Surrogate Data Testing Research Articles

Testing dynamic correlations and nonlinearity in bivariate time series through information measures and surrogate data analysis.

The increasing availability of time series data depicting the evolution of physical system properties has prompted the development of methods focused on extracting insights into the system behavior over time, discerning whether it stems from deterministic or stochastic dynamical systems. Surrogate data testing plays a crucial role in this process by facilitating robust statistical assessments. This ensures that the observed results are not mere occurrences by chance, but genuinely reflect the inherent characteristics of the underlying system. The initial process involves formulating a null hypothesis, which is tested using surrogate data in cases where assumptions about the underlying distributions are absent. A discriminating statistic is then computed for both the original data and each surrogate data set. Significantly deviating values between the original data and the surrogate data ensemble lead to the rejection of the null hypothesis. In this work, we present various surrogate methods designed to assess specific statistical properties in random processes. Specifically, we introduce methods for evaluating the presence of autodependencies and nonlinear dynamics within individual processes, using Information Storage as a discriminating statistic. Additionally, methods are introduced for detecting coupling and nonlinearities in bivariate processes, employing the Mutual Information Rate for this purpose. The surrogate methods introduced are first tested through simulations involving univariate and bivariate processes exhibiting both linear and nonlinear dynamics. Then, they are applied to physiological time series of Heart Period (RR intervals) and respiratory flow (RESP) variability measured during spontaneous and paced breathing. Simulations demonstrated that the proposed methods effectively identify essential dynamical features of stochastic systems. The real data application showed that paced breathing, at low breathing rate, increases the predictability of the individual dynamics of RR and RESP and dampens nonlinearity in their coupled dynamics.

Revisiting nonlinearity of heart rate variability in healthy aging

Aging is commonly regarded as a physiological process in which the dynamic complexity of physiological time series and organ systems is gradually lost. This notion is derived from the identification of a decline of nonlinear measures with the advance of aging. However, additional research on cardiovascular control studied through heart rate variability (HRV), i.e., the instantaneous changes in heart rate, shows that despite the constriction of its statistical distribution, the nonlinear organization remains present in advanced age. Here, we used surrogate data testing to investigate the presence of nonlinear information in HRV time series from a publicly available database of 1121 healthy human subjects from 18 to 92 years old. We also studied the influence of basic clinical features, such as sex, body mass index (BMI), and mean heart rate (HR), on such nonlinear information. We found that the percentage of nonlinear time series after 30 years of age diminishes significantly (p < 0.01). Furthermore, larger BMI and HR are associated with the presence of more linear information in HRV, while the female sex is associated with the manifestation of nonlinear information. This work provides a common background for the contextualized interpretation of nonlinear testing and shows that the nonlinear content of HRV time series diminishes through aging.

Neural Cross-Frequency Coupling Functions in Sleep

The human brain presents a heavily connected complex system. From a relatively fixed anatomy, it can enable a vast repertoire of functions. One important brain function is the process of natural sleep, which alters consciousness and voluntary muscle activity. On neural level, these alterations are accompanied by changes of the brain connectivity. In order to reveal the changes of connectivity associated with sleep, we present a methodological framework for reconstruction and assessment of functional interaction mechanisms. By analyzing EEG (electroencephalogram) recordings from human whole night sleep, first, we applied a time–frequency wavelet transform to study the existence and strength of brainwave oscillations. Then we applied a dynamical Bayesian inference on the phase dynamics in the presence of noise. With this method we reconstructed the cross-frequency coupling functions, which revealed the mechanism of how the interactions occur and manifest. We focus our analysis on the delta-alpha coupling function and observe how this cross-frequency coupling changes during the different sleep stages. The results demonstrated that the delta-alpha coupling function was increasing gradually from Awake to NREM3 (non-rapid eye movement), but only during NREM2 and NREM3 deep sleep it was significant in respect of surrogate data testing. The analysis on the spatially distributed connections showed that this significance is strong only for within the single electrode region and in the front-to-back direction. The presented methodological framework is for the whole-night sleep recordings, but it also carries general implications for other global neural states.

Ordinal pattern-based complexity analysis of high-dimensional chaotic time series.

The ordinal pattern-based complexity-entropy plane is a popular tool in nonlinear dynamics for distinguishing stochastic signals (noise) from deterministic chaos. Its performance, however, has mainly been demonstrated for time series from low-dimensional discrete or continuous dynamical systems. In order to evaluate the usefulness and power of the complexity-entropy (CE) plane approach for data representing high-dimensional chaotic dynamics, we applied this method to time series generated by the Lorenz-96 system, the generalized Hénon map, the Mackey-Glass equation, the Kuramoto-Sivashinsky equation, and to phase-randomized surrogates of these data. We find that both the high-dimensional deterministic time series and the stochastic surrogate data may be located in the same region of the complexity-entropy plane, and their representations show very similar behavior with varying lag and pattern lengths. Therefore, the classification of these data by means of their position in the CE plane can be challenging or even misleading, while surrogate data tests based on (entropy, complexity) yield significant results in most cases.

Nonlinear Dynamics of Heart Rate Variability after Acutely Induced Myocardial Ischemia by Percutaneous Transluminal Coronary Angioplasty.

Several heart rate variability (HRV) characteristics of patients with myocardial ischemia are associated with a higher mortality risk. However, the immediate effect of acute ischemia on the HRV nonlinear dynamical behavior is unknown. The objective of this work is to explore the presence of nonlinearity through surrogate data testing and describe the dynamical behavior of HRV in acutely induced ischemia by percutaneous transluminal coronary angioplasty (PTCA) with linear and recurrence quantification analysis (RQA). Short-term electrocardiographic recordings from 68 patients before and after being treated with elective PTCA were selected from a publicly available database. The presence of nonlinear behavior was confirmed by determinism and laminarity in a relevant proportion of HRV time series, in up to 29.4% during baseline conditions and 30.9% after PTCA without statistical difference between these scenarios. After PTCA, the mean value and standard deviation of HRV time series decreased, while determinism and laminarity values increased. Here, the diminishment in overall variability caused by PTCA is not accompanied by a change in nonlinearity detection. Therefore, the presence of nonlinear behavior in HRV time series is not necessarily in agreement with the change of traditional and RQA measures.

Modified multiscale sample entropy and cross-sample entropy based on horizontal visibility graph

As a crucial method of the feature extraction, the complexity measurement has a wide range of applications in the field of nonlinear time series research. This paper presents an innovative multiscale sample entropy for measuring the complexity of time series based on the horizontal visibility graph. The modified multiscale sample entropy has been proven to be robust on two artificial time series, and is capable of reducing the undefined entropy generated as a result of the increase in scale. We apply the modified multiscale sample entropy to the diagnosis of epilepsy. Using a novel data processing algorithm that combines frequency bands with decomposition, feature vectors are constructed for Electroencephalography (EEG) signals through the proposed entropy calculation algorithm, and different classes of subjects are categorized based on K-Nearest Neighbors, Support Vector Machine, and Artificial Neural Network. In the meantime, we propose an improved horizontal visibility graph-based multiscale cross-sample entropy method to measure the synchronization between two time series. It shows robustness in artificial data and decreases the appearance of undefined entropy to a certain extent. It is possible to extract the characteristics of sleep EEG signals and divide the subjects’ sleep stages using this method. Furthermore, this paper introduces the surrogate data test and the proposed methods have the ability to detect the nonlinearity and synchronization in simulations and in real-world experiments. Experimental results demonstrate that the two proposed frameworks are effective in monitoring human health and in assessing physical status through EEG signals.

A singular value decomposition entropy approach to assess the impact of Covid-19 on the informational efficiency of the WTI crude oil market

This work investigates the impact of the Covid-19 outbreak on crude oil market efficiency. The approach is based on the singular value decomposition (SVD) entropy. Iso-distributional surrogate data test was used to contrast the results against random patterns, and phase randomization based on Fourier transform was used to assess nonlinearities. The analysis considered the WTI market and focused on the Covid-19 pandemic period January 2020–November 2021 and contrasted with the long preceding period from January 2000 to date. It was found that the crude oil market was informationally efficient most of the time with small sporadic deviations from efficiency in the pre-Covid-19 years. The Covid-19 period exhibited the largest deviations from efficiency, mainly in the first months of the outbreak, accompanied by a marked reduction of nonlinear components. The analysis was conducted for different scales, and the results showed that the deviations from efficiency were more pronounced for quarterly scales. For the sake of comparison, the analysis was also carried out on the trading volume dynamics and the results showed that the market activity is not fully random. The dynamics of the trading volume exhibited significant deviations from the randomness behavior when the crude oil market was efficient, and a behavior that was consistent with nonlinear patterns. The opposite behavior was noted for stages when the crude oil market showed strong deviations from efficiency. Overall, the findings of this study suggest an increasing opportunity for crude oil price predictions and abnormal returns during the Covid-19 pandemic.

Recurrence Quantitative Analysis of Wavelet-Based Surrogate Data for Nonlinearity Testing in Heart Rate Variability.

Exploring the presence of nonlinearity through surrogate data testing provides insights into the nature of physical and biological systems like those obtained from heart rate variability (HRV). Short-term HRV time series are of great clinical interest to study autonomic impairments manifested in chronic diseases such as the end stage renal disease (ESRD) and the response of patients to treatment with hemodialysis (HD). In contrast to Iterative Amplitude Adjusted Fourier Transform (IAAFT), the Pinned Wavelet Iterative Amplitude Adjusted Fourier Transform (PWIAAFT) surrogates preserve nonstationary behavior in time series, a common characteristic of HRV. We aimed to test synthetic data and HRV time series for the existence of nonlinearity. Recurrence Quantitative Analysis (RQA) indices were used as discriminative statistics in IAAFT and PWIAAFT surrogates of linear stationary and nonstationary processes. HRV time series of healthy subjects and 29 ESRD patients before and after HD were tested in this setting during an active standing test. Contrary to PWIAAFT, linear nonstationary time series may be erroneously regarded as nonlinear according to the IAAFT surrogates. Here, a lower proportion of HRV time series was classified as nonlinear with PWIAAFT, compared to IAAFT, confirming that the nonstationarity condition influences the testing of nonlinear behavior in HRV. A contribution of nonlinearity was found in the HRV data of healthy individuals. A lower proportion of nonlinear time series was also found in ESRD patients, but statistical significance was not found. Although this proportion tends to be lower in ESRD patients, as much as 60% of time series proved to be nonlinear in healthy subjects. Given the important contribution of nonlinearity in HRV data, a nonlinear point of view is required to achieve a broader understanding of cardiovascular physiology.

Enhanced symplectic geometry mode decomposition and its application to rotating machinery fault diagnosis under variable speed conditions

Tacholess order tracking (TLOT) has been one of the most powerful and applicable rotating machinery fault diagnosis methods. However, it is still a challenge to accurately estimate the instantaneous phase of the reference shaft under variable speed conditions. Although current available signal decomposition methods can deal with non-stationary vibration signal, they are probably interfered by some tough problems, such as prior knowledge requirement or heavy computational burden. In this paper, the aforementioned problems are addressed and an adaptive harmonic components extraction framework is proposed. Firstly, the vibration signal is low-pass filtered and down-sampled for computation speed acceleration. Harmonic components are subsequently extracted by enhanced symplectic geometry mode decomposition (ESGMD), which is based on Cramer-von Mises criterion. Secondly, surrogate data test is applied for pseudo components identification, thereby interferences induced by background noise can be filtered out adaptively. Finally, Hilbert transform is applied to obtain the instantaneous phase of the decomposed fundamental harmonic component, and thereby TLOT is conducted to realize fault diagnosis. The effectiveness of the proposed method has been validated by both simulated and experimental tests. The results exhibit that the proposed method outperforms conventional approaches in harmonic components extraction for rotating machinery fault diagnosis under variable speed conditions.

Characterization of ground oscillations induced by underground mining

We examine ground acceleration during M1.5 and M2.0 seismic events induced by underground mining at Upper Silesian coal basin and Legnica Glogow copper mine, respectively, using methods of nonlinear time series analysis, in order to confirm its stochastic nature. Recorded time series are firstly embedded into the adequate phase space using the mutual information and box-assisted methods. After this, we performed stationarity test, by which we confirmed that the examined ground acceleration belongs to a group of stationary processes. Surrogate data testing is applied then, which resulted in following: (1) horizontal ground acceleration at Legnica Glogow copper mine represents stationary linear stochastic processes with Gaussian inputs, (2) ground acceleration at Upper Silesian coal basin originates from a stationary Gaussian linear process that has been distorted by a monotonic, instantaneous, time-independent non-linear function, (3) vertical ground acceleration at Legnica Glogow copper mine could not be ascribed to any of the examined processes, probably due to high level of instrumental or background noise. Low values of determinism coefficient (c≤0.7), negative values of maximum Lyapunov exponent and quick saturation of neighboring points distance with the increase of embedding dimension indicate the absence of determinism in the observed ground acceleration time series.

Testing for nonlinearity in nonstationary time series: A network-based surrogate data test

The classical surrogate data tests, which are used to differentiate linear noise processes from nonlinear processes, are not suitable for nonstationary time series. In this paper, we propose a surrogate data test that can be applied on both stationary time series as well as nonstationary time series with short-term fluctuations. The method is based on the idea of constructing a network from the time series, employing a generalized symbolic dynamics method introduced in this work, and using any one of the several easily computable network parameters as discriminating statistics. The construction of the network is designed to remove the long-term trends in the data automatically. The network-based test statistics pick up only the short-term variations, unlike the discriminating statistics of the traditional methods, which are influenced by nonstationary trends in the data. The method is tested on several systems generated by linear or nonlinear processes and with deterministic or stochastic trends, and in all cases it is found to be able to differentiate between linear stochastic processes and nonlinear processes quite accurately, especially in cases where the common methods would lead to false rejections of the null hypothesis due to nonstationarity being interpreted as nonlinearity. The method is also found to be robust to the presence of experimental or dynamical noise of a moderate level in an otherwise nonlinear system.

Changes in the dynamics of seismic process observed in the fixed time windows; case study for southern California 1980–2020

In the present work we investigated changes in the extent of regularity (randomness) of seismic process in fixed time span windows. A comparison with a set of randomized catalogues was accomplished basing on spatial, temporal and energetic characteristics of a seismic process. Increments of cumulative times, increments of cumulative distances and increments of cumulative seismic energies have been calculated from the southern California earthquake catalogue, 1980 to 2020.The multivariate Mahalanobis' distance calculation, combined with the surrogate data testing procedure, was chosen as the analysis method. An analysis of variability in the extent of regularity of a seismic process has been accomplished for different completeness magnitude thresholds and sliding windows of different time spans.Analysing the features of temporal, spatial and energetic variability, in periods of supposedly aftershock activity, we found that the original seismic process is significantly different from a random process. Such periods, containing windows with nonrandom seismicity, are always ended by a series of windows in which a seismic process is indistinguishable from a random one. This was shown at different magnitude thresholds, comparing the original catalogue with the set of randomized catalogues.It was also found that at small magnitude thresholds (M2.6 and M3.0), the fixed time span windows with a seismic process significantly different from the random process might have occurred also prior to four large (M > 7.0) earthquakes in the considered catalogue. The amount of the released seismic energy in these windows is essentially smaller than in the ones after strong earthquakes of smaller magnitudes. Relying on our results we suggest that causes of regularity in the seismic process prior and after large earthquakes are probably different.At larger-magnitude thresholds, the total number of fixed time windows with a seismic process different from the random one gradually decreases. Moreover, at M3.8 and M4.2 thresholds there are practically no windows with regular seismic process prior to four large catalogue earthquakes. In the periods between strong earthquakes, mostly in the periods of relatively small earthquakes generation, the percentage of windows in which the seismic process is indistinguishable from the random one essentially increases with increasing magnitude threshold.

Cross-Scale Causality and Information Transfer in Simulated Epileptic Seizures.

An information-theoretic approach for detecting causality and information transfer was applied to phases and amplitudes of oscillatory components related to different time scales and obtained using the wavelet transform from a time series generated by the Epileptor model. Three main time scales and their causal interactions were identified in the simulated epileptic seizures, in agreement with the interactions of the model variables. An approach consisting of wavelet transform, conditional mutual information estimation, and surrogate data testing applied to a single time series generated by the model was demonstrated to be successful in the identification of all directional (causal) interactions between the three different time scales described in the model. Thus, the methodology was prepared for the identification of causal cross-frequency phase–phase and phase–amplitude interactions in experimental and clinical neural data.

Multifractal Dynamics in Executive Control When Adapting to Concurrent Motor Tasks.

There is some evidence that an improved understanding of executive control in the human movement system could be gained from explorations based on scale-free, fractal analysis of cyclic motor time series. Such analyses capture non-linear fractal dynamics in temporal fluctuations of motor instances that are believed to reflect how executive control enlist a coordination of multiple interactions across temporal scales between the brain, the body and the task environment, an essential architecture for adaptation. Here by recruiting elite rugby players with high motor skills and submitting them to the execution of rhythmic motor tasks involving legs and arms concurrently, the main attempt was to build on the multifractal formalism of movement control to show a marginal need of effective adaptation in concurrent tasks, and a preserved adaptability despite complexified motor execution. The present study applied a multifractal analytical approach to experimental time series and added surrogate data testing based on shuffled, ARFIMA, Davies&Harte and phase-randomized surrogates, for assessing scale-free behavior in repeated motor time series obtained while combining cycling with finger tapping and with circling. Single-tasking was analyzed comparatively. A focus-based multifractal-DFA approach provided Hurst exponents (H) of individual time series over a range of statistical moments H(q), q = [−15 15]. H(2) quantified monofractality and H(-15)-H(15) provided an index of multifractality. Despite concurrent tasking, participants showed great capacity to keep the target rhythm. Surrogate data testing showed reasonable reliability in using multifractal formalism to decipher movement control behavior. The global (i.e., monofractal) behavior in single-tasks did not change when adapting to dual-task. Multifractality dominated in cycling and did not change when cycling was challenged by upper limb movements. Likewise, tapping and circling behaviors were preserved despite concurrent cycling. It is concluded that the coordinated executive control when adapting to dual-motor tasking is not modified in people having developed great motor skills through physical training. Executive control likely emerged from multiplicative interactions across temporal scales which puts emphasis on multifractal approaches of the movement system to get critical cues on adaptation. Extending such analyses to less skilled people is appealing in the context of exploring healthy and diseased movement systems.

Optimal COVID-19 infection spread under low temperature, dry air, and low UV radiation

The COVID-19 pandemic, caused by the novel coronavirus SARS-CoV-2, is spreading rapidly throughout the world, causing many deaths and severe economic damage. It is believed that hot and humid conditions do not favor the novel coronavirus, yet this is still under debate due to many uncertainties associated with the COVID-19 data. Here we propose surrogate data tests to examine the preference of this virus to spread under different climate conditions. We find, by mainly studying the relative number of COVID-19 deaths, that the disease is significantly (above the 95% confidence level) more common when the temperature is ∼10 °C, the relative humidity is ∼60%, the specific humidity is ∼5 g kg−1, and the ultraviolet radiation is less than ∼50 kJ m−2 (per hour). We also find, but less significantly, that the relative number of COVID-19 deaths is high when the wind is weak and low when the wind is strong. The results are supported based on global and regional data, spanning the time period from January to December 2020. The COVID-19 data includes the daily reported new cases and the daily deaths; for both, the population size is either taken into account or ignored.

Modifications in the Topological Structure of EEG Functional Connectivity Networks during Listening Tonal and Atonal Concert Music in Musicians and Non-Musicians.

The present work aims to demonstrate the hypothesis that atonal music modifies the topological structure of electroencephalographic (EEG) connectivity networks in relation to tonal music. To this, EEG monopolar records were taken in musicians and non-musicians while listening to tonal, atonal, and pink noise sound excerpts. EEG functional connectivities (FC) among channels assessed by a phase synchronization index previously thresholded using surrogate data test were computed. Sound effects, on the topological structure of graph-based networks assembled with the EEG-FCs at different frequency-bands, were analyzed throughout graph metric and network-based statistic (NBS). Local and global efficiency normalized (vs. random-network) measurements (NLE|NGE) assessing network information exchanges were able to discriminate both music styles irrespective of groups and frequency-bands. During tonal audition, NLE and NGE values in the beta-band network get close to that of a small-world network, while during atonal and even more during noise its structure moved away from small-world. These effects were attributed to the different timbre characteristics (sounds spectral centroid and entropy) and different musical structure. Results from networks topographic maps for strength and NLE of the nodes, and for FC subnets obtained from the NBS, allowed discriminating the musical styles and verifying the different strength, NLE, and FC of musicians compared to non-musicians.

Multifractal and Entropy-Based Analysis of Delta Band Neural Activity Reveals Altered Functional Connectivity Dynamics in Schizophrenia.

Dynamic functional connectivity (DFC) was established in the past decade as a potent approach to reveal non-trivial, time-varying properties of neural interactions – such as their multifractality or information content –, that otherwise remain hidden from conventional static methods. Several neuropsychiatric disorders were shown to be associated with altered DFC, with schizophrenia (SZ) being one of the most intensely studied among such conditions. Here we analyzed resting-state electroencephalography recordings of 14 SZ patients and 14 age- and gender-matched healthy controls (HC). We reconstructed dynamic functional networks from delta band (0.5–4 Hz) neural activity and captured their spatiotemporal dynamics in various global network topological measures. The acquired network measure time series were made subject to dynamic analyses including multifractal analysis and entropy estimation. Besides group-level comparisons, we built a classifier to explore the potential of DFC features in classifying individual cases. We found stronger delta-band connectivity, as well as increased variance of DFC in SZ patients. Surrogate data testing verified the true multifractal nature of DFC in SZ, with patients expressing stronger long-range autocorrelation and degree of multifractality when compared to controls. Entropy analysis indicated reduced temporal complexity of DFC in SZ. When using these indices as features, an overall cross-validation accuracy surpassing 89% could be achieved in classifying individual cases. Our results imply that dynamic features of DFC such as its multifractal properties and entropy are potent markers of altered neural dynamics in SZ and carry significant potential not only in better understanding its pathophysiology but also in improving its diagnosis. The proposed framework is readily applicable for neuropsychiatric disorders other than schizophrenia.

Information theoretic measures of perinatal cardiotocography synchronization.

We examined the use of bivariate mutual information (MI) and its conditional variant transfer entropy (TE) to address synchronization of perinatal uterine pressure (UP) and fetal heart rate (FHR). We used a nearest-neighbour based Kraskov entropy estimator, suitable to the non-Gaussian distributions of the UP and FHR signals. Moreover, the estimates were robust to noise by use of surrogate data testing. Estimating degree of synchronicity and UP-FHR delay length is useful since they are physiological correlates to fetal hypoxia. Mutual information of the UP-FHR discriminated normal and pathological fetuses early (160 min before delivery) and discriminated normal and metabolic acidotic fetuses slightly later (110 min before delivery), with higher mutual information for progressively pathological classes. The delay in mutual information transfer was also discriminating in the last 50 min of labour. Transfer entropy discriminated normal and pathological cases 110 min before delivery with lower TE values and longer information transfer delays in pathological cases, to our knowledge, the first report of this phenomena in the literature.

Existence of Long Memory Phenomenon in Air Pollutant Concentrations using Surrogate Data

This study investigated the existence of long memory phenomenon in air pollutant concentrations specifically the ozone concentration obtained at six monitoring stations in Peninsular Malaysia. The main objective was to select the best method in detecting the long memory. Four methods used in this study were Rescaled Range (R/S) method, Aggregated Variance (V/S) method, Aggregated Absolute Value (A/S) method and Peng’s (P/S) method. Surrogate data testing was used to verify the existence of long memory. The average estimated Hurst value obtained by using VS and PS method are found to be near to the actual Hurst value compared to RS and AS method. The biased and MSE value also showed that the VS and PS method is the most appropriate method in estimating the H value. Based on the result obtained, it can be concluded that long memory exists in ozone concentration data used in the study. The VS and PS method are the best method in detecting the long memory phenomenon.

Multifractal and entropy analysis of resting-state electroencephalography reveals spatial organization in local dynamic functional connectivity

Functional connectivity of the brain fluctuates even in resting-state condition. It has been reported recently that fluctuations of global functional network topology and those of individual connections between brain regions expressed multifractal scaling. To expand on these findings, in this study we investigated if multifractality was indeed an inherent property of dynamic functional connectivity (DFC) on the regional level as well. Furthermore, we explored if local DFC showed region-specific differences in its multifractal and entropy-related features. DFC analyses were performed on 62-channel, resting-state electroencephalography recordings of twelve young, healthy subjects. Surrogate data testing verified the true multifractal nature of regional DFC that could be attributed to the presumed nonlinear nature of the underlying processes. Moreover, we found a characteristic spatial distribution of local connectivity dynamics, in that frontal and occipital regions showed stronger long-range correlation and higher degree of multifractality, whereas the highest values of entropy were found over the central and temporal regions. The revealed topology reflected well the underlying resting-state network organization of the brain. The presented results and the proposed analysis framework could improve our understanding on how resting-state brain activity is spatio-temporally organized and may provide potential biomarkers for future clinical research.