Phase transitions and self-organized criticality in networks of stochastic spiking neurons

Brochini, Ludmila; Costa, Ariadne de Andrade; Abadi, Miguel; Roque, Antônio C.; Stolfi, Jorge; Kinouchi, Osame

doi:10.1038/srep35831

Cited by 102 publications

(171 citation statements)

References 53 publications

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“…Notice that this mean-field result is also relevant to the quenched case since, as can be seen in Fig. 5e, we have σ * → λ c = 1 for large K. This slight supercriticality has been called selforganized supercriticality (SOSC) by Brochini et al [23]. Curiously, superavalanches (the so called dragon kings) and supercriticality have also been observed in experiments [11].…”

Section: The Time Series λT and Its Fluctuationsmentioning

confidence: 68%

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Correlations induced by depressing synapses in critically self-organized networks with quenched dynamics

et al. 2017

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In a recent work, mean-field analysis and computer simulations were employed to analyze critical self-organization in networks of excitable cellular automata where randomly chosen synapses in the network were depressed after each spike (the so-called annealed dynamics). Calculations agree with simulations of the annealed version, showing that the nominal branching ratio σ converges to unity in the thermodynamic limit, as expected of a self-organized critical system. However, the question remains whether the same results apply to the biological case where only the synapses of firing neurons are depressed (the so-called quenched dynamics). We show that simulations of the quenched model yield significant deviations from σ = 1 due to spatial correlations. However, the model is shown to be critical, as the largest eigenvalue of the synaptic matrix approaches unity in the thermodynamic limit, that is, λc = 1 . We also study the finite size effects near the critical state as a function of the parameters of the synaptic dynamics.

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Section: The Time Series λT and Its Fluctuationsmentioning

confidence: 68%

“…Finally, the case with a = 0 only produces SelfOrganized Supercriticality (SOSC [23]). However, for large number of synapses K, as suggested by biology, networks which are almost critical are obtained, and this can be sufficient to deal with the power laws found in experiments.…”

Section: Discussionmentioning

confidence: 99%

Correlations induced by depressing synapses in critically self-organized networks with quenched dynamics

et al. 2017

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“…We use discrete-time stochastic integrate-and-fire neurons [14,27,28]. A Boolean variable denotes if a neuron fires (X[t] = 1) or not (X[t] = 0) at time t. The membrane potentials of neurons in E and I populations evolve as:…”

Section: The Modelmentioning

confidence: 99%

Synaptic balance due to homeostatically self-organized quasicritical dynamics

Girardi‐Schappo

Brochini

Costa

et al. 2020

Phys. Rev. Research

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Recent experiments suggested that homeostatic regulation of synaptic balance leads the visual system to recover and maintain a regime of power-law avalanches. Here we study an excitatory/inhibitory (E/I) mean-field neuronal network that has a critical point with power-law avalanches and synaptic balance. When short term depression in inhibitory synapses and firing threshold adaptation are added, the system hovers around the critical point. This homeostatically self-organized quasi-critical (SOqC) dynamics generates E/I synaptic current cancellation in fast time scales, causing fluctuation-driven asynchronous-irregular (AI) firing. We present the full phase diagram of the model without adaptation varying external input versus synaptic coupling.This system has a rich dynamical repertoire of spiking patterns: synchronous regular (SR), asynchronous regular (AR), synchronous irregular (SI), slow oscillations (SO) and AI. It also presents dynamic balance of synaptic currents, since inhibitory currents try and compensate excitatory currents over time, resulting in both of them scaling linearly with external input.Our model thus unifies two different perspectives on cortical spontaneous activity: both critical avalanches and fluctuation-driven AI firing arise from SOqC homeostatic adaptation, and are indeed two sides of the same coin.

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Section: Introductionmentioning

confidence: 99%

“…A growing body of evidence in the past few decades has emerged suggesting that many 2 disparate natural and particularly biological phenomena reside in a critical regime of 3 dynamics on the cusp between order and disorder [1][2][3][4][5][6][7][8][9][10]. This seemingly ubiquitous 4 phenomena has sparked a renaissance of new ideas attempting to understand the 5 self-organizing nature of our world [11]. More specifically, it has been shown that 6 critical models, and in particular the Ising model at criticality, model the statistics of 7 brain dynamics quite well [12][13][14][15], which combined with evidence of critical variables in 8 brain dynamics has led to the emergence of the critical brain hypothesis [8,10].…”

Section: Introductionmentioning

confidence: 99%

The emergence of integrated information, complexity, and consciousness at criticality

Khajehabdollahi

Abeyasinghe²,

Owen

et al. 2019

Preprint

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Using the critical Ising model of the brain, integrated information as a measure of consciousness is measured in toy models of generic neural networks. Monte Carlo simulations are run on 159 random weighted networks analogous to small 5-node neural network motifs. The integrated information generated by this sample of small Ising models is measured across the model parameter space. It is observed that integrated information, as a type of order parameter not unlike a concept like magnetism, undergoes a phase transition at the critical point in the model. This critical point is demarcated by the peaks of the generalized susceptibility of integrated information, a point where the 'consciousness' of the system is maximally susceptible to perturbations and on the boundary between an ordered and disordered form. This study adds further evidence to support that the emergence of consciousness coincides with the more universal patterns of self-organized criticality, evolution, the emergence of complexity, and the integration of complex systems. Author summaryUnderstanding consciousness through a scientific and mathematical language is slowly coming into reach and so testing and grounding these emerging ideas onto empirical observations and known systems is a first step to properly framing this ancient problem. This paper in particular explores the Integrated Information Theory of Consciousness framed within the physics of the Ising model to understand how and when consciousness, or integrated information, can arise in simple dynamical systems. The emergence of consciousness is treated like the emergence of other classical macroscopic observables in physics such as magnetism and understood as a dynamical phase of matter. Our findings show that the sensitivity of consciousness in a complex system is maximized when the system is undergoing a phase transition, also known as a critical point. This result, combined with a body of evidence highlighting the privelaged state of critical systems suggests that, like many other complex phenomenon, consciousness may simply follow from/emerge out of the tendency of a system to self-organize to criticality. January 4, 2019 1/12illustrate the control exhibited by the choice of connectivity onto the order parameters 127 across the uniformly sampled random networks, whereas the susceptibilities quantify the 128 mean fluctuations of those order parameters within each random network, averaged 129 across all random networks. These summary statistics give first-order insights into the 130 diagnosis and control of simple neural networks. We note that at the critical 131 temperature, denoted roughly by the peaks of χ, the susceptibility of Φ, χ Φ also peaks. 132 When looking at Φ across different simulations, σ 2 J (Φ), we observe that there seems to 133 be two transition points. One transition point at low temperatures leading into a 134 plateau region followed by a second transition close to the classical critical point where 135 January 4, 2019 4/12

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Phase transitions and self-organized criticality in networks of stochastic spiking neurons

Cited by 102 publications

References 53 publications

Correlations induced by depressing synapses in critically self-organized networks with quenched dynamics

Correlations induced by depressing synapses in critically self-organized networks with quenched dynamics

Synaptic balance due to homeostatically self-organized quasicritical dynamics

The emergence of integrated information, complexity, and consciousness at criticality

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