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.
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".
The project that created the Research, Innovation and Dissemination Center for Neuromathematics (RIDC NeuroMat) in 2013 has been renewed by the São Paulo Research Foundation for a six-year term, and in this context we launch a series to connect our past and current trajectory. This series has been called "First 5, Next 6", a direct reference to content produced by our team within the center renewal process, especially a presentation to FAPESP's International Assessment Committee in 2017. The first part of this text is informed by NeuroMat's Statement of Impact, again a document prepared in the renewal process.
This month on "Jornal da USP" website, there was a report on the relevance of comics in the context of scientific diffusion. In this context, "Os Braços de Nildo e Rony" is a comic book by Antonio Galves, professor of the Institute of Mathematics and Statistics (IME-USP) and coordinator of RIDC NeuroMat. The material seeks to guide patients who have suffered a traumatic injury of the brachial plexus, a set of nerves that makes communication between the upper limbs and the brain. The injuries affect many victims of traffic accidents, mainly involving motorcycles. Jornal da USP, 20/02/2019. (In Portuguese.)
Ludmila Brochini, Ariadne de Andrade Costa, Miguel Abadi, Antônio C. Roque, Jorge Stolfi and Osame Kinouchi
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 Φ(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 Φ. 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 located at 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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