The Temporal Structures and Functional Significance of Scale-free Brain Activity

Electrophysiological signals exhibit both periodic and aperiodic properties. Periodic oscillations have been linked to numerous physiological, cognitive, behavioral and disease states. Emerging evidence demonstrates that the aperiodic component has putative physiological interpretations and that it dynamically changes with age, task demands and cognitive states. Electrophysiological neural activity is typically analyzed using canonically defined frequency bands, without consideration of the aperiodic (1/f-like) component. We show that standard analytic approaches can conflate periodic parameters (center frequency, power, bandwidth) with aperiodic ones (offset, exponent), compromising physiological interpretations. To overcome these limitations, we introduce an algorithm to parameterize neural power spectra as a combination of an aperiodic component and putative periodic oscillatory peaks. This algorithm requires no a priori specification of frequency bands. We validate this algorithm on simulated data, and demonstrate how it can be used in applications ranging from analyzing age-related changes in working memory to large-scale data exploration and analysis.

Parameterizing neural power spectra into periodic and aperiodic components.

Scale-free brain activity: past, present, and future

Aging is associated with performance decrements across multiple cognitive domains. The neural noise hypothesis, a dominant view of the basis of this decline, posits that aging is accompanied by an increase in spontaneous, noisy baseline neural activity. Here we analyze data from two different groups of human subjects: intracranial electrocorticography from 15 participants over a 38 year age range (15-53 years) and scalp EEG data from healthy younger (20-30 years) and older (60-70 years) adults to test the neural noise hypothesis from a 1/f noise perspective. Many natural phenomena, including electrophysiology, are characterized by 1/f noise. The defining characteristic of 1/f is that the power of the signal frequency content decreases rapidly as a function of the frequency (f) itself. The slope of this decay, the noise exponent (χ), is often <-1 for electrophysiological data and has been shown to approach white noise (defined as χ = 0) with increasing task difficulty. We observed, in both electrophysiological datasets, that aging is associated with a flatter (more noisy) 1/f power spectral density, even at rest, and that visual cortical 1/f noise statistically mediates age-related impairments in visual working memory. These results provide electrophysiological support for the neural noise hypothesis of aging. Significance statement: Understanding the neurobiological origins of age-related cognitive decline is of critical scientific, medical, and public health importance, especially considering the rapid aging of the world's population. We find, in two separate human studies, that 1/f electrophysiological noise increases with aging. In addition, we observe that this age-related 1/f noise statistically mediates age-related working memory decline. These results significantly add to this understanding and contextualize a long-standing problem in cognition by encapsulating age-related cognitive decline within a neurocomputational model of 1/f noise-induced deficits in neural communication.

https://www.jneurosci.org/content/jneuro/35/38/13257.full.pdf

Age-Related Changes in 1/f Neural Electrophysiological Noise.

Inferring synaptic excitation/inhibition balance from field potentials.

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/fx, 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/fx 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.

/pdf/simulated-power-spectral-density-psd-of-background-55brjpwsp7.pdf

Simulated power spectral density (PSD) of background electrocorticogram (ECoG)

http://core.ac.uk/download/pdf/12093196.pdf

Global existence of small classical solutions to nonlinear Schrödinger equations

Escape dynamics and equilibria selection by iterative cycle decomposition

We prove the existence of non-trivial stable solutions to Landau-Lifshitz-Maxwell equations with the Neumann boundary condition for large anisotropies and small domains, where the domains are non-simply connected and rotationally invariant around an axis. The Landau-Lifshitz-Maxwell equations describe ferromagnets including the demagnetizing field effect.

Stable solutions to Landau-Lifshitz-Maxwell equations

This paper studies the adaptive learning dynamics over multiple locations. Our focus is to show that, to observe the average performance of other locations is necessary or efficient. Through the analysis of information structure, the result about convergence and stochastic stability can be obtained. And, for a large class of information structures and games, only Pareto efficient symmetric outcome can emerge in the unique stochastically stable equilibrium. In the Prisoner's Dilemma, for example, observability and mutual linkage between different locations can guarantee that in each location, both players must ultimately cooperate most of the time.

Jian Zhai

Papers

Simulated power spectral density (PSD) of background electrocorticogram (ECoG)

Global existence of small classical solutions to nonlinear Schrödinger equations

Escape dynamics and equilibria selection by iterative cycle decomposition

Stable solutions to Landau-Lifshitz-Maxwell equations

The Efficiency of Observability and Mutual Linkage