Universal probability distribution function for bursty transport in plasma turbulence

Fluctuation scaling in the visual cortex at threshold

Fluctuation scaling relates trial-to-trial variability to the average response by a power function in many physical processes. Here we address whether fluctuation scaling holds in sensory psychophysics and its functional role in visual processing. We report experimental evidence of fluctuation scaling in human color vision and form perception at threshold. Subjects detected thresholds in a psychophysical masking experiment that is considered a standard reference for studying suppression between neurons in the visual cortex. For all subjects, the analysis of threshold variability that results from the masking task indicates that fluctuation scaling is a global property that modulates detection thresholds with a scaling exponent that departs from 2, β=2.48±0.07. We also examine a generalized version of fluctuation scaling between the sample kurtosis K and the sample skewness S of threshold distributions. We find that K and S are related and follow a unique quadratic form K=(1.19±0.04)S^{2}+(2.68±0.06) that departs from the expected 4/3 power function regime. A random multiplicative process with weak additive noise is proposed based on a Langevin-type equation. The multiplicative process provides a unifying description of fluctuation scaling and the quadratic S-K relation and is related to on-off intermittency in sensory perception. Our findings provide an insight into how the human visual system interacts with the external environment. The theoretical methods open perspectives for investigating fluctuation scaling and intermittency effects in a wide variety of natural, economic, and cognitive phenomena.

Discriminating between Light- and Heavy-Tailed Distributions with Limit Theorem

In this paper we propose an algorithm to distinguish between light- and heavy-tailed probability laws underlying random datasets. The idea of the algorithm, which is visual and easy to implement, is to check whether the underlying law belongs to the domain of attraction of the Gaussian or non-Gaussian stable distribution by examining its rate of convergence. The method allows to discriminate between stable and various non-stable distributions. The test allows to differentiate between distributions, which appear the same according to standard Kolmogorov–Smirnov test. In particular, it helps to distinguish between stable and Student’s t probability laws as well as between the stable and tempered stable, the cases which are considered in the literature as very cumbersome. Finally, we illustrate the procedure on plasma data to identify cases with so-called L-H transition.

Stochastic modeling of intermittent scrape-off layer plasma fluctuations

Single-point measurements of fluctuations in the scrape-off layer of magnetized plasmas are generally found to be dominated by large-amplitude bursts which are associated with radial motion of bloblike structures. A stochastic model for these fluctuations is presented, with the plasma density given by a random sequence of bursts with a fixed wave form. When the burst events occur in accordance to a Poisson process, this model predicts a parabolic relation between the skewness and kurtosis moments of the plasma fluctuations. In the case of an exponential wave form and exponentially distributed burst amplitudes, the probability density function for the fluctuation amplitudes is shown to be a Gamma distribution with the scale parameter given by the average burst amplitude, and the shape parameter given by the ratio of the burst duration and waiting times.