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Locally finite ultrametric spaces and labeled trees
It is shown that a locally finite ultrametric space ( X , d ) is generated by a labeled tree if and only if for every open ball B ⊆ X there is a point c ...
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Hereditary properties of finite ultrametric spaces
A characterization of finite homogeneous ultrametric spaces and finite ultrametric spaces generated by unrooted labeled trees has been made in terms...
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Minimum Spanning Paths and Hausdorff Distance in Finite Ultrametric Spaces
AbstractIt is shown that a minimum weight spanning tree of a finite ultrametric space can be always found in the form of path. As a canonical...
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Constructions of Urysohn Universal Ultrametric Spaces
AbstractIn this paper, we give new constructions of Urysohn universal ultrametric spaces. We first characterize a Urysohn universal ultrametric...
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Coarse structure of ultrametric spaces with applications
We show how to decompose all separable ultrametric spaces into a “Lego” combinations of scaled versions of full simplices. To do this we introduce...
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Labeled Trees Generating Complete, Compact, and Discrete Ultrametric Spaces
We investigate the interrelations between labeled trees and ultrametric spaces generated by these trees. The labeled trees, which generate complete...
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A Chip-Firing and a Riemann-Roch Theorem on an Ultrametric Space
A Riemann-Roch theorem on an edge-weighted infinite graph with local finiteness was established by the present authors in [1], where the spectral gap...
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On Quasisymmetric Map**s Between Ultrametric Spaces
AbstractIn 1980 P. Tukia and J. Väisälä in seminal paper [
23 ] extended a concept of quasisymmetric map** known from the theory of quasiconformal... -
Isometries of ultrametric normed spaces
We show that the group of isometries of an ultrametric normed space can be seen as a kind of a fractal. Then, we apply this description to study...
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The Space of Equidistant Phylogenetic Cactuses
An equidistant X - cactus is a type of rooted, arc-weighted, directed acyclic graph with leaf set X , that is used in biology to represent the...
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On Some Extremal Properties of Finite Ultrametric Spaces
We characterize finite ultrametric spaces having the strictly n -ary representing trees and finite ultrametric spaces having the representing trees...
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Finite Ultrametric Balls
The necessary and sufficient conditions under which a given family ℱ of subsets of finite set X coincides with the family B X of all balls generated...
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Tropical Logistic Regression Model on Space of Phylogenetic Trees
Classification of gene trees is an important task both in the analysis of multi-locus phylogenetic data, and assessment of the convergence of Markov...
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Bipartite graphs and best proximity pairs
We say that a bipartite graph G ( A , B ) with the fixed parts A and B is proximinal if there is a semimetric space ( X , d ) such that A and B are disjoint...
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Toward Ultrametric Modeling of the Epidemic Spread
AbstractAn ultrametric model of epidemic spread of infections based on the classical SIR model is proposed. Ultrametrics on a set of individuals is...
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Ramsey partitions of metric spaces
We investigate the existence of metric spaces which, for any coloring with a fixed number of colors, contain monochromatic isomorphic copies of a...
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The Noncommutative Space of Penrose Tilings
In this chapter, we study the space parameterizing inequivalent Penrose tilings from the point of view of Noncommutative Geometry. This chapter is a...
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Banach Space Representations
In this chapter, we present the Schneider-Teitelbaum duality between Banach space representations and Iwasawa modules.