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".

NeuroMat's scientific achievements during the first years and for the next steps

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.

Scientists and cartoonists unite to spread science

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.)

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