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Invariant ultrametrics and Markov processes on the finite adèle ring of ℚ
This article introduces several rotation and additive invariant ultrametrics on the finite adèle ring A f of the rational numbers ℚ. Symmetry,...
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Applications of ball spaces theory: fixed point theorems in semimetric spaces and ball convergence
In the paper, we apply some of the results from the theory of ball spaces in semimetric setting. This allows us to obtain fixed point theorems which...
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Perfect elimination orderings for symmetric matrices
We introduce a new class of structured symmetric matrices by extending the notion of perfect elimination ordering from graphs to weighted graphs or...
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Quasi-metric antipodal spaces and maximal Gromov hyperbolic spaces
Hyperbolic fillings of metric spaces are a well-known tool for proving results on extending quasi-Moebius maps between boundaries of Gromov...
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Tropical Principal Component Analysis and Its Application to Phylogenetics
Principal component analysis is a widely used method for the dimensionality reduction of a given data set in a high-dimensional Euclidean space. Here...
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Minkowski Distances and Standardisation for Clustering and Classification on High-Dimensional Data
There are many distance-based methods for classification and clustering, and for data with a high number of dimensions and a lower number of...
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Intuitionistic Fuzzy Sets Generated by Archimedean Metrics and Ultrametrics
For a nonempty universe E it is shown that the standard intutitionistic fuzzy sets (IFSs) over E are generated by Manhattan metric. For several other...
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p-Adic Gaussian Random Variables
The paper is devoted to characterization theorems for idempotent distributions on the p -adic number field ℚ p in terms of functional relations for 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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Edge Elimination and Weighted Graph Classes
Edge-weighted graphs play an important role in the theory of Robinsonian matrices and similarity theory, particularly via the concept of level...
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Forty Years of Fuzzy Metrics
Kramosil and Michalek gave in 1975 a concept of fuzzy metric M on a set X which extends to the fuzzy setting the concept of probabilistic metric...
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Approximate Coalgebra Homomorphisms and Approximate Solutions
Terminal coalgebras \(\nu F\) of finitary endofunctors F on categories called strongly lfp are proved to carry a canonical ultrametric on their...
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Lipschitz free p-spaces for 0 < p < 1
This paper initiates the study of the structure of a new class of p -Banach spaces, 0 < p < 1, namely the Lipschitz free p -spaces (alternatively called...
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Estimating Tropical Principal Components Using Metropolis Hasting Algorithm
Principal component analysis is one of the most popular unsupervised learning methods for reducing the dimension of a given data set in a...
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Pseudodifferential Operators and Markov Processes on Adèles
In this article a class of Markov processes on the ring of finite adèles of the rational numbers are introduced. A class of non-Archimedean metrics...
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Phylogenetics beyond biology
Evolutionary processes have been described not only in biology but also for a wide range of human cultural activities including languages and law. In...
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Penalty-Based Aggregation of Strings
Whereas the field of aggregation theory has historically studied aggregation on bounded posets (mainly the aggregation of real numbers), different...