Hysteresis, neural avalanches, and critical behavior near a first-order transition of a spiking neural network

Abstract

Many experimental results, both in vivo and in vitro, support the idea that the brain cortex operates near a critical point and at the same time works as a reservoir of precise spatiotemporal patterns. However, the mechanism at the basis of these observations is still not clear. In this paper we introduce a model which combines both these features, showing that scale-free avalanches are the signature of a system posed near the spinodal line of a first-order transition, with many spatiotemporal patterns stored as dynamical metastable attractors. Specifically, we studied a network of leaky integrate-and-fire neurons whose connections are the result of the learning of multiple spatiotemporal dynamical patterns, each with a randomly chosen ordering of the neurons. We found that the network shows a first-order transition between a low-spiking-rate disordered state (down), and a high-rate state characterized by the emergence of collective activity and the replay of one of the stored patterns (up). The transition is characterized by hysteresis, or alternation of up and down states, depending on the lifetime of the metastable states. In both cases, critical features and neural avalanches are observed. Notably, critical phenomena occur at the edge of a discontinuous phase transition, as recently observed in a network of glow lamps.

Modeling neuronal avalanches and long-range temporal correlations at the emergence of collective oscillations: continuously varying exponents mimic M/EEG results

“…Moreover, the exponents are related to the those ruling the distributions of avalanche size and duration [27,9,26]:…”

Single-cell membrane potential fluctuations evince network scale-freeness and quasicriticality

“…The scaling relation is another power-law ⟨ ⟩( ) ∝ predicting how the measured size of avalanches increase geometrically with increasing duration (on average). For any data set which has three power-laws, ⟨ ⟩( ) ∝ (scaling relation), ( ) ∝ − (size distribution), and ( ) ∝ − (duration distribution), the scaling relation exponent is predicted by the other two exponents by ≈ = ( −1) ( −1) (Scarpetta et al, 2018). Note that = 1 is a trivial value because it implies ⟨ ⟩( ) ∝ and that would suggest individual avalanches were just noise symmetric about a constant value.…”

“…Another statistic crucial to signatures of criticality measures the relationship between the power-laws describing size and duration of avalanches (Sethna et al, 2001;Beggs and Timme, 2012;Friedman et al, 2012). If the average avalanche size also scales with duration according to ⟨ ⟩( ) ∝ , then the exponent is not independent, but rather depends on the exponents and β according to = ( − 1)/( − 1) irrespective of criticality (Scarpetta et al, 2018). For critical systems this condition is enforced because avalanche profiles follows the same shape for all durations which means that this prediction is believed to be more precise than for noncritical systems and the exact values are important (Sethna et al, 2001;Nishimori and Ortiz, 2011).…”

“…Qualitatively, these were reflected in the network activity. As the presence of these paradoxical behaviors may indicate the presence of second phase-transition tuned by the balance of excitation to inhibition (Shew et al, 2011;Poil et al, 2012;Kello, 2013;Hesse and Gross, 2014;Larremore et al, 2014;Scarpetta et al, 2018) several key results differ strongly and thus are reported separately for these regions of parameter space.…”

“…It is known that so long as three requirements are met the scaling relation will be marginally obeyed: Avalanche size and durations must be power-law distributed (with exponents and respectively) and average size must scale with duration according to a power-law with exponent . Given those three requirements one can derive a prediction for the scaling exponent, = ( − 1)/( − 1) without needing to assume criticality (Scarpetta et al, 2018). However, without any other assumptions one expects and to be independent so plotting one against the other should make a point-cloud that is symmetrical, not stretched along a trendline (Figure 3).…”