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.

Análise de volatilidade, integração de preços e previsibilidade para o mercado brasileiro de camarão

The present paper has the purpose of investigate the dynamics of the volatility structure in the shrimp prices in the Brazilian fish market. Therefore, a description of the initial aspects of the shrimp price series was made. From this information, statistics tests were made and selected univariate models to be price predictors. Then, it was verified the existence of relationship of long-term equilibrium between the Brazilian and American imported shrimp and if, confirmed the relationship, whether or not there is a causal link between these assets, considering that the two countries had presented trade relations over the years. It is presented as an exploratory research of applied nature with quantitative approach. The database was collected through direct contact with the Companhia de Entrepostos e Armazéns Gerais de São Paulo (CEAGESP) and on the official website of American import, National Marine Fisheries Service - National Oceanic and Atmospheric Administration (NMFS- NOAA). The results showed that the great variability in the active price is directly related with the gain and loss of the market agents. The price series presents a strong seasonal and biannual effect. The average structure of price of shrimp in the last 12 years was R$ 11.58 and external factors besides the production and marketing (U.S. antidumping, floods and pathologies) strongly affected the prices. Among the tested models for predicting prices of shrimp, four were selected, which through the prediction methodologies of one step forward of horizon 12, proved to be statistically more robust. It was found that there is weak evidence of long-term equilibrium between the Brazilian and American shrimp, where equivalently, was not found a causal link between them. We concluded that the dynamic pricing of commodity shrimp is strongly influenced by external productive factors and that these phenomena cause seasonal effects in the prices. There is no relationship of long-term stability between the Brazilian and American shrimp prices, but it is known that Brazil imports USA production inputs, which somehow shows some dependence productive. To the market agents, the risk of interferences of the external prices cointegrated to Brazilian is practically inexistent. Through statistical modeling is possible to minimize the risk and uncertainty embedded in the fish market, thus, the sales and marketing strategies for the Brazilian shrimp can be consolidated and widespread