Motivated by the work of Li and Meneveau [Phys. Rev. Lett. 95, 164502 (2005)], we propose and solve a model for the Lagrangian evolution of both longitudinal and transverse velocity and temperature increments for Boussinesq convection. From this model, the short-time evolution of an initially imposed Gaussian joint probability density function (PDF) of both velocity and temperature increments i...

We introduce and discuss the concept of Gaussian probability density function (pdf) for the n-dimensional hyperbolic space which has been proposed as an environment for coding and decoding signals. An upper bound for the error probability of signal transmission associated with the hyperbolic distance is established. The pdf and the upper bound were developed using Poincaré models for the hyperb...

A theory of the probability distribution function (PDF) tails of the blob density in plasma edge turbulence is provided. A simplified model of the fast convective radial transport is used. The theoretically predicted PDF tails corroborate earlier measurements of edge transport, further confirming the strongly non-Gaussian feature of edge transport. It is found that increasing the cross sectiona...

The probability density function ~PDF! of the roughness, i.e., of the temporal variance, of 1/f a noise signals is studied. Our starting point is the generalization of the model of Gaussian, time periodic, 1/f noise, discussed in our recent Letter @Phys. Rev. Lett. 87, 240601 ~2001!#, to arbitrary power law. We investigate three main scaling regions (a<1/2, 1/2,a<1, and 1,a), distinguished by t...

A basic task of exploratory data analysis is the characterisation of “structure” in multivariate datasets. For bivariate Gaussian distributions, natural measures of dependence (the predictive relationship between individual variables) and compactness (the degree of concentration of the probability density function (pdf) around a low-dimensional axis) are respectively provided by ordinary least-...

In this letter, we propose a new approach to speech enhancement based on a complex Laplacian probability density function (pdf). With a use of a goodness-of-fit (GOF) test, we discover that the complex Laplacian pdf is more desirable to describe noisy speech distribution than the conventional Gaussian pdf for speech enhancement. The likelihood ratio (LR) is computed and then applied to computat...

For a known weak signal in additive white noise, the asymptotic performance of a locally optimum processor (LOP) is shown to be given by the Fisher information (FI) of a standardized even probability density function (PDF) of noise in three cases: (i) the maximum signal-tonoise ratio (SNR) gain for a periodic signal; (ii) the optimal asymptotic relative efficiency (ARE) for signal detection; (i...

Moghaddam et al. (Moghaddam and Pentland, 1997) first proposed to perform object detection by modelling the marginal probability density function (pdf) of high dimensional features of appearance. Based on gaussian hypotheses, their approach is however not robust to outliers that can occur in images due, for instance, to cluttered backgrounds or partial occlusions. In (Dahyot et al., 2004), robu...

The evolution of probability distribution functions (PDFs) of continuous density, velocity and velocity derivatives ( deformation tensor) fields in the theory of cosmological gravitational instability are considered. We show that in the Newtonian theory the dynamical equations cannot be reduced to the closed set of Lagrangian equations. Since continuous fields from galaxy surveys need sufficien...