Neural oscillation

795:, whereas delayed-feedback oscillations arise when components of a system affect each other after significant time delays. Limit-cycle oscillations can be complex but there are powerful mathematical tools for analyzing them; the mathematics of delayed-feedback oscillations is primitive in comparison. Linear oscillators and limit-cycle oscillators qualitatively differ in terms of how they respond to fluctuations in input. In a linear oscillator, the frequency is more or less constant but the amplitude can vary greatly. In a limit-cycle oscillator, the amplitude tends to be more or less constant but the frequency can vary greatly. A 1465:

activity when activated by visual stimuli. The frequency of these oscillations was in the range of 40 Hz and differed from the periodic activation induced by the grating, suggesting that the oscillations and their synchronization were due to internal neuronal interactions. Similar findings were shown in parallel by the group of Eckhorn, providing further evidence for the functional role of neural synchronization in feature binding. Since then, numerous studies have replicated these findings and extended them to different modalities such as EEG, providing extensive evidence of the functional role of

1649: 588:, subtypes of cortical cells fire bursts of spikes (brief clusters of spikes) rhythmically at preferred frequencies. Bursting neurons have the potential to serve as pacemakers for synchronous network oscillations, and bursts of spikes may underlie or enhance neuronal resonance. Many of these neurons can be considered intrinsic oscillators, namely, neurons that generate their oscillations intrinsically, as their oscillation frequencies can be modified by local applications of glutamate in-vivo. 398: 1082: 38: 2026: 1217:. Induced activity generally reflects the activity of numerous neurons: amplitude changes in oscillatory activity are thought to arise from the synchronization of neural activity, for instance by synchronization of spike timing or membrane potential fluctuations of individual neurons. Increases in oscillatory activity are therefore often referred to as event-related synchronization, while decreases are referred to as event-related desynchronization. 1034: 1804:(BCIs). For example, a non-invasive BCI can be created by placing electrodes on the scalp and then measuring the weak electric signals. Although individual neuron activities cannot be recorded through non-invasive BCI because the skull damps and blurs the electromagnetic signals, oscillatory activity can still be reliably detected. The BCI was introduced by Vidal in 1973 as challenge of using EEG signals to control objects outside human body. 1050: 819: 1066: 225:

observed as the spectral intensity decreases from the summation of these neurons firing, which can be utilized to differentiate cognitive function or neural isolation. However, new non-linear methods have been used that couple temporal and spectral entropic relationships simultaneously to characterize how neurons are isolated, (the signal's inability to propagate to adjacent neurons), an indicator of impairment (e.g., hypoxia).

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modulations, such as an asymmetry of the intracellular currents that propagate forward and backward down the dendrites. Under this assumption, asymmetries in the dendritic current would cause asymmetries in oscillatory activity measured by EEG and MEG, since dendritic currents in pyramidal cells are generally thought to generate EEG and MEG signals that can be measured at the scalp.

261:(30–70 Hz), and high gamma (70–150 Hz) frequency bands. Faster rhythms such as gamma activity have been linked to cognitive processing. Indeed, EEG signals change dramatically during sleep. In fact, different sleep stages are commonly characterized by their spectral content. Consequently, neural oscillations have been linked to cognitive states, such as 1019:. These ongoing rhythms can change in different ways in response to perceptual input or motor output. Oscillatory activity may respond by increases or decreases in frequency and amplitude or show a temporary interruption, which is referred to as phase resetting. In addition, external activity may not interact with ongoing activity at all, resulting in an additive response. 114:. Oscillatory activity in groups of neurons generally arises from feedback connections between the neurons that result in the synchronization of their firing patterns. The interaction between neurons can give rise to oscillations at a different frequency than the firing frequency of individual neurons. A well-known example of macroscopic neural oscillations is 1661: 221:, also referred to as local synchronization. In addition to local synchronization, oscillatory activity of distant neural structures (single neurons or neural ensembles) can synchronize. Neural oscillations and synchronization have been linked to many cognitive functions such as information transfer, perception, motor control and memory. 1481:, and the disruption of the oscillatory synchronization leads to impairment of behavioral discrimination of chemically similar odorants in bees, and to more similar responses across odors in downstream β-lobe neurons. Recent follow-up of this work has shown that oscillations create periodic integration windows for 59: 1526:

activity when subjects made a movement. Using intra-cortical recordings, similar changes in oscillatory activity were found in the motor cortex when the monkeys performed motor acts that required significant attention. In addition, oscillations at spinal level become synchronised to beta oscillations

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Single-cell intrinsic oscillators serve as valuable tools for decoding temporally-encoded sensory information. This information is encoded through inter-spike intervals, and intrinsic oscillators can act as 'temporal rulers' for precisely measuring these intervals. One notable mechanism for achieving

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Next to evoked activity, neural activity related to stimulus processing may result in induced activity. Induced activity refers to modulation in ongoing brain activity induced by processing of stimuli or movement preparation. Hence, they reflect an indirect response in contrast to evoked responses. A

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The Kuramoto model is widely used to study oscillatory brain activity, and several extensions have been proposed that increase its neurobiological plausibility, for instance by incorporating topological properties of local cortical connectivity. In particular, it describes how the activity of a group

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Neural field models are another important tool in studying neural oscillations and are a mathematical framework describing evolution of variables such as mean firing rate in space and time. In modeling the activity of large numbers of neurons, the central idea is to take the density of neurons to the

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adopt a variety of abstractions in order to describe complex oscillatory dynamics observed in brain activity. Many models are used in the field, each defined at a different level of abstraction and trying to model different aspects of neural systems. They range from models of the short-term behaviour

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rarely all fire at exactly the same moment, i.e. fully synchronized. Instead, the probability of firing is rhythmically modulated such that neurons are more likely to fire at the same time, which gives rise to oscillations in their mean activity. (See figure at top of page.) As such, the frequency of

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approximately 100 times per minute. Although all of the heart's cells have the ability to generate action potentials that trigger cardiac contraction, the sinoatrial node normally initiates it, simply because it generates impulses slightly faster than the other areas. Hence, these cells generate the

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Cross-frequency coupling (CFC) describes the coupling (statistical correlation) between a slow wave and a fast wave. There are many kinds, generally written as A-B coupling, meaning the A of a slow wave is coupled with the B of a fast wave. For example, phase–amplitude coupling is where the phase of

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Phase resetting occurs when input to a neuron or neuronal ensemble resets the phase of ongoing oscillations. It is very common in single neurons where spike timing is adjusted to neuronal input (a neuron may spike at a fixed delay in response to periodic input, which is referred to as phase locking)

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Neuronal spiking can be classified by its activity pattern. The excitability of neurons can be subdivided in Class I and II. Class I neurons can generate action potentials with arbitrarily low frequency depending on the input strength, whereas Class II neurons generate action potentials in a certain

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A neural network model describes a population of physically interconnected neurons or a group of disparate neurons whose inputs or signalling targets define a recognizable circuit. These models aim to describe how the dynamics of neural circuitry arise from interactions between individual neurons.

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After the BCI challenge, in 1988, alpha rhythm was used in a brain rhythm based BCI for control of a physical object, a robot. Alpha rhythm based BCI was the first BCI for control of a robot. In particular, some forms of BCI allow users to control a device by measuring the amplitude of oscillatory

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across the surface of the motor cortex along dominant spatial axes characteristic of the local circuitry of the motor cortex. It has been proposed that motor commands in the form of travelling waves can be spatially filtered by the descending fibres to selectively control muscle force. Simulations

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If a group of neurons engages in synchronized oscillatory activity, the neural ensemble can be mathematically represented as a single oscillator. Different neural ensembles are coupled through long-range connections and form a network of weakly coupled oscillators at the next spatial scale. Weakly

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The opposite of neuron synchronization is neural isolation, which is when electrical activity of neurons is not temporally synchronized. This is when the likelihood of the neuron to reach its threshold potential for the signal to propagate to the next neuron decreases. This phenomenon is typically

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Both single neurons and groups of neurons can generate oscillatory activity spontaneously. In addition, they may show oscillatory responses to perceptual input or motor output. Some types of neurons will fire rhythmically in the absence of any synaptic input. Likewise, brain-wide activity reveals

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A tremor is an involuntary, somewhat rhythmic, muscle contraction and relaxation involving to-and-fro movements of one or more body parts. It is the most common of all involuntary movements and can affect the hands, arms, eyes, face, head, vocal cords, trunk, and legs. Most tremors occur in the

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if one is interested in stimulus processing; however, spontaneous activity is considered to play a crucial role during brain development, such as in network formation and synaptogenesis. Spontaneous activity may be informative regarding the current mental state of the person (e.g. wakefulness,

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and when performing slow finger movements. These findings may indicate that the human brain controls continuous movements intermittently. In support, it was shown that these movement discontinuities are directly correlated to oscillatory activity in a cerebello-thalamo-cortical loop, which may

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The functional role of synchronized oscillatory activity in the brain was mainly established in experiments performed on awake kittens with multiple electrodes implanted in the visual cortex. These experiments showed that groups of spatially segregated neurons engage in synchronous oscillatory

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hypothesis. According to this idea, synchronous oscillations in neuronal ensembles bind neurons representing different features of an object. For example, when a person looks at a tree, visual cortex neurons representing the tree trunk and those representing the branches of the same tree would

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are obtained from an electroencephalogram by stimulus-locked averaging, i.e. averaging different trials at fixed latencies around the presentation of a stimulus. As a consequence, those signal components that are the same in each single measurement are conserved and all others, i.e. ongoing or

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and may also occur in neuronal ensembles when the phases of their neurons are adjusted simultaneously. Phase resetting is fundamental for the synchronization of different neurons or different brain regions because the timing of spikes can become phase locked to the activity of other neurons.

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oscillations does not need to match the firing pattern of individual neurons. Isolated cortical neurons fire regularly under certain conditions, but in the intact brain, cortical cells are bombarded by highly fluctuating synaptic inputs and typically fire seemingly at random. However, if the

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because ongoing brain oscillations may not be symmetric and thus amplitude modulations may result in a baseline shift that does not average out. This model implies that slow event-related responses, such as asymmetric alpha activity, could result from asymmetric brain oscillation amplitude

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Synchronization of neuronal firing may serve as a means to group spatially segregated neurons that respond to the same stimulus in order to bind these responses for further joint processing, i.e. to exploit temporal synchrony to encode relations. Purely theoretical formulations of the

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reflecting their summed activity. Figure illustrates how synchronized patterns of action potentials may result in macroscopic oscillations that can be measured outside the scalp. When these neural oscillation patterns of synchronization break down, a reduction of signal intensity

1628:: for instance, stage N1 refers to the transition of the brain from alpha waves (common in the awake state) to theta waves, whereas stage N3 (deep or slow-wave sleep) is characterized by the presence of delta waves. The normal order of sleep stages is N1 → N2 → N3 → N2 → REM. 1472:

Gilles Laurent and colleagues showed that oscillatory synchronization has an important functional role in odor perception. Perceiving different odors leads to different subsets of neurons firing on different sets of oscillatory cycles. These oscillations can be disrupted by

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studies suggest that visual perception is dependent on both the phase and amplitude of cortical oscillations. For instance, the amplitude and phase of alpha activity at the moment of visual stimulation predicts whether a weak stimulus will be perceived by the subject.

459:(MEG). The electric potentials generated by single neurons are far too small to be picked up outside the scalp, and EEG or MEG activity always reflects the summation of the synchronous activity of thousands or millions of neurons that have similar spatial orientation. 570:, different oscillatory varieties of these neuronal models can be determined, allowing for the classification of types of neuronal responses. The oscillatory dynamics of neuronal spiking as identified in the Hodgkin–Huxley model closely agree with empirical findings. 429:

in membrane potential. These rhythmic changes in membrane potential do not reach the critical threshold and therefore do not result in an action potential. They can result from postsynaptic potentials from synchronous inputs or from intrinsic properties of neurons.

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A model of a biological neuron is a mathematical description of the properties of nerve cells, or neurons, that is designed to accurately describe and predict its biological processes. One of the most successful neuron models is the Hodgkin–Huxley model, for which

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is a coupling between theta wave and gamma wave in the hippocampal network. During a theta wave, 4 to 8 non-overlapping neuron ensembles are activated in sequence. This has been hypothesized to form a neural code representing multiple items in a temporal frame

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A group of neurons can also generate oscillatory activity. Through synaptic interactions, the firing patterns of different neurons may become synchronized and the rhythmic changes in electric potential caused by their action potentials may accumulate

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activity in the absence of an explicit task, such as sensory input or motor output, and hence also referred to as resting-state activity. It is opposed to induced activity, i.e. brain activity that is induced by sensory stimuli or motor responses.

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of coupled phase oscillators is one of the most abstract and fundamental models used to investigate neural oscillations and synchronization. It captures the activity of a local system (e.g., a single neuron or neural ensemble) by its circular

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at all levels of organization. Three different levels have been widely recognized: the micro-scale (activity of a single neuron), the meso-scale (activity of a local group of neurons) and the macro-scale (activity of different brain regions).

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often increases during increased mental activity such as during object representation. Because induced responses may have different phases across measurements and therefore would cancel out during averaging, they can only be obtained using

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Neural oscillations have been most widely studied in neural activity generated by large groups of neurons. Large-scale activity can be measured by techniques such as EEG. In general, EEG signals have a broad spectral content similar to

1144:, are part of spontaneous activity. Statistical analysis of power fluctuations of alpha activity reveals a bimodal distribution, i.e. a high- and low-amplitude mode, and hence shows that resting-state activity does not just reflect a 164:

published in 1890 his observations of spontaneous electrical activity of the brain of rabbits and dogs that included rhythmic oscillations altered by light, detected with electrodes directly placed on the surface of the brain. Before

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that deals with large-scale systems. Models based on these principles have been used to provide mathematical descriptions of neural oscillations and EEG rhythms. They have for instance been used to investigate visual hallucinations.

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to describe how neural activity evolves over time. In particular, it aims to relate dynamic patterns of brain activity to cognitive functions such as perception and memory. In very abstract form, neural oscillations can be analyzed

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Neuronal spiking is generally considered the basis for information transfer in the brain. For such a transfer, information needs to be coded in a spiking pattern. Different types of coding schemes have been proposed, such as

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tremor. It is argued that tremors are likely to be multifactorial in origin, with contributions from neural oscillations in the central nervous systems, but also from peripheral mechanisms such as reflex loop resonances.

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activity, are extensively linked to memory function. Theta rhythms are very strong in rodent hippocampi and entorhinal cortex during learning and memory retrieval, and they are believed to be vital to the induction of

1446:(NPLL). In this mechanism, cortical oscillators undergo modulation influenced by the firing rates of thalamocortical 'phase detectors,' which, in turn, gauge the disparity between the cortical and sensory periodicity. 62:

Autocorrelations and spike raster plots of two single-units recorded from the secondary somatosensory cortex of a monkey. The top neuron is oscillating spontaneously at approximately 30 Hz. The bottom neuron is not

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Eckhorn R, Bauer R, Jordan W, Brosch M, Kruse W, Munk M, Reitboeck HJ (1988). "Coherent oscillations: a mechanism of feature linking in the visual cortex? Multiple electrode and correlation analyses in the cat".

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with one another via synapses and affect the timing of spike trains in the post-synaptic neurons. Depending on the properties of the connection, such as the coupling strength, time delay and whether coupling is

1863: 1388:. Central pattern generators are neuronal circuits that—when activated—can produce rhythmic motor patterns in the absence of sensory or descending inputs that carry specific timing information. Examples are 1748:

is disrupted. The thalamic loss of input allows the frequency of the thalamo-cortical column to slow into the theta or delta band as identified by MEG and EEG by machine learning. TCD can be treated with

125:). More than 50 years later, intrinsic oscillatory behavior was encountered in vertebrate neurons, but its functional role is still not fully understood. The possible roles of neural oscillations include 1383:

Synchronized firing of neurons also forms the basis of periodic motor commands for rhythmic movements. These rhythmic outputs are produced by a group of interacting neurons that form a network, called a

681: – the major immune cells of the brain – have been shown to play an important role in shaping network connectivity, and thus, influencing neuronal network oscillations both 1329:

recordings providing increasing evidence for a close relation between synchronous oscillatory activity and a variety of cognitive functions such as perceptual grouping and attentional top-down control.

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Bressloff PC, Cowan JD (2003) Spontaneous pattern formation in primary visual cortex. In: J Hogan, AR Krauskopf, M di Bernado, RE Wilson (Eds.), Nonlinear dynamics and chaos: where do we go from here?

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and is thought to play a key role in processing neural information. Numerous experimental studies support a functional role of neural oscillations; a unified interpretation, however, is still lacking.

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Ahissar, E. & Vaadia, E. Oscillatory activity of single units in a somatosensory cortex of an awake monkey and their possible role in texture analysis. Proc Natl Acad Sci USA 87, 8935-8939 (1990).

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Suffczynski P, Kalitzin S, Pfurtscheller G, Lopes da Silva FH (December 2001). "Computational model of thalamo-cortical networks: dynamical control of alpha rhythms in relation to focal attention".

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Simulations using the Kuramoto model with realistic long-range cortical connectivity and time-delayed interactions reveal the emergence of slow patterned fluctuations that reproduce resting-state

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Ahissar, E., Haidarliu, S., and Zacksenhouse, M. (1997). Decoding temporally encoded sensory input by cortical oscillations and thalamic phase comparators. Proc Natl Acad Sci USA 94, 11633-11638.

868:, or highly idealized neuron models such as the leaky integrate-and-fire neuron, originally developed by Lapique in 1907. Such models only capture salient membrane dynamics such as spiking or 857:. The model is so successful at describing these characteristics that variations of its "conductance-based" formulation continue to be utilized in neuron models over a half a century later. 417:

resulting from changes in the electric membrane potential. Neurons can generate multiple action potentials in sequence forming so-called spike trains. These spike trains are the basis for

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binding-by-synchrony hypothesis were proposed first, but subsequently extensive experimental evidence has been reported supporting the potential role of synchrony as a relational code.

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play an important role in producing neural ensemble synchrony by generating a narrow window for effective excitation and rhythmically modulating the firing rate of excitatory neurons.

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in clinical trials and in quantifying effects in pre-clinical studies. These biomarkers are often named "EEG biomarkers" or "Neurophysiological Biomarkers" and are quantified using

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probability of a large group of neurons firing is rhythmically modulated at a common frequency, they will generate oscillations in the mean field. (See also figure at top of page.)

960: 1598:. Tight coordination of single-neuron spikes with local theta oscillations is linked to successful memory formation in humans, as more stereotyped spiking predicts better memory. 7121: 5462:

Gray CM, König P, Engel AK, Singer W (March 1989). "Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties".

1727: 957: 903:. Similarly, it was shown that simulations of neural networks with a phenomenological model for neuronal response failures can predict spontaneous broadband neural oscillations. 3395:"Exploring mechanisms of spontaneous functional connectivity in MEG: how delayed network interactions lead to structured amplitude envelopes of band-pass filtered oscillations" 434:

frequency band, which is relatively insensitive to changes in input strength. Class II neurons are also more prone to display sub-threshold oscillations in membrane potential.

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alone and hence ignores the amplitude of oscillations (amplitude is constant). Interactions amongst these oscillators are introduced by a simple algebraic form (such as a

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Although neural oscillations in human brain activity are mostly investigated using EEG recordings, they are also observed using more invasive recording techniques such as

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Local interactions between neurons can result in the synchronization of spiking activity and form the basis of oscillatory activity. In particular, models of interacting

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Mureşan RC, Jurjuţ OF, Moca VV, Singer W, Nikolić D (March 2008). "The oscillation score: an efficient method for estimating oscillation strength in neuronal activity".

1427:. Neural oscillations could create periodic time windows in which input spikes have larger effect on neurons, thereby providing a mechanism for decoding temporal codes. 5949:

Murthy VN, Fetz EE (December 1996). "Oscillatory activity in sensorimotor cortex of awake monkeys: synchronization of local field potentials and relation to behavior".

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Ahissar, E., Nelinger, G., Assa, E., Karp, O. & Saraf-Sinik, I. Thalamocortical loops as temporal demodulators across senses. Communications Biology 6, 562 (2023).

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Whittington MA, Traub RD, Kopell N, Ermentrout B, Buhl EH (December 2000). "Inhibition-based rhythms: experimental and mathematical observations on network dynamics".

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The functions of neural oscillations are wide-ranging and vary for different types of oscillatory activity. Examples are the generation of rhythmic activity such as a

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is an example of a limit-cycle oscillation in that the frequency of beats varies widely, while each individual beat continues to pump about the same amount of blood.

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on a much slower time scale. That is, the concentration levels of certain neurotransmitters are known to regulate the amount of oscillatory activity. For instance,

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Wendling F, Bellanger JJ, Bartolomei F, Chauvel P (October 2000). "Relevance of nonlinear lumped-parameter models in the analysis of depth-EEG epileptic signals".

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loops tend to cause oscillatory activity where frequency is inversely related to the delay time. An example of such a feedback loop is the connections between the

1033: 627:. Certain network structures promote oscillatory activity at specific frequencies. For example, neuronal activity generated by two populations of interconnected 6333:

Heitmann S, Boonstra T, Gong P, Breakspear M, Ermentrout B (2015). "The rhythms of steady posture: Motor commands as spatially organized oscillation patterns".

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measures. Coherent activity of large-scale brain activity may form dynamic links between brain areas required for the integration of distributed information.

1893: 1365:. In the absence of extrinsic neural and hormonal control, cells in the SA node will rhythmically discharge. The sinoatrial node is richly innervated by the 581:

behavior that does not result in action potentials, may also contribute to oscillatory activity by facilitating synchronous activity of neighboring neurons.

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The Hodgkin–Huxley model is too complicated to understand using classical mathematical techniques, so researchers often turn to simplifications such as the

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coupled oscillators can generate a range of dynamics including oscillatory activity. Long-range connections between different brain structures, such as the

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and consists of nonlinear differential equations that approximate the electrical characteristics of a neuron, including the generation and propagation of

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arise from interactions between individual neurons, to models of how behaviour can arise from abstract neural modules that represent complete subsystems.

1254:-locked to the stimulus or event. Evoked activity is often considered to be independent from ongoing brain activity, although this is an ongoing debate. 447:). That is, synchronized firing patterns result in synchronized input into other cortical areas, which gives rise to large-amplitude oscillations of the 4664:

Makeig S, Westerfield M, Jung TP, Enghoff S, Townsend J, Courchesne E, Sejnowski TJ (January 2002). "Dynamic brain sources of visual evoked responses".

938:. Instead of modelling individual neurons, this approach approximates a group of neurons by its average properties and interactions. It is based on the 784:

Noise-driven harmonic oscillators realistically simulate alpha rhythm in the waking EEG as well as slow waves and spindles in the sleep EEG. Successful

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Stopfer M, Bhagavan S, Smith BH, Laurent G (November 1997). "Impaired odour discrimination on desynchronization of odour-encoding neural assemblies".

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Shusterman V, Troy WC (June 2008). "From baseline to epileptiform activity: a path to synchronized rhythmicity in large-scale neural networks".

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Llinás RR (December 1988). "The intrinsic electrophysiological properties of mammalian neurons: insights into central nervous system function".

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Dement W, Kleitman N (November 1957). "Cyclic variations in EEG during sleep and their relation to eye movements, body motility, and dreaming".

1680:. These pathological oscillations often consist of an aberrant version of a normal oscillation. For example, one of the best known types is the 1065: 311:

Neural oscillations are commonly studied within a mathematical framework and belong to the field of "neurodynamics", an area of research in the

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involves determining how oscillations are generated and what their roles are. Oscillatory activity in the brain is widely observed at different

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Napoli, Nicholas J.; Demas, Matthew; Stephens, Chad L.; Kennedy, Kellie D.; Harrivel, Angela R.; Barnes, Laura E.; Pope, Alan T. (2020-03-03).

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at which it spikes. Often, a neuron's firing rate depends on the summed activity it receives. Frequency changes are also commonly observed in

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MacLeod K, Bäcker A, Laurent G (October 1998). "Who reads temporal information contained across synchronized and oscillatory spike trains?".

4648: 3625: 3106: 1159:. The temporal evolution of resting state networks is correlated with fluctuations of oscillatory EEG activity in different frequency bands. 6088:

Salenius S, Portin K, Kajola M, Salmelin R, Hari R (June 1997). "Cortical control of human motoneuron firing during isometric contraction".

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MacLeod K, Laurent G (November 1996). "Distinct mechanisms for synchronization and temporal patterning of odor-encoding neural assemblies".

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Ongoing brain activity may also have an important role in perception, as it may interact with activity related to incoming stimuli. Indeed,

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hands. In some people, tremor is a symptom of another neurological disorder. Many different forms of tremor have been identified, such as

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algorithms were based on such models. Several other EEG components are better described by limit-cycle or delayed-feedback oscillations.

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Mäkinen V, Tiitinen H, May P (February 2005). "Auditory event-related responses are generated independently of ongoing brain activity".

1779: 527:. In a whole-brain network model with realistic anatomical connectivity and propagation delays between brain areas, oscillations in the 4301:

Fox MD, Raichle ME (September 2007). "Spontaneous fluctuations in brain activity observed with functional magnetic resonance imaging".

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Pfurtscheller G, Lopes da Silva FH (November 1999). "Event-related EEG/MEG synchronization and desynchronization: basic principles".

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emerge from the partial synchronisation of subsets of brain areas oscillating in the gamma-band (generated at the mesoscopic level).

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of sensory features in perception, such as the shape and color of an object. Neural oscillations also play an important role in many

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Bozinovski S (August 1990). "Mobile robot trajectory control: From fixed rails to direct bioelectric control.". In Kaynak O (ed.).

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oscillation, which is typical of generalized or absence epileptic seizures, and which resembles normal sleep spindle oscillations.

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are critical in the generation of action potentials. The dynamics of these ion channels have been captured in the well-established

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Lebedev MA, Nicolelis MA (April 2017). "Brain-Machine Interfaces: From Basic Science to Neuroprostheses and Neurorehabilitation".

4346:"Electroencephalographic signatures of attentional and cognitive default modes in spontaneous brain activity fluctuations at rest" 5914:

Pfurtscheller G, Aranibar A (June 1977). "Event-related cortical desynchronization detected by power measurements of scalp EEG".

3655:"Microglia contribute to neuronal synchrony despite endogenous ATP-related phenotypic transformation in acute mouse brain slices" 2742:

Varela F, Lachaux JP, Rodriguez E, Martinerie J (April 2001). "The brainweb: phase synchronization and large-scale integration".

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have shown that ongoing wave activity in cortex can elicit steady muscle force with physiological levels of EEG-EMG coherence.

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spontaneous activity, are averaged out. That is, event-related potentials only reflect oscillations in brain activity that are

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and in somatosensory perception. However, recent findings argue against a clock-like function of cortical gamma oscillations.

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play an important role here. Because all brain areas are bidirectionally coupled, these connections between brain areas form

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Rubino D, Robbins KA, Hatsopoulos NG (December 2006). "Propagating waves mediate information transfer in the motor cortex".

6045:"Synchronization between motor cortex and spinal motoneuronal pool during the performance of a maintained motor task in man" 3489:"In vitro neurons in mammalian cortical layer 4 exhibit intrinsic oscillatory activity in the 10- to 50-Hz frequency range" 7381: 233:, but also reveal oscillatory activity in specific frequency bands. The first discovered and best-known frequency band is 3704:"Resting GABA concentration predicts peak gamma frequency and fMRI amplitude in response to visual stimulation in humans" 1801: 1795: 372: 5255:

Dimitrijevic MR, Gerasimenko Y, Pinter MM (November 1998). "Evidence for a spinal central pattern generator in humans".

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Tallon-Baudry C, Bertrand O (April 1999). "Oscillatory gamma activity in humans and its role in object representation".

2810:"Oscillatory properties of guinea-pig inferior olivary neurones and their pharmacological modulation: an in vitro study" 1621: 1199:

is not so common because the frequency of oscillatory activity is often related to the time delays between brain areas.

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concentration has been shown to be positively correlated with frequency of oscillations in induced stimuli. A number of

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Wehr M, Laurent G (November 1996). "Odour encoding by temporal sequences of firing in oscillating neural assemblies".

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Singer W (1993). "Synchronization of cortical activity and its putative role in information processing and learning".

4907:"Magnetoencephalography - Theory, instrumentation, and applications to noninvasive studies of the working human brain" 1739: 778: 663:

that support oscillatory activity. Oscillations recorded from multiple cortical areas can become synchronized to form

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discovered electrical activity in the cerebral hemispheres of rabbits and monkeys and presented his findings in 1875.

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that describes how action potentials are initiated and propagated by means of a set of differential equations. Using

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are thought to have properties that define early connectivity of circuits and synapses between cells in the retina.

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in the 1990s when the studies of the visual system of the brain by Gray, Singer and others appeared to support the

752: 664: 559: 337: 217:. In large-scale oscillations, amplitude changes are considered to result from changes in synchronization within a 170: 1648: 1262:

It has recently been proposed that even if phases are not aligned across trials, induced activity may still cause

861: 777:, and vibrations of every sort. They generally arise when a physical system is perturbed by a small degree from a 7557: 2198:

Fries P (October 2005). "A mechanism for cognitive dynamics: neuronal communication through neuronal coherence".

1558:, which is associated with the cerebellum. These oscillations are also observed in motor output of physiological 1528: 1385: 1378: 1184: 873: 603: 585: 516: 491:

Neural oscillation can also arise from interactions between different brain areas coupled through the structural

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and information transfer in the brain. Spike trains can form all kinds of patterns, such as rhythmic spiking and

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Oscillations have been commonly reported in the motor system. Pfurtscheller and colleagues found a reduction in

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oscillators. Harmonic oscillations appear very frequently in nature—examples are sound waves, the motion of a

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Buhusi CV, Meck WH (October 2005). "What makes us tick? Functional and neural mechanisms of interval timing".

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or by interactions between neurons. In individual neurons, oscillations can appear either as oscillations in

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Bozinovski S, Sestakov M, Bozinovska L (November 1988). "Using EEG alpha rhythm to control a mobile robot.".

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have diffuse projections throughout the brain influencing concentration levels of neurotransmitters such as

332:. When studied in a more physiologically realistic setting, oscillatory activity is generally studied using 214: 99: 924: 757:

Oscillations can often be described and analyzed using mathematics. Mathematicians have identified several

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Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society

6235:"Network structure of the human musculoskeletal system shapes neural interactions on multiple time scales" 5162: 4759: 3975: 3037:

Vansteensel MJ, Pels EG, Bleichner MG, Branco MP, Denison T, Freudenburg ZV, et al. (November 2016).

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at the cost of biophysical detail, but are more computationally efficient, enabling simulations of larger

716: 456: 452: 390: 368: 324: 305: 198: 190: 111: 75: 425:, and often display oscillatory activity. Oscillatory activity in single neurons can also be observed in 7572: 7115: 1238: 1121: 620: 448: 352: 329: 273: 58: 50: 5804:

Ahissar E, Zacksenhouse M (2001). "Chapter 6 Temporal and spatial coding in the rat vibrissal system".

2389:"Alpha-Band Oscillations Enable Spatially and Temporally Resolved Tracking of Covert Spatial Attention" 4945: 2694:

Engel AK, Singer W (January 2001). "Temporal binding and the neural correlates of sensory awareness".

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Schnitzler A, Gross J (April 2005). "Normal and pathological oscillatory communication in the brain".

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Coenen A, Fine E, Zayachkivska O (2014). "Adolf Beck: a forgotten pioneer in electroencephalography".

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or the occurrence of specific other events, such as moving a body part, i.e. events that do not form

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Catterall, W. A., Raman, I. M., Robinson, H. P. C., Sejnowski, T. J., Paulsen, O. (2 October 2012).

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oscillate in synchrony to form a single representation of the tree. This phenomenon is best seen in

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during relaxed wakefulness and which increases when the eyes are closed. Other frequency bands are:

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Laufs H, Krakow K, Sterzer P, Eger E, Beyerle A, Salek-Haddadi A, Kleinschmidt A (September 2003).

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Pravdich-Neminsky VV (1913). "Ein Versuch der Registrierung der elektrischen Gehirnerscheinungen".

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behavior: a fast rhythm generated by individual spikes and a slower rhythm generated by the bursts.

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Neural oscillations are observed throughout the central nervous system at all levels, and include

7506: 7401: 7076: 7045: 6865: 6746:"Retinal waves are likely to instruct the formation of eye-specific retinogeniculate projections" 6666: 6627: 6362:"A dendritic mechanism for decoding traveling waves: principles and applications to motor cortex" 6315: 6133:"Coherent oscillations in monkey motor cortex and hand muscle EMG show task-dependent modulation" 6113: 5839: 5786: 5743: 5692: 5641: 5590: 5539: 5495: 5288: 5237: 4981: 4787: 4762:, Ilmoniemi RJ, Curio G (May 2007). "A novel mechanism for evoked responses in the human brain". 4740: 4697: 4621: 4575: 4326: 4234: 4097: 4024: 3948: 3835: 2964: 2909: 2767: 2719: 2641: 2579: 2534: 2369: 2312: 2266: 2223: 2158: 2060:"Intrinsic electrical properties of mammalian neurons and CNS function: a historical perspective" 1587: 1540: 1509: 1397: 1305: 1208:

well-studied type of induced activity is amplitude change in oscillatory activity. For instance,

1155:(BOLD) signal reveal correlation patterns that are linked to resting state networks, such as the 1016: 842: 636: 567: 401: 91: 6419:

Allum JH, Dietz V, Freund HJ (May 1978). "Neuronal mechanisms underlying physiological tremor".

5153:

Singer W, Gray CM (1995). "Visual feature integration and the temporal correlation hypothesis".

4156:"Generative models of cortical oscillations: neurobiological implications of the kuramoto model" 1493:

are more effective in activating Kenyon cells only at specific phases of the oscillatory cycle.

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through local interactions between excitatory and inhibitory neurons. In particular, inhibitory

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or spikes. Some types of neurons have the tendency to fire at particular frequencies, either as

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Gross J, Timmermann L, Kujala J, Dirks M, Schmitz F, Salmelin R, Schnitzler A (February 2002).

5867:"Is gamma-band activity in the local field potential of V1 cortex a "clock" or filtered noise?" 3923:

Abbott, Larry (1999). "Lapicque's introduction of the integrate-and-fire model neuron (1907)".

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alertness) and is often used in sleep research. Certain types of oscillatory activity, such as

37: 7200: 7179: 7152: 7035: 7004: 6963: 6922: 6857: 6814: 6777: 6723: 6658: 6608: 6544: 6485: 6436: 6401: 6307: 6272: 6215: 6158: 6105: 6070: 6025: 5986:"Oscillations in local field potentials of the primate motor cortex during voluntary movement" 5966: 5931: 5896: 5827: 5817: 5778: 5735: 5684: 5633: 5582: 5531: 5487: 5441: 5397: 5337: 5280: 5229: 5180: 5135: 5097: 5079: 5038: 5020: 4973: 4965: 4887: 4836: 4779: 4732: 4689: 4644: 4613: 4567: 4532: 4483: 4434: 4385: 4318: 4283: 4226: 4187: 4089: 4054: 4013:"Broadband macroscopic cortical oscillations emerge from intrinsic neuronal response failures" 3993: 3940: 3886: 3827: 3784: 3743: 3684: 3621: 3595: 3528: 3469: 3426: 3375: 3340: 3291: 3242: 3183: 3158: 3102: 3076: 3019: 3011: 2956: 2948: 2874: 2839: 2759: 2711: 2676: 2633: 2526: 2470: 2418: 2361: 2304: 2258: 2215: 2150: 2091: 2014: 1996: 1853: 1775: 1723: 1443: 1436: 1339: 1321:

which reflect the synchronous activity of local groups of neurons, but has also been shown in

1176: 939: 916: 854: 758: 743:, and have a pronounced effect on amplitude of different brain waves, such as alpha activity. 672: 504: 496: 468: 414: 384: 312: 107: 95: 6176:

Boonstra TW, Danna-Dos-Santos A, Xie HB, Roerdink M, Stins JF, Breakspear M (December 2015).

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Conway BA, Halliday DM, Farmer SF, Shahani U, Maas P, Weir AI, Rosenberg JR (December 1995).

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Fell J, Axmacher N (February 2011). "The role of phase synchronization in memory processes".

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Danner SM, Hofstoetter US, Freundl B, Binder H, Mayr W, Rattay F, Minassian K (March 2015).

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Cardin JA, Carlén M, Meletis K, Knoblich U, Zhang F, Deisseroth K, et al. (June 2009).

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Neural oscillations are sensitive to several drugs influencing brain activity; accordingly,

1700: 1242: 1125: 850: 818: 668: 656: 545: 320: 277: 186: 174: 46: 45:. Upper panel shows spiking of individual neurons (with each dot representing an individual 7225: 6942:"Breaking the silence: brain-computer interfaces (BCI) for communication and motor control" 4503:"Prestimulus oscillatory activity in the alpha band predicts visual discrimination ability" 3393:

Cabral J, Luckhoo H, Woolrich M, Joensson M, Mohseni H, Baker A, et al. (April 2014).

2441:"Decoding object-based auditory attention from source-reconstructed MEG alpha oscillations" 1824:

A non-inclusive list of types of oscillatory activity found in the central nervous system:

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Specific types of neural oscillations may also appear in pathological situations, such as

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that play an important role in generating membrane potential oscillations. In particular,

512: 463: 301: 218: 103: 308:. Quantitative models can estimate the strength of neural oscillations in recorded data. 6999: 6982: 6900: 6845: 6701: 6646: 6520: 6377: 6250: 6193: 6001: 5723: 5672: 5621: 5570: 5475: 5375: 5268: 5215: 5176: 5131: 4922: 4677: 4361: 3815: 3719: 3679: 3654: 3575: 3504: 3457: 3266:

Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences

3220: 2999: 2619: 2347: 2029: This article incorporates text from this source, which is available under the 1984: 849:

won the 1963 Nobel Prize in physiology or medicine. The model is based on data from the

6917: 6884: 6772: 6745: 6718: 6685: 6628:"Human memory strength is predicted by theta-frequency phase-locking of single neurons" 6603: 6578: 6480: 6455: 6396: 6361: 6267: 6234: 6210: 6177: 6153: 6132: 6065: 6044: 5891: 5866: 5392: 5359: 5332: 5307: 5276: 5092: 5057: 5033: 5000: 4882: 4855: 4831: 4807:"Asymmetric amplitude modulations of brain oscillations generate slow evoked responses" 4806: 4527: 4502: 4478: 4453: 4429: 4404: 4278: 4253: 4182: 4155: 4049: 4012: 3904:

Lapicque, LM (1907). "Recherches quantitatives sur l'excitation electrique des nerfs".

3881: 3854: 3738: 3703: 3335: 3310: 3286: 3261: 3237: 3204: 3153: 3128: 3071: 3038: 2834: 2809: 2465: 2413: 2388: 2086: 2059: 2009: 1969:"Activation Complexity: A Cognitive Impairment Tool for Characterizing Neuro-isolation" 1968: 1681: 1555: 1536: 1353: 1313: 1297: 1145: 979: 973: 965: 885: 807: 724: 348: 242: 126: 7240: 6539: 6504: 5813: 5224: 5199: 4946:"Neural Cross-Frequency Coupling: Connecting Architectures, Mechanisms, and Functions" 4609: 4563: 4380: 4345: 3989: 3936: 3371: 2983: 2707: 1369:, which up or down regulates the spontaneous firing frequency of the pacemaker cells. 995:

of interacting neurons can become synchronized and generate large-scale oscillations.

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Hyafil, Alexandre; Giraud, Anne-Lise; Fontolan, Lorenzo; Gutkin, Boris (2015-11-01).

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Ermentrout B (1994). "An introduction to neural oscillators". In F Ventriglia (ed.).

3779: 3762: 3556: 3523: 3488: 3411: 3394: 2913: 2672: 2538: 2162: 1888: 1843: 1637: 1613: 1497: 1490: 1413: 1400:, Most evidence for central pattern generators comes from lower animals, such as the 1251: 1196: 1072: 984: 846: 796: 791:

Limit-cycle oscillations arise from physical systems that show large deviations from

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that places a strong focus on the dynamic character of neural activity in describing

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is another form of rhythmic spiking. Spiking patterns are considered fundamental for

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Lebedev M (2016). "Augmentation of sensorimotor functions with neural prostheses".

6741: 6670: 6471: 6117: 6056: 5882: 5747: 5594: 5499: 5241: 4985: 4906: 4822: 4579: 4518: 4469: 4420: 4269: 4101: 3871: 3839: 3326: 2968: 2825: 2456: 2316: 2270: 2227: 1940: 1920: 1750: 1704: 1578: 1358: 1349: 1309: 1136: 1129: 896: 785: 480: 142: 7210: 5292: 3641: 3311:"Neuronal mechanisms and attentional modulation of corticothalamic α oscillations" 3129:"Neurophysiological and computational principles of cortical rhythms in cognition" 137:. Over the last decades more insight has been gained, especially with advances in 6386: 6346: 5629: 5016: 3177: 2511: 2494: 2146: 519:. This thalamocortical network is able to generate oscillatory activity known as 6178:"Muscle networks: Connectivity analysis of EMG activity during postural control" 5308:"Human spinal locomotor control is based on flexibly organized burst generators" 3802:

Buzsáki G, Draguhn A (June 2004). "Neuronal oscillations in cortical networks".

3205:"Driving fast-spiking cells induces gamma rhythm and controls sensory responses" 1910: 1754: 1554:

Oscillatory rhythms at 10 Hz have been recorded in a brain area called the

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Simulation of a neural mass model showing network spiking during the onset of a

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Neural oscillations in humans were observed by researchers as early as 1924 (by

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Brainwaves, repetitive patterns of neural activity in the central nervous system

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