Rhythms of the Brain by György Buzsaki: Review and Excerpts

Spike-waves

Buzsaki presents a difficult subject in a commendably clear manner. It is an exemplary piece of scientific writing produced by one of the grand old men of brain wave research. A growing literature, which has expanded significantly since the book’s publication in 2006, suggests neural oscillations are not “noise” or novelties for someone interested in the minutiae of neuroscience, but fundamental to understanding perception, peak performance, emotional regulation, memory formation, the organization of the various “levels” of the brain, a variety of psychiatric illnesses, and consciousness itself.

“There is no good reason to assume that the brain is organized in accordance with the concepts of folk psychology.”

—Cornelius H. Vanderwolf

“Berger called the large-amplitude rhythm (approximately 10 waves per second, or 10 hertz), which was induced by eye closure in the awake, calm subject, the “alpha” rhythm because he observed this rhythm first. He named the faster, smaller amplitude waves, present when the eyes were open, ‘beta’ waves. Paradoxically, Berger’s recordings provided firm physical evidence against his idea that waves generated by one brain could somehow be detected by another brain.”

“Assuredly, neuronal oscillators are quite complex. Nevertheless, the principles that govern their operation are not fundamentally different from those of oscillators in other physical systems.”

“The intimate relationship between space and time is packaged into the concept of “spacetime” (x, y, z, t dimensions). Oscillations can be conceived of and dis- played in terms of either space or time. The phase-plane of a sinusoid harmonic oscillator 8 is a circle. We can walk the perimeter of the circle once, twice, or billion of times and yet we always get back to our starting point….”

“Linear causation works most of the time, and it is the foundation of many essential operations from catching a ball to solving a mysterious murder case. Causation can also fail. For example, in an oscillatory system, most or all neurons with reciprocal, one-way connections or no direct connections may discharge with a zero time lag (i.e., simultaneously), making linear causation impossible….

If the second ball starts moving in the same direction after the arrival of the first ball, we conclude from the timing of the events that the first ball caused the second one to move. However, derivation of such a conclusion depends critically on the exact timing of the events. We make the inference of causality only if the second ball begins to move within 70 milliseconds after the first ball reaches it.”

“Although in this case a simple cause–effect (unexpected object–braking) relationship exists, mental reconstruction offers a different cause. The brain takes into consideration the conduction velocities of its own hardware and compensates for it. For example, touching your nose and toe at the same physical time (or touching your nose with your toe) feels simultaneous even though neuronal events in the cerebrum, representing the touch of two body parts, are delayed by several tens of milliseconds.”

“ ‘Representation’ of external reality is therefore a continual adjustment of the brain’s self-generated patterns by outside influences, a process called “experience” by psychologists. From the above perspective, therefore, the engineering term “calibration” is synonymous with “experience.”

“A quick glance through the Cycles makes it clear that the title Rhythms of the Brain is a bit grandiose relative to the modest content of the book. Many important topics are omitted or glossed over. The vital oscillations generated by the spinal cord and brainstem are completely ignored, and the bulk of the discussion is centered on cortical systems of the mammalian brain. Circadian and other long period oscillations are discussed only as they pertain to the faster neuronal events.”

“The basic circuit capable of the aforementioned control functions is recognizable in all vertebrate brains, small and large. During the course of evolution, the basic circuit is not fundamentally modified, but instead, multiple parallel circuits, consisting of intermediate and longer chains of neurons, are superimposed on the existing wiring. No matter what fraction of the brain web we are investigating, neuronal loops are the principal organization at nearly all levels. A physicist would call this multi-level, self-similar organization a fractal of loops.”

“For the sake of simplicity, let us start with just 50 neurons. To link each of these neurons to all other neurons would require 1,225 bidirectional connections. But we know that this is not the brain’s choice. Neurons are not connected to all other neurons but only to a fraction of them. What is the minimum number of links that can connect each neuron to at least one of its partners? The general solution to this sort of a problem is the most famous in graph theory. It took the genius of two mathematicians, Paul Erdös and Alfréd Rényi, to solve this puzzle. They showed, that using just 98 randomly placed links, a mere 8 percent of the 1,225 all-to-all connections, we can connect all 50 nodes (neurons).”

“The number of random links required to keep the synaptic path length short increases much less than the size of the network. In other words, the larger the network, the greater the impact of each random link on the effective connectivity of the network.”

“By examining the accessibility of the websites on the Internet, his team realized that traffic is directed mostly toward a handful of busy sites, for example, the search engine Google and the popular e-store Amazon.com. These popular hubs are visited orders of magnitude more frequently than, say, my website. Barabási argued that many real-world networks, including the Web, evolve by some rules but they cannot be described by illustrating a typical, representative example. Instead, the connections in these ‘scale-free’ networks obey a statistical rule called the power law.”

“In scale-free systems, things are different. In systems governed by power law statistics, there is no peak at an average value, and a select small group can have the largest effect. For example, if we drop a vase on the floor, it will break into fragments of varying size. There will be a lot of debris but also a number of reasonably large fragments. If we collect all the pieces, from the microscopic ones to the large, and plot their numbers as a function of size on a log–log scale, we will get an oblique line: a power law for fractures. No one fragment can be considered as the characteristic size. There is no “typical example” in a scale-free system. A power law implies that there is no such thing as a normal or characteristic size scale and that there is no qualitative difference between the larger and smaller pieces or events.”

“Giulio Tononi, Olaf Sporns, and Gerald Edelman from the Neurosciences Institute in La Jolla, California, searched for a structure-based metric that could more objectively define ‘neuronal complexity’ and capture the relationship between functional segregation and global integration of function in the brain. Using the concepts of statistical entropy and mutual information, they estimated the relative statistical independence of model systems with various connectivity structures. Not surprisingly, they found that statistical independence is low when system constituents are either completely independent (segregated) or completely dependent (integrated).”

“Its robust local tensegrity organization has allowed continuous growth from the small brain of a tree shrew to the giant brain of the whale… The cerebral cortex is a scalable and robust spherical structure. 33 Its modular plan is identical in all mammals, with five layers of principal cells and a thin superficial layer containing mostly distal apical dendrites and horizontal axons.”

“Tensegrity dynamics can be maintained only if the excitatory effects are balanced by equally effective inhibitory forces, provided by specialized inhibitory neurons. If only excitatory cells were present in the brain, neurons could not create form or order or secure some autonomy for themselves. Principal cells can do only one thing: excite each other. In the absence of inhibition, any external input, weak or strong, would generate more or less the same one-way pattern, an avalanche of excitation involving the whole population.”

“A textbook example of a state transition is the shift between water and ice.  A slight change in temperature (an externally imposed influence) can shift the state in either direction. If a system, for example, a neural network, can self-organize in such a way as to maintain itself near the phase transition, it can stay in this ‘sensitized’ or metastable state until perturbed.”

“For example, the thalamus, basal ganglia, and the cerebellum possess a low degree of variability in their neuron types. In contrast, cortical structures have evolved not only five principal-cell types but also numerous classes of GABAergic inhibitory interneurons.”

“How can such a minority group keep in check the excitatory effects brought about by the majority principal cells in cortical networks? Interneurons deploy numerous mechanisms to meet this challenge. In contrast to the typically weak synaptic connections between principal cells, principal cell–interneuron connections are strong. In the return direction, a typical interneuron innervates a principal cell with 5–15 synaptic terminals (or boutons). Furthermore, almost half of the inhibitory terminals are placed at strategically critical positions for controlling action potential output.”

“The primary role of the interneuron networks is to coordinate timing of the action potentials. This task becomes more and more complex as the brain grows because neurons are placed farther apart from each other.”

“The seismologists’ task is literally identical to that of a neurologist who attempts to localize the source of an epileptic seizure from scalp recordings. The source localization problem or, as engineers call it, the “inverse problem” is the task of recovering the elements and location of the neural field generators based on the spatially averaged activity detected by the scalp electrodes. However, surface recordings provide only limited information about the structures and neuron groups from which the hypersynchronous epileptic activity emanates, and the inverse problem does not have a unique solution.”

“The complex EEG or MEG waveform can be reproduced by an appropriate combination of sine waves. This method is similar to the trick used by electronic synthesizers that can make convincing acoustical forgeries of everything from trombones to harps. It is done by a mathematical process called Fourier synthesis, named after the French mathematician Joseph Fourier. 32 The reverse process, called Fourier analysis, takes the complex EEG or MEG signal and decomposes it into the sine waves that make it up. After the signal is decomposed into sine waves, a compressed representation of the relative dominance of the various frequencies can be constructed. This frequency versus incidence illustration is known as the power spectrum. The Fourier method transforms the signal, defined in the time domain, into one defined in the frequency domain.”

“For example, random noise is defined as uncorrelated because it is similar only to itself, and any small amount of temporal shift results in no correlation with the unshifted signal at all. In contrast, oscillating signals go in and out of phase when shifted in time.”

“Coherence is the measure of the state in which two signals maintain a fixed phase relationship with each other or with a third signal that serves as a reference for each. The phase differences are often used to infer the direction of the force, although in most cases such inference is not possible…”

Page 109 lists several key definitions.

“Karl Friston emphasized the importance of short-lived transients in his “labile brain” series (Friston, 2000). According to Friston, brain dynamics move from a stable incoherence through dynamic instability to complete entrainment. A similar idea is echoed by the chaotic organization of Walter Freeman’s “wave packets” (Freeman and Rogers, 2002; Freeman et al., 2003) and the “neural moment” of transient synchrony of Hopfield and Brody (2001). It is not clear, though, how stable incoherence (high entropy) can be maintained in an interconnected system, e.g., the brain. As Sporns et al. (2000a, b, 2002) have pointed out, high-complexity and high-entropy conditions require very different architectures.”

“Perhaps what makes music fundamentally different from (white) noise for the observer is that music has temporal patterns that are tuned to the brain’s ability to detect them because it is another brain that generates these patterns. The long-time and large-scale note structure of Bach’s First Brandenburg Concerto is quite similar to the latest hit played by a rock station or to Scott Joplin’s Piano Rags. 26 On the other hand, both high temporal predictability, such as the sound of dripping water, and total lack of predictability, such as John Cage’s stochastic “music” (essentially white noise) are quite annoying to most of us.”

“Psychophysical law that comes to mind in connection with the 1/f nature of cortical EEG is that of Weber and Fechner: the magnitude of a subjective sensation (a cognitive unit) increases proportionally to the logarithm of the stimulus intensity (a physical unit). For example, if a just-noticeable change in a visual sensation is produced by the addition of one candle to an original illumination of 100 candles, 10 candles will be required to detect a change in sensation when the original illumination is 1,000 candles. 28 According to Rodolfo Llinás at New York University, Weber’s law also underlies the octave tonal structure of music perception and production. He goes even further by suggesting that quale, 29 the feeling character of sensation, may “derive from electrical architectures embedded in neuronal circuits capable of such logarithmic order.”

“Pausing with this thought for a second, the math is not as simple as it looks. The seductively simple 1/f α function is, in fact, a very complex one. Every new computation forward takes into consideration the entire past history of the system. The response of a neuron depends on the immediate discharge history of the neuron and the long-term history of the connectivity of the network into which it is embedded. Assuming 100 independent neurons with spiking and nonspiking binary states, more than 10 30 different spike combinations are possible. However, only a very small fraction of these combinations can be realized in the brain because neurons are interconnected; thus, they are not independent constituents.”

“A household example of a relaxation oscillator is a dripping faucet. If the faucet is not turned off completely, it behaves like a metronome, generating water spheres and annoying sounds at regular intervals. The energy source that maintains the oscillation is the water pressure, whereas the balance between gravity and local viscosity determines the drop size. If the pressure is reduced, the interval between the drops increases; thus, the oscillator slows down, but the drop size remains the same. The frequency of the relaxation oscillator is calculated from the intervals between the pulses (water drops).”

“A good piano has good resonance because it amplifies the sound. Oftentimes, resonance is unwelcome because it amplifies events we want to avoid. Engineers of bridges and skyscrapers constantly struggle with unwanted resonance.”

“Resonant properties of neurons constrain them to respond most effectively to inputs at biologically important frequencies such as those associated with brain oscillations.”

“The astonishing conclusion from contemporary biophysics is that every part of the neuron can function as a resonator-oscillator. All the neuron needs is channel, activity with opposing actions and feedback to sustain the ying-yang game. Thus, a single neuron consists of myriads of potential resonators whose properties differ due to the different channel properties and densities of the membrane along the somatodendritic and axonal surface.”

“In its broad definition, synchrony refers to the concurrence of events in time, a relation that exists when things occur simultaneously, such as two or many neurons firing within a short time interval. Events that occur at different times are asynchronous. Although this definition of synchrony is found in most textbooks, it is not particularly useful. For two observers to have expectations of something occurring “at the same time” is meaningful only if they see the same clock. Furthermore, a “discrete time window” should be defined for the judgment of simultaneity. Otherwise, it is impossible to name the time at which something occurs…

If the same tune is played at the same time on the radio in both London and New York City, and the London broadcast is transmitted through the Internet, the tunes played by a radio and a computer in New York will not be judged as being simultaneous by a human listener. The same is true for an observer neuron that receives inputs from other neurons with different physical distances. If the difference in travel time of the action potentials from the presynaptic neurons is too long, the target neuron may treat them as asynchronous (separate) events.”

“For real neurons, however, the integration time window is much harder to determine and depends on a variety of factors, such as replenishment of the neurotransmitter in the presynaptic terminal, the actual resistance of the membrane, receptor types, the immediate spiking history of the neuron, and the state of the various conductances in general. When the neuron is very active, it becomes leaky and can integrate over a much shorter window than at times of low activity….

The slower the rhythm, the wider is the window of opportunity for synchronization. In a wider time window, more neurons can be recruited from larger brain areas because synaptic and axonal conductance delays are less limiting; thus, the spatial extent of synchrony is much larger in the case of a slow rhythm.”

“The optimal performance of man-made devices can be notoriously deteriorated by the presence of noise. But noise is not necessarily bad. An oft-quoted beneficial aspect of noise in bistable systems, for example, neurons, is its ability to amplify hidden periodic signals under certain conditions.”

“Noise can maintain spontaneous activity in computer models of neural networks. Signals become detectable due to resonance between the weak deterministic signal and stochastic noise.”

“Although signal amplification through noise appears advantageous for the brain, it has its own problems. A critical issue is the source of noise. Classical theories, in which the brain is viewed as a stimulus-driven device, assumed that spike response variability in response to an invariant input derives from unreliable individual neurons. 31 According to such view, a neuronal population can represent consistent and coherent decisions, but single cells within the population can cast different votes. These individually incongruent opinions are usually regarded as wasted action potentials from the representational point of view and are considered the source of synaptic noise. From the “population code” perspective, stochastic resonance is a clever mechanism because it can “recycle” the wasted action potentials. However, in contrast to the population code model, numerous recent works emphasize that action potentials are used sparingly in the brain, and spiking of neurons is much more reliable than previously thought.”

“Hebb’s cell assembly is a transient coalition of neurons, much like the dynamic interactions among jazz musicians. Members of the cell assembly are brought together by Hebb’s synaptic plasticity rule, on the basis of temporal relations among them: “When an axon of cell A is near enough to excite a cell B and repeatedly or persistently takes part in firing it, some growth process or metabolic change takes place in one or both cells such that A’s efficiency, as one of the cells firing B, is increased.”

“For example, in the hippocampus, spike transmission from pyramidal cell to interneuron is low at both low and high frequencies and highest at 15–40 hertz, which is the typical discharge frequency of an activated pyramidal neuron. In other words, a single but strongly “activated” pyramidal cell can exert an equal or larger effect in discharging its basket neurons than several dozen other presynaptic neurons discharging the same number of spikes because they target different, rather than the same, synapses. In essence, the high-frequency discharge of a pyramidal cell in its receptive field “enslaves” its basket cells through resonance tuning. In turn, the output of the basket cells suppresses the activity of the surrounding pyramidal neurons. Such “winner-take-all” or “rich-gets-richer” mechanisms are abundant in complex systems, from automatons to Bill Gates’s empire, and analogous mechanisms may be responsible for the segregation of neurons in networks strongly interconnected by excitatory collaterals.”

“Perhaps the most spectacular example of low-energy coupling, known to all physics and engineering majors, is the synchronization of Christiaan Huygens’s pendulum clocks. Huygens’s striking observation was that when two identical clocks were hung next to each other on the wall, their pendula became time-locked after some period. Synchrony did not happen when the clocks were placed on different walls in the room. Huygens’s clocks entrained because the extremely small vibrations of the wall that held both clocks were large enough that each rhythm affected the other.”

“However, when very large numbers of neurons come together with some time jitter, their integrated output, in principle, can be so smooth that the population may appear to behave like a sinusoid oscillator. In fact, this principle is routinely exploited by electric engineers to construct reliable sinusoid (i.e., harmonic) generators without the inconvenience of the inertia inherent in real sinusoid generators.”

“There are two requirements for an oscillator: opposing forces and positive feedback. Systems with opposing forces but without feedback can maintain only a transient oscillation with decreasing amplitude, a phenomenon called resonance. Neurons and networks with these properties preferentially treat inputs whose frequency matches their own resonance. Neuronal oscillators belong to the family of limit cycle or weakly chaotic oscillators. Two well-defined oscillators, harmonic and relaxation types, have numerous examples in the brain. Harmonic oscillators are good long-term predictors because their phase is constant. Relaxation oscillators can synchronize quickly and efficiently. Brain oscillators tend to exploit and combine these properties.”

“However, the information theory strategy cannot account for important functions of the brain that do not require immediate environmental inputs, including various the hard-to-define types of mental processing and sleep. I take a different approach in this book, beginning with the examination of the unperturbed, resting-sleeping brain and examining its evolving state changes.”

“The pattern of thalamic connectivity coevolved with the neocortex. However, cortical representations grew much more rapidly. For example, the number of thalamocortical neurons in the mouse is only an order of magnitude less than the number of target neurons in the cortex, whereas in the human brain the ratio is less than one to a thousand. Even though thalamic growth did not keep up with the fast development of the neocortex, higher order nuclei in primates are relatively larger than the first-order relays, indicating that allocation of divergent cortical–thalamic–cortical connections is more important for the evolution of the mammalian brain than enhancing the bandwidth capacity of primary sensory pathways.”

“This is interesting because the same cortical inputs can produce a diametrically opposite change in the network state, depending on the short-term history of the network. The mechanisms responsible for bringing the active network back to silence are not well understood. A combination of various factors, including decreasing. Input resistance of neurons, activity-dependent K + currents, and gain of inhibition over excitation, are considered opposing forces of excitation that collectively revert the network into a silent state. Anesthetics that increase K + conductance or potentiate the action of GABA can prolong the down state. In contrast, cortical neurons in the waking brain stay virtually constantly in the upstate. A major reason for this is that a main action of subcortical neurotransmitters is to decrease K + conductance of cortical neurons”

“The strong cholinergic activity during REM sleep and in the waking brain is mainly responsible for the lack of down states in cortical neurons. The most prominent oscillation of the waking brain is the family of alpha rhythms that occur selectively in every sensory and motor thalamocortical system in the absence of sensory inputs. Nevertheless, alpha oscillations are not simply a result of sensory disengagement but may reflect internal mental processing.”

“Similarly, Robert Stickgold and coleagues at Harvard Medical School found that the magnitude of memory enhancement after sleep was positively correlated with the amount of early-night slow-wave sleep, although it was also correlated with late-night REM sleep. Moreover, behavioral performance also increased after a daytime nap, which is dominated by slow-wave sleep.  Perhaps the most spectacular result in this area of research is the demonstration of sleep facilitation of creative insight. Did you ever wake up with the right answer to a problem that you could not solve the night before? To bring this folk psychology belief into the lab, Born’s team asked their subjects to generate number sequences that included a hidden rule—the second sequence was identical to the last in the series. Uncovering the hidden rule was possible only after several trials. The subjects were given only two trials before going to bed, not knowing about the hidden rule. A night’s sleep triggered insight of the rule the following morning in most subjects, whereas the same amount of time spent in waking during the day had little effect. These experiments provided the first controlled laboratory experiments for the widely known anecdotes of several famous scientists, writers, and musicians that sleep catalyzes the creative process. 14 The potential physiological basis of such associations are discussed in Cycle 12.”

“Brains of yogis and Zen practitioners, therefore, provide unexploited opportunities to examine the effects of long-termbehavioral training on brain rhythms. Unfortunately, it is difficult to obtain consent of highly trained contemplative yogis and students of Zen to participate in laboratory experiments. Not surprisingly, quantitative studies are rare. Nevertheless, the available evidence is telling. When absorbed in the Samadhi of Yoga meditation, when the self-versus-environment distinction disappears, external stimulation is largely ineffective in blocking alpha oscillations, whereas continued blocking without habituation is observed in Zen meditators. Both types of practice increase both the power and the spatial extent of alpha oscillations, and the magnitude of changes correlates with the extent of training. Beginners show increases of alpha power activity over the occipital area, whereas in intermediate meditators the extent of oscillating cortical area is increased and the frequency of alpha oscillations is decreased. After decades of training, large-amplitude theta-frequency rhythm may dominate over a large extent of the scalp.”

“Imagine that the brain and the body would mature separately in a laboratory, and only several years later we would connect them. This newly united brain–body child would not be able to walk, talk, or even scratch her nose. Local stimulation of her hand or foot would trigger generalized startle reactions, as is the case in premature babies, rather than a spatially localized motor response that characterizes a full-term baby. The reason is that the motor or sensory relations generated by the brain grown in isolation would not match.”

“The primacy of movement-induced sensory feedback may also underlie more complex processes such as development of social communication and speech. Songbirds, such as the extensively studied zebra finches, learn their songs from their fathers. This process is more serendipitous, though, than a well-thought-out learning algorithm. The young birds do not start with the first syllables of the father’s song and acquire the rest piece by piece. Instead, each bird “babbles” some sounds, and it is these self-generated “syllables” from which the birds expand to learn a species-specific adult song. Each bird starts out with a unique seed syllable. Analogously, babbling in human babies also reflects a self-organized intrinsic dynamics.”

“If all currently active neurons to a particular face were selectively and instantaneously eliminated in the inferotemporal cortex in my brain, I would not suffer from face recognition problems because neighboring neurons would instantaneously take over the response properties of the eliminated cells. 18 Another objection that can be added to the list of criticisms is that purely feedforward circuits with closed ends do not really exist in the brain.”

“An alternative to the hierarchical connectionist model of object recognition is a more egalitarian solution: binding by temporal coherence. The key idea of this model, usually attributed to Peter Milner, a colleague of Donald Hebb at McGill University in Montreal, and to the German theoretical physicist Christoph von der Malsburg at the University of Heildelberg, Germany, is that spatially distributed cell groups should synchronize their responses when activated by a single object. n this new scheme, connectivity is no longer the main variable; rather, it is the temporal synchrony of neurons, representing the various attributes of the object, that matters. The different stimulus features, embedded in the activity of distributed cell assemblies, can be combined by mutual horizontal links.”

“Neurons with overlapping receptive fields and similar response properties synchronize robustly with zero time lag, whereas neurons that do not share the same receptive fields do not synchronize. Importantly, it is the response features of the neurons, rather than their spatial separation, that determine the vigor of synchrony. Neurons several millimeters apart in the same or different stages of the visual system and even across the two cerebral hemispheres have been shown to come together in time transiently by gamma-frequency synchronization”

“Instead, the attributes of the object are generated by the observer’s brain. As Gestalt psychologists have known for long, the whole is often faster recognized than its parts, indicating that object recognition is not simply representation of elementary features but the result of bottom-up and top-down interactions, in harmony with the architectural organization of the cerebral cortex.”

“A particular striking correlation between working memory and gamma oscillation was observed by subdural grid recordings. Working memory is a hypothetical mechanism that enables us keep stimuli “in mind” after they are no longer available. The amount of information to be held at any given time is referred to as memory load, for example, the number of ‘nonsense’ syllables to be stored when trying to repeat a toast salutation in a foreign language.

The longer the string of the syllables, the larger the memory load. Experiments in epileptic patients, equipped with large numbers of subdural electrodes for diagnostic purposes, showed that gamma power increased linearly with memory load at multiple, distributed sites, especially above the prefrontal cortex. The power remained at the elevated level during the retention period but fell back quickly to baseline level after the working memory information was no longer needed.”

“There are two fundamental requirements for affecting synaptic strength: sufficiently strong depolarization of the postsynaptic neuron and appropriate timing between presynaptic activity and the discharge of the post-synaptic neuron. 38 Because both mechanisms are affected by the gamma oscillation–mediated synchronization, adjustment of synaptic strength is a perpetual process in the cortex.”

“It is important to recognize that once synchrony is established on a single gamma cycle, the two sites can remain synchronous for several cycles even without further synchronizing events. This is the major advantage of oscillatory synchrony and the main reason why synchrony can be established by relatively weak connections and few spikes.”

“Model systems are always a trade-off, giving up some direct relevance for simplicity. Consider olfactory perception in insects as a model for visual perception in higher mammals. Yet, these entirely different sensory systems have at least one thing in common: stimulus-induced gamma oscillations. The technical advantages of using insects over mammals are enormous…

[In locusts] Different odorants activate different sets of cells, indicative of some spatial representation of odors. However, many neurons respond to several odorants, and the temporal patterns of spike responses are characteristic to different odorants and concentrations. Laurent observed that at a certain time after the odorant presentation, the individual spikes become phase-locked to the induced gamma cycles as well as to other simultaneously recorded neurons.”

“Gamma oscillations have been hypothesized to offer a solution to the century old ‘binding problem’ of perception. Because different features of an object, such as color, texture, distance, spatial position, and smell, are processed in separate parts of the cortex by different sets of neurons, one should explain how they are bound into a complex representation in a matter of 200 milliseconds or so to ‘reconstruct’ the physical object. An earlier solution of the binding problem is a hierarchical feature extraction in feedforward networks, the product of which is a set of ‘gnostic’ neurons at the top.”

“[Penfield] stimulated various sites of the surface of the neocortex of epileptic patients and asked them to narrate their experience. The stimulations evoked dream-like sensations, combining the actual situation and assumed recalled memories. Repeated stimulation of the same cortical site typically produced different experiences, while stimulation of some other sites could evoke the same experience. A possible explanation of the stimulation results is that the stimulation effects were combined with the ongoing trajectories of neuronal activity.”

“The variation of our motor and cognitive abilities is present at multiple time scales, extending from periods of tens of milliseconds to hours. The brain-state variability to a large extent is internally coordinated even in the waking brain.”

“Virtually all neocortical regions project to the perirhinal and entorhinal cortices, and the neocortical information is funneled to the hippocampus by these structures. Thus, according to the brain hierarchy formula, the hippocampus is the ultimate association structure, receiving the highest order neuronal information”

“But even giants can make (small) mistakes. A few decades after Ramón y Cajal outlined the direction of the main hippocampal output, it was discovered that the subcortical projection of the hippocampus is not the most significant output projection. Instead, the principal hippocampal efferents return to the subicular complex and to the deep layers of the entorhinal cortex, from where the information is routed back to the neocortex. Thus, the principal direction of neocortex–paleocortex traffic is not downward to the archipallium but upward to the neocortex.”

“Let’s begin with some theoretical speculation. The computational properties of recursive organization, such as the extensive CA3 recurrent system, meet the requirements of an “autoassociator.” By its computational definition, an autoassociator is a self-correcting network that can recreate a previously stored pattern that most closely resembles the current input pattern, even if it is only a fragment of the stored version.”

“At the very least, the synaptic interactions among neurons should account for the trial-to-trial variability of phase precession. An analogy may be helpful here to illustrate the differences between the pacemaker and cell assembly models. Imagine musicians of an orchestra playing their parts in isolation, supervised by a metronome timer only. Once all the musicians have played their parts separately, the recorded pieces are combined into a single set. have to convince the reader that the quality of the metronome-paced cut-and-paste piece would never match the quality of a real, concert hall performance, where interactions among musicians are available at a much finer time scale than supplied by the metronome-supplied beat (figure 11.15).”

“Seeing a dog for the first time in life is an episode. However, after seeing many different dogs and pictures of dogs, the universal features assume a semantic meaning: a common name. 113 Neuron members of an omnidirectional or explicit assembly collectively define or symbolize the ‘meaning’ of an item. Such explicit, higher order representation is invariant to the conditions that created it.”

“The most prominent collective pattern of hippocampal neurons is theta oscillation, a sustained rhythm associated with explorative navigation.”

“A major motivation for studying the mechanisms of oscillatory coupling is to use such understanding for describing the direction and strength of functional connectivity between brain areas of interest. Unfortunately, there is no general mathematical or computational theory of oscillatory networks of multiple interacting oscillators.”

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