Proper gromov transforms of metrics are metrics

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Proper gromov transforms of metrics are metrics
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 non-expansive map f : X R, the one-parameter family of the Gromov transforms D,f of D relative to f and that starts with D for large values of and ends with an additive metric for = 0 consists exclusively of metrics. It is expected that this result will help to better understand some standard tree reconstruction procedures considered in phylogenetic analyis. Keywords and Phrases: Metrics, additive metrics, additive metrics, ultra metrics Farris transforms, Gromov transforms, phylogenetic analysis, phylogenetic combinatorics
Andreas W. M. Dress
Added 16 Dec 2010
Updated 16 Dec 2010
Type Journal
Year 2002
Authors Andreas W. M. Dress
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