Convexity in Tree Spaces
| Autor: | Bo Lin, Bernd Sturmfels, Ruriko Yoshida, Xiaoxian Tang |
|---|---|
| Přispěvatelé: | Operations Research (OR) |
| Rok vydání: | 2017 |
| Předmět: |
Computational Geometry (cs.CG)
FOS: Computer and information sciences Geodesic geodesic triangle General Mathematics Billera–Holmes–Vogtman metric tropical convexity 0102 computer and information sciences Space (mathematics) 01 natural sciences Convexity Combinatorics Mathematics - Metric Geometry FOS: Mathematics Mathematics - Combinatorics Mathematics::Metric Geometry phylogenetic tree 0101 mathematics Quantitative Biology - Populations and Evolution Ultrametric space Mathematics Discrete mathematics Linear space 010102 general mathematics Populations and Evolution (q-bio.PE) Metric Geometry (math.MG) Orthant ultrametric CAT(0) space 010201 computation theory & mathematics FOS: Biological sciences polytope Metric (mathematics) Computer Science - Computational Geometry Combinatorics (math.CO) Tree (set theory) |
| Zdroj: | SIAM Journal on Discrete Mathematics. 31:2015-2038 |
| ISSN: | 1095-7146 0895-4801 |
| DOI: | 10.1137/16m1079841 |
| Popis: | We study the geometry of metrics and convexity structures on the space of phylogenetic trees, which is here realized as the tropical linear space of all \ ultrametrics. The ${\rm CAT}(0)$-metric of Billera-Holmes-Vogtman arises from the theory of orthant spaces. While its geodesics can be computed by the Owen-Provan algorithm, geodesic triangles are complicated. We show that the dimension of such a triangle can be arbitrarily high. Tropical convexity and the tropical metric behave better. They exhibit properties desirable for geometric statistics, such as geodesics of small depth. Comment: 21 pages, 5 figures; Theorem 13 is now proved in all dimensions |
| Databáze: | OpenAIRE |
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