Related papers: Spatially Varying Anisotropy for Gaussian Random F…
The article studies non-Gaussian extensions of a recently discovered link between certain Gaussian random fields, expressed as solutions to stochastic partial differential equations (SPDEs), and Gaussian Markov random fields. The focus is…
Astronomical observations suggest that the Universe may be anisotropic on the largest scales. In order to model this situation, we develop a new approach to cosmology that allows for large-scale anisotropy to emerge from the growth of…
This paper addresses the inference of spatial dependence in the context of a recently proposed framework. More specifically, the paper focuses on the estimation of model parameters for a class of generalized Gibbs random fields, i.e.,…
An important aspect of modeling spatially-referenced data is appropriately specifying the covariance function of the random field. A practitioner working with spatial data is presented a number of choices regarding the structure of the…
We consider anisotropic self-similar random fields, in particular, the fractional Brownian sheet. This Gaussian field is an extension of fractional Brownian motion. We prove some properties of covariance function for self-similar fields…
The dynamics of large-scale geophysical fluids is primarily governed by the balance between the Coriolis force and the pressure gradient. This phenomenon, known as geostrophic equilibrium, is the basis for the geostrophic model, which has…
Obtaining high-resolution maps of precipitation data can provide key insights to stakeholders to assess a sustainable access to water resources at urban scale. Mapping a nonstationary, sparse process such as precipitation at very high…
We present Gaussian Splatting Anisotropic Visibility Field (GAVIS), a novel framework for uncertainty quantification and active mapping in 3DGS. Our key insight is that regions unseen from the training views yield unreliable predictions…
The COBE satellite's maps of the cosmic microwave background (CMB) anisotropy do not have the resolution to discriminate between theories of cosmic structure formation based on inflation, and those based on field ordering following a…
We present results obtained from a finite-element simulation of seismic displacement fields and of gravity gradients generated by those fields. The displacement field is constructed by a plane wave model with a 3D isotropic stochastic field…
We report an experimental assessment of surface kinetic roughening properties that are anisotropic in space. Working for two specific instances of silicon surfaces irradiated by ion-beam sputtering under diverse conditions (with and without…
Motivated by the modeling of the spatial structure of the velocity field of three-dimensional turbulent flows, and the phenomenology of cascade phenomena, a linear dynamics has been recently proposed able to generate high velocity gradients…
In this paper we present a general framework in which one can rigorously study the effect of spatio-temporal noise on traveling waves, stationary patterns and oscillations that are invariant under the action of a finite-dimensional set of…
Spartan Spatial Random Fields (SSRFs) are generalized Gibbs random fields, equipped with a coarse-graining kernel that acts as a low-pass filter for the fluctuations. SSRFs are defined by means of physically motivated spatial interactions…
Gaussian random fields pervade all areas of science. However, it is often the departures from Gaussianity that carry the crucial signature of the nonlinear mechanisms at the heart of diverse phenomena, ranging from structure formation in…
We develop, simulate and extend an initial proposition by Chaves et al. concerning a random incompressible vector field able to reproduce key ingredients of three-dimensional turbulence in both space and time. In this article, we focus on…
In this work, we argue that Gaussian splatting is a suitable unified representation for autonomous robot navigation in large-scale unstructured outdoor environments. Such environments require representations that can capture complex…
Millimeter-wave radar offers unique advantages in adverse weather but suffers from low spatial fidelity, severe azimuth ambiguity, and clutter-induced spurious returns. Existing methods mainly focus on improving spatial perception…
We study the sample paths properties of Operator scaling Gaussian random fields. Such fields are anisotropic generalizations of anisotropic self-similar random fields as anisotropic Fractional Brownian Motion. Some characteristic properties…
It is desirable to create 3D object models and 3D maps from 2D input images for applications such as navigation, virtual tourism, and urban planning. The traditional methods of creating 3D maps, (such as photogrammetry), require a large…