Quantum affine Cartan matrices, Poincare series of binary polyhedral groups, and reflection representations

We first review some invariant theoretic results about the finite subgroups of SU(2) in a quick algebraic way by using the McKay correspondence and quantum affine Cartan matrices. By the way it turns out that some parameters (a,b,h;p,q,r) that one usually associates with such a group and hence with a simply-laced Coxeter-Dynkin diagram have a meaningful definition for the non-simply-laced diagrams, too, and as a byproduct we extend Saito's formula for the determinant of the Cartan matrix to all cases. Returning to invariant theory we show that for each irreducible representation i of a binary tetrahedral, octahedral, or icosahedral group one can find a homomorphism into a finite complex reflection group whose defining reflection representation restricts to i.Comment: 19 page

Forming norms: informing diagnosis and management in sports medicine

Clinicians aim to identify abnormalities, and distinguish harmful from harmless abnormalities. In sports medicine, measures of physical function such as strength, balance and joint flexibility are used as diagnostic tools to identify causes of pain and disability and monitor progression in response to an intervention. Comparing results from clinical measures against ‘normal’ values guides decision-making regarding health outcomes. Understanding ‘normal’ is therefore central to appropriate management of disease and disability. However, ‘normal’ is difficult to clarify and definitions are dependent on context. ‘Normal’ in the clinical setting is best understood as an appropriate state of physical function. Particularly as disease, pain and sickness are expected occurrences of being human, understanding ‘normal’ at each stage of the lifespan is essential to avoid the medicalisation of usual life processes. Clinicians use physical measures to assess physical function and identify disability. Accurate diagnosis hinges on access to ‘normal’ reference values for such measures. However our knowledge of ‘normal’ for many clinical measures in sports medicine is limited. Improved knowledge of normal physical function across the lifespan will assist greatly in the diagnosis and management of pain, disease and disability

Oxygen Fugacity of the Upper Mantle of Mars. Evidence from the Partitioning Behavior of Vanadium in Y980459 (Y98) and other Olivine-Phyric Shergottites

Using partitioning behavior of V between olivine and basaltic liquid precisely calibrated for martian basalts, we determined the redox state of primitive (olivine-rich, high Mg#) martian basalts near their liquidus. The combination of oxidation state and incompatible element characteristics determined from early olivine indicates that correlations between fO2 and other geochemical characteristics observed in many martian basalts is also a fundamental characteristic of these primitive magmas. However, our data does not exhibit the range of fO2 observed in these previous studies.. We conclude that the fO2 for the martian upper mantle is approximately IW+1 and is incompatible-element depleted. It seems most likely (although clearly open to interpretation) that these mantle-derived magmas assimilated a more oxidizing (>IW+3), incompatible-element enriched, lower crustal component as they ponded at the base of the martian crust

Plasticity and Genetic Diversity May Allow Saltcedar to Invade Cold Climates in North America

Two major mechanisms have been proposed to explain the ability of introduced populations to colonize over large habitat gradients, despite significant population bottlenecks during introduction: (1) Broad environmental tolerance-successful invaders possess life history traits that confer superior colonizing ability and/or phenotypic plasticity, allowing acclimation to a wide range of habitats. (2) Local adaptation-successful invaders rapidly adapt to local selective pressures. However, even with bottlenecks, many introduced species exhibit surprisingly high levels of genetic variation and thus the potential for evolutionary increases in invasive traits and plasticity. Here we assess the invasive potential of Tamarix ramosissima, by examining the degree of genetic differentiation within and among populations from the latitudinal extremes of its introduced range. Using growth chamber experiments we examined ecologically important variation in seedlings, both in trait means and their reaction norms across temperature environments. Although we found no genetic variation for gas exchange traits, within or among populations, we did find significant genetic variation for growth traits, both in the trait means and in the degree of plasticity in these traits. Northern ecotypes invested more in roots relative to southern ecotypes but only under low temperatures. Both ecotypes increased shoot investment in warm temperatures. Increased root investment in cold temperatures by northern ecotypes may increase their first winter survival. Genetic differences in seedling root investment may contribute to the ability of this species to successfully tolerate and invade a broader latitudinal range. Our data support a model in which both plasticity and adaptive evolution can contribute to the invasive potential of introduced species

Making Sense of the Legendre Transform

The Legendre transform is an important tool in theoretical physics, playing a critical role in classical mechanics, statistical mechanics, and thermodynamics. Yet, in typical undergraduate or graduate courses, the power of motivation and elegance of the method are often missing, unlike the treatments frequently enjoyed by Fourier transforms. We review and modify the presentation of Legendre transforms in a way that explicates the formal mathematics, resulting in manifestly symmetric equations, thereby clarifying the structure of the transform algebraically and geometrically. Then we bring in the physics to motivate the transform as a way of choosing independent variables that are more easily controlled. We demonstrate how the Legendre transform arises naturally from statistical mechanics and show how the use of dimensionless thermodynamic potentials leads to more natural and symmetric relations.Comment: 11 pages, 3 figure

Suicide and accidental death in Australia’s rural farming communities: a review of the literature

Introduction: Australia's farmers constitute a heterogeneous group within the rural population. This literature review incorporates four broad areas: an understanding of farming communities, families and individuals and the contexts in which they live and work; an exploration of the challenges to morbidity and mortality that these communities face; a description of the patterns of suicide and accidental death in farming communities; and an outline of what is missing from the current body of research. Recommendations will be made on how these gaps may be addressed. Methods: In developing this comprehensive literature review, a snowballing and saturation approach was adopted. Initial search terms included suicid*, farm*, accident*, fatal*, death, sudden death, rural OR remote, Australia and NOT Australia. Databases searched included SCOPUS, PubMed, Proquest and SafetyLit; research from 1995 onwards was examined for relevance. Earlier seminal texts were also included. Reference lists of retrieved articles were searched and citations explored for further relevant research material. The primary focus was on Australian peer-reviewed research with supplementary grey literature. International material was used as examples. Results: The literature variously describes farmers as members of both rural farming communities and farming families, and as individuals within an occupational classification. Within each of these classifications, there is evidence of the cumulative impact of a multiplicity of social, geographical and psychological factors relating to work, living and social arrangements that impact the health and wellbeing of Australia's farmers and their families, particularly accidental death and suicide. Research consistently demonstrates traumatic death to be at a greater rate than in the general Australian population, with reductions found more recently in some modes of farming-related accidental death. Patterns of accidental death and suicide are commonly linked to the changing shape of contemporary farming. Suicide rates are also frequently described in relation to lethality and accessibility of means. The limitations of suicide and accidental death data are considerable. Conclusion: While there is consistent reporting of heightened levels of risk for suicide and accidental death in farming communities the limitations of the research remain significant. There are substantial gaps in current knowledge, and the body of research to date lacks clarity, inclusiveness and contextual specificity. Absent from the literature is any investigation of the impact of these frequently preventable deaths on the families and communities in which they occur. Recommendations for future research are suggested

Kochen-Specker Vectors

We give a constructive and exhaustive definition of Kochen-Specker (KS) vectors in a Hilbert space of any dimension as well as of all the remaining vectors of the space. KS vectors are elements of any set of orthonormal states, i.e., vectors in n-dim Hilbert space, H^n, n>3 to which it is impossible to assign 1s and 0s in such a way that no two mutually orthogonal vectors from the set are both assigned 1 and that not all mutually orthogonal vectors are assigned 0. Our constructive definition of such KS vectors is based on algorithms that generate MMP diagrams corresponding to blocks of orthogonal vectors in R^n, on algorithms that single out those diagrams on which algebraic 0-1 states cannot be defined, and on algorithms that solve nonlinear equations describing the orthogonalities of the vectors by means of statistically polynomially complex interval analysis and self-teaching programs. The algorithms are limited neither by the number of dimensions nor by the number of vectors. To demonstrate the power of the algorithms, all 4-dim KS vector systems containing up to 24 vectors were generated and described, all 3-dim vector systems containing up to 30 vectors were scanned, and several general properties of KS vectors were found.Comment: 19 pages, 6 figures, title changed, introduction thoroughly rewritten, n-dim rotation of KS vectors defined, original Kochen-Specker 192 (117) vector system translated into MMP diagram notation with a new graphical representation, results on Tkadlec's dual diagrams added, several other new results added, journal version: to be published in J. Phys. A, 38 (2005). Web page: http://m3k.grad.hr/pavici

Towards a global model of accounting education

Purpose - The purpose of this paper is to examine the accounting education systems in three countries - Australia, Japan and Sri Lanka - to inform the development and testing (by application) of a Global Model of Accounting Education

Comparative RNAi Screens in C. elegans and C. briggsae Reveal the Impact of Developmental System Drift on Gene Function

Although two related species may have extremely similar phenotypes, the genetic networks underpinning this conserved biology may have diverged substantially since they last shared a common ancestor. This is termed Developmental System Drift (DSD) and reflects the plasticity of genetic networks. One consequence of DSD is that some orthologous genes will have evolved different in vivo functions in two such phenotypically similar, related species and will therefore have different loss of function phenotypes. Here we report an RNAi screen in C. elegans and C. briggsae to identify such cases. We screened 1333 genes in both species and identified 91 orthologues that have different RNAi phenotypes. Intriguingly, we find that recently evolved genes of unknown function have the fastest evolving in vivo functions and, in several cases, we identify the molecular events driving these changes. We thus find that DSD has a major impact on the evolution of gene function and we anticipate that the C. briggsae RNAi library reported here will drive future studies on comparative functional genomics screens in these nematodes