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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 entity-to-character 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:
Foreword ix
Preface xi
Ancestor-descendant relations and incompatible data:
Motivation for research in discrete mathematics
G. F. Estabrook 1
Krohn-Rhodes theory, hierarchies & evolution
C. L. Nehaniv and J. Rhodes 29
Inferring evolutionary trees from polymorphic characters,
and an analysis of the Indo-European family of languages
M. L. Bonet, C. A. Phillips, T. J. Warnow, and S. Yooseph 43
Reconciled trees and incongruent gene and species trees
R. D. Page and M. Charleston 57
Comparison of annotating duplication, tree mapping, and
copying as methods to compare gene trees with species trees
O. Eulenstein, B. G. Mirkin, and M. Vingron 71
Fitting models of intron evolution to aldehyde dehydrogenase
data
A. Rzhetsky, F. J. Ayala, L. C. Hsu, C. Chang, and
A. Yoshida 95
Dissimilarity maps and substitution models: Some new results
V. L. Moulton, M. A. Steel, and C. Tuffley 111
The performance of the neighbor-joining method of phylogeny
reconstruction
K. Atteson 133
Concerning the NJ algorithm and its unweighted version, UNJ
O. Gascuel 149
Order distances in tree reconstruction
A. Guenoche 171
Circular orders of tree metrics, and their uses for the
reconstruction and fitting of phylogenetic trees
V. Makarenkov and B. Leclerc 183
Estimation of missing distances in path-length matrices:
Problems and solutions
P.-A. Landry and F.-J. Lapointe 209
Complexity issues in hierarchical optimization
P. M. Pardalos and X. Deng 219
Nesticity
P. Hansen and D. de Werra 225
Phylogeny graphs of arbitrary digraphs
F. S. Roberts and L. Sheng 233
Agreement metrics for trees revisited
E. M. Kubicka, G. Kubicki, and F. R. McMorris 239
Sparse dynamic programming for maximum agreement subtree
problem
T. M. Przytycka 249
The median function on weak hierarchies
F. R. McMorris and R. C. Powers 265
Towards a theory of holistic clustering
A. W. Dress 271
On hierarchies and hierarchical classes models
I. Van Mechelen, S. Rosenberg, and P. De Boeck 291
The construction of globally optimal ordered partitions
L. Hubert, P. Arabie, and J. Meulman 299
Multiple trees: Fitting two or more tree structures to
proximity data
D. Carroll and G. De Soete 313
Linear embedding of binary hierarchies and its applications
B. G. Mirkin 331
Learning algorithms generating multigranular hierarchies
A. Meystel 357
Index 385
Index of Volumes
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