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Related papers: Uniform Consistency of Generalized Fr\'echet Means

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For most optimisation methods an essential assumption is the vector space structure of the feasible set. This condition is not fulfilled if we consider optimisation problems over the sphere. We present an algorithm for solving a special…

Computation · Statistics 2018-02-27 Gabriele Eichfelder , Thomas Hotz , Johannes Wieditz

In the paper we define the convergence of compact fuzzy sets as a convergence of alpha-cuts in the topology of compact subsets of a metric space. Furthermore we define typical convergences of fuzzy variables and show relations with…

Probability · Mathematics 2009-04-06 Adam Bzowski , Michal K. Urbanski

We investigate measures of complexity of function classes based on continuity moduli of Gaussian and Rademacher processes. For Gaussian processes, we obtain bounds on the continuity modulus on the convex hull of a function class in terms of…

Probability · Mathematics 2007-05-23 Olivier Bousquet , Vladimir Koltchinskii , Dmitry Panchenko

The aim of this paper is to present some structural equations for generalized quasi-Einstein metrics which was defined recently by Catino in [12]. In addition, supposing that the Riemannian manifold is Einstein we shall show that it is a…

Differential Geometry · Mathematics 2012-09-13 Abdênago Barros , Ernani Ribeiro

We establish finite-sample error bounds in expectation for transformed Fr\'echet means in Hadamard spaces under minimal assumptions. Transformed Fr\'echet means provide a unifying framework encompassing classical and robust notions of…

Statistics Theory · Mathematics 2025-11-11 Christof Schötz

In light of the log-Brunn-Minkowski conjecture, various attempts have been made to define the geometric mean of convex bodies. Many of these constructions are fairly complex and/or fail to satisfy some natural properties one would expect of…

Metric Geometry · Mathematics 2024-05-02 René Brandenberg , Florian Grundbacher

Any measure $\mu$ on a CAT(k) space M that is stratified as a finite union of manifolds and has local exponential maps near the Fr\'echet mean $\bar\mu$ yields a continuous "tangential collapse" from the tangent cone of M at $\bar\mu$ to a…

Metric Geometry · Mathematics 2023-11-17 Jonathan C. Mattingly , Ezra Miller , Do Tran

Weintroduce a new class of mappings called cyclic p-$\phi$-contraction mappings and investigate the existence and uniqueness of fixed point for such mappings defined on metric spaces, uniformly convex Banach spaces, or reflex ive Banach…

Functional Analysis · Mathematics 2026-02-19 Seyyed Mohammad Sadegh Nabavi Sales

Mathai-Quillen forms are used to give an integral formula for the Lefschetz number of a smooth map of a closed manifold. Applied to the identity map, this formula reduces to the Chern-Gauss-Bonnet theorem. The formula is computed explicitly…

Differential Geometry · Mathematics 2007-05-23 Mihail Frumosu , Steven Rosenberg

This paper is devoted to the study of the T-tensor associated with a spherically symmetric Finsler metric $F=u\phi(r,s)$ on \(\mathbb{R}^n\). We derive a general expression for the T-tensor in terms of the scalar function \(\phi(r, s)\) and…

Differential Geometry · Mathematics 2026-01-23 Salah G. Elgendi

In this paper, we study a new class of Finsler metrics, F=\alpha\phi(b^2,s), s:=\beta/\alpha, defined by a Riemannian metric \alpha and 1-form \beta. It is called general (\alpha, \beta) metric. In this paper, we assume \phi be coefficient…

Differential Geometry · Mathematics 2017-06-28 A. Ala , A. Behzadi , M. Rafiei-Rad

A $\phi$-exponential distribution is a generalization of an exponential distribution associated to functions $\phi$ in an appropriate class, and the space of $\phi$-exponential distributions has a dually flat structure. We study features of…

Metric Geometry · Mathematics 2011-10-03 Asuka Takatsu

In this paper, we consider certain topological properties along with certain types of mappings on these spaces defined by the notion of ideal convergence. In order to do that, we primarily follow in the footsteps of the earlier studies of…

General Topology · Mathematics 2023-01-03 Pratulananda Das , Upasana Samanta , Shou Lin

Given a map $\phi:X\rightarrow Y$ between $F$-analytic manifolds over a local field $F$ of characteristic $0$, we introduce an invariant $\epsilon_{\star}(\phi)$ which quantifies the integrability of pushforwards of smooth compactly…

Algebraic Geometry · Mathematics 2024-09-17 Itay Glazer , Yotam I. Hendel , Sasha Sodin

This paper is devoted to the complete convergence study of the finite-element approximation of Maxwell's equations in the case where the magnetic permeability is constant. Standard linear finite elements for the space discretization are…

Numerical Analysis · Mathematics 2020-07-06 Larisa Beilina , Vitoriano Ruas

We study (generalized) cones over metric spaces, both in Riemannian and Lorentzian signature. In particular, we establish synthetic lower Ricci curvature bounds \`a la Lott-Villani-Sturm and Ohta in the metric measure case, and \`a la…

Differential Geometry · Mathematics 2026-03-25 Matteo Calisti , Christian Ketterer , Clemens Sämann

We solve the problem of best approximation by partial isometries of given rank to an arbitrary rectangular matrix, when the distance is measured in any unitarily invariant norm. In the case where the norm is strictly convex, we parametrize…

Functional Analysis · Mathematics 2016-11-08 Jorge Antezana , Eduardo Chiumiento

We consider two statistical problems at the intersection of functional and non-Euclidean data analysis: the determination of a Fr\'echet mean in the Wasserstein space of multivariate distributions; and the optimal registration of deformed…

Statistics Theory · Mathematics 2020-12-17 Yoav Zemel , Victor M. Panaretos

In this paper, generalized metrics mean metrics taking values in general linearly ordered Abelian groups. Using the Hahn fields, we first prove that for every generalized metric space, if the set of the Archimedean equivalence classes of…

Metric Geometry · Mathematics 2022-07-22 Yoshito Ishiki

We prove generalized Gaffney inequalities and the discrete compactness for finite element differential forms on $s$-regular domains, including general Lipschitz domains. In computational electromagnetism, special cases of these results have…

Numerical Analysis · Mathematics 2018-07-18 Juncai He , Kaibo Hu , Jinchao Xu