Solving Non-Uniqueness in Agglomerative Hierarchical Clustering Using Multidendrograms

In agglomerative hierarchical clustering, pair-group methods suffer from a problem of non-uniqueness when two or more distances between different clusters coincide during the amalgamation process. The traditional approach for solving this drawback has been to take any arbitrary criterion in order to break ties between distances, which results in different hierarchical classifications depending on the criterion followed. In this article we propose a variable-group algorithm that consists in grouping more than two clusters at the same time when ties occur. We give a tree representation for the results of the algorithm, which we call a multidendrogram, as well as a generalization of the Lance andWilliams’ formula which enables the implementation of the algorithm in a recursive way. The authors thank A. Arenas for discussion and helpful comments. This work was partially supported by DGES of the Spanish Government Project No. FIS2006–13321–C02–02 and by a grant of Universitat Rovira i Virgili.     

Choroidal and iris angioarchitecture of the newt: A scanning electron-microscopic study of vascular corrosion casts

The corrosion cast technique provided for the first time an excellent three-dimensional visualization of the vascular pattern of the choroid and iris in the newt eye. The results show the presence of a single arterial afference to the choroidal and iris capillaries: the ophthalmic artery is the origin fo both ciliary arteries and the long posterior ciliary artery. Slightly behind the equatorial circumference of the eyeball the venous drainage consists of a single vessel on the dorsal side and two distinct vessels on the ventral one. It receives blood from both iris and choroid. The surface of the plastic endocasts shows some details of fine luminal structures of the endothelial cells. Shallow depressions may be regarded as imprints of endothelial cell nuclei, and they are distinctly different for arteries and capillaries. The angioarchitecture of the newt eye differs from that of brain in that hairpin-shaped capillary loops are not observed at all.