On Invariant Notions of Segre Varieties in Binary Projective Spaces

Invariant notions of a class of Segre varieties \Segrem(2) of PG(2^m - 1, 2) that are direct products of $m$ copies of PG(1, 2), $m$ being any positive integer, are established and studied. We first demonstrate that there exists a hyperbolic quadric that contains \Segrem(2) and is invariant under its projective stabiliser group \Stab{m}{2}. By embedding PG(2^m - 1, 2) into \PG(2^m - 1, 4), a basis of the latter space is constructed that is invariant under \Stab{m}{2} as well. Such a basis can be split into two subsets whose spans are either real or complex-conjugate subspaces according as $m$ is even or odd. In the latter case, these spans can, in addition, be viewed as indicator sets of a \Stab{m}{2}-invariant geometric spread of lines of PG(2^m - 1, 2). This spread is also related with a \Stab{m}{2}-invariant non-singular Hermitian variety. The case $m=3$ is examined in detail to illustrate the theory. Here, the lines of the invariant spread are found to fall into four distinct orbits under \Stab{3}{2}, while the points of PG(7, 2) form five orbits.Comment: 18 pages, 1 figure; v2 - version accepted in Designs, Codes and Cryptograph

Functional responses can unify invasion ecology.

We contend that invasion ecology requires a universal, measurable trait of species and their interactions with resources that predicts key elements of invasibility and ecological impact; here, we advocate that functional responses can help achieve this across taxonomic and trophic groups, among habitats and contexts, and can hence help unify disparate research interests in invasion ecology

Threats to the validity of the Collegiate Learning Assessment (CLA+) as a measure of critical thinking skills and implications for Learning Gain

The University of Reading Learning Gain project is a three-year longitudinal project to test and evaluate a range of available methodologies and to draw conclusions on what might be the right combination of instruments for the measurement of Learning Gain in higher education. This paper analyses the validity of a measure of critical thinking skills, the Collegiate Learning Assessment (CLA+) and the implications of using this standardised test as a proxy for Learning Gain. The paper reviews five inferences regarding the interpretations and use of test scores: construct representation, scoring, generalisation, extrapolation and decision-making. Each section reviews some of the available evidence in support of the claims the CLA+ makes and the threats to their validity. The possible impact of these issues on Learning Gain in the UK is considered

United States Valuation of EQ-5D-5L Health States Using an International Protocol

Objective To derive a US-based value set for the EQ-5D-5L questionnaire using an international, standardized protocol developed by the EuroQol Group. Methods Respondents from the US adult population were quota-sampled on the basis of age, sex, ethnicity, and race. Trained interviewers guided participants in completing composite time trade-off (cTTO) and discrete choice experiment (DCE) tasks using the EuroQol Valuation Technology software and routine quality control measures. Data were modeled using a Tobit model for cTTO data, a mixed logit model for DCE data, and a hybrid model that combined cTTO and DCE data. Model performance was compared on the basis of logical ordering of coefficients, statistical significance, parsimony, and theoretical considerations. Results Of 1134 respondents, 1062, 1099, and 1102 respondents provided useable cTTO, DCE, and cTTO or DCE responses, respectively, on the basis of quality control criteria and interviewer judgment. Respondent demographic characteristics and health status were similar to the 2015 US Census. The Tobit model was selected as the preferred model to generate the value set. Values ranged from −0.573 (55 555) to 1 (11 111), with 20% of all predicted health states scores less than 0 (ie, worse than dead). Conclusions A societal value set for the EQ-5D-5L was developed that can be used for economic evaluations and decision making in US health systems. The internationally established, standardized protocol used to develop this US-based value set was recommended by the EuroQol Group and can facilitate cross-country comparisons

Perturbation theory for large Stokes number particles in random velocity fields

We derive a perturbative approach to study, in the large inertia limit, the dynamics of solid particles in a smooth, incompressible and finite-time correlated random velocity field. We carry on an expansion in powers of the inverse square root of the Stokes number, defined as the ratio of the relaxation time for the particle velocities and the correlation time of the velocity field. We describe in this limit the residual concentration fluctuations of the particle suspension, and determine the contribution to the collision statistics produced by clustering. For both concentration fluctuations and collision velocities, we analyze the differences with the compressible one-dimensional case.Comment: Latex, 12 pages, 2 eps figures include

Le magmatisme de la région de Kwyjibo, Province\ud du Grenville (Canada) : intérêt pour les\ud minéralisations de type fer-oxydes associées

The granitic plutons located north of the Kwyjibo property in Quebec’s Grenville Province are of\ud Mesoproterozoic age and belong to the granitic Canatiche Complex . The rocks in these plutons are calc-alkalic, K-rich,\ud and meta- to peraluminous. They belong to the magnetite series and their trace element characteristics link them to\ud intraplate granites. They were emplaced in an anorogenic, subvolcanic environment, but they subsequently underwent\ud significant ductile deformation. The magnetite, copper, and fluorite showings on the Kwyjibo property are polyphased\ud and premetamorphic; their formation began with the emplacement of hydraulic, magnetite-bearing breccias, followed by\ud impregnations and veins of chalcopyrite, pyrite, and fluorite, and ended with a late phase of mineralization, during\ud which uraninite, rare earths, and hematite were emplaced along brittle structures. The plutons belong to two families:\ud biotite-amphibole granites and leucogranites. The biotite-amphibole granites are rich in iron and represent a potential\ud heat and metal source for the first, iron oxide phase of mineralization. The leucogranites show a primary enrichment in\ud REE (rare-earth elements), F, and U, carried mainly in Y-, U-, and REE-bearing niobotitanates. They are metamict and\ud underwent a postmagmatic alteration that remobilized the uranium and the rare earths. The leucogranites could also be\ud a source of rare earths and uranium for the latest mineralizing events