Related papers: Sparsity for isotropic spherical random fields

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…

Gaussian Markov random fields (GMRFs) are frequently used as computationally efficient models in spatial statistics. Unfortunately, it has traditionally been difficult to link GMRFs with the more traditional Gaussian random field models as…

We study spherically symmetric spacetimes for matter distributions with isotropic pressures. We generate new exact solutions to the Einstein field equations which also contains isotropic pressures. We develop an algorithm that produces a…

Random fields play a central role in the analysis of spatially correlated data and, as a result, have a significant impact on a broad array of scientific applications. This paper studies the cepstral random field model, providing recursive…

Gaussian random fields have been one of the most popular tools for analyzing spatial data. However, many geophysical and environmental processes often display non-Gaussian characteristics. In this paper, we propose a new class of spatial…

In the first part of the series papers, we set out to answer the following question: given specific restrictions on a set of samplers, what kind of signal can be uniquely represented by the corresponding samples attained, as the foundation…

In this paper, we are concerned with sample path properties of isotropic spherical Gaussian fields on $\S^2$. In particular, we establish the property of strong local nondeterminism of an isotropic spherical Gaussian field based on the…

Cosmological simulations play a crucial role in elucidating the effect of physical parameters on the statistics of fields and on constraining parameters given information on density fields. We leverage diffusion generative models to address…

A flexible model for non-stationary Gaussian random fields on hypersurfaces is introduced.The class of random fields on curves and surfaces is characterized by an amplitude spectral density of a second order elliptic differential…

Known algorithms for manipulating octagons do not preserve their sparsity, leading typically to quadratic or cubic time and space complexities even if no relation among variables is known when they are all bounded. In this paper, we present…

Instance sparsification is well-known in the world of exact computation since it is very closely linked to the Exponential Time Hypothesis. In this paper, we extend the concept of sparsification in order to capture subexponential time…

Motivated by the need to better understand the properties of sparse cutting-planes used in mixed integer programming solvers, the paper [2] studied the idealized problem of how well a polytope is approximated by the use of sparse valid…

We show that sparse spherical harmonic expansions can be efficiently recovered from a small number of randomly chosen samples on the sphere. To establish the main result, we verify the restricted isometry property of an associated…

Several extensions of General Relativity and high energy physics include scalar fields as extra degrees of freedom. In the search for predictions in the non-linear regime of cosmological evolution, the community makes use of numerical…

Geometric reconstruction of opaque surfaces from images is a longstanding challenge in computer vision, with renewed interest from volumetric view synthesis algorithms using radiance fields. We leverage the geometry field proposed in recent…

In this paper we will consider the problem of the numerical simulation of non-Gaussian, scalar random fields with a prescribed correlation structure provided either by a theoretical model or computed on a set of observational data.…

The next generation of galaxy surveys, aiming to observe millions of galaxies, are expensive both in time and cost. This raises questions regarding the optimal investment of this time and money for future surveys. In a previous work, it was…

The problem of how to find a sparse representation of a signal is an important one in applied and computational harmonic analysis. It is closely related to the problem of how to reconstruct a sparse vector from its projection in a much…

We develop a technique for the reconstruction of the potential for a scalar field or a tachyon field, reproducing a given cosmological evolution in a closed and open isotropic cosmological models. Such potentials are explicitly written down…

Random feature methods have been successful in various machine learning tasks, are easy to compute, and come with theoretical accuracy bounds. They serve as an alternative approach to standard neural networks since they can represent…