for those regions are also analyzed. The generalized Hurst exponents for India and the two regions are 1.27, 0.74 and 0.91, which are significantly high from their shuffled data counterparts i.e. 0.50, 0.51 and 0.51 respectively. This finding reveals that methane gas concentration over time show multifractal nature which in turn establishes the presence of long-range temporal correlations in the data. The width of the Multifractal spectrum for India and the two regions are found to be 0.76, 1.38 and 1.01 respectively. This result shows that strength of correlation is different for the two regions selected, which we suggest may be due to the different methane emission process of the considered regions. Comparison of the results with that of shuffled data signify that the correlation is purely due to the methane production dynamics and not a result of mere statistics.

Studying Complex Adaptive Systems With Internal States: A Recurrence Network Approach to the Analysis of Multivariate Time-Series Data Representing Self-Reports of Human Experience

We discuss formal, theoretical and practical issues with the statistical analysis of multivariate time series data that represent self-reports of human experience, often referred to as Ecological Momentary Assessment (EMA) data, or, Experience Sampling Method (ESM) data. We argue such time series likely violate the assumptions required for valid statistical inference, such as the memoryless-ness property (due to the presence of long-range temporal correlations) and ergodicity (due to non-stationarity and non-homogeneity of central moments). Moreover, we consider the common practice of interpreting outcomes of self-reports as if they were outcomes of classical physical measurements as extremely problematic and suggest to consider them as records of the temporal evolution of observables of a complex adaptive system with internal state dynamics. We propose to address some of these issues by analyzing the Change Profile instead of the observed time series, using recurrence-bases analyses, specifically, (multiplex) recurrence networks. We analyze a publicly available data set in which 4 participants rated 6 questions about their self-esteem and physical self, twice a day over a period of 512 days and introduce the concept of recurrence networks weighted by recurrence time. The edge weights represent either recurrence times or recurrence time frequencies and results show the scaling relation between vertex degree and vertex strength (the weighted variant of vertex degree), is associated to the scaling relation between frequency and spectral power based on the ‘raw’ time series. In addition, we present a new spiral layout for recurrence networks that might be more appropriate when the detection of critical periods, regime shifts and tipping points requires insight in the temporal order in which those events occur. We conclude a complex systems approach to analyzing multivariate time series of self-reports of human experience is preferred over and above fitting statistical models like the Gaussian Graphical Model, or its derivatives.

Working memory performance inversely predicts spontaneous delta and theta-band scaling relations

Electrophysiological studies have strongly implicated theta-band activity in human working memory processes. Concurrently, work on spontaneous, non-task-related oscillations has revealed the presence of long-range temporal correlations (LRTCs) within sub-bands of the ongoing EEG, and has begun to demonstrate their functional significance. However, few studies have yet assessed the relation of LRTCs (also called scaling relations) to individual differences in cognitive abilities. The present study addressed the intersection of these two literatures by investigating the relation of narrow-band EEG scaling relations to individual differences in working memory ability, with a particular focus on the theta band. Fifty-four healthy adults completed standardized assessments of working memory and separate recordings of their spontaneous, non-task-related EEG. Scaling relations were quantified in each of the five classical EEG frequency bands via the estimation of the Hurst exponent obtained from detrended fluctuation analysis. A multilevel modeling framework was used to characterize the relation of working memory performance to scaling relations as a function of general scalp location in Cartesian space. Overall, results indicated an inverse relationship between both delta and theta scaling relations and working memory ability, which was most prominent at posterior sensors, and was independent of either spatial or individual variability in band-specific power. These findings add to the growing literature demonstrating the relevance of neural LRTCs for understanding brain functioning, and support a construct- and state-dependent view of their functional implications.

Modulation of cortical neural dynamics during thalamic deep brain stimulation in patients with essential tremor

Although thalamic deep brain stimulation is an effective treatment for patients with essential tremor, little is known about its effect on cortical neural dynamics. Therefore, we investigated long-range temporal correlations and spectral power in electroencephalographic recordings of patients during OFF versus ON bilateral thalamic deep brain stimulation in comparison with healthy controls. Cortical dynamics were analyzed in the range of 6-30 Hz. We found the presence of long-range temporal correlations up to 20 s in patients and controls. Thalamic deep brain stimulation was associated with increased long-range temporal correlations in the high beta band (21-30 Hz) and decreased power in the low beta band (13-20 Hz) compared with OFF stimulation and healthy controls. Long-range temporal correlations in the 6-10 Hz range were increased with OFF stimulation compared with the controls. Importantly, deep brain stimulation-induced changes in long-range temporal correlations within 6-10 Hz and in the beta ranges (13-20, 21-30 Hz) were correlated with OFF-ON changes in the tremor severity and with the disease duration, respectively. The differential reactivity of long-range temporal correlations and spectral power to deep brain stimulation might suggest that both measures reflect distinct aspects of cortical dynamics and might represent biomarkers for stimulation-induced modulations of neural dynamics in electroencephalography. The fact that long-range temporal correlations, but not spectral power, were correlated with clinical information might suggest long-range temporal correlations as a potential marker for disease severity in essential tremor.

Long-Range Temporal Correlations in Resting-State Alpha Oscillations Predict Human Timing-Error Dynamics

Human behavior is imperfect. This is notably clear during repetitive tasks in which sequences of errors or deviations from perfect performance result. These errors are not random, but show patterned fluctuations with long-range temporal correlations that are well described using power-law spectra P(f)∝1/f(β), where β is the power-law scaling exponent describing the decay in temporal correlations. The neural basis of temporal correlations in such behaviors is not known. Interestingly, long-range temporal correlations are a hallmark of amplitude fluctuations in resting-state neuronal oscillations. Here, we investigated whether the temporal dynamics in brain and behavior are related. Thirty-nine subjects' eyes-open rest EEG was measured. Next, subjects reproduced without feedback a 1 s interval by tapping with their right index finger. In line with previous reports, we found evidence for the presence of long-range temporal correlations both in the amplitude modulation of resting-state oscillations in multiple frequency bands and in the timing-error sequences. Frequency scaling exponents of finger tapping and amplitude modulation of oscillations exhibited large individual differences. Neuronal dynamics of resting-state alpha-band oscillations (9-13 Hz) recorded at precentral sites strongly predicted scaling exponents of tapping behavior. The results suggest that individual variation in resting-state brain dynamics offer a neural explanation for individual variation in the error dynamics of human behavior.

Adaptive time-varying detrended fluctuation analysis

Detrended fluctuation analysis (DFA) is a technique commonly used to assess and quantify the presence of long-range temporal correlations (LRTCs) in neurophysiological time series. Convergence of the method is asymptotic only and therefore its application assumes a constant scaling exponent. However, most neurophysiological data are likely to involve either spontaneous or experimentally induced scaling exponent changes. We present a novel extension of the DFA method that permits the characterisation of time-varying scaling exponents. The effectiveness of the methodology in recovering known changes in scaling exponents is demonstrated through its application to synthetic data. The dependence of the method on its free parameters is systematically explored. Finally, application of the methodology to neurophysiological data demonstrates that it provides experimenters with a way to identify previously un-recognised changes in the scaling exponent in the data. We suggest that this methodology will make it possible to go beyond a simple demonstration of the presence of scaling to an appreciation of how it may vary in response to either intrinsic changes or experimental perturbations.

Adaptive time-varying detrended fluctuations analysis: a new method for characterizing time-varying scaling parameters in physiological time series

Detrended fluctuations analysis (DFA) [1] is a technique commonly used to assess the presence of long-range temporal correlations (LRTCs) in physiological time series. The method is based on assessing the parameters of the linear regression in the loglog space of the residuals of the detrended signal over different box sizes; providing an estimate of the Hurst exponent. Convergence of the method is asymptotic only [2] and therefore its application requires lengthy time series assuming a stationary scaling exponent. Methods for dealing with nonstationarities due to, e.g., data manipulation (e.g., stitching), addition of random outliers or the presence of different standard deviations or correlations assume the superposition of independent processes and rely on a graphical interpretation of changes in the slope of the residuals at various box sizes [3]. However, most neurophysiological experiments involve a task or neurophysiological perturbations. These may disrupt the LRTCs in unexpected and interesting ways. It is therefore of importance to devise a robust method for tracking changes in the parameter that best characterizes LRTCs. We derived analytical formulations for the bias and variance of the error committed when using the scaling exponent obtained by DFA on a given time-series to predict the scaling exponent of the same time-series but shifted by one sample (assuming the scaling exponent is stationary at a very short time scale). These results make it possible to define a Kalman filter for tracking fluctuations in scaling exponents over a longer time scale. Estimates for the measurement noise of the filter are obtained by pooling DFA estimates of the signal across a small number of time shifts. Robust estimates of the state vector are obtained by augmenting the filter with a smoothing procedure. Simulation results with surrogate time series demonstrate that this technique makes it possible to accurately recover changing scaling exponents even in the presence of rapid fluctuations (see Figure ​Figure1).1). It therefore provides a robust mechanism with which experimenters may be able to measure changes in the strength of LRTCs within their data. This may help move the debate concerning scale-free behavior of time series on from a simple demonstration of the existence of LRTCs to an appreciation of how their magnitude may vary systematically in response to experiments. Figure 1 Comparison between standard DFA (black line, value obtained over whole record) and adaptive time-varying DFA (green line). The actual scaling exponent is shown in red.

Detecting the presence of long-range temporal correlations in a time-varying measure of phase synchrony

Time-averaged coherence between human EEG and EMG signals has been found to increase with age of subject [1]. This is indicative of the underlying physiological system progressively reaching a level of synchrony, which allows it to perform tasks with efficiency. Recent experiments [2] have shown that physiological signals such as the EEG show long-range temporal correlations (LRTCs), implying that the brain may be poised in a critical state. It has been suggested that self-organization to such a critical state reflects a developing interaction of neuronal groups over a range of scales [3]. Since synchrony is an important method of communication between different neuronal groups it is of interest to determine whether its time course could reveal the presence of critical dynamics. To our knowledge, the only paper to have tackled this issue is [4], in which scale-free dynamics are suggested in fMRI and MEG data. This is done by demonstrating power laws in the probability distribution of phase-locked intervals between signals from related channels. Here, we present our own methodology, which relies on searching for LRTCs in a measure of instantaneous synchrony between two signals. We first compute the analytical phases of two signals through the Hilbert Transform. The differential of the phase is taken to obtain a frequency measure, and the difference of these time series is calculated to provide an instantaneous synchrony level between the original signals. Detrended fluctuation analysis is then performed to ascertain the presence of LRTCs through an estimation of the Hurst exponent. LRTCs exist when the exponent is greater than 0.5 (a value of 0.5 indicates uncorrelated noise). To demonstrate the method, we replicate the findings of [4] on the Ising model, which passes a transition from subcritical to supercritical behavior at a known parameter value. As shown in Figure ​Figure1,1, as the temperature in the Ising model is increased the system passes through a critical state (2.2-2.4) at which a non-trivial exponent is obtained (α=0.63). At non-critical temperatures, the exponent indicates a signal similar to white noise. Figure 1 DFA exponents of synchrony between two regions in Ising model when the system undergoes transition from subcritical to supercritical state. The peak in DFA values is observed in the theoretically critical range of this system, 2.2-2.4. Error bars are ... The methodology presented here displays greater generality than that described in [4]. Specifically, it avoids the use of an arbitrary threshold to determine the boundary of synchronization, and does not use time averaging in assessing instantaneous synchrony. The construction of a time-varying phase synchrony measure between two signals and the determination of whether synchrony in a system is in a critical state has significant implications for understanding the development of the nervous system, when applied to neurophysiological data.

Influence of filters in the detrended fluctuation analysis of digital electroencephalographic data

The technique named detrended fluctuation analysis (DFA) has been used to reveal the presence of long-range temporal correlations (LRTC) and scaling behavior (SB) in electroencephalographic (EEG) recordings. The occurrence of these phenomena seems to be a salient characteristic of the healthy human brain and alterations in different pathologies has been described. Here we show how the filtering stages implemented in the systems for digital EEG influence the estimation of the DFA parameters used to characterize the brain signals. In consequence, we conclude that it is important to consider these filtering effects before interpreting the results obtained from digital EEG recordings.

Long-range temporal correlations in electroencephalographic oscillations: Relation to topography, frequency band, age and gender

Presence of long-range temporal correlations in neuronal oscillations is thought to be beneficial for a reliable transfer of information in neuronal networks. In the present study long-range temporal correlations in electroencephalographic (EEG) neuronal oscillations were characterized with respect to their topography, frequency-band specificity (α and β oscillations), gender and age. EEG was recorded in 91 normal subjects (age 20–65 years) in a resting condition. The amplitude of ongoing α and β oscillations was extracted with band-pass filtering and Hilbert transform, and long-range temporal correlations were analyzed with detrended fluctuation analysis. The topography of long-range temporal correlations was comparable for α and β oscillations, showing largest scaling exponents in the occipital and parietal areas. This topography was partially similar to that of the power distribution and a weak positive correlation was observed between long-range temporal correlations and power of neuronal oscillations. Long-range temporal correlations were stronger in α than β oscillations, but only in a few electrode locations in the left hemisphere. In both frequency bands long-range temporal correlations were stronger in males than in females and were largely unaffected by the age of the subjects. It is hypothesized that the idling state of the occipital areas in the closed-eyes condition may explain both large power values and pronounced long-range temporal correlations in this region.

Long-range temporal correlations in alpha and beta oscillations: effect of arousal level and test–retest reliability

Objective: The aim of the present study was to evaluate test–retest reliability and condition sensitivity of long-range temporal correlations in the amplitude dynamics of electroencephalographic alpha and beta oscillations. Methods: Twelve normal subjects were measured two times with a test–retest interval of several days. Open- and closed-eyes conditions were used, representing different levels of arousal. The amplitude of the alpha and beta oscillations was extracted with bandpass filtering and the Hilbert transform. The long-range temporal correlations were quantified with detrended fluctuation analysis. Results: The amplitude dynamics of the alpha and beta oscillations demonstrated power-law long-range temporal correlations lasting for tens of seconds. These correlations were degraded in the open- compared to the closed-eyes condition. Test–retest statistics demonstrated that the long-range temporal correlations had significant reliability, which was greatest in the closed-eyes condition. Conclusions: The presence of long-range temporal correlations indicates that the amplitude of neuronal oscillations at a given time is dependent on the amplitude at times as remote in the past as tens of seconds. The reliability of long-range temporal correlations suggests that the mechanisms generating the amplitude fluctuations are not perturbed over several days. The systematic changes in the scaling exponents at different levels of arousal indicate that these changes occur on many time scales (5–80 s) as a result of modifications in the intrinsic dynamics of the neuronal oscillations. Significance: This study demonstrates that the dynamics of spontaneous neuronal oscillations possess long-range temporal correlations with properties suitable for functional and clinical studies.

Long-range temporal correlations in epileptogenic and non-epileptogenic human hippocampus

Epileptogenic human hippocampus generates spontaneous energy fluctuations with a wide range of amplitude and temporal variation, which are often assumed to be entirely random. However, the temporal dynamics of these fluctuations are poorly understood, and the question of whether they exhibit persistent long-range temporal correlations (LRTC) remains unanswered. In this paper we use detrended fluctuation analysis (DFA) to show that the energy fluctuations in human hippocampus show LRTC with power-law scaling, and that these correlations differ between epileptogenic and non-epileptogenic hippocampus. The analysis shows that the energy fluctuations exhibit slower decay of the correlations in the epileptogenic hippocampus compared with the non-epileptogenic hippocampus. The DFA-derived scaling exponents demonstrate that there are LRTC of energy fluctuations in human hippocampus, and that the temporal persistence of energy fluctuations is characterized by a bias for large (small) energy fluctuations to be followed by large (small) energy fluctuations. Furthermore, we find that in the period of time leading up to seizures there is no change in the scaling exponents that characterize the LRTC of energy fluctuations. The fact that the LRTC of energy fluctuations do not change as seizures approach provides evidence that the local neuronal network dynamics do not change in the period before seizures, and that seizures in mesial temporal lobe epilepsy may be triggered by an influence that is external to the hippocampus. The presence of LRTC with power-law scaling does not imply a specific mechanism, but the finding that temporal correlations decay more slowly in epileptogenic hippocampus provides electrophysiologic evidence that the underlying neuronal dynamics are different within the epileptogenic hippocampus compared with contralateral hippocampus. We briefly discuss possible neurobiological mechanisms for LRTC of the energy fluctuations in hippocampus.