DIMACS: Series in Discrete Mathematics and Theoretical Computer Science 1997; 388 pp; hardcover Volume: 37 ISBN10: 0821807625 ISBN13: 9780821807620 List Price: US$101 Member Price: US$80.80 Order Code: DIMACS/37
 The mathematical approach to the study of hierarchies presents the theoretical basis for many important areas of current scientific investigation. Biology has benefited from this research and has also stimulated the mathematical study of hierarchies. This collection presents papers devoted to theoretical, algorithmical, and application issues related to (1) reconstructing hierarchies (trees or ranking) from (dis)similarity or entitytocharacter data, (2) using hierarchies for modeling evolution and other processes, and (3) combining (gene) trees. The papers in this volume provide a contemporary sample of many new results in hierarchy theory with applications in biology, psychology, data analysis, and systems engineering. Features:  Mathematical treatment of hierarchies in several interconnected frameworks: set systems, linear subspaces, graph objects, and tree metrics.
 The relationship of hierarchies to many issues of current applicationfrom learning robots to wavelets to intron evolution to the evolution of language.
 Solutions to several important problems.
Copublished with the Center for Discrete Mathematics and Theoretical Computer Science beginning with Volume 8. Volumes 17 were copublished with the Association for Computer Machinery (ACM). Readership Graduate students and research mathematicians working in discrete mathematics, computational biology, and data analysis. Table of Contents  G. F. Estabrook  Ancestordescendant relations and incompatible data: Motivation for research in discrete mathematics
 C. L. Nehaniv and J. L. Rhodes  KrohnRhodes theory, hierarchies & evolution
 M. Bonet, C. Phillips, T. Warnow, and S. Yooseph  Inferring evolutionary trees from polymorphic characters, and an analysis of the IndoEuropean family of languages
 R. D. M. Page and M. A. Charleston  Reconciled trees and incongruent gene and species trees
 O. Eulenstein, B. Mirkin, and M. Vingron  Comparison of annotating duplication, tree mapping, and copying as methods to compare gene trees with species trees
 A. Rzhetsky, F. J. Ayala, L. C. Hsu, C. Chang, and A. Yoshida  Fitting models of intron evolution to aldehyde dehydrogenase data
 V. Moulton, M. Steel, and C. Tuffley  Dissimilarity maps and substitution models: Some new results
 K. Atteson  The performance of the neighborjoining method of phylogeny reconstruction
 O. Gascuel  Concerning the NJ algorithm and its unweighted version, UNJ
 A. Guénoche  Order distances in tree reconstruction
 V. Makarenkov and B. Leclerc  Circular orders of tree metrics, and their uses for the reconstruction and fitting of phylogenetic trees
 P.A. Landry and F.J. Lapointe  Estimation of missing distances in pathlength matrices: Problems and solutions
 P. M. Pardalos and X. Deng  Complexity issues in hierarchical optimization
 P. Hansen and D. de Werra  Nesticity
 F. S. Roberts and L. Sheng  Phylogeny graphs of arbitrary digraphs
 E. Kubicka, G. Kubicki, and F. R. McMorris  Agreement metrics for trees revisited
 T. M. Przytycka  Sparse dynamic programming for maximum agreement subtree problem
 F. R. McMorris and R. C. Powers  The median function on weak hierarchies
 A. W. M. Dress  Towards a theory of holistic clustering
 I. van Mechelen, S. Rosenberg, and P. De Boeck  On hierarchies and hierarchical classes models
 L. Hubert, P. Arabie, and J. Meulman  The construction of globally optimal ordered partitions
 J. D. Carroll and G. De Soete  Multiple trees: Fitting two or more tree structures to proximity data
 B. Mirkin  Linear embedding of binary hierarchies and its applications
 A. Meystel  Learning algorithms generating multigranular hierarchies
 Index
