Experimental results for the evolution of the probability distribution function (PDF) of a scalar mixed by a turbulent flow in a channel are presented. The sequence of PDF from an initial skewed distribution to a sharp Gaussian is found to be nonuniversal. The route toward homogeneization depends on the ratio between the cross sections of the dye injector and the channel. In connection with thi...

We analytically compute the probability distribution function (PDF) of the local Reynolds stress ( R) for forced Hasegawa-Mima turbulence. With the assumption that the PDF tail is due to an instanton with the spatial form given by the modon solution, the tail of the PDF of R is found to be a stretched, non-Gaussian exponential, with the specific form exp[-cR(3/2)] ( c is a constant). We relate ...

Probabilistic aspects of regional ocean model predictability is analyzed using the probability density function (PDF) of the irreversible predictability time (IPT) (called τ PDF) computed from an unconstrained ensemble of stochastic perturbations in initial conditions, winds, and open boundary conditions. Two-attractors (a chaotic attractor and a small-amplitude stable limit cycle) are found in...

The paper deals with the particle filter in state estimation of a discrete-time nonlinear non-Gaussian system. The goal of the paper is to design a sample size adaptation technique to guarantee the quality of an empirical probability density function (pdf) which approximates a target filtering pdf. The quality is measured by inaccuracy (cross-information) between the empirical pdf and the filte...

The determination of Cramer-Rao lower bound (CRLB) as an optimality criterion for the problem of channel estimation in wireless communication is a very important issue. Several CRLBs on channel estimation have been derived for Gaussian noise. However, a practical channel is affected by not only Gaussian background noise but also non-Gaussian noise such as impulsive interference. This paper deri...

The sum of two randomly-phased sine waves and Gaussian noise arises in various fields of communications. In this paper, a Laguerre series and also a power series are introduced, for the envelope PDF of this random process. Moreover, tight upper bounds are derived for the truncation error of these two infinite series. Comparison of these two upper bounds show that the Laguerre series is superior...

In this paper, we present a noisy version of the algebraic geometric approach of identifying parameters of discrete-time linear hybrid system. Two approximate ways of estimating hybrid parameters are considered: one is using MSE criteria, while the other is based on the information divergence that measures the distance between the error probability density function (PDF) of the identified model...

In this paper, a recently developed Bayesian method called ensemble learning is applied to independent component analysis (ICA). Ensemble learning is a computationally eecient approximation for exact Bayesian analysis. In general, the posterior probability density function (pdf) is a complex high dimensional function whose exact treatment is diicult. In ensemble learning, the posterior pdf is a...

We consider the tails of probability density function (PDF) for the velocity that satisfies Burgers equation driven by a Gaussian large-scale force. The saddle-point approximation is employed in the path integral so that the calculation of the PDF tails boils down to finding the special field-force configuration (instanton) that realizes the extremum of probability. For the PDFs of velocity and...

Particle random motion can exhibit both anomalous diffusion and non-Gaussian statistics in some physical systems. Anomalous diffusion is quantified by a deviation from alpha=1 in a power law for a particle's mean-square displacement, MSD proportional, variant(Deltat)alpha. A deviation from Gaussian statistics for a probability distribution function (PDF) is quantified by fitting to a kappa func...