The single-point probability distribution function ~PDF! for a passive scalar with an imposed mean gradient is studied here. Elementary models are introduced involving advection diffusion of a passive scalar by a velocity field consisting of a deterministic or random shear flow with a transverse time-periodic transverse sweep. Despite the simplicity of these models, the PDFs exhibit scalar inte...

This paper introduces an on-line particle-filtering-based framework for failure prognosis in nonlinear, non-Gaussian systems. This framework uses a nonlinear state-space model of the plant (with unknown time-varying parameters) and a particle filtering (PF) algorithm to estimate the probability density function (pdf) of the state in real-time. The state pdf estimate is then used to predict the ...

This work shows how the probability density function (PDF) of the turbulent velocity fluctuation can be estimated from the deconvolution of ensemble averaged cross-correlation and auto-correlation functions of PIV recordings. Once the PDF is known, the mean displacement, the Reynolds stresses as well as higher order moments can reliable be estimated. The approach was tested on synthetic PIV ima...

Logistic regression is the most common method used to model binary response data. When the response is binary, it typically takes the form of 1/0, with 1 generally indicating a success and 0 a failure. However, the actual values that 1 and 0 can take vary widely, depending on the purpose of the study. For example, for a study of the odds of failure in a school setting, 1 may have the value of f...

Characterization of the joint (among wavebands) probability density function (pdf) of hyperspectral imaging (HSI) data is crucial for several applications, including the design of constant false alarm rate (CFAR) detectors and statistical classifiers. HSI data are vector (or equivalently multivariate) data in a vector space with dimension equal to the number of spectral bands. As a result, the ...

This1 chapter addresses the problems of minimum mean square error (MMSE) estimation in non-Gaussian linear and nonlinear systems. In many scientific and practical problems (such as control, astronomy, economic data analysis, communication and radar surveillance), estimation of time-varying system state using a sequence of noisy measurements is performed using the dynamic state-space (DSS) model...

We show that the tails of the single-point velocity probability distribution function (PDF) are generally non-Gaussian in developed turbulence. By using instanton formalism for the Navier-Stokes equation, we establish the relation between the PDF tails of the velocity and those of the external forcing. In particular, we show that a Gaussian random force having correlation scale L and correlatio...

Introduction The MR diffusion technique allows probing the microstructure of biological tissues. Anisotropic diffusion is commonly studied using diffusion tensor imaging (DTI). Analysis of the MR signal as a bi-exponential decay with definition of a slow compartment and of a fast compartment has also been proposed (1). When restrictions or hindrance of the water molecules movements are present,...

The dynamics of a one-dimensional self-gravitating medium, with initial density almost uniform is studied. Numerical experiments are performed with ordered and with Gaussian random initial conditions. The phase space portraits are shown to be qualitatively similar to shock waves, in particular with initial conditions of Brownian type. The PDF of the mass distribution is investigated. Submitted ...

A class of filters based on histograms are presented. The signal probability density function is estimated and filtering is performed in the pdf domain. Such filters can be designed to preserve signal features such as sharp edges while suppressing stochastic variations. One particular histogram filter scheme is evaluated and compared to a median filter and a normal gaussian blurring filter.