Abstract
The activity of a sparse network of leaky integrate-and-fire neurons is carefully revisited with reference to a regime of a bona-fide asynchronous dynamics. The study is preceded by a finite-size scaling analysis, carried out to identify a setup where collective synchronization is negligible. The comparison between quenched and annealed networks reveals the emergence of substantial differences when the coupling strength is increased, via a scenario somehow reminiscent of a phase transition. For sufficiently strong synaptic coupling, quenched networks exhibit a highly bursting neural activity, well reproduced by a self-consistent approach, based on the assumption that the input synaptic current is the superposition of independent renewal processes. The distribution of interspike intervals turns out to be relatively long-tailed; a crucial feature required for the self-sustainment of the bursting activity in a regime where neurons operate on average (much) below threshold. A semi-quantitative analogy with Ornstein-Uhlenbeck processes helps validating this interpretation. Finally, an alternative explanation in terms of Poisson processes is offered under the additional assumption of mutual correlations among excitatory and inhibitory spikes.
Highlights
The characterization of the spiking activity of neuronal networks is a long-standing problem even with reference to the asynchronous regime: simple from a dynamical point of view, but extremely relevant for understanding cortex dynamics [1,2]
One of the main results of this paper is that the synaptic current can be accurately represented as the superposition of independent identical renewal processes (RPs), each characterized by a suitable interspike intervals (ISIs) distribution
We show that the correlations due to the long-tailed ISI distribution can be equivalently represented as long-term memory in the symbolic representation of inhibitory versus excitatory spikes
Summary
The characterization of the spiking activity of neuronal networks is a long-standing problem even with reference to the asynchronous regime: simple from a dynamical point of view, but extremely relevant for understanding cortex dynamics [1,2]. Under the additional simplifying assumption of a piecewise linear dynamics [as in leaky integrate-and-fire (LIF) neurons], a solution can be analytically determined and its stability assessed [4] This approach turns out to be relatively accurate for small coupling strengths, the same is no longer true for stronger coupling From a statistical-mechanics point of view, this choice will help in better understanding the dynamics of the system, since it is known that quenched and annealed systems may exhibit different properties from one another [16] This happens in the present model above a “critical” synaptic coupling strength (namely, J ≈ 0.25). IV, we first introduce the two self-consistent approaches implemented to characterize the neural activity The former one, based on the distribution of ISIs, provides a rather accurate description. VI we summarize the main results and focus on the still open problems
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