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.     

Zur Blutdruckwirkung von Aludrin und Adrenalin

Summary The depressor action of small doses of adrenaline on the blood pressure (B.P.) of the decapitated cat may be abolished by pretreatment with pilocarpine; atropine restores the original depressor action. The fall in B.P. due to adrenaline after ergotamine once more becomes an increase when pilocarpine has been given earlier. After atropine a fall in B.P. again occurs. This effect of pilocarpine and atropine on a depressor response has already been described in the case of Aludrine (N-isopropyl-noradrenaline) byFromherz.     

Über ein Chromoplastin aus reifenden Tomaten

Summary (1) By precipitation with ammonium sulfate, streptomycin, or calcium salts, we obtained from the pulp of tomatoes a substance containing carotinoids. The behaviour of this substance was analogous to that of chloroplst-substance and to that of animal cytoplasmatic nucleoproteins. Like these it contains proteins, lipids, and very probably nucleic acids. We regard this substance as achromoplastine.(2) Experiments with slices of green tomatoes show that the changing over of the chlorophyll content into the carotinoid content is inhibited by the presence of streptomycin.(3) Streptomycin inhibits the formation of chlorophyll in etiolated separated cabbage leafs, just as this drug inhibits the formation of chlorophyll in growing seeds.(4) The development of anthocyanides is not influenced by streptomycin.