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

Leonardo Dalla Porta and Mauro Copelli

We revisit the CROS (“CRitical OScillations”) model which was recently proposed as an attempt to reproduce both scale-invariant neuronal avalanches and long-range temporal correlations. With excitatory and inhibitory stochastic neurons locally connected in a two-dimensional disordered network, the model exhibits a transition where alpha-band oscillations emerge. Precisely at the transition, the fluctuations of the network activity have nontrivial detrended fluctuation analysis (DFA) exponents, and avalanches (defined as supra-threshold activity) have power law distributions of size and duration. We show that, differently from previous results, the exponents governing the distributions of avalanche size and duration are not necessarily those of the mean-field directed percolation universality class (3/2 and 2, respectively). Instead, in a narrow region of parameter space, avalanche exponents obtained via a maximum-likelihood estimator vary continuously and follow a linear relation, in good agreement with results obtained from M/EEG data. In that region, moreover, the values of avalanche and DFA exponents display a spread with positive correlations, reproducing human MEG results.

A mathematical model for short-term plasticity

The RIDC NeuroMat research team has put forward a rigorous mathematical model for short-term plasticity. This type of plasticity has been the object of studies since at least the mid 90s, and recent paper by Antonio Galves, Eva Löcherbach, Christophe Pouzat and Errico Presutti has now proposed a simple probabilistic model describing this phenomenon within a large network of neurons.

Packing arborescences in random digraphs

Carlos Hoppen, Roberto F. Parente and Cristiane M. Sato

We study the problem of packing arborescences in the random digraph D(n, p), where each possible arc is included uniformly at random with probability p = p(n). Let λ(D(n, p)) denote the largest integer λ ≥ 0 such that, for all 0 ≤ ≤ λ, we have −1 i=0 ( − i)|{v : din(v) = i}| ≤ . We show that the maximum number of arc-disjoint arborescences in D(n, p) is λ(D(n, p)) a.a.s. We also give tight estimates for λ(D(n, p)) depending on the range of p. Keywords: random graph, random digraph, edge-disjoint spanning tree, spanning tree, packing arborescence.

Stochastic oscillations and dragon king avalanches in self-organized quasi-critical systems

Osame Kinouchi, Ludmila Brochini, Ariadne A. Costa, João Guilherme Ferreira Campos and Mauro Copelli

In the last decade, several models with network adaptive mechanisms (link deletion-creation, dynamic synapses, dynamic gains) have been proposed as examples of self-organized criticality (SOC) to explain neuronal avalanches. However, all these systems present stochastic oscillations hovering around the critical region that are incompatible with standard SOC. Here we make a linear stability analysis of the mean field fixed points of two self-organized quasi-critical systems: a fully connected network of discrete time stochastic spiking neurons with firing rate adaptation produced by dynamic neuronal gains and an excitable cellular automata with depressing synapses. We find that the fixed point corresponds to a stable focus that loses stability at criticality. We argue that when this focus is close to become indifferent, demographic noise can elicit stochastic oscillations that frequently fall into the absorbing state. This mechanism interrupts the oscillations, producing both power law avalanches and dragon king events, which appear as bands of synchronized firings in raster plots. Our approach differs from standard SOC models in that it predicts the coexistence of these different types of neuronal activity.

A system of interacting neurons with short term plasticity

Today RIDC NeuroMat will hold another one of its seminars. This time, the NeuroMat distinguished associate investigators Eva Löcherbach will present "A system of interacting neurons with short term plasticity".

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