Power-law statistics and universal scaling in the absence of criticality

Touboul, Jonathan; Destexhe, Alain

doi:10.1103/physreve.95.012413

Cited by 186 publications

(242 citation statements)

References 79 publications

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“…In contrast, absence of power laws may also be due to genuine deviations from critical dynamics as we show above. To test how sub-sampling affects the discrimination between cortical states and their critical properties, we modeled a realistic spiking neuron network (see Methods) which is capable of generating population dynamics that closely resemble those seen in physiological recordings [35,53,61,62]. Depending on the overall drive, the network can exhibit irregular bouts of synchronized bursts (synchronous irregular state [61], SI, low input) or largely desynchronized activity (asynchronous irregular state [61], AI, high input), akin to the physiological states shown in this study (Fig 9A and 9B).…”

Section: Resultsmentioning

confidence: 99%

Spontaneous cortical activity is transiently poised close to criticality

Hahn¹,

Ponce‐Alvarez²,

Monier³

et al. 2017

PLoS Comput Biol

109

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Brain activity displays a large repertoire of dynamics across the sleep-wake cycle and even during anesthesia. It was suggested that criticality could serve as a unifying principle underlying the diversity of dynamics. This view has been supported by the observation of spontaneous bursts of cortical activity with scale-invariant sizes and durations, known as neuronal avalanches, in recordings of mesoscopic cortical signals. However, the existence of neuronal avalanches in spiking activity has been equivocal with studies reporting both its presence and absence. Here, we show that signs of criticality in spiking activity can change between synchronized and desynchronized cortical states. We analyzed the spontaneous activity in the primary visual cortex of the anesthetized cat and the awake monkey, and found that neuronal avalanches and thermodynamic indicators of criticality strongly depend on collective synchrony among neurons, LFP fluctuations, and behavioral state. We found that synchronized states are associated to criticality, large dynamical repertoire and prolonged epochs of eye closure, while desynchronized states are associated to sub-criticality, reduced dynamical repertoire, and eyes open conditions. Our results show that criticality in cortical dynamics is not stationary, but fluctuates during anesthesia and between different vigilance states.

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Section: Resultsmentioning

confidence: 99%

Spontaneous cortical activity is transiently poised close to criticality

Hahn¹,

Ponce‐Alvarez²,

Monier³

et al. 2017

PLoS Comput Biol

109

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“…However, avalanches do not usually appear (or are not searched for) in such modeling approaches (see, however, (18,45,46)). …”

Section: Significance Statementmentioning

confidence: 99%

“…To date, we do not have a theoretical understanding of why results are compatible with branching-process exponents. In particular, it is not clear to us if a branching process could possibly emerge as an effective description of the actual (synchronization) dynamics in the vicinity of the phase transition, or whether the exponent values appear as a generic consequence of the way temporally-defined avalanches are measured (see (46)). These issues deserve to be carefully scrutinized in future work.…”

Section: A4) Up-state Phasementioning

confidence: 99%

“…A number of features of criticality, including scale invariance, have been conjectured to be functionally convenient and susceptible to be exploited by biological (as well as artificial) computing devices. Thus, the hypothesis that the brain actually works at the borderline of a phase transition has gained momentum in recent years (20)(21)(22), even if some skepticism remains (46). However, what these phases are, and what the nature of the putative critical point is, are questions that still remain to be fully settled.…”

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confidence: 99%

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Landau–Ginzburg theory of cortex dynamics: Scale-free avalanches emerge at the edge of synchronization

Santo

Villegas

Burioni

et al. 2018

Proc. Natl. Acad. Sci. U.S.A.

180

187

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Understanding the origin, nature and functional significance of complex patterns of neural activity, as recorded by diverse electrophysiological and neuroimaging techniques, is a central challenge in Neuroscience. Such patterns include collective oscillations, emerging out of neural synchronization, as well as highly-heterogeneous outbursts of activity interspersed by periods of quiescence, called "neuronal avalanches". Much debate has been generated about the possible scale-invariance or criticality of such avalanches, and its relevance for brain function. Aimed at shedding light onto this, here we analyze the large-scale collective properties of the cortex by using a mesoscopic approach, following the principle of parsimony of Landau-Ginzburg. Our model is similar to that of Wilson-Cowan for neural dynamics but, crucially, including stochasticity and space; synaptic plasticity and inhibition are considered as possible regulatory mechanisms. Detailed analyses uncover a phase diagram including down-states, synchronous, asynchronous, and up-state phases, and reveal that empirical findings for neuronal avalanches are consistently reproduced by tuning our model to the edge of synchronization. This reveals that the putative criticality of cortical dynamics does not correspond to a quiescent-to-active phase transition, as usually assumed in theoretical approaches, but to a synchronization phase transition, at which incipient oscillations and scalefree avalanches coexist. Furthermore, our model also accounts for up and down states as they occur, e.g. during deep sleep. The present approach constitutes a framework to rationalize the possible collective phases and phase transitions of cortical networks in simple terms, thus helping shed light into basic aspects of brain functioning from a very broad perspective.Cortical dynamics | Neuronal avalanches | Criticality | Synaptic plasticity T he cerebral cortex exhibits spontaneous activity even in the absence of any task or external stimuli (1-3). A salient aspect of this, so-called, resting-state dynamics, as revealed by in vivo and in vitro measurements, is that it exhibits outbursts of electrochemical activity, characterized by brief episodes of coherence -during which many neurons fire within a narrow time window-interspaced by periods of relative quiescence, giving rise to collective oscillatory rhythms (4, 5). Shedding light on the origin, nature, and functional meaning of such an intricate dynamics is a fundamental challenge in Neuroscience (6).Upon experimentally enhancing the spatio-temporal resolution of activity recordings, Beggs and Plenz made the remarkable finding that, actually, synchronized outbursts of neural activity could be decomposed into complex spatio-temporal patterns, thereon named "neuronal avalanches" (7). The sizes and durations of such avalanches were reported to be distributed as power-laws, i.e. to be organized in a scale-free way, limited only by network size (7). Furthermore, they obey finite-size scaling (8), a trademark of scale invariance...

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“…Such distributions were found in the statistics of spontaneous avalanches in cortical tissue recorded with multi-electrode arrays 1,7,8 and, more recently, in the auditory system. 9 In addition to this evidence, distinct potential mechanisms for the emergence of power-law like distributions have been suggested as well, 10,11 and the emergence of power-law avalanche distributions has even been questioned in some experiments. 12 As a result, the avalanche criticality hypothesis 1,13 has remained controversial.…”

Section: Introductionmentioning

confidence: 99%

Avalanche and edge-of-chaos criticality do not necessarily co-occur in neural networks

Kanders

Lorimer

Stoop

2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

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There are indications that for optimizing neural computation, neural networks may operate at criticality. Previous approaches have used distinct fingerprints of criticality, leaving open the question whether the different notions would necessarily reflect different aspects of one and the same instance of criticality, or whether they could potentially refer to distinct instances of criticality. In this work, we choose avalanche criticality and edge-of-chaos criticality and demonstrate for a recurrent spiking neural network that avalanche criticality does not necessarily entrain dynamical edge-of-chaos criticality. This suggests that the different fingerprints may pertain to distinct phenomena. In biological neural networks, scale-free avalanches of neuronal firing events have suggested that such networks might preferably operate at criticality, in particular, since theoretical studies of artificial neural networks and of cellular automata have highlighted some potential computational benefits of such a state. In these studies, notions of either edge-of-chaos criticality or avalanche criticality were adhered to. Here, using a recurrent neural network of more realistic neurons compared with what has been considered previously, we scrutinize whether these two manifestations of criticality are necessarily co-occurring. Based on a realistic paradigm of neural networks, we show that a positive largest Lyapunov exponent-indicating chaotic dynamics of the networkis conserved as we tune the network from subcritical to critical and to supercritical avalanche behavior. This demonstrates that avalanche criticality does not necessarily co-occur with edge-of-chaos criticality.

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Power-law statistics and universal scaling in the absence of criticality

Cited by 186 publications

References 79 publications

Spontaneous cortical activity is transiently poised close to criticality

Spontaneous cortical activity is transiently poised close to criticality

Landau–Ginzburg theory of cortex dynamics: Scale-free avalanches emerge at the edge of synchronization

Avalanche and edge-of-chaos criticality do not necessarily co-occur in neural networks

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