The ECoG background activity of cerebral cortex in states of rest and slow wave sleep resembles broadband noise. The power spectral density (PSD) then may often conform to a power-law distribution: a straight line in coordinates of log power vs. log frequency. The exponent, x, of the distribution, 1/f(x), ranges between 2 and 4. These findings are explained with a model of the neural source of the background activity in mutual excitation among pyramidal cells. The dendritic response of a population of interactive excitatory neurons to an impulse input is a rapid exponential rise and a slow exponential decay, which can be fitted with the sum of two exponential terms. When that function is convolved as the kernel with pulses from a Poisson process and summed, the resulting "brown" or "black noise conforms to the ECoG time series and the PSD in rest and sleep. The PSD slope is dependent on the rate of rise. The variation in the observed slope is attributed to variation in the level of the background activity that is homeostatically regulated by the refractory periods of the excitatory neurons. Departures in behavior from rest and sleep to action are accompanied by local peaks in the PSD, which manifest emergent nonrandom structure in the ECoG, and which prevent reliable estimation of the 1/f(x) exponents in active states. We conclude that the resting ECoG truly is low-dimensional noise, and that the resting state is an optimal starting point for defining and measuring both artifactual and physiological structures emergent in the activated ECoG.

In this paper, we consider the averaging principle for one dimensional stochastic Burgers equation with slow and fast time-scales. Under some suitable conditions, we show that the slow component strongly converges to the solution of the corresponding averaged equation. Meanwhile, when there is no noise in the slow component equation, we also prove that the slow component weakly converges to the solution of the corresponding averaged equation with the order of convergence 1 − r, for any 0 < r < 1.

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The organization of human brain networks can be measured by capturing correlated brain activity with functional MRI data. There have been a variety of studies showing that human functional connectivities undergo an age-related change over development. In the present study, we employed resting-state functional MRI data to construct functional network models. Principal component analysis was performed on the FC matrices across all the subjects to explore meaningful components especially correlated with age. Coefficients across the components, edge features after a newly proposed feature reduction method as well as temporal features based on fALFF, were extracted as predictor variables and three different regression models were learned to make prediction of brain age. We observed that individual's functional network architecture was shaped by intrinsic component, age-related component and other components and the predictive models extracted sufficient information to provide comparatively accurate predictions of brain age.

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In this paper, we establish the large deviation principle for 3D stochastic primitive equations with small perturbation multiplicative noise. The proof is mainly based on the weak convergence approach.