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.

Participação de mulheres na história da Escola Mista no Pará - 1870/1901

This study aims to problematize the history of mixed schools in Pará, from 1870 to 1901, highlighting women participation that helped to build them. The analytical focus of the research fell on the changes and the continuities of the mixed school in Pará. The object of analysis is the Paraense mixed schools, formed by women. The study also brings out arguments that the mixed school was set up in variable forms, concepts, times and spaces, in an overlapping with the inclusion of women in educational universe, either through education, professionalization or teaching in schools of girls and boys. The documentary sources privileged by the study are: the educational law, the newspapers, the government reports and the journals of education, which were examined in a confrontation between what was said and done. The evidential method helped the documentary reading revealed that, in small lines, the linkages built in the search for clues and signs of Paraense mixed schools was assembled with the participation of women, from the perception that historical knowledge is indirect, conjectural. Evidences indicated that the school for both sexes, legally established in the Province of Grão-Pará in 1870, gave the signals of the junction of girls and boys in school, at a time when the presence of women in education was suggested. Mutations related to the educational organization, with the introduction of mixed school in the following decade had a closer relationship with restrictive settings and more effective integration of women in that school. The inaccuracies of the Republican mixed school have revealed, through winding paths, that signal of contradictions between the modern discourse and conservative practices regarding this school, in communion with the expansion of the mixed school throughout the state, including in groups schools, observing the presence of effective women teachers in the regency of such schools and an expansion of students in relation to the equity between the sexes

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.