Related papers: Sparsity for isotropic spherical random fields
The atmospheres of planets (including Earth) and the outer layers of stars have often been treated in radiative transfer as plane-parallel media, instead of spherical shells, which can lead to inaccuracy, e.g. limb darkening. We give an…
This paper proposes parametric and non-parametric hypothesis testing algorithms for detecting anisotropy -- rotational variance of the covariance function in random fields. Both algorithms are based on resampling mechanisms, which enable…
The paper deals with cosmological solutions describing different phases of the Universe for the homogeneous and isotropic FLRW model of the Universe with torsion. Normally, torsion field is not suitable for maximally symmetric space time…
Two algorithms are proposed to simulate space-time Gaussian random fields with a covariance function belonging to an extended Gneiting class, the definition of which depends on a completely monotone function associated with the spatial…
Spherical Whittle--Mat\'ern Gaussian random fields are considered as solutions to fractional elliptic stochastic partial differential equations on the sphere. Approximation is done with surface finite elements. While the non-fractional part…
Embeddings provide compact representations of signals in order to perform efficient inference in a wide variety of tasks. In particular, random projections are common tools to construct Euclidean distance-preserving embeddings, while…
We consider and analyze applying a spectral inverse iteration algorithm and its subspace iteration variant for computing eigenpairs of an elliptic operator with random coefficients. With these iterative algorithms the solution is sought…
A compressed sensing scheme for near-field imaging of corrugations of relative sparse Fourier components is proposed. The scheme employs random sparse measurement of near field to recover the angular spectrum of the scattered field. It is…
Applying a transformation to a non-Gaussian field can enhance the information content of the resulting power spectrum, by reducing the correlations between Fourier modes. In the context of weak gravitational lensing, it has been shown that…
We present a ${\Gamma}$-convergence approximation for the total anisotropic length of a partition. This theoretical result gives rise to a numerical method which allows the study of minimal partitions with respect to different anisotropies.…
Gaussian Markov random fields (GMRFs) are useful in a broad range of applications. In this paper we tackle the problem of learning a sparse GMRF in a high-dimensional space. Our approach uses the l1-norm as a regularization on the inverse…
We review old and new uses of exchangeability, emphasizing the general theme of exchangeable representations of complex random structures. Illustrations of this theme include processes of stochastic coalescence and fragmentation; continuum…
A new line of research uses compression methods to measure the similarity between signals. Two signals are considered similar if one can be compressed significantly when the information of the other is known. The existing compression-based…
We extend field-level inference to jointly constrain the cosmological parameters $\{A,\omega_{\rm cdm},H_0\}$, in both real and redshift space. Our analyses are based on mock data generated using a perturbative forward model, with noise…
The problem of constructing flexible stochastic models to describe the variability in shape of solid particles is challenging. Natural objects often exhibit mono- or multi-fractal features, i.e. irregular shapes and self-similar patterns.…
Approximating field variables and data vectors from sparse samples is a key challenge in computational science. Widely used methods such as gappy proper orthogonal decomposition and empirical interpolation rely on linear approximation…
We study the energy landscape of a model of a single particle on a random potential, that is, we investigate the topology of level sets of smooth random fields on $\mathbb R^{N}$ of the form $X_N(x) +\frac\mu2 \|x\|^2,$ where $X_{N}$ is a…
The matter density field exhibits a nearly lognormal probability density distribution (PDF) after entering into the nonlinear regime. Recently, it has been shown that the shape of the power spectrum of a logarithmically transformed density…
We show that an isotropic random field on $SU(2)$ is not necessarily isotropic as a random field on $S^3$, although the two spaces can be identified. The ambiguity is due to the fact that the notion of isotropy on a group and on a sphere…
The scattering of scalar waves by a set of scatterers is considered. It is proven that the scattered field can be represented as an integral supported by any smooth surface enclosing the scatterers. This is a generalization of the series…