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

Oregon, My Oregon

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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

Moral, wasteful, frugal, or thrifty? Identifying consumer identities to understand and manage pro-environmental behaviour

Moral motives are important for pro-environmental behavior. But such behavior is not only motivated by moral or environmental concerns. We examined what higher order motives, other than morality, may be important for understanding pro-environmental behavior, by studying consumer identities. In three studies (N = 877) four consumer identities were distinguished: moral, wasteful, frugal, and thrifty. Frugal and moral consumer identities were most salient and were the strongest predictors of pro-environmental behaviors, but in different ways. Frugality, which is related to, but distinct from thriftiness, was particularly important for behaviors associated with waste reduction of any kind (including money). The findings suggest that people adopt the same behavior for different reasons, in ways consistent with their consumer identities. People manage multiple consumer identities simultaneously, and environmental policy is likely to be more effective if it addresses these multiple identities

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

First Odin sub-mm retrievals in the tropical upper troposphere: ice cloud properties

International audienceMore accurate global measurements of the amount of ice in thicker clouds are needed to validate atmospheric models and sub-mm radiometry can be an important component in this respect. A cloud ice retrieval scheme for the first such instrument in space, Odin-SMR, is presented here. Several advantages of sub-mm observations are shown, such as low influence of particle shape and orientation, and a high dynamic range of the retrievals. In the case of Odin-SMR, only cloud ice above ?12.5 km can be measured. The present retrieval scheme gives a detection threshold of about 4 g/m2 above 12.5 km and does not saturate even for thickest observed clouds (>500 g/m2). The main retrieval uncertainties are the assumed particle size distribution and cloud inhomogeneity effects. The overall retrieval accuracy is estimated to be ~75%. The retrieval error is judged to have large random components and to be significantly lower than this value for averaged results, but high fixed errors can not be excluded. However, a firm lower value can always be provided. Initial results are found to be consistent with similar Aura MLS retrievals, but show important differences to corresponding data from atmospheric models. This first retrieval algorithm is limited to lowermost Odin-SMR tangent altitudes, and further development should improve the detection threshold and the vertical resolution. It should also be possible to decrease the retrieval uncertainty associated with cloud inhomogeneities by detailed analysis of other data sets

Expansion and Rehabilitation of the State Fish Pier in Gloucester, Massachusetts

The State Fish Pier in Gloucester, Massachusetts, has been expanded and rehabilitated to provide an upgraded facility to support the local fishing industry. Expansion consisted of a new Finger Pier and solid fill extension of the existing pier. Rehabilitation consisted of replacing a deteriorated wharf with a new higher load carrying wharf. Subsurface conditions ranged from rock outcrops exposed at low tide at some locations to thick marine deposits overlying rock at other locations. Foundation support for the new Finger Pier and rehabilitated wharf consisted of concrete filled steel pipe piles, a portion of which had to he socketed into bedrock due to lack of soil overburden. Compression and tension load tests were performed to verify the pile design capacities

2D-1D Wavelet Reconstruction As A Tool For Source Finding In Spectroscopic Imaging Surveys

Today, image denoising by thresholding of wavelet coefficients is a commonly used tool for 2D image enhancement. Since the data product of spectroscopic imaging surveys has two spatial and one spectral dimension, the techniques for denoising have to be adapted to this change in dimensionality. In this paper we will review the basic method of denoising data by thresholding wavelet coefficients and implement a 2D-1D wavelet decomposition to obtain an efficient way of denoising spectroscopic data cubes. We conduct different simulations to evaluate the usefulness of the algorithm as part of a source finding pipeline.Comment: 8 pages, 7 figures, 1 table, accepted for publication in PASA Special Issue on Source Finding and Visualizatio