Related papers: A strong optimality result for anisotropic self--s…

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…

We provide a comprehensive study of interrelations between different measures of smoothness of functions on various domains and smoothness properties of approximation processes. Two general approaches to this problem have been developed:…

We present a general probabilistic perspective on Gaussian filtering and smoothing. This allows us to show that common approaches to Gaussian filtering/smoothing can be distinguished solely by their methods of computing/approximating the…

This article improves on existing methods to estimate the spectral density of stationary and nonstationary time series assuming a Gaussian process prior. By optimising an appropriate eigendecomposition using a smoothing spline covariance…

An important operation in geometry processing is finding the correspondences between pairs of shapes. The Gromov-Hausdorff distance, a measure of dissimilarity between metric spaces, has been found to be highly useful for nonrigid shape…

In nonparametric regression problems involving multiple predictors, there is typically interest in estimating an anisotropic multivariate regression surface in the important predictors while discarding the unimportant ones. Our focus is on…

We show relation between sign of Gaussian curvature of cuspidal edge and geometric invariants through types of singularities of Gauss map. Moreover, we define and characterize positivity/negativity of cusps of Gauss maps by geometric…

In tribology, it is of importance to properly characterize the topography of rough surfaces. In this work, the three-dimensional topographies of plain grinding surfaces are measured through a white light interferometer, and their…

The recent advancements in 3D Gaussian splatting (3D-GS) have not only facilitated real-time rendering through modern GPU rasterization pipelines but have also attained state-of-the-art rendering quality. Nevertheless, despite its…

We give a characterization of vertex-monotone properties with sharp thresholds in a Poisson random geometric graph or hypergraph. As an application we show that a geometric model of random k-SAT exhibits a sharp threshold for…

We consider nonparametric testing in a non-asymptotic framework. Our statistical guarantees are exact in the sense that Type I and II errors are controlled for any finite sample size. Meanwhile, one proposed test is shown to achieve minimax…

We propose an explicit way to generate a large class of Operator scaling Gaussian random fields (OSGRF). Such fields are anisotropic generalizations of selfsimilar fields. More specifically, we are able to construct any Gaussian field…

We study Gauss curvature for random Riemannian metrics on a compact surface, lying in a fixed conformal class; our questions are motivated by comparison geometry. Next, analogous questions are considered for the scalar curvature in…

Adjoint methods can speed up stellarator optimisation by providing gradient information more efficiently compared to finite-difference evaluations. Adjoint methods are herein applied to vacuum magnetic fields, with objective functions…

Building on the foundation work of Brown, Milton and Torquato, we present a tractable approach to analyse the effective permittivity of anisotropic two-phase structures. This methodology accounts for successive dipolar interactions,…

By considering gauge transformations on the macroscopic Maxwell's equations, a two dimensional gauge field, with its pseudo magnetic field in the real space, is identified as tilted anisotropy in the constitutive parameters. We show that…

Measures of the non-Gaussianity of a random field depend on how accurately one is able to measure the field. If a signal measured at a certain point is to be averaged with its surroundings, or coarse-grained, the magnitude of its…

This paper introduces a material-aware strength-of-connection measure for smoothed aggregation algebraic multigrid methods, aimed at improving robustness for scalar partial differential equations with heterogeneous and anisotropic material…

Motivated by the problem of testing for the existence of a signal of known parametric structure and unknown ``location'' (as explained below) against a noisy background, we obtain for the maximum of a centered, smooth random field an…

We study the rigidity results for self-shrinkers in Euclidean space by restriction of the image under the Gauss map. The geometric properties of the target manifolds carry into effect. In the self-shrinking hypersurface situation Theorem…