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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.
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