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.

Relações de cooperação em consórcios públicos de regiões metropolitanas: análises do CONDIAM/PB e consórcio grande Recife

With the disorganized decentralization occurred in Brazil after the 1988 Constitution, municipalities have risen to the level of federal entities. This phenomenon became known as "municipalism" also brought some negative effects such as low capacity financial, economic and political of these entities. In the face of this reality , the municipalities sought in models of collaborative features to address public policy issues ultrarregionais, one of these models are the Public Consortia. Characterized as the organization of all federal entities that aim to solve public policy implementation alone that they could not, or spend great resources for such. This reality of the municipalities have an aggravating factor when looking at the situation in Metropolitan Regions (MRs). This is because the RMs has a historical process of formation that does not encourage cooperation, since that were created top-down during the military regime. Furthermore, the metropolitan municipalities have significant power asymmetries, localist vision, rigidity earmarked revenues, different scenarios conurbation, difficulty standardization of concepts and others that contribute to the vision of low cooperation of these metropolitan areas. Thus, the problem of this work is in the presence of collaborative arrangements, such as the Public Consortia in metropolitan areas, which are seen as areas of low cooperation. To elucidate this research was used for analysis the cases of CONDIAM/PB and Consórcio Grande Recife/PE, because they are apparently antagonistic, but with some points of similarity. The cases has as foundation the Theory of Common Resources, which provides the possibility of collective action through the initiative of individuals. This theory has as its methodology for analyzing the picture IAD Framework, which proposes its analysis based on three axes: external variables, the arena of action and results. The nature of the method of this research was classified as exploratory and descriptive. For the stage of date analysis, was used the method of document analysis and content, Further than of separation of the cases according to theur especificities. At the end of the study, noted that the CONDIAM/PB was a strategy of municipal government of Joao Pessoa to attract funds from the Federal Government for the purpose of to build a landfill, and over the years the ideology of cooperation was left aside, the prevailing view localist municipalities. In the case of Consórcio Grande Recife/PE, members act with some degree of cooperation, especially the collaborative aspect of the region, however, still prevails with greater strength the power of the state of Pernambuco in the decisions and paths of the consortium. Thus, was conclude that the Public Consortia analyzed are an experience of collaborative arrangement, from the initiative of members, as the theory of common resources says, but has not actually signed as a practice of collective action to overcome the dilemmas faced by metropolitan areas