The power-law size distributions obtained experimentally for neuronal avalanches are an important evidence of criticality inthe 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 observedexperimentally. 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 neuronaltissue tens of thousands of neurons can be found. Here we investigate the consequences of undersampling in models withthree 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 thepower laws observed in critical systems. Distributions from subcritical systems are also modified, but the shape of theundersampled distributions is more similar to that of a fully sampled system. Undersampled supercritical systems canrecover 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 isinsensitive to sampling density due to the lack of a well-defined neighborhood. We conjecture that neuronal avalanchesrecorded from local field potentials avoid undersampling effects due to the nature of this signal, but the same does not holdfor spike avalanches. We conclude that undersampled branching-process-like models in these topologies fail to reproducethe statistics of spike avalanches.
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