Intertangled stochastic motifs in networks of excitatory-inhibitory units

Abstract

A stochastic model of excitatory and inhibitory interactions which bears universality traits is introduced and studied. The endogenous component of noise, stemming from finite size corrections, drives robust inter-nodes correlations, that persist at large large distances. Anti-phase synchrony at small frequencies is resolved on adjacent nodes and found to promote the spontaneous generation of long-ranged stochastic patterns, that invade the network as a whole. These patterns are lacking under the idealized deterministic scenario, and could provide novel hints on how living systems implement and handle a large gallery of delicate computational tasks.PACS numbers: 02.50. Ey, 87.18.Sn, 87.18.Tt Living systems execute an extraordinary plethora of complex functions, that result from the intertwined interactions among key microscopic actors [1]. Positive and negative feedbacks appear to orchestrate the necessary degree of macroscopic coordination [2], by propagating information to distant sites while supporting the processing steps that underly categorization and decisionmaking. Excitatory and inhibitory circuits play, in this respect, a role of paramount importance. As an example, networks of excitatory and inhibitory neurons constitute the primary computational units in the brain cortex [3][4][5]. They can flexibly adjust to different computational modalities, as triggered by distinct external stimuli [6,7]. Genetic regulation is also relying on sophisticated inhibitory and excitatory loops [8][9][10][11]. Specific genes are customarily assigned to the nodes of a given constellation, which can be abstractly pictured as a complex network [12][13][14]. Weighted edges between adjacent nodes encode for the characteristics of the interaction. Simple deterministic models can be put forward to reproduce at the mesoscopic, coarse grained level, the prototypical evolution of excitatory and inhibitory units, organized in two mutually competing populations. Continuous variables are customarily introduced to quantify the activity of each selected population. Non linearities prove crucial to adequately represent the threshold mechanism of activation that modulates, from neurons to genes, the system response [15,16]. One can then assemble large networks with designated topology, by replicating the aforementioned module on each node of the collection and incorporating the specific nature of the coupling [17]. Stationary patterns [18] of asynchronous activity for the scrutinized species can eventually emerge, following symmetry breaking instabilities that necessitate a fine tuning of the parameters involved. These patterns could define the basic architectural units for natural systems to perform efficient computations [19][20][21].As opposed to the deterministic formulation, an individual-based description -hence intrinsically stochastic for any finite population -can be invoked [22,23]. This amounts to characterizing the microscopic dynamics via transition rates, that govern the interactions among individuals and with the surro...

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