Synchronization in random balanced networks

Molino, Luis Carlos García del; Pakdaman, Khashayar; Touboul, Jonathan; Wainrib, Gilles

doi:10.1103/physreve.88.042824

Cited by 32 publications

(46 citation statements)

References 18 publications

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“…Some time after we initially publicized the present results, a very recent work [74] examined the case with g 0 ≈ 0, ∞ for our networks. The authors developed a perturbative mean-field theory combined with the approach of [66]. Although they gained insights into the behavior of the model analytically, their theory still largely relies on heuristic approximate calculations, and its application is limited to nearly deterministic dynamics with small fluctuations.…”

Section: Discussionmentioning

confidence: 99%

Spontaneous and stimulus-induced coherent states of critically balanced neuronal networks

Hayakawa

Fukai

2020

Phys. Rev. Research

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How the information microscopically processed by individual neurons is integrated and used in organizing the macroscopic behavior of an animal is a central question in neuroscience. Coherence of neuronal dynamics over different scales has been suggested as a clue to the mechanisms underlying this integration. Balanced strong excitation and inhibition can amplify microscopic fluctuations to a macroscopic level and may provide a mechanism for generating coherent macroscopic dynamics from microscopic neuronal dynamics. Previous theories of brain dynamics, however, have been restricted to cases in which the balanced excitation and inhibition have constrained the macroscopic population-averaged activities to constant values, that is, to cases with no macroscopic degrees of freedom. In the present study, we investigate balanced neuronal networks with a non-zero number of macroscopic degrees of freedom that are coupled to microscopic degrees of freedom. In these networks, the microscopic fluctuations in the network dynamics are amplified by the strong excitation and inhibition to drive the macroscopic dynamics, while the macroscopic dynamics determine the statistics of the microscopic fluctuations. We develop a novel type of mean-field theory applicable to this class of interscale interactions, for which an analytical approach has previously been unknown. Irregular macroscopic rhythms similar to those observed in the brain emerge spontaneously as a result of such interactions. Microscopic inputs to a small number of neurons effectively entrain the whole network through the amplification mechanism. The neuronal responses of the network undergo a transition to coherent states in a probabilistic manner, as the magnitude of either the balanced excitation and inhibition or the external inputs is increased. Our mean-field theory successfully predicts the behavior of this model. Furthermore, our numerical results indicate that the coherent dynamics can be used for state-dependent read-out of information from the network. In conclusion, our results show a novel form of neuronal information processing that bridges different scales, and advance our understanding of the circuit mechanisms of brain computing.

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Section: Discussionmentioning

confidence: 99%

Spontaneous and stimulus-induced coherent states of critically balanced neuronal networks

Hayakawa

Fukai

2020

Phys. Rev. Research

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“…Inspired by the universality of random matrices, in 1984 Bohigas, Gianonni and Schimt [8] formulated their celebrated statement (called "BGS conjecture") concerning quantum chaotic systems: Spectrum of time-reversal invariant systems whose classical analogue are K-systems show the same statistical properties as predicted by Gaussian orthogonal ensembles. Furthermore, Gaussian ensembles proved to be powerful tools to study statistical properties in many applications [27][28][29][30].…”

Section: What Is Quantum Chaos?mentioning

confidence: 99%

About the Concept of Quantum Chaos

Gomez

Losada

Lombardi

2017

Entropy

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Abstract:The research on quantum chaos finds its roots in the study of the spectrum of complex nuclei in the 1950s and the pioneering experiments in microwave billiards in the 1970s. Since then, a large number of new results was produced. Nevertheless, the work on the subject is, even at present, a superposition of several approaches expressed in different mathematical formalisms and weakly linked to each other. The purpose of this paper is to supply a unified framework for describing quantum chaos using the quantum ergodic hierarchy. Using the factorization property of this framework, we characterize the dynamical aspects of quantum chaos by obtaining the Ehrenfest time. We also outline a generalization of the quantum mixing level of the kicked rotator in the context of the impulsive differential equations.

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“…Using Dynamical Mean-Field Theory (DMFT) SCS showed that if the standard deviation of the weight distribution is sufficiently large, the dynamics bifurcate from fixed point to asynchronous chaos. The SCS model in its original form or in its discrete time version has been used in numerous studies in theoretical and computational neuroscience [15][16][17][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Asynchronous Rate Chaos in Spiking Neuronal Circuits

Harish¹,

Hansel

2015

Preprint

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The brain exhibits temporally complex patterns of activity with features similar to those of chaotic systems. Theoretical studies over the last twenty years have described various computational advantages for such regimes in neuronal systems. Nevertheless, it still remains unclear whether chaos requires specific cellular properties or network architectures, or whether it is a generic property of neuronal circuits. We investigate the dynamics of networks of excitatory-inhibitory (EI) spiking neurons with random sparse connectivity operating in the regime of balance of excitation and inhibition. Combining Dynamical Mean-Field Theory with numerical simulations, we show that chaotic, asynchronous firing rate fluctuations emerge generically for sufficiently strong synapses. Two different mechanisms can lead to these chaotic fluctuations. One mechanism relies on slow I-I inhibition which gives rise to slow subthreshold voltage and rate fluctuations. The decorrelation time of these fluctuations is proportional to the time constant of the inhibition. The second mechanism relies on the recurrent E-I-E feedback loop. It requires slow excitation but the inhibition can be fast. In the corresponding dynamical regime all neurons exhibit rate fluctuations on the time scale of the excitation. Another feature of this regime is that the population-averaged firing rate is substantially smaller in the excitatory population than in the inhibitory population. This is not necessarily the case in the I-I mechanism. Finally, we discuss the neurophysiological and computational significance of our results. Author SummaryCortical circuits exhibit complex temporal patterns of spiking and are exquisitely sensitive to small perturbations in their ongoing activity. These features are all suggestive of an underlying chaotic dynamics. Theoretical works have indicated that a rich dynamical reservoir can endow neuronal circuits with remarkable computational capabilities. Nevertheless, the mechanisms underlying chaos in circuits of spiking neurons remain unknown. We combine analytical calculations and numerical simulations to investigate this fundamental issue. Our key result is that chaotic firing rate fluctuations on the time scales of the synaptic dynamics emerge generically from the network collective dynamics. Our results PLOS Computational Biology |

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Synchronization in random balanced networks

Cited by 32 publications

References 18 publications

Spontaneous and stimulus-induced coherent states of critically balanced neuronal networks

Spontaneous and stimulus-induced coherent states of critically balanced neuronal networks

About the Concept of Quantum Chaos

Asynchronous Rate Chaos in Spiking Neuronal Circuits

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