Related papers: Integrated shape-sensitive functional metrics
Intermediate dimensions were recently introduced to interpolate between the Hausdorff and box-counting dimensions of fractals. Firstly, we show that these intermediate dimensions may be defined in terms of capacities with respect to certain…
In this paper, we analyze metrical approximations of functions $F :\Lambda times X \rightarrow Y$ by trigonometric polynomials and $\rho$-periodic type functions, where $\emptyset \neq \Lambda \subseteq {\mathbb R}^{n},$ $X$ and $Y $are…
In this paper we study an abstract framework for computing shape derivatives of functionals subject to PDE constraints. We revisit the Lagrangian approach using the implicit function theorem in an abstract setting tailored for applications…
Finite mixture models have long been used across a variety of fields in engineering and sciences. Recently there has been a great deal of interest in quantifying the convergence behavior of the \emph{mixing measure}, a fundamental object…
3D shape analysis has been largely focused on traditional 3D representations of point clouds and meshes, but the discrete nature of these data makes the analysis susceptible to variations in input resolutions. Recent development of neural…
We propose a means of computing fitted frames on the boundary and in the interior of objects and using them to provide the basis for producing geometric features from them that are not only alignment-free but most importantly can be made to…
A general framework for integration over certain infinite dimensional spaces is first developed using projective limits of a projective family of compact Hausdorff spaces. The procedure is then applied to gauge theories to carry out…
Neural signed distance functions (SDFs) have been a vital representation to represent 3D shapes or scenes with neural networks. An SDF is an implicit function that can query signed distances at specific coordinates for recovering a 3D…
We study a new class of distances between Radon measures similar to those studied in a recent paper of Dolbeault-Nazaret-Savar\'e [DNS]. These distances (more correctly pseudo-distances because can assume the value $+\infty$) are defined…
This paper introduces the notion of stochastic simulation-gap function, which formally quantifies the gap between an approximate mathematical model and a high-fidelity stochastic simulator. Since controllers designed for the mathematical…
\textit{Implicit neural representations} (INRs) have emerged as a promising framework for representing signals in low-dimensional spaces. This survey reviews the existing literature on the specialized INR problem of approximating…
The direct and inverse theorems are established for the best approximation in the weighted $L^p$ space on the unit sphere of $\RR^{d+1}$, in which the weight functions are invariant under finite reflection groups. The theorems are stated…
A comprehensive theory of the effect of Orlicz-Sobolev maps, between Euclidean spaces, on subsets with zero or finite Hausdorff measure is offered. Arbitrary Orlicz-Sobolev spaces embedded into the space of continuous function and Hausdorff…
We introduce a new metric on the ideal space of an AF algebra that metrizes the Fell topology. The novelty of this metric lies in the use of a Hamming distance type metric in its construction. Furthermore, this metric captures more of the…
In [Heimann, Lehrenfeld, Preu{\ss}, SIAM J. Sci. Comp. 45(2), 2023, B139 - B165] new geometrically unfitted space-time Finite Element methods for partial differential equations posed on moving domains of higher-order accuracy in space and…
We study holomorphic isometries between bounded symmetric domains with respect to the Bergman metrics up to a normalizing constant. In particular, we first consider a holomorphic isometry from the complex unit ball into an irreducible…
One of the most natural and challenging issues in discrete complex analysis is to prove the convergence of discrete holomorphic functions to their continuous counterparts. This article is to solve the open problem in the general setting. To…
As commonly used implicit geometry representations, the signed distance function (SDF) is limited to modeling watertight shapes, while the unsigned distance function (UDF) is capable of representing various surfaces. However, its inherent…
The classical and extensively-studied Fr\'echet distance between two curves is defined as an inf max, where the infimum is over all traversals of the curves, and the maximum is over all concurrent positions of the two agents. In this…
A labeled metric space is intuitively speaking a metric space together with a special set of points to be understood as the geometric boundary of the space. We study basic properties of a recently introduced labeled Gromov-Hausdorff…