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.

Toothache and social and economic conditions among adolescents in Northeastern Brazil

O objetivo deste estudo foi relacionar dor de dente com condição socioeconômica, acesso aos serviços de saúde bucal e estilo de vida em adolescentes do município de Sobral, Ceará, desenvolvido com delineamento transversal analítico, com amostra composta por 688 indivíduos. A prevalência de dor de dente no grupo pesquisado foi de 31,8%. Para avaliar a relação entre as variáveis independentes e a dor de dente, realizou-se teste de associação pelo qui-quadrado, estimando-se a razão de prevalências por meio da regressão de Poisson. Os fatores que mais demonstraram relação com a dor de dente foram severidade da cárie, motivo do atendimento odontológico relacionado com urgência, frequência ao dentista e recebimento de escova na escola. Observou-se que a alta prevalência de dor de dente em adolescentes está diretamente relacionada às condições de acesso, assim como às características das ações desenvolvidas pelos serviços de saúde. Assim como há necessidade da implantação de serviços vinculados à promoção de saúde, pautados pela equidade e integralidade, é necessária a implantação de serviços de urgência que não simplesmente intervenham na dor de forma mutiladora, mas a encarem como mecanismo de estímulo ao desenvolvimento de procedimentos de prevenção das doenças bucais.

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.