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.

Uma metodologia para redução de incertezas em sistema de medição de vazão de óleo e gás

The objective of this research is to discuss about the need for implementation of new alternatives for the implementation on the metrological control: on the findings of initial and subsequent measurements, the control procedures of measurement uncertainty applied in assessing the loss or remains found in handling operations of bulk liquids, when used turbine meters used in measuring the tax on the business of Petrobras, due to the current environment of legal metrology and scientific, both domestic and international. We aim, with these alternatives: standardizing the minimization of random and systematic errors, the estimate of the remaining errors, as well as the management control of metrological calibration procedures, control of measurement uncertainty, and contribute to the change in the form of performance of legal metrology and scientific disseminating new information to change management of metrological control, objectively focused on aspects of supervision in implementing these activities in the control of the uncertainties of measurement used in our processes in the fiscal measurement system Petrobras. Results are presented, information and comments on the influence of measurement uncertainty in the current results of the fiscal and transfer of custody. This will emphasize the need, among other things, improvement and expansion of metrological control monitored by setting a better meet demand, calibration equipment and measuring instruments for Petrobras. Finally, we intend to establish the need for improving the method of evaluation of the data meter applied to the current management control of measurement uncertainty by proposing a methodology for addressing the problem, as well as highlighting the expected results.