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.

Estudo sobre a mortalidade e sobrevivência de micro e pequenas empresas natalenses e seus impactos nas políticas públicas pró-empreendedorismo

The principal purpose of this research was to investigate discriminant factors of survival and failure of micro and small businesses, and the impacts of these factors in the public politics for entrepreneurship in the State of Rio Grande do Norte. The data were ceded by SEBRAE/RN and the Commercial Committee of the Rio Grande do Norte State and it included the businesses that were registered in 2000, 2001 and 2002. According to the theoretical framework 3 groups of factors were defined Business Financial Structure, Entrepreneurial Preparation and Entrepreneurial Behavior , and the factors were studied in order to determine whether they are discriminant or not of the survival and business failure. A quantitative research was applied and advanced statistical techniques were used multivariate data analysis , beginning with the factorial analysis and after using the discriminant analysis. As a result, canonical discriminant functions were found and they partially explained the survival and business failure in terms of the factors and groups of factors. The analysis also permitted the evaluation of the public politics for entrepreneurship and it was verified, according to the view of the entrepreneurs, that these politics were weakly effective to avoid business failure. Some changes in the referred politics were suggested based on the most significant factors found.