Related papers: Capturing, Ordering and Gaussianity in 2D

Random fields in nature often have, to a good approximation, Gaussian characteristics. For such fields, the relative densities of umbilical points -- topological defects which can be classified into three types -- have certain fixed values.…

One of the key advantages of 3D rendering is its ability to simulate intricate scenes accurately. One of the most widely used methods for this purpose is Gaussian Splatting, a novel approach that is known for its rapid training and…

Many questions about triangles and quadrilaterals with rational sides, diagonals and areas can be reduced to solving certain Diophantine equations. We look at a number of such questions including the question of approximating arbitrary…

The curse of dimensionality is a common phenomenon which affects analysis of datasets characterized by large numbers of variables associated with each point. Problematic scenarios of this type frequently arise in classification algorithms…

I review what bispectra and trispectra look like in real space, in terms of the sign of particular shaped triangles and tetrahedrons. Having an equilateral density bispectrum of positive sign corresponds to having concentrated overdensities…

Random fields in nature often have, to a good approximation, Gaussian characteristics. We present the mathematical framework for a new and simple method for investigating the non-Gaussian contributions, based on counting the maxima and…

Among the topics we discuss are certain joint densities (for sides and for angles), acuteness probabilities and bivariate Rice moments.

This study proposes a radically alternate approach for extracting quantitative information from schlieren images. The method uses a scaled, derivative enhanced Gaussian process model to obtain true density estimates from two corresponding…

High dimensional data analysis is known to be as a challenging problem. In this article, we give a theoretical analysis of high dimensional classification of Gaussian data which relies on a geometrical analysis of the error measure. It…

We consider the signed density of the extremal points of (two-dimensional) scalar fields with a Gaussian distribution. We assign a positive unit charge to the maxima and minima of the function and a negative one to its saddles. At first, we…

Dark matter caustics have specific density profiles and, therefore, precisely calculable gravitational lensing properties. We present a formalism which simplifies the relevant calculations, and apply it to four specific cases. In the first…

We study the regularity of densities of distributions that are polynomial images of the standard Gaussian measure on $\mathbb{R}^n$. We assume that the degree of a polynomial is fixed and that each variable enters to a power bounded by…

This paper presents a new approach to the estimation of the deformation of an isotropic Gaussian random field on $\mathbb{R}^2$ based on dense observations of a single realization of the deformed random field. Under this framework we…

We study the isoperimetric problem in Euclidean space endowed with a density. We first consider piecewise constant densities and examine particular cases related to the characteristic functions of half-planes, strips and balls. We also…

Constraints on cosmological parameters from large-scale structure have traditionally been obtained from two-point statistics. However, non-linear structure formation renders these statistics insufficient in capturing the full information…

We investigate the complex Gaussian as well as non-Gaussian distributed random analytical and entire functions (complex entire random field) and calculate their domain of definiteness (radius of convergence) as well as some important…

We provide several diagrams for the graphical determination of certain elements of a Gaussian beam based on prior knowledge of other elements. For example, these diagrams allow us to determine the plane of the beam waist and the Rayleigh…

This brief paper develops a probability density that models processes for which the physical mechanism is unknown. It has desirable properties which are not realized by densities derived from Gaussian process or other classic methods. In…

We study distributions of random vectors whose components are second order polynomials in Gaussian random variables. Assuming that the law of such a vector is not absolutely continuous with respect to Lebesgue measure, we derive some…

A simple and efficient method for characterization of multidimensional Gaussian states is suggested and experimentally demonstrated. Our scheme shows analogies with tomography of finite dimensional quantum states, with the covariance matrix…