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

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

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

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

Comparison between early Odin-SMR, Aura MLS and CloudSat retrievals of cloud ice mass in the upper tropical troposphere

International audienceEmerging microwave satellite techniques are expected to provide improved global measurements of cloud ice mass. CloudSat, Aura MLS and Odin-SMR fall into this category and early cloud ice retrievals from these instruments are compared. The comparison follows the SMR retrieval product and is made for partial ice water columns above 12 km. None of the retrievals shows a significant degree of false cloud detections, the ratio between local mean values from the instruments is fairly constant and a consistent view of the geographical distribution of cloud ice is obtained. However, important differences on the absolute levels exist, where the overall mean is 9.6, 4.2 and 3.7 g m?2 for CloudSat, SMR and MLS, respectively. Assumptions about the particle size distribution (PSD) are a consideration for all three instruments and constitute the dominating retrieval uncertainty for CloudSat. The mean for CloudSat when applying the same PSD as for MLS and SMR was estimated to 6.3 g m?2. A second main consideration for MLS and SMR are the effects caused by the poorer spatial resolution: a possible vertical misplacement of retrieved values and an impact of cloud inhomogeneities. The latter effect was found to be the dominating retrieval uncertainty for SMR, giving a possible mean value range of 2.3?8.9 g m?2. The comparison indicates a common retrieval accuracy in the order of 70%. Already this number should suffice for improved validations of cloud ice parametrisation schemes in atmospheric models, but a substantially better consistency between the datasets should be attainable through an increased understanding of main retrieval error sources

Source detection using a 3D sparse representation: application to the Fermi gamma-ray space telescope

The multiscale variance stabilization Transform (MSVST) has recently been proposed for Poisson data denoising. This procedure, which is nonparametric, is based on thresholding wavelet coefficients. We present in this paper an extension of the MSVST to 3D data (in fact 2D-1D data) when the third dimension is not a spatial dimension, but the wavelength, the energy, or the time. We show that the MSVST can be used for detecting and characterizing astrophysical sources of high-energy gamma rays, using realistic simulated observations with the Large Area Telescope (LAT). The LAT was launched in June 2008 on the Fermi Gamma-ray Space Telescope mission. The MSVST algorithm is very fast relative to traditional likelihood model fitting, and permits efficient detection across the time dimension and immediate estimation of spectral properties. Astrophysical sources of gamma rays, especially active galaxies, are typically quite variable, and our current work may lead to a reliable method to quickly characterize the flaring properties of newly-detected sources.Comment: Accepted. Full paper will figures available at http://jstarck.free.fr/aa08_msvst.pd

Semi-supervised clustering on heterogeneous information networks

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Kepler Cycle 1 Observations of Low Mass Stars: New Eclipsing Binaries, Single Star Rotation Rates, and the Nature and Frequency of Starspots

We have analyzed Kepler light curves for 849 stars with T_eff < 5200 K from our Cycle 1 Guest Observer program. We identify six new eclipsing binaries, one of which has an orbital period of 29.91 d, and two of which are probably W UMa variables. In addition, we identify a candidate "warm Jupiter" exoplanet. We further examine a subset of 670 sources for variability. Of these objects, 265 stars clearly show periodic variability that we assign to rotation of the low-mass star. At the photometric precision level provided by Kepler, 251 of our objects showed no evidence for variability. We were unable to determine periods for 154 variable objects. We find that 79% of stars with T_eff < 5200 K are variable. The rotation periods we derive for the periodic variables span the range 0.31 < P_rot < 126.5 d. A considerable number of stars with rotation periods similar to the solar value show activity levels that are 100 times higher than the Sun. This is consistent with results for solar-like field stars. As has been found in previous studies, stars with shorter rotation periods generally exhibit larger modulations. This trend flattens beyond P_rot = 25 d, demonstrating that even long period binaries may still have components with high levels of activity and investigating whether the masses and radii of the stellar components in these systems are consistent with stellar models could remain problematic. Surprisingly, our modeling of the light curves suggests that the active regions on these cool stars are either preferentially located near the rotational poles, or that there are two spot groups located at lower latitudes, but in opposing hemispheres.Comment: 48 pages, 11 figure