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pro vyhledávání: '"Tuzhilin, Alexey"'
The purpose of this article is to demonstrate the connection between the properties of the Gromov--Hausdorff distance and the Borsuk conjecture. The Borsuk number of a given bounded metric space $X$ is the infimum of cardinal numbers $n$ such that $X
Externí odkaz:
http://arxiv.org/abs/2203.04030
It is shown that any bounded metric space can be isometrically embedded into the Gromov--Hausdorff metric class GH. This result is a consequence of local geometry description of the class GH in a sufficiently small neighborhood of a generic metric sp
Externí odkaz:
http://arxiv.org/abs/2203.02904
Autor:
Ivanov, Alexander, Tuzhilin, Alexey
The aim of this paper is to demonstrate relations between Gromov-Hausdorff distance properties and the Borsuk Conjecture. The Borsuk number of a given bounded metric space $X$ is the infimum of cardinal numbers $n$ such that $X$ can be partitioned in
Externí odkaz:
http://arxiv.org/abs/2203.05991
Autor:
Bogaty, Semeon A., Tuzhilin, Alexey A.
The paper is devoted to the study of the Gromov-Hausdorff proper class, consisting of all metric spaces considered up to isometry. In this class, a generalized Gromov-Hausdorff pseudometric is introduced and the geometry of the resulting space is inv
Externí odkaz:
http://arxiv.org/abs/2110.06101
Autor:
Ji, Yibo, Tuzhilin, Alexey A.
We calculate the Gromov--Hausdorff distance between a line segment and a circle in the Euclidean plane. To do that, we introduced a few new notions like round spaces and nonlinearity degree of a metric space.
Comment: 14 pages, 4 figures
Comment: 14 pages, 4 figures
Externí odkaz:
http://arxiv.org/abs/2101.05762
Autor:
Tuzhilin, Alexey A.
The course was given at Peking University, Fall 2019. We discuss the following subjects: (1) Introduction to general topology, hyperspaces, metric and pseudometric spaces, graph theory. (2) Graphs in metric spaces, minimum spanning tree, Steiner mini
Externí odkaz:
http://arxiv.org/abs/2012.00756
Autor:
Lê, Hông Vân, Tuzhilin, Alexey A.
Publikováno v:
In: Barbaresco F., Nielsen F. (eds) Geometric Structures of Statistical Physics, Information Geometry, and Learning, p. 120-138, SPIGL 2020. Springer Proceedings in Mathematics & Statistics, vol 361. Springer, Cham
In this paper, first, we survey the concept of diffeological Fisher metric and its naturality, using functorial language of probability morphisms, and slightly extending L\^e's theory in \cite{Le2020} to include weakly $C^k$-diffeological statistical
Externí odkaz:
http://arxiv.org/abs/2011.13418
In the present paper we investigate the Gromov--Hausdorff distances between a bounded metric space $X$ and so called simplex, i.e., a metric space all whose non-zero distances are the same. In the case when the simplex's cardinality does not exceed t
Externí odkaz:
http://arxiv.org/abs/1907.03828
We have constructed a realization of rectilinear geodesic (in the sense of~\cite{Memoli2018}), lying in Gromov-Hausdorff space, as a shortest geodesic w.r.t. the Hausdorff distance in an ambient metric space.
Comment: 5 pages, 1 figure
Comment: 5 pages, 1 figure
Externí odkaz:
http://arxiv.org/abs/1904.09281
Autor:
Ivanov, Alexander1,2 alexandr.o.ivanov@gmail.com, Tuzhilin, Alexey1 tuz@mech.math.msu.su
Publikováno v:
Matematicki Vesnik. Mar2024, Vol. 76 Issue 1, p136-148. 13p.
