Using a non-perturbative method developed in a previous work (paper II), we derive the probability distribution P(δR) of the density contrast within spherical cells in the quasi-linear regime for some non-Gaussian initial conditions. We describe three such models. The first one is a straightforward generalization of the Gaussian scenario. It can be seen as a phenomenological description of a de...

Recovering a set of independent sources which are linearly mixed is the main task of the blind source separation. Utilizing different methods such as infomax principle, mutual information and maximum likelihood leads to simple iterative procedures such as natural gradient algorithms. These algorithms depend on a nonlinear function (known as score or activation function) of source distributions....

Nonlinear/non-Gaussian filtering has broad applications in many areas of life sciences where either the dynamic is nonlinear and/or the probability density function of uncertain state is non-Gaussian. In such problems, the accuracy of the estimated quantities depends highly upon how accurately their posterior pdf can be approximated. In low dimensional state spaces, methods based on Sequential ...

In this paper, we present an analytical approach in obtaining the probability density function (pdf) of the random decision variable Y , formed at the output of power-cubic all-optical nonlinear preprocessor followed by the photodetector. Our approach can be used to accurately evaluate the performance of ultrafast pulse detection in the presence of Gaussian noise. Through rigorous Monte-Carlo s...

The dynamics of a tracer particle in a stationary driven granular gas is investigated. We show how to transform the linear Boltzmann equation, describing the dynamics of the tracer into a master equation for a continuous Markov process. The transition rates depend on the stationary velocity distribution of the gas. When the gas has a Gaussian velocity probability distribution function (PDF), th...

The stochastic radiation transfer is considered in a participating planar finite continuously fluctuating medium characterized by non-Gaussian variability. The problem is considered for diffuse-reflecting boundaries with quadratic Rayleigh scattering. Random variable transformation (RVT) technique is used to get the complete average for the solution functions that are represented by the probabi...

In this paper, we present an analytical approach in obtaining the probability density function (pdf) of the random decision variable Y , formed at the output of power-cubic all-optical nonlinear preprocessor followed by the photodetector. Our approach can be used to accurately evaluate the performance of ultrafast pulse detection in the presence of Gaussian noise. Through rigorous Monte-Carlo s...

Estimation of the power spectral density (PSD) of noise is crucial for retrieving speech in a noisy environment. 3 novel methods for estimating the non-white noise PSD of noisy speech based on a generalized gamma distribution and 3 criterions are proposed, which are minimum mean square error (MMSE), maximum a posteriori (MAP) and Maximum likelihood estimation (MLE). Because of the highly non-st...

We present a detailed investigation of the probability density function (PDF) of order parameter fluctuations in the finite two-dimensional XY (2dXY ) model. In the low temperature critical phase of this model, the PDF approaches a universal non-Gaussian limit distribution in the limit T → 0. Our analysis resolves the question of temperature dependence of the PDF in this regime, for which confl...

Probability density functions (pdfs) are employed to evaluate the distribution of velocities in the global ocean. This study computes pdfs of ocean surface velocity using altimetric data from the TOPEX/Poseidon satellite. Results show that the shape of the observed pdfs changes with the size of the domain over which they are calculated: if data are drawn from a small region of the ocean, the pd...