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.     

On the limitations of comparing mean square forecast errors

Linear models are invariant under non-singular, scale-preserving linear transformations, whereas mean square forecast errors (MSFEs) are not. Different rankings may result across models or methods from choosing alternative yet isomorphic representations of a process. One approach can dominate others for comparisons in levels, yet lose to another for differences, to a second for cointegrating vectors and to a third for combinations of variables. The potential for switches in ranking is related to criticisms of the inadequacy of MSFE against encompassing criteria, which are invariant under linear transforms and entail MSFE dominance. An invariant evaluation criterion which avoids misleading outcomes is examined in a Monte Carlo study of forecasting methods.     

Growth hormone signal transduction

Growth hormone (GH) promotes animal growth by stimulating bone and cartilage cell proliferation, and influences carbohydrate and lipid metabolism. Some of these effects are brought about indirectly via somatomedin induction in hepatocytes, others by acting directly on the target cells. In either case, GH first binds to specific receptors on cells to trigger a sequence of biochemical events culminating in a biological response. Recently much has been learnt about the molecular structure of GH receptor, its binding to ligand, and the ensuing signal transduction events.     

Periodic paralysis in quarter horses: a sodium channel mutation disseminated by selective breeding.

We recently reported on a linkage study within a Quarter Horse lineage segregating hyperkalaemic periodic paralysis (HYPP), an autosomal dominant condition showing potassium-induced attacks of skeletal muscle paralysis. HYPP co-segregated with the equine adult skeletal muscle sodium channel alpha subunit gene, the same gene that causes human HYPP. We now describe the Phe to Leu mutation in transmembrane domain IVS3 which courses the horse disease. This represents the first application of molecular genetics to an important horse disease, and the data will provide an opportunity for control or eradication of this condition.     

Short alanine-based peptides may form 3(10)-helices and not alpha-helices in aqueous solution.

Short alanine peptides, containing 16 or 17 residues, appear to form alpha-helices in aqueous solution. But the main spectroscopic analyses used on helical peptides (circular dichroism and nuclear magnetic resonance) cannot distinguish between an alpha-helix (in which the ith residue is hydrogen-bonded to residue i + 4; ref. 9) and the next most common peptide helix, the 3(10)-helix10 (i-->i + 3 hydrogen-bonding). To address this problem we have designed single and doubly spin-labelled analogues of alanine-based peptides in which the nitroxide spin label forms an unbranched side chain extending from the sulphur atom of a cysteine residue. Here we report the circular dichroism, Fourier-transform infrared and electron-spin resonance spectra of these peptides under helix-forming conditions. The infrared absorbance gives an amide I' band with a frequency that is substantially different from that observed for alpha-helices. The electron-spin resonance spectra of doubly labelled helices show that the ranking of distances between side chains, around a single turn (residues 4-8), is inconsistent with an alpha-helical structure. Our experiments suggest that the more likely peptide geometry is a 3(10)-helix.