Proper Gromov transforms of metrics are metrics

被引：2

作者：

Dress, A ^{[1
]}

机构：

[1] Univ Bielefeld, GK Strukturbildungsprozesse, FSP Mathematisierung, D-33501 Bielefeld, Germany

来源：

APPLIED MATHEMATICS LETTERS | 2002年 / 15卷 / 08期

关键词：

metrics; additive metrics; Delta additive metrics; ultra metrics; Farris transforms; Gromov transforms; phylogenetic analysis; phylogenetic combinatorics;

D O I：

10.1016/S0893-9659(02)00075-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In phylogenetic analysis, a standard problem is to approximate a given metric by an additive metric. Here it is shown that, given a metric D defined on some finite set X and a nonexpansive map f : X --> R, the one-parameter family of the Gromov transforms D-Delta,D-f of D relative to f and A that starts with D for large values of A and ends with an additive metric for Delta = 0 consists exclusively of metrics. It is expected that this result will help to better understand some standard tree reconstruction procedures considered in phylogenetic analysis. (C) 2002 Elsevier Science Ltd. All rights reserved.

引用

页码：995 / 999

页数：5