arXiv subjects

L. Brochini

Publications and source records attributed to L. Brochini.

3 recordsLinked to original sources

arXiv2018

Metastability and Multiscale Extinction Time on a Finite System of Interacting Stochastic Chains

We studied metastability and extinction time of a finite system with a large number of interacting components in discrete time by means of analytical and numerical investigation. The system is markovian with respect to the potential profile of the components, which are subject to leakage and gain effects simultaneously. We show that the only invariant measure is the null configuration, that the system ceases activity almost surely in a finite time and that extinction time presents a cutoff behavior. Moreover, there is a critical parameter determined by leakage and gain below which the extinction time does not depend on the system size. Above such critical ratio, the extinction time depends on the number of components and the system tends to stabilize around a unique metastable state. Furthermore, the extinction time presents infinitely many scales with respect to the system size.

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arXiv2018

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

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. This phenomenology has been called self-organized quasi-criticality (SOqC). Here we make a linear stability analysis of the mean field fixed points of two SOqC 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.

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arXiv2016

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

Phase transitions and critical behavior are crucial issues both in theoretical and experimental neuroscience. We report analytic and computational results about phase transitions and self-organized criticality (SOC) in networks with general stochastic neurons. The stochastic neuron has a firing probability given by a smooth monotonic function $\Phi(V)$ of the membrane potential $V$, rather than a sharp firing threshold. We find that such networks can operate in several dynamic regimes (phases) depending on the average synaptic weight and the shape of the firing function $\Phi$. In particular, we encounter both continuous and discontinuous phase transitions to absorbing states. At the continuous transition critical boundary, neuronal avalanches occur whose distributions of size and duration are given by power laws, as observed in biological neural networks. We also propose and test a new mechanism to produce SOC: the use of dynamic neuronal gains -- a form of short-term plasticity probably in the axon initial segment (AIS) -- instead of depressing synapses at the dendrites (as previously studied in the literature). The new self-organization mechanism produces a slightly supercritical state, that we called SOSC, in accord to some intuitions of Alan Turing.

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