Phase synchronization of chaotic oscillators

Climatic and dam-induced impacts on river water temperature: Assessment and management implications

In a changing climate with a warming trend in air temperature, river water temperature increases as a result of heat exchange with the atmosphere. Moreover, of the different types of anthropogenic activity impacting rivers, the construction of dams appears to have multi-dimensional effects on the river environment, and it especially affects the thermal condition of rivers. The aim of the study is to identify and assess the impact of these two distinct sources of water temperature distortion in relation to the natural thermal conditions of rivers. In the study, linear trend analysis and a complex wavelet transform are used. The analysis focuses on daily river water temperature data for time periods before and after the construction of selected reservoirs in the Polish Carpathians, and on daily air temperature data for neighboring meteorological stations. Three rivers were selected for analysis: (1) Dunajec River, 22km downstream of the Czorsztyn-Sromowce Wyżne reservoir complex, (2) Ropa River, 16km downstream of the Klimkówka Reservoir, and (3) Wisłok River, 33km downstream of the Besko Reservoir. Research has shown that the significant increasing trends identified for water temperature are weaker than analogous trends in air temperature. The Czorsztyn-Sromowce Wyżne and Klimkówka reservoirs appear to exert considerable influence on natural air-water temperature synchronization, because the phase difference increases 5-fold in comparison with conditions prior to the construction of the reservoirs. The weakening of the natural air-water temperature synchrony implies diminished impact of air temperature on stream water temperature. However, this creates an opportunity for preparing appropriate management practices mitigating an increasing temperature trend in order to shape more favorable (natural) thermal conditions for native aquatic biota in impounded rivers.

Assessment of Multivariate Neural Time Series by Phase Synchrony Clustering in a Time-Frequency-Topography Representation

Most EEG phase synchrony measures are of bivariate nature. Those that are multivariate focus on producing global indices of the synchronization state of the system. Thus, better descriptions of spatial and temporal local interactions are still in demand. A framework for characterization of phase synchrony relationships between multivariate neural time series is presented, applied either in a single epoch or over an intertrial assessment, relying on a proposed clustering algorithm, termed Multivariate Time Series Clustering by Phase Synchrony, which generates fuzzy clusters for each multivalued time sample and thereupon obtains hard clusters according to a circular variance threshold; such cluster modes are then depicted in Time-Frequency-Topography representations of synchrony state beyond mere global indices. EEG signals from P300 Speller sessions of four subjects were analyzed, obtaining useful insights of synchrony patterns related to the ERP and even revealing steady-state artifacts at 7.6 Hz. Further, contrast maps of Levenshtein Distance highlight synchrony differences between ERP and no-ERP epochs, mainly at delta and theta bands. The framework, which is not limited to one synchrony measure, allows observing dynamics of phase changes and interactions among channels and can be applied to analyze other cognitive states rather than ERP versus no ERP.

Disruption of frontal-parietal connectivity during conscious sedation by propofol administration

The sedative state is a transitional state from wakefulness to general anesthesia. However, little is understood regarding the mechanism of conscious sedation, different from general anesthesia while maintaining wakefulness. In this study, we aimed to investigate changes in functional connectivity of the parietal-frontal network, implicated in wakefulness during conscious sedation induced by propofol infusion. The electroencephalography was obtained at the frontal and parietal areas of adult volunteers who maintain wakefulness during low-dose propofol infusion (1.5 mg/kg/h) over 1 h. Spectral Granger causality (GC) (δ, θ, α, β, and γ frequency bands) and time-domain GC were calculated during each stage of awake (before propofol administration), sedation, and recovery (after discontinuation of propofol). We also calculated the phase-locking index and compared it with GC during each stage. A decrease in GC from the frontal to parietal areas was observed particularly in the low-frequency bands during propofol administration. Contrary to the GC changes in the frontoparietal direction, GC from the parietal to frontal areas was increased in the high-frequency bands during propofol administration and significantly decreased after discontinuation of propofol. In summary, we showed that frontal-parietal neural networks were significantly changed differently by the frequency of the brain rhythm and the directions of connections during sedation by propofol administration. Our result suggests that the alteration of brain interaction may induce sedative state lying between awake and general anesthesia.

Understanding transient uncoupling induced synchronization through modified dynamic coupling

An important aspect of the recently introduced transient uncoupling scheme is that it induces synchronization for large values of coupling strength at which the coupled chaotic systems resist synchronization when continuously coupled. However, why this is so is an open problem? To answer this question, we recall the conventional wisdom that the eigenvalues of the Jacobian of the transverse dynamics measure whether a trajectory at a phase point is locally contracting or diverging with respect to another nearby trajectory. Subsequently, we go on to highlight a lesser appreciated fact that even when, under the corresponding linearised flow, the nearby trajectory asymptotically diverges away, its distance from the reference trajectory may still be contracting for some intermediate period. We term this phenomenon transient decay in line with the phenomenon of the transient growth. Using these facts, we show that an optimal coupling region, i.e., a region of the phase space where coupling is on, should ideally be such that at any of the constituent phase point either the maximum of the real parts of the eigenvalues is negative or the magnitude of the positive maximum is lesser than that of the negative minimum. We also invent and employ a modified dynamics coupling scheme-a significant improvement over the well-known dynamic coupling scheme-as a decisive tool to justify our results.

Heightened Background Cortical Synchrony in Patients With Epilepsy: EEG Phase Synchrony Analysis During Awake and Sleep Stages Using Novel Ensemble Measure

INTRODUCTION

Excessive cortical synchrony within neural ensembles has been implicated as an important mechanism driving epileptiform activity. The current study measures and compares background electroencephalographic (EEG) phase synchronization in patients having various types of epilepsies and healthy controls during awake and sleep stages.

METHODS

A total of 120 patients with epilepsy (PWE) subdivided into 3 groups (juvenile myoclonic epilepsy [JME], temporal lobe epilepsy [TLE], and extra-temporal lobe epilepsy [Ex-TLE]; n = 40 in each group) and 40 healthy controls were subjected to overnight polysomnography. EEG phase synchronization (SI) between the 8 EEG channels was assessed for delta, theta, alpha, sigma, and high beta frequency bands using ensemble measure on 10-second representative time windows and compared between patients and controls and also between awake and sleep stages. Mean ± SD of SI was compared using 2-way analysis of variance followed by pairwise comparison ( P ≤ .05).

RESULTS

In both delta and theta bands, the SI was significantly higher in patients with JME, TLE, and Ex-TLE compared with controls, whereas in alpha, sigma, and high beta bands, SI was comparable between the groups. On comparison of SI between sleep stages, delta band: progressive increase in SI from wake ⇒ N1 ⇒ N2 ⇒ N3, whereas REM (rapid eye movement) was comparable to wake; theta band: decreased SI during N2 and increase during N3; alpha band: SI was highest in wake and lower in N1, N2, N3, and REM; and sigma and high beta bands: progressive increase in SI from wake ⇒ N1 ⇒ N2 ⇒ N3; however, sigma band showed lower SI during REM.

CONCLUSION

This study found an increased background cortical synchronization in PWE compared with healthy controls in delta and theta bands during wake and sleep. This background hypersynchrony may be an important property of epileptogenic brain circuitry in PWE, which enables them to effortlessly generate a paroxysmal EEG depolarization shift.

Brain Network Regional Synchrony Analysis in Deafness

Deafness, the most common auditory disease, has greatly affected people for a long time. The major treatment for deafness is cochlear implantation (CI). However, till today, there is still a lack of objective and precise indicator serving as evaluation of the effectiveness of the cochlear implantation. The goal of this EEG-based study is to effectively distinguish CI children from those prelingual deafened children without cochlear implantation. The proposed method is based on the functional connectivity analysis, which focuses on the brain network regional synchrony. Specifically, we compute the functional connectivity between each channel pair first. Then, we quantify the brain network synchrony among regions of interests (ROIs), where both intraregional synchrony and interregional synchrony are computed. And finally the synchrony values are concatenated to form the feature vector for the SVM classifier. What is more, we develop a new ROI partition method of 128-channel EEG recording system. That is, both the existing ROI partition method and the proposed ROI partition method are used in the experiments. Compared with the existing EEG signal classification methods, our proposed method has achieved significant improvements as large as 87.20% and 86.30% when the existing ROI partition method and the proposed ROI partition method are used, respectively. It further demonstrates that the new ROI partition method is comparable to the existing ROI partition method.

Robust generalized Mittag-Leffler synchronization of fractional order neural networks with discontinuous activation and impulses

Fractional order system is playing an increasingly important role in terms of both theory and applications. In this paper we investigate the global existence of Filippov solutions and the robust generalized Mittag-Leffler synchronization of fractional order neural networks with discontinuous activation and impulses. By means of growth conditions, differential inclusions and generalized Gronwall inequality, a sufficient condition for the existence of Filippov solution is obtained. Then, sufficient criteria are given for the robust generalized Mittag-Leffler synchronization between discontinuous activation function of impulsive fractional order neural network systems with (or without) parameter uncertainties, via a delayed feedback controller and M-Matrix theory. Finally, four numerical simulations demonstrate the effectiveness of our main results.

Capacitive coupling synchronizes autonomous microfluidic oscillators

Even identically designed autonomous microfluidic oscillators have device-to-device oscillation variability that arises due to inconsistencies in fabrication, materials, and operation conditions. This work demonstrates, experimentally and theoretically, that with appropriate capacitive coupling these microfluidic oscillators can be synchronized. The size and characteristics of the capacitive coupling needed and the range of input flow rate differences that can be synchronized are also characterized. In addition to device-to-device variability, there is also within-device oscillation noise that arises. An additional advantage of coupling multiple fluidic oscillators together is that the oscillation noise decreases. The ability to synchronize multiple autonomous oscillators is also a first step towards enhancing their usefulness as tools for biochemical research applications where multiplicate experiments with identical temporal-stimulation conditions are required.

Detection of generalized synchronization using echo state networks

Generalized synchronization between coupled dynamical systems is a phenomenon of relevance in applications that range from secure communications to physiological modelling. Here, we test the capabilities of reservoir computing and, in particular, echo state networks for the detection of generalized synchronization. A nonlinear dynamical system consisting of two coupled Rössler chaotic attractors is used to generate temporal series consisting of time-locked generalized synchronized sequences interleaved with unsynchronized ones. Correctly tuned, echo state networks are able to efficiently discriminate between unsynchronized and synchronized sequences even in the presence of relatively high levels of noise. Compared to other state-of-the-art techniques of synchronization detection, the online capabilities of the proposed Echo State Network based methodology make it a promising choice for real-time applications aiming to monitor dynamical synchronization changes in continuous signals.

Analysis of chimera states as drive-response systems

Chimera states are spatiotemporal segregations – stably coexisting coherent and incoherent groups – that can occur in systems of identical phase oscillators. Here we demonstrate that this remarkable phenomenon can also be understood in terms of Pecora and Carroll’s drive-response theory. By calculating the conditional Lyapunov exponents, we show that the incoherent group acts to synchronize the coherent group; the latter playing the role of a response. We also compare the distributions of finite-time conditional Lyapunov exponents to the characteristic distribution that was reported previously for chimera states. The present analysis provides a unifying explanation of the inherently frustrated dynamics that gives rise to chimera states.

A Novel Multivariate Sample Entropy Algorithm for Modeling Time Series Synchronization

Approximate and sample entropy (AE and SE) provide robust measures of the deterministic or stochastic content of a time series (regularity), as well as the degree of structural richness (complexity), through operations at multiple data scales. Despite the success of the univariate algorithms, multivariate sample entropy (mSE) algorithms are still in their infancy and have considerable shortcomings. Not only are existing mSE algorithms unable to analyse within- and cross-channel dynamics, they can counter-intuitively interpret increased correlation between variates as decreased regularity. To this end, we first revisit the embedding of multivariate delay vectors (DVs), critical to ensuring physically meaningful and accurate analysis. We next propose a novel mSE algorithm and demonstrate its improved performance over existing work, for synthetic data and for classifying wake and sleep states from real-world physiological data. It is furthermore revealed that, unlike other tools, such as the correlation of phase synchrony, synchronized regularity dynamics are uniquely identified via mSE analysis. In addition, a model for the operation of this novel algorithm in the presence of white Gaussian noise is presented, which, in contrast to the existing algorithms, reveals for the first time that increasing correlation between different variates reduces entropy.

Coupled Lorenz oscillators near the Hopf boundary: Multistability, intermingled basins, and quasiriddling

We investigate the dynamics of coupled identical chaotic Lorenz oscillators just above the subcritical Hopf bifurcation. In the absence of coupling, the motion is on a strange chaotic attractor and the fixed points of the system are all unstable. With the coupling, the unstable fixed points are converted into chaotic attractors, and the system can exhibit a multiplicity of coexisting attractors. Depending on the strength of the coupling, the motion of the individual oscillators can be synchronized (both in and out of phase) or desynchronized and in addition there can be mixed phases. We find that the basins have a complex structure: the state that is asymptotically reached shows extreme sensitivity to initial conditions. The basins of attraction of these different states are characterized using a variety of measures and depending on the strength of the coupling, they are intermingled or quasiriddled.

Insensitivity of synchronization to network structure in chaotic pendulum systems with time-delay coupling

It has been generally believed that both time delay and network structure could play a crucial role in determining collective dynamical behaviors in complex systems. In this work, we study the influence of coupling strength, time delay, and network topology on synchronization behavior in delay-coupled networks of chaotic pendulums. Interestingly, we find that the threshold value of the coupling strength for complete synchronization in such networks strongly depends on the time delay in the coupling, but appears to be insensitive to the network structure. This lack of sensitivity was numerically tested in several typical regular networks, such as different locally and globally coupled ones as well as in several complex networks, such as small-world and scale-free networks. Furthermore, we find that the emergence of a synchronous periodic state induced by time delay is of key importance for the complete synchronization.

Amplification through chaotic synchronization in spatially extended beam-plasma systems

In this paper, we have studied the relationship between chaotic synchronization and microwave signal amplification in coupled beam-plasma systems. We have considered a 1D particle-in-cell numerical model of unidirectionally coupled beam-plasma oscillatory media being in the regime of electron pattern formation. We have shown the significant gain of microwave oscillation power in coupled beam-plasma media being in the different regimes of generation. The discovered effect has a close connection with the chaotic synchronization phenomenon, so we have observed that amplification appears after the onset of the complete time scale synchronization regime in the analyzed coupled spatially extended systems. We have also provided the numerical study of physical processes in the chain of beam-plasma systems leading to the chaotic synchronization and the amplification of microwave oscillations power, respectively.

Phase synchronization of baroclinic waves in a differentially heated rotating annulus experiment subject to periodic forcing with a variable duty cycle

A series of laboratory experiments in a thermally driven, rotating fluid annulus are presented that investigate the onset and characteristics of phase synchronization and frequency entrainment between the intrinsic, chaotic, oscillatory amplitude modulation of travelling baroclinic waves and a periodic modulation of the (axisymmetric) thermal boundary conditions, subject to time-dependent coupling. The time-dependence is in the form of a prescribed duty cycle in which the periodic forcing of the boundary conditions is applied for only a fraction δ of each oscillation. For the rest of the oscillation, the boundary conditions are held fixed. Two profiles of forcing were investigated that capture different parts of the sinusoidal variation and δ was varied over the range 0.1≤δ≤1. Reducing δ was found to act in a similar way to a reduction in a constant coupling coefficient in reducing the width of the interval in forcing frequency or period over which complete synchronization was observed (the "Arnol'd tongue") with respect to the detuning, although for the strongest pulse-like forcing profile some degree of synchronization was discernible even at δ=0.1. Complete phase synchronization was obtained within the Arnol'd tongue itself, although the strength of the amplitude modulation of the baroclinic wave was not significantly affected. These experiments demonstrate a possible mechanism for intraseasonal and/or interannual "teleconnections" within the climate system of the Earth and other planets that does not rely on Rossby wave propagation across the planet along great circles.

Synchronization of world economic activity

Common dynamical properties of business cycle fluctuations are studied in a sample of more than 100 countries that represent economic regions from all around the world. We apply the methodology of multivariate singular spectrum analysis (M-SSA) to identify oscillatory modes and to detect whether these modes are shared by clusters of phase- and frequency-locked oscillators. An extension of the M-SSA approach is introduced to help analyze structural changes in the cluster configuration of synchronization. With this novel technique, we are able to identify a common mode of business cycle activity across our sample, and thus point to the existence of a world business cycle. Superimposed on this mode, we further identify several major events that have markedly influenced the landscape of world economic activity in the postwar era.

Self-similarity in explosive synchronization of complex networks

We report that explosive synchronization of networked oscillators (a process through which the transition to coherence occurs without intermediate stages but is rather characterized by a sudden and abrupt jump from the network's asynchronous to synchronous motion) is related to self-similarity of synchronous clusters of different size. Self-similarity is revealed by destructing the network synchronous state during the backward transition and observed with the decrease of the coupling strength between the nodes of the network. As illustrative examples, networks of Kuramoto oscillators with different topologies of links have been considered. For each one of such topologies, the destruction of the synchronous state goes step by step with self-similar configurations of interacting oscillators. At the critical point, the invariance of the phase distribution in the synchronized cluster with respect to the cluster size is reported.

A robust statistical framework for instantaneous electroencephalogram phase and frequency estimation and analysis

OBJECTIVE

The instantaneous phase (IP) and instantaneous frequency (IF) of the electroencephalogram (EEG) are considered as notable complements for the EEG spectrum. The calculation of these parameters commonly includes narrow-band filtering, followed by the calculation of the signal's analytical form. The calculation of the IP and IF is highly susceptible to the filter parameters and background noise level, especially in low analytical signal amplitudes. The objective of this study is to propose a robust statistical framework for EEG IP/IF estimation and analysis.

APPROACH

Herein, a Monte Carlo estimation scheme is proposed for the robust estimation of the EEG IP and IF. It is proposed that any EEG phase-related inference should be reported as an average with confidence intervals obtained by repeating the IP and IF estimation under infinitesimal variations (selected by an expert), in algorithmic parameters such as the filter's bandwidth, center frequency and background noise level. In the second part of the paper, a stochastic model consisting of the superposition of narrow-band foreground and background EEG is used to derive analytically probability density functions of the instantaneous envelope (IE) and IP of EEG signals, which justify the proposed Monte Carlo scheme.

MAIN RESULTS

The instantaneous analytical envelope of the EEG, which has been empirically used in previous studies, is shown to have a fundamental impact on the accuracy of the EEG phase contents. It is rigorously shown that the IP/IF estimation quality highly depends on the IE and any phase/frequency interpretations in low IE are statistically unreliable and require a hypothesis test.

SIGNIFICANCE

The impact of the proposed method on previous studies, including time-domain phase synchrony, phase resetting, phase locking value and phase amplitude coupling are studied with examples. The findings of this research can set forth new standards for EEG phase/frequency estimation and analysis techniques.

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.

Synchronization and collective swimming patterns in fish (Hemigrammus bleheri)

In this work, we address the case of red nose tetra fish Hemigrammus bleheri swimming in groups in a uniform flow, giving special attention to the basic interactions and cooperative swimming of a single pair of fish. We first bring evidence of synchronization of the two fish, where the swimming modes are dominated by 'out-phase' and 'in-phase' configurations. We show that the transition to this synchronization state is correlated with the swimming speed (i.e. the flow rate), and thus with the magnitude of the hydrodynamic pressure generated by the fish body during each swimming cycle. From a careful spatio-temporal analysis corresponding to those synchronized modes, we characterize the distances between the two individuals in a pair in the basic schooling pattern. We test the conclusions of the analysis of fish pairs with a second set of experiments using groups of three fish. By identifying the typical spatial configurations, we explain how the nearest neighbour interactions constitute the building blocks of collective fish swimming.

Coordination of Slow Waves With Sleep Spindles Predicts Sleep-Dependent Memory Consolidation in Schizophrenia

Study Objectives

Schizophrenia patients have correlated deficits in sleep spindle density and sleep-dependent memory consolidation. In addition to spindle density, memory consolidation is thought to rely on the precise temporal coordination of spindles with slow waves (SWs). We investigated whether this coordination is intact in schizophrenia and its relation to motor procedural memory consolidation.

Methods

Twenty-one chronic medicated schizophrenia patients and 17 demographically matched healthy controls underwent two nights of polysomnography, with training on the finger tapping motor sequence task (MST) on the second night and testing the following morning. We detected SWs (0.5-4 Hz) and spindles during non-rapid eye movement (NREM) sleep. We measured SW-spindle phase-amplitude coupling and its relation with overnight improvement in MST performance.

Results

Patients did not differ from controls in the timing of SW-spindle coupling. In both the groups, spindles peaked during the SW upstate. For patients alone, the later in the SW upstate that spindles peaked and the more reliable this phase relationship, the greater the overnight MST improvement. Regression models that included both spindle density and SW-spindle coordination predicted overnight improvement significantly better than either parameter alone, suggesting that both contribute to memory consolidation.

Conclusion

Schizophrenia patients show intact spindle-SW temporal coordination, and these timing relationships, together with spindle density, predict sleep-dependent memory consolidation. These relations were seen only in patients suggesting that their memory is more dependent on optimal spindle-SW timing, possibly due to reduced spindle density. Interventions to improve memory may need to increase spindle density while preserving or enhancing the coordination of NREM oscillations.

Function Projective Dual Synchronization with Uncertain Parameters of Hyperchaotic Systems

Function projective dual synchronization between two pairs of hyperchaotic systems with fully unknown parameters for drive and response systems is investigated. On the basis of the Lyapunov stability theory, a suitable and effective adaptive control law and parameters update rule for unknown parameters are designed, such that function projective dual synchronization between the hyperchaotic Chen system and the hyperchaotic Lü system with unknown parameters is achieved. Theoretical analysis and numerical simulations are presented to demonstrate the validity and feasibility of the proposed method.

Synchronous behaviour of two interacting oscillatory systems undergoing quasiperiodic route to chaos

Thermoacoustic instability, caused by a positive feedback between the unsteady heat release and the acoustic field in a combustor, is a major challenge faced in most practical combustors such as those used in rockets and gas turbines. We employ the synchronization theory for understanding the coupling between the unsteady heat release and the acoustic field of a thermoacoustic system. Interactions between coupled subsystems exhibiting different collective dynamics such as periodic, quasiperiodic, and chaotic oscillations are addressed. Even though synchronization studies have focused on different dynamical states separately, synchronous behaviour of two coupled systems exhibiting a quasiperiodic route to chaos has not been studied. In this study, we report the first experimental observation of different synchronous behaviours between two subsystems of a thermoacoustic system exhibiting such a transition as reported in Kabiraj et al. [Chaos 22, 023129 (2012)]. A rich variety of synchronous behaviours such as phase locking, intermittent phase locking, and phase drifting are observed as the dynamics of such subsystem change. The observed synchronization behaviour is further characterized using phase locking value, correlation coefficient, and relative mean frequency. These measures clearly reveal the boundaries between different states of synchronization.

Brain networking analysis in migraine with and without aura

Background

To apply effective connectivity by means of nonlinear Granger Causality (GC) and brain networking analysis to basal EEG and under visual stimulation by checkerboard gratings with 0.5 and 2.0 cpd as spatial frequency in migraine with aura (MA) and without aura (MO), and to compare these findings with Blood Oxygen Level Dependent (BOLD) signal changes.

Methods

Nineteen asymptomatic MA and MO patients and 11 age and sex matched controls (C) were recorded by 65 EEG channels. The same visual stimulation was employed to evaluate BOLD signal changes in a subgroup of MA and MO. The GC and brain networking were applied to EEG signals.

Results

A different pattern of reduced vs increased GC respectively in MO and MA patients, emerged in resting state. During visual stimulation, both MA and MO showed increased information transfer toward the fronto-central regions, while MA patients showed a segregated cluster of connections in the posterior regions, and an increased bold signal in the visual cortex, more evident at 2 cpd spatial frequency.

Conclusions

The wealth of information exchange in the parietal-occipital regions indicates a peculiar excitability of the visual cortex, a pivotal condition for the manifestation of typical aura symptoms.

Electronic supplementary material

The online version of this article (10.1186/s10194-017-0803-5) contains supplementary material, which is available to authorized users.

Quantitative heartbeat coupling measures in human-horse interaction

We present a study focused on a quantitative estimation of a human-horse dynamic interaction. A set of measures based on magnitude and phase coupling between heartbeat dynamics of both humans and horses in three different conditions is reported: no interaction, visual/olfactory interaction and grooming. Specifically, Magnitude Squared Coherence (MSC), Mean Phase Coherence (MPC) and Dynamic Time Warping (DTW) have been used as estimators of the amount of coupling between human and horse through the analysis of their heart rate variability (HRV) time series in a group of eleven human subjects, and one horse. The rationale behind this study is that the interaction of two complex biological systems go towards a coupling process whose dynamical evolution is modulated by the kind and time duration of the interaction itself. We achieved a congruent and consistent statistical significant difference for all of the three indices. Moreover, a Nearest Mean Classifier was able to recognize the three classes of interaction with an accuracy greater than 70%. Although preliminary, these encouraging results allow a discrimination of three distinct phases in a real human-animal interaction opening to the characterization of the empirically proven relationship between human and horse.

Experimental phase synchronization detection in non-phase coherent chaotic systems by using the discrete complex wavelet approach

Phase synchronization may emerge from mutually interacting non-linear oscillators, even under weak coupling, when phase differences are bounded, while amplitudes remain uncorrelated. However, the detection of this phenomenon can be a challenging problem to tackle. In this work, we apply the Discrete Complex Wavelet Approach (DCWA) for phase assignment, considering signals from coupled chaotic systems and experimental data. The DCWA is based on the Dual-Tree Complex Wavelet Transform (DT-CWT), which is a discrete transformation. Due to its multi-scale properties in the context of phase characterization, it is possible to obtain very good results from scalar time series, even with non-phase-coherent chaotic systems without state space reconstruction or pre-processing. The method correctly predicts the phase synchronization for a chemical experiment with three locally coupled, non-phase-coherent chaotic processes. The impact of different time-scales is demonstrated on the synchronization process that outlines the advantages of DCWA for analysis of experimental data.

Automated Detection of Epileptic Biomarkers in Resting-State Interictal MEG Data

Certain differences between brain networks of healthy and epilectic subjects have been reported even during the interictal activity, in which no epileptic seizures occur. Here, magnetoencephalography (MEG) data recorded in the resting state is used to discriminate between healthy subjects and patients with either idiopathic generalized epilepsy or frontal focal epilepsy. Signal features extracted from interictal periods without any epileptiform activity are used to train a machine learning algorithm to draw a diagnosis. This is potentially relevant to patients without frequent or easily detectable spikes. To analyze the data, we use an up-to-date machine learning algorithm and explore the benefits of including different features obtained from the MEG data as inputs to the algorithm. We find that the relative power spectral density of the MEG time-series is sufficient to distinguish between healthy and epileptic subjects with a high prediction accuracy. We also find that a combination of features such as the phase-locked value and the relative power spectral density allow to discriminate generalized and focal epilepsy, when these features are calculated over a filtered version of the signals in certain frequency bands. Machine learning algorithms are currently being applied to the analysis and classification of brain signals. It is, however, less evident to identify the proper features of these signals that are prone to be used in such machine learning algorithms. Here, we evaluate the influence of the input feature selection on a clinical scenario to distinguish between healthy and epileptic subjects. Our results indicate that such distinction is possible with a high accuracy (86%), allowing the discrimination between idiopathic generalized and frontal focal epilepsy types.

Spontaneous exchange of leader-laggard relationship in mutually coupled synchronized semiconductor lasers

We investigate the instantaneous behavior of synchronized temporal wave forms in two mutually coupled semiconductor lasers numerically and experimentally. The temporal wave forms of two lasers are synchronized with a propagation delay time, with one laser oscillating in advance of the other, known as the leader-laggard relationship. The leader-laggard relationship can be determined by measuring the cross-correlation between the two temporal wave forms with the propagation delay time. The leader can be identified when the optical carrier frequency of the leader laser is higher than that of the other laser. However, spontaneous exchange between the leader and laggard lasers can be observed in low-frequency fluctuations by short-term cross-correlation measurements, even for a fixed initial optical frequency detuning. The spontaneous exchange of the leader-laggard relationship originates from alternation of partial optical frequency locking between the two lasers. This observation is analyzed using a phase space trajectory on steady-state solutions for mutually coupled lasers with optical frequency detuning.

Directional information flow in patients with Alzheimer's disease. A source-space resting-state MEG study

In a recent magnetoencephalography (MEG) study, we found posterior-to-anterior information flow over the cortex in higher frequency bands in healthy subjects, with a reversed pattern in the theta band. A disruption of information flow may underlie clinical symptoms in Alzheimer's disease (AD). In AD, highly connected regions (hubs) in posterior areas are mostly disrupted. We therefore hypothesized that in AD the information flow from these hub regions would be disturbed. We used resting-state MEG recordings from 27 early-onset AD patients and 26 healthy controls. Using beamformer-based virtual electrodes, we estimated neuronal oscillatory activity for 78 cortical regions of interest (ROIs) and 12 subcortical ROIs of the AAL atlas, and calculated the directed phase transfer entropy (dPTE) as a measure of information flow between these ROIs. Group differences were evaluated using permutation tests and, for the AD group, associations between dPTE and general cognition or CSF biomarkers were determined using Spearman correlation coefficients. We confirmed the previously reported posterior-to-anterior information flow in the higher frequency bands in the healthy controls, and found it to be disturbed in the beta band in AD. Most prominently, the information flow from the precuneus and the visual cortex, towards frontal and subcortical structures, was decreased in AD. These disruptions did not correlate with cognitive impairment or CSF biomarkers. We conclude that AD pathology may affect the flow of information between brain regions, particularly from posterior hub regions, and that changes in the information flow in the beta band indicate an aspect of the pathophysiological process in AD.

Horizontal visibility graph transfer entropy (HVG-TE): A novel metric to characterize directed connectivity in large-scale brain networks

We propose a new measure, horizontal visibility graph transfer entropy (HVG-TE), to estimate the direction of information flow between pairs of time series. HVG-TE quantifies the transfer entropy between the degree sequences of horizontal visibility graphs derived from original time series. Twenty-one Rössler attractors unidirectionally coupled in the posterior-to-anterior direction were used to simulate 21-channel Electroencephalography (EEG) brain networks and validate the performance of the HVG-TE. We showed that the HVG-TE is robust to different levels of coupling strengths between the coupled Rössler attractors, a wide range of time delays, different sample sizes, the effects of noise and linear mixing, and the choice of reference for EEG data. We also applied HVG-TE to EEG data in 20 healthy controls and compared its performance to a recently introduces phase-based TE measure (PTE). We found that compared with PTE, HVG-TE consistently detected stronger posterior-to-anterior information flow patterns in the alpha-band (8-13Hz) EEG brain networks for three different references. Moreover, in contrast to PTE, HVG-TE does not require an assumption on the periodicity of input signals, therefore it can be more widely applicable, even for non-periodic signals. This study shows that the HVG-TE is a directed connectivity measure to characterise the direction of information flow in large-scale brain networks.

Generalized synchronization between chimera states

Networks of coupled oscillators in chimera states are characterized by an intriguing interplay of synchronous and asynchronous motion. While chimera states were initially discovered in mathematical model systems, there is growing experimental and conceptual evidence that they manifest themselves also in natural and man-made networks. In real-world systems, however, synchronization and desynchronization are not only important within individual networks but also across different interacting networks. It is therefore essential to investigate if chimera states can be synchronized across networks. To address this open problem, we use the classical setting of ring networks of non-locally coupled identical phase oscillators. We apply diffusive drive-response couplings between pairs of such networks that individually show chimera states when there is no coupling between them. The drive and response networks are either identical or they differ by a variable mismatch in their phase lag parameters. In both cases, already for weak couplings, the coherent domain of the response network aligns its position to the one of the driver networks. For identical networks, a sufficiently strong coupling leads to identical synchronization between the drive and response. For non-identical networks, we use the auxiliary system approach to demonstrate that generalized synchronization is established instead. In this case, the response network continues to show a chimera dynamics which however remains distinct from the one of the driver. Hence, segregated synchronized and desynchronized domains in individual networks congregate in generalized synchronization across networks.

Consistency of heterogeneous synchronization patterns in complex weighted networks

Synchronization within the dynamical nodes of a complex network is usually considered homogeneous through all the nodes. Here we show, in contrast, that subsets of interacting oscillators may synchronize in different ways within a single network. This diversity of synchronization patterns is promoted by increasing the heterogeneous distribution of coupling weights and/or asymmetries in small networks. We also analyze consistency, defined as the persistence of coexistent synchronization patterns regardless of the initial conditions. Our results show that complex weighted networks display richer consistency than regular networks, suggesting why certain functional network topologies are often constructed when experimental data are analyzed.

Synchronization of oscillators through time-shifted common inputs

Shared upstream dynamical processes are frequently the source of common inputs in various physical and biological systems. However, due to finite signal transmission speeds and differences in the distance to the source, time shifts between otherwise common inputs are unavoidable. Since common inputs can be a source of correlation between the elements of multi-unit dynamical systems, regardless of whether these elements are directly connected with one another or not, it is of importance to understand their impact on synchronization. As a canonical model that is representative for a variety of different dynamical systems, we study limit-cycle oscillators that are driven by stochastic time-shifted common inputs. We show that if the oscillators are coupled, time shifts in stochastic common inputs do not simply shift the distribution of the phase differences, but rather the distribution actually changes as a result. The best synchronization is therefore achieved at a precise intermediate value of the time shift, which is due to a resonance-like effect with the most probable phase difference that is determined by the deterministic dynamics.

Efficient Computation of Functional Brain Networks: toward Real-Time Functional Connectivity

Functional Connectivity has demonstrated to be a key concept for unraveling how the brain balances functional segregation and integration properties while processing information. This work presents a set of open-source tools that significantly increase computational efficiency of some well-known connectivity indices and Graph-Theory measures. PLV, PLI, ImC, and wPLI as Phase Synchronization measures, Mutual Information as an information theory based measure, and Generalized Synchronization indices are computed much more efficiently than prior open-source available implementations. Furthermore, network theory related measures like Strength, Shortest Path Length, Clustering Coefficient, and Betweenness Centrality are also implemented showing computational times up to thousands of times faster than most well-known implementations. Altogether, this work significantly expands what can be computed in feasible times, even enabling whole-head real-time network analysis of brain function.

Flocking ferromagnetic colloids

Assemblages of microscopic colloidal particles exhibit fascinating collective motion when energized by electric or magnetic fields. The behaviors range from coherent vortical motion to phase separation and dynamic self-assembly. Although colloidal systems are relatively simple, understanding their collective response, especially under out-of-equilibrium conditions, remains elusive. We report on the emergence of flocking and global rotation in the system of rolling ferromagnetic microparticles energized by a vertical alternating magnetic field. By combing experiments and discrete particle simulations, we have identified primary physical mechanisms, leading to the emergence of large-scale collective motion: spontaneous symmetry breaking of the clockwise/counterclockwise particle rotation, collisional alignment of particle velocities, and random particle reorientations due to shape imperfections. We have also shown that hydrodynamic interactions between the particles do not have a qualitative effect on the collective dynamics. Our findings shed light on the onset of spatial and temporal coherence in a large class of active systems, both synthetic (colloids, swarms of robots, and biopolymers) and living (suspensions of bacteria, cell colonies, and bird flocks).

A novel method linking neural connectivity to behavioral fluctuations: Behavior-regressed connectivity

BACKGROUND

During an experimental session, behavioral performance fluctuates, yet most neuroimaging analyses of functional connectivity derive a single connectivity pattern. These conventional connectivity approaches assume that since the underlying behavior of the task remains constant, the connectivity pattern is also constant.

NEW METHOD

We introduce a novel method, behavior-regressed connectivity (BRC), to directly examine behavioral fluctuations within an experimental session and capture their relationship to changes in functional connectivity. This method employs the weighted phase lag index (WPLI) applied to a window of trials with a weighting function. Using two datasets, the BRC results are compared to conventional connectivity results during two time windows: the one second before stimulus onset to identify predictive relationships, and the one second after onset to capture task-dependent relationships.

RESULTS

In both tasks, we replicate the expected results for the conventional connectivity analysis, and extend our understanding of the brain-behavior relationship using the BRC analysis, demonstrating subject-specific BRC maps that correspond to both positive and negative relationships with behavior. Comparison with Existing Method(s): Conventional connectivity analyses assume a consistent relationship between behaviors and functional connectivity, but the BRC method examines performance variability within an experimental session to understand dynamic connectivity and transient behavior.

CONCLUSION

The BRC approach examines connectivity as it covaries with behavior to complement the knowledge of underlying neural activity derived from conventional connectivity analyses. Within this framework, BRC may be implemented for the purpose of understanding performance variability both within and between participants.