Ward's Hierarchical Clustering Method: Clustering Criterion and Agglomerative Algorithm

The Ward error sum of squares hierarchical clustering method has been very widely used since its first description by Ward in a 1963 publication. It has also been generalized in various ways. However there are different interpretations in the literature and there are different implementations of the Ward agglomerative algorithm in commonly used software systems, including differing expressions of the agglomerative criterion. Our survey work and case studies will be useful for all those involved in developing software for data analysis using Ward's hierarchical clustering method.Comment: 20 pages, 21 citations, 4 figure

Degenerating families of dendrograms

Dendrograms used in data analysis are ultrametric spaces, hence objects of nonarchimedean geometry. It is known that there exist $p$-adic representation of dendrograms. Completed by a point at infinity, they can be viewed as subtrees of the Bruhat-Tits tree associated to the $p$-adic projective line. The implications are that certain moduli spaces known in algebraic geometry are $p$-adic parameter spaces of (families of) dendrograms, and stochastic classification can also be handled within this framework. At the end, we calculate the topology of the hidden part of a dendrogram.Comment: 13 pages, 8 figure

Evaluation of cosmic ray rejection algorithms on single-shot exposures

To maximise data output from single-shot astronomical images, the rejection of cosmic rays is important. We present the results of a benchmark trial comparing various cosmic ray rejection algorithms. The procedures assess relative performances and characteristics of the processes in cosmic ray detection, rates of false detections of true objects and the quality of image cleaning and reconstruction. The cosmic ray rejection algorithms developed by Rhoads (2000), van Dokkum (2001), Pych (2004) and the IRAF task xzap by Dickinson are tested using both simulated and real data. It is found that detection efficiency is independent of the density of cosmic rays in an image, being more strongly affected by the density of real objects in the field. As expected, spurious detections and alterations to real data in the cleaning process are also significantly increased by high object densities. We find the Rhoads' linear filtering method to produce the best performance in detection of cosmic ray events, however, the popular van Dokkum algorithm exhibits the highest overall performance in terms of detection and cleaning.Comment: 12 pages, 4 figures, accepted for publication in PAS

Mumford dendrograms and discrete p-adic symmetries

In this article, we present an effective encoding of dendrograms by embedding them into the Bruhat-Tits trees associated to $p$-adic number fields. As an application, we show how strings over a finite alphabet can be encoded in cyclotomic extensions of $\mathbb{Q}_p$ and discuss $p$-adic DNA encoding. The application leads to fast $p$-adic agglomerative hierarchic algorithms similar to the ones recently used e.g. by A. Khrennikov and others. From the viewpoint of $p$-adic geometry, to encode a dendrogram $X$ in a $p$-adic field $K$ means to fix a set $S$ of $K$-rational punctures on the $p$-adic projective line $\mathbb{P}^1$. To $\mathbb{P}^1\setminus S$ is associated in a natural way a subtree inside the Bruhat-Tits tree which recovers $X$, a method first used by F. Kato in 1999 in the classification of discrete subgroups of $\textrm{PGL}_2(K)$. Next, we show how the $p$-adic moduli space $\mathfrak{M}_{0,n}$ of $\mathbb{P}^1$ with $n$ punctures can be applied to the study of time series of dendrograms and those symmetries arising from hyperbolic actions on $\mathbb{P}^1$. In this way, we can associate to certain classes of dynamical systems a Mumford curve, i.e. a $p$-adic algebraic curve with totally degenerate reduction modulo $p$. Finally, we indicate some of our results in the study of general discrete actions on $\mathbb{P}^1$, and their relation to $p$-adic Hurwitz spaces.Comment: 14 pages, 6 figure

A systematic review and critical appraisal of quality indicators to assess optimal palliative care for older people with dementia

© The Author(s) 2019Background: A challenge for commissioners and providers of end-of-life care in dementia is to translate recommendations for good or effective care into quality indicators that inform service development and evaluation. Aim: To identify and critically evaluate quality indicators for end-of-life care in dementia. Results: We found 8657 references, after de-duplication. In all, 19 publications describing 10 new and 3 updated sets of indicators were included in this review. Ultimately, 246 individual indicators were identified as being relevant to dementia end-of-life care and mapped against EAPC guidelines. Conclusions: We systematically derived and assessed a set of quality indicators using a robust framework that provides clear definitions of aspects of palliative care, which are dementia specific, and strengthens the theoretical underpinning of new complex interventions in end-of-life care in dementia.Peer reviewedFinal Published versio

Does perception of automation undermine pro-environmental behaviour? Findings from three everyday settings

The global deployment of technology to aid mitigation of climate change has great potential but the realisation of much of this potential depends on behavioural response. A culturally pervasive reliance on and belief in technology raises the risk that dependence on technology will hamper human actions of mitigation. Theory suggests that ‘green’ behaviour may be undermined by automated technology but empirical investigation has been lacking. We examined the effect of the prospect of automation on three everyday behaviours with environmental impact. Based on evidence from observational and experimental studies, we demonstrated that the prospect of automation can undermine even simple actions for sustainability. Further, we examined the process by which automated technology influences behaviour and suggest that automation may impair personal responsibility for action

Spectral Classification of Galaxies

We investigate the integrated spectra of a sample of 24 normal galaxies. A principal component analysis suggests that most of the variance present in the spectra is due to the differences in morphology of the galaxies in the sample. We show that spectroscopic parameters extracted from the spectra, like the amplitude of the 4000 \AA~ break or of the CN band, correlate well with Hubble types and are useful for quantitative classification.Comment: 7 pages uuencoded compressed PostScript file. To appear in Vistas in Astronomy, special issue on Artificial Neural Networks in Astronom

Health-related quality-of-life outcome measures in paediatric palliative care: A systematic review of psychometric properties and feasibility of use

BACKGROUND: The number of children worldwide requiring palliative care services is increasing due to advances in medical care and technology. The use of outcome measures is important to improve the quality and effectiveness of care. AIM: To systematically identify health-related quality-of-life outcome measures that could be used in paediatric palliative care and examine their feasibility of use and psychometric properties. DESIGN: A systematic literature review and analysis of psychometric properties. DATA SOURCES: PsychInfo, Medline and EMBASE were searched from 1 January 1990 to 10 December 2014. Hand searches of the reference list of included studies and relevant reviews were also performed. RESULTS: From 3460 articles, 125 papers were selected for full-text assessment. A total of 41 articles met the eligibility criteria and examined the psychometric properties of 22 health-related quality-of-life measures. Evidence was limited as at least half of the information on psychometric properties per instrument was missing. Measurement error was not analysed in any of the included articles and responsiveness was only analysed in one study. The methodological quality of included studies varied greatly. CONCLUSION: There is currently no 'ideal' outcome assessment measure for use in paediatric palliative care. The domains of generic health-related quality-of-life measures are not relevant to all children receiving palliative care and some domains within disease-specific measures are only relevant for that specific population. Potential solutions include adapting an existing measure or developing more individualized patient-centred outcome and experience measures. Either way, it is important to continue work on outcome measurement in this field