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.

Desenvolvimento de uma rota química alternativa de síntese de SrCo0,8Fe0,2O3- e LaNi0,3Co0,7O3- para aplicação na reação de oxidação do CO

This thesis focuses on the coprecipitation synthesis method for preparation of ceramic materials with perovskite structure, their characterization and application as catalytic material in the reaction of converting CO to CO2 developing a methodological alternative route of synthesis from the middle via oxalate coprecipitation material SrCo0,8Fe0,2O3-d. In order to check the influence of this method, it was also synthesized using a combined citrate - EDTA complexing method. The material was characterized by: X-ray diffraction (XRD), Rietveld refinement method, thermogravimetry and differential thermo analysis (TG / DTA), scanning (SEM) and transmission (TEM) electron microscopy, particle size distribution and surface analysis method BET. Both methods led to post-phase synthesis, with pH as a relevant parameter. The synthesis based on the method via oxalate coprecipitation among particles led to the crystalline phase as those obtained using a combined citrate - EDTA complexing method under the same conditions of heat treatment. The nature of the reagent used via oxalate coprecipitation method produced a material with approximately 80 % lower than the average size of crystallites. Moreover, the via oxalate coprecipitation method precursors obtained in the solid state at low temperature (~ 26 oC), shorter synthesis, greater thermal stability and a higher yield of around 90-95 %, maintaining the same order of magnitude the crystallite size that the combined citrate - EDTA complexing method. For purposes of comparing the catalytic properties of the material was also synthesized by the using a combined citrate - EDTA complexing method. The evaluation of catalytic materials SrCo0,8Fe0,2O3-d LaNi0,3Co0,7O3-d was accompanied on the oxidation of CO to CO2 using a stainless steel tubular reactor in the temperature range of 75-300 oC. The conversion CO gas was evaluated in both materials on the results shaved that the firm conversion was loves for the material LaNi0,3Co0,7O3-d