Proper Gromov transforms of metrics are metrics

Dress A (2002)
Applied Mathematics Letters 15(8): 995-999.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
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.
Stichworte
Farris transforms; Gromov transforms; phylogenetic analysis; phylogenetic combinatorics; additive metrics; ultra metrics; Delta additive metrics; metrics
Erscheinungsjahr
2002
Zeitschriftentitel
Applied Mathematics Letters
Band
15
Ausgabe
8
Seite(n)
995-999
ISSN
0893-9659
Page URI
https://pub.uni-bielefeld.de/record/1613617

Zitieren

Dress A. Proper Gromov transforms of metrics are metrics. Applied Mathematics Letters. 2002;15(8):995-999.
Dress, A. (2002). Proper Gromov transforms of metrics are metrics. Applied Mathematics Letters, 15(8), 995-999. https://doi.org/10.1016/S0893-9659(02)00075-7
Dress, A. (2002). Proper Gromov transforms of metrics are metrics. Applied Mathematics Letters 15, 995-999.
Dress, A., 2002. Proper Gromov transforms of metrics are metrics. Applied Mathematics Letters, 15(8), p 995-999.
A. Dress, “Proper Gromov transforms of metrics are metrics”, Applied Mathematics Letters, vol. 15, 2002, pp. 995-999.
Dress, A.: Proper Gromov transforms of metrics are metrics. Applied Mathematics Letters. 15, 995-999 (2002).
Dress, Andreas. “Proper Gromov transforms of metrics are metrics”. Applied Mathematics Letters 15.8 (2002): 995-999.

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