Related papers: ECoG observations of power-law scaling in the huma…
We perform an experimental study of the time behavior of the $\alpha$-wave events occuring in human electroencephalographic signals. We find that the fraction of the time spent in an $\alpha$-burst of time size $\tau$ exhibits a scaling…
Power laws, that is, power spectral densities (PSDs) exhibiting 1/f^alpha behavior for large frequencies f, have commonly been observed in neural recordings. Power laws in noise spectra have not only been observed in microscopic recordings…
Converging research suggests that the resting brain operates at the cusp of dynamic instability signified by scale-free temporal correlations. We asked if the scaling properties of these correlations differ between amplitude and phase…
Electrophysiological signals (electroencephalography, EEG, and magnetoencephalography , MEG), as many natural processes, exhibit scale-invariance properties resulting in a power-law (1/f) spectrum. Interestingly, EEG and MEG differ in their…
There are several mathematical models yielding 1/f noise. For example, 1/f spectrum can be obtained from stochastic sequence of pulses having power-law distribution of pulse durations or from nonlinear stochastic differential equations. We…
Power-law scaling in coarse-grained data suggests critical dynamics, but the true source of this scaling often remains unclear. Here, we analyze neural activity recorded during spatial navigation, reproducing power-law scaling under a…
Many complex systems display self-organized critical states characterized by 1/f frequency scaling of power spectra. Global variables such as the electroencephalogram, scale as 1/f, which could be the sign of self-organized critical states…
Particles are accelerated to very high, non-thermal energies in solar and space plasma environments. While energy spectra of accelerated electrons often exhibit a power law, it remains unclear how electrons are accelerated to high energies…
The fluctuation properties of the human electroencephalogram (EEG) time series are studied using detrended fluctuation analysis. For all 128 channels in each of 18 subjects studied, it is found that the standard deviation of the…
Historically, the analysis of stimulus-dependent time-frequency patterns has been the cornerstone of most electroencephalography (EEG) studies. The abnormal oscillations in high-frequency waves associated with psychotic disorders during…
Neural scaling laws underlie many of the recent advances in deep learning, yet their theoretical understanding remains largely confined to linear models. In this work, we present a systematic analysis of scaling laws for quadratic and…
This article studies the scaling limit of a class of shot-noise fields defined on an independently marked stationary Poisson point process and with a power law response function. Under appropriate conditions, it is shown that the shot-noise…
Power spectra of awake resting state EEG recordings in humans typically have an Alpha peak at around 10 Hz riding a decreasing background "Xi process". Normal and pathological variations may have more than one peak or none. The single…
We investigate the dynamical properties of electroencephalogram (EEG) signals of human in sleep. By using a modified random walk method, We demonstrate that the scale-invariance is embedded in EEG signals after a detrending procedure.…
The resistive or non-resistive nature of the extracellular space in the brain is still debated, and is an important issue for correctly modeling extracellular potentials. Here, we first show theoretically that if the medium is resistive,…
Power spectral density scaling with frequency $f$ as $1/f^\beta$ and $\beta \approx 1$ is widely found in natural and socio-economic systems. Consequently, it has been suggested that such self-similar spectra reflect the universal dynamics…
We report an empirical determination of the probability density functions $P_{\text{data}}(r)$ of the number $r$ of earthquakes in finite space-time windows for the California catalog. We find a stable power law tail $P_{\text{data}}(r)…
The brain projects require the collection of massive electrophysiological data, aiming to the longitudinal, sectional, or populational neuroscience studies. Quality metrics automatically label the data after centralized preprocessing.…
We investigate the apparent power-law scaling of the pseudo phase space density (PPSD) in CDM halos. We study fluid collapse, using the close analogy between the gas entropy and the PPSD in the fluid approximation. Our hydrodynamic…
The power-law distribution is ubiquitous and its mechanism seems to be various. We find a general mechanism for the distribution. The distribution of a geometrically growing system can be approximated by a log - completely squared chi…