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Biomedical subjects

B Mirkin

Publications and source records attributed to B Mirkin.

4 recordsLinked to original sources
PubMed1998

Duplication-based measures of difference between gene and species trees.

In the framework of a duplication-based method for comparing gene and species trees, the concepts of "duplication" and "loss" are reformulated in set-theoretic terms. A number of related tree dissimilarity measures is suggested, and relations between them are analyzed. For any node in the species tree, the number of gene duplications for which it is a "non-child" loss coincides with the number of times when the node's parent is an intermediate between the mapping images of a gene node and its parent. This implies that the total number of losses is equal to the number of intermediate nodes plus the number of one-side duplications and, thus, provides an alternative proof for a conjecture made by Mirkin, Muchnik, and Smith (1995). Another formula proven involves crossings (incompatible gene-species node pairs): the number of losses equals the number of crossings plus the number of duplications.

Animals↗
PubMed1995

A biologically consistent model for comparing molecular phylogenies.

In the framework of the problem of combining different gene trees into a unique species phylogeny, a model for duplication/speciation/loss events along the evolutionary tree is introduced. The model is employed for embedding a phylogeny tree into another one via the so-called duplication/speciation principle requiring that the gene duplicated evolves in such a way that any of the contemporary species involved bears only one of the gene copies diverged. The number of biologically meaningful elements in the embedding result (duplications, losses, information gaps) is considered a (asymmetric) dissimilarity measure between the trees. The model duplication concept is compared with that one defined previously in terms of a mapping procedure for the trees. A graph-theoretic reformulation of the measure is derived.

Evolution, Molecular↗
PubMed1993

Consensus functions and patterns in molecular sequences.

In recent years, methods of consensus, developed for the solution of problems in the social sciences, have become widely used in molecular biology. We study a method of consensus originally due to Waterman et al. (Waterman, Galas and Arratis. 1984. Pattern recognition in several sequences: consensus and alignment. Bull. math. Biol. 46, 515-527) which is used to identify patterns or features in a molecular sequence where a pattern can vary in position within a given window. We show that some well-known consensus methods of the social sciences, the median and the mean, are special cases of this method for certain choices of the parameters used in it and give a precise account of the parameters for which these special cases arise. We also show that the specific parameters used in the method of Waterman et al. make their method equivalent to the media procedure which is widely used in the social sciences.

Base Sequence↗