A data-based power transformation for compositional data

Compositional data analysis is carried out either by neglecting the compositional constraint and applying standard multivariate data analysis, or by transforming the data using the logs of the ratios of the components. In this work we examine a more general transformation which includes both approaches as special cases. It is a power transformation and involves a single parameter, {\alpha}. The transformation has two equivalent versions. The first is the stay-in-the-simplex version, which is the power transformation as defined by Aitchison in 1986. The second version, which is a linear transformation of the power transformation, is a Box-Cox type transformation. We discuss a parametric way of estimating the value of {\alpha}, which is maximization of its profile likelihood (assuming multivariate normality of the transformed data) and the equivalence between the two versions is exhibited. Other ways include maximization of the correct classification probability in discriminant analysis and maximization of the pseudo R-squared (as defined by Aitchison in 1986) in linear regression. We examine the relationship between the {\alpha}-transformation, the raw data approach and the isometric log-ratio transformation. Furthermore, we also define a suitable family of metrics corresponding to the family of {\alpha}-transformation and consider the corresponding family of Frechet means.Comment: Published in the proceddings of the 4th international workshop on Compositional Data Analysis. http://congress.cimne.com/codawork11/frontal/default.as

IUE observations of the chromospheric activity-age relation in young solar-type stars

Ultraviolet data obtained with the IUE spacecraft are presented for a dozen solar-type stars in the field. The stars are of spectral type F6 V - G1 V; on the basis of their high Li content, they range in age from 0.1 to 2.8 Gyr. The evolution of transition regions and chromospheric emission with stellar age is studied along with the surface distribution of magnetically active regions as revealed by rotational modulation of UV emission line fluxes

Rotational modulation of the chromospheric activity in the young solar-type star, X-1 Orionis

The IUE satellite was used to observe one of the youngest G stars (GO V) for which Duncan (1981) derives an age of 6 x 10 to the 8th power years from the Li abundance. Rotational modulation was looked for in the emission flux in the chromospheric and transition region lines of this star. Variations in the Ca 11 K-lines profile were studied with the CHF telescope at Mauna Kea. Results show that the same modulation of the emission flux of Ca 11 due to stellar rotation is present in the transition region feature of C IV and probably of He II. For other UV lines the modulation is not apparent, due to a more complex surface distribution of the active areas or supergranulation network, or a shorter lifetime of the conditions which give rise to these features, or to the uncertainities in the measured line strengths. The Mg II emission flux is constant to within + or - 3.4% implying a rather uniform distribution of Mg II emission areas. The Ca II emission not only shows a measurable variation in intensity but also variations in detailed line profile shape when observed at high resolution

How to Measure Group Selection in Real-world Populations

Multilevel selection and the evolution of cooperation are fundamental to the formation of higher-level organisation and the evolution of biocomplexity, but such notions are controversial and poorly understood in natural populations. The theoretic principles of group selection are well developed in idealised models where a population is neatly divided into multiple semi-isolated sub-populations. But since such models can be explained by individual selection given the localised frequency-dependent effects involved, some argue that the group selection concepts offered are, even in the idealised case, redundant and that in natural conditions where groups are not well-defined that a group selection framework is entirely inapplicable. This does not necessarily mean, however, that a natural population is not subject to some interesting localised frequency-dependent effects – but how could we formally quantify this under realistic conditions? Here we focus on the presence of a Simpson’s Paradox where, although the local proportion of cooperators decreases at all locations, the global proportion of cooperators increases. We illustrate this principle in a simple individual-based model of bacterial biofilm growth and discuss various complicating factors in moving from theory to practice of measuring group selection

Improved classification for compositional data using the α\alpha-transformation

In compositional data analysis an observation is a vector containing non-negative values, only the relative sizes of which are considered to be of interest. Without loss of generality, a compositional vector can be taken to be a vector of proportions that sum to one. Data of this type arise in many areas including geology, archaeology, biology, economics and political science. In this paper we investigate methods for classification of compositional data. Our approach centres on the idea of using the $\alpha$-transformation to transform the data and then to classify the transformed data via regularised discriminant analysis and the k-nearest neighbours algorithm. Using the $\alpha$-transformation generalises two rival approaches in compositional data analysis, one (when $\alpha=1$) that treats the data as though they were Euclidean, ignoring the compositional constraint, and another (when $\alpha=0$) that employs Aitchison's centred log-ratio transformation. A numerical study with several real datasets shows that whether using $\alpha=1$ or $\alpha=0$ gives better classification performance depends on the dataset, and moreover that using an intermediate value of $\alpha$ can sometimes give better performance than using either 1 or 0.Comment: This is a 17-page preprint and has been accepted for publication at the Journal of Classificatio

A dynamic scheme for generating number squeezing in Bose-Einstein condensates through nonlinear interactions

We develop a scheme to generate number squeezing in a Bose-Einstein condensate by utilizing interference between two hyperfine levels and nonlinear atomic interactions. We describe the scheme using a multimode quantum field model and find agreement with a simple analytic model in certain regimes. We demonstrate that the scheme gives strong squeezing for realistic choices of parameters and atomic species. The number squeezing can result in noise well below the quantum limit, even if the initial noise on the system is classical and much greater than that of a poisson distribution.Comment: 4 pages, 3 figure

The adaptation of cognitive behavioural therapy for adult Maori clients with depression: A pilot study

A semistructured cognitive behavioural therapy (CBT) programme for depression was adapted for use with Maori adult clients with depression. Adaptations were developed in consultation with an advisory group consisting of Maori clinical psychologists and kaumatua with experience working in mental health services. The programme was piloted with 2 participants who were clients of a Maori mental health service. The programme builds on a more traditional CBT treatment programme by integrating concepts such as whakatauki, whanaungatanga, whanau involvement, and whakapapa into the therapeutic context. Despite limitations the results demonstrate considerable promise. Depressive symptoms increased substantially in both cases and both clients reflected positively on the adaptations incorporated into therapy

Lifting a Weak Poisson Bracket to the Algebra of Forms

We detail the construction of a weak Poisson bracket over a submanifold of a smooth manifold M with respect to a local foliation of this submanifold. Such a bracket satisfies a weak type Jacobi identity but may be viewed as a usual Poisson bracket on the space of leaves of the foliation. We then lift this weak Poisson bracket to a weak odd Poisson bracket on the odd tangent bundle, interpreted as a weak Koszul bracket on differential forms on M. This lift is achieved by encoding the weak Poisson structure into a homotopy Poisson structure on an extended manifold, and lifting the Hamiltonian function that generates this structure. Such a construction has direct physical interpretation. For a generic gauge system, the submanifold may be viewed as a stationary surface or a constraint surface, with the foliation given by the foliation of the gauge orbits. Through this interpretation, the lift of the weak Poisson structure is simply a lift of the action generating the corresponding BRST operator of the system