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.

Avaliação da remoção catalítica de compostos orgânicos monoaromáticos em água utilizando materiais nanoestruturados de sílica

Statistics of environmental protection agencies show that the soil has been contaminated with problems often resulting from leaks, spills and accidents during exploration, refining, transportation and storage oil operations and its derivatives. These, gasoline noteworthy, verified by releasing, to get in touch with the groundwater, the compounds BTEX (benzene, toluene, ethylbenzene and xylenes), substances which are central nervous system depressants and causing leukemia. Among the processes used in remediation of soil and groundwater contaminated with organic pollutants, we highlight those that use hydrogen peroxide because they are characterized by the rapid generation of chemical species of high oxidation power, especially the hydroxyl radical ( OH), superoxide (O2 -) and peridroxil (HO2 ), among other reactive species that are capable of transforming or decomposing organic chemicals. The pH has a strong effect on the chemistry of hydrogen peroxide because the formation of different radicals directly depends on the pH of the medium. In this work, the materials MCM-41 and Co-MCM-41 were synthesized and used in the reaction of BTEX removal in aqueous media using H2O2. These materials were synthesized by the hydrothermal method and the techniques used to characterize were: XRD, TG/DTG, adsorption/desorption N2, TEM and X-Ray Fluorescence. The catalytic tests were for 5 h of reaction were carried out in reactors of 20 mL, which was accompanied by the decomposition of hydrogen peroxide by molecular absorption spectrophotometry in the UV-Vis, in addition to removal of organic compounds BTEX was performed as gas chromatography with detection photoionization and flame ionization and by static headspace sampler. The characterizations proved that the materials were successfully synthesized. The catalytic tests showed satisfactory results, and the reactions containing BTEX + Co-MCM-41 + H2O2 at pH = 12.0 had the highest percentages of removal for the compounds studied