Related papers: Distance-squared mappings
Divergence functions are measures of distance or dissimilarity between probability distributions that serve various purposes in statistics and applications. We propose decompositions of Wasserstein and Cram\'er distances$-$which compare two…
Starting from kicked equations of motion with derivatives of non-integer orders, we obtain "fractional" discrete maps. These maps are generalizations of well-known universal, standard, dissipative, kicked damped rotator maps. The main…
Motivated by recent progress of structural optimization problems, the paper presents a new method for constructing the distance function to the boundary of given sets of interest, which simplifies the optimization procedure. We extend the…
We establish a characterization of the extraordinary dimension of perfect maps between metrizable spaces.
This paper studies the properties of convergence of distances between points and the existence and uniqueness of best proximity and fixed points of the so-called semi-cyclic impulsive self-mappings on the union of a number of nonempty…
We consider mappings satisfying an upper bound for the distortion of families of curves. We establish lower bounds for the distortion of distances under such mappings. As applications, we obtain theorems on the discreteness of the limit…
In the recent development in a various disciplines of physics, it is noted the need for including the deformed versions of the exponential functions. In this paper, we consider the deformations which have two purposes: to have them like…
Geometric properties of the fixed point set $Fix(f)$ of a self-mapping $f$ on a metric or a generalized metric space is an attractive issue. The set $Fix(f)$ can contain a geometric figure (a circle, an ellipse, etc.) or it can be a…
We provide a general framework to study convergence properties of families of maps. For manifolds $M$ and $N$ where $M$ is equipped with a volume form $\mathcal{V}$ we consider families of maps in the collection $\{(\phi, B) : B \subset M,…
Proximity maps and regions are defined based on the relative allocation of points from two or more classes in an area of interest and are used to construct random graphs called proximity catch digraphs (PCDs) which have applications in…
The Dirichlet-to-Neumann maps connect boundary values of harmonic functions. It is an amazing fact that the square of the non-local Dirichlet-to-Neumann map for the uniform conductivity 1 on the unit disc equals minus the local(!) Laplace…
With the help of a given distance matrix of size $n$, we construct an infinite family of distances $d_p$ (where $p \geq 2$) on the complex projective space $\mathbb{P}(\mathbb{C}^n)$ modelling the space of pure states of an $n$-level…
Computing the distance function to some surface or line is a problem that occurs very frequently. There are several ways of computing a relevant approximation of this function, using for example technique originating from the approximation…
Distance metric learning is a branch of machine learning that aims to learn distances from the data, which enhances the performance of similarity-based algorithms. This tutorial provides a theoretical background and foundations on this…
The domains of mesh functions are strict subsets of the underlying space of continuous independent variables. Spaces of partial maps between topological spaces admit topologies which do not depend on any metric. Such topologies…
Distance-hereditary graphs are known to be the graphs that are totally decomposable for the split decomposition. We characterise distance-hereditary graphs whose complement is also distance-hereditary by their split decomposition and by…
This paper studies first the differential inequalities that make it possible to build a global theory of pseudo-holomorphic functions in the case of one or several complex variables. In the case of one complex dimension, we prove that the…
Differentiable rendering is an essential operation in modern vision, allowing inverse graphics approaches to 3D understanding to be utilized in modern machine learning frameworks. Explicit shape representations (voxels, point clouds, or…
Optimal transportation distances are valuable for comparing and analyzing probability distributions, but larger-scale computational techniques for the theoretically favorable quadratic case are limited to smooth domains or regularized…
Based on a local approximation of the Riemannian distance on a manifold by a computationally cheap dissimilarity measure, a time discrete geodesic calculus is developed, and applications to shape space are explored. The dissimilarity…