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.     

Quantum Mechanics and other Fields of Science

In recent times, a particular attention has been devoted to thesignificance of Quantum Theory for other disciplines. The articlescollected in this issue discuss some interesting cases,characterized by an interaction between Quantum Theory andother fields. Some basic notrons of the mathematical formalismof the theory are here summarized.     

Unit roots versus other types of time heterogeneity,parameter time dependence and superexogeneity

This paper stresses the restrictive nature of the standard unit root/cointegration assumptions and examines a more general type of time heterogeneity, which might characterize a number of economic variables, and which results in parameter time dependence and misleading statistical inference. We show that in such cases ‘operational’ models cannot be obtained, and the estimation of time‐varying parameter models becomes necessary. For instance, economic processes subject to endemic change can only be adequately modelled in a state space form. This is a very important point, because unstable models will break down when used for forecasting purposes. We also discuss a new test for the null of cointegration developed by Quintos and Phillips (1993), which is based on parameter constancy in cointegrating regressions. Finally, we point out that, if it is possible to condition on a subset of superexogenous variables, parameter instability can be handled by estimating a restricted system. Copyright © 2002 John Wiley & Sons, Ltd.     

Proton-induced dismutation of superoxide in aprotic media by bile pigments

Summary Cyclic voltammetry of molecular oxygen in aprotic media (dimethylformamide) and in the presence of bilirubin and other bile pigments shows that superoxide anion ( ) undergoes proton-induced dismutation. Lactam hydrogens of bile pigments are sufficiently acid to induce disproportionation to O₂ and H₂O₂. Because of its characteristic lipophilic behavior, a biological role for natural bilirubin similar to that of other non-enzymatic lipophilic scavengers of is suggested.     

Effect of beta-adrenergic blockade on intramuscular triglyceride mobilization during exercise

Summary It was shown in the rat that mobilization of intramuscular triglyceride during exercise is controlled by the adrenergic system.Acknowledgments. The work was supported by the Polish Academy of Sciences, grant No. 10.4.2.01.3.2.     

Presence of natural killer cells in Peyer's patches of the mouse

Summary Natural cell-mediated cytotoxicity of normal murine Peyer's patch cells against Ehrlich ascites carcinoma was found in a short-term⁵¹Cr release assay. Peyer's patch and lymph node cells showed natural cytotoxicity at approximately the same level.Acknowledgments. This work was supported by grant No. 10.5 from the Polish Academy of Sciences.     

Diurnal rhythm of active calcium transport in rat intestine

Summary The active calcium transport along the small intestine of adult rat was shown to exhibit daily rhythmic variations of considerable amplitude. Both the light-dark cycle and the time of food presentation acted as synchronizers of the rhythm observed.This work has been supported by Polish Academy of Sciences within the project MR II.1.1.6.     

In vitro inactivation of corpora allata of the bugOncopeltus fasciatus by precocene II

Summary Corpora allata fromOncopeltus fasciatus incubated in vitro in medium containing 10^–5.35 M (1 g/ml) of precocene II lose their ability to secrete juvenile hormone when reimplanted into last instar larvae.Acknowledgments. We thank Mr K. Dorn, Mrs L. Dolezal, Mrs V. Nötzli-Graf, Mr K.H. Trautmann and Mr A. Schuler for technical help, Dr W. Vogel and Dr A. Dübendorfer for valuable discussions.