Optimal income crossover for a two-class model using particle swarm optimization.

Personal income distribution may exhibit a two-class structure, such that the lower income class of the population (85-98%) is described by exponential Boltzmann-Gibbs distribution, whereas the upper income class (2-15%) has a Pareto power-law distribution. We propose a method, based on a theoretical and numerical optimization scheme, which allows us to determine the crossover income between the distributions, the temperature of the Boltzmann-Gibbs distribution, and the Pareto index. Using this method, the Brazilian income distribution data provided by the National Household Sample Survey was studied. The data was stratified into two dichotomies (sex/gender and color/race), so the model was tested using different subsets along with accessing the economic differences between these groups. Last, we analyze the temporal evolution of the parameters of our model and the Gini coefficient discussing the implication on the Brazilian income inequality. In this paper, we propose an optimization method to find a continuous two-class income distribution, which is able to delimit the boundaries of the two distributions. It also gives a measure of inequality which is a function that depends only on the Pareto index and the percentage of people in the high-income region. We found a temporal dynamics relation, that may be general, between the Pareto and the percentage of people described by the Pareto tail.

Measuring neuronal avalanches in disordered systems with absorbing states.

Power-law-shaped avalanche-size distributions are widely used to probe for critical behavior in many different systems, particularly in neural networks. The definition of avalanche is ambiguous. Usually, theoretical avalanches are defined as the activity between a stimulus and the relaxation to an inactive absorbing state. On the other hand, experimental neuronal avalanches are defined by the activity between consecutive silent states. We claim that the latter definition may be extended to some theoretical models to characterize their power-law avalanches and critical behavior. We study a system in which the separation of driving and relaxation time scales emerges from its structure. We apply both definitions of avalanche to our model. Both yield power-law-distributed avalanches that scale with system size in the critical point as expected. Nevertheless, we find restricted power-law-distributed avalanches outside of the critical region within the experimental procedure, which is not expected by the standard theoretical definition. We remark that these results are dependent on the model details.

Griffiths phase and long-range correlations in a biologically motivated visual cortex model.

Activity in the brain propagates as waves of firing neurons, namely avalanches. These waves' size and duration distributions have been experimentally shown to display a stable power-law profile, long-range correlations and 1/f (b) power spectrum in vivo and in vitro. We study an avalanching biologically motivated model of mammals visual cortex and find an extended critical-like region - a Griffiths phase - characterized by divergent susceptibility and zero order parameter. This phase lies close to the expected experimental value of the excitatory postsynaptic potential in the cortex suggesting that critical be-havior may be found in the visual system. Avalanches are not perfectly power-law distributed, but it is possible to collapse the distributions and define a cutoff avalanche size that diverges as the network size is increased inside the critical region. The avalanches present long-range correlations and 1/f (b) power spectrum, matching experiments. The phase transition is analytically determined by a mean-field approximation.

Critical avalanches and subsampling in map-based neural networks coupled with noisy synapses.

Many different kinds of noise are experimentally observed in the brain. Among them, we study a model of noisy chemical synapse and obtain critical avalanches for the spatiotemporal activity of the neural network. Neurons and synapses are modeled by dynamical maps. We discuss the relevant neuronal and synaptic properties to achieve the critical state. We verify that networks of functionally excitable neurons with fast synapses present power-law avalanches, due to rebound spiking dynamics. We also discuss the measuring of neuronal avalanches by subsampling our data, shedding light on the experimental search for self-organized criticality in neural networks.

A brief history of excitable map-based neurons and neural networks.

This review gives a short historical account of the excitable maps approach for modeling neurons and neuronal networks. Some early models, due to Pasemann (1993), Chialvo (1995) and Kinouchi and Tragtenberg (1996), are compared with more recent proposals by Rulkov (2002) and Izhikevich (2003). We also review map-based schemes for electrical and chemical synapses and some recent findings as critical avalanches in map-based neural networks. We conclude with suggestions for further work in this area like more efficient maps, compartmental modeling and close dynamical comparison with conductance-based models.

Nonuniversal behavior for aperiodic interactions within a mean-field approximation.

We study the spin-1/2 Ising model on a Bethe lattice in the mean-field limit, with the interaction constants following one of two deterministic aperiodic sequences, the Fibonacci or period-doubling one. New algorithms of sequence generation were implemented, which were fundamental in obtaining long sequences and, therefore, precise results. We calculate the exact critical temperature for both sequences, as well as the critical exponents beta, gamma, and delta . For the Fibonacci sequence, the exponents are classical, while for the period-doubling one they depend on the ratio between the two exchange constants. The usual relations between critical exponents are satisfied, within error bars, for the period-doubling sequence. Therefore, we show that mean-field-like procedures may lead to nonclassical critical exponents.