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.

Contribuições para a análise de sinais neuronais e biomédicos

Following the new tendency of interdisciplinarity of modern science, a new field called neuroengineering has come to light in the last decades. After 2000, scientific journals and conferences all around the world have been created on this theme. The present work comprises three different subareas related to neuroengineering and electrical engineering: neural stimulation; theoretical and computational neuroscience; and neuronal signal processing; as well as biomedical engineering. The research can be divided in three parts: (i) A new method of neuronal photostimulation was developed based on the use of caged compounds. Using the inhibitory neurotransmitter GABA caged by a ruthenium complex it was possible to block neuronal population activity using a laser pulse. The obtained results were evaluated by Wavelet analysis and tested by non-parametric statistics. (ii) A mathematical method was created to identify neuronal assemblies. Neuronal assemblies were proposed as the basis of learning by Donald Hebb remain the most accepted theory for neuronal representation of external stimuli. Using the Marcenko-Pastur law of eigenvalue distribution it was possible to detect neuronal assemblies and to compute their activity with high temporal resolution. The application of the method in real electrophysiological data revealed that neurons from the neocortex and hippocampus can be part of the same assembly, and that neurons can participate in multiple assemblies. (iii) A new method of automatic classification of heart beats was developed, which does not rely on a data base for training and is not specialized in specific pathologies. The method is based on Wavelet decomposition and normality measures of random variables. Throughout, the results presented in the three fields of knowledge represent qualification in neural and biomedical engineering

Obtenção e caracterização do sistema compósito alginato de sódio-dióxido de titânio em formas de pó e de membrana

The alginates are copolymers of 1→4-linked β-D-mannuronic acid (M) and α-Lguluronic acid (G) residues that are arranjed in a block structure along a linear chain. Titanium dioxide, TiO2, is a ceramic material and can exist in three distinct crystallography forms: anatase, brookite and rutile. composites of organic and inorganic materials have better properties than the components alone. Thus, this study aims to synthesize, characterize and analyze the composite NaAlg-TiO2 in the form of powder and film. The synthesis of composite powders was performed using the sol-gel process and obtain the composite film was performed using the slow evaporation process, then the composites were analyzed by infrared spectroscopy, fluorescence x ray, thermal analysis, attenuated total reflection (ATR), x ray diffraction and impedance spectroscopy. The X ray diffraction patterns of composite powders show that with increasing calcination temperature, there were no complete transition of rutile-anatase crystalline phase, since at all temperatures studied (300, 500, 700, 900 and 1100ºC) were observed peaks of anatase phase. Thermal analysis shows that at 400°C caused the decomposition of sodium alginate in sodium carbonate and above 600°C, we observe an exothermic peak related to the decomposition of sodium carbonate and in the presence of titanium dioxide becomes sodium titanate. The XRD results confirm the formation of sodium carbonate at 700ºC and the formation sodium titanate in the temperature range 900-1100ºC. The sodium titanate influenced the electrical properties of the material, because with increasing temperature there was a decrease in conductivity, probably due to the creation of Ti vacancies, since the sodium can induce the reduction of surface Ti4+ ions into Ti3+ species. The infrared spectra of the composites in the form of powder and film showed a small shift in the bands compared to the spectrum of pure alginate, indicating that these shifts, even small ones, have evidence of miscibility between the polymer and ceramic material