Simulations of vortex tube dynamics reveal that the non-Gaussian nature of turbulent fluctuation originates in the effect of random advection. A similar non-Gaussian distribution is found numerically in a simplified statistical model of random advection. An analytical solution is obtained in the mean-field case.

For continuous sources the rate-distortion function has been found for a Laplace source with an absolute error distortion d(x, x̂) = |x x̂| [2], exponential source with absolute error distortion [3] and Gaussian source with square error distortion d(x, x̂) = |x x̂|2 [1]. In this paper, we will enlarge this set of known cases by considering the rate-distortion problem for generalized Gaussian (GG) d...

Statistical modeling plays an important role in various research areas. It provides a way to connect the data with the statistics. Based on the statistical properties of the observed data, an appropriate model can be chosen that leads to a promising practical performance. The Gaussian distribution is the most popular and dominant probability distribution used in statistics, since it has an anal...

The mixture of Gaussian distributions, a soft version of k-means ( [2]), is considered a stateof-the-art clustering algorithm. It is widely used in computer vision for selecting classes, e.g., color[4, 1, 5],texture[1, 9], shapes [12, 10]. In this algorithm, each class is described by a Gaussian distribution, defined by its mean and covariance. The data is described by a weighted sum of these G...

This paper describes an improved Constant False Alarm Rate (CFAR) ship detection algorithm in spaceborne synthetic aperture radar (SAR) image based on Alphastable distribution model. Typically, the CFAR algorithm uses the Gaussian distribution model to describe statistical characteristics of a SAR image background clutter. However, the Gaussian distribution is only valid for multilook SAR image...

The vast majority of HMM–based speech recognition systems use Gaussian mixture models as the state distribution model. The use of these distributions is motivated more by ease of training, decoding and the fact that a sufficient number of Gaussian components may be used to approximate any distribution, than some underlying aspect of the data being modelled. If distributions were selected that b...

We discuss the distribution of the gravitational force created by a Poissonian distribution of field sources (stars, galaxies,...) in different dimensions of space d. In d = 3, when the particle number N → +∞, it is given by a Lévy law called the Holtsmark distribution. It presents an algebraic tail for large fluctuations due to the contribution of the nearest neighbor. In d = 2, for large but ...

Following the discovery of the cosmic microwave background, the hot big-bang model has become the standard cosmological model. In this theory, small primordial fluctuations are subsequently amplified by gravity to form the large-scale structure seen today. Different theories for unified models of particle physics, lead to different predictions for the statistical properties of the primordial fl...

In aggregation applications, individual privacy is a crucial factor to determine the effectiveness, for which the noise-addition method (i.e., a random noise value is added to the true value) is a simple yet powerful approach. However, improper additive noise could result in bias for the aggregate result. It demands an optimal noise distribution to reduce the deviation. In this paper, we develo...

We compute analytically, for large N, the probability distribution of the number of positive eigenvalues (the index N+) of a random N x N matrix belonging to Gaussian orthogonal (beta=1), unitary (beta=2) or symplectic (beta=4) ensembles. The distribution of the fraction of positive eigenvalues c=N+/N scales, for large N, as P(c,N) approximately = exp[-betaN(2)Phi(c)] where the rate function Ph...