Complex of phylogenetic trees

Definition 9.28. For a positive integer n > 3, the above procedure describes a cubical complex Tn, called the complex of phylogenetic trees. 

The standard reference for the introduction of the complexes of phylogenetic trees is Billera, Holmes, Vogtmann, [BHVOl], where several of their aspects were investigated. 

For many years the phylogenetic tree was believed to possess two main branches the prokaryotes and the eukaryotes. Largely because of Carl Woese s pioneering work with rRNA sequences, it has become apparent that the relationships among currently existing life forms are more complex than the two-domain model implies. Small ribosomal subunit RNA molecules are especially useful for probing phylogenetic relationships because ... 

In the classification setting, every example is assumed to be independent of every other example. However, there are cases where dependencies exist between examples and the label corresponding to such dependent examples forms a complex object. The structured-prediction problem attempts to predict a complex object such as a protein interaction network, phylogenetic tree, a binding site on a protein, etc. In short, a structured-prediction problem D is a classification problem where y e Y (the space of fhe label on an example) has a structure. For a finite set of data structures, the learning algorithm searches for the structured output that minimizes the expected cost E[c/,(j )] of example x [44] where cosf measures fhe dissimilarify between the example and a proposed structured output. 

Evolutionary Relationships of RC The types of RC complexes, in terms of the presence or absence of the cytochrome subunit, are summarized in Fig. 4-f together with the type of soluble cytochrome C2 and quinone species in the membrane. The phylogenetic tree was based on 16S ribosomal RNA sequence (4) and the information described above (7,8). 

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