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

Comparison between the first 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 first cloud ice retrievals from these instruments are compared. The comparison is made for partial ice water columns above 12 km, following the SMR retrieval product. None of the instruments shows significant false cloud detections and a consistent view of the geographical distribution of cloud ice is obtained, but differences on the absolute levels exist. CloudSat gives the lowest values, with an overall mean of 2.12 g/m2. A comparable mean for MLS is 4.30 g/m2. This relatively high mean can be an indication of overestimation of the vertical altitude of cloud ice by the MLS retrievals. The vertical response of SMR has also some uncertainty, but this does not affect the comparison between MLS and CloudSat. SMR observations are sensitive to cloud inhomogeneities inside the footprint and some compensation is required. Results in good agreement with CloudSat, both in regard of the mean and probability density functions, are obtained for a weak compensation, while a simple characterisation of the effect indicates the need for stronger compensation. The SMR mean was found to be 1.89/2.62/4.10 g/m2 for no/selected/strongest compensation, respectively. Assumptions about the particle size distribution are a consideration for all three instruments, and constitute the dominating retrieval uncertainty for CloudSat. The comparison indicates a retrieval accuracy of about 40% (3.1±1.2 g/m2). This number is already very small compared to uncertainties of cloud ice parametrisation in atmospheric models, but can be decreased further through a better understanding of main retrieval error sources