Displaying similar documents to “Best approximation of coincidence points in metric trees”

Remarks on best approximation in R-trees

William Kirk, Bancha Panyanak (2009)

Annales UMCS, Mathematica

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An R-tree is a geodesic space for which there is a unique arc joining any two of its points, and this arc is a metric segment. If X is a closed convex subset of an R-tree Y, and if T: X → 2Y is a multivalued mapping, then a point z for which [...] is called a point of best approximation. It is shown here that if T is an ε-semicontinuous mapping whose values are nonempty closed convex subsets of Y, and if T has at least two distinct points of best approximation, then T must have a fixed...

Compact widths in metric trees

Asuman Güven Aksoy, Kyle Edward Kinneberg (2011)

Banach Center Publications

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The definition of n-width of a bounded subset A in a normed linear space X is based on the existence of n-dimensional subspaces. Although the concept of an n-dimensional subspace is not available for metric trees, in this paper, using the properties of convex and compact subsets, we present a notion of n-widths for a metric tree, called Tn-widths. Later we discuss properties of Tn-widths, and show that the compact width is attained. A relationship between the compact widths and Tn-widths...

Some results on metric trees

Asuman Güven Aksoy, Timur Oikhberg (2010)

Banach Center Publications

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Using isometric embedding of metric trees into Banach spaces, this paper will investigate barycenters, type and cotype, and various measures of compactness of metric trees. A metric tree (T, d) is a metric space such that between any two of its points there is a unique arc that is isometric to an interval in ℝ. We begin our investigation by examining isometric embeddings of metric trees into Banach spaces. We then investigate the possible images x₀ = π((x₁ + ... + xₙ)/n), where π is...

Analyzing sets of phylogenetic trees using metrics

Damian Bogdanowicz (2011)

Applicationes Mathematicae

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The reconstruction of evolutionary trees is one of the primary objectives in phylogenetics. Such a tree represents historical evolutionary relationships between different species or organisms. Tree comparisons are used for multiple purposes, from unveiling the history of species to deciphering evolutionary associations among organisms and geographical areas. In this paper, we describe a general method for comparing phylogenetic trees and give some basic properties of the Matching Split...

On a matching distance between rooted phylogenetic trees

Damian Bogdanowicz, Krzysztof Giaro (2013)

International Journal of Applied Mathematics and Computer Science

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The Robinson-Foulds (RF) distance is the most popular method of evaluating the dissimilarity between phylogenetic trees. In this paper, we define and explore in detail properties of the Matching Cluster (MC) distance, which can be regarded as a refinement of the RF metric for rooted trees. Similarly to RF, MC operates on clusters of compared trees, but the distance evaluation is more complex. Using the graph theoretic approach based on a minimum-weight perfect matching in bipartite graphs,...

Some Results on Maps That Factor through a Tree

Roger Züst (2015)

Analysis and Geometry in Metric Spaces

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We give a necessary and sufficient condition for a map deffned on a simply-connected quasi-convex metric space to factor through a tree. In case the target is the Euclidean plane and the map is Hölder continuous with exponent bigger than 1/2, such maps can be characterized by the vanishing of some integrals over winding number functions. This in particular shows that if the target is the Heisenberg group equipped with the Carnot-Carathéodory metric and the Hölder exponent of the map...

The dual form of Knaster-Kuratowski-Mazurkiewicz principle in hyperconvex metric spaces and some applications

George Isac, George Xian-Zhi Yuan (1999)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In this paper, we first establish the dual form of Knaster- Kuratowski-Mazurkiewicz principle which is a hyperconvex version of corresponding result due to Shih. Then Ky Fan type matching theorems for finitely closed and open covers are given. As applications, we establish some intersection theorems which are hyperconvex versions of corresponding results due to Alexandroff and Pasynkoff, Fan, Klee, Horvath and Lassonde. Then Ky Fan type best approximation theorem and Schauder-Tychonoff...

The triangles method to build X -trees from incomplete distance matrices

Alain Guénoche, Bruno Leclerc (2001)

RAIRO - Operations Research - Recherche Opérationnelle

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A method to infer X -trees (valued trees having X as set of leaves) from incomplete distance arrays (where some entries are uncertain or unknown) is described. It allows us to build an unrooted tree using only 2 n -3 distance values between the n elements of X , if they fulfill some explicit conditions. This construction is based on the mapping between X -tree and a weighted generalized 2-tree spanning X .