Recovering S1S^1-invariant metrics on S2S^2 from the equivariant spectrum

We prove an inverse spectral result for $S^1$-invariant metrics on $S^2$ based on the so-called asymptotic equivariant spectrum. This is roughly the spectrum together with large weights of the $S^1$ action on the eigenspaces. Our result generalizes an inverse spectral result of the first and last named authors, together with Victor Guillemin, concerning $S^1$-invariant metrics on $S^2$ which are invariant under the antipodal map. We use higher order terms in the asymptotic expansion of a natural spectral measure associated with the Laplacian and the $S^1$ action.Comment: 16 pages; minor revisions throughout following comments from referee

Hearing Delzant polytopes from the equivariant spectrum

Let M^{2n} be a symplectic toric manifold with a fixed T^n-action and with a toric K\"ahler metric g. Abreu asked whether the spectrum of the Laplace operator $\Delta_g$ on $\mathcal{C}^\infty(M)$ determines the moment polytope of M, and hence by Delzant's theorem determines M up to symplectomorphism. We report on some progress made on an equivariant version of this conjecture. If the moment polygon of M^4 is generic and does not have too many pairs of parallel sides, the so-called equivariant spectrum of M and the spectrum of its associated real manifold M_R determine its polygon, up to translation and a small number of choices. For M of arbitrary even dimension and with integer cohomology class, the equivariant spectrum of the Laplacian acting on sections of a naturally associated line bundle determines the moment polytope of M.Comment: 23 pages, 9 figures; v2 is published versio

Long-term effects of school quality on health and lifestyle: evidence from comprehensive schooling reforms in England

Members of the National Child Development Study cohort attended very different types of secondary schools, as their schooling lay within the transition period of the comprehensive education reform in England and Wales. This provides a natural setting to explore the impact of educational attainment and of school quality on health and health-related behavior later in life. We use a combination of matching methods and parametric regressions to deal with selection effects and to evaluate differences in adult health outcomes and health-related behavior for cohort members exposed to the old selective and to the new comprehensive educational systems

Quality of schooling and inequality of opportunity in health

This paper explores the role of quality of schooling as a source of inequality of opportunity in health. Substantiating earlier literature that links differences in education to health disparities, the paper uses variation in quality of schooling to test for inequality of opportunity in health. Analysis of the 1958 NCDS cohort exploits the variation in type and quality of schools generated by the comprehensive schooling reforms in England and Wales. The analysis provides evidence of a statistically significant and economically sizable association between some dimensions of quality of education and a range of health and health-related outcomes. For some outcomes the association persists, over and above the effects of measured ability, social development, academic qualifications and adult socioeconomic status and lifestyle

O túmulo da rainha Santa Isabel

Num dos seus diálogos sobre pintura, redigidos em 1548, Francisco de Holanda registou que nenhuma outra arte como esta exerce tão importante efeito regenerador sobre os homens, uma vez que os conduz às melhores emoções e lhes mostra de maneira suave as durezas da condição humana: ao melancolizado provoca alegria; o contente e o alterado [leva] ao conhecimento da miséria humana; ao desaustinado move-o à compunção; o mundano à penitência, o [indevoto e pouco] contemplativo à contemplação e medo e vergonha. Ela nos mostra a morte e o que somos, mais suavemente que doutra maneira; ela os tormentos e perigos dos Infernos; ela, quanto é possível, nos representa a glória e paz dos bem-aventurados, e aquela incompreensível imagem do Senhor Deus1. Mas a virtude da pintura estaria também, segundo o referido pintor, no facto de pôr diante dos olhos as imagens dos grandes acontecimentos, os feitos dos grandes homens e a formosura das mulheres; de dar vida aos mortos e de lhes perpetuar a memória muito para além da sua temporal existência2. Se acharmos nós que todas estas virtualidades são extensíveis a outros domínios das artes plásticas, nomeadamente à escultura, então encontramos aí uma boa síntese sobre a natureza e a vocação de tais artes