相关论文: Distances Induced by Barbilian's Metrization Proce…

We discuss how metric limits and rescalings of K\"ahler-Einstein metrics connect with Algebraic Geometry, mostly in relation to the study of moduli spaces of varieties, and singularities. Along the way, we describe some elementary examples,…

Metrics on the space of sets of trajectories are important for scientists in the field of computer vision, machine learning, robotics, and general artificial intelligence. However, existing notions of closeness between sets of trajectories…

The basic theory of semi-measures on locally compact Abelian groups is extended to prove the existence of a generalised Eberlein decomposition into such semi-measures.

We consider the metric transformation of metric measure spaces/pyramids. We clarify the conditions to obtain the convergence of the sequence of transformed spaces from that of the original sequence, and, conversely, to obtain the…

Given a probability measure with density, Fermat distances and density-driven metrics are conformal transformations of the Euclidean metric that shrink distances in high density areas and enlarge distances in low density areas. Although…

This paper is a companion paper to [Lipman and Daubechies 2011]. We provide numerical procedures and algorithms for computing the alignment of and distance between two disk type surfaces. We provide a convergence analysis of the discrete…

This article presents a novel mathematical formalism for advanced manifold--metric pairs, enhancing the frameworks of geometry and topology. We construct various D-dimensional manifolds and their associated metric spaces using functional…

We introduce a rigorous, physically appealing, and practical way to measure distances between exchange-only correlations of interacting many-electron systems, which works regardless of their size and inhomogeneity. We show that this…

Longitude determination at sea gained increasing commercial importance in the late Middle Ages, spawned by a commensurate increase in long-distance merchant shipping activity. Prior to the successful development of an accurate marine…

The idea of measuring distance between languages seems to have its roots in the work of the French explorer Dumont D'Urville \cite{Urv}. He collected comparative words lists of various languages during his voyages aboard the Astrolabe from…

The aim of this work is to study the problem of prior elicitation for the Mallows model with Spearman's distance, a popular distance-based model for rankings or permutation data. Previous Bayesian inference for such model has been limited…

This paper is the first of three in which I study the moduli space of isometry classes of (compact) globally hyperbolic spacetimes (with boundary). I introduce a notion of Gromov-Hausdorff distance which makes this moduli space into a…

We introduce a general class of distances (metrics) between Markov chains, which are based on linear behaviour. This class encompasses distances given topologically (such as the total variation distance or trace distance) as well as by…

The regularization of propagators by means of a complex metric is considered. (The paper is an English translation of the first of two articles in Russian published by the author in 1987-88: V.D. Ivashchuk, Regularization by…

We describe a method of defining a Hermitian metric on Kobayashi hyperbolic manifolds. The metric is distance decreasing under holomorphic mappings, up to a multiplicative constant. This method is distinct from the classical construction of…

Systematic surveys of astronomical objects often lead to discoveries, but always provide invaluable information for statistical studies of well-defined samples. They also promote follow-up investigations of individual objects or classes.…

We discuss how the redshift (Mattig) method in Friedmann cosmology relates to dynamical distance indicators based on Newton's gravity (Teerikorpi 2011). It belongs to the class of indicators where the relevant length inside the system is…

In this paper we study the differential systems on Leibniz algebroids. We introduce a class of almost metriplectic manifolds as a special case of Leibniz manifolds. Also, the notion of almost metriplectic algebroid is introduced. These…

Graphs are interesting structures: extremely useful to depict real-life problems, extremely easy to understand given a sketch, extremely complicated to represent formally, extremely complicated to compare. Phylogeny is the study of the…

We describe a novel procedure to map the field equations of nonlinear Ricci-based metric-affine theories of gravity, coupled to scalar matter described by a given Lagrangian, into the field equations of General Relativity coupled to a…