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On neural substrates of cognition: Theory, experiments and application in brain computer interfaces


Abstract and Figures

Recent experiments with high-resolution brain imaging techniques provide an amazing view on the complex spatio-temporal dynamics of cortical processes. There is ample of evidence pointing to frequent transitions between periods of large-scale synchronization and intermittent desynchronization at alpha-theta rates (period length of 0.1 s to 0.25s). These observations have been interpreted based on the cinematic model of cognitive processing. In the corresponding mathematical theories, brains are perceived as open thermodynamic systems converting noisy sensory data into meaningful knowledge. We employ a graph-theoretic model called neuropercolation, which extends the concept of phase transitions to large interactive populations of nerve cells. We show that normal brains operate at the edge of criticality, where phase transitions are manifested via intermittent phase synchronization. Cortical phase transitions are viewed as neural correlates of cognition and serve as basis for non-invasive cognitive monitoring using novel brain-computer interfaces.
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On Neural Substrates of Cognition
Theory, Experiments and Application in Brain Computer Interfaces
Robert Kozma
Department of Mathematical Sciences
University of Memphis
Memphis, TN 38152, USA
Walter J. Freeman
Division of Neuroscience
University of California at Berkeley
Berkeley, CA 94720, USA
Abstract Recent experiments with high-
resolution brain imaging techniques provide an
amazing view on the complex spatio-temporal
dynamics of cortical processes. There is ample of
evidence pointing to frequent transitions between
periods of large-scale synchronization and
intermittent desynchronization at alpha-theta rates
(period length of 0.1 s to 0.25s). These observations
have been interpreted based on the cinematic model
of cognitive processing. In the corresponding
mathematical theories, brains are perceived as open
thermodynamic systems converting noisy sensory
data into meaningful knowledge. We employ a
graph-theoretic model called neuropercolation,
which extends the concept of phase transitions to
large interactive populations of nerve cells. We show
that normal brains operate at the edge of criticality,
where phase transitions are manifested via
intermittent phase synchronization. Cortical phase
transitions are viewed as neural correlates of
cognition and serve as basis for non-invasive
cognitive monitoring using novel brain-computer
KeywordsEEG, Phase Transition, Brain Computer
Interface (BCI), High-density Array.
Brain computer interfaces (BCIs) explore the
possibility to establish a communication channel
between brains and external devices such as computers.
The potential benefits are enormous. In clinical setting
BCIs can help to diagnose, predict, and treat cognitive
diseases at an early stage; they can also drastically
improve the quality of life of physically disabled
people. These clinical methods are often invasive, i.e.,
they involve the placement of implants on brains by
opening the scull (Yamakawa, 2012). In everyday life,
noninvasive BCIs are increasingly popular, for
example, the entertainment industry, and they have the
potential to serve as personal assistants in physical
training and exercises. BCIs are young and immature
technologies, and they are still at the very early stage of
their development. Clearly, a large number of
technological challenges must be solved before BCIs
widespread proliferation in broad segments of the
Here we focus on noninvasive devices, when the BCI
electrodes are located on the scull far away from the
cortical neurons. Extracting meaningful information
from the signals of such electrodes may seem daunting.
Indeed, significant exponents of the neuroscience
community consider the obstacles impenetrable and the
related activities outright foolish. The impossibility of
the task has been compared to the burlesque assignment
of Keystone Cops who try to eavesdrop on a single
conservation from outside a giant football stadium
(Marcus and Koch, 2014).
Or one may compare the situation to the case of a
group of free men of fishing trade installing a dense
array of flotation-sensors on the surface of a lake. They
keep applying ever more sophisticated tools and models
to their multi-channel bobbing-record. Methods, which
can indeed catch some statistical signs of at least the
movements of some of the creatures beneath the surface
they are monitoring. These swirls and eddies, they
proclaim, are the real secret of the piece of nature that is
the lake. Keystone Cops and free fishermen illustrate
the prevalent view concerning the apparent
impossibility of brain monitoring using noninvasive
devices. However, increasing experimental evidence
indicates that, in spite of the difficulties, this task can be
solved (Kozma and Freeman, 2014).
Noninvasive BCIs using EEG electrodes placed on
the scalp provide a feasible method for measuring the
brain electrical activity, for a review; see (Liao et al.,
2012). In recent years, EEG sensors and sensing circuit
designs have enabled the integration of sensors into
portable multimodal acquisition devices to measure a
wide variety of physiological signals. In this essay we
describe the experimentally documented intermittent
phase synchronization-desynchronization effects
carrying cognitive content. Then we introduce
neuropercolation as a mathematical approach to model
the synchronization transitions. We conclude with the
need for future developments of high-density scalp
EEG arrays for building efficient BCI devices.
Various brain imaging technologies can be used to
monitor cognitive functions, including functional
magnetic resonance imaging (fMRI), positron emission
tomography (PET), electroencephalograms (EEGs),
near-infrared spectroscopy (NIRS), and others
(Mazaheri and Jensen, 2006).
Figure 1. Illustration of the cognitive cycle, according to the
cinematic theory of cognition. Top: 64 superimposed band-pass
filtered ECoG signals. The 64 analytic amplitudes show drastic
reduction during an intermittent singularity (blue bars). These are the
null spikes (within the vertical blue bars), which are spatially and
temporally localized. Bottom: During the singularity, phase cones
convey the transition from microscopic disorder to macroscopic
order. The amplitudes are high between the blue bars, and they
correspond to the metastable AM patterns carrying the cognitive
During the past years, strong evidence has emerged
in the literature about the existence of sudden jumps in
measured cortical activities. Lehmann identifies
microstates in brain activity and jumps between them
(Lehman, 1998). Rapid switches in EEG activity have
been described by (Freeman et al., 2003, Stam, 2003).
A comprehensive overview of stability, metastability,
and transitions in brain activity is given in (Le Van
Quyen 2001; Werner 2007). Mathematical theory of
heteroclinic channels in winnerless competition is a
powerful approach of modeling sudden switches in
cognitive behavior (Rabinovich et al., 2012). Chaotic
itinerancy is a mathematical theory that describes the
trajectory of a dynamical system, which intermittently
visits “attractor ruins” as it traverses across the
landscape (Tsuda, 2001).
Here we summarize the cinematic theory of
cognition based on experimental studies of sudden
transitions in brain dynamics using electrocorticograms
(ECoGs). ECoGs indicate the presence of spatio-
temporal dynamics over the cortical surface in the form
of amplitude modulation (AM) patterns, which
intermittently collapse at the theta rates and give rise to
rapidly propagating phase modulated (PM) patterns.
The observed dynamics has been shown to be of
cognitive relevance carrying useful information on the
meaning of sensory information perceived by the
In the terminology of cinematic theory, the
metastable AM patters are the frames and the sudden
transitions through singularity represent the shutter, see
Fig. 1. This result is based on a 64-channel intracranial
experiment, where the analytic amplitudes (AA) and
analytic phases (AP) are obtained following Hilbert
transformation of the beta-gamma filtered ECoG
signals. Intensive work has been conducted to describe
dynamic transitions in cognitive processing as part of
the action-perception (Freeman and Quiroga, 2013).
Recent scalp EEG studies evidence that AM and PM
patterns are observable by non-intrusive experimental
techniques as well (Ruiz et al., 2010).
Neuropercolation is a family of probabilistic models
based on the mathematical theory of probabilistic
cellular automata on lattices and random graphs.
Neuropercolation is motivated by the structural and
dynamical properties of large-scale neural populations.
Neuropercolation extends the concept of phase
transitions to interactive neural populations exhibiting
frequent sudden transitions in their spatio-temporal
dynamics. Neuropercolation develops equations for the
probability distributions of macroscopic state variables
using percolation theory as an alternative to models
based on differential equations (Kozma et al., 2005;
Puljic and Kozma, 2008).
Neuropercolation is a natural domain for modeling
collective properties of brain networks, especially near
critical states, when the behavior of the system changes
abruptly with the variation of some parameter.
Neuropercolation incorporates the following major
generalizations based on the features of the neuropil,
the filamentous neural tissue in the cortex.
Noisy interaction: The dynamics of the interacting
neural populations is inherently non-deterministic
due to dendritic noise and other random effects in
the nervous tissue and external noise acting on the
population. Neuropercolation includes a small
random component, which can act as a control
Long axonal effects: In neural populations, most of
the connections are short, but there are a relatively
few long-range connections mediated by long
axons. The effect of long-range axons is similar to
small-world phenomena.
Inhibition: The cortex contains excitatory and
inhibitory connections. Inhibition contributes to the
emergence of sustained narrow-band oscillations in
the neural tissue. Inhibition is modeled by the
interaction of excitatory and inhibitory populations
in neuropercolation models.
Multi-layer neuropercolation models have been
built for implementing hierarchical models of cortical
populations (Freeman 2001; Kozma and Puljic, 2013).
The results indicate that multi-layer neuropercolation
reproduces intermittent phase transitions observed in
brains. Long axons communicating across mesoscopic
cortical distances control the rapid switching from one
pattern to another. The functional advantage of a
network structure with overlapping hubs, similar to the
observed “Rich Club” has been analyzed based on the
pioneer neurons concept.
The human scalp EEG contains massive information
that is correlated with higher cognitive functions.
Samples taken from arrays of electrodes show that the
information is in the form of spatiotemporal patterns of
briefly stationary bursts of electric potential differences
(Freeman and Quiroga, 2013). The bursts are generated
by masses of cortical neurons located 10-30 mm below
the scalp surface. They are signals that are
contaminated by electrical noise from scalp muscles
located 2-5 mm beneath the scalp surface.
Theoretical considerations indicate the need for a
high-density array with spatial resolution in the range of
3-5 mm. In order to produce robust spatial power
spectral densities, it is required to have a linear array of
64 electrodes. The spacing requirement is based on
analyses of the spatial frequencies imposed on the scalp
EEG by the gyri and sulci of the cortex (Ramon et al.,
2009); the typical width and length of gyri are on the
order of 10 and 30 cm, giving a spatial Nyquist
frequency of 0.2 cycles/mm. The temporal Nyquist
frequency of 2000 Hz is based on the need for temporal
precision in measurements of the phase of signals in the
high gamma and epsilon ranges, respectively 30-80 Hz
and 80-200 Hz.
Figure 2. Illustration of the high-density EEG array combined with
model studies using hierarchical neuropercolation model exhibiting
repeated phase transitions. The required massive simulations and
hypothesis generation is best performed using a dedicated FPGA chip
device. The experimental device is a headband of length about 25-30
cm, placed along the forehead. Both approaches lead to temporal-
spatial patterns (insets), which can be described as trajectories in a
phase space. This approach allows direct comparison between
experiment and model, generating and testing several hypotheses
about the relevance of phase transitions in complex neurodynamic
systems for explaining cognitive state changes. The approach is a
generalization based on ECoG experiments on learning and strategy
change in gerbils (Ohl et al., 2001).
Previous studies have shown that the PSDt of the
EEG is fA, where the exponent is 2<A<4, while on
average the EMG PSDt conforms to fB, where B = 0
(Freeman et al., 2003). Therefore the EMG imposes a
plateau onto the combined PSDt, with an inflection at a
high frequency, fH, on transit from fA to fB above fH.
Subjects can be trained by biofeedback, on seeing the
PSDt, to minimize EMG and reveal the signals in the
upper gamma ranges.
BCI technology is developed based on noninvasive
scalp electroencephalogram (EEG). Main conclusions
are as follows:
The proposed approach is based on the monitoring
of the experimentally documented intermittent
phase synchronization-desynchronization effects,
which carry the cognitive content.
We introduce an integrated experimental and
modeling approach using neuropercolation. The
neuropercolation model is used to interpret the
experimental data in real time using massive
parallel computing on a chip.
The information extracted from high-density EEG
array manifests neural correlates of higher
cognitive behaviors.
This work has been supported in part by DARPA
Physical Intelligence Program, Dr. Srinivasa Narayan,
and NSF CRCNS Program.
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... Despite the reported successes and breakthroughs in this field, there still exist some problems. First, most studies have focused on the recovery of motor ability, and the use of BCIs and AI for cognitive training is still at a very early stage (81). Second, clinical BCI applications are still very limited, and some important issues need to be solved before BCIs could be considered effective systems for rehabilitation in clinical settings. ...
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Brain-computer interfaces (BCIs) have shown great prospects as real-time bidirectional links between living brains and actuators. Artificial intelligence (AI), which can advance the analysis and decoding of neural activity, has turbocharged the field of BCIs. Over the past decade, a wide range of BCI applications with AI assistance have emerged. These "smart" BCIs including motor and sensory BCIs have shown notable clinical success, improved the quality of paralyzed patients' lives, expanded the athletic ability of common people and accelerated the evolution of robots and neurophysiological discoveries. However, despite technological improvements, challenges remain with regard to the long training periods, real-time feedback, and monitoring of BCIs. In this article, the authors review the current state of AI as applied to BCIs and describe advances in BCI applications, their challenges and where they could be headed in the future.
... Freeman has proposed a cinematographic or cinematic model of cognitive dynamics (Freeman, 2006). According to this model the cortical code that supports cognition consists of repetitive spatial frames of metastable amplitude modulation (AM) patterns (Freeman 2000a(Freeman ,b, 2003(Freeman , 2004a(Freeman ,b, 2005a(Freeman , 2006 that are analogous to the movie frames, while the rapid transition from one AM pattern to the other acts as the shutter (Freeman & Quian-Quiroga, 2013;Kozma & Freeman, 2014). Freeman proved experimentally that AM patterns (frames) embody the meaning of the stimuli rather than be their representations (Freeman, 1992;Barrie et al., 1996). ...
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Walter Jackson Freeman III (January 30, 1927 – April 24, 2016) was a true explorer, a Renaissance Man, who transcended the boundaries of disciplines and scientific knowledge. He has revolutionized the field of neuroscience, by bringing into it many pioneering ideas on brain dynamics. The authors of this brief essay address the main legacy of Walter Freeman through their framework of Operational Architectonics of brain-mind functioning that encompasses Freeman's mass action in the nervous system in the form of nested, dynamic neuronal assemblies and his cinematic model of cognitive dynamics, leading to emergence of consciousness. According to Operational Architectonics theory, the hierarchy of phenomenal world (features, patterns, objects, scenes) has its electrophysiological equivalent in an operational hierarchy of neuronal assemblies and nested spatial-temporal conglomerates of them in the form of operational modules (with different size and lifespan), which correspond to the phenomenal entities of different complexity. ABBREVIATIONS AM = Amplitude modulation; EEG = Electroencephalogram; EPSP = Excitatory postsynaptic potential; IPSP = inhibitory postsynaptic potential; OA = Operational architectonics; OM = Operational module; RTP = Rapid transitional period; OST = Operational space–time; IPST = Internal physical space–time; PST = Phenomenal (subjective) space-time. 2 Like other true explorers, we don't know what we will find, and we don't yet have the proper framework in which to describe whatever is there. This broad view from an open mind is my legacy. Walter Jackson Freeman (2007a)
... According to Freeman, the cortical code consists of repetitive spatial frames of metastable amplitude modulation (AM) patterns (Freeman 2000a(Freeman , b, 2003(Freeman , 2004a(Freeman , b, 2005(Freeman , 2006bFreeman et al. , 2003aFreeman and Rogers 2002). In this model, the AM patterns are the movie frames, while the rapid transition from one AM pattern to the other acts as the shutter (Freeman and Quian-Quiroga 2013;Davis et al. 2013;Kozma and Freeman 2014). This work extends attractor theory in the presence of self-organizing, far-from-equilibrium thermodynamics, following Haken's synergetics and Prigogine's 'dissipative structures' that feed on energy (Freeman 2007(Freeman , 2008. 4. The role of phase transitions on cortical dynamics. ...
Walter J. Freeman was a giant of the field of neuroscience whose visionary work contributed various experimental and theoretical breakthroughs to brain research in the past 60 years. He has pioneered a number of Electroencephalogram and Electrocorticogram tools and approaches that shaped the field, while “Freeman Neurodynamics” is a theoretical concept that is widely known, used, and respected among neuroscientists all over the world. His recent death is a profound loss to neuroscience and biomedical engineering. Many of his revolutionary ideas on brain dynamics have been ahead of their time by decades. We summarize his following groundbreaking achievements: (1) Mass Action in the Nervous System, from microscopic (single cell) recordings, through mesoscopic populations, to large-scale collective brain patterns underlying cognition; (2) Freeman–Kachalsky model of multi-scale, modular brain dynamics; (3) cinematic theory of cognitive dynamics; (4) phase transitions in cortical dynamics modeled with random graphs and quantum field theory; (5) philosophical aspects of intentionality, consciousness, and the unity of brain–mind–body. His work has been admired by many of his neuroscientist colleagues and followers. At the same time, his multidisciplinary approach combining advanced concepts of control theory and the mathematics of nonlinear systems and chaos, poses significant challenges to those who wish to thoroughly understand his message. The goal of this commemorative paper is to review key aspects of Freeman’s neurodynamics and to provide some handles to gain better understanding about Freeman’s extraordinary intellectual achievement.
... Neuropercolation develops equations for the probability distributions of macroscopic state variables generalizing percolation theory as an alternative to differential equations [35]. Neuropercolation results are interpreted in the context of recent experimental findings on the dynamics and structure of the cortex, indicating that brains operate at the edge of criticality, with phase transitions appearing intermittently, several times per second [36][37][38]. In the cinematic theory of cognition, brains compute with metastable coherent patterns as frames, intermittently interrupted by desynchronization episodes acting as the shutter [36]. ...
In this work, we describe operational principles of a pattern-based computing paradigm based on the neuropercolation model, which can be used as associative memory supporting sensory processing and pattern recognition. Neuropercolation extends the concept of phase transitions to interactive populations exhibiting frequent transients in their spatio-temporal dynamics, which can be viewed as manifestations of an asynchronous computer working with a sequence of meta-stable spatial patterns, in a bid to unravel the limitations of Turing computing principles. The model is motivated by the structural and dynamical properties of large-scale neural populations in the cerebral cortex and it implements basic building blocks of neurodynamics following the hierarchy of Freeman K-sets.
The hypothesis that foci that are visualized with fMRI are signs of hubs rather than modules can be tested by combining hemodynamic imaging (Buxton, Introduction to functional magnetic resonance imaging: principles and techniques, Cambridge University Press, Cambridge, 2001, [1]) with EEG imaging (Barlow, The electroencephalogram: its patterns and origins, MIT Press, Cambridge, 1993, [2], Pfurtscheller, Functional brain imaging. Hans Huber Publishers, Lewiston, 1988, [3]) and MEG (Hamalainen, JAMA, Rev Mod Phys 65:413–497, 1993, [4]). Experimental data indicate that the necessary macroscopic frames with beta-gamma carrier frequencies are readily found in human volunteers engaged in cognitive tasks by several research groups.
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Electrical dipoles oriented perpendicular to the cortical surface are the primary source of the scalp EEGs and MEGs. Thus, in particular, gyri and sulci structures on the cortical surface have a definite possibility to influence the EEGs and MEGs. This was examined by comparing the spatial power spectral density (PSD) of the upper portion of the human cortex in MRI slices to that of simulated scalp EEGs and MEGs. The electrical activity was modeled with 2,650 dipolar sources oriented normal to the local cortical surface. The resulting scalp potentials were calculated with a finite element model of the head constructed from 51 segmented sagittal MR images. The PSD was computed after taking the fast Fourier transform of scalp potentials. The PSD of the cortical contour in each slice was also computed. The PSD was then averaged over all the slices. This was done for sagittal and coronal view both. The PSD of EEG and MEG showed two broad peaks, one from 0.05 to 0.22cycles/cm (wavelength 20–4.545cm) and the other from 0.22 to 1.2cycles/cm (wavelength 4.545–0.834cm). The PSD of the cortex showed a broad peak from 0.08 to 0.32cycles/cm (wavelength 12.5–3.125cm) and other two peaks within the range of 0.32 to 0.9cycles/cm (wavelength 3.125–1.11cm). These peaks are definitely due to the gyri structures and associated larger patterns on the cortical surface. Smaller peaks in the range of 1–3cycles/cm were also observed which are possibly due to sulci structures. These results suggest that the spatial information was present in the EEG and MEG at the spatial frequencies of gyri. This also implies that the practical Nyquist frequency for sampling scalp EEGs should be 3.0cycles/cm and an optimal interelectrode spacing of about 3mm is needed for extraction of cortical patterns from scalp EEGs in humans.
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Dynamical properties of neural populations are studied using probabilistic cellular automata. Previous work demonstrated the emergence of critical behavior as the function of system noise and density of long-range axonal connections. Finite-size scaling theory identified critical properties, which were consistent with properties of a weak Ising universality class. The present work extends the studies to neural populations with excitatory and inhibitory interactions. It is shown that the populations can exhibit narrow-band oscillations when confined to a range of inhibition levels, with clear boundaries marking the parameter region of prominent oscillations. Phase diagrams have been constructed to characterize unimodal, bimodal, and quadromodal oscillatory states. The significance of these findings is discussed in the context of large-scale narrow-band oscillations in neural tissues, as observed in electroencephalographic and magnetoencephalographic measurements.
Pathology of heart cells in some arrgythmias was studied by nonlinear dynamic analysis developed recently. On the basis of computer simulation, the authors suggested that some arrhythmias might be due to nonlinerarity of cellular ionic channel. Relation between arrhythmial due to digitalis Poisioning and bifurcation solution of nonlinear dynamic equation was discussed in details.
The scalp and cortex lie like pages of an open book on which the cortex enciphers vast quantities of information and knowledge. They are recorded and analyzed as temporal and spatial patterns in the electroencephalogram and electrocorticogram. This book describes basic tools and concepts needed to measure and decipher the patterns extracted from the EEG and ECoG. This book emphasizes the need for single trial analysis using new methods and paradigms, as well as large, high-density spatial arrays of electrodes for pattern sampling. The deciphered patterns reveal neural mechanisms by which brains process sensory information into precepts and concepts. It describes the brain as a thermodynamic system that uses chemical energy to construct knowledge. The results are intended for use in the search for the neural correlates of intention, attention, perception and learning; in the design of human brain-computer interfaces enabling mental control of machines; and in exploring and explaining the physicochemical foundation of biological intelligence. © Springer Science+Business Media New York 2013. All rights are reserved.
We propose a subdural electrode array guided by a φ 0.3 mm SMA guidewire for a minimally-invasive method of electrocorticogram recording. The measured electric characteristics show that the proposed electrodes are compatible with the application of electrocorticogram recording. Somatosensory evoked potential is measured by the proposed method in the animal test in vivo. The results confirm that the proposed electrode array is available for the ECoG recording under a minimally invasive surgery.
Sensory information processing and cognition in brains are modeled using dynamic systems theory. The brain's dynamic state is described by a trajectory evolving in a high-dimensional state space. We introduce a hierarchy of random cellular automata as the mathematical tools to describe the spatio-temporal dynamics of the cortex. The corresponding brain model is called neuropercolation which has distinct advantages compared to traditional models using differential equations, especially in describing spatio-temporal discontinuities in the form of phase transitions. Phase transitions demarcate singularities in brain operations at critical conditions, which are viewed as hallmarks of higher cognition and awareness experience. The introduced Monte-Carlo simulations obtained by parallel computing point to the importance of computer implementations using very large-scale integration (VLSI) and analog platforms.
Prior studies of multichannel ECoG from animals showed that beta and gamma oscillations carried perceptual information in both local and global spatial patterns of amplitude modulation, when the subjects were trained to discriminate conditioned stimuli (CS). Here the hypothesis was tested that similar patterns could be found in the scalp EEG human subjects trained to discriminate simultaneous visual-auditory CS. Signals were continuously recorded from 64 equispaced scalp electrodes and band-pass filtered. The Hilbert transform gave the analytic phase, which segmented the EEG into temporal frames, and the analytic amplitude, which expressed the pattern in each frame as a feature vector. Methods applied to the ECoG were adapted to the EEG for systematic search of the beta-gamma spectrum, the time period after CS onset, and the scalp surface to locate patterns that could be classified with respect to type of CS. Spatial patterns of EEG amplitude modulation were found from all subjects that could be classified with respect to stimulus combination type significantly above chance levels. The patterns were found in the beta range (15-22 Hz) but not in the gamma range. They occurred in three short bursts following CS onset. They were non-local, occupying the entire array. Our results suggest that the scalp EEG can yield information about the timing of episodically synchronized brain activity in higher cognitive function, so that future studies in brain-computer interfacing can be better focused. Our methods may be most valuable for analyzing data from dense arrays with very high spatial and temporal sampling rates.