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.     

Effects of vitamin B12 on plasma melatonin rhythm in humans: increased light sensitivity phase-advances the circadian clock?

Vitamin B12 (methylcobalamin) was administered orally (3 mg/day) to 9 healthy subjects for 4 weeks. Nocturnal melatonin levels after exposure to bright light (ca. 2500 lx) were determined, as well as the levels of plasma melatonin over 24 h. The timing of sleep was also recorded. Vitamin B12 was given blind to the subjects and crossed over with placebo. We found that the 24-h melatonin rhythm was significantly phase-advanced (1.1 h) in the vitamin B12 trial as compared with that in the placebo trial. In addition, the 24-h mean of plasma melatonin level was much lower in the vitamin B12 trial than with the placebo. Furthermore, the nocturnal melatonin levels during bright light exposure were significantly lower in the vitamin B12 trial than with the placebo. On the other hand, vitamin B12 did not affect the timing of sleep. These findings raise the possibility that vitamin B12 phase-advances the human circadian rhythm by increasing the light sensitivity of the circadian clock.     

Seasonality in human sleep.

The timing of sleep and sleep EEG parameters in 10 healthy male subjects were investigated in four seasons under controlled conditions. The phase of nocturnal sleep was delayed about one and a half hours in winter as compared to that in summer. The duration of stage 4 sleep decreased and REM sleep increased significantly in winter compared with summer. The seasonality in the timing of sleep can be explained by photoperiodic time cues, but the changes in sleep EEG parameters are difficult to explain in terms of photoperiod.     

A ground‐level ozone forecasting model for Santiago,Chile

A physically based model for ground‐level ozone forecasting is evaluated for Santiago, Chile. The model predicts the daily peak ozone concentration, with the daily rise of air temperature as input variable; weekends and rainy days appear as interventions. This model was used to analyse historical data, using the Linear Transfer Function/Finite Impulse Response (LTF/FIR) formalism; the Simultaneous Transfer Function (STF) method was used to analyse several monitoring stations together. Model evaluation showed a good forecasting performance across stations—for low and high ozone impacts—with power of detection (POD) values between 70 and 100%, Heidke's Skill Scores between 40% and 70% and low false alarm rates (FAR). The model consistently outperforms a pure persistence forecast. Model performance was not sensitive to different implementation options. The model performance degrades for two‐ and three‐days ahead forecast, but is still acceptable for the purpose of developing an environmental warning system at Santiago. Copyright © 2002 John Wiley & Sons, Ltd.