19 citations · 33 across the 8 of their papers we have counts for
9 papers
Bi-Lipschitz embeddings of -free spaces into Euclidean spaces
Vladimir Zolotov
-free spaces is a wide class of metric spaces including finite dimensional Alexandrov spaces of non-negative curvature, complete Berwald spaces of nonnegative flag curvature,…
Self-contracted curves in spaces with weak lower curvature bound
Nina Lebedeva, Shin-ichi Ohta, Vladimir Zolotov
We show that bounded self-contracted curves are rectifiable in metric spaces with weak lower curvature bound in a sense we introduce in this article. This class of spaces is wide a…
Sets with small angles in self-contracted curves
Vladimir Zolotov
We study metric spaces with bounded rough angles. E. Le Donne, T. Rajala and E. Walsberg implicitly used this notion to show that infinite snowflakes can not be isometrically embed…
Finite flat spaces
Vladimir Zolotov
We say that a finite metric space can be embedded almost isometrically into a class of metric spaces , if for every there exists an embedding of into one of the e…
Bipolar comparison
Nina Lebedeva, Anton Petrunin, Vladimir Zolotov
We define a new type of metric comparison similar to the comparison of Alexandrov. We show that it has strong connections to continuity of optimal transport between regular measure…
Dimension of a snowflake of a finite Euclidean subspace
Vladimir Zolotov
Let be an -point subset of a Euclidean space and . The classical theorem of Schoenberg implies that the snowflake space can be isometrically embedded into E…
Analysis and Optimization of fastText Linear Text Classifier
Vladimir Zolotov, David Kung
The paper [1] shows that simple linear classifier can compete with complex deep learning algorithms in text classification applications. Combining bag of words (BoW) and linear cla…
Markov Type constants, flat tori and Wasserstein spaces
Vladimir Zolotov
Let denote the Markov type constant at time of a metric space , where . We show that in each of the following cases: (a) a…
Extensions of isometric embeddings of Pseudo-Euclidean metric polyhedra
Pavel Galashin, Vladimir Zolotov
We extend the results of B. Minemyer by showing that any indefinite metric polyhedron (either compact or not) with the vertex degree bounded from above admits an isometric simplici…