Undersampled Critical Branching Processes on Small-World and Random Networks Fail to Reproduce the Statistics of Spike Avalanches

The power-law size distributions obtained experimentally for neuronal avalanches are an important evidence of criticality in the brain. This evidence is supported by the fact that a critical branching process exhibits the same exponent t~3=2. Models at criticality have been employed to mimic avalanche propagation and explain the statistics observed experimentally. However, a crucial aspect of neuronal recordings has been almost completely neglected in the models: undersampling. While in a typical multielectrode array hundreds of neurons are recorded, in the same area of neuronal tissue tens of thousands of neurons can be found. Here we investigate the consequences of undersampling in models with three different topologies (two-dimensional, small-world and random network) and three different dynamical regimes (subcritical, critical and supercritical). We found that undersampling modifies avalanche size distributions, extinguishing the power laws observed in critical systems. Distributions from subcritical systems are also modified, but the shape of the undersampled distributions is more similar to that of a fully sampled system. Undersampled supercritical systems can recover the general characteristics of the fully sampled version, provided that enough neurons are measured. Undersampling in two-dimensional and small-world networks leads to similar effects, while the random network is insensitive to sampling density due to the lack of a well-defined neighborhood. We conjecture that neuronal avalanches recorded from local field potentials avoid undersampling effects due to the nature of this signal, but the same does not hold for spike avalanches. We conclude that undersampled branching-process-like models in these topologies fail to reproduce the statistics of spike avalanches.

O papel sócio empreendedor da ONG Sodireitos em defesa dos direitos sexuais e migratórios na Amazônia

This paper presents a case study from the Society for the Defense of Sexual and Migrate Rivers Amazônia - Sodireitos, whose central problem is to understand how it the works the social entrepreneur of the NGO Sodireitos in defense of sexual rights and migrate rivers in Amazônia. The central objective is to analyze the practices Social Entrepreneurship at the NGO Sodireitos on sexual rights and migrate rivers. The method adopted examined the entire creation process at the NGO the present day. Primary and secondary dates were used allowing the viewing of the dynamic intervention Social Sodireitos practiced by the fields of human rights and migrate rivers. Categories of analyses were given, and possible perceive in works of the strong Sodireitos flags that converge to social entrepreneurship as a guideline in the search for a model of human development, social and mainstay vel.