Phase synchronization of chaotic oscillators

Mode decomposition-based time-varying phase synchronization for fMRI

Recently, there has been significant interest in measuring time-varying functional connectivity (TVC) between different brain regions using resting-state functional magnetic resonance imaging (rs-fMRI) data. One way to assess the relationship between signals from different brain regions is to measure their phase synchronization (PS) across time. However, this requires the a priori choice of type and cut-off frequencies for the bandpass filter needed to perform the analysis. Here we explore alternative approaches based on the use of various mode decomposition (MD) techniques that provide a more data driven solution to this issue. These techniques allow for the data driven decomposition of signals jointly into narrow-band components at different frequencies, thus fulfilling the requirements needed to measure PS. We explore several variants of MD, including empirical mode decomposition (EMD), bivariate EMD (BEMD), noise-assisted multivariate EMD (na-MEMD), and introduce the use of multivariate variational mode decomposition (MVMD) in the context of estimating time-varying PS. We contrast the approaches using a series of simulations and application to rs-fMRI data. Our results show that MVMD outperforms other evaluated MD approaches, and further suggests that this approach can be used as a tool to reliably investigate time-varying PS in rs-fMRI data.

Synergetic synchronized oscillation by distributed neural integrators to induce dynamic equilibrium in energy dissipation systems

The synchronization phenomenon is common to many natural mechanical systems. Joint friction and damping in humans and animals are associated with energy dissipation. A coupled oscillator model is conventionally used to manage multiple joint torque generations to form a limit cycle in an energy dissipation system. The coupling term design and the frequency and phase settings become issues when selecting the oscillator model. The relative coupling relationship between oscillators needs to be predefined for unknown dynamics systems, which is quite challenging problem. We present a simple distributed neural integrators method to induce the limit cycle in unknown energy dissipation systems without using a coupled oscillator. The results demonstrate that synergetic synchronized oscillation could be produced that adapts to different physical environments. Finding the balanced energy injection by neural inputs to form dynamic equilibrium is not a trivial problem, when the dynamics information is not priorly known. The proposed method realized self-organized pattern generation to induce the dynamic equilibrium for different mechanical systems. The oscillation was managed without using the explicit phase or frequency knowledge. However, phase, frequency, and amplitude modulation emerged to form an efficient synchronized limit cycle. This type of distributed neural integrator can be used as a source for regulating multi-joint coordination to induce synergetic oscillations in natural mechanical systems.

Alterations in a cross-hemispheric circuit associates with novelty discrimination deficits in mouse models of neurodegeneration

A major pathological hallmark of neurodegenerative diseases, including Alzheimer's, is a significant reduction in the white matter connecting the two cerebral hemispheres, as well as in the correlated activity between anatomically corresponding bilateral brain areas. However, the underlying circuit mechanisms and the cognitive relevance of cross-hemispheric (CH) communication remain poorly understood. Here, we show that novelty discrimination behavior activates CH neurons and enhances homotopic synchronized neural oscillations in the visual cortex. CH neurons provide excitatory drive required for synchronous neural oscillations between hemispheres, and unilateral inhibition of the CH circuit is sufficient to impair synchronous oscillations and novelty discrimination behavior. In the 5XFAD and Tau P301S mouse models, CH communication is altered, and novelty discrimination is impaired. These data reveal a hitherto uncharacterized CH circuit in the visual cortex, establishing a causal link between this circuit and novelty discrimination behavior and highlighting its impairment in mouse models of neurodegeneration.

The global neuronal workspace as a broadcasting network

A new strategy for moving forward in the characterization of the global neuronal workspace (GNW) is proposed. According to Dehaene, Changeux, and colleagues (Dehaene, 2014, pp. 304, 312; Dehaene & Changeux, 2004, 2005), broadcasting is the main function of the GNW. However, the dynamic network properties described by recent graph theoretic GNW models are consistent with many large-scale communication processes that are different from broadcasting. We propose to apply a different graph theoretic approach, originally developed for optimizing information dissemination in communication networks, which can be used to identify the pattern of frequency and phase-specific directed functional connections that the GNW would exhibit only if it were a broadcasting network.

Mirroring of synchronization in a bi-layer master-slave configuration of Kuramoto oscillators

The phenomenon of mirroring of synchronization is investigated in dynamically dissimilar, unidirectionally coupled, bi-layer master-slave configuration of globally coupled Kuramoto oscillators. The dynamics of the master layer depends solely on the distribution of the natural frequencies of its oscillators. On the other hand, the slave layer dynamics depends not only on the distribution of the natural frequencies of its oscillators but also on the unidirectional coupling with the master layer. The standard Kuramoto order parameter is used to study synchronization in the individual layers and of the bi-layer network. A transition to a completely mirroring state is observed in the dynamics of the slave layer, as the mirroring coefficient in the unidirectional coupling is increased. We derive analytically and verify numerically the conditions for the slave layer to fully mimic the synchronization properties of the master layer. It is further shown that while the master and slave layers are individually synchronized, the bi-layer network exhibits a state of frustrated synchronization.

Synchronization in a multilevel network using the Hamilton-Jacobi-Bellman (HJB) technique

This paper presents the optimal control and synchronization problem of a multilevel network of Rössler chaotic oscillators. Using the Hamilton-Jacobi-Bellman technique, the optimal control law with a three-state variable feedback is designed such that the trajectories of all the Rössler oscillators in the network are optimally synchronized at each level. Furthermore, we provide numerical simulations to demonstrate the effectiveness of the proposed approach for the cases of one and three networks. A perfect correlation between the MATLAB and PSpice results was obtained, thus allowing the experimental validation of our designed controller and shows the effectiveness of the theoretical results.

Huygens synchronization of medial septal pacemaker neurons generates hippocampal theta oscillation

Episodic learning and memory retrieval are dependent on hippocampal theta oscillation, thought to rely on the GABAergic network of the medial septum (MS). To test how this network achieves theta synchrony, we recorded MS neurons and hippocampal local field potential simultaneously in anesthetized and awake mice and rats. We show that MS pacemakers synchronize their individual rhythmicity frequencies, akin to coupled pendulum clocks as observed by Huygens. We optogenetically identified them as parvalbumin-expressing GABAergic neurons, while MS glutamatergic neurons provide tonic excitation sufficient to induce theta. In accordance, waxing and waning tonic excitation is sufficient to toggle between theta and non-theta states in a network model of single-compartment inhibitory pacemaker neurons. These results provide experimental and theoretical support to a frequency-synchronization mechanism for pacing hippocampal theta, which may serve as an inspirational prototype for synchronization processes in the central nervous system from Nematoda to Arthropoda to Chordate and Vertebrate phyla.

Anticipating measure synchronization in coupled Hamiltonian systems with machine learning

A model-free approach is proposed for anticipating the occurrence of measure synchronization in coupled Hamiltonian systems. Specifically, by the technique of parameter-aware reservoir computing in machine learning, we demonstrate that the machine trained by the time series of coupled Hamiltonian systems at a handful of coupling parameters is able to predict accurately not only the critical coupling for the occurrence of measure synchronization, but also the variation of the system order parameters around the transition point. The capability of the model-free technique in anticipating measure synchronization is exemplified in Hamiltonian systems of two coupled oscillators and also in a Hamiltonian system of three globally coupled oscillators where partial synchronization arises. The studies pave a way to the model-free, data-driven analysis of measure synchronization in large-size Hamiltonian systems.

Analysis of the Relationship Between Motor Imagery and Age-Related Fatigue for CNN Classification of the EEG Data

Background

The aging of the world population poses a major health challenge, and brain–computer interface (BCI) technology has the potential to provide assistance and rehabilitation for the elderly.

Objectives

This study aimed to investigate the electroencephalogram (EEG) characteristics during motor imagery by comparing young and elderly, and study Convolutional Neural Networks (CNNs) classification for the elderly population in terms of fatigue analysis in both frontal and parietal regions.

Methods

A total of 20 healthy individuals participated in the study, including 10 young and 10 older adults. All participants completed the left- and right-hand motor imagery experiment. The energy changes in the motor imagery process were analyzed using time–frequency graphs and quantified event-related desynchronization (ERD) values. The fatigue level of the motor imagery was assessed by two indicators: (θ + α)/β and θ/β, and fatigue-sensitive channels were distinguished from the parietal region of the brain. Then, rhythm entropy was introduced to analyze the complexity of the cognitive activity. The phase-lock values related to the parietal and frontal lobes were calculated, and their temporal synchronization was discussed. Finally, the motor imagery EEG data was classified by CNNs, and the accuracy was discussed based on the analysis results.

Result

For the young and elderly, ERD was observed in C3 and C4 channels, and their fatigue-sensitive channels in the parietal region were slightly different. During the experiment, the rhythm entropy of the frontal lobe showed a decreasing trend with time for most of the young subjects, while there was an increasing trend for most of the older ones. Using the CNN classification method, the elderly achieved around 70% of the average classification accuracy, which is almost the same for the young adults.

Conclusion

Compared with the young adults, the elderly are less affected by the level of cognitive fatigue during motor imagery, but the classification accuracy of motor imagery data in the elderly may be slightly lower than that in young persons. At the same time, the deep learning method also provides a potentially feasible option for the application of motor-imagery BCI (MI-BCI) in the elderly by considering the ERD and fatigue phenomenon together.

Spatiotemporal patterns of firearm acquisition in the United States in different presidential terms

This study develops mathematical tools and approaches to investigate spatiotemporal patterns of firearm acquisition in the U.S. complemented by hypothesis testing and statistical analysis. First, state-level and nation-level instant background check (BC) data are employed as proxy of firearm acquisition corresponding to 1999-2021. The relative-phase time-series of BC in each U.S. state is recovered and utilized to calculate the time-series of the U.S. states' synchronization degree. We reveal that U.S. states present a high-level degree of synchronization except in 2010-2011 and after 2018. Comparing these results with respect to a sitting U.S. president provides additional information: specifically, any two presidential terms are characterized by statistically different synchronization degrees except G. W. Bush's first term and B. H. Obama's second term. Next, to detail variations of BC, short-time Fourier transform, dimensionality reduction techniques, and diffusion maps are implemented within a time-frequency representation. Firearm acquisition in the high frequency band is described by a low-dimensional embedding, in the form of a plane with two embedding coordinates. Data points on the embedding plane identify separate clusters that signify state transitions in the original BC data with respect to different time windows. Through this analysis, we reveal that the frequency content of the BC data has a time-dependent characteristic. By comparing the diffusion map at hand with respect to a presidential term, we find that at least one of the embedding coordinates presents statistically significant variations between any two presidential terms except B. H. Obama's first term and D. J. Trump's pre-COVID term. The results point at a possible interplay between firearm acquisition in the U.S. and a presidential term.

Experimental investigation on the synchronization characteristics of a pitch-plunge aeroelastic system exhibiting stall flutter

This study focuses on characterizing the bifurcation scenario and the underlying synchrony behavior in a nonlinear aeroelastic system under deterministic as well as stochastic inflow conditions. Wind tunnel experiments are carried out for a canonical pitch-plunge aeroelastic system subjected to dynamic stall conditions. The system is observed to undergo a subcritical Hopf bifurcation, giving way to large-amplitude limit cycle oscillations (LCOs) in the stall flutter regime under the deterministic flow conditions. At this condition, we observe intermittent phase synchronization between pitch and plunge modes near the fold point, whereas synchronization via phase trapping is observed near the Hopf point. Repeating the experiments under stochastic inflow conditions, we observe two different aeroelastic responses: low amplitude noise-induced random oscillations (NIROs) and high-amplitude random LCOs (RLCOs) during stall flutter. The present study shows asynchrony between pitch and plunge modes in the NIRO regime. At the onset of RLCOs, asynchrony persists even though the relative phase distribution changes. With further increase in the flow velocity, we observe intermittent phase synchronization in the flutter regime. To the best of the authors' knowledge, this is the first study reporting the experimental evidence of phase synchronization between pitch and plunge modes of an aeroelastic system, which is of great interest to the nonlinear dynamics community. Furthermore, given the ubiquitous presence of stall behavior and stochasticity in a variety of engineering systems, such as wind turbine blades, helicopter blades, and unmanned aerial vehicles, the present findings will be directly beneficial for the efficient design of futuristic aeroelastic systems.

Causal Inference in Time Series in Terms of Rényi Transfer Entropy

Uncovering causal interdependencies from observational data is one of the great challenges of a nonlinear time series analysis. In this paper, we discuss this topic with the help of an information-theoretic concept known as Rényi’s information measure. In particular, we tackle the directional information flow between bivariate time series in terms of Rényi’s transfer entropy. We show that by choosing Rényi’s parameter α, we can appropriately control information that is transferred only between selected parts of the underlying distributions. This, in turn, is a particularly potent tool for quantifying causal interdependencies in time series, where the knowledge of “black swan” events, such as spikes or sudden jumps, are of key importance. In this connection, we first prove that for Gaussian variables, Granger causality and Rényi transfer entropy are entirely equivalent. Moreover, we also partially extend these results to heavy-tailed α-Gaussian variables. These results allow establishing a connection between autoregressive and Rényi entropy-based information-theoretic approaches to data-driven causal inference. To aid our intuition, we employed the Leonenko et al. entropy estimator and analyzed Rényi’s information flow between bivariate time series generated from two unidirectionally coupled Rössler systems. Notably, we find that Rényi’s transfer entropy not only allows us to detect a threshold of synchronization but it also provides non-trivial insight into the structure of a transient regime that exists between the region of chaotic correlations and synchronization threshold. In addition, from Rényi’s transfer entropy, we could reliably infer the direction of coupling and, hence, causality, only for coupling strengths smaller than the onset value of the transient regime, i.e., when two Rössler systems are coupled but have not yet entered synchronization.

Determining states of consciousness in the electroencephalogram based on spectral, complexity, and criticality features

This study was based on the contemporary proposal that distinct states of consciousness are quantifiable by neural complexity and critical dynamics. To test this hypothesis, it was aimed at comparing the electrophysiological correlates of three meditation conditions using nonlinear techniques from the complexity and criticality framework as well as power spectral density. Thirty participants highly proficient in meditation were measured with 64-channel electroencephalography (EEG) during one session consisting of a task-free baseline resting (eyes closed and eyes open), a reading condition, and three meditation conditions (thoughtless emptiness, presence monitoring, and focused attention). The data were analyzed applying analytical tools from criticality theory (detrended fluctuation analysis, neuronal avalanche analysis), complexity measures (multiscale entropy, Higuchi's fractal dimension), and power spectral density. Task conditions were contrasted, and effect sizes were compared. Partial least square regression and receiver operating characteristics analysis were applied to determine the discrimination accuracy of each measure. Compared to resting with eyes closed, the meditation categories emptiness and focused attention showed higher values of entropy and fractal dimension. Long-range temporal correlations were declined in all meditation conditions. The critical exponent yielded the lowest values for focused attention and reading. The highest discrimination accuracy was found for the gamma band (0.83-0.98), the global power spectral density (0.78-0.96), and the sample entropy (0.86-0.90). Electrophysiological correlates of distinct meditation states were identified and the relationship between nonlinear complexity, critical brain dynamics, and spectral features was determined. The meditation states could be discriminated with nonlinear measures and quantified by the degree of neuronal complexity, long-range temporal correlations, and power law distributions in neuronal avalanches.

Partial event coincidence analysis for distinguishing direct and indirect coupling in functional network construction

Correctly identifying interaction patterns from multivariate time series presents an important step in functional network construction. In this context, the widespread use of bivariate statistical association measures often results in a false identification of links because strong similarity between two time series can also emerge without the presence of a direct interaction due to intermediate mediators or common drivers. In order to properly distinguish such direct and indirect links for the special case of event-like data, we present here a new generalization of event coincidence analysis to a partial version thereof, which is aimed at excluding possible transitive effects of indirect couplings. Using coupled chaotic systems and stochastic processes on two generic coupling topologies (star and chain configuration), we demonstrate that the proposed methodology allows for the correct identification of indirect interactions. Subsequently, we apply our partial event coincidence analysis to multi-channel EEG recordings to investigate possible differences in coordinated alpha band activity among macroscopic brain regions in resting states with eyes open (EO) and closed (EC) conditions. Specifically, we find that direct connections typically correspond to close spatial neighbors while indirect ones often reflect longer-distance connections mediated via other brain regions. In the EC state, connections in the frontal parts of the brain are enhanced as compared to the EO state, while the opposite applies to the posterior regions. In general, our approach leads to a significant reduction in the number of indirect connections and thereby contributes to a better understanding of the alpha band desynchronization phenomenon in the EO state.

Learning Coupled Oscillators System with Reservoir Computing

In this paper, we reconstruct the dynamic behavior of the ring-coupled Lorenz oscillators system by reservoir computing. Although the reconstruction of various complex chaotic attractors has been well studied by using various neural networks, little attention has been paid to whether the spatio-temporal structure of some special attractors can be maintained in long-term prediction. Reservoir computing has been shown to be effective for model-free prediction, so we want to investigate whether reservoir computing can restore the rotational symmetry of the original ring-coupled Lorenz system. We find that although the state prediction of the trained reservoir computer will gradually deviate from the actual trajectory of the original system, the associated spatio-temporal structure is maintained in the process of reconstruction. Specifically, we show that the rotational symmetric structure of periodic rotating waves, quasi-periodic torus, and chaotic rotating waves is well maintained.

Asymptotically local synchronization in interdependent networks with unidirectional interlinks

Synchronization in complex networks has been investigated for decades. Due to the particularity of the interlinks between networks, the synchronization in interdependent networks has received increasing interest. Since the interlinks are not always symmetric in interdependent networks, we focus on the synchronization in unidirectional interdependent networks to study the control scheme. The mathematical model is put forward and some factors are taken into consideration, such as different coupling functions and strengths. Firstly, the feasibility of the control scheme is proved theoretically by using Lyapunov stability theory and verified by simulations. Then, we find that the synchronization could be maintained in one sub-network by utilizing our control scheme while the nodes in the other sub-network are in chaos. The result indicates that the influence of interlinks can be decreased and the proposed scheme can guarantee the synchronization in one sub-network at least. Moreover, we also discuss the robust of our control scheme against the cascading failure. The scheme is verified by simulations to be effective while the disturbances occur.

Phase-based causality analysis with partial mutual information from mixed embedding

Instantaneous phases extracted from multivariate time series can retain information about the relationships between the underlying mechanisms that generate the series. Although phases have been widely used in the study of nondirectional coupling and connectivity, they have not found similar appeal in the study of causality. Herein, we present a new method for phase-based causality analysis, which combines ideas from the mixed embedding technique and the information-theoretic approach to causality in coupled oscillatory systems. We then use the introduced method to investigate causality in simulated datasets of bivariate, unidirectionally paired systems from combinations of Rössler, Lorenz, van der Pol, and Mackey-Glass equations. We observe that causality analysis using the phases can capture the true causal relation for coupling strength smaller than the analysis based on the amplitudes can capture. On the other hand, the causality estimation based on the phases tends to have larger variability, which is attributed more to the phase extraction process than the actual phase-based causality method. In addition, an application on real electroencephalographic data from an experiment on elicited human emotional states reinforces the usefulness of phases in causality identification.

Sinusoidal and nonsinusoidal patterns in amplitude envelope synchronization

In this work, amplitude envelope synchronization (AES), as a general phenomenon characterized with highly correlated amplitude envelope but uncorrelated phases and frequencies in coupled nonidentical nonlinear systems, is investigated theoretically and numerically. Two different types of AES patterns, including sinusoidal and nonsinusoidal, are widely observable in coupled periodic and/or chaotic oscillators. They both come from modulation of phase mismatch on amplitude but show different patterns due to different behaviors of phase mismatch. With increase of frequency mismatch, the system tends to crossover from nonsinusoidal to sinusoidal AES. With the aid of synchronization manifold and transverse stability analyses of the AES state, the physical mechanism and scale relations for the AES are well revealed. We expect that all these results could uncover the generality of AES in coupled nonlinear oscillators and help to understand the rich dynamics of phase and amplitude coupling in multidisciplinary fields.

Phase and frequency linear response theory for hyperbolic chaotic oscillators

We formulate a linear phase and frequency response theory for hyperbolic flows, which generalizes phase response theory for autonomous limit cycle oscillators to hyperbolic chaotic dynamics. The theory is based on a shadowing conjecture, stating the existence of a perturbed trajectory shadowing every unperturbed trajectory on the system attractor for any small enough perturbation of arbitrary duration and a corresponding unique time isomorphism, which we identify as phase such that phase shifts between the unperturbed trajectory and its perturbed shadow are well defined. The phase sensitivity function is the solution of an adjoint linear equation and can be used to estimate the average change of phase velocity to small time dependent or independent perturbations. These changes in frequency are experimentally accessible, giving a convenient way to define and measure phase response curves for chaotic oscillators. The shadowing trajectory and the phase can be constructed explicitly in the tangent space of an unperturbed trajectory using co-variant Lyapunov vectors. It can also be used to identify the limits of the regime of linear response.

Phase irregularity: A conceptually simple and efficient approach to characterize electroencephalographic recordings from epilepsy patients

The severe neurological disorder epilepsy affects almost 1% of the world population. For patients who suffer from pharmacoresistant focal-onset epilepsy, electroencephalographic (EEG) recordings are essential for the localization of the brain area where seizures start. Apart from the visual inspection of the recordings, quantitative EEG signal analysis techniques proved to be useful for this purpose. Among other features, regularity versus irregularity and phase coherence versus phase independence allowed characterizing brain dynamics from the measured EEG signals. Can phase irregularities also characterize brain dynamics? To address this question, we use the univariate coefficient of phase velocity variation, defined as the ratio of phase velocity standard deviation and the mean phase velocity. Beyond that, as a bivariate measure we use the classical mean phase coherence to quantify the degree of phase locking. All phase-based measures are combined with surrogates to test null hypotheses about the dynamics underlying the signals. In the first part of our analysis, we use the Rössler model system to study our approach under controlled conditions. In the second part, we use the Bern-Barcelona EEG database which consists of focal and nonfocal signals extracted from seizure-free recordings. Focal signals are recorded from brain areas where the first seizure EEG signal changes can be detected, and nonfocal signals are recorded from areas that are not involved in the seizure at its onset. Our results show that focal signals have less phase variability and more phase coherence than nonfocal signals. Once combined with surrogates, the mean phase velocity proved to have the highest discriminative power between focal and nonfocal signals. In conclusion, conceptually simple and easy to compute phase-based measures can help to detect features induced by epilepsy from EEG signals. This holds not only for the classical mean phase coherence but even more so for univariate measures of phase irregularity.

Anticipating synchrony in dynamical systems using information theory

Synchronization in coupled dynamical systems has been a well-known phenomenon in the field of nonlinear dynamics for a long time. This phenomenon has been investigated extensively both analytically and experimentally. Although synchronization is observed in different areas of our real life, in some cases, this phenomenon is harmful; consequently, an early warning of synchronization becomes an unavoidable requirement. This paper focuses on this issue and proposes a reliable measure ( R), from the perspective of the information theory, to detect complete and generalized synchronizations early in the context of interacting oscillators. The proposed measure R is an explicit function of the joint entropy and mutual information of the coupled oscillators. The applicability of R to anticipate generalized and complete synchronizations is justified using numerical analysis of mathematical models and experimental data. Mathematical models involve the interaction of two low-dimensional, autonomous, chaotic oscillators and a network of coupled Rössler and van der Pol oscillators. The experimental data are generated from laboratory-scale turbulent thermoacoustic systems.

Topological synchronization of chaotic systems

A chaotic dynamics is typically characterized by the emergence of strange attractors with their fractal or multifractal structure. On the other hand, chaotic synchronization is a unique emergent self-organization phenomenon in nature. Classically, synchronization was characterized in terms of macroscopic parameters, such as the spectrum of Lyapunov exponents. Recently, however, we attempted a microscopic description of synchronization, called topological synchronization, and showed that chaotic synchronization is, in fact, a continuous process that starts in low-density areas of the attractor. Here we analyze the relation between the two emergent phenomena by shifting the descriptive level of topological synchronization to account for the multifractal nature of the visited attractors. Namely, we measure the generalized dimension of the system and monitor how it changes while increasing the coupling strength. We show that during the gradual process of topological adjustment in phase space, the multifractal structures of each strange attractor of the two coupled oscillators continuously converge, taking a similar form, until complete topological synchronization ensues. According to our results, chaotic synchronization has a specific trait in various systems, from continuous systems and discrete maps to high dimensional systems: synchronization initiates from the sparse areas of the attractor, and it creates what we termed as the 'zipper effect', a distinctive pattern in the multifractal structure of the system that reveals the microscopic buildup of the synchronization process. Topological synchronization offers, therefore, a more detailed microscopic description of chaotic synchronization and reveals new information about the process even in cases of high mismatch parameters.

Interictal epileptiform discharges in focal epilepsy are preceded by increase in low-frequency oscillations

OBJECTIVE

Interictal epileptiform discharges (IEDs) constitute a diagnostic signature of epilepsy. These events reflect epileptogenic hypersynchronization. Previous studies indicated that IEDs arise from slow neuronal activation accompanied by metabolic and hemodynamic changes. These might induce cortical inhibition followed hypersynchronization at IED onset. As cortical inhibition is mediated by low-frequency oscillations, we aimed to analyze the role of low-frequency oscillations prior the IED using magnetencephalography (MEG).

METHODS

Low-frequency (1-8 Hz) oscillations pre-IED ([-1000 milliseconds (ms), IED onset]) were analyzed using MEG in 14 focal epilepsy patients (median age = 23 years, range = 7-46 age). Occurrence of local pre-IED oscillations was analyzed using Beamformer Dynamical Imaging of Coherent Sources (DICS) and event-related desynchronization/synchronization (ERD-ERS) maps constructed using cluster-based permutation tests. The development of pre-IED oscillations was characterized using Hilbert transformation.

RESULTS

All patients exhibited statistically significant increase in delta (1-4 Hz) and/or theta (4-8 Hz) oscillations pre-IED compared to baseline [-2000 ms, -1000 ms]. Furthermore, all patients exhibited low-frequency power increase up to IED onset.

CONCLUSIONS

We demonstrated consistently occurring, low-frequency oscillations prior to IED onset.

SIGNIFICANCE

As low-frequency activity mediates cortical inhibition, our study demonstrates that a focal inhibition precedes hypersynchronization at IED onset.

Noninvasive inference methods for interaction and noise intensities of coupled oscillators using only spike time data

Identifying interactions is essential for understanding self-organized systems because they are a source of order, function, and complexity. However, distinguishing interaction and noise effect is generally difficult because they both critically affect the stability of an ordered state. We propose methods that enable us to simultaneously infer both interaction and noise intensities. Our methods use only the time series of periodic events such as spike time data and do not require any external stimuli. Moreover, it is not necessary to assume a function form to fit. We numerically demonstrate that our methods yield reasonable inference even for a relatively short time series. These features are particularly beneficial for application in biological and chemical complex systems.

Measurements of interaction intensity are generally achieved by observing responses to perturbations. In biological and chemical systems, external stimuli tend to deteriorate their inherent nature, and thus, it is necessary to develop noninvasive inference methods. In this paper, we propose theoretical methods to infer coupling strength and noise intensity simultaneously in two well-synchronized noisy oscillators through observations of spontaneously fluctuating events such as neural spikes. A phase oscillator model is applied to derive formulae relating each of the parameters to spike time statistics. Using these formulae, each parameter is inferred from a specific set of statistics. We verify these methods using the FitzHugh–Nagumo model as well as the phase model. Our methods do not require external perturbations and thus can be applied to various experimental systems.

Recurrence-Based Synchronization Analysis of Weakly Coupled Bursting Neurons Under External ELF Fields

We investigate the response characteristics of a two-dimensional neuron model exposed to an externally applied extremely low frequency (ELF) sinusoidal electric field and the synchronization of neurons weakly coupled with gap junction. We find, by numerical simulations, that neurons can exhibit different spiking patterns, which are well observed in the structure of the recurrence plot (RP). We further study the synchronization between weakly coupled neurons in chaotic regimes under the influence of a weak ELF electric field. In general, detecting the phases of chaotic spiky signals is not easy by using standard methods. Recurrence analysis provides a reliable tool for defining phases even for noncoherent regimes or spiky signals. Recurrence-based synchronization analysis reveals that, even in the range of weak coupling, phase synchronization of the coupled neurons occurs and, by adding an ELF electric field, this synchronization increases depending on the amplitude of the externally applied ELF electric field. We further suggest a novel measure for RP-based phase synchronization analysis, which better takes into account the probabilities of recurrences.

Phase synchronization and measure of criticality in a network of neural mass models

Synchronization has an important role in neural networks dynamics that is mostly accompanied by cognitive activities such as memory, learning, and perception. These activities arise from collective neural behaviors and are not totally understood yet. This paper aims to investigate a cortical model from this perspective. Historically, epilepsy has been regarded as a functional brain disorder associated with excessive synchronization of large neural populations. Epilepsy is believed to arise as a result of complex interactions between neural networks characterized by dynamic synchronization. In this paper, we investigated a network of neural populations in a way the dynamics of each node corresponded to the Jansen-Rit neural mass model. First, we study a one-column Jansen-Rit neural mass model for four different input levels. Then, we considered a Watts-Strogatz network of Jansen-Rit oscillators. We observed an epileptic activity in the weak input level. The network is considered to change various parameters. The detailed results including the mean time series, phase spaces, and power spectrum revealed a wide range of different behaviors such as epilepsy, healthy, and a transition between synchrony and asynchrony states. In some points of coupling coefficients, there is an abrupt change in the order parameters. Since the critical state is a dynamic candidate for healthy brains, we considered some measures of criticality and investigated them at these points. According to our study, some markers of criticality can occur at these points, while others may not. This occurrence is a result of the nature of the specific order parameter selected to observe these markers. In fact, The definition of a proper order parameter is key and must be defined properly. Our view is that the critical points exhibit clear characteristics and invariance of scale, instead of some types of markers. As a result, these phase transition points are not critical as they show no evidence of scaling invariance.

Analysis of respiratory kinematics: a method to characterize breaths from motion signals

Breathing motion (respiratory kinematics) can be characterized by the interval and depth of each breath, and by magnitude-synchrony relationships between locations. Such characteristics and their breath-by-breath variability might be useful indicators of respiratory health. To enable breath-by-breath characterization of respiratory kinematics, we developed a method to detect breaths using motion sensors. In 34 volunteers who underwent maximal exercise testing, we used 8 motion sensors to record upper rib, lower rib and abdominal kinematics at 3 exercise stages (rest, lactate threshold and exhaustion). We recorded volumetric air flow signals using clinical exercise laboratory equipment and synchronized them with kinematic signals. Using instantaneous phase landmarks from the analytic representation of kinematic and flow signals, we identified individual breaths and derived respiratory rate (RR) signals at 1Hz. To evaluate the fidelity of kinematics-derived RR, we calculated bias, limits of agreement, and cross-correlation coefficients (CCC) relative to flow-derived RR. To identify coupling between kinematics and flow, we calculated the Shannon entropy of the relative frequency with which flow landmarks were distributed over the phase of the kinematic cycle. We found good agreement in the kinematics-derived and flow-derived RR signals [bias (95% limit of agreement) = 0.1 (± 7) breaths/minute; CCC median (IQR) = 0.80 (0.48 - 0.91)]. In individual signals, kinematics and flow were well-coupled (entropy 0.9-1.4 across sensors), but the relationship varied within (by exercise stage) and between individuals. The final result was that the flow landmarks did not consistently localize to any particular phase of the kinematic signals (entropy 2.2-3.0 across sensors). The Analysis of Respiratory Kinematics method can yield highly resolved respiratory rate signals by separating individual breaths. This method will facilitate characterization of clinically significant breathing motion patterns on a breath-by-breath basis. The relationship between respiratory kinematics and flow is much more complex than expected, varying between and within individuals.

Intermingled attractors in an asymmetrically driven modified Chua oscillator

Understanding the asymptotic behavior of a dynamical system when system parameters are varied remains a key challenge in nonlinear dynamics. We explore the dynamics of a multistable dynamical system (the response) coupled unidirectionally to a chaotic drive. In the absence of coupling, the dynamics of the response system consists of simple attractors, namely, fixed points and periodic orbits, and there could be chaotic motion depending on system parameters. Importantly, the boundaries of the basins of attraction for these attractors are all smooth. When the drive is coupled to the response, the entire dynamics becomes chaotic: distinct multistable chaos and bistable chaos are observed. In both cases, we observe a mixture of synchronous and desynchronous states and a mixture of synchronous states only. The response system displays a much richer, complex dynamics. We describe and analyze the corresponding basins of attraction using the required criteria. Riddled and intermingled structures are revealed.

Wavelet-Based Biphase Analysis of Brain Rhythms in Automated Wake-Sleep Classification

Many studies in the field of sleep have focused on connectivity and coherence. Still, the nonstationary nature of electroencephalography (EEG) makes many of the previous methods unsuitable for automatic sleep detection. Time-frequency representations and high-order spectra are applied to nonstationary signal analysis and nonlinearity investigation, respectively. Therefore, combining wavelet and bispectrum, wavelet-based bi-phase (Wbiph) was proposed and used as a novel feature for sleep-wake classification. The results of the statistical analysis with emphasis on the importance of the gamma rhythm in sleep detection show that the Wbiph is more potent than coherence in the wake-sleep classification. The Wbiph has not been used in sleep studies before. However, the results and inherent advantages, such as the use of wavelet and bispectrum in its definition, suggest it as an excellent alternative to coherence. In the next part of this paper, a convolutional neural network (CNN) classifier was applied for the sleep-wake classification by Wbiph. The classification accuracy was 97.17% in nonLOSO and 95.48% in LOSO cross-validation, which is the best among previous studies on sleep-wake classification.

Optimizing phase variability threshold for automated synchrogram analysis of cardiorespiratory interactions in amateur cyclists

We propose a procedure suitable for automated synchrogram analysis for setting the threshold below which phase variability between two marker event series is of such a negligible amount that the null hypothesis of phase desynchronization can be rejected. The procedure exploits the principle of maximizing the likelihood of detecting phase synchronization epochs and it is grounded on a surrogate data approach testing the null hypothesis of phase uncoupling. The approach was applied to assess cardiorespiratory phase interactions between heartbeat and inspiratory onset in amateur cyclists before and after 11-week inspiratory muscle training (IMT) at different intensities and compared to a more traditional approach to set phase variability threshold. The proposed procedure was able to detect the decrease in cardiorespiratory phase locking strength during vagal withdrawal induced by the modification of posture from supine to standing. IMT had very limited effects on cardiorespiratory phase synchronization strength and this result held regardless of the training intensity. In amateur athletes training, the inspiratory muscles did not limit the decrease in cardiorespiratory phase synchronization observed in the upright position as a likely consequence of the modest impact of this respiratory exercise, regardless of its intensity, on cardiac vagal control. This article is part of the theme issue 'Advanced computation in cardiovascular physiology: new challenges and opportunities'.

Direction of information flow between brain regions in ADHD and healthy children based on EEG by using directed phase transfer entropy

Directed information flow between brain regions might be disrupted in children with Attention Deficit Hyperactivity Disorder (ADHD) which is related to the behavioral characteristics of ADHD. This paper aims to investigate the different information pathways of brain networks in children with ADHD in comparison with healthy subjects. EEG recordings were obtained from 61 children with ADHD and 60 healthy children without neurological disorders during attentional visual task. Effective connectivity among all scalp channels was calculated using directed phase transfer entropy (dPTE) for delta, theta, alpha, beta, and lower-gamma frequency bands. Group differences were evaluated using permutation tests in connectivity between regions. Significant posterior to anterior patterns of information flow in theta frequency bands were found in healthy subjects (p-value < 0.05), while disrupted pattern flow, in an opposite way, was found in ADHD children. In the beta band, information flow in pathways between anterior regions was significantly higher in healthy individuals than in the ADHD group. These differences are more indicated in connectivity that leads from frontal and central regions to the right frontal regions of the brain (F8 electrode). Furthermore, connections from central and lateral parietal areas to Pz electrode areas are statistically significant and higher in healthy children in this band. In the delta band, internal connections in the anterior region show a significant difference between the two groups, as this amount is higher in the ADHD group. Our analysis may provide new insights into information flow in brain regions of ADHD children in comparison with healthy children.

Connectivity Analysis for Multivariate Time Series: Correlation vs. Causality

The study of the interdependence relationships of the variables of an examined system is of great importance and remains a challenging task. There are two distinct cases of interdependence. In the first case, the variables evolve in synchrony, connections are undirected and the connectivity is examined based on symmetric measures, such as correlation. In the second case, a variable drives another one and they are connected with a causal relationship. Therefore, directed connections entail the determination of the interrelationships based on causality measures. The main open question that arises is the following: can symmetric correlation measures or directional causality measures be applied to infer the connectivity network of an examined system? Using simulations, we demonstrate the performance of different connectivity measures in case of contemporaneous or/and temporal dependencies. Results suggest the sensitivity of correlation measures when temporal dependencies exist in the data. On the other hand, causality measures do not spuriously indicate causal effects when data present only contemporaneous dependencies. Finally, the necessity of introducing effective instantaneous causality measures is highlighted since they are able to handle both contemporaneous and causal effects at the same time. Results based on instantaneous causality measures are promising; however, further investigation is required in order to achieve an overall satisfactory performance.

Sex Differences in Magnetoencephalography-Identified Functional Connectivity in the Human Connectome Project Connectomics of Brain Aging and Dementia Cohort

Introduction: The human brain shows modest traits of sexual dimorphism, with the female brain, on average, 10% smaller than the male brain. These differences do not imply a lowered cognitive performance, but suggest a more optimal brain organization in women. Here we evaluate the patterns of functional connectivity (FC) in women and men from the Connectomics of Brain Aging and Dementia sample. Methods: We used phase locking values to calculate FC from the magnetoencephalography time series in a sample of 138 old adults (87 females and 51 males). We compared the FC patterns between sexes, with the intention of detecting regions with different levels of connectivity. Results: We found a frontal cluster, involving anterior cingulate and the medial frontal lobe, where women showed higher FC values than men. Involved connections included the following: (1) medial parietal areas, such as posterior cingulate cortices and precunei; (2) right insula; and (3) medium cingulate and paracingulate cortices. Moreover, these differences persisted when considering only cognitively intact individuals, but not when considering only cognitively impaired individuals. Discussion: Increased anteroposterior FC has been identified as a biomarker for increased risk of developing cognitive impairment or dementia. In our study, cognitively intact women showed higher levels of FC than their male counterparts. This result suggests that neurodegenerative processes could be taking place in these women, but the changes are undetected by current diagnosis tools. FC, as measured here, might be valuable for early identification of this neurodegeneration.

The diagnosis of amnestic mild cognitive impairment by combining the characteristics of brain functional network and support vector machine classifier

BACKGROUND

Amnestic mild cognitive impairment (aMCI) is an essential stage of early detection and potential intervention for Alzheimer's disease (AD). Patients with aMCI exhibit partially abnormal functional brain connectivity and it is suggested that these features may represent a new diagnostic marker of early AD.

NEW METHOD

In this paper, we constructed two brain network models, a phase synchronization index (PSI) undirected network and a directed transfer function (DTF) directed network, to evaluate the cognitive function in patients with aMCI. We then built SVM classification models using the network clustering coefficient, global efficiency and average node degree as features to distinguish between aMCI patients and controls.

RESULTS

Our results reveal a classification accuracy and AUC of 66.6 ± 1.7% and 0.7475 and 80.0 ± 2.2% and 0.7825, respectively, for the two network models (PSI and DTF). As the directed network model performed better than the undirected model, we introduced an improved graph theory feature, efficiency density, which resulted in an increased classification accuracy and AUC value 86.6 ± 2.6% and 0.8295, respectively.

COMPARISON WITH EXISTING METHODS

The analysis of network models and the directionality of information flow is suitable for analysis of nonlinear EEG signals for assessment of the functional state of the brain. Compared with traditional network features, our proposed improved features more comprehensively evaluate transmission efficiency and density of the brain.

CONCLUSION

In this study, we demonstrate that an improved efficiency density feature is helpful for enhancing classification the accuracy of aMCI. Moreover, directed brain network models exhibit better classification for aMCI diagnosis than undirected networks.

Socio-Motor Improvisation in Schizophrenia: A Case-Control Study in a Sample of Stable Patients

Improvising is essential for human development and is one of the most important characteristics of being human. However, how mental illness affects improvisation remains largely unknown. In this study we focused on socio-motor improvisation in individuals with schizophrenia, one of the more debilitating mental disorder. This represents the ability to improvise gestures during an interaction to promote sustained communication and shared attention. Using a novel paradigm called the mirror game and recently introduced to study joint improvisation, we recorded hand motions of two people mirroring each other. Comparing Schizophrenia patients and healthy controls skills during the game, we found that improvisation was impaired in schizophrenia patients. Patients also exhibited significantly higher difficulties to being synchronized with someone they follow but not when they were leaders of the joint improvisation game. Considering the correlation between socio-motor synchronization and socio-motor improvisation, these results suggest that synchronization does not only promote affiliation but also improvisation, being therefore an interesting key factor to enhance social skills in a clinical context. Moreover, socio-motor improvisation abnormalities were not associated with executive functioning, one traditional underpinning of improvisation. Altogether, our results suggest that even if both mental illness and improvisation differ from normal thinking and behavior, they are not two sides of the same coin, providing a direct evidence that being able to improvise in individual situations is fundamentally different than being able to improvise in a social context.

Synchronization of a Network Composed of Stochastic Hindmarsh–Rose Neurons

An algorithm for synchronization of a network composed of interconnected Hindmarsh–Rose neurons is presented. Delays are present in the interconnections of the neurons. Noise is added to the controlled input of the neurons. The synchronization algorithm is designed using convex optimization and is formulated by means of linear matrix inequalities via the stochastic version of the Razumikhin functional. The recovery and the adaptation variables are also synchronized; this is demonstrated with the help of the minimum-phase property of the Hindmarsh–Rose neuron. The results are illustrated by an example.

Functional Connectivity Analysis in Motor-Imagery Brain Computer Interfaces

Motor Imagery BCI systems have a high rate of users that are not capable of modulating their brain activity accurately enough to communicate with the system. Several studies have identified psychological, cognitive, and neurophysiological measures that might explain this MI-BCI inefficiency. Traditional research had focused on mu suppression in the sensorimotor area in order to classify imagery, but this does not reflect the true dynamics that underlie motor imagery. Functional connectivity reflects the interaction between brain regions during the MI task and resting-state network and is a promising tool in improving MI-BCI classification. In this study, 54 novice MI-BCI users were split into two groups based on their accuracy and their functional connectivity was compared in three network scales (Global, Large and Local scale) during the resting-state, left vs. right-hand motor imagery task, and the transition between the two phases. Our comparison of High and Low BCI performers showed that in the alpha band, functional connectivity in the right hemisphere was increased in High compared to Low aptitude MI-BCI users during motor imagery. These findings contribute to the existing literature that indeed connectivity might be a valuable feature in MI-BCI classification and in solving the MI-BCI inefficiency problem.

Phase tipping: how cyclic ecosystems respond to contemporary climate

We identify the phase of a cycle as a new critical factor for tipping points (critical transitions) in cyclic systems subject to time-varying external conditions. As an example, we consider how contemporary climate variability induces tipping from a predator–prey cycle to extinction in two paradigmatic predator–prey models with an Allee effect. Our analysis of these examples uncovers a counterintuitive behaviour, which we call phase tipping or P-tipping, where tipping to extinction occurs only from certain phases of the cycle. To explain this behaviour, we combine global dynamics with set theory and introduce the concept of partial basin instability for attracting limit cycles. This concept provides a general framework to analyse and identify easily testable criteria for the occurrence of phase tipping in externally forced systems, and can be extended to more complicated attractors.

Technical aspects of cardiorespiratory estimation using subspace projections and cross entropy

BACKGROUND

Respiratory sinus arrhythmia (RSA) is a form of cardiorespiratory coupling. Its quantification has been suggested as a biomarker to diagnose different diseases. Two state-of-the-art methods, based on subspace projections and entropy, are used to estimate the RSA strength and are evaluated in this paper. Their computation requires the selection of a model order, and their performance is strongly related to the temporal and spectral characteristics of the cardiorespiratory signals.

OBJECTIVE

To evaluate the robustness of the RSA estimates to the selection of model order, delays, changes of phase and irregular heartbeats as well as to give recommendations for their interpretation on each case.

APPROACH

Simulations were used to evaluate the model order selection when calculating the RSA estimates explained before, as well as 3 different scenarios that can occur in signals acquired in non-controlled environments and/or from patient populations: the presence of irregular heartbeats; the occurrence of delays between heart rate variability (HRV) and respiratory signals; and the changes over time of the phase between HRV and respiratory signals.

MAIN RESULTS

It was found that using a single model order for all the calculations suffices to characterize the RSA estimates correctly. In addition, the RSA estimation in signals containing more than 5 irregular heartbeats in a period of 5 minutes might be misleading. Regarding the delays between HRV and respiratory signals, both estimates are robust. For the last scenario, the two approaches tolerate phase changes up to 54°, as long as this lasts less than one fifth of the recording duration.

SIGNIFICANCE

Guidelines are given to compute the RSA estimates in non-controlled environments and patient populations.

Measuring Synchronization between Spikes and Local Field Potential Based on the Kullback-Leibler Divergence

Neurophysiological studies have shown that there is a close relationship between spikes and local field potential (LFP), which reflects crucial neural coding information. In this paper, we used a new method to evaluate the synchronization between spikes and LFP. All possible phases of LFP from −π to π were first binned into a freely chosen number of bins; then, the probability of spikes falling in each bin was calculated, and the deviation degree from the uniform distribution based on the Kullback–Leibler divergence was calculated to define the synchronization between spikes and LFP. The simulation results demonstrate that the method is rapid, basically unaffected by the total number of spikes, and can adequately resist the noise of spike trains. We applied this method to the experimental data of patients with intractable epilepsy, and we observed the synchronization between spikes and LFP in the formation of memory. These results show that our proposed method is a powerful tool that can quantitatively measure the synchronization between spikes and LFP.

Connectivity of EEG synchronization networks increases for Parkinson's disease patients with freezing of gait

Freezing of gait (FoG), a paroxysmal gait disturbance commonly experienced by patients with Parkinson's disease (PD), is characterized by sudden episodes of inability to generate effective forward stepping. Recent studies have shown an increase in beta frequency of local-field potentials in the basal-ganglia during FoG, however, comprehensive research on the synchronization between different brain locations and frequency bands in PD patients is scarce. Here, by developing tools based on network science and non-linear dynamics, we analyze synchronization networks of electroencephalography (EEG) brain waves of three PD patient groups with different FoG severity. We find higher EEG amplitude synchronization (stronger network links) between different brain locations as PD and FoG severity increase. These results are consistent across frequency bands (theta, alpha, beta, gamma) and independent of the specific motor task (walking, still standing, hand tapping) suggesting that an increase in severity of PD and FoG is associated with stronger EEG networks over a broad range of brain frequencies. This observation of a direct relationship of PD/FoG severity with overall EEG synchronization together with our proposed EEG synchronization network approach may be used for evaluating FoG propensity and help to gain further insight into PD and the pathophysiology leading to FoG.

Reconstruction of Pulse Wave and Respiration from Wrist Accelerometer During Sleep

OBJECTIVE

Nocturnal recordings of heart rate and respiratory rate usually require several separate sensors or electrodes attached to different body parts -- a disadvantage for at-home screening tests and for large cohort studies. In this paper, we demonstrate that a state-of-the-art accelerometer placed at subjects' wrists can be used to derive reliable signal reconstructions of heartbeat (pulse wave intervals) and respiration during sleep.

METHODS

Based on 226 full-night recordings, we evaluate the performance of our signal reconstruction methodology with respect to polysomnography. We use a phase synchronization analysis metrics that considers individual heartbeats or breaths.

RESULTS

The quantitative comparison reveals that pulse-wave signal reconstructions are generally better than respiratory signal reconstructions. The best quality is achieved during deep sleep, followed by light sleep N2 and REM sleep. In addition, a suggested internal evaluation of multiple derived reconstructions can be used to identify time periods with highly reliable signals, particularly for pulse waves. Furthermore, we find that pulse-wave reconstructions are hardly affected by apnea and hypopnea events.

CONCLUSION

During sleep, pulse wave and respiration signals can simultaneously be reconstructed from the same accelerometer recording at the wrist without the need for additional sensors. Reliability can be increased by internal evaluation if the reconstructed signals are not needed for the whole sleep duration.

SIGNIFICANCE

The presented methodology can help to determine sleep characteristics and improve diagnostics and treatment of sleep disorders in the subjects' normal sleep environment.

Binary mixtures of locally coupled mobile oscillators

Synchronized behavior in a system of coupled dynamic objects is a fascinating example of an emerged cooperative phenomena which has been observed in systems as diverse as a group of insects, neural networks, or networks of computers. In many instances, however, the synchronization is undesired because it may lead to system malfunctioning, as in the case of Alzheimer's and Parkinson's diseases, for example. Recent studies of static networks of oscillators have shown that the presence of a small fraction of so-called contrarian oscillators can suppress the undesired network synchronization. On the other hand, it is also known that the mobility of the oscillators can significantly impact their synchronization dynamics. Here, we combine these two ideas-the oscillator mobility and the presence of heterogeneous interactions-and study numerically binary mixtures of phase oscillators performing two-dimensional random walks. Within the framework of a generalized Kuramoto model, we introduce two phase-coupling schemes. The first one is invariant when the types of any two oscillators are swapped, while the second model is not. We demonstrate that the symmetric model does not allow for a complete suppression of the synchronized state. However, it provides means for a robust control of the synchronization timescale by varying the overall number density and the composition of the mixture and the strength of the off-diagonal Kuramoto coupling constant. Instead, the asymmetric model predicts that the coherent state can be eliminated within a subpopulation of normal oscillators and evoked within a subpopulation of the contrarians.

Measuring Phase-Amplitude Coupling Based on the Jensen-Shannon Divergence and Correlation Matrix

Phase-amplitude coupling (PAC) measures the relationship between the phase of low-frequency oscillations (LFO) and the amplitude of high-frequency oscillations (HFO). It plays an important functional role in neural information processing and cognition. Thus, we propose a novel method based on the Jensen-Shannon (JS) divergence and correlation matrix. The method takes the amplitude distributions of the HFO located in the corresponding phase bins of the LFO as multichannel inputs to construct a correlation matrix, where the elements are calculated based on the JS divergence between pairs of amplitude distributions. Then, the omega complexity extracted from the correlation matrix is used to estimate the PAC strength. The simulation results demonstrate that the proposed method can effectively reflect the PAC strength and slightly vary with the data length. Moreover, it outperforms five frequently used algorithms in the performance against additive white Gaussian noise and spike noise and the ability of detecting PAC in wide frequency ranges. To validate our proposed method with real data, it was applied to analyze the local field potential recorded from the dorsomedial striatum in a male Sprague-Dawley rat. It can replicate previous results obtained with other PAC metrics. In conclusion, these results suggest that our proposed method is a powerful tool for measuring the PAC between neural oscillations.

Viewing Ambiguous Social Interactions Increases Functional Connectivity between Frontal and Temporal Nodes of the Social Brain

Social behavior is coordinated by a network of brain regions, including those involved in the perception of social stimuli and those involved in complex functions, such as inferring perceptual and mental states and controlling social interactions. The properties and function of many of these regions in isolation are relatively well understood, but less is known about how these regions interact while processing dynamic social interactions. To investigate whether the functional connectivity between brain regions is modulated by social context, we collected fMRI data from male monkeys (Macaca mulatta) viewing videos of social interactions labeled as "affiliative," "aggressive," or "ambiguous." We show activation related to the perception of social interactions along both banks of the superior temporal sulcus, parietal cortex, medial and lateral frontal cortex, and the caudate nucleus. Within this network, we show that fronto-temporal functional connectivity is significantly modulated by social context. Crucially, we link the observation of specific behaviors to changes in functional connectivity within our network. Viewing aggressive behavior was associated with a limited increase in temporo-temporal and a weak increase in cingulate-temporal connectivity. By contrast, viewing interactions where the outcome was uncertain was associated with a pronounced increase in temporo-temporal, and cingulate-temporal functional connectivity. We hypothesize that this widespread network synchronization occurs when cingulate and temporal areas coordinate their activity when more difficult social inferences are being made.SIGNIFICANCE STATEMENT Processing social information from our environment requires the activation of several brain regions, which are concentrated within the frontal and temporal lobes. However, little is known about how these areas interact to facilitate the processing of different social interactions. Here we show that functional connectivity within and between the frontal and temporal lobes is modulated by social context. Specifically, we demonstrate that viewing social interactions where the outcome was unclear is associated with increased synchrony within and between the cingulate cortex and temporal cortices. These findings suggest that the coordination between the cingulate and temporal cortices is enhanced when more difficult social inferences are being made.

The organization of functional neurocognitive networks in focal epilepsy correlates with domain-specific cognitive performance

Understanding and diagnosing cognitive impairment in epilepsy remains a prominent challenge. New etiological models suggest that cognitive difficulties might not be directly linked to seizure activity, but are rather a manifestation of a broader brain pathology. Consequently, treating seizures is not sufficient to alleviate cognitive symptoms, highlighting the need for novel diagnostic tools. Here, we investigated whether the organization of three intrinsic, resting-state functional connectivity networks was correlated with domain-specific cognitive test performance. Using individualized EEG source reconstruction and graph theory, we examined the association between network small worldness and cognitive test performance in 23 patients with focal epilepsy and 17 healthy controls, who underwent a series of standardized pencil-and-paper and digital cognitive tests. We observed that the specific networks robustly correlated with test performance in distinct cognitive domains. Specifically, correlations were evident between the default mode network and memory in patients, the central-executive network and executive functioning in controls, and the salience network and social cognition in both groups. Interestingly, the correlations were evident in both groups, but in different domains, suggesting an alteration in these functional neurocognitive networks in focal epilepsy. The present findings highlight the potential clinical relevance of functional brain network dysfunction in cognitive impairment.

Dynamics in two interacting subpopulations of nonidentical phase oscillators

Chimera states refer to the dynamical states in which the inherent symmetry of the system is broken. The system composed of two interacting identical subpopulations of phase oscillators provides a platform to study chimera states. In this system, different types of chimera states have been identified and the transitions between them have been investigated. However, the parameter space is not fully explored in this system. In this work, we study a system comprised of two interacting subpopulations of nonidentical phase oscillators. Through numerical simulations and theoretical analyses, we find three symmetry-reserving states, including incoherent state, in-phase synchronous state, and antiphase synchronous state, and three types of symmetry-breaking states, including in-phase chimera states, antiphase chimera states, and weak chimera states. The stability diagrams of these dynamical states are explored on different parameter planes and transition scenarios amongst these states are investigated. We find that the weak chimera states act as the bridge between in-phase and antiphase chimera states. We also observe the existence of a period-two chimera state, chaotic chimera state, and drifting chimera states.

Phase/Amplitude Synchronization of Brain Signals During Motor Imagery BCI Tasks

In the last decade, functional connectivity (FC) has been increasingly adopted based on its ability to capture statistical dependencies between multivariate brain signals. However, the role of FC in the context of brain-computer interface applications is still poorly understood. To address this gap in knowledge, we considered a group of 20 healthy subjects during an EEG-based hand motor imagery (MI) task. We studied two well-established FC estimators, i.e. spectral- and imaginary-coherence, and we investigated how they were modulated by the MI task. We characterized the resulting FC networks by extracting the strength of connectivity of each EEG sensor and we compared the discriminant power with respect to standard power spectrum features. At the group level, results showed that while spectral-coherence based network features were increasing in the sensorimotor areas, those based on imaginary-coherence were significantly decreasing. We demonstrated that this opposite, but complementary, behavior was respectively determined by the increase in amplitude and phase synchronization between the brain signals. At the individual level, we eventually assessed the potential of these network connectivity features in a simple off-line classification scenario. Taken together, our results provide fresh insights into the oscillatory mechanisms subserving brain network changes during MI and offer new perspectives to improve BCI performance.