相关论文: Definitions of distance function in radial basis f…

Decoupled fractional Laplacian wave equation can describe the seismic wave propagation in attenuating media. Fourier pseudospectral implementations, which solve the equation in spatial frequency domain, are the only existing methods for…

In this paper, we determine explicit bases for Riemann--Roch spaces of linearized function fields, and we give a lower bound for the minimum distance of generalized algebraic geometry codes. As a consequence, we construct generalized…

By employing the differential structure recently developed by N. Gigli, we first give a notion of functions of bounded variation ($BV$) in terms of suitable vector fields on a complete and separable metric measure space $(\mathbb{X},d,\mu)$…

We study the regularity of the distance function to the boundary of a domain in $\mathbb{R}^n$, with respect to the Minkowski functional of a convex polytope. We obtain the regularity of the distance function in certain cases. We also…

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…

If $X$ is a convex surface in a Euclidean space, then the squared intrinsic distance function $\dist^2(x,y)$ is DC (d.c., delta-convex) on $X\times X$ in the only natural extrinsic sense. An analogous result holds for the squared distance…

We present a novel type of neural fields that uses general radial bases for signal representation. State-of-the-art neural fields typically rely on grid-based representations for storing local neural features and N-dimensional linear…

Although recovering an Euclidean distance matrix from noisy observations is a common problem in practice, how well this could be done remains largely unknown. To fill in this void, we study a simple distance matrix estimate based upon the…

Sleeve functions are generalizations of the well-established ridge functions that play a major role in the theory of partial differential equation, medical imaging, statistics, and neural networks. Where ridge functions are non-linear,…

This paper presents a comprehensive experimental validation of a recently developed Ray Deflection Function (RDF) approach, which offers a new framework for modeling surface roughness effects in optical systems. Through detailed geometrical…

Some response surface functions in complex engineering systems are usually highly nonlinear, unformed, and expensive-to-evaluate. To tackle this challenge, Bayesian optimization, which conducts sequential design via a posterior distribution…

We introduce fractional flat space, described by a continuous geometry with constant non-integer Hausdorff and spectral dimensions. This is the analogue of Euclidean space, but with anomalous scaling and diffusion properties. The basic tool…

We consider a ramification of the deep BSDE loss functional designed to apply for BSDEs on bounded domains, i.e. with random (unbounded) time horizons. We derive a general convergence rate of the loss functional; precisely for a class of…

We apply the techniques of computable model theory to the distance function of a graph. This task leads us to adapt the definitions of several truth-table reducibilities so that they apply to functions as well as to sets, and we prove…

We give an accessible introduction and elaboration on the methods used in obtaining a geodesic, which is the curve of shortest length connecting two points lying on the surface of a function. This is found through computing what's known as…

In this paper, we introduce a new approach for soft robot shape formation and morphing using approximate distance fields. The method uses concepts from constructive solid geometry, R-functions, to construct an approximate distance function…

Over the past decade, a number of algorithms for full-field elastic strain estimation from neutron and X-ray measurements have been published. Many of the recently published algorithms rely on modelling the unknown strain field as a…

Motivated by information geometry, a distance function on the space of stochastic matrices is advocated. Starting with sequences of Markov chains the Bhattacharyya angle is advocated as the natural tool for comparing both short and long…

We present a practical approach to solving distance-based optimization problems using optical computing hardware. The objective is to minimize an energy function defined as the weighted sum of squared differences between measured distances…

Distance function is a main metrics of measuring the affinity between two data points in machine learning. Extant distance functions often provide unreachable distance values in real applications. This can lead to incorrect measure of the…