Zobrazeno 1 - 10
of 22
pro vyhledávání: '"Tombari, Francesca"'
Autor:
Fajstrup, Lisbeth, Fasy, Brittany Terese, Li, Wenwen, Mezrag, Lydia, Rask, Tatum, Tombari, Francesca, Urbančič, Živa
The Gromov--Hausdorff distance measures the similarity between two metric spaces by isometrically embedding them into an ambient metric space. In this work, we introduce an analogue of this distance for metric spaces endowed with directed structures.
Externí odkaz:
http://arxiv.org/abs/2408.14394
One of the most animated themes of multidimensional persistence is the comparison between invariants. The matching distance between persistent Betti numbers functions (or rank invariants), is among the most studied metrics in this context, particular
Externí odkaz:
http://arxiv.org/abs/2312.04201
In this article, we propose a topological model to encode partial equivariance in neural networks. To this end, we introduce a class of operators, called P-GENEOs, that change data expressed by measurements, respecting the action of certain sets of t
Externí odkaz:
http://arxiv.org/abs/2308.13357
In this paper, we discuss certain circumstances in which the category of tame functors inherits an abelian category structure with minimal resolutions and a model category structure with minimal cofibrant replacements. We also present a structure the
Externí odkaz:
http://arxiv.org/abs/2301.04079
In this paper we exploit the concept of extended Pareto grid to study the geometric properties of the matching distance for $\mathbb{R}^2$-valued regular functions defined on a Riemannian closed manifold. In particular, we prove that in this case the
Externí odkaz:
http://arxiv.org/abs/2210.16718
Under certain conditions, Koszul complexes can be used to calculate relative Betti diagrams of vector space-valued functors indexed by a poset, without the explicit computation of global minimal relative resolutions. In relative homological algebra o
Externí odkaz:
http://arxiv.org/abs/2209.05923
We introduce a construction called realisation which transforms posets into posets. We show that realisations share several key features with upper semilattices. For example, we define local dimensions of points in a poset and show that these numbers
Externí odkaz:
http://arxiv.org/abs/2112.12209
The aim of this article is to describe a new perspective on functoriality of persistent homology and explain its intrinsic symmetry that is often overlooked. A data set for us is a finite collection of functions, called measurements, with a finite do
Externí odkaz:
http://arxiv.org/abs/2002.05972
Motivated by applications in Topological Data Analysis, we consider decompositions of a simplicial complex induced by a cover of its vertices. We study how the homotopy type of such decompositions approximates the homotopy of the simplicial complex i
Externí odkaz:
http://arxiv.org/abs/2002.03409
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