Performance of different synchronization measures in real data: a case study on electroencephalographic signals

Decrease of coherence between the respiration and parasympathetic control of the heart rate with aging

The study of coordinated behavior between different systems of the human body provides useful information on the functioning of the body. The peculiarities of interaction and coordinated dynamics of the heart rate and respiration are of particular interest. We investigated the coherence of the processes of respiration and autonomic control of the heart rate for people of different ages in the awake state, in sleep with rapid eye movement, and in deep sleep. Our analysis revealed a monotonic decrease in the coherence of these processes with increasing age. This can be explained by age-related changes in the system of autonomic control of circulation. For all age groups, we found a qualitatively similar dynamics of the coherence between the studied processes during a transition from the awake state to sleep.

EEG Synchronization-Parameters in Patients With Subcortical Arteriosclerotic Encephalopathy and Gait Disorder

PURPOSE

Subcortical arteriosclerotic encephalopathy (SAE) is characterized by extensive white matter lesions in the MRI. Clinical symptoms are cognitive impairment, ranging from mild deficits to vascular dementia, impaired executive functioning, and gait disorders. In the EEG of SAE patients with vascular dementia, the lower frequencies are increased. However, it is unclear whether EEG changes also exist in SAE patients with gait disorders but without vascular dementia.

METHODS

The authors analyzed the EEGs of 50 nondemented patients with SAE and gait disorders and 50 healthy controls applying pointwise transinformation as a measure of synchronization.

RESULTS

Hundred seconds of waking EEG that appeared unaltered in visual analysis were sufficient to prove changes in synchronization. The authors found a decrease in the mean level of synchronization, combined with an elongation of synchronization time in all examined brain areas. These effects correlated slightly with the extent of subcortical lesions.

CONCLUSIONS

Changes in EEG synchronization in patients with SAE and gait disorders seem to occur independently of cognitive function. The causal relationship of the changes in EEG synchronization and gait disorders remains to be clarified. The results of this study might point to a decrease in coupling efficiency in these patients, with the increase in synchronization duration as a possible compensatory mechanism. Because a time-efficient signal transmission particularly during gait execution is crucial, reduced efficiency might contribute to an impairment of postural stabilization. The study results might indicate a neuronal network for planning and execution of motor activity and particularly gait, extending from the frontal over the central to the parietal cortex.

Infant functional networks are modulated by state of consciousness and circadian rhythm

Functional connectivity networks are valuable tools for studying development, cognition, and disease in the infant brain. In adults, such networks are modulated by the state of consciousness and the circadian rhythm; however, it is unknown if infant brain networks exhibit similar variation, given the unique temporal properties of infant sleep and circadian patterning. To address this, we analyzed functional connectivity networks calculated from long-term EEG recordings (average duration 20.8 hr) from 19 healthy infants. Networks were subject specific, as intersubject correlations between weighted adjacency matrices were low. However, within individual subjects, both sleep and wake networks were stable over time, with stronger functional connectivity during sleep than wakefulness. Principal component analysis revealed the presence of two dominant networks; visual sleep scoring confirmed that these corresponded to sleep and wakefulness. Lastly, we found that network strength, degree, clustering coefficient, and path length significantly varied with time of day, when measured in either wakefulness or sleep at the group level. Together, these results suggest that modulation of healthy functional networks occurs over ∼24 hr and is robust and repeatable. Accounting for such temporal periodicities may improve the physiological interpretation and use of functional connectivity analysis to investigate brain function in health and disease.

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.

Dissociation of the G protein βγ from the Gq-PLCβ complex partially attenuates PIP2 hydrolysis

Phospholipase C β (PLCβ), which is activated by the Gq family of heterotrimeric G proteins, hydrolyzes the inner membrane lipid phosphatidylinositol 4,5-bisphosphate (PIP2), generating diacylglycerol and inositol 1,4,5-triphosphate (IP3). Because Gq and PLCβ regulate many crucial cellular processes and have been identified as major disease drivers, activation and termination of PLCβ signaling by the Gαq subunit have been extensively studied. Gq-coupled receptor activation induces intense and transient PIP2 hydrolysis, which subsequently recovers to a low-intensity steady-state equilibrium. However, the molecular underpinnings of this equilibrium remain unclear. Here, we explored the influence of signaling crosstalk between Gq and Gi/o pathways on PIP2 metabolism in living cells using single-cell and optogenetic approaches to spatially and temporally constrain signaling. Our data suggest that the Gβγ complex is a component of the highly efficient lipase Gαq_GTP-PLCβ-Gβγ. We found that over time, Gβγ dissociates from this lipase complex, leaving the less-efficient Gαq_GTP-PLCβ lipase complex and allowing the significant partial recovery of PIP2 levels. Our findings also indicate that the subtype of the Gγ subunit in Gβγ fine-tunes the lipase activity of Gq-PLCβ, in which cells expressing Gγ with higher plasma membrane interaction show lower PIP2 recovery. Given that Gγ shows cell- and tissue-specific subtype expression, our findings suggest the existence of tissue-specific distinct Gq-PLCβ signaling paradigms. Furthermore, these results also outline a molecular process that likely safeguards cells from excessive Gq signaling.

Fast and effective pseudo transfer entropy for bivariate data-driven causal inference

Identifying, from time series analysis, reliable indicators of causal relationships is essential for many disciplines. Main challenges are distinguishing correlation from causality and discriminating between direct and indirect interactions. Over the years many methods for data-driven causal inference have been proposed; however, their success largely depends on the characteristics of the system under investigation. Often, their data requirements, computational cost or number of parameters limit their applicability. Here we propose a computationally efficient measure for causality testing, which we refer to as pseudo transfer entropy (pTE), that we derive from the standard definition of transfer entropy (TE) by using a Gaussian approximation. We demonstrate the power of the pTE measure on simulated and on real-world data. In all cases we find that pTE returns results that are very similar to those returned by Granger causality (GC). Importantly, for short time series, pTE combined with time-shifted (T-S) surrogates for significance testing strongly reduces the computational cost with respect to the widely used iterative amplitude adjusted Fourier transform (IAAFT) surrogate testing. For example, for time series of 100 data points, pTE and T-S reduce the computational time by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$82\%$$\end{document}82% with respect to GC and IAAFT. We also show that pTE is robust against observational noise. Therefore, we argue that the causal inference approach proposed here will be extremely valuable when causality networks need to be inferred from the analysis of a large number of short time series.

Antagonistic muscle prefatigue weakens the functional corticomuscular coupling during isometric elbow extension contraction

OBJECTIVE

During muscle fatigue, acute changes in the interaction between the sensorimotor cortex and peripheral neurons have been widely studied. However, it is still unclear about the effect of antagonist muscle prefatigue on corticomuscular coupling and central modulation. The purpose of this study was to investigate the changes in the magnitude of electroencephalogram-electromyography (EEG-EMG) coherence and phase synchronization index (PSI) induced by antagonistic muscle prefatigue.

METHODS

Twelve young male volunteers conducted a 30-s long, nonfatiguing isometric elbow extension with a target force level of 20% maximum voluntary contraction (MVC) before and after a fatiguing sustained elbow flexion contraction at 20% MVC until task failure. Coherence and PSI between the EEG recorded over the sensorimotor cortex and the surface EMG of the triceps brachii (TB) muscle were quantified for the pre- and post-fatigue elbow extension contractions.

RESULTS

Coherence and PSI in the gamma frequency band (35-60 Hz) were found significantly decreased in the postfatigue elbow extension contraction than the prefatigue contraction. The power of the EEG in the beta and gamma band were significantly increased, while the EMG power showed no significant changes when the antagonistic muscle was prefatigued. PSI in the gamma frequency band between the EMG of the TB muscle and the EEG were found significantly decreased during postfatigue elbow extension contraction compared with prefatigue contraction.

CONCLUSION

Antagonistic muscle prefatigue led to significantly lower gamma band corticomuscular coherence and phase coupling during an isometric elbow extension position task. The lower corticomuscular coupling may indicate a central modulation mechanism of antagonist muscle prefatigue that related to decreased descending common drive or joint instability compensation modulation mechanism.

Revisiting the global workspace orchestrating the hierarchical organization of the human brain

A central challenge in neuroscience is how the brain organizes the information necessary to orchestrate behaviour. Arguably, this whole-brain orchestration is carried out by a core subset of integrative brain regions, a 'global workspace', but its constitutive regions remain unclear. We quantified the global workspace as the common regions across seven tasks as well as rest, in a common 'functional rich club'. To identify this functional rich club, we determined the information flow between brain regions by means of a normalized directed transfer entropy framework applied to multimodal neuroimaging data from 1,003 healthy participants and validated in participants with retest data. This revealed a set of regions orchestrating information from perceptual, long-term memory, evaluative and attentional systems. We confirmed the causal significance and robustness of our results by systematically lesioning a generative whole-brain model. Overall, this framework describes a complex choreography of the functional hierarchical organization of the human brain.

Causality and Information Transfer Between the Solar Wind and the Magnetosphere-Ionosphere System

An information-theoretic approach for detecting causality and information transfer is used to identify interactions of solar activity and interplanetary medium conditions with the Earth's magnetosphere-ionosphere systems. A causal information transfer from the solar wind parameters to geomagnetic indices is detected. The vertical component of the interplanetary magnetic field (Bz) influences the auroral electrojet (AE) index with an information transfer delay of 10 min and the geomagnetic disturbances at mid-latitudes measured by the symmetric field in the H component (SYM-H) index with a delay of about 30 min. Using a properly conditioned causality measure, no causal link between AE and SYM-H, or between magnetospheric substorms and magnetic storms can be detected. The observed causal relations can be described as linear time-delayed information transfer.

EEG-Based Sleep Staging Analysis with Functional Connectivity

Sleep staging is important in sleep research since it is the basis for sleep evaluation and disease diagnosis. Related works have acquired many desirable outcomes. However, most of current studies focus on time-domain or frequency-domain measures as classification features using single or very few channels, which only obtain the local features but ignore the global information exchanging between different brain regions. Meanwhile, brain functional connectivity is considered to be closely related to brain activity and can be used to study the interaction relationship between brain areas. To explore the electroencephalography (EEG)-based brain mechanisms of sleep stages through functional connectivity, especially from different frequency bands, we applied phase-locked value (PLV) to build the functional connectivity network and analyze the brain interaction during sleep stages for different frequency bands. Then, we performed the feature-level, decision-level and hybrid fusion methods to discuss the performance of different frequency bands for sleep stages. The results show that (1) PLV increases in the lower frequency band (delta and alpha bands) and vice versa during different stages of non-rapid eye movement (NREM); (2) alpha band shows a better discriminative ability for sleeping stages; (3) the classification accuracy of feature-level fusion (six frequency bands) reaches 96.91% and 96.14% for intra-subject and inter-subjects respectively, which outperforms decision-level and hybrid fusion methods.

Clinical application of intraoperative trial-free online-based language mapping for patients with refractory epilepsy

OBJECTIVE

The objective of the study was to develop and clinically test a trial-free online-based language mapping method for localizing the eloquent cortex easily in epilepsy operation.

METHODS

Nine patients with refractory epilepsy were included in this study according to the results of preoperative evaluation for their epileptogenic zones (EZs) located adjacent to the eloquent cortex. When patients were awakened up from general anesthesia during operation, the trial-free online-based language-mapping paradigm was performed. All positive points marked on the cortex in each test were labeled and superimposed together as the result of functional mapping for each patient. The eloquent cortex was mapped according to the results obtained both from the intraoperative trial-free task localization method and the traditional electrical cortical stimulation (ECS).

RESULTS

All patients completed this paradigms twice within 10 min. Based on the results of mapping, the EZs were tried to fully resected on the premise of preserving the mapped eloquent cortex as much as possible. The postoperative follow-up showed the outcome of Engel I in six patients and Engel II in three patients, whereas only two patients had aphemia after surgery and recovered within one week and three months, respectively.

SIGNIFICANCE

The intraoperative trial-free online-based language mapping method was primarily identified to be safe and effective. This novel method seems to be promising and worthy of improvement.

Explicit Granger causality in kernel Hilbert spaces

Granger causality (GC) is undoubtedly the most widely used method to infer cause-effect relations from observational time series. Several nonlinear alternatives to GC have been proposed based on kernel methods. We generalize kernel Granger causality by considering the variables' cross-relations explicitly in Hilbert spaces. The framework is shown to generalize the linear and kernel GC methods and comes with tighter bounds of performance based on Rademacher complexity. We successfully evaluate its performance in standard dynamical systems, as well as to identify the arrow of time in coupled Rössler systems, and it is exploited to disclose the El Niño-Southern Oscillation phenomenon footprints on soil moisture globally.

Motor Imagery Hand Movement Direction Decoding Using Brain Computer Interface to Aid Stroke Recovery and Rehabilitation

Motor Imagery (MI)-based Brain Computer Interface (BCI) system is a potential technology for active neurorehabilitation of stroke patients by complementing the conventional passive rehabilitation methods. Research to date mainly focused on classifying left vs. right hand/foot MI of stroke patients. Though a very few studies have reported decoding imagined hand movement directions using electroencephalogram (EEG)-based BCI, the experiments were conducted on healthy subjects. Our work analyzes MI-based brain cortical activity from EEG signals and decodes the imagined hand movement directions in stroke patients. The decoded direction (left vs. right) of hand movement imagination is used to provide control commands to a motorized arm support on which patient's affected (paralyzed) arm is placed. This enables the patient to move his/her stroke-affected hand towards the intended (imagined) direction that aids neuroplasticity in the brain. The synchronization measure called Phase Locking Value (PLV), extracted from EEG, is the neuronal signature used to decode the directional movement of the MI task. Event-related desynchronization/synchronization (ERD/ERS) analysis on Mu and Beta frequency bands of EEG is done to select the time bin corresponding to the MI task. The dissimilarities between the two directions of MI tasks are identified by selecting the most significant channel pairs that provided maximum difference in PLV features. The training protocol has an initial calibration session followed by a feedback session with 50 trials of MI task in each session. The feedback session extracts PLV features corresponding to most significant channel pairs which are identified in the calibration session and is used to predict the direction of MI task in left/right direction. An average MI direction classification accuracy of 74.44% is obtained in performing the training protocol and 68.63% from the prediction protocol during feedback session on 16 stroke patients.

The Endocannabinoid System Activation as a Neural Network Desynchronizing Mediator for Seizure Suppression

The understanding that hyper-excitability and hyper-synchronism in epilepsy are indissociably bound by a cause-consequence relation has only recently been challenged. Thus, therapeutic strategies for seizure suppression have often aimed at inhibiting excitatory circuits and/or activating inhibitory ones. However, new approaches that aim to desynchronize networks or compromise abnormal coupling between adjacent neural circuitry have been proven effective, even at the cost of enhancing local neuronal activation. Although most of these novel perspectives targeting circuitry desynchronization and network coupling have been implemented by non-pharmacological devices, we argue that there may be endogenous neurochemical systems that act primarily in the desynchronization component of network behavior rather than dampening excitability of individual neurons. This review explores the endocannabinoid system as one such possible pharmacological landmark for mimicking a form of "on-demand" desynchronization analogous to those proposed by deep brain stimulation in the treatment of epilepsy. This essay discusses the evidence supporting the role of the endocannabinoid system in modulating the synchronization and/or coupling of distinct local neural circuitry; which presents obvious implications on the physiological setting of proper sensory-motor integration. Accordingly, the process of ictogenesis involves pathological circuit coupling that could be avoided, or at least have its spread throughout the containment of other areas, if such endogenous mechanisms of control could be activated or potentiated by pharmacological intervention. In addition, we will discuss evidence that supports not only a weaker role played on neuronal excitability but the potential of the endocannabinoid system strengthening its modulatory effect, only when circuitry coupling surpasses a level of activation.

Differentiation of pain levels by deploying various EEG synchronization features and dynamic ensemble selection mechanism

OBJECTIVE

The target of this study is measuring the pain intensity in an objective manner by analysing the electroencephalogram (EEG) signals. Although this problem has attracted researchers' attention, increasing the resolution of this measurement, by increasing the number of pain states, significantly decreases the accuracy of pain level classification problem.

APPROACH

To overcome this drawback, we adopt state-of-the-art synchronization schemes to measure the linear, nonlinear and generalized synchronization between different EEG channels. 32 subjects executed the Cold Pressor Task (CPT) and experienced five defined levels of pain while recording their EEGs. Due to high number of synchronization features from 34 channels, the most discriminative features were selected using greedy overall relevancy (GOR) method. The selected features are applied to a dynamic ensemble selection system.

MAIN RESULTS

Our experiment provides 85.6% accuracy over the five classes, which significantly outperforms the results of past research. Moreover, we observe that the selected features belong to the channels placed over the ridge of cortex, the area responsible for processing somatic sensation arisen from nociceptive temperature. As expected, we noted that continuing the painful stimulus for minutes engaged regions beyond the sensorimotor cortex, e.g., the prefrontal cortex.

SIGNIFICANCE

We conclude that the amount of synchronization between scalp EEG channels is an informative tool in revealing the pain sensation.

Refined nonuniform embedding for coupling detection in multivariate time series

State-space reconstruction is essential to analyze the dynamics and internal interactions of complex systems. However, it is difficult to estimate high-dimensional conditional mutual information and select the optimal time delays in most existing nonuniform state-space reconstruction methods. Therefore, we propose a nonuniform embedding method framed in information theory for state-space reconstruction. We use a low-dimensional approximation of conditional mutual information criterion for time delay selection, which is effectively solved by the particle swarm optimization algorithm. The obtained embedded vector has relatively strong independence and low redundancy, which better characterizes multivariable complex systems and detects coupling within complex systems. In addition, the proposed nonuniform embedding method exhibits good performance in coupling detection of linear stochastic, nonlinear stochastic, chaotic systems. In the actual application, the importance of small airports that cause delay propagation has been demonstrated by constructing the delay propagation network.

Non-Uniform Embedding Scheme and Low-Dimensional Approximation Methods for Causality Detection

Information causality measures have proven to be very effective in uncovering the connectivity patterns of multivariate systems. The non-uniform embedding (NUE) scheme has been developed to address the “curse of dimensionality”, since the estimation relies on high-dimensional conditional mutual information (CMI) terms. Although the NUE scheme is a dimension reduction technique, the estimation of high-dimensional CMIs is still required. A possible solution is the utilization of low-dimensional approximation (LA) methods for the computation of CMIs. In this study, we aim to provide useful insights regarding the effectiveness of causality measures that rely on NUE and/or on LA methods. In a comparative study, three causality detection methods are evaluated, namely partial transfer entropy (PTE) defined using uniform embedding, PTE using the NUE scheme (PTENUE), and PTE utilizing both NUE and an LA method (LATE). Results from simulations on well known coupled systems suggest the superiority of PTENUE over the other two measures in identifying the true causal effects, having also the least computational cost. The effectiveness of PTENUE is also demonstrated in a real application, where insights are presented regarding the leading forces in financial data.

Disentangling synchrony from serial dependency in paired-event time series

Quantifying synchronization phenomena based on the timing of events has recently attracted a great deal of interest in various disciplines such as neuroscience or climatology. A multitude of similarity measures has been proposed for this purpose, including event synchronization (ES) and event coincidence analysis (ECA) as two widely applicable examples. While ES defines synchrony in a data-adaptive local way that does not distinguish between different timescales, ECA requires selecting a specific scale for analysis. In this paper, we use slightly modified versions of both ES and ECA that address previous issues with respect to proper normalization and boundary treatment, which are particularly relevant for short time series with low temporal resolution. By numerically studying threshold crossing events in coupled autoregressive processes, we identify a practical limitation of ES when attempting to study synchrony between serially dependent event sequences exhibiting event clustering in time. Practical implications of this observation are demonstrated for the case of functional network representations of climate extremes based on both ES and ECA, while no marked differences between both measures are observed for the case of epileptic electroencephalogram data. Our findings suggest that careful event detection along with diligent preprocessing is recommended when applying ES while less crucial for ECA. Despite the lack of a general modus operandi for both event definition and detection of synchronization, we suggest ECA as a widely robust method, especially for time-resolved synchronization analyses of event time series from various disciplines.

Comparison of mobile and clinical EEG sensors through resting state simultaneous data collection

Development of mobile sensors brings new opportunities to medical research. In particular, mobile electroencephalography (EEG) devices can be potentially used in low cost screening for epilepsy and other neurological and psychiatric disorders. The necessary condition for such applications is thoughtful validation in the specific medical context. As part of validation and quality assurance, we developed a computer-based analysis pipeline, which aims to compare the EEG signal acquired by a mobile EEG device to the one collected by a medically approved clinical-grade EEG device. Both signals are recorded simultaneously during 30 min long sessions in resting state. The data are collected from 22 patients with epileptiform abnormalities in EEG. In order to compare two multichannel EEG signals with differently placed references and electrodes, a novel data processing pipeline is proposed. It allows deriving matching pairs of time series which are suitable for similarity assessment through Pearson correlation. The average correlation of 0.64 is achieved on a test dataset, which can be considered a promising result, taking the positions shift due to the simultaneous electrode placement into account.

When Sinus Tachycardia Becomes Too Much: Negative Effects of Excessive Upright Tachycardia on Cardiac Output in Vasovagal Syncope, Postural Tachycardia Syndrome, and Inappropriate Sinus Tachycardia

BACKGROUND

Upright posture reduces venous return, stroke volume, and cardiac output (CO) while causing reflex sinus rate (heart rate [HR]) increase. Yet, in inappropriate sinus tachycardia (IST), postural tachycardia syndrome (POTS), and vasovagal syncope (VVS), symptomatic excessive HR occurs. We hypothesized that CO reaches maximum as function of HR in all.

METHODS

We recruited 12 healthy controls, 9 IST, 30 VVS, and 30 POTS patients (13-23years) selected randomly by disorder not by HR, each fulfilled appropriate diagnostic criteria. Subjects were instrumented for electrocardiography, beat-to-beat blood pressure, respiratory rate, CO-Modelflow algorithm, and central blood volume from impedance cardiography; 10-minute data were collected supine; subjects were tilted head-up for ≤10 minutes. We computed phase differences, ΔΦ, between fluctuations of HR (ΔHR) and CO (ΔCO) tabulating data when phases were synchronized, determined by a squared nonlinear phase synchronization index >0.5, describing extent/validity of CO/HR coupling. We graphed results supine, 1-minute post-tilt-up, mid-tilt, and pre-tilt-down using polar coordinates (HR-radius, ΔΦ-angle) plotting cos(ΔΦ) versus HR to determine if transition HR exists at which in-phase shifts to antiphase above which CO decreases when HR further increases.

RESULTS

At baseline HR, diastolic and mean arterial pressures in IST and POTS were higher versus controls. Upright HR increased most in POTS then IST and VVS, with diverse changes in CO, SVR, and central blood volume. Each patient grouping was separately and collectively analyzed for HR change showing transition from in-phase to anti-phase (ΔΦ) as HR increased: HRtransition=115±6 (IST), 123±8 (POTS), 124±7 (VVS), P=ns. Controls never reached transitional HR.

CONCLUSIONS

Excessive HR independently and equivalently reduces upright CO, in IST, POTS, and VVS.

Dynamics and sources of response variability and its coordination in visual cortex

The trial-to-trial response variability in sensory cortices and the extent to which this variability can be coordinated among cortical units have strong implications for cortical signal processing. Yet, little is known about the relative contributions and dynamics of defined sources to the cortical response variability and their correlations across cortical units. To fill this knowledge gap, here we obtained and analyzed multisite local field potential (LFP) recordings from visual cortex of turtles in response to repeated naturalistic movie clips and decomposed cortical across-trial LFP response variability into three defined sources, namely, input, network, and local fluctuations. We found that input fluctuations dominate cortical response variability immediately following stimulus onset, whereas network fluctuations dominate the response variability in the steady state during continued visual stimulation. Concurrently, we found that the network fluctuations dominate the correlations of the variability during the ongoing and steady-state epochs, but not immediately following stimulus onset. Furthermore, simulations of various model networks indicated that (i) synaptic time constants, leading to oscillatory activity, and (ii) synaptic clustering and synaptic depression, leading to spatially constrained pockets of coherent activity, are both essential features of cortical circuits to mediate the observed relative contributions and dynamics of input, network, and local fluctuations to the cortical LFP response variability and their correlations across recording sites. In conclusion, these results show how a mélange of multiscale thalamocortical circuit features mediate a complex stimulus-modulated cortical activity that, when naively related to the visual stimulus alone, appears disguised as high and coordinated across-trial response variability.

Coupling in complex systems as information transfer across time scales

Complex systems such as the human brain or the Earth's climate consist of many subsystems interacting in intricate, nonlinear ways. Moreover, variability of such systems extends over broad ranges of spatial and temporal scales and dynamical phenomena on different scales also influence each other. In order to explain how to detect cross-scale causal interactions, we review information-theoretic formulation of the Granger causality in combination with computational statistics (surrogate data method) and demonstrate how this method can be used to infer driver-response relations from amplitudes and phases of coupled nonlinear dynamical systems. Considering complex systems evolving on multiple time scales, the reviewed methodology starts with a wavelet decomposition of a multi-scale signal into quasi-oscillatory modes of a limited bandwidth, described using their instantaneous phases and amplitudes. Then statistical associations, in particular, causality relations between phases or between phases and amplitudes on different time scales are tested using the conditional mutual information. As an application, we present the analysis of cross-scale interactions and information transfer in the dynamics of the El Niño Southern Oscillation. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'.

Reorganization of Large-Scale Functional Networks During Low-Frequency Electrical Stimulation of the Cortical Surface

We investigated the functional network reorganization caused by low-frequency electrical stimulation (LFES) of human brain cortical surface. Intracranial EEG data from subdural grid positions were analyzed in 16 pre-surgery epileptic patients. LFES was performed by injecting current pulses (10[Formula: see text]mA, 0.2[Formula: see text]ms pulse width, 0.5[Formula: see text]Hz, 25 trials) into all adjacent electrode contacts. Dynamic functional connectivity analysis was carried out on two frequency bands (low: 1–4[Formula: see text]Hz; high: 10–40[Formula: see text]Hz) to investigate the early, high frequency and late, low frequency responses elicited by the stimulation. The centralization increased in early compared to late responses, suggesting a more prominent role of direct neural links between primarily activated areas and distant brain regions. Injecting the current into the seizure onset zone (SOZ) evoked a more integrated functional topology during the early (N1) period of the response, whereas during the late (N2) period — regardless of the stimulation site — the connectedness of the SOZ was elevated compared to the non-SOZ tissue. The abnormal behavior of the epileptic sub-network during both part of the responses supports the idea of the pathogenic role of impaired inhibition and excitation mechanisms in epilepsy.

Evaluation of synchronization measures for capturing the lagged synchronization between EEG channels: A cognitive task recognition approach

During cognitive, perceptual and sensory tasks, connectivity profile changes across different regions of the brain. Variations of such connectivity patterns between different cognitive tasks can be evaluated using pairwise synchronization measures applied to electrophysiological signals, such as electroencephalography (EEG). However, connectivity-based task recognition approaches achieving viable recognition performance have been lacking from the literature. By using several synchronization measures, we identify time lags between channel pairs during different cognitive tasks. We employed mutual information, cross correntropy, cross correlation, phase locking value, cosine similarity and nonlinear interdependence measures. In the training phase, for each type of cognitive task, we identify the time lags that maximize the average synchronization between channel pairs. These lags are used to calculate pairwise synchronization values with which we construct the train and test feature vectors for recognition of the cognitive task carried out using Fisher's linear discriminant (FLD) analysis. We tested our framework in a motor imagery activity recognition scenario on PhysioNet Motor Movement/Imagery and BCI Competition-III Ⅳa datasets. For PhysioNet dataset, average performance results ranging between % 51 and % 61 across 20 subjects. For BCI Competition-Ⅲ dataset, we achieve an average recognition performance of % 76 which is above the minimum reliable communication rate (% 70). We achieved an average accuracy over the minimum reliable communication rate on the BCI Competition-Ⅲ dataset. Performance levels were lower on the PhysioNet dataset. These results indicate that a viable task recognition system is achievable using pairwise synchronization measures evaluated at the proper task specific lags.

Universal Cointegration and Its Applications

Cointegration focuses on whether the long-term linear relationship between two or more time series is stationary even if this linear relationship does not exist or is not strong for the short term. Identifying the potential cointegration is important for economics, ecology, meteorology, neuroscience, and much more. Classic methods only considered or restricted in cointegration where the order of integration of all time series is 1. We introduce a method based on searching the vector to minimize the absolute correlation of convergent cross-mapping that can explore the universal cointegration and its extent. The proposed method can be applied to time series whose order of integration is not 1, cases that are not covered by classic cointegration. The proposed method is first illustrated and validated through time series generated by mathematical models in which the underlying relationships are known and then applied to three real-world examples.

Badminton players show a lower coactivation and higher beta band intermuscular interactions of ankle antagonist muscles during isokinetic exercise

Previous studies have suggested that skilled athletes may show a specific muscle activation pattern with a lower antagonist coactivation level. Based on the point, we hypothesize that the coupling of antagonistic muscles may be different between badminton players and non-skilled individuals during exercises. The current work was designed to verify the hypothesis. Ten male college students and eight male badminton players performed three maximal voluntary isometric contractions (MVC) and a set of three maximal concentric ankle dorsiflexion and plantar flexions at an angular velocity of 30°, 60°, 120°, and 180°/s. Surface electromyography (EMG) was recorded from the tibialis anterior (TA) and lateral gastrocnemius (LG) muscles during the test. Normalized average EMG amplitude and phase synchronization index (PSI) between surface EMG of TA and LG were calculated. Antagonist muscle coactivation was significantly lower (from 22.1% ± 9.4 and 10.7% ± 3.7 at 30°/s to 22.4% ± 9.7 and 10.6% ± 2.5 at 180°/s for non-players and badminton players group, respectively), and PSI in beta frequency band was significantly higher (from 0.42 ± 0.06 and 0.47 ± 0.15 at 30°/s to 0.35 ± 0.12 and 0.49 ± 0.14 at 180°/s) in the badminton player group compared with the non-player group during isokinetic ankle dorsiflexion contraction. No significant difference was found in antagonist muscle coactivation and PSI between two group subjects during ankle plantar flexion. The decrease of antagonist coactivation may indicate an optimal motor control style to increase the contraction efficiency, while the increase coupling of antagonistic muscles may help to ensure joint stability to compensate for the decrease of antagonist coactivation. Graphical abstract Significant difference of observed indexes between non-players and badminton players.

Early glioma is associated with abnormal electrical events in cortical cultures

The prodromal stages of some neurological diseases have a distinct electrical profile which can potentially be leveraged for early diagnosis, predicting disease recurrence, monitoring of disease progression, and better understanding of the disease pathology. Gliomas are tumors that originate from glial cells present in the brain and spinal cord. Healthy glial cells support normal neuronal function and play an important role in modulating the regular electrical activity of neurons. However, gliomas can disrupt the normal electrical dynamics of the brain. Though experimental and clinical studies suggest that glioma and injury to glial cells disrupt electrical dynamics of the brain, whether these disruptions are present during the earliest stages of glioma and glial injury are unclear. The primary aim of this study is to investigate the effect of early in vitro glial pathology (glioma and glial injury in specific) on neuronal electrical activity. In particular, we investigated the effect of glial pathology on neural synchronization: an important phenomenon that underlies several central neurophysiological processes (ScienceDirect, 2018 ). We used two in vitro disease samples: (a) a sample in which cortical cultures were treated with anti-mitotic agents that deplete glial cells and (b) a glioma sample in which healthy cortical cells were cultured with CRL-2303 (an aggressive glioma cell line). Healthy cortical culture samples were used as controls. Cultures were established over a glass dish embedded with microelectrodes that permits simultaneous measurement of extracellular electrical activity from multiple sites of the culture. We observed that healthy cortical cultures produce spontaneous and synchronized oscillations which were attenuated in the absence of glial cells. The presence of glioma was associated with the emergence of two types of "abnormal electrical activity" each with distinct amplitude and frequency profile. Our results indicate that even early stages of glioma and glial injury are associated with distinct changes in neuronal electrical activity. Graphical abstract.

Inferring directed networks using a rank-based connectivity measure

Inferring the topology of a network using the knowledge of the signals of each of the interacting units is key to understanding real-world systems. One way to address this problem is using data-driven methods like cross-correlation or mutual information. However, these measures lack the ability to distinguish the direction of coupling. Here, we use a rank-based nonlinear interdependence measure originally developed for pairs of signals. This measure not only allows one to measure the strength but also the direction of the coupling. Our results for a system of coupled Lorenz dynamics show that we are able to consistently infer the underlying network for a subrange of the coupling strength and link density. Furthermore, we report that the addition of dynamical noise can benefit the reconstruction. Finally, we show an application to multichannel electroencephalographic recordings from an epilepsy patient.

The meaning of "coherent" and its quantification in coherent hemodynamics spectroscopy

We have recently introduced a new technique, coherent hemodynamics spectroscopy (CHS), which aims at characterizing a specific kind of tissue hemodynamics that feature a high level of covariation with a given physiological quantity. In this study, we carry out a detailed analysis of the significance of coherence and phase synchronization between oscillations of arterial blood pressure (ABP) and total hemoglobin concentration ([Hbt]), measured with near-infrared spectroscopy (NIRS) during a typical protocol for CHS, based on a cyclic thigh cuff occlusion and release. Even though CHS is based on a linear time invariant model between ABP (input) and NIRS measurands (outputs), for practical reasons in a typical CHS protocol, we induce finite "groups" of ABP oscillations, in which each group is characterized by a different frequency. For this reason, ABP (input) and NIRS measurands (output) are not stationary processes, and we have used wavelet coherence and phase synchronization index (PSI), as a metric of coherence and phase synchronization, respectively. PSI was calculated by using both the wavelet cross spectrum and the Hilbert transform. We have also used linear coherence (which requires stationary process) for comparison with wavelet coherence. The method of surrogate data is used to find critical values for the significance of covariation between ABP and [Hbt]. Because we have found similar critical values for wavelet coherence and PSI by using five of the most used methods of surrogate data, we propose to use the data-independent Gaussian random numbers (GRNs), for CHS. By using wavelet coherence and wavelet cross spectrum, and GRNs as surrogate data, we have found the same results for the significance of coherence and phase synchronization between ABP and [Hbt]: on a total set of 20 periods of cuff oscillations, we have found 17 coherent oscillations and 17 phase synchronous oscillations. Phase synchronization assessed with Hilbert transform yielded similar results with 14 phase synchronous oscillations. Linear coherence and wavelet coherence overall yielded similar number of significant values. We discuss possible reasons for this result. Despite the similarity of linear and wavelet coherence, we argue that wavelet coherence is preferable, especially if one wants to use baseline spontaneous oscillations, in which phase locking and coherence between signals might be only temporary.

Synchronization of infra-slow oscillations of brain potentials with respiration

We study the synchronization of infra-slow oscillations in human scalp electroencephalogram signal with the respiratory signal. For the cases of paced respiration with a fixed frequency and linearly increasing frequency, we reveal the phase and frequency locking of infra-slow oscillations of brain potentials by respiration. It is shown that for different brain areas, the infra-slow oscillations and respiration can exhibit synchronous regimes of different orders.

Detecting directional couplings from multivariate flows by the joint distance distribution

The identification of directional couplings (or drive-response relationships) in the analysis of interacting nonlinear systems is an important piece of information to understand their dynamics. This task is especially challenging when the analyst's knowledge of the systems reduces virtually to time series of observations. Spurred by the success of Granger causality in econometrics, the study of cause-effect relationships (not to be confounded with statistical correlations) was extended to other fields, thus favoring the introduction of further tools such as transfer entropy. Currently, the research on old and new causality tools along with their pitfalls and applications in ever more general situations is going through a time of much activity. In this paper, we re-examine the method of the joint distance distribution to detect directional couplings between two multivariate flows. This method is based on the forced Takens theorem, and, more specifically, it exploits the existence of a continuous mapping from the reconstructed attractor of the response system to the reconstructed attractor of the driving system, an approach that is increasingly drawing the attention of the data analysts. The numerical results with Lorenz and Rössler oscillators in three different interaction networks (including hidden common drivers) are quite satisfactory, except when phase synchronization sets in. They also show that the method of the joint distance distribution outperforms the lowest dimensional transfer entropy in the cases considered. The robustness of the results to the sampling interval, time series length, observational noise, and metric is analyzed too.

Causality, dynamical systems and the arrow of time

Using several methods for detection of causality in time series, we show in a numerical study that coupled chaotic dynamical systems violate the first principle of Granger causality that the cause precedes the effect. While such a violation can be observed in formal applications of time series analysis methods, it cannot occur in nature, due to the relation between entropy production and temporal irreversibility. The obtained knowledge, however, can help to understand the type of causal relations observed in experimental data, namely, it can help to distinguish linear transfer of time-delayed signals from nonlinear interactions. We illustrate these findings in causality detected in experimental time series from the climate system and mammalian cardio-respiratory interactions.

Prediction of microsleeps using pairwise joint entropy and mutual information between EEG channels

Microsleeps are involuntary and brief instances of complete loss of responsiveness, typically of 0.5-15 s duration. They adversely affect performance in extended attention-driven jobs and can be fatal. Our aim was to predict microsleeps from 16 channel EEG signals. Two information theoretic concepts - pairwise joint entropy and mutual information - were independently used to continuously extract features from EEG signals. k-nearest neighbor (kNN) with k = 3 was used to calculate both joint entropy and mutual information. Highly correlated features were discarded and the rest were ranked using Fisher score followed by an average of 3-fold cross-validation area under the curve of the receiver operating characteristic (AUC_ROC). Leave-one-out method (LOOM) was performed to test the performance of microsleep prediction system on independent data. The best prediction for 0.25 s ahead was AUCROC, sensitivity, precision, geometric mean (GM), and φ of 0.93, 0.68, 0.33, 0.75, and 0.38 respectively with joint entropy using single linear discriminant analysis (LDA) classifier.

Comparison of six methods for the detection of causality in a bivariate time series

In this comparative study, six causality detection methods were compared, namely, the Granger vector autoregressive test, the extended Granger test, the kernel version of the Granger test, the conditional mutual information (transfer entropy), the evaluation of cross mappings between state spaces, and an assessment of predictability improvement due to the use of mixed predictions. Seven test data sets were analyzed: linear coupling of autoregressive models, a unidirectional connection of two Hénon systems, a unidirectional connection of chaotic systems of Rössler and Lorenz type and of two different Rössler systems, an example of bidirectionally connected two-species systems, a fishery model as an example of two correlated observables without a causal relationship, and an example of mediated causality. We tested not only 20000 points long clean time series but also noisy and short variants of the data. The standard and the extended Granger tests worked only for the autoregressive models. The remaining methods were more successful with the more complex test examples, although they differed considerably in their capability to reveal the presence and the direction of coupling and to distinguish causality from mere correlation.

Determining synchrony between behavioral time series: An application of surrogate data generation for establishing falsifiable null-hypotheses

Synchrony between interacting systems is an important area of nonlinear dynamics in physical systems. Recently psychological researchers from multiple areas of psychology have become interested in nonverbal synchrony (i.e., coordinated motion between two individuals engaged in dyadic information exchange such as communication or dance) as a predictor and outcome of psychological processes. An important step in studying nonverbal synchrony is systematically and validly differentiating synchronous systems from nonsynchronous systems. However, many current methods of testing and quantifying nonverbal synchrony will show some level of observed synchrony even when research participants have not interacted with one another. In this article we demonstrate the use of surrogate data generation methodology as a means of testing new null-hypotheses for synchrony between bivariate time series such as those derived from modern motion tracking methods. Hypotheses generated by surrogate data generation methods are more nuanced and meaningful than hypotheses from standard null-hypothesis testing. We review four surrogate data generation methods for testing for significant nonverbal synchrony within a windowed cross-correlation (WCC) framework. We also interpret the null-hypotheses generated by these surrogate data generation methods with respect to nonverbal synchrony as a specific use of surrogate data generation, which can then be generalized for hypothesis testing of other psychological time series. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

Non-linear auto-regressive models for cross-frequency coupling in neural time series

We address the issue of reliably detecting and quantifying cross-frequency coupling (CFC) in neural time series. Based on non-linear auto-regressive models, the proposed method provides a generative and parametric model of the time-varying spectral content of the signals. As this method models the entire spectrum simultaneously, it avoids the pitfalls related to incorrect filtering or the use of the Hilbert transform on wide-band signals. As the model is probabilistic, it also provides a score of the model “goodness of fit” via the likelihood, enabling easy and legitimate model selection and parameter comparison; this data-driven feature is unique to our model-based approach. Using three datasets obtained with invasive neurophysiological recordings in humans and rodents, we demonstrate that these models are able to replicate previous results obtained with other metrics, but also reveal new insights such as the influence of the amplitude of the slow oscillation. Using simulations, we demonstrate that our parametric method can reveal neural couplings with shorter signals than non-parametric methods. We also show how the likelihood can be used to find optimal filtering parameters, suggesting new properties on the spectrum of the driving signal, but also to estimate the optimal delay between the coupled signals, enabling a directionality estimation in the coupling.

Neural oscillations synchronize information across brain areas at various anatomical and temporal scales. Of particular relevance, slow fluctuations of brain activity have been shown to affect high frequency neural activity, by regulating the excitability level of neural populations. Such cross-frequency-coupling can take several forms. In the most frequently observed type, the power of high frequency activity is time-locked to a specific phase of slow frequency oscillations, yielding phase-amplitude-coupling (PAC). Even when readily observed in neural recordings, such non-linear coupling is particularly challenging to formally characterize. Typically, neuroscientists use band-pass filtering and Hilbert transforms with ad-hoc correlations. Here, we explicitly address current limitations and propose an alternative probabilistic signal modeling approach, for which statistical inference is fast and well-posed. To statistically model PAC, we propose to use non-linear auto-regressive models which estimate the spectral modulation of a signal conditionally to a driving signal. This conditional spectral analysis enables easy model selection and clear hypothesis-testing by using the likelihood of a given model. We demonstrate the advantage of the model-based approach on three datasets acquired in rats and in humans. We further provide novel neuroscientific insights on previously reported PAC phenomena, capturing two mechanisms in PAC: influence of amplitude and directionality estimation.

Quantifying team cooperation through intrinsic multi-scale measures: respiratory and cardiac synchronization in choir singers and surgical teams

A highly localized data-association measure, termed intrinsic synchrosqueezing transform (ISC), is proposed for the analysis of coupled nonlinear and non-stationary multivariate signals. This is achieved based on a combination of noise-assisted multivariate empirical mode decomposition and short-time Fourier transform-based univariate and multivariate synchrosqueezing transforms. It is shown that the ISC outperforms six other combinations of algorithms in estimating degrees of synchrony in synthetic linear and nonlinear bivariate signals. Its advantage is further illustrated in the precise identification of the synchronized respiratory and heart rate variability frequencies among a subset of bass singers of a professional choir, where it distinctly exhibits better performance than the continuous wavelet transform-based ISC. We also introduce an extension to the intrinsic phase synchrony (IPS) measure, referred to as nested intrinsic phase synchrony (N-IPS), for the empirical quantification of physically meaningful and straightforward-to-interpret trends in phase synchrony. The N-IPS is employed to reveal physically meaningful variations in the levels of cooperation in choir singing and performing a surgical procedure. Both the proposed techniques successfully reveal degrees of synchronization of the physiological signals in two different aspects: (i) precise localization of synchrony in time and frequency (ISC), and (ii) large-scale analysis for the empirical quantification of physically meaningful trends in synchrony (N-IPS).

The Effects of rTMS Combined with Motor Training on Functional Connectivity in Alpha Frequency Band

It has recently been reported that repetitive transcranial magnetic stimulation combined with motor training (rTMS-MT) could improve motor function in post-stroke patients. However, the effects of rTMS-MT on cortical function using functional connectivity and graph theoretical analysis remain unclear. Ten healthy subjects were recruited to receive rTMS immediately before application of MT. Low frequency rTMS was delivered to the dominant hemisphere and non-dominant hand performed MT over 14 days. The reaction time of Nine-Hole Peg Test and electroencephalography (EEG) in resting condition with eyes closed were recorded before and after rTMS-MT. Functional connectivity was assessed by phase synchronization index (PSI), and subsequently thresholded to construct undirected graphs in alpha frequency band (8–13 Hz). We found a significant decrease in reaction time after rTMS-MT. The functional connectivity between the parietal and frontal cortex, and the graph theory statistics of node degree and efficiency in the parietal cortex increased. Besides the functional connectivity between premotor and frontal cortex, the degree and efficiency of premotor cortex showed opposite results. In addition, the number of connections significantly increased within inter-hemispheres and inter-regions. In conclusion, this study could be helpful in our understanding of how rTMS-MT modulates brain activity. The methods and results in this study could be taken as reference in future studies of the effects of rTMS-MT in stroke patients.

Adaptive Spatial Filter Based on Similarity Indices to Preserve the Neural Information on EEG Signals during On-Line Processing

This work presents a new on-line adaptive filter, which is based on a similarity analysis between standard electrode locations, in order to reduce artifacts and common interferences throughout electroencephalography (EEG) signals, but preserving the useful information. Standard deviation and Concordance Correlation Coefficient (CCC) between target electrodes and its correspondent neighbor electrodes are analyzed on sliding windows to select those neighbors that are highly correlated. Afterwards, a model based on CCC is applied to provide higher values of weight to those correlated electrodes with lower similarity to the target electrode. The approach was applied to brain computer-interfaces (BCIs) based on Canonical Correlation Analysis (CCA) to recognize 40 targets of steady-state visual evoked potential (SSVEP), providing an accuracy (ACC) of 86.44 ± 2.81%. In addition, also using this approach, features of low frequency were selected in the pre-processing stage of another BCI to recognize gait planning. In this case, the recognition was significantly (p<0.01) improved for most of the subjects (ACC≥74.79%), when compared with other BCIs based on Common Spatial Pattern, Filter Bank-Common Spatial Pattern, and Riemannian Geometry.

Directionality indices: Testing information transfer with surrogate correction

Directionality indices can be used as an indicator of the asymmetry in coupling between systems and have found particular application in relation to neurological systems. The directionality index between two systems is a function of measures of information transfer in both directions. Here we illustrate that before inferring the directionality of coupling it is first necessary to consider the use of appropriate tests of significance. We propose a surrogate corrected directionality index which incorporates such testing. We also highlight the differences between testing the significance of the directionality index itself versus testing the individual measures of information transfer in each direction. To validate the approach we compared two different methods of estimating coupling, both of which have previously been used to estimate directionality indices. These were the modeling-based evolution map approach and a conditional mutual information (CMI) method for calculating dynamic information rates. For the CMI-based approach we also compared two different methods for estimating the CMI, an equiquantization-based estimator and a k-nearest neighbors estimator.

Mapping the Information Trace in Local Field Potentials by a Computational Method of Two-Dimensional Time-Shifting Synchronization Likelihood Based on Graphic Processing Unit Acceleration

The local field potential (LFP) is a signal reflecting the electrical activity of neurons surrounding the electrode tip. Synchronization between LFP signals provides important details about how neural networks are organized. Synchronization between two distant brain regions is hard to detect using linear synchronization algorithms like correlation and coherence. Synchronization likelihood (SL) is a non-linear synchronization-detecting algorithm widely used in studies of neural signals from two distant brain areas. One drawback of non-linear algorithms is the heavy computational burden. In the present study, we proposed a graphic processing unit (GPU)-accelerated implementation of an SL algorithm with optional 2-dimensional time-shifting. We tested the algorithm with both artificial data and raw LFP data. The results showed that this method revealed detailed information from original data with the synchronization values of two temporal axes, delay time and onset time, and thus can be used to reconstruct the temporal structure of a neural network. Our results suggest that this GPU-accelerated method can be extended to other algorithms for processing time-series signals (like EEG and fMRI) using similar recording techniques.

Simple phalanx pattern leads to energy saving in cohesive fish schooling

The question of how individuals in a population organize when living in groups arises for systems as different as a swarm of microorganisms or a flock of seagulls. The different patterns for moving collectively involve a wide spectrum of reasons, such as evading predators or optimizing food prospection. Also, the schooling pattern has often been associated with an advantage in terms of energy consumption. In this study, we use a popular aquarium fish, the red nose tetra fish, Hemigrammus bleheri, which is known to swim in highly cohesive groups, to analyze the schooling dynamics. In our experiments, fish swim in a shallow-water tunnel with controlled velocity, and stereoscopic video recordings are used to track the 3D positions of each individual in a school, as well as their tail-beating kinematics. Challenging the widespread idea of fish favoring a diamond pattern to swim more efficiently [Weihs D (1973) Nature 241:290-291], we observe that when fish are forced to swim fast-well above their free-swimming typical velocity, and hence in a situation where efficient swimming would be favored-the most frequent configuration is the "phalanx" or "soldier" formation, with all individuals swimming side by side. We explain this observation by considering the advantages of tail-beating synchronization between neighbors, which we have also characterized. Most importantly, we show that schooling is advantageous as compared with swimming alone from an energy-efficiency perspective.