Determining the statistical properties of stochastic nonlinear systems is of major interest across many disciplines. Currently, there are no general efficient methods to deal with this challenging problem that involves high dimensionality, low regularity and random frequencies. We propose a framework for stochastic analysis in nonlinear dynamical systems based on goal-oriented probability densi...

Normal dynamics in a quasi-one-dimensional channel of length L (→∞) of N hard spheres are analyzed. The spheres are heterogeneous: each has a diffusion coefficient D that is drawn from a probability density function (PDF), W∼D(-γ) for small D, where 0≤γ<1. The initial spheres' density ρ is nonuniform and scales with the distance (from the origin) l as ρ∼l(-α), 0≤α≤1. An approximation for the N-...

In this paper, an analytical approach for evaluating performance of dual-hop cooperative link over shadowed Ricean fading channels is presented. New lower bound expressions for the probability density function (PDF), cumulative distribution function (CDF) and average bit error probability (ABEP) for system with channel state information (CSI) relay are derived. Some numerical results are presen...

Abstract: This paper is concerned with the analysis of exact symbol error probability (SEP) for cooperative diversity using amplify-and-forward (AF) relaying over independent and non-identical Nakagami-m fading channels. The mathematical formulations for Probability Density Function (pdf) and Moment Generating Function (MGF) of a cooperative link have been derived for calculating symbol error p...

We investigate the non-perturbative results of multi-dimensional forced Burgers equation coupled to the continuity equation. In the inviscid limit, we derive the exact exponents of two-point density correlation functions in the universal region in arbitrary dimensions. We then find the universal generating function and the tails of the probability density function (PDF) for the longitudinal vel...

In this correspondence, we compare the expectation maximization (EM) algorithm with another iterative approach, namely, the iterative conditional estimation (ICE) algorithm, which was formally introduced in the field of statistical segmentation of images. We show that in case the probability density function (PDF) belongs to the exponential family, the EM algorithm is one particular case of the...

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.

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...

A large eddy simulation (LES)/probability density function (PDF) method is proposed for modeling turbulent spray combustion. The PDF method has the advantage that the chemical source term appears closed but requires models for the small scale mixing process. The transport equation for the joint-scalar PDF is high dimensional and solved using a Lagrangian technique. A stable and consistent numer...

The slope stability is a very important problem in geotechnical engineering. This paper presents an approach for slope reliability analysis based on the maximum-entropy method. The key idea is to implement the maximum entropy principle in estimating the probability density function. The performance function is formulated by the Simplified Bishop’s method to estimate the slope failure probabilit...