Open loop optogenetic control of simulated cortical epileptiform activity.

We present a model for the use of open loop optogenetic control to inhibit epileptiform activity in a meso scale model of the human cortex. The meso scale cortical model first developed by Liley et al. (2001) is extended to two dimensions and the nature of the seizure waves is studied. We adapt to the meso scale a 4 state functional model of Channelrhodopsin-2 (ChR2) ion channels. The effects of pulsed and constant illumination on the conductance of these ion channels is presented. The inhibitory cell population is targeted for the application of open loop control. Seizure waves are successfully suppressed and the inherent properties of the optogenetic channels ensures charge balance in the cortex, protecting it from damage.

Spatial patterning of the neonatal EEG suggests a need for a high number of electrodes.

There is an increasing demand for source analysis of neonatal EEG, but currently there is inadequate knowledge about i) the spatial patterning of neonatal scalp EEG and hence ii) the number of electrodes needed to capture neonatal EEG in full spatial detail. This study addresses these issues by using a very high density (2.5mm interelectrode spacing) linear electrode array to assess the spatial power spectrum, by using a high density (64 electrodes) EEG cap to assess the spatial extent of the common oscillatory bouts in the neonatal EEG and by using a neonatal size spherical head model to assess the effects of source depth and skull conductivities on the spatial frequency spectrum. The linear array recordings show that the spatial power spectrum decays rapidly until about 0.5-0.8 cycles per centimeter. The dense array EEG recordings show that the amplitude of oscillatory events decays within 4-6 cm to the level of global background activity, and that the higher frequencies (12-20 Hz) show the most rapid spatial decline in amplitude. Simulation with spherical head model showed that realistic variation in skull conductivity and source depths can both introduce orders of magnitude difference in the spatial frequency of the scalp EEG. Calculation of spatial Nyquist frequencies from the spatial power spectra suggests that an interelectrode distance of about 6-10mm would suffice to capture the full spatial texture of the raw EEG signal at the neonatal scalp without spatial aliasing or under-sampling. The spatial decay of oscillatory events suggests that a full representation of their spatial characteristics requires an interelectrode distance of 10-20mm. The findings show that the conventional way of recording neonatal EEG with about 10 electrodes ignores most spatial EEG content, that increasing the electrode density is necessary to improve neonatal EEG source localization and information extraction, and that prospective source models will need to carefully consider the neonatally relevant ranges of tissue conductivities and source depths when source localizing cortical activity in neonates.

The emergence of mind and emotion in the evolution of neocortex.

The most deeply transformative concept for the growth of 21st Century psychiatry is the constellation of the chaotic dynamics of the brain. Brains are no longer seen as rational systems that are plagued with emotional disorders reflecting primitives inherited from our animal ancestors. Brains are dynamical systems that continually create patterns by acting intentionally into the environment and shaping themselves in accord with the sensory consequences of their intended actions. Emotions are now seen not as reversions to animal behaviors but as the sources of force and energy that brains require for the actions they take to understand the world and themselves. Humans are unique in experiencing consciousness of their own actions, which they experience as conscience: guilt, shame, pride and joy. Chaotic brain dynamics strives always for unity and harmony, but as a necessary condition for adaptation to a changing world, it repeatedly lapses into disorder. The successes are seen in the normal unity of consciousness; the failures are seen in the disorders that we rightly label the schizophrenias and the less severe character disorders. The foundation for healthy unity is revealed by studies in the evolution of brains, in particular the way in which neocortex of mammals emerged from the primitive allocortex of reptiles. The amazing facts of brain dynamics are now falling into several places. The power-law connectivity of cortex supports the scale-free dynamics of the global workspace in brains ranging from mouse to whale. That dynamics in humans holds the secrets of speech and symbol utilization. By recursive interactions in vast areas of human neocortex the scale-free connectivity supports our unified consciousness. Here in this dynamics are to be sought the keys to understanding and treating the disorders that uniquely plague the human mind.

Controversies in epilepsy: debates held during the Fourth International Workshop on Seizure Prediction.

Debates on six controversial topics were held during the Fourth International Workshop on Seizure Prediction (IWSP4) convened in Kansas City, KS, USA, July 4-7, 2009. The topics were (1) Ictogenesis: Focus versus Network? (2) Spikes and Seizures: Step-relatives or Siblings? (3) Ictogenesis: A Result of Hyposynchrony? (4) Can Focal Seizures Be Caused by Excessive Inhibition? (5) Do High-Frequency Oscillations Provide Relevant Independent Information? (6) Phase Synchronization: Is It Worthwhile as Measured? This article, written by the IWSP4 organizing committee and the debaters, summarizes the arguments presented during the debates.

Similarities between simulated spatial spectra of scalp EEG, MEG and structural MRI.

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 0.22 cycles/cm (wavelength 20-4.545 cm) and the other from 0.22 to 1.2 cycles/cm (wavelength 4.545-0.834 cm). The PSD of the cortex showed a broad peak from 0.08 to 0.32 cycles/cm (wavelength 12.5-3.125 cm) and other two peaks within the range of 0.32 to 0.9 cycles/cm (wavelength 3.125-1.11 cm). These peaks are definitely due to the gyri structures and associated larger patterns on the cortical surface. Smaller peaks in the range of 1-3 cycles/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 3.0 cycles/cm and an optimal interelectrode spacing of about 3 mm is needed for extraction of cortical patterns from scalp EEGs in humans.

Power spectral density changes and language lateralization during covert object naming tasks measured with high-density EEG recordings.

Our objective was to study changes in EEG time-domain power spectral density (PSDt) and localization of language areas during covert object naming tasks in human subjects with epilepsy. EEG data for subjects with epilepsy were acquired during the covert object naming tasks using a net of 256 electrodes. The trials required each subject to provide the names of common objects presented every 4 seconds on slides. Each trial comprised the 1.0 second before and 3.0 seconds after initial object presentation. PSDt values at baseline and during tasks were calculated in the theta, alpha, beta, low gamma, and high gamma bands. The spatial contour plots reveal that PSDt values during object naming were 10-20% higher than the baseline values for different bands. Language was lateralized to left frontal or temporal areas. In all cases, the Wada test disclosed language lateralization to the left hemisphere as well.

A pseudo-equilibrium thermodynamic model of information processing in nonlinear brain dynamics.

Computational models of brain dynamics fall short of performance in speed and robustness of pattern recognition in detecting minute but highly significant pattern fragments. A novel model employs the properties of thermodynamic systems operating far from equilibrium, which is analyzed by linearization near adaptive operating points using root locus techniques. Such systems construct order by dissipating energy. Reinforcement learning of conditioned stimuli creates a landscape of attractors and their basins in each sensory cortex by forming nerve cell assemblies in cortical connectivity. Retrieval of a selected category of stored knowledge is by a phase transition that is induced by a conditioned stimulus, and that leads to pattern self-organization. Near self-regulated criticality the cortical background activity displays aperiodic null spikes at which analytic amplitude nears zero, and which constitute a form of Rayleigh noise. Phase transitions in recognition and recall are initiated at null spikes in the presence of an input signal, owing to the high signal-to-noise ratio that facilitates capture of cortex by an attractor, even by very weak activity that is typically evoked by a conditioned stimulus.

Simulating cortical background activity at rest with filtered noise.

Phase slip and beat phenomena are ubiquitous in many forms of wave superposition. Likewise, it is trivially true that cumulative summation of individual random events gives rise to "brown noise" (1/f(2) power spectrum). This paper presents a simulation that relates these phenomena with cortical function. We report that phase interference in the distributed frequencies of oscillation in bandpass-filtered brown noise gives null power spikes like those in the electrocorticograms (ECoG) from test subjects. The null spikes coincide with the onsets of frames in which the spatial amplitude patterns are classifiable with respect to conditioned stimuli. We report similarity in the waveforms and amplitude distributions of null spikes upon filtering brown noise in bands corresponding to the theta, alpha, beta and gamma ranges in experimental and simulated ECoG. We estimate a threshold in null spike minimal amplitudes below which perceptual frames having gamma oscillations may recur at theta rates.

Intermittent spatio-temporal desynchronization and sequenced synchrony in ECoG signals.

Electrocorticographic (ECoG) signals from the brain surface typically exhibit high synchrony across large cortical areas, interrupted by brief periods of desynchronization exhibiting propagating phase discontinuities, across which spatial patterns of phase emerge in selected frequency bands. Experiments with rabbits trained using classical conditioning paradigms indicated that such desynchronization periods demarcate cognitive processing in the subjects; the ECoG in the frames between such periods revealed spatial patterns of amplitude modulation that were classified with respect to sensory stimuli that the rabbits had been trained to recognize. The present work describes intermittent synchrony and desynchronization of ECoG signals measured over the visual cortex. We analyze the analytic amplitude (AA) and analytic phase (AP) of the signals bandpassed over the beta band (12.5-25 Hz) and theta band (3-7 Hz) using the Hilbert transform. The AP of analytic signals evaluated using a Shannon-based synchronization index in theta band exhibits phase synchronization for varying time periods averaging about 1 s, interrupted by desynchronization periods of duration about 0.1 s. Synchronization periods in the beta-band last <100 ms, with interruptions by desynchronization lasting one-tenth that, in which the analytic amplitude drops drastically. During these "null spikes," the analytic phase is undefined, and the spatial and temporal phase differences show high dispersion. Detailed examination of the bandpass filtered ECoG confirms the presence of a shared mean frequency in a frame of synchronized oscillation, at which frequency the spatial pattern of the AP has the form of a cone. Between frames the AA approaches zero. The form of the null spike resembles a tornado (a vortex), as shown in sequential frames by a rotating spatial pattern of amplitude in the filtered ECoG.

The place of 'codes' in nonlinear neurodynamics.

A key problem in cognitive science is to explain the neural mechanisms of the rapid transposition between stimulus energy and abstract concept--between the specific and the generic--in both material and conceptual aspects, not between neural and psychic aspects. Three approaches by researchers to a solution in terms of neural codes are considered. Materialists seek rate and frequency codes in the interspike intervals of trains of action potentials induced by stimuli and carried by topologically organized axonal lines. Cognitivists refer to the symbol grounding problem and search for symbolic codes in firings of hierarchically organized feature-detector neurons of phonemes, lines, odorants, pressures, etc., that object-detector neurons bind into representations of probabilities of stimulus occurrence. Dynamicists seek neural correlates of stimuli and associated behaviors in spatial patterns of oscillatory fields of dendritic activity that self-organize and evolve as trajectories through high-dimensional brain state space; the codes are landscapes of chaotic attractors. Unlike codes in DNA and the periodic table, these codes have neither alphabet nor syntax. They are epistemological metaphors required by experimentalists to measure neural activity and by engineers to model brain functions. Here I review the central neural mechanisms of olfaction as a paradigm for use of codes to explain how brains create cortical activities that mediate sensation, perception, comprehension, prediction, decision, and action or inaction.

Indirect biological measures of consciousness from field studies of brains as dynamical systems.

Consciousness fully supervenes when the 1.5 kgm mass of protoplasm in the head directs the body into material and social environments and engages in reciprocity. While consciousness is not susceptible to direct measurement, a limited form exercised in animals and pre-lingual children can be measured indirectly with biological assays of arousal, intention and attention. In this essay consciousness is viewed as operating simultaneously in a field at all levels ranging from subatomic to social. The relations and transpositions between levels require sophisticated mathematical treatments that are largely still to be devised. In anticipation of those developments the available experimental data are reviewed concerning the state variables in several levels that collectively constitute the substrate of biological consciousness. The basic metaphors are described that represent the neural machinery of transposition in consciousness. The processes are sketched by which spatiotemporal neural activity patterns emerge as fields that may represent the contents of consciousness. The results of dynamical analysis are discussed in terms serving to distinguish between the neural point processes dictated by the neuron doctrine vs. continuously variable neural fields generated by neural masses in cortex.

Cinematic Operation of the Cerebral Cortex Interpreted via Critical Transitions in Self-Organized Dynamic Systems.

Measurements of local field potentials over the cortical surface and the scalp of animals and human subjects reveal intermittent bursts of beta and gamma oscillations. During the bursts, narrow-band metastable amplitude modulation (AM) patters emerge for a fraction of a second and ultimately dissolve to the broad-band random background activity. The burst process depends on previously learnt conditioned stimuli (CS), thus different AM patterns may emerge in response to different CS. This observation leads to our cinematic theory of cognition when perception happens in discrete steps manifested in the sequence of AM patterns. Our article summarizes findings in the past decades on experimental evidence of cinematic theory of cognition and relevant mathematical models. We treat cortices as dissipative systems that self-organize themselves near a critical level of activity that is a non-equilibrium metastable state. Criticality is arguably a key aspect of brains in their rapid adaptation, reconfiguration, high storage capacity, and sensitive response to external stimuli. Self-organized criticality (SOC) became an important concept to describe neural systems. We argue that transitions from one AM pattern to the other require the concept of phase transitions, extending beyond the dynamics described by SOC. We employ random graph theory (RGT) and percolation dynamics as fundamental mathematical approaches to model fluctuations in the cortical tissue. Our results indicate that perceptions are formed through a phase transition from a disorganized (high entropy) to a well-organized (low entropy) state, which explains the swiftness of the emergence of the perceptual experience in response to learned stimuli.

Origin, structure, and role of background EEG activity. Part 4: Neural frame simulation.

OBJECTIVE: To develop a method for simulating background EEG based on the premise that the self-organized activity from synaptic interaction among populations of neurons creates sustained fluctuations that can be modeled with the filtered output of a random number generator. METHODS: The logarithm of the amplitude of activity was weighted in accordance with 1/f, the log frequency in both temporal (PSD(T)) and spatial (PSD(X)) power spectral densities. The activity was spatially smoothed by volume conduction. Further deviation from full randomness was by sustained spatial coherence averaging 25% of total power. The departure from the background state to an active state, as seen in the awake EEG, was simulated by adding segments that were 90% correlated while attenuating by 50% the uncorrelated background activity in those segments. Spatial amplitude modulation was imposed on the correlated noise to create signals that simulated AM patterns. RESULTS: The statistical properties of the EEG that were replicated (Freeman, 2004a,b, 2005) included the PSD(T), PSD(X), point spread function (PSF), partitioning of the variance with PCA, and the percentages of correct classification of AM patterns. CONCLUSIONS: The origin of background EEG was traced to self-sustaining mutual excitation among pyramidal cells creating stable noise that was filtered by self-organized criticality to give 1/f(2) PSD, by inhibitory feedback to give oscillations in the classic clinical bands, and by volume conduction to give smoothing. The essential change that identified a frame in EEG was transient synchrony by phase transition among cortical populations in beta and gamma bands of the PSD(T). SIGNIFICANCE: This simulation can provide test data with which to optimize techniques for noninvasively extracting information from the EEG for diagnosis and treatment evaluation of neuropsychiatric disorders and for operation by paraplegics of prosthetic devices.

Fine spatiotemporal structure of phase in human intracranial EEG.

OBJECTIVE: To transfer to the clinic for humans the technology and theory for high-resolution EEG analysis that have been developed in the laboratory with animals. METHODS: EEGs were recorded at high spatial resolution from a 1 x 1 cm 8 x 8 electrode array on the right inferior temporal gyrus of a patient undergoing preoperative monitoring for epilepsy surgery. Cosines were fitted to EEG segments to measure frequency and phase and compute location, size, latency, phase velocity, duration, and recurrence rate of radially symmetric spatial patterns called phase cones. The Hilbert transform was also used to get high temporal resolution. RESULTS: In the awake state, the power spectral density (PSD) showed power-law decrease in log power with log frequency at 1/falpha, alpha approximately 2, but with peaks in the standard empirical ranges. The phase in beta and gamma ranges had spatial gradients in conic form. Resetting of these stable spatial patterns of phase cones was spatially coincident at intermittent discontinuities ('phase slip') recurring at theta rates. Cones had half power diameters from 2 to 50+ mm; their durations had power-law distributions with values ranging from 6 to 300+ ms depending on length of the analysis window. In slow wave sleep PSD decreased at 1/falpha, alpha approximately 3,with loss of beta-gamma spectral peaks and diminished or absent oscillations and spatiotemporal phase structure. CONCLUSIONS: Spatiotemporal structures in awake human and rabbit EEG showed striking similarities. The only clear differences were ascribable to differing scales of measurement. These fine spatiotemporal structures of EEG were diminished or lost in slow wave sleep. SIGNIFICANCE: The fine structure indicates that neocortical stability is sustained at self-organized criticality; that synaptic input in the awake state drives neocortex away from criticality causing beta-gamma oscillations in re-stabilizing 'neural avalanches'; and that diminished input in slow wave sleep allows return toward criticality but with some added risk of instability and seizure.

A cinematographic hypothesis of cortical dynamics in perception.

The aim of this study was to measure and classify spatial patterns in sensory cortical EEGs relating to conditioned stimuli (CSs) in order to test the hypothesis, based on clinical reports, that cortical dynamics is not continuous but operates in steps that resemble frames in a cinema. Recent advances in the application of the Hilbert Transform to intracranial recordings of the EEG in animals have revealed markers for repetitive phase transitions in neocortex at frame rates in the theta band. The frames were sought in multichannel EEGs that had been recorded from 8x8 high-density arrays that were fixed on primary sensory cortices of rabbits trained to discriminate visual, auditory or somatic conditioned stimuli with reinforcement (CS+) or without (CS-). Localization of frames in EEGs was by use of a new index, H(e)(t), called "pragmatic information". Each spatial pattern was represented by a feature vector from the 64 analytic amplitudes at a maximal value of H(e)(t) from the Hilbert transform and expressed as a 64x1 feature vector specifying a point in 64-space. Classification with respect to CS+/- was by calculation of Euclidean distances of points from centers of gravity of clusters after preprocessing by nonlinear mapping. Stable spatial patterns were found in the form of amplitude modulation (AM) of aperiodic waveforms that included all channels. The impact of a CS on a sensory neocortex reorganized background EEG into two types of sequential patterns of coordinated activity, initially local and modality-specific, later global. The initial stage of phase transitions required 3-7 ms. Large-scale cortical activity then reorganized itself repeatedly and reliably over relatively immense cortical distances within the cycle duration of the center frequency of oscillation. The size, texture, timing, and duration of the AM patterns support the hypothesis that these frames may provide the basis for multisensory percepts (Gestalts).

Breathing as a Fundamental Rhythm of Brain Function.

Ongoing fluctuations of neuronal activity have long been considered intrinsic noise that introduces unavoidable and unwanted variability into neuronal processing, which the brain eliminates by averaging across population activity (Georgopoulos et al., 1986; Lee et al., 1988; Shadlen and Newsome, 1994; Maynard et al., 1999). It is now understood, that the seemingly random fluctuations of cortical activity form highly structured patterns, including oscillations at various frequencies, that modulate evoked neuronal responses (Arieli et al., 1996; Poulet and Petersen, 2008; He, 2013) and affect sensory perception (Linkenkaer-Hansen et al., 2004; Boly et al., 2007; Sadaghiani et al., 2009; Vinnik et al., 2012; Palva et al., 2013). Ongoing cortical activity is driven by proprioceptive and interoceptive inputs. In addition, it is partially intrinsically generated in which case it may be related to mental processes (Fox and Raichle, 2007; Deco et al., 2011). Here we argue that respiration, via multiple sensory pathways, contributes a rhythmic component to the ongoing cortical activity. We suggest that this rhythmic activity modulates the temporal organization of cortical neurodynamics, thereby linking higher cortical functions to the process of breathing.

Origin, structure, and role of background EEG activity. Part 3. Neural frame classification.

OBJECTIVE: To show that cortical responses to conditioned stimuli (CS) include intermittently induced spatial patterns of amplitude modulation (AM) of beta-gamma oscillation called frames. METHODS: EEGs were recorded from 8x8 high-density arrays fixed on primary sensory cortices of rabbits trained to discriminate CS with reinforcement (CS+) from those without (CS-). EEG frames were located with a pragmatic information index, H(e). The spatial patterns of the first 3 frames on each of 37-40 trials were measured by the square of 64 analytic amplitudes from the Hilbert transform to give points in 64-space. The questions were asked: Did the frames from CS+ trials and CS- trials differ within each sequential group? Did the 3 frames differ from each other (form 3 clusters of points)? RESULTS: EEG frames that were identified by high H(e) had AM patterns that could be classified with respect to CS+ and CS- well above chance levels. Two stages of correct frame classification occurred on each trial: 40-130 ms after CS onset with a gamma carrier frequency, and 450-550 ms with a beta carrier frequency. Peak power in the beta frames was double that in gamma frames, and mean pattern surface area of beta frames was nearly 4-fold greater. CONCLUSIONS: Under the impact of a CS on a sensory neocortex, the background EEG activity reorganized in sequential frames of coordinated activity, first local and modality-specific, thereafter global. SIGNIFICANCE: The size, texture and duration of these AM patterns indicate that spatial patterns of human beta frames may be accessible with high-density scalp arrays for correlation with phenomenological reports by human subjects.

Metastability, instability, and state transition in neocortex.

Mesoscopic patterns of neural activity were sought in multichannel EEGs of rabbits that were trained to respond to conditioned stimuli (CSs) in visual, auditory and somatic modalities. Spatiotemporal patterns were sought of oscillations in the beta and gamma ranges. The techniques required for preprocessing EEGs in search of global patterns were diametrically opposed to those needed for localization of modular EEG signals. Frames were found in the form of intermittent spatial patterns of phase and amplitude modulation (AM and PM) of carrier waves in beta and gamma ranges that served to classify EEG frames with respect to CSs. A model based on the intentional action-perception cycle is proposed to complement the information processing model.

Ndn, volume transmission, and self-organization in brain dynamics.

Fields of neural activity are seen in synchronized oscillations that are detected at mesoscopic scales in syntheses of multicellular recordings of action potentials and electroencephalograms (EEGs) over broad areas of cerebral cortex. The waves often have large-scale, highly textured spatial patterns of cortical activity, formed in the context of associative learning under classical and operant conditioning in rabbits. The patterns show spatial amplitude modulation of shared oscillations of carrier waves in the beta and gamma ranges of the EEG, with recurrence at frame rates in the alpha and theta ranges. The frames also show spatial phase modulation that is inconsistent with driving of the oscillations by focal pacemakers. The hypothesis is developed that the synchronization manifests continuous distributions of activity in cortical neuropil that modulate firings of selected neural networks embedded in the neuropil. Five interactive agencies have been postulated to explain the mechanism for the field synchrony: electric fields; magnetic fields; electromagnetic fields (radio waves); diffusion chemical gradients; and order parameters that control self-organization of large populations of neurons by widespread synaptic interaction constituting negative and positive feedback. Only the last interactive agency fits the data. The points are emphasized that these field patterns in frames require interactive neural dynamics that is modulated in respect to global operations mediating arousal, attention, selective emotional stance, wake, sleep, learn, habituate, dishabituate, etc., and that these operations require differing but complementary fields that form by massive parallel feed-forward architectures of brainstem neuromodulatory nuclei. An example is given using histamine of the neural discharges of brainstem nuclei that do not require fine spatiotemporal texturing of their firing; they operate by nonsynaptic release of neuromodulators that effect changes in background state, such that textured patterns of cortical activity can form and update in flexible adaptations of brains to their environments. These systems instantiate volume transmission by nonsynaptic diffusion transmission, in concert with the self-organization of the textured neural activity that supports cognition.

Mechanism and significance of global coherence in scalp EEG.

What distinguishes animals from robots is the neurodynamics of intention. The mechanism is the action-perception cycle that creates and applies knowledge. Knowledge is the condensed, categorized information brains accumulate over lifetimes of experience. Vertebrate intention emerged in the Ordovician period as a tool to prowl first olfactory environments, then environments of other modalities. Action necessitates remembering space-time trajectories. Hence the sensory, motor, and hippocampal cortices interact intimately. Brains create the contextual richness of relevant knowledge almost instantly by exploiting the capacity of cortical neuropil to transit between a gas-like phase with sparse, random firing and a liquid-liked phase of high-energy, narrow band oscillation synchronized widely. They express remembrances in spatial patterns of amplitude modulation (AM) of beta and gamma waves.