Beta: bursts of cognition

Beta oscillations are linked to the control of goal-directed processing of sensory information and the timing of motor output. Recent evidence demonstrates they are not sustained but organized into intermittent high-power bursts mediating timely functional inhibition. This implies there is a considerable moment-to-moment variation in the neural dynamics supporting cognition. Beta bursts thus offer new opportunities for studying how sensory inputs are selectively processed, reshaped by inhibitory cognitive operations and ultimately result in motor actions. Recent method advances reveal diversity in beta bursts that provide deeper insights into their function and the underlying neural circuit activity motifs. We propose that brain-wide, spatiotemporal patterns of beta bursting re ﬂ ect various cognitive operations and that their dynamics reveal nonlinear aspects of cortical processing.

Beta oscillations are linked to the control of goal-directed processing of sensory information and the timing of motor output.Recent evidence demonstrates they are not sustained but organized into intermittent high-power bursts mediating timely functional inhibition.This implies there is a considerable moment-tomoment variation in the neural dynamics supporting cognition.Beta bursts thus offer new opportunities for studying how sensory inputs are selectively processed, reshaped by inhibitory cognitive operations and ultimately result in motor actions.Recent method advances reveal diversity in beta bursts that provide deeper insights into their function and the underlying neural circuit activity motifs.We propose that brain-wide, spatiotemporal patterns of beta bursting reflect various cognitive operations and that their dynamics reveal nonlinear aspects of cortical processing.

Beta oscillations are transient and reflect executive control
Brain dynamics are naturally rhythmic, with countless neurons syncing and harmonizing electrical activity across various frequencies [1].Beta band oscillations , in particular, are linked to top-down executive control processes that implement goal-directed behavior [2][3][4][5][6][7][8][9][10][11].In most studies, spectral analysis measures are averaged over repeated trials to increase the inherently low signal-to-noise ratio.This results in seemingly sustained oscillations that are slowly modulated.However, variation across trials may reflect meaningful neural dynamics rather than noise.Indeed, recent single-trial analyses have revealed that primarily beta (but also other) oscillations are organized in brief high-power bursts of much shorter duration (10s to 100s of milliseconds) than the cognitive tasks themselves [12][13][14][15].
The earliest systematic evidence for beta bursting comes from the motor cortex-thalamusbasal ganglia loop during movement planning and execution [15][16][17][18][19][20][21][22][23].Here, beta bursts are correlated with suppression of movement and reduction of movement speed [22,23].However, several studies also propose that prefrontal beta bursts provide transient inhibition in the executive control of working memory (WM) [13,24,25].This evidence, together with the established role of beta oscillations in top-down processing, may suggest a general role for beta bursts in cognition.
Here, we first discuss why the transient nature of beta oscillations considerably changes how we think about cognitive processes and models.Then, we review recent evidence that beta bursts, often emerging in prefrontal and premotor areas, provide transient inhibition suitable for a general role in top-down executive control in various cognitive functions.We highlight how recent advances in burst analysis point towards a diversity in their origin and function, and how burst analysis may help give insights into the underlying circuit mechanisms.Next, we discuss how these findings yield novel insights into the nonlinear network interactions that support executive functions.Finally, we point out important future research directions building on these insights.

Highlights
Brief beta bursts, rather than sustained oscillations, support cognition by providing transient, functional inhibition.
Analyzing the timing of beta bursts helps establish neural correlates of cognitive behavior on a single trial level.
The intermittent and nonlinear nature of beta bursts provides novel insights into interareal interactions.
Diversity of beta burst types may reflect differences in circuit-level origins and may yield insights into the underlying activity motifs and function.
We suggest that spatiotemporal patterns of beta bursting implement cognitive control operations underlying goaldirected behavior.

Why do bursts matter?
Before providing evidence for the involvement of beta bursts in cognitive control, we put forward six arguments for why intermittent oscillations have important implications for cognition.We will revisit these points as we review the experimental evidence in subsequent sections.
First, the intermittent nature of oscillations implies that cognition and executive control are supported by frequent switching between discrete transient states rather than continuously and slowly changing dynamics (Figure 1A).This has fundamental implications on how we conceptualize brain functions underpinning goal-directed behavior, as it suggests that the functions themselves emerge from a set of discrete operations reflected in transient states.
Second, as bursts reflect abrupt transitions between low-and high-amplitude oscillations, they are a hallmark of nonlinear brain dynamics.Unlike Gaussian signals, the amplitude of oscillations does not follow smooth fluctuations.Instead, it is subject to abrupt shifts with considerably higher likelihood of large-power, extreme events than expected by a normal distribution.As we shall see, this has several potentially important implications.transient bursts of activity.The variation in timing of bursts may be characterized either as an average burst rate (top; [13]), by studying interburst intervals (IBIs) [14,15,45]) or variability across trials measured by the Fano factor [14,53]. (B) Average power difference between two conditions (blue and black) may have distinct underlying causes that can be accessed by single-trial burst analysis [13,14,106].(C) Beta bursts may be further distinguished by their waveforms to find different phenotypes, for instance, by using clustering algorithms or principal component analysis [41,101,104].(D) Each individual burst can be characterized with additional features such as central frequency, duration and frequency span by, for example, fitting 2D Gaussian in the joint time-frequency domain [13].See also Box 1 in the main text.
Third, as a consequence of the first two points, intermittent oscillations cast new light on largescale interactions in the brain.The collective coordinated dynamics between regions may offer computational versatility, with transient brain-wide interactions providing a dynamical substrate for flexible cognition [26].In this view, new event-based analysis methods (enabled by the transient nature of bursts) or information theoretical measures better capture the dynamical nature of interactions between nonlinear nodes than conventional spectral coherence and linear correlations [27,28].
Fourth, intermittent oscillations encourage new ways to examine experimental data (Box 1).The modulation of average band power by cognitive states could be driven by various characteristics of the underlying bursts, including their amplitude, frequency range, rate, and duration, providing additional insights into the underlying mechanisms (Figure 1B-D).The temporal distribution of bursts in trials casts new light on neural variability (Figure 1A).In addition, the precise timing of oscillatory bursts in single trials offers opportunities for event-based analyses such as temporal colocalization of neural correlates with behavior [22,23], with bursts in other regions or with other neural measures, such as spike rates [24,29,30].Establishing a relationship between spiking and oscillatory bursts renders bursts as a proxy for population spiking or activity motifs.On the other hand, it is important to ensure that the seemingly intermittent oscillations are truly intermittent(on-off) and not simply continuously modulated in amplitude, to make correct conceptual inferences [31,32].
Fifth, future computational and cognitive models should account for the transient and intermittent operational dynamics reflected in bursty oscillations.This is relevant for all models that study the link between brain dynamics and function.In other words, intermittent activity poses constraints not only on the implementational level but also on the possible computational algorithms adopted.Burst analyses reveal that intermittent beta bursts are not limited to a particular cognitive process but occur during all phases of a cognitive task and at rest [13].

Box 1. Burst detection and characterization
Oscillatory bursts constitute events of high power and thus their identification boils down to detecting whether power temporarily exceeds a certain threshold [13][14][15].This approach comes in different flavors depending on how the instantaneous band power is estimated, how the detection threshold is determined, and what constraints are defined.Band power is obtained directly in the temporal domain by filtering the data in specific frequency bands, or in the spectrotemporal domain by extracting time-frequency (TF) maps.Next, to find and calibrate the burst-defining threshold, the band power signal is typically normalized relative to its estimated center (median or mean) over a selected period: a given trial, multiple trials or taskrelated trial epochs.The threshold itself is typically expressed as the multiplicity of the median [14] or the standard deviation of the signal's band power above its mean [13,17].The actual power threshold can be decided based on the distribution following the 1/f fitting procedure [127,128], as the cut-off that maximizes the correlation of the generated burst frequency with band power [14,17] or by using surrogate data to validate the extracted power fluctuations as actual burst events [15,129].Finally, there are typically additional constraints applied, such as the minimal duration [13].
Individual bursts can be further characterized by their duration, central frequency, frequency span or amplitude.To estimate these parameters it was originally proposed to characterize burst events in the joint TF space by locally fitting 2D Gaussian (mixture models) to detected bursts [13].Burst TF centroids can also be directly extracted from spectrograms as local maxima [14].For each TF centroid, burst duration and frequency span can then be determined, for example, as full-width-at-half-maximum.With additional spatial dimension, spatiotemporal burst dynamics can also be captured [102].Finally, a characterization of temporal burst waveforms by means of their 20-dimensional principal component projections has been suggested [101].Some alternatives to band-power-thresholding approaches have been proposed.Transient neural oscillations could potentially be better characterized with a cycle-by-cycle analysis, exclusively in the time domain, than by using conventional spectral representations [46].Matching pursuit represents another time-domain method, involving the iterative fitting of a signal with a dictionary of oscillatory waveforms, which could correspond to bursts and other transient events [130].Finally, Hidden Markov Models have been employed to represent a signal as probabilistic transitions between a set of discrete states, some of which correspond to rhythmic burst-like events [98,104,105].
High-power states revealed in trial averages merely imply that the bursts are more consistently aligned in a particular phase of the trial (Figure 1A).Theories about the function of beta oscillations must therefore account for this.Here, we propose that beta bursts reflect so-called functional inhibition (in analogy to the more established role of alpha power in occipital and parieto-occipital areas [33,34]).In this regard, the brain is continuously balancing excitatory and inhibitory operations, and only some of this functional inhibition, and thus beta bursts, are related to the cognitive process being studied.

Beta bursts provide functional inhibition in cognition
Having established why intermittent oscillations have broad implications for how we study cognition, we now review evidence that beta bursts reflect functional inhibition in cognitive functions such as WM, attention, and action selection.By functional inhibition we imply an operational effect of disrupting task-related computations, which is not necessarily implemented as inhibition of activity on the neural level.Given the limited knowledge of the circuit origins of beta bursts, current data leave open whether beta mechanistically mediates this operational inhibition or merely reflects its correlation.
Beta bursts for executive control of WM In a series of studies, we have established that beta bursts correlate with inhibitory executive functions in WM [13,24,25,[53][54][55][56][57][58].We used intracranial recordings in prefrontal cortex of nonhuman primates to test predictions from a computational model [58].This confirmed that beta bursts reflected intermittent inhibition during various stages of WM control such as encoding, read-out, or selective deletion of information (Figure 2A,B) [13,24].Beta bursts were spatially and temporally anticorrelated with gamma bursts (40-100 Hz), which were in turn associated with elevated spiking informative of the WM contents.The gamma bursts thus reflected spiking on the population level, and their pattern could largely explain the variability of spiking in single neurons across trials [53].Beta bursting was instead associated with both reduced spiking and reduced gamma bursting.It was suppressed at times and cortical locations in which information was encoded into or selectively read out from WM [13]; that is, when gamma/spiking was high.These patterns also suggested a division of labor between deep layers dominated by beta and superficial cortical layers dominated by gamma activity in control and retention of WM, respectively [55].As content held in WM was updated, the patterns of beta and gamma bursting were again consistent with beta bursting as an inhibitory correlate: beta dictating when active processing occurred and gamma reflecting the active processing itself [54].Moreover, following the end of each trial, beta bursting was highly elevated specifically on locations that had stored WM information in spiking during the trial itself [24].This distinction between sites indicates that a surge of beta bursting clears out WM in preparation for the next trial (Figure 2B), rather than beta reflecting some baseline idling rhythm the network returns to.This view is supported by a recent study where diminished beta power rebound in patients with obsessive compulsive disorder correlated with impaired ability to remove information from WM [59].Recently, more evidence for the similar motifs of dynamic beta burst modulation correlated with WM control operations has been reported in human MEG recordings [60].In particular, beta bursting was reduced during the encoding of stimuli, and more so for relevant than for irrelevant stimuli.Similarly, beta bursts were suppressed during encoding and then elevated during subsequent retention of WM content in intracranial recordings from the endbrain of crows [61]; the analog of the mammalian prefrontal cortex (PFC).This suggests that beta bursts could have a similar functional role irrespective of differences in supporting neural architectures.
As for the origins of prefrontal beta bursts related to WM, we have speculated [57] that they may be generated in the thalamic-basal ganglia loops, analogously to motor planning [38,39,42,62,63].Recent evidence from rats indeed suggests that beta bursts in thalamic nucleus reuniens precede prefrontal and hippocampal beta bursts during WM performance [64].Avg.

burst rate Frequency
Non-responding pop.
Responding pop.information to be held over a retention period, before the information is read out and compared with a test probe.A single-trial time-frequency decomposition (top) reveals gamma and beta bursts with elevated spiking during gamma and decreased spiking during beta bursts.The trial averaged burst rates (bottom) are anticorrelated between the two bands [13].(B) Beta burst rates are selectively reduced during encoding in cortical locations with responsive neuronal populations (red) compared with cortical locations with unresponsive neurons, consistent with the role of beta bursting in controlling encoding.In the post-trial period the relationship is reversed, beta bursting is instead much higher in cortical locations with responsive neurons.This is in line with the role of beta in clearing out WM contents for the next trial [24].(C) Spatial computing is implemented by spatiotemporal patterns of beta bursting [25].A cell assembly responding to a certain stimulus is recurrently connected and distributed spatially in cortex (left).By applying distinct spatial patterns of inhibitory beta bursting in, for example, the encoding of the first (middle) and second (right) item, the brain can exert top-down control and decide which parts of the assembly get activated by each stimulus in the sequence.In this way the network can access information related to the first and second item without knowledge of the underlying cell assemblies.Space is used as an additional encoding dimension that attributes functional cognitive status to neural representations of WM (see Box 2 in the main text).
We stress that the intermittent nature of beta (and gamma) oscillations is conceptually important in this context because it implies that WM is supported by transient inhibition and reactivation processes.In line with our arguments for the relevance of bursts, this suggests that cognitive processes may indeed be discrete.Transient activity lends support to models that rely not only on sustained patterns of spiking activity to retain information, but also on alternative mechanisms such as temporary encoding of information in synapses or cellular mechanisms [58,[65][66][67][68][69].
Evidence that beta bursts reflect the control of individual items held in WM raises the question of how such oscillations, accounting for population activity within hundreds of microns, can be selective enough to target individual items that are represented by specific patterns (ensembles) of individual neurons on a fine spatial scale (Figure 2C).To answer this, we proposed the concept of Spatial computing (Box 2), where network space is utilized as an additional coding dimension, and provided supporting neural evidence by analyzing beta, gamma, and spiking patterns [25].In this concept, it is the spatiotemporal pattern of inhibition, reflected in beta bursts during various cognitive processes such as encoding or comparing two WM items, which is controlled rather than individual neurons (Figure 2C, Box 2).Although beta bursting was analyzed on the mesoscale within the PFC [25], the spatial patterning of inhibition could in principle be functionally exploited at any scale.In subsequent sections, we review evidence that cognitive strategies may also be reflected in spatiotemporal patterns of inhibitory beta bursts in brain-wide networks.

Box 2. Spatial computing
Prior work has demonstrated that oscillatory bursts, which incorporate the activity of hundreds of thousands of neurons, control items held in WM during encoding, prioritization and comparisons to test probes [13,24].Spatial computing addresses the question of how such spatially imprecise bursts can selectively target one out of several memory representations held in WM [25], and how this control process knows which neurons to up-and downregulate when, for instance, reading out one of several items held in WM.That would seem to require a cognitive homunculus inside the brain with knowledge of the preferences of all neurons [131,132].Flexibility in using WM implies that executive control should generalize memory operations to novel items and it should not rely on detailed information as to which specific neurons represent concrete items.For example, there could be a need to access the first or second item in the sequence without really knowing the actual memory content (item identity) or which neurons represent it.These problems may be solved by using cortical space as an additional encoding dimension [132].As an example, two items encoded sequentially could be accompanied by distinct patterns of top-down induced beta bursting during encoding.These patterns then dictate which subsets of item-selective neurons currently represent each item and where they are located in network space (Figure 2C).This enables subsequent item-specific read-out, by upregulating activity in the respective parts of the network.We propose that this way control processes generalize beyond the specific memory items they have been trained on in the first place.Similarly, the status of a mental representation may be updated over time by changing the imposed beta patterns.
The top-down beta activity in turn imposes shared low-dimensional spiking activity associated with the controlled execution of a task rather than with processing the stimulus.Such low-dimensional activity has indeed been linked to task execution in several studies [25,[133][134][135][136].Spatial computing predicts that low-dimensional subspaces are shared more strongly between nearby neurons than predicted by their connectivity, as they are imposed by spatial patterns of beta.Thus, in this view, the allocation of individual neurons to different subspaces can also flexibly change between tasks.Analysis of spiking, gamma and beta patterns revealed low-dimensional patterns in oscillatory bursting that were stable across recording sessions but distinct between different WM tasks [25].The finding that executive WM control functions are observable in spatial patterns of beta bursting (and thus spatially separated) in the cortical sheet implies in turn that the proposed beta bursting mechanism has sufficient spatial precision to target individual WM items for selective memory operations such as deletion or read-out.
Conceptually similar ideas were recently suggested for predictive coding [111], where the cortical landscape of inhibition may suppress predictable inputs and focus processing on unpredicted inputs.We speculate that the proposed Spatial computing may be a general principle for implementing cognitive strategies through spatiotemporal inhibition, limiting the space of possible computations by dictating when and where sensory processing (reflected in gamma) takes place.
Beta bursts reflect functional inhibition in other cognitive tasks Cortical beta bursts have been linked to other executive control processes beyond WM.Here, we review evidence that they provide analogous functional inhibition in memory, executive functions and attention.
Several studies using transcranial stimulations have linked trial-by-trial beta power to attention and memory formation [70].First, lower beta power in the inferior frontal gyrus led to improved subsequent recall in long-term memory formation, suggesting a similar role as prefrontal beta bursting during WM encoding [70].Second, parietal single-trial beta power has also been linked to neural excitability [71] (monitored by phosphene perception) and successful performance on discrimination tasks with visual crowding [72,73], where perceiving targets in the peripheral vision is impaired by the presence of nearby flankers.On trials with a strong crowding, which require a more focused top-down filter to correctly perceive the target, elevated beta power was associated with better performance [73].Similarly, stimulation specifically at beta frequencies over parietal areas improved performance [72].
Upon the prediction of upcoming tactile stimuli, contralateral beta power over the somatosensory cortex in human MEG is suppressed, and stronger suppression is linked to faster response times [4].The rate of short-lasting beta events in somatosensory cortex, rather than their exact duration or amplitude, is modulated by attention and anticorrelated with tactile stimulus detection performance [14,74].A supportive modeling study proposed that somatosensory beta events are the result of transient activation from the higher-order thalamus [12].Collectively these findings share interesting similarities to the inhibitory role of occipital beta bursts for anticipated distractors in WM [60].PFC beta bursts reflect switches between exogenous to endogenous attention by selectively reducing spiking in neurons selective to the exogenous stimuli [29].Taken together across cortical areas and cognitive modalities, beta bursts may act as spatiotemporal filters that modulate information flow on a brain-wide scale by providing transient functional inhibition.This inhibitory role of beta in cognition also generalizes to mental control in a 'Think/No-Think' task where learned word pair associations occasionally need to be prevented from retrieval at the last moment [75].Successful stopping of such mental action was linked to brief increases in averaged beta power in electroencephalogram (EEG) electrodes over right frontal areas.Similarly, directed forgetting, where a 'Forget cue' informs subjects that a given word stimulus will not be prompted later and thus encourages subjects to forget the word, leads to similar beta increases [76].This is an interesting parallel to the elevated beta bursting in the PFC of monkeys clearing out WM at the end of each trial [24].Beta bursting in the putative right inferior frontal cortex of human subjects measured with EEG has been linked to action stopping [77][78][79].Combining both directed forgetting and action stopping in the same experiment, the use of EEG and neural decoders demonstrated that the neural correlates of the two tasks highly overlap [76].This is consistent with theories suggesting cognitive control evolved from motor control, deploying analogous cortico-thalamic-basal ganglia loops to regulate cortical excitability in both regimes [57,80,81].Indeed, there is ample evidence for a shared neural machinery between inhibition of actions and inhibition in cognition [63], ultimately manifested as transiently elevated beta power.Thus, the functional inhibition mediated by beta across modalities may also have shared neural origins.
Regardless, in terms of underlying machinery, action stopping is better understood than disruption of cognition processes, partly because of the more direct connection to observable behavior.Thus, existing studies on action stopping may inspire future cognitive research.The temporal order in which beta bursts in the right inferior frontal cortex and in the basal ganglia-thalamus loop [50,[77][78][79][82][83][84] are induced during successful action stopping may provide valuable insights into how executive commands arise.Some, but not all, of these studies reported beta burst properties as single-trial correlates of action stopping [77,78,[82][83][84].Still, we should be careful with such a parallel since enhanced beta bursting over frontal regions was also reported following unexpected sensory events and during error coding [85,86], implying that this inhibitory effect may not be strictly under top-down control.However, evidence suggests that surprise activates a global suppressive network that temporarily pauses the ongoing action and leads to motor slowing [87].Thus, excessive frontal beta bursting following surprise and during error processing could hypothetically be linked to suppression of motor action.
Taken together, beta bursts appear to provide functional inhibition in a wide range of cognitive processes and cortical areas.However, there have been conflicting findings regarding whether the inhibitory role of beta bursts is reflected in reduced firing rates [13,24,29,88].We propose that functional inhibition may be implemented in different ways on the neural or circuit level, for example, by reducing overall firing rates, by increasing spiking in a population of inhibitory neurons, or by disrupting the information content in neuronal spiking without changing the overall level of population activity.There is a clear need for future studies to shed more light on how the presumed functional inhibition is implemented and provide insights into the underlying neural mechanisms.

Diversity in beta bursts, diversity in function?
In several tasks, it is hard to explain the modulation of beta bursting from the perspective of functional inhibition.This is either due to the nature of the task, with no clear prediction on when inhibition should occur, or because the outcomes of the experiments have been interpreted as beta performing active processing [85,86,[89][90][91].Therefore, we discuss here whether various beta burst phenotypes can be identified and correlated with a more diverse set of functions.In fact, there has been a long-standing debate about the functional role of beta oscillations [10,11,92].This debate could potentially be resolved by considering whether distinct types of beta bursts have different functions.
First, beta oscillations in a wide range of frequencies have often been treated as the same rhythm.However, both low and high frequency peaks in the beta band have been commonly reported and referred to as beta-1 and beta-2, respectively, with partly varying functional correlates [92][93][94].Likewise, tracking the central frequency of cortical beta activity measured intracranially reveals shifts in the central frequency of bursts over the course of an experimental task [24,89], or even within single bursts [95].Distinct beta frequencies may also reflect the origins of the underlying bursts with faster frequencies arising in the higher areas in the cortical hierarchy [56,[96][97][98].In addition, instantaneous dopamine levels modulate the central frequency of beta oscillations in cortex and basal ganglia [99] in humans and non-human primates, consistent with instantaneous frequency reflecting the level of excitation.Thus, differences in the central frequency of bursts may sometimes reflect changes in excitation, but other times reflect oscillations generated by distinct neural processes with potentially different functional roles.
Similarly, differentiating beta bursts based on waveform morphology or other features suggests some functional heterogeneity even within a single task [100][101][102][103].This complexity may provide a potential way forward in the debate on the function of beta oscillations.By recognizing and categorizing variability in beta waveforms [41,44,46,95,101,104], central frequency and duration of bursts [13,14,105], their origin [106], relationship to spikes [24,42], direction of propagation [102] and other metrics we may gain deeper insights into circuit level mechanisms underlying different beta bursts.As recently suggested in the context of gamma oscillations [107], individual burst phenotypes may then be used as proxies for transient activation motifs of the underlying neural circuits (Figure 3A).For example, these motifs could be concerned with varying participating neuron subgroups or a distinction between locally generated bursts and those imposed by other areas.Therefore, studying different beta burst phenotypes and the associated motifs would offer insights not only into their neural origins but also into their functional roles.
Still, we argue that to obtain a more integrative perspective on the mechanistic origins and as well as functional implications of different beta bursts more effort should be invested into computational modelling.Currently, two types of computational mechanisms explaining the transient nature of bursts have been suggested.Either they are driven by transient inputs or the result of fluctuating, transient dynamics within the simulated networks themselves.In the former case, beta events can arise depending on how transient thalamic input currents are integrated in the network [12,18,74] or by transiently driving an oscillatory response in the connected inhibitory and excitatory neural populations [62].In the latter case, the oscillations are generated by similar interactions between inhibitory and excitatory populations, but their transient nature is due to spontaneous flip-flop behavior of the network occasionally visiting states that generate the oscillations [58,108].It remains unknown which of these models, if any, builds on correct assumptions.Likewise, it is unknown how beta bursts arise as a mediator of an executive command that cascades to other regions of the brain.Therefore, having discussed earlier the potentially distinct functional roles of different burst phenotypes, it is important to establish how they propagate or coincide in two connected brain regions.Next, we discuss novel insights that crossregional analysis of beta bursts reveal about interareal interactions and how they shift from moment to moment.

Beta bursts in interareal interactions
Cognition is thought to emerge from large-scale interactions, with abrupt transitions between global network states underlying the flexibility of mental operations [26,109] (Box 3).Beta synchronizes over large distances [110] and conveys top-down executive information from prefrontal regions to motor and sensory areas [2][3][4]8,111].Growing evidence for the intermittent nature of beta promises to offer a better understanding of such large-scale interactions and to bring about a change in how we analyze them.
First, the transient nature of beta allows us to track moment-to-moment changes in interactions between brain regions.In fact, if beta bursts can provide insights into the activity motifs in the underlying circuit, as suggested earlier, these burst events enable a detailed analysis of the directionality and timing of interactions on an event-by-event basis (Figure 3B).For example, such an event-based approach revealed that the direction of communication between cortical areas and basal ganglia, inferred from spiking activity, reversed during beta bursts in non-human primates [112].Furthermore, transient parietal beta oscillations were linked to the time of routing of information in perceptual decision making in non-human primates [113].The moment-to-Box 3. Nonlinear brain dynamics and bursts The brain is a nonlinear system, which in simple terms implies that it does not follow the principle of proportionalityits response does not depend on the input strength.This nonlinear input-output transform defines the fundamental behavior of neurons, often conceptualized as threshold units following an all-or-nothing law.Although networks composed of such units inherit nonlinear processing capabilities, their dynamics could sometimes be reduced and linearized.This raises a relevant question of whether nonlinearities characterize intrinsic global dynamics in the brain.There has been a lot of evidence suggesting that the neural activity, captured at different scales, from spiking to MEG recordings, presents a range of nonlinear complex behaviors, often spontaneously arising even without any external stimuli [118,129,137,138].Consequently, the brain is described as a complex system that has emergent properties through nonlinear interactions of its parts, from neurons and local circuits to networks and brain areas.It cannot be understood by a simple sum or superposition of these parts.Its rich functionality builds on the coordination dynamics within and between system components.If they were the result of a linear superposition of activity at smaller scales, say neuronal ensembles, then collectively the fluctuations would be described by a Gaussian distribution.However, there is growing evidence for the heavy tailed distributions, for the beta band activity among others [129].This implies that extreme fluctuations are more frequent than those predicted by models where activity diffuses linearly [139].Beta bursts are the manifestation of such fluctuations and on a macroscale they are accompanied by abrupt global state changes with different populations of neurons and subsets of networks being coactivated, thereby collectively contributing to large-scale interactions, reflected in the dynamic beta bursting connectome (Figure 3D).The global nonlinear coordination dynamics facilitates such fast transient coupling between some neural networks and decoupling between others [26,109,139], which is hypothesized to underlie our cognitive flexibility among others.Studying the brain as a complex nonlinear dynamical system has helped explain emergent phenomena in neural activity and paved the way for computational theories that reconcile biological findings across scales.
moment direction of interactions can also be derived from the propagation of bursts (Figure 3C), which was recently demonstrated to form travelling wave patterns [102].It was observed that sensorimotor beta bursts measured with MEG in humans moved along two principal directions with distinct behavioral correlates.Relatedly, beta waves propagating along a few principal directions in higher order cortex of non-human primates have also been linked to reward processing and WM performance [114,115].
Second, beta bursts measured with MEG in humans shed light on large scale interactions and how brain networks perform abrupt coordinated switches from one global brain state to another.Global patterns of beta band power correlations correspond to a subset of resting state networks, including those associated with executive functions [97,116].In later studies, it was argued that these correlations can be explained by coincident interareal beta bursts (Figure 3D), which was thus proposed to drive global network coordination shaping the beta bursting connectome [27,98].These resting state beta burst patterns are functionally relevant as they could predict beta patterns during the execution of motor as well as WM tasks [117].Importantly, the activations of these networks reflect the nature of burst dynamicsthey are transient and abruptly switch on short-time scales [118,119], which suggests underlying nonlinear dynamics [26,109].In consequence, traditional methods measuring interactions between oscillatory nodes in these functional global brain networks, such as synchrony and linear correlations, are likely to miss burst-driven event-like interactions and do not account for nonlinear coupling effects induced by transiently aligning bursts [27,120].Some studies indeed indicate that burst coincidence is a better indicator of the resting state networks than coherence [27,98], and that coherence may suggest spurious synchrony arising from high-power events like bursts [121].The assumption behind classical synchrony-based measures rests on individual regions having sustained oscillations that transiently align in phase (not necessarily with zero-phase lag) with other regions to form flexible interactions rather than transient overlapping windows (bursts) of activity [122].From a functional perspective, interactions built on the transient coactivations of bursts would be robust as they do not have to rely on phase alignment or millisecond-level synchronization between the oscillatory networks.The interactions would still be selective by the controllable co-occurrence of bursting windows and the specificity of cell assemblies or cell types recruited for population beta bursts (Figure 3B,D).Thus, there is a need to extend our brain signal analysis toolbox with methods that account for the event-based nature of bursts [123], their coincidences (even occurring across different frequency ranges), and inherent nonlinear components [28].
How these transient global network states reflecting functional inhibition are dynamically formed and coordinated, on the top of the local circuit mechanisms discussed earlier, remains an open question.Several studies indicated that the timing of cortical beta bursts is coordinated by subthalamic and thalamic structures [63,64,74,77,82].In rats, for example, driving the thalamic nucleus reuniens by optogenetic techniques generated similar patterns of coordinated beta bursting in prefrontal cortex and hippocampus as during WM performance [64].We thus speculate that similar cortico-subcortical interactions underlying movement regulations may also be involved in the coordinated activation of various networks involved in cognitive tasks.

Concluding remarks
We have reviewed evidence that beta is manifested as brief bursts that reflect functional inhibition and thus have an analogous role in cognition as in motor planning and execution [80,81].We propose that brain-wide spatiotemporal beta burst patterns reflect cognitive strategies, which we refer to as Spatial computing (Box 2).These patterns are a correlate of the functional inhibition that orchestrates the execution of cognitive strategies by first shaping sensory processing (reflected in transient gamma activity) and ultimately controlling motor outputs.The transient dynamics of bursts implies that these functional operations may be discrete rather than continuous.The growing evidence for a fundamental role of beta burst patterns in executive cognitive functions opens several new research avenues in cognitive neuroscience (see Outstanding questions).We also envisage a need to continue studies that shed light on the potential diversity in function of beta bursts, beyond inhibition, as well as their circuit-level origin.While we have focused here on beta bursts, transient activity in other bands and how they relate to beta will also be important directions of future research [13,25,36,95,[124][125][126].
In studies on motor behavior in health and disease, beta burst analysis has already had substantial impact [15,38].In comparison with motor behavior, it is experimentally more challenging to disentangle the timing of cognitive processes.However, we still foresee a similar trend towards event-based beta burst analysis in cognitive research as it can cast more light on relevant inhibitory processes, especially if the circuit activity motif such as the activation of subsets of neurons may eventually be inferred from bursting patterns.Importantly, since cognition emerges on the systems level via interareal interactions, the potential of beta bursts to generate novel insights about how transient constellations of network states are formed and globally coordinated is particularly valuable.
In conclusion, we propose that beta bursts provide both experimental and computational studies with a window through which to explore the real-time organization and execution of cognitive functions.To fully leverage this potential there is a need to address the outstanding questions with new experimental paradigms, analytical methods and modeling approaches.

Figure 1 .
Figure 1.Oscillatory bursts underlie band power changes across trials and provide insights into neural dynamics.(A) Average power across trials suggests slowly changing dynamics, whereas single-trial analysis reveals

Figure 2 .
Figure 2. Beta bursts in executive control of working memory (WM).(A) A simple WM task requires encoding of

Figure 3 .
Figure 3. Bursts as windows into the underlying circuit activity and interactions.(A) Bursts may reflect moment-tomoment state changes in the underlying neural population activity.Burst onsets may provide insights into the transient activation of different neuron species (left).By simultaneously extracting burst phenotypes, deeper insights into the transient activation of distinct cell assemblies may be obtained (right), providing insights into transitions in the neural population activity.(B) The dynamics sketched in (A) could, when analyzing multiple connected regions together, provide insights into nonlinear interactions across cortical areas [black (a) and blue (b)].The presence of interactions (left) or shifts in their directionality (middle, right) might be inferred from the burst patterns in the two regions [112].(C) The direction of interactions between areas [black (a), blue (b), and red (c)] can alternatively be studied by analyzing the temporal propagation of bursts [102].(D) Interactions are not necessarily reflected in correlations of average power or burst rates (top) between two areas [black (a) and blue (b)].They can instead be studied based on how single bursts align from trial to trial (bottom).