Structural (operational) synchrony of EEG alpha activity during an auditory memory task

Ensemble of coupling forms and networks among brain rhythms as function of states and cognition

The current paradigm in brain research focuses on individual brain rhythms, their spatiotemporal organization, and specific pairwise interactions in association with physiological states, cognitive functions, and pathological conditions. Here we propose a conceptually different approach to understanding physiologic function as emerging behavior from communications among distinct brain rhythms. We hypothesize that all brain rhythms coordinate as a network to generate states and facilitate functions. We analyze healthy subjects during rest, exercise, and cognitive tasks and show that synchronous modulation in the micro-architecture of brain rhythms mediates their cross-communications. We discover that brain rhythms interact through an ensemble of coupling forms, universally observed across cortical areas, uniquely defining each physiological state. We demonstrate that a dynamic network regulates the collective behavior of brain rhythms and that network topology and links strength hierarchically reorganize with transitions across states, indicating that brain-rhythm interactions play an essential role in generating physiological states and cognition.

Functional Complex Networks Based on Operational Architectonics: Application on Electroencephalography-Brain-computer Interface for Imagined Speech

A new method for analyzing brain complex dynamics and states is presented. This method constructs functional brain graphs and is comprised of two pylons: (a) Operational architectonics (OA) concept of brain and mind functioning. (b) Network neuroscience. In particular, the algorithm utilizes OA framework for a non-parametric segmentation of EEGs, which leads to the identification of change points, namely abrupt jumps in EEG amplitude, called Rapid Transition Processes (RTPs). Subsequently, the time coordinates of RTPs are used for the generation of undirected weighted complex networks fulfilling a scale-free topology criterion, from which various network metrics of brain connectivity are estimated. These metrics form feature vectors, which can be used in machine learning algorithms for classification and/or prediction. The method is tested in classification problems on an EEG-based BCI data set, acquired from individuals during imagery pronunciation tasks of various words/vowels. The classification results, based on a Naïve Bayes classifier, show that the overall accuracies were found to be above chance level in all tested cases. This method was also compared with other state-of-the-art computational approaches commonly used for functional network generation, exhibiting competitive performance. The method can be useful to neuroscientists wishing to enhance their repository of brain research algorithms.

Altered electroencephalography functional connectivity in depression during the emotional face-word Stroop task

OBJECTIVE

Depression is a severe mental disorder. However, the neural mechanisms underlying affective interference (difficulties in directing attention away from negative distractors) in depression patients are still not well-understood. In particular, the connections between brain regions remain unclear. Using the emotional face-word Stroop task, we aimed to reveal the altered electroencephalography (EEG) functional connectivity in patients with depression, using concepts from event-related potentials (ERPs) and time series clustering.

APPROACH

In this study, the EEG signals of ten healthy participants and ten depression patients were collected from a 64-sensor cap. Subsequently, EEG signals were segmented into temporal windows corresponding to the ERPs. For each duration, the dynamic time warping algorithm was used to calculate the similarities between EEG signals from different electrodes, and differences of these similarities were compared between the groups. Finally, hierarchical clustering was used to identify functionally connected regions and examine changes in depression.

MAIN RESULTS

It was observed that during the time interval of 400-600 ms (N450 components), depression patients had more long-range connections than did healthy control patients and exhibited abnormal functional connectivity via the superior and middle frontal gyrus, specifically, the dorsolateral prefrontal cortex (DL-PFC, Brodmann's area 8 and 9), which is related to the control and resolution of affective interference. Moreover, the functionally connected region of depression patients was much larger than that of healthy participants, which is caused by brain resource reorganization.

SIGNIFICANCE

These findings thus provide new insights into the neural mechanisms of depression and further identify the DL-PFC and connections between certain electrodes as quantitative indicators of depression.

Consciousness: a unique way of processing information

In this article, I argue that consciousness is a unique way of processing information, in that: it produces information, rather than purely transmitting it; the information it produces is meaningful for us; the meaning it has is always individuated. This uniqueness allows us to process information on the basis of our personal needs and ever-changing interactions with the environment, and consequently to act autonomously. Three main basic cognitive processes contribute to realize this unique way of information processing: the self, attention and working memory. The self, which is primarily expressed via the central and peripheral nervous systems, maps our body, the environment, and our relations with the environment. It is the primary means by which the complexity inherent to our composite structure is reduced into the "single voice" of a unique individual. It provides a reference system that (albeit evolving) is sufficiently stable to define the variations that will be used as the raw material for the construction of conscious information. Attention allows for the selection of those variations in the state of the self that are most relevant in the given situation. Attention originates and is deployed from a single locus inside our body, which represents the center of the self, around which all our conscious experiences are organized. Whatever is focused by attention appears in our consciousness as possessing a spatial quality defined by this center and the direction toward which attention is focused. In addition, attention determines two other features of conscious experience: periodicity and phenomenal quality. Self and attention are necessary but not sufficient for conscious information to be produced. Complex forms of conscious experiences, such as the various modes of givenness of conscious experience and the stream of consciousness, need a working memory mechanism to assemble the basic pieces of information selected by attention.

Topodynamics of metastable brains

The brain displays both the anatomical features of a vast amount of interconnected topological mappings as well as the functional features of a nonlinear, metastable system at the edge of chaos, equipped with a phase space where mental random walks tend towards lower energetic basins. Nevertheless, with the exception of some advanced neuro-anatomic descriptions and present-day connectomic research, very few studies have been addressing the topological path of a brain embedded or embodied in its external and internal environment. Herein, by using new formal tools derived from algebraic topology, we provide an account of the metastable brain, based on the neuro-scientific model of Operational Architectonics of brain-mind functioning. We introduce a "topodynamic" description that shows how the relationships among the countless intertwined spatio-temporal levels of brain functioning can be assessed in terms of projections and mappings that take place on abstract structures, equipped with different dimensions, curvatures and energetic constraints. Such a topodynamical approach, apart from providing a biologically plausible model of brain function that can be operationalized, is also able to tackle the issue of a long-standing dichotomy: it throws indeed a bridge between the subjective, immediate datum of the naïve complex of sensations and mentations and the objective, quantitative, data extracted from experimental neuro-scientific procedures. Importantly, it opens the door to a series of new predictions and future directions of advancement for neuroscientific research.

Statistical detection of EEG synchrony using empirical bayesian inference

There is growing interest in understanding how the brain utilizes synchronized oscillatory activity to integrate information across functionally connected regions. Computing phase-locking values (PLV) between EEG signals is a popular method for quantifying such synchronizations and elucidating their role in cognitive tasks. However, high-dimensionality in PLV data incurs a serious multiple testing problem. Standard multiple testing methods in neuroimaging research (e.g., false discovery rate, FDR) suffer severe loss of power, because they fail to exploit complex dependence structure between hypotheses that vary in spectral, temporal and spatial dimension. Previously, we showed that a hierarchical FDR and optimal discovery procedures could be effectively applied for PLV analysis to provide better power than FDR. In this article, we revisit the multiple comparison problem from a new Empirical Bayes perspective and propose the application of the local FDR method (locFDR; Efron, 2001) for PLV synchrony analysis to compute FDR as a posterior probability that an observed statistic belongs to a null hypothesis. We demonstrate the application of Efron's Empirical Bayes approach for PLV synchrony analysis for the first time. We use simulations to validate the specificity and sensitivity of locFDR and a real EEG dataset from a visual search study for experimental validation. We also compare locFDR with hierarchical FDR and optimal discovery procedures in both simulation and experimental analyses. Our simulation results showed that the locFDR can effectively control false positives without compromising on the power of PLV synchrony inference. Our results from the application locFDR on experiment data detected more significant discoveries than our previously proposed methods whereas the standard FDR method failed to detect any significant discoveries.

Attention and working memory: two basic mechanisms for constructing temporal experiences

Various kinds of observations show that the ability of human beings to both consciously relive past events – episodic memory – and conceive future events, entails an active process of construction. This construction process also underpins many other important aspects of conscious human life, such as perceptions, language, and conscious thinking. This article provides an explanation of what makes the constructive process possible and how it works. The process mainly relies on attentional activity, which has a discrete and periodic nature, and working memory, which allows for the combination of discrete attentional operations. An explanation is also provided of how past and future events are constructed.

PHENOMENOLOGICAL ARCHITECTURE OF A MIND AND OPERATIONAL ARCHITECTONICS OF THE BRAIN: THE UNIFIED METASTABLE CONTINUUM

In our contribution we will observe phenomenal architecture of a mind and operational architectonics of the brain and will show their intimate connectedness within a single integrated metastable continuum. The notion of operation of different complexity is the fundamental and central one in bridging the gap between brain and mind: it is precisely by means of this notion that it is possible to identify what at the same time belongs to the phenomenal conscious level and to the neurophysiological level of brain activity organization, and what mediates between them. Implications for linguistic semantics, self-organized distributed computing algorithms, artificial machine consciousness, and diagnosis of dynamic brain diseases will be discussed briefly.

Optimal detection of functional connectivity from high-dimensional EEG synchrony data

Computing phase-locking values between EEG signals is a popular method for quantifying functional connectivity. However, this method involves large-scale, high-resolution datasets, which impose a serious multiple testing problem. Standard multiple testing methods fail to exploit the information from the complex dependence structure that varies across hypotheses in spectral, temporal, and spatial dimensions and result in a severe loss of power. They tend to control the false positives at the cost of hiding true positives. We introduce a new approach, called optimal discovery procedure (ODP) for identifying synchrony that is statistically significant. ODP maximizes the number of true positives for a given number of false positives, and thus offers a theoretical optimum for detecting significant synchrony in a multiple testing situation. We demonstrate the utility of this method with PLV data obtained from a visual search study. We also present simulation analysis to confirm the validity and relevance of using ODP in comparison with the standard FDR method for given configurations of true synchrony. We also compare the effectiveness of ODP with our previously published investigation of hierarchical FDR method (Singh and Phillips, 2010).

Dynamic task-specific brain network connectivity in children with severe reading difficulties

We investigated patterns of sensor-level functional connectivity derived from single-trial whole-head magnetoencephalography data during a pseudoword reading and a letter-sound naming task in children with reading difficulties (RD) and children with no reading impairments (NI). The Phase Lag Index (PLI), a linear and nonlinear estimator, computed for each pair of sensors, was used to construct graphs and obtain estimates of local and global network efficiency according to graph theory. In the 8-13 Hz (alpha band) and 20-30 Hz (gamma band) range, RD students showed significantly lower global efficiency than NI children, for the entire MEG recording epoch. RD students also displayed reduced local network efficiency in the alpha band. Correlations between phonological decoding ability and graph metrics were particularly evident during the task that posed significant demands for phonological decoding, and followed distinct time courses depending on signal frequency. Results are consistent with the notion of task-dependent, aberrant long- and short-range functional connectivity in RD children.

Persistent operational synchrony within brain default-mode network and self-processing operations in healthy subjects

Based on the theoretical analysis of self-consciousness concepts, we hypothesized that the spatio-temporal pattern of functional connectivity within the default-mode network (DMN) should persist unchanged across a variety of different cognitive tasks or acts, thus being task-unrelated. This supposition is in contrast with current understanding that DMN activated when the subjects are resting and deactivated during any attention-demanding cognitive tasks. To test our proposal, we used, in retrospect, the results from our two early studies (Fingelkurts, 1998; Fingelkurts et al., 2003). In both studies for the majority of experimental trails we indeed found a constellation of operationally synchronized cortical areas (indexed as DMN) that was persistent across all studied experimental conditions in all subjects. Furthermore, we found three major elements comprising this DMN: two symmetrical occipito-parieto-temporal and one frontal spatio-temporal patterns. This new data directly supports the notion that DMN has a specific functional connotation - it provides neurophysiologic basis for self-processing operations, namely first-person perspective taking and an experience of agency.

Brain-mind operational architectonics imaging: technical and methodological aspects

This review paper deals with methodological and technical foundations of the Operational Architectonics framework of brain and mind functioning. This theory provides a framework for mapping and understanding important aspects of the brain mechanisms that constitute perception, cognition, and eventually consciousness. The methods utilized within Operational Architectonics framework allow analyzing with an incredible detail the operational behavior of local neuronal assemblies and their joint activity in the form of unified and metastable operational modules, which constitute the whole hierarchy of brain operations, operations of cognition and phenomenal consciousness.

Neuromagnetic functional coupling during dichotic listening of speech sounds

The present magnetoencephalography (MEG) study tested the hypothesis of a phase synchronization (functional coupling) of cortical alpha rhythms (about 6-12 Hz) within a "speech" cortical neural network comprising bilateral primary auditory cortex and Wernicke's areas, during dichotic listening (DL) of consonant-vowel (CV) syllables. Dichotic stimulation was done with the CV-syllable pairs /da/-/ba/ (true DL, yielded by stimuli having high spectral overlap) and /da/-/ka/ (sham DL, obtained with stimuli having poor spectral overlap). Whole-head MEG activity (165 sensors) was recorded from 10 healthy right-handed non-musicians showing right ear advantage in a speech DL task. Functional coupling of alpha rhythms was defined as the spectral coherence at the following bands: alpha 1 (about 6-8 Hz), alpha 2 (about 8-10 Hz), and alpha 3 (about 10-12) with respect to the peak of individual alpha frequency. Results showed an inverse pattern of functional coupling: during DL of speech sounds, spectral coherence of the high-band alpha rhythms increased between left auditory and Wernicke's areas with respect to sham DL, whereas it decreased between left and right auditory areas. The increase of functional coupling within the left hemisphere would underlie the processing of the syllable presented to the right ear, which arrives to the left auditory cortex without the interference of the other syllable presented to the left ear. Conversely, the decrease of inter-hemispherical coupling of the high-band alpha might be due to the fact that the two auditory cortices do not receive the same information from the ears during DL. These results suggest that functional coupling of alpha rhythms can constitute a neural substrate for the lateralization of auditory stimuli during DL.

Human cortical circuits for central executive function emerge by theta phase synchronization

Dynamic networking of brain regions is suggested to be one of the key factors involved in various brain computations. Central executive function typically requires instantaneous coordination among the medial prefrontal regions and other distant regions, depending on the on-going task situation. In human scalp-recorded electroencephalography (EEG), the medial prefrontal area is estimated to be the current source of the theta rhythm, while there is no direct evidence that the theta rhythm is involved in the dynamic networking of central executive circuits. Here we hypothesize that the central executive circuit over the prefrontal and task-related cortices is dynamically linked by theta synchronization. By using simultaneous functional magnetic resonance imaging (fMRI) and EEG, we elucidated cortical circuits emerging with theta phase synchronization during free pacing repeated subtraction. Theta phase synchronization in the scalp EEG was found to emerge at two major clusters of electrode pairs, between the right frontal and left parietal sites and between the frontal and right parietal sites. The phase synchronization of two clusters is accompanied by fMRI responses in the cortical regions responsible for central executive function, working memory, visual imagery and cognitive action sequence. Here we report the first evidence that theta phase synchronization dynamically coordinates the central executive circuits, including the medial prefrontal cortex and relevant cortical regions.

Opioid withdrawal results in an increased local and remote functional connectivity at EEG alpha and beta frequency bands

Withdrawal may be a natural model to study craving and compulsive drug seeking, since craving can be viewed as a conditioned dysphoric state. It has been suggested that functional connectivity between brain areas may be of major value in explaining excessive craving and compulsive drug seeking by providing essential link between psychological and biological processes. Considering that withdrawal initiates a widespread activation of cortical regions responsible for compulsive drug seeking and desire for the drug, we predict that withdrawal would result in a significant increase in functional cortical connectivity. We applied the novel operational architectonics approach that enables us to estimate both local and remote functional cortical connectivity by means of EEG structural synchrony measure. In 13 withdrawal opioid-dependent patients we found the evidence that local and remote cortical functional connectivity was indeed significantly enhanced (for both alpha and beta frequency oscillations). Additionally, statistical relationship between functional connectivity and the severity of opioid withdrawal has been found.

Impaired functional connectivity at EEG alpha and theta frequency bands in major depression

Recent reports on functional brain imaging in major depression have lead to an assumption that observed psychopathology might be related to an altered brain functional connectivity. Our hypothesis was that an increase in brain functional connectivity occurs in major depression. As a measure of functional connectivity, the electroencephalogram (EEG) structural synchrony approach was used in 12 medication-free depressive outpatients and 10 control subjects. Differences in the number and strength of structurally synchronized EEG patterns were compared between groups. In depressive patients the number and strength of short cortex functional connections were significantly larger for the left than for the right hemisphere, while the number and strength of long functional connections were significantly larger for the right than for the left hemisphere. Some of the functional connections were positively correlated with the severity of depression, thus being predictive. These were short-range anterior, posterior, and left hemisphere functional connections for the alpha frequency band and short-range anterior functional connections for the theta frequency band. The topology of the most representative functional connections among all patients with major depression indicated that the right anterior and left posterior brain parts may discriminate depressive patients from healthy controls. The obtained data support our hypothesis that there is an increase in brain functional connectivity in major depression. This finding was interpreted within the semantic framework, where different specialization of left (monosemantic context) and right (polysemantic context) hemispheres is functionally insufficient in patients with depression.

Cortex functional connectivity as a neurophysiological correlate of hypnosis: an EEG case study

Cortex functional connectivity associated with hypnosis was investigated in a single highly hypnotizable subject in a normal baseline condition and under neutral hypnosis during two sessions separated by a year. After the hypnotic induction, but without further suggestions as compared to the baseline condition, all studied parameters of local and remote functional connectivity were significantly changed. The significant differences between hypnosis and the baseline condition were observable (to different extent) in five studied independent frequency bands (delta, theta, alpha, beta, and gamma). The results were consistent and stable after 1 year. Based on these findings we conclude that alteration in functional connectivity of the brain may be regarded as a neuronal correlate of hypnosis (at least in very highly hypnotizable subjects) in which separate cognitive modules and subsystems may be temporarily incapable of communicating with each other normally.

Timing in cognition and EEG brain dynamics: discreteness versus continuity

This article provides an overview of recent developments in solving the timing problem (discreteness vs. continuity) in cognitive neuroscience. Both theoretical and empirical studies have been considered, with an emphasis on the framework of operational architectonics (OA) of brain functioning (Fingelkurts and Fingelkurts in Brain Mind 2:291-29, 2001; Neurosci Biobehav Rev 28:827-836, 2005). This framework explores the temporal structure of information flow and interarea interactions within the network of functional neuronal populations by examining topographic sharp transition processes in the scalp EEG, on the millisecond scale. We conclude, based on the OA framework, that brain functioning is best conceptualized in terms of continuity-discreteness unity which is also the characteristic property of cognition. At the end we emphasize where one might productively proceed for the future research.

Cortical memory mechanisms and language origins

We have previously proposed that cortical auditory-vocal networks of the monkey brain can be partly homologized with language networks that participate in the phonological loop. In this paper, we suggest that other linguistic phenomena like semantic and syntactic processing also rely on the activation of transient memory networks, which can be compared to active memory networks in the primate. Consequently, short-term cortical memory ensembles that participate in language processing can be phylogenetically tracked to more simple networks present in the primate brain, which became increasingly complex in hominid evolution. This perspective is discussed in the context of two current interpretations of language origins, the "mirror-system hypothesis" and generativist grammar.

Cognition- and memory-related ERD/ERS responses in the auditory stimulus modality

In the year 1994, Krause et al. published an initial report of acoustically elicited electroencephalogram (EEG) event-related desynchronization (ERD)/ event-related synchronization (ERS) responses. Later, Krause et al. reported of distinct ERD/ERS responses during an auditory memory task: the encoding of acoustic material elicited alpha-frequency ERS whereas retrieval or recognition of the same stimulus material evoked alpha ERD. The research group of Krause and co-workers has published several reports on acoustically evoked ERD/ERS responses utilizing various cognitive tasks and diverse stimuli. Recently, also clinical studies have been initiated. This chapter reviews, summarizes, and discusses the findings on cognition- and memory-related ERD/ERS responses specifically in the auditory stimulus modality.

Functional connectivity in the brain--is it an elusive concept?

Even though functional brain connectivity is an influential concept in modern cognitive neuroscience, it is a very controversial notion. This is why further theoretical and methodological clarification are needed to help define precisely what is meant by functional connectivity and to help frame-associated issues. In this review we present the neurophysiological concept of functional connectivity, which utilizes in a plausible manner the notion of neural assemblies, as well as local and large-scale levels of description. Here functional connectivity is the mechanism for the coordination of activity between different neural assemblies in order to achieve a complex cognitive task or perceptual process. Our theoretical and empirical findings offer new insights into possible implications of the concept of functional connectivity for cognitive neuroscience.

New perspectives in pharmaco-electroencephalography

Recent research emphasizes that majority of brain disorders and psychiatric problems are accompanied by disruption in the temporal structure of brain activity. From this perspective, disruption is viewed as a disorder of the metastable balance between large-scale integration and independent processing in the brain, in favor of either independent or hyper-ordered processing. This paper proposes that the future of psychopharmacology lies in its ability to design the psychotropic drugs which can restore the normal temporal structure and metastable structure of brain activity. Quantitative electroencephalography (QEEG) is one of the key complex technologies utilized in psychopharmacology for this purpose. However, conventional approaches for EEG analysis used in clinical practice are not suitable for studying temporal structure of brain activity. To overcome this limitation, and in order to reveal dynamic and temporal characteristics of brain activity, the advanced analysis of EEG micro-structure should be used.

Extending the global workspace theory to emotion: phenomenality without access

Recent accounts on the global workspace theory suggest that consciousness involves transient formations of functional connections in thalamo-cortico-cortical networks. The level of connectivity in these networks is argued to determine the state of consciousness. Emotions are suggested to play a role in shaping consciousness, but their involvement in the global workspace theory remains elusive. In the present study, the role of emotion in the neural workspace theory of consciousness was scrutinized by investigating, whether unconscious (masked) and conscious (unmasked) display of emotional compared to neutral facial expressions would differentially modulate EEG coherence. EEG coherence was measured by means of computing an average EEG coherence value between the frontal, parietal, and midline scalp sites. Objective awareness checks evidenced that conscious identification of the masked facial expressions was precluded. Analyses revealed reductions in EEG coherence in the lower frequency range for the masked as compared to unmasked neutral facial expressions. Crucially, a decline in EEG coherence was not observed for the emotional facial expressions. In other words, the level of EEG coherence did apparently vary as a function of awareness, but not when emotion was involved. The current finding suggests that EEG coherence is modulated by unconscious emotional processes, which extends common views on the global workspace architecture of consciousness.

Making complexity simpler: multivariability and metastability in the brain

This article provides a retrospective, current, and prospective overview on developments in brain research and neuroscience. Both theoretical and empirical studies are considered, with emphasis in the concept of multivariability and metastability in the brain. In this new view on the human brain, the potential multivariability of the neuronal networks appears to be far from continuous in time, but confined by the dynamics of short-term local and global metastable brain states. The article closes by suggesting some of the implications of this view in future multidisciplinary brain research.

Local and remote functional connectivity of neocortex under the inhibition influence

The current paper focuses on a relatively new and promising area of the study of EEG transformations during brain information processing based on the reduction of the signal to the discrete quasi-stationary segment sequences which may reflect individual brain microstates or discrete operations. In this framework, the complex brain functions require integration of several operations throughout the whole neocortex. However, the role of inhibitory brain systems in such processes is still unsettled. The effects of a single dose (30 microg/kg) of lorazepam on the operational activity of neuronal populations and on the temporal binding between them were examined in a double-blind randomized crossover placebo-controlled study with eight healthy volunteers. EEG measures at 20 channels were evaluated on two occasions: (1) eyes closed, (2) eyes open. In short, we conducted a two-by-two factorial study where one factor manipulated GABAergic neurotransmission (lorazepam vs. placebo), and the other factor was simply brain state (eyes closed vs. eyes opened). We were primarily interested in the main effect of lorazepam. In the present study, a connection between the mesoscopic level, described by the local functional processes (neuronal assemblies or populations) and the macroscopic level, described as a sequence of metastable brain states (remote functionally synchronized neuronal populations) was established. The role of inhibitory brain systems facilitated by lorazepam in the operational dynamics of neuronal populations and in the process of EEG structural synchrony (SS) (topological peculiarities) was addressed for the first time. It was shown that GABA signaling reorganized the dynamics of local neuronal populations and the remote functional connectivity between them.

Enhancement of GABA-related signalling is associated with increase of functional connectivity in human cortex

Structural or operational synchrony analysis with EEG was conducted in order to detect functional interaction between cortical areas during an enhanced inhibition induced by the GABAergic agonist lorazepam in a double-blind, randomized, placebo-controlled, cross-over study in eight healthy human subjects. Specifically, we investigated whether a neuronal inhibitory system in the brain mediates functional decoupling of cortical areas. Single-dose lorazepam administration resulted in a widespread increase in the inter-area functional connectivity and an increase in the strength of functional long-range and interhemispheric connections. These results suggest that inhibition can be an efficient mechanism for synchronization of large neuronal populations.