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Random fields are useful mathematical tools for representing natural phenomena with complex dependence structures in space and/or time. In particular, the Gaussian random field is commonly used due to its attractive properties and…
Random Wavelet Series form a class of random processes with multifractal properties. We give three applications of this construction. First, we synthesize a random function having any given spectrum of singularities satisfying some…
This article presents an efficient algorithm to generate a discrete uniform distribution on a set of $p$ elements using a biased random source for $p$ prime. The algorithm generalizes Von Neumann's method and improves computational…
A novel approach to unstructured quadrilateral mesh generation for planar domains is presented. Away from irregular vertices, the resulting meshes have the properties of nearly conformal grids. The technique is based on a theoretical…
In this paper, we generalise the formula for the fourth moment of a random determinant to account for entries with asymmetric distribution. We also derive the second moment of a random Gram determinant.
This paper proposes a unified approach to enable the study of diverse distributions in the real, complex, quaternion and octonion cases, simultaneously. In particular, the central, nonsingular matricvariate and matrix multivariate Pearson…
Variational inference is a powerful tool for approximate inference, and it has been recently applied for representation learning with deep generative models. We develop the variational Gaussian process (VGP), a Bayesian nonparametric…
In this paper introduces a new family of continuous distributions namely the Poison transmuted-G family of distribution is proposed by inducing two addition parameter on the base line G distribution. Some of its mathematical properties…
Gaussian random number generators attract a widespread interest due to their applications in several fields. Important requirements include easy implementation, tail accuracy, and, finally, a flat spectrum. In this work, we study the…
Let $[\mathcal{P}]$ be the points of a Poisson process on $\mathbb{R}^d$ and $F$ a probability distribution with support on the non-negative integers. Models are formulated for generating translation invariant random graphs with vertex set…
An expression for the joint probability distribution of the principal curvatures at an arbitrary point in the ensemble of isosurfaces defined on isotropic Gaussian random fields on Rn is derived. The result is obtained by deriving symmetry…
From a suitable integral representation of the Laplace transform of a positive semi-definite quadratic form of independent real random variables with not necessarily identical densities a univariate integral representation is derived for…
Many engineering systems are subject to spatially distributed uncertainty, i.e. uncertainty that can be modeled as a random field. Altering the mean or covariance of this uncertainty will in general change the statistical distribution of…
In probability theory, there is a tendency to treat one random variable with a given distribution as being just as good as any other. By and large this is fine because probability is (mostly) concerned with distributional properties of…
The AMAS group at the Paul Scherrer Institute developed an object oriented library for high performance simulation of high intensity ion beam transport with space charge. Such particle-in-cell (PIC) simulations require a method to generate…
The paper considers the classical Goodness of Fit test. It suggests to use the Gamma distribution for the approximation of the distribution of the Pearson statistics with unknown parameters estimated from raw data. The parameters of these…
Consider a graph on randomly scattered points in an arbitrary space, with two points $x,y$ connected with probability $\phi(x,y)$. Suppose the number of points is large but the mean number of isolated points is $O(1)$. We give general…
Random unitary matrices find a number of applications in quantum information science, and are central to the recently defined boson sampling algorithm for photons in linear optics. We describe an operationally simple method to directly…
The existence of invariant generators for distributions satisfying a compatibility condition with the symmetry algebra is proved.
Pyrosequencing is emerging as one of the important next-generation sequencing technologies. We derive the statistical distributions of this technique in terms of nucleotide probabilities of the target sequences. We give exact distributions…