Properties of a square root transformation regression model

We consider the problem of modelling the conditional distribution of a response given a vector of covariates x when the response is a compositional data vector u. That is, u is defined on the unit simplex [...] This definition of the unit simplex differs subtly from that of Aitchison (1982), as we relax the con- dition that the components of u must be strictly positive. Under this scenario, use of the ratio (or logratio) to compare different compositions is not ideal since it is undefined in some instances, and subcompositional analysis is also not appropriate due to the possibility of division by zero. It has long been recognised that the square root transformation [...] transforms compositional data (including zeros) onto the surface of the (p-1)-dimensional hyperspher

Downstream benefits vs upstream costs of land use change for water-yield and salt-load targets in the Macquarie Catchment, NSW

The net present value (NPV) of downstream economic benefits of changes in water-yield (W) and salt-load (S) of mean annual river flow received by a lower catchment from an upper catchment are described as a 3-dimensional (NPV,W, S) surface, where dNPV/dW > 0 and dNPV/d(S/W) < 0. Upstream changes in land use (i.e. forest clearing or forest establishment, which result in higher or lower water-yields, respectively) are driven by economic consequences for land owners. This paper defines conditions under which costs of strategic upstream land use changes could be exceeded by compensations afforded by downstream benefits from altered water-yields and/or lower salt loads. The paper presents methods, and preliminary calculations for an example river, quantifying the scope for such combinations, and raising the question of institutional designs to achieve mutually beneficial upstream and downstream outcomes. Examples refer to the Macquarie River downstream of Dubbo, NSW, and Little River, an upstream tributary.policy, markets, upstream, downstream, water, salinity, Land Economics/Use,

Improving well-being and outcomes for looked after children in Wales: a context sensitive review of interventions

Improving outcomes for looked after children and young people has been a longstanding concern in Wales. This article reports the findings of a scoping study which sought to identify interventions aimed at improving outcomes for looked after children that are effective or promising. The study was commissioned by an independent funding body to inform a £5 million investment programme for Wales. It comprised a rapid review of literature, informed through consultation with an expert advisory panel and groups of young people who had been in care. The article outlines the rapid review method, provides details of shortlisted interventions and describes the interventions subsequently approved for investment. It concludes that although there are many promising interventions which address the factors associated with poor outcomes for looked after children, the evidence base is weak. It is argued that decision-making on interventions should be informed by appraisal of the empirical evidence available, but should also be guided by professional judgement that considers the needs, priorities and preferences of service users, carers, practitioners and policy-makers

Computing a Knot Invariant as a Constraint Satisfaction Problem

We point out the connection between mathematical knot theory and spin glass/search problem. In particular, we present a statistical mechanical formulation of the problem of computing a knot invariant; p-colorability problem, which provides an algorithm to find the solution. The method also allows one to get some deeper insight into the structural complexity of knots, which is expected to be related with the landscape structure of constraint satisfaction problem.Comment: 6 pages, 3 figures, submitted to short note in Journal of Physical Society of Japa

Spanning Trees on Lattices and Integration Identities

For a lattice $\Lambda$ with $n$ vertices and dimension $d$ equal or higher than two, the number of spanning trees $N_{ST}(\Lambda)$ grows asymptotically as $\exp(n z_\Lambda)$ in the thermodynamic limit. We present exact integral expressions for the asymptotic growth constant $z_\Lambda$ for spanning trees on several lattices. By taking different unit cells in the calculation, many integration identities can be obtained. We also give $z_{\Lambda (p)}$ on the homeomorphic expansion of $k$-regular lattices with $p$ vertices inserted on each edge.Comment: 15 pages, 3 figures, 1 tabl

Cytotoxicity of alpha-particle-emitting astatine-211-labelled antibody in tumour spheroids: no effect of hyperthermia.

The high linear energy transfer, alpha-particle-emitting radionuclide astatine-211 (211At) is of interest for certain therapeutic applications; however, because of the 55- to 70-microm path length of its alpha-particles, achieving homogeneous tracer distribution is critical. Hyperthermia may enhance the therapeutic efficacy of alpha-particle endoradiotherapy if it can improve tracer distribution. In this study, we have investigated whether hyperthermia increased the cytotoxicity of an 211At-labelled monoclonal antibody (MAb) in tumour spheroids with a radius (approximately 100 microm) greater than the range of 211At alpha-particles. Hyperthermia for 1 h at 42 degrees C was used because this treatment itself resulted in no regrowth delay. Radiolabelled chimeric MAb 81C6 reactive with the extracellular matrix antigen tenascin was added to spheroids grown from the D-247 MG human glioma cell line at activity concentrations ranging from 0.125 to 250 kBq ml(-1). A significant regrowth delay was observed at 125 and 250 kBq ml(-1) in both hyperthermia-treated and untreated spheroids. For groups receiving hyperthermia, no increase in cytotoxicity was seen compared with normothermic controls at any activity concentration. These results and those from autoradiographs indicate that hyperthermia at 42 degrees C for 1 h had no significant effect on the uptake or distribution of this antitenascin MAb in D-247 MG spheroids

A Directional Mixed Effects Model for Compositional Expenditure Data

Compositional data are vectors of proportions defined on the unit simplex and this type of constrained data occur frequently in Government surveys. It is also possible for the compositional data to be correlated due to the clustering or grouping of the observations within small domains or areas. We propose a new class of the mixed model for compositional data based on the Kent distribution for directional data, where the random effects also have Kent distributions. One useful property of the new directional mixed model is that the marginal mean direction has a closed form and is interpretable. The random effects enter the model in a multiplicative way via the product of a set of rotation matrices and the conditional mean direction is a random rotation of the marginal mean direction. In small area estimation settings, the mean proportions are usually of primary interest and these are shown to be simple functions of the marginal mean direction. For estimation, we apply a quasi-likelihood method which results in solving a new set of generalized estimating equations and these are shown to have low bias in typical situations. For inference, we use a nonparametric bootstrap method for clustered data which does not rely on estimates of the shape parameters (shape parameters are difficult to estimate in Kent models). We analyze data from the 2009–2010 Australian Household Expenditure Survey CURF (confidentialized unit record file). We predict the proportions of total weekly expenditure on food and housing costs for households in a chosen set of domains. The new approach is shown to be more tractable than the traditional approach based on the logratio transformation