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On ultrametrics, b-metrics, w-distances, metric-preserving functions, and fixed point theorems
In this article, new classes of functions based on new variations of metric-preserving functions are defined. Necessary and sufficient conditions for...
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An Embedding, An Extension, and An Interpolation of Ultrametrics\(^*\)
AbstractThe notion of ultrametrics can be considered as a zero-dimensional analogue of ordinary metrics, and it is expected to prove...
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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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Ultrametrics and Surface Singularities
The present lecture notes give an introduction to works of García Barroso, González Pérez, Ruggiero and the author. The starting point of those works...
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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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Three-Way Symbolic Tree-Maps and Ultrametrics
Three-way dissimilarities are a generalization of (two-way) dissimilarities which can be used to indicate the lack of homogeneity or resemblance...
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Order preserving hierarchical agglomerative clustering
Partial orders and directed acyclic graphs are commonly recurring data structures that arise naturally in numerous domains and applications and are...
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Expanding the Class of Global Objective Functions for Dissimilarity-Based Hierarchical Clustering
Recent work on dissimilarity-based hierarchical clustering has led to the introduction of global objective functions for this classical problem....
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Tropical Geometric Variation of Tree Shapes
We study the behavior of phylogenetic tree shapes in the tropical geometric interpretation of tree space. Tree shapes are formally referred to as...
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Tree Topologies along a Tropical Line Segment
Tropical geometry with the max-plus algebra has been applied to statistical learning models over tree spaces because geometry with the tropical...
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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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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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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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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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Tropical Data Science over the Space of Phylogenetic Trees
Phylogenomics is a new field which applies to tools in phylogenetics to genome data. Due to a new technology and increasing amount of data, we face...
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Statistical Approach on the Economic System
Masanao AokiAoki, M. was a great scholar who sincerely challenged to exit from the secular world fettered by the representative method of economic...
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Tropical medians by transportation
Fermat–Weber points with respect to an asymmetric tropical distance function are studied. It turns out that they correspond to the optimal solutions...
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Functional Clustering on a Circle Using von Mises Mixtures
This paper addresses the question of clustering density curves around a unit circle by approximating each such curve by a mixture of an appropriate...
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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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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 ...