Phase synchronization of chaotic oscillators

Effects of Gastrin-releasing Peptide on Hippocampal Neural Networks in Vascular Dementia Rats

Gastrin-releasing peptide (GRP) has been confirmed to exhibit a variety of physiological functions in the brain and play a role in many neurological diseases. Our previous research found that GRP could restore the impaired synaptic plasticity and the spatial learning and memory impairments induced by vascular dementia (VD). However, the specific mechanisms of GRP affecting hippocampus, especially the effects on the neuronal oscillations were still poorly understood. In this study, we examined the effects of GRP on the changes of the interactions between theta and gamma oscillations in the hippocampal CA3-CA1 pathway of VD rats and explored the potential electrophysiological mechanism. To this purpose, local field potentials (LFPs) simultaneously collected from hippocampal CA3 and CA1 were measured by the power spectrum, phase synchronization, phase-phase coupling (PPC) and phase-amplitude coupling (PAC). We found that GRP substantially restored the phase synchronization of the theta and gamma oscillations. The GRP also significantly improved the strength of theta-gamma cross-frequency coupling (including theta-gamma PPC and theta-gamma PAC) in the CA3-CA1 network. The results indicated that GRP could alleviate the changes of neural activities in hippocampal CA3-CA1 pathway induced by VD. This might be an electrophysiological mechanism for GRP preventing cognitive impairments induced by VD.

Linear and Nonlinear EEG-Based Functional Networks in Anxiety Disorders

Electrocortical network dynamics are integral to brain function. Linear and nonlinear connectivity applications enrich neurophysiological investigations into anxiety disorders. Discrete EEG-based connectivity networks are unfolding with some homogeneity for anxiety disorder subtypes. Attenuated delta/theta/beta connectivity networks, pertaining to anterior-posterior nodes, characterize panic disorder. Nonlinear measures suggest reduced connectivity of ACC as an executive neuro-regulator in germane "fear circuitry networks" might be more central than considered. Enhanced network complexity and theta network efficiency at rest define generalized anxiety disorder, with similar tonic hyperexcitability apparent in social anxiety disorder further extending to task-related/state functioning. Dysregulated alpha connectivity and integration of mPFC-ACC/mPFC-PCC relays implicated with attentional flexibility and choice execution/congruence neurocircuitry are observed in trait anxiety. Conversely, state anxiety appears to recruit converging delta and beta connectivity networks as panic, suggesting trait and state anxiety are modulated by discrete neurobiological mechanisms. Furthermore, EEG connectivity dynamics distinguish anxiety from depression, despite prevalent clinical comorbidity. Rethinking mechanisms implicated in the etiology, maintenance, and treatment of anxiety from the perspective of EEG network science across micro- and macroscales serves to shed light and move the field forward.

A practical method for estimating coupling functions in complex dynamical systems

A foremost challenge in modern network science is the inverse problem of reconstruction (inference) of coupling equations and network topology from the measurements of the network dynamics. Of particular interest are the methods that can operate on real (empirical) data without interfering with the system. One such earlier attempt (Tokuda et al. 2007 Phys. Rev. Lett. 99, 064101. (doi:10.1103/PhysRevLett.99.064101)) was a method suited for general limit-cycle oscillators, yielding both oscillators' natural frequencies and coupling functions between them (phase equations) from empirically measured time series. The present paper reviews the above method in a way comprehensive to domain-scientists other than physics. It also presents applications of the method to (i) detection of the network connectivity, (ii) inference of the phase sensitivity function, (iii) approximation of the interaction among phase-coherent chaotic oscillators, and (iv) experimental data from a forced Van der Pol electric circuit. This reaffirms the range of applicability of the method for reconstructing coupling functions and makes it accessible to a much wider scientific community. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'.

A Brief Introduction to Nonlinear Time Series Analysis and Recurrence Plots

Nonlinear time series analysis gained prominence from the late 1980s on, primarily because of its ability to characterize, analyze, and predict nontrivial features in data sets that stem from a wide range of fields such as finance, music, human physiology, cognitive science, astrophysics, climate, and engineering. More recently, recurrence plots, initially proposed as a visual tool for the analysis of complex systems, have proven to be a powerful framework to quantify and reveal nontrivial dynamical features in time series data. This tutorial review provides a brief introduction to the fundamentals of nonlinear time series analysis, before discussing in greater detail a few (out of the many existing) approaches of recurrence plot-based analysis of time series. In particular, it focusses on recurrence plot-based measures which characterize dynamical features such as determinism, synchronization, and regime changes. The concept of surrogate-based hypothesis testing, which is crucial to drawing any inference from data analyses, is also discussed. Finally, the presented recurrence plot approaches are applied to two climatic indices related to the equatorial and North Pacific regions, and their dynamical behavior and their interrelations are investigated.

Synchronous patterns and intermittency in a network induced by the rewiring of connections and coupling

The connection architecture plays an important role in the synchronization of networks, where the presence of local and nonlocal connection structures are found in many systems, such as the neural ones. Here, we consider a network composed of chaotic bursting oscillators coupled through a Watts-Strogatz-small-world topology. The influence of coupling strength and rewiring of connections is studied when the network topology is varied from regular to small-world to random. In this scenario, we show two distinct nonstationary transitions to phase synchronization: one induced by the increase in coupling strength and another resulting from the change from local connections to nonlocal ones. Besides this, there are regions in the parameter space where the network depicts a coexistence of different bursting frequencies where nonstationary zig-zag fronts are observed. Regarding the analyses, we consider two distinct methodological approaches: one based on the phase association to the bursting activity where the Kuramoto order parameter is used and another based on recurrence quantification analysis where just a time series of the network mean field is required.

Emotional Transfer in Human-Horse Interaction: New Perspectives on Equine Assisted Interventions

Equine assisted interventions (EAIs) include all therapeutic interventions aimed at improving human wellbeing through the involvement of horses. Due to the prominent emotional involvement traditionally characterizing their relation with humans, horses developed sophisticated communicative skills, which fostered their ability to respond to human emotional states. In this review, we hypothesize that the proximate causation of successful interventions could be human-animal mutual coordination, through which the subjects bodily and, most importantly, emotionally come into contact. We propose that detecting emotions of other individuals and developing the capacity to fine-tune one's own emotional states accordingly (emotional transfer mechanism), could represent the key engine triggering the positive effects of EAIs. We provide a comprehensive analysis of horses' socio-emotional competences according to recent literature and we propose a multidisciplinary approach to investigate this inter-specific match. By considering human and horse as a unique coupling system during the interaction, it would be possible to objectively measure the degree of coordination through the analysis of physiological variables of both human and animal. Merging the state of art on human-horse relationship with the application of novel methodologies, could help to improve standardized protocols for animal assisted interventions, with particular regard to the emotional states of subjects involved.

Cluster Synchronization for Neutral Stochastic Delay Networks via Intermittent Adaptive Control

This paper studies the problem of cluster synchronization at exponential rates in both the mean square and almost sure senses for neutral stochastic coupled neural networks with time-varying delay via a periodically intermittent pinning adaptive control strategy. The network topology can be symmetric or asymmetric, with each network node being described by neutral stochastic delayed neural networks. When considering the exponential stabilization in the mean square sense for neutral stochastic delay system, the delay integral inequality approach is used to circumvent the obstacle arising from the coexistence of random disturbance, neutral item, and time-varying delay. The almost surely exponential stabilization is also analyzed with the nonnegative semimartingale convergence theorem. Sufficient criteria on cluster synchronization at exponential rates in both the mean square and almost sure senses of the underlying networks under the designed control scheme are derived. The effectiveness of the obtained theoretical results is illustrated by two examples.

Sources of intraspecific variation in the collective tempo and synchrony of ant societies

Populations of independently oscillating agents can sometimes synchronize. In the context of animal societies, conspicuous synchronization of activity is known in some social insects. However, the causes of variation in synchrony within and between species have received little attention. We repeatedly assessed the short-term activity cycle of ant colonies (Temnothorax rugatulus) and monitored the movements of individual workers and queens within nests. We detected persistent differences between colonies in the waveform properties of their collective activity oscillations, with some colonies consistently oscillating much more erratically than others. We further demonstrate that colony crowding reduces the rhythmicity (i.e., the consistent timing) of oscillations. Workers in both erratic and rhythmic colonies spend less time active than completely isolated workers, but workers in erratic colonies oscillate out of phase with one another. We further show that the queen's absence can impair the ability of colonies to synchronize worker activity and that behavioral differences between queens are linked with the waveform properties of their societies.

Chaotic synchronization of two optical cavity modes in optomechanical systems

The synchronization of the motion of microresonators has attracted considerable attention. In previous studies, the microresonators for synchronization were studied mostly in the linear regime. While the important problem of synchronizing nonlinear microresonators was rarely explored. Here we present theoretical methods to synchronize the motions of chaotic optical cavity modes in an optomechanical system, where one of the optical modes is strongly driven into chaotic motion and transfers chaos to other weakly driven optical modes via a common mechanical resonator. This mechanical mode works as a common force acting on each optical mode, which, thus, enables the synchronization of states. We find that complete synchronization can be achieved in two identical chaotic cavity modes. For two arbitrary nonidentical chaotic cavity modes, phase synchronization can also be achieved in the strong-coupling small-detuning regime.

Mechanism for explosive synchronization of neural networks

Here we investigate the mechanism for explosive synchronization (ES) of a complex neural network composed of nonidentical neurons and coupled by Newman-Watts small-world matrices. We find a range of nonlocal connection probabilities for which the network displays an abrupt transition to phase synchronization, characterizing ES. The mechanism behind the ES is the following: As the coupling parameter is varied in a network of distinct neurons, ES is likely to occur due to a bistable regime, namely a chaotic nonsynchronized and a regular phase-synchronized state in the phase space. In this case, even small coupling changes make possible a transition between them. The onset of ES occurs via a saddle-node bifurcation of a periodic orbit that leads the network dynamics to display a locally stable phase-synchronized state. The presence of this regime is accompanied by a hysteresis loop on the network dynamics as the coupling parameter is adiabatically increased and decreased. The end of the hysteresis loop is marked by a frontier crisis of the chaotic attractor which also determines the end of the coupling strength interval where ES is possible.

EMD-Based, Mean-Phase Coherence Analysis to Assess Instantaneous Phase-Synchrony Dynamics in Epilepsy Patients

In this paper, an adaptive, non-linear, analytical methodology is proposed in order to quantitatively evaluate the instantaneous phase-synchrony dynamics in epilepsy patients. A group of finite neuronal oscillators is extracted from a multichannel electrocorticographic (ECoG) data, using the empirical mode decomposition (EMD). The instantaneous phases of the extracted oscillators are measured using the Hilbert transform in order to be utilized in the mean-phase coherence analysis. Finally, the dynamical evolution of phase-synchrony among the extracted neuronal oscillators within 1-600 Hz frequency range is assessed using eigenvalue decomposition. A different phasesynchrony dynamics was observed in two patients with frontal vs. temporal lobe epilepsy, as their seizures evolve. However, experimental results demonstrated a hypersynchrony level at seizure offset for both types of epilepsy during the ictal periods. This result suggests that hypersynchronization of the epileptic network may be a crucial, self-regulatory mechanism by which the brain terminate seizures.

Brain Functional Connectivity Through Phase Coupling of Neuronal Oscillations: A Perspective From Magnetoencephalography

Magnetoencephalography has gained an increasing importance in systems neuroscience thanks to the possibility it offers of unraveling brain networks at time-scales relevant to behavior, i.e., frequencies in the 1-100 Hz range, with sufficient spatial resolution. In the first part of this review, we describe, in a unified mathematical framework, a large set of metrics used to estimate MEG functional connectivity at the same or at different frequencies. The different metrics are presented according to their characteristics: same-frequency or cross-frequency, univariate or multivariate, directed or undirected. We focus on phase coupling metrics given that phase coupling of neuronal oscillations is a putative mechanism for inter-areal communication, and that MEG is an ideal tool to non-invasively detect such coupling. In the second part of this review, we present examples of the use of specific phase methods on real MEG data in the context of resting state, visuospatial attention and working memory. Overall, the results of the studies provide evidence for frequency specific and/or cross-frequency brain circuits which partially overlap with brain networks as identified by hemodynamic-based imaging techniques, such as functional Magnetic Resonance (fMRI). Additionally, the relation of these functional brain circuits to anatomy and to behavior highlights the usefulness of MEG phase coupling in systems neuroscience studies. In conclusion, we believe that the field of MEG functional connectivity has made substantial steps forward in the recent years and is now ready for bringing the study of brain networks to a more mechanistic understanding.

Causal stability and synchronization

Synchronization of chaos arises between coupled dynamical systems and is very well understood as a temporal phenomenon, which leads the coupled systems to converge or develop a dependence with time. In this work, we provide a complementary spatial perspective to this phenomenon by introducing the novel idea of causal stability. We then propose and prove a causal stability synchronization theorem as a necessary and sufficient condition for complete synchronization. We also provide an empirical criterion to identify synchronizing variables in coupled identical chaotic dynamical systems based on intrasystem causal influences estimated using time series data of the driving system alone. For this, a recently proposed measure, Compression-Complexity Causality (CCC), is used. The sign and magnitude of the estimated CCC value capture the nature of dynamical influences from each variable to rest of the subsystem and are thus able to determine whether or not the variable, when used to couple another system, will drive that system to synchronization.

Using wavelet analysis to investigate synchronization

Wavelet analysis is shown to be a more robust technique than previously used methods in the investigation of synchronization. The highlight of the technique is that it encompasses most of the information obtained by conventional methods into a single picture, while giving a deeper insight into the dynamics of the system. Order parameters derived from continuous wavelet transform coefficients are proposed, which can be used in the quantification of measure synchronization in Hamiltonian systems and identical synchronization in dissipative systems, irrespective of the nature of coupling, the nature of synchronization (complete or partial, quasiperiodic or chaotic), and the number of coupled subsystems.

Coupling Between Leg Muscle Activation and EEG During Normal Walking, Intentional Stops, and Freezing of Gait in Parkinson's Disease

In this paper, we apply novel techniques for characterizing leg muscle activation patterns via electromyograms (EMGs) and for relating them to changes in electroencephalogram (EEG) activity during gait experiments. Specifically, we investigate changes of leg-muscle EMG amplitudes and EMG frequencies during walking, intentional stops, and unintended freezing-of-gait (FOG) episodes. FOG is a frequent paroxysmal gait disturbance occurring in many patients suffering from Parkinson's disease (PD). We find that EMG amplitudes and frequencies do not change significantly during FOG episodes with respect to walking, while drastic changes occur during intentional stops. Phase synchronization between EMG signals is most pronounced during walking in controls and reduced in PD patients. By analyzing cross-correlations between changes in EMG patterns and brain-wave amplitudes (from EEGs), we find an increase in EEG-EMG coupling at the beginning of stop and FOG episodes. Our results may help to better understand the enigmatic pathophysiology of FOG, to differentiate between FOG events and other gait disturbances, and ultimately to improve diagnostic procedures for patients suffering from PD.

Emergence of oscillatory coexistence with exponentially decayed waiting times in a coupled cyclic competition system

Interpatch migration between two environments is generally considered as a spatial concept and can affect species biodiversity in each patch by inducing flux of population such as inflow and outflow quantities of species. In this paper, we explore the effect of interpatch migration, which can be generally considered as a spatial concept and may affect species biodiversity between two different patches in the perspective of the macroscopic level by exploiting the coupling of two systems, where each patch is occupied by cyclically competing three species who can stably coexist by exhibiting periodic orbits. For two simple scenarios of interpatch migration either single or all species migration, we found that two systems with independently stable coexisting species in each patch are eventually synchronized, and oscillatory behaviors of species densities in two patches become identical, i.e., the synchronized coexistence emerges. In addition, we find that, whether single or all species interpatch migration occurs, the waiting time for the synchronization is exponentially decreasing as the coupling strength is intensified. Our findings suggest that the synchronized behavior of species as a result of migration between different patches can be easily predicted by the coupling of systems and additional information such as waiting times and sensitivity of initial densities.

Influence of Time Delay in Signal Transmission on Synchronization between Two Coupled FitzHugh-Nagumo Neurons

In this paper, the energy method is employed to analytically investigate the influence of time delay in signal transmission on synchronization between two coupled FitzHugh-Nagumo (FHN) neurons. Unlike pre-existing methods that deal with synchronization problems, our major idea is to consider the change rate of the energy of the synchronization error system, since the original system’s synchronization is equivalent to the disappearance of the energy of the error system. In rewriting the original coupled system in the corresponding energy coordinates based on the energy method, we find that the change rate of energy of the error system can be divided into two parts (periodic and non-periodic). The synchronization criterion for the original system can then be obtained by letting the non-periodic part of the change rate of the energy be less than zero. The correctness of the analysis is illustrated with numerical simulations. Our analytical results show that time delay in signal transmission has very significant effects on the synchronization between two FHN neurons. If the time delay in signal transmission is not taken into account in the two coupled FHN neurons, synchronous spikes cannot be achieved in the system for any given coupling strength. By adjusting the value of the time delay in signal transmission, the neural system can freely switch between neural rest and synchronous spikes. This means that time delay in signal transmission is crucial for the occurrence of synchronous spikes in the FHN neural system, which contributes to our understanding of the interaction between neurons. We analytically show the influence of the time delay on the synchronization between two FHN neurons, which was seldom considered by other researchers.

Magnetoencephalography applied to the study of Alzheimer's disease

Magnetoencephalography (MEG) is a relatively modern neuroimaging technique able to study normal and pathological brain functioning with temporal resolution in the order of milliseconds and adequate spatial resolution. Although its clinical applications are still relatively limited, great advances have been made in recent years in the field of dementia and Alzheimer's disease (AD) in particular. In this chapter, we briefly describe the physiological phenomena underlying MEG brain signals and the different metrics that can be computed from these data in order to study the alterations disrupting brain activity not only in demented patients, but also in the preclinical and prodromal stages of the disease. Changes in non-linear brain dynamics, power spectral properties, functional connectivity and network topological changes observed in AD are narratively summarized in the context of the pathophysiology of the disease. Furthermore, the potential of MEG as a potential biomarker to identify AD pathology before dementia onset is discussed in the light of current knowledge and the relationship between potential MEG biomarkers and current established hallmarks of the disease is also reviewed. To this aim, findings from different approaches such as resting state or during the performance of different cognitive paradigms are discussed.Lastly, there is an increasing interest in current scientific literature in promoting interventions aimed at modifying certain lifestyles, such as nutrition or physical activity among others, thought to reduce or delay AD risk. We discuss the utility of MEG as a potential marker of the success of such interventions from the available literature.

Excessive phase synchronization in cortical activation during locomotion in persons with Parkinson's disease

INTRODUCTION

Parkinson's disease (PD) is characterized by gait disturbances, which become severe during the advanced stages of the disease. Though gait impairments in Parkinson's disease have been extensively described in terms of spatiotemporal gait parameters, little is known regarding associated patterns of cortical activity. The objective of the present study is to test if interhemispheric synchronization differs between participants with PD and healthy elderly controls (NPD). We analyzed electroencephalography (EEG) signals recorded during bilateral movements, i.e., locomotion and hand tapping.

METHODS

Fifteen participants with PD ('OFF' their anti-parkinsonian medications) and eight NPD were assessed during quiet standing, straight-line walking, turning, and hand tapping tasks. Using a 32-electrode EEG array, we quantified the synchronization in periodic cortical activation between the brain hemispheres (interhemispheric phase synchronization; inter-PS). Theta, alpha, beta, and gamma bands were evaluated.

RESULTS

In all bands, inter-PS was significantly higher for the PD group as compared with the NPD group during standing and walking (p < 0.001) and during bimanual tasks (p = 0.026).

CONCLUSIONS

Persons with PD exhibit increased inter-PS as compared with NPD participants. These findings support previous evidence from animal studies, that bilateral cortical hypersynchronization emerges from the asymmetric neural degeneration that is at the base of the disease. Future studies should elucidate the long-term temporal development of this hypersynchronization and its clinical relevance (e.g., can it 'serve' as prodromal marker?).

Bistable Firing Pattern in a Neural Network Model

Excessively high, neural synchronization has been associated with epileptic seizures, one of the most common brain diseases worldwide. A better understanding of neural synchronization mechanisms can thus help control or even treat epilepsy. In this paper, we study neural synchronization in a random network where nodes are neurons with excitatory and inhibitory synapses, and neural activity for each node is provided by the adaptive exponential integrate-and-fire model. In this framework, we verify that the decrease in the influence of inhibition can generate synchronization originating from a pattern of desynchronized spikes. The transition from desynchronous spikes to synchronous bursts of activity, induced by varying the synaptic coupling, emerges in a hysteresis loop due to bistability where abnormal (excessively high synchronous) regimes exist. We verify that, for parameters in the bistability regime, a square current pulse can trigger excessively high (abnormal) synchronization, a process that can reproduce features of epileptic seizures. Then, we show that it is possible to suppress such abnormal synchronization by applying a small-amplitude external current on > 10% of the neurons in the network. Our results demonstrate that external electrical stimulation not only can trigger synchronous behavior, but more importantly, it can be used as a means to reduce abnormal synchronization and thus, control or treat effectively epileptic seizures.

Tracking Control of a Class of Chaotic Systems

This paper investigates the asymptotic tracking control problem of the chaotic system. Firstly, a reference system is presented, the output of which can asymptotically track a given command. Then, a both physically implementable and simple controller is designed, by which the given chaotic system synchronizes the reference system, and thus the output of such chaotic systems can asymptotically track the given command. It should be pointed out that the output of the given chaotic system can asymptotically track arbitrary desired periodic orbits. Finally, several illustrative examples are taken as example to show the validity and effectiveness of the obtained results.

Brain networks and their relevance for stroke rehabilitation

Stroke has long been regarded as focal disease with circumscribed damage leading to neurological deficits. However, advances in methods for assessing the human brain and in statistics have enabled new tools for the examination of the consequences of stroke on brain structure and function. Thereby, it has become evident that stroke has impact on the entire brain and its network properties and can therefore be considered as a network disease. The present review first gives an overview of current methodological opportunities and pitfalls for assessing stroke-induced changes and reorganization in the human brain. We then summarize principles of plasticity after stroke that have emerged from the assessment of networks. Thereby, it is shown that neurological deficits do not only arise from focal tissue damage but also from local and remote changes in white-matter tracts and in neural interactions among wide-spread networks. Similarly, plasticity and clinical improvements are associated with specific compensatory structural and functional patterns of neural network interactions. Innovative treatment approaches have started to target such network patterns to enhance recovery. Network assessments to predict treatment response and to individualize rehabilitation is a promising way to enhance specific treatment effects and overall outcome after stroke.

Synchronization of pitch and plunge motions during intermittency route to aeroelastic flutter

Interaction of fluid forces with flexible structures is often prone to dynamical instabilities, such as aeroelastic flutter. The onset of this instability is marked by sustained large amplitude oscillations and is detrimental to the structure's integrity. Therefore, investigating the possible physical mechanisms behind the onset of flutter instability has attracted considerable attention within the aeroelastic community. Recent studies have shown that in the presence of oncoming fluctuating flows, the onset of flutter instability is presaged by an intermediate regime of oscillations called intermittency. Further, based on the intensity of flow fluctuations and the relative time scales present in the flow, qualitatively different types of intermittency at different flow regimes have been reported hitherto. However, the coupled interaction between the pitch (torsion) and plunge (bending) modes during the transition to aeroelastic flutter has not been explored. With this, we demonstrate with a mathematical model that the onset of flutter instability under randomly fluctuating flows occurs via a mutual phase synchronization between the pitch and the plunge modes. We show that at very low values of mean flow speeds, the response is by and large noisy and, consequently, a phase asynchrony between the modes is present. Interestingly, during the regime of intermittency, we observe the coexistence of patches of synchronized periodic bursts interspersed amidst a state of desynchrony between the pitch and the plunge modes. On the other hand, at the onset of flutter, we observe a complete phase synchronization between the pitch and plunge modes. This study concludes by utilizing phase locking value as a quantitative measure to demarcate different states of synchronization in the aeroelastic response.

Synchronization of chaotic systems and their machine-learning models

Recent advances have demonstrated the effectiveness of a machine-learning approach known as "reservoir computing" for model-free prediction of chaotic systems. We find that a well-trained reservoir computer can synchronize with its learned chaotic systems by linking them with a common signal. A necessary condition for achieving this synchronization is the negative values of the sub-Lyapunov exponents. Remarkably, we show that by sending just a scalar signal, one can achieve synchronism in trained reservoir computers and a cascading synchronization among chaotic systems and their fitted reservoir computers. Moreover, we demonstrate that this synchronization is maintained even in the presence of a parameter mismatch. Our findings possibly provide a path for accurate production of all expected signals in unknown chaotic systems using just one observational measure.

U1 snRNA over-expression affects neural oscillations and short-term memory deficits in mice

Small nuclear RNAs (snRNAs) and other RNA spliceosomal components are involved in neurological and psychiatric disorders. U1 snRNA has recently been demonstrated to be altered in pathology in some neurodegenerative diseases, but whether it has a causative role is not clear. Here we have studied this by overexpressing U1 snRNA in mice and measured their hippocampal oscillatory patterns and brain functions. Novel object recognition test showed that the recognition index was significantly decreased in the U1 snRNA over-expression mice compared to that in the C57BL mice. U1 snRNA over-expression regulated not only the pattern of neural oscillations but also the expression of neuron excitatory and inhibitory proteins. Here we show that U1 snRNA over-expression contains the shrinkage distribution of theta-power, theta-phase lock synchronization, and theta and low-gamma cross-frequency coupling in the hippocampus. The alternations of neuron receptors by the U1 snRNA overexpression also modulated the decreasing of recognition index, the energy distribution of theta power spectrum with the reductions of theta phase synchronization and phase-amplitude coupling between theta and low-gamma. Linking these all together, our results suggest that U1 snRNA overexpression particularly causes a deficit in short-term memory. These findings make a bedrock of our research that U1 snRNA bridges the gap about the mechanism behind short-term memory based on the molecular and mesoscopic level.

Human Heart Rhythms Synchronize While Co-sleeping

Human physiological systems have a major role in maintenance of internal stability. Previous studies have found that these systems are regulated by various types of interactions associated with physiological homeostasis. However, whether there is any interaction between these systems in different individuals is not well-understood. The aim of this research was to determine whether or not there is any interaction between the physiological systems of independent individuals in an environment where they are connected with one another. We investigated the heart rhythms of co-sleeping individuals and found evidence that in co-sleepers, not only do independent heart rhythms appear in the same relative phase for prolonged periods, but also that their occurrence has a bidirectional causal relationship. Under controlled experimental conditions, this finding may be attributed to weak cardiac vibration delivered from one individual to the other via a mechanical bed connection. Our experimental approach could help in understanding how sharing behaviors or social relationships between individuals are associated with interactions of physiological systems.

Mixed mode oscillations and phase locking in coupled FitzHugh-Nagumo model neurons

We study the dynamics of a low-dimensional system of coupled model neurons as a step towards understanding the vastly complex network of neurons in the brain. We analyze the bifurcation structure of a system of two model neurons with unidirectional coupling as a function of two physiologically relevant parameters: the external current input only to the first neuron and the strength of the coupling from the first to the second neuron. Leveraging a timescale separation, we prove necessary conditions for multiple timescale phenomena observed in the coupled system, including canard solutions and mixed mode oscillations. For a larger network of model neurons, we present a sufficient condition for phase locking when external inputs are heterogeneous. Finally, we generalize our results to directed trees of model neurons with heterogeneous inputs.

Warped phase coherence: An empirical synchronization measure combining phase and amplitude information

The entrainment between weakly coupled nonlinear oscillators, as well as between complex signals such as those representing physiological activity, is frequently assessed in terms of whether a stable relationship is detectable between the instantaneous phases extracted from the measured or simulated time-series via the analytic signal. Here, we demonstrate that adding a possibly complex constant value to this normally null-mean signal has a non-trivial warping effect. Among other consequences, this introduces a level of sensitivity to the amplitude fluctuations and average relative phase. By means of simulations of Rössler systems and experiments on single-transistor oscillator networks, it is shown that the resulting coherence measure may have an empirical value in improving the inference of the structural couplings from the dynamics. When tentatively applied to the electroencephalogram recorded while performing imaginary and real movements, this straightforward modification of the phase locking value substantially improved the classification accuracy. Hence, its possible practical relevance in brain-computer and brain-machine interfaces deserves consideration.

Phosphofructokinase controls the acetaldehyde-induced phase shift in isolated yeast glycolytic oscillators

The response of oscillatory systems to external perturbations is crucial for emergent properties such as synchronisation and phase locking and can be quantified in a phase response curve (PRC). In individual, oscillating yeast cells, we characterised experimentally the phase response of glycolytic oscillations for external acetaldehyde pulses and followed the transduction of the perturbation through the system. Subsequently, we analysed the control of the relevant system components in a detailed mechanistic model. The observed responses are interpreted in terms of the functional coupling and regulation in the reaction network. We find that our model quantitatively predicts the phase-dependent phase shift observed in the experimental data. The phase shift is in agreement with an adaptation leading to synchronisation with an external signal. Our model analysis establishes that phosphofructokinase plays a key role in the phase shift dynamics as shown in the PRC and adaptation time to external perturbations. Specific mechanism-based interventions, made possible through such analyses of detailed models, can improve upon standard trial and error methods, e.g. melatonin supplementation to overcome jet-lag, which are error-prone, specifically, since the effects are phase dependent and dose dependent. The models by Gustavsson and Goldbeter discussed in the text can be obtained from the JWS Online simulation database: (https://jjj.bio.vu.nl/models/gustavsson5 and https://jjj.bio.vu.nl/models/goldbeter1).

Symmetries in the time-averaged dynamics of networks: Reducing unnecessary complexity through minimal network models

Complex networks are the subject of fundamental interest from the scientific community at large. Several metrics have been introduced to characterize the structure of these networks, such as the degree distribution, degree correlation, path length, clustering coefficient, centrality measures, etc. Another important feature is the presence of network symmetries. In particular, the effect of these symmetries has been studied in the context of network synchronization, where they have been used to predict the emergence and stability of cluster synchronous states. Here, we provide theoretical, numerical, and experimental evidence that network symmetries play a role in a substantially broader class of dynamical models on networks, including epidemics, game theory, communication, and coupled excitable systems; namely, we see that in all these models, nodes that are related by a symmetry relation show the same time-averaged dynamical properties. This discovery leads us to propose reduction techniques for exact, yet minimal, simulation of complex networks dynamics, which we show are effective in order to optimize the use of computational resources, such as computation time and memory.

Application of fractional calculus to combined modified function projective synchronization of different systems

This paper presents the analysis of fractional order dynamical system of combined modified function projective synchronization of different systems. Initially, we formulate the model in fractional order and then investigate their associated properties. We then investigate the chaotic behavior of different systems by considering the fractional order parameter. To obtain the simulation results of the models, we use the Runge-Kutta order four scheme and Adams-Bashforth scheme. The obtained results are discussed in detail for the various values of the fractional order parameters. The obtained graphical results reveal the significance of the fractional order modeling.

Amnestic Mild Cognitive Impairment Is Associated With Frequency-Specific Brain Network Alterations in Temporal Poles

There is general agreement that the neuropathological processes leading to Alzheimer’s disease (AD) begin decades before the clinical onset. In order to detect early topological changes, we applied functional connectivity and network analysis to magnetoencephalographic (MEG) data obtained from 16 patients with amnestic Mild Cognitive Impairment (aMCI), a prodromal stage of AD, and 16 matched healthy control (HCs). Significant differences between the two groups were found in the theta band, which is associated with memory processes, in both temporal poles (TPs). In aMCI, the degree and betweenness centrality (BC) were lower in the left superior TP, whereas in the right middle TP the BC was higher. A statistically significant negative linear correlation was found between the BC of the left superior TP and a delayed recall score, a sensitive marker of the “hippocampal memory” deficit in early AD. Our results suggest that the TPs, which are involved early in AD pathology and belong to the memory circuitry, have an altered role in the functional network in aMCI.

Phase coherence between precipitation in South America and Rossby waves

The dominant mode of intraseasonal precipitation variability during the South American monsoon is the so-called precipitation dipole between the South Atlantic convergence zone (SACZ) and southeastern South America (SESA). It affects highly populated areas that are of substantial importance for the regional food supplies. Previous studies using principal components analysis or complex networks were able to describe and characterize this variability pattern, but crucial questions regarding the responsible physical mechanism remain open. Here, we use phase synchronization techniques to study the relation between precipitation in the SACZ and SESA on the one hand and southern hemisphere Rossby wave trains on the other hand. In combination with a conceptual model, this approach demonstrates that the dipolar precipitation pattern is caused by the southern hemisphere Rossby waves. Our results thus show that Rossby waves are the main driver of the monsoon season variability in South America, a finding that has important implications for synoptic-scale weather forecasts.

Noise-Assisted Multivariate EMD-Based Mean-Phase Coherence Analysis to Evaluate Phase-Synchrony Dynamics in Epilepsy Patients

Spatiotemporal evolution of synchrony dynamics among neuronal populations plays an important role in decoding complicated brain function in normal cognitive processing as well as during pathological conditions such as epileptic seizures. In this paper, a non-linear analytical methodology is proposed to quantitatively evaluate the phase-synchrony dynamics in epilepsy patients. A set of finite neuronal oscillators was adaptively extracted from a multi-channel electrocorticographic (ECoG) dataset utilizing noise-assisted multivariate empirical mode de-composition (NA-MEMD). Next, the instantaneous phases of the oscillatory functions were extracted using the Hilbert transform in order to be utilized in the mean-phase coherence analysis. The phase-synchrony dynamics were then assessed using eigenvalue decomposition. The extracted neuronal oscillators were grouped with respect to their frequency range into wideband (1-600 Hz), ripple (80-250 Hz), and fast-ripple (250-600 Hz) bands in order to investigate the dynamics of ECoG activity in these frequency ranges as seizures evolve. Drug-refractory patients with frontal and temporal lobe epilepsy demonstrated a reduction in phase-synchrony around seizure onset. However, the network phase-synchrony started to increase toward seizure end and achieved its maximum level at seizure offset for both types of epilepsy. This result suggests that hyper-synchronization of the epileptic network may be an essential self-regulatory mechanism by which the brain terminates seizures.

Generalized synchronization in a conservative and nearly conservative systems of star network

We report the coexistence of synchronized and unsynchronized states in a mutually coupled star network of nearly conservative non-identical oscillators. Generalized synchronization is observed between the central oscillator with the peripherals, and phase synchronization is found among the peripherals in weakly dissipative systems. However, the basin size of the synchronization region decreases as dissipation strength is increased. We have demonstrated these phenomena with the help of Duffing and Lorenz84 oscillators with conservative, nearly conservative, and dissipative properties. The observed results are robust against the network size.

NREM Sleep and Antiepileptic Medications Modulate Epileptiform Activity by Altering Cortical Synchrony

INTRODUCTION

The activating role of non-rapid eye movement (NREM) sleep on epileptic cortex and conversely, the seizure remission brought about by antiepileptic medications, has been attributed to their effects on neuronal synchrony. This study aims to understand the role of neural synchrony of NREM sleep in promoting interictal epileptiform discharges (IEDs) in patients with epilepsy (PWE) by assessing the peri-IED phase synchrony during awake and sleep states. It also studies the role played by antiepileptic drugs (AEDs) on EEG desynchronization in the above cohort.

METHODS

A total of 120 PWE divided into 3 groups (each n = 40; juvenile myoclonic epilepsy [JME], temporal lobe epilepsy [TLE]. and extratemporal lobe epilepsy [Ex-TLE]) were subjected to overnight polysomnography. Each patient group was subdivided into drug-naive and on treatment (Each n = 20). EEG phase synchronization analysis was performed to compare peri-IED phase synchronization indices (SI) during awake and sleep stages and between drug naïve and on treatment groups in 4 frequency bands, namely delta, theta, alpha, and beta. The mean ± SD of peri-IED SI among various subgroups was compared employing a multilevel mixed effects modeling approach.

RESULTS

Patients with JME had increased peri-IED cortical synchrony in N3 sleep stage, whereas patients with partial epilepsy had increased IED cortical synchrony in N1 sleep stage. On the other hand, peri-IED synchrony was lower during wake and REM sleep. We also found that peri-IED synchronization in patients with JME was higher in drug-naive patients compared with those on sodium valproate monotherapy in theta, alpha, and beta bands.

CONCLUSION

The findings of this study suggest that sleep stages can alter cortical synchrony in patients with JME and focal epilepsy, with NREM IEDs being more synchronized and wake/REM IEDs being less synchronized. Furthermore, it also suggests that AEDs alleviate seizures in PWE by inhibiting cortical synchrony.

Dynamic low frequency EEG phase synchronization patterns during proactive control of task switching

Cognitive flexibility is critical for humans living in complex societies with ever-growing multitasking demands. Yet the low-frequency neural dynamics of distinct task-specific and domain-general mechanisms sub-serving mental flexibility are still ill-defined. Here we estimated phase electroencephalogram synchronization by using inter-trial phase coherence (ITPC) at the source space while twenty six young participants were intermittently cued to switch or repeat their perceptual categorization rule of Gabor gratings varying in color and thickness (switch task). Therefore, the aim of this study was to examine whether a proactive control is associated with connectivity only in the frontoparietal theta network, or also involves distinct neural connectivity within the delta band, as distinct neural signatures while preparing to switch or repeat a task set, respectively. To this end, we focused the analysis on late-latencies (from 500 to 800 msec post-cue onset), since they are known to be associated with top-down cognitive control processes. We confirmed that proactive control during a task switch was associated with frontoparietal theta connectivity. But importantly, we also found a distinct role of delta band oscillatory synchronization in proactive control, engaging more posterior frontotemporal regions as opposed to frontoparietal theta connectivity. Additionally, we built a regression model by using the ITPC results in delta and theta bands as predictors, and the behavioral accuracy in the switch task as the criterion, obtaining significant results for both frequency bands. All these findings support the existence of distinct proactive cognitive control processes related to functionally distinct though highly complementary theta and delta frontoparietal and temporoparietal oscillatory networks at late-latency temporal scales.

Efficient determination of synchronization domains from observations of asynchronous dynamics

We develop an approach for a fast experimental inference of synchronization properties of an oscillator. While the standard technique for determination of synchronization domains implies that the oscillator under study is forced with many different frequencies and amplitudes, our approach requires only several observations of a driven system. Reconstructing the phase dynamics from data, we successfully determine synchronization domains of noisy and chaotic oscillators. Our technique is especially important for experiments with living systems where an external action can be harmful and shall be minimized.

Mean field phase synchronization between chimera states

We study two-layer networks of identical phase oscillators. Each individual layer is a ring network for which a non-local intra-layer coupling leads to the formation of a chimera state. The number of oscillators and their natural frequencies is in general different across the layers. We couple the phases of individual oscillators in one layer to the phase of the mean field of the other layer. This coupling from the mean field to individual oscillators is done in both directions. For a sufficient strength of this inter-layer coupling, the phases of the mean fields lock across the two layers. In contrast, both layers continue to exhibit chimera states with no locking between the phases of individual oscillators across layers, and the two mean field amplitudes remain uncorrelated. Hence, the networks' mean fields show phase synchronization which is analogous to the one between low-dimensional chaotic oscillators. The required coupling strength to achieve this mean field phase synchronization increases with the mismatches in the network sizes and the oscillators' natural frequencies.

The blessing of Dimensionality: Feature Selection outperforms functional connectivity-based feature transformation to classify ADHD subjects from EEG patterns of phase synchronisation

Functional connectivity (FC) characterizes brain activity from a multivariate set of N brain signals by means of an NxN matrix A, whose elements estimate the dependence within each possible pair of signals. Such matrix can be used as a feature vector for (un)supervised subject classification. Yet if N is large, A is highly dimensional. Little is known on the effect that different strategies to reduce its dimensionality may have on its classification ability. Here, we apply different machine learning algorithms to classify 33 children (age [6-14 years]) into two groups (healthy controls and Attention Deficit Hyperactivity Disorder patients) using EEG FC patterns obtained from two phase synchronisation indices. We found that the classification is highly successful (around 95%) if the whole matrix A is taken into account, and the relevant features are selected using machine learning methods. However, if FC algorithms are applied instead to transform A into a lower dimensionality matrix, the classification rate drops to less than 80%. We conclude that, for the purpose of pattern classification, the relevant features should be selected among the elements of A by using appropriate machine learning algorithms.

Novel analysis of fNIRS acquired dynamic hemoglobin concentrations: application in young children with autism spectrum disorder

A novel analysis of the spatial complexity of functional connectivity (SCFC) was proposed to investigate the spatial complexity of multiple dynamic functional connectivity series in an fNIRS study, using an approach combining principal component analysis and normalized entropy. The analysis was designed to describe the complex spatial features of phase synchrony based dynamic functional connectivity (dFC), which are unexplained in traditional approaches. The feasibility and validity of this method were verified in a sample of young patients with autism spectrum disorders (ASD). Our results showed that there were information exchange deficits in the right prefrontal cortex (PFC) of children with ASD, with markedly higher interregion SCFCs between the right PFC and other brain regions than those of normal controls. Furthermore, the global SCFC was significantly higher in young patients with ASD, along with considerably higher intraregion SCFCs in the prefrontal and temporal lobes which represents more diverse information exchange in these areas. The study suggests a novel method to analyze the fNIRS required dynamic hemoglobin concentrations by using concepts of SCFC. Moreover, the clinical results extend our understanding of ASD pathology, suggesting the crucial role of the right PFC during the information exchange process.

Optimizing the detection of nonstationary signals by using recurrence analysis

Recurrence analysis and its quantifiers are strongly dependent on the evaluation of the vicinity threshold parameter, i.e., the threshold to regard two points close enough in phase space to be considered as just one. We develop a new way to optimize the evaluation of the vicinity threshold in order to assure a higher level of sensitivity to recurrence quantifiers to allow the detection of even small changes in the dynamics. It is used to promote recurrence analysis as a tool to detect nonstationary behavior of time signals or space profiles. We show that the ability to detect small changes provides information about the present status of the physical process responsible to generate the signal and offers mechanisms to predict future states. Here, a higher sensitive recurrence analysis is proposed as a precursor, a tool to predict near future states of a particular system, based on just (experimentally) obtained signals of some available variables of the system. Comparisons with traditional methods of recurrence analysis show that the optimization method developed here is more sensitive to small variations occurring in a signal. The method is applied to numerically generated time series as well as experimental data from physiology.

Stabilization of dynamics of oscillatory systems by nonautonomous perturbation

Synchronization and stability under periodic oscillatory driving are well understood, but little is known about the effects of aperiodic driving, despite its abundance in nature. Here, we consider oscillators subject to driving with slowly varying frequency, and investigate both short-term and long-term stability properties. For a phase oscillator, we find that, counterintuitively, such variation is guaranteed to enlarge the Arnold tongue in parameter space. Using analytical and numerical methods that provide information on time-variable dynamical properties, we find that the growth of the Arnold tongue is specifically due to the growth of a region of intermittent synchronization where trajectories alternate between short-term stability and short-term neutral stability, giving rise to stability on average. We also present examples of higher-dimensional nonlinear oscillators where a similar stabilization phenomenon is numerically observed. Our findings help support the case that in general, deterministic nonautonomous perturbation is a very good candidate for stabilizing complex dynamics.

Phase definition to assess synchronization quality of nonlinear oscillators

This paper proposes a phase definition, named the vector field phase, which can be defined for systems with arbitrary finite dimension and is a monotonically increasing function of time. The proposed definition can properly quantify the dynamics in the flow direction, often associated with the null Lyapunov exponent. Numerical examples that use benchmark periodic and chaotic oscillators are discussed to illustrate some of the main features of the definition, which are that (i) phase information can be obtained either from the vector field or from a time series, (ii) it permits not only detection of phase synchronization but also quantification of it, and (iii) it can be used in the phase synchronization of very different oscillators.