Spectral analysis and zeta determinant on the deformed spheres

We consider a class of singular Riemannian manifolds, the deformed spheres $S^N_k$, defined as the classical spheres with a one parameter family $g[k]$ of singular Riemannian structures, that reduces for $k=1$ to the classical metric. After giving explicit formulas for the eigenvalues and eigenfunctions of the metric Laplacian $\Delta_{S^N_k}$, we study the associated zeta functions $\zeta(s,\Delta_{S^N_k})$. We introduce a general method to deal with some classes of simple and double abstract zeta functions, generalizing the ones appearing in $\zeta(s,\Delta_{S^N_k})$. An application of this method allows to obtain the main zeta invariants for these zeta functions in all dimensions, and in particular $\zeta(0,\Delta_{S^N_k})$ and $\zeta'(0,\Delta_{S^N_k})$. We give explicit formulas for the zeta regularized determinant in the low dimensional cases, $N=2,3$, thus generalizing a result of Dowker \cite{Dow1}, and we compute the first coefficients in the expansion of these determinants in powers of the deformation parameter $k$.Comment: 1 figur

Why measure inequality?

A large body of literature is devoted to the measurement of income inequality, yet little attention is given to the question, Why measure inequality? However, the reasons for measurement bear importantly on whether and how measurement should be done. Upon examination, normative measures are found to be of questionable value. Descriptive measures, by contrast, may be useful, but the appropriate measure depends on the field of application rather than on general, a priori principles of the sort that are emphasized in the existing measurement literature. Measures of poverty are also considered, and similar conclusions are reached. Copyright Springer 2005income distribution, inequality, inequality measurement, poverty, poverty measurement, progressivity, redistribution, social welfare function,

Genetic diversity fuels gene discovery for tobacco and alcohol use.

Tobacco and alcohol use are heritable behaviours associated with 15% and 5.3% of worldwide deaths, respectively, due largely to broad increased risk for disease and injury1–4. These substances are used across the globe, yet genome-wide association studies have focused largely on individuals of European ancestries5. Here we leveraged global genetic diversity across 3.4 million individuals from four major clines of global ancestry (approximately 21% non-European) to power the discovery and fine-mapping of genomic loci associated with tobacco and alcohol use, to inform function of these loci via ancestry-aware transcriptome-wide association studies, and to evaluate the genetic architecture and predictive power of polygenic risk within and across populations. We found that increases in sample size and genetic diversity improved locus identification and fine-mapping resolution, and that a large majority of the 3,823 associated variants (from 2,143 loci) showed consistent effect sizes across ancestry dimensions. However, polygenic risk scores developed in one ancestry performed poorly in others, highlighting the continued need to increase sample sizes of diverse ancestries to realize any potential benefit of polygenic prediction

Health-status outcomes with invasive or conservative care in coronary disease

BACKGROUND In the ISCHEMIA trial, an invasive strategy with angiographic assessment and revascularization did not reduce clinical events among patients with stable ischemic heart disease and moderate or severe ischemia. A secondary objective of the trial was to assess angina-related health status among these patients. METHODS We assessed angina-related symptoms, function, and quality of life with the Seattle Angina Questionnaire (SAQ) at randomization, at months 1.5, 3, and 6, and every 6 months thereafter in participants who had been randomly assigned to an invasive treatment strategy (2295 participants) or a conservative strategy (2322). Mixed-effects cumulative probability models within a Bayesian framework were used to estimate differences between the treatment groups. The primary outcome of this health-status analysis was the SAQ summary score (scores range from 0 to 100, with higher scores indicating better health status). All analyses were performed in the overall population and according to baseline angina frequency. RESULTS At baseline, 35% of patients reported having no angina in the previous month. SAQ summary scores increased in both treatment groups, with increases at 3, 12, and 36 months that were 4.1 points (95% credible interval, 3.2 to 5.0), 4.2 points (95% credible interval, 3.3 to 5.1), and 2.9 points (95% credible interval, 2.2 to 3.7) higher with the invasive strategy than with the conservative strategy. Differences were larger among participants who had more frequent angina at baseline (8.5 vs. 0.1 points at 3 months and 5.3 vs. 1.2 points at 36 months among participants with daily or weekly angina as compared with no angina). CONCLUSIONS In the overall trial population with moderate or severe ischemia, which included 35% of participants without angina at baseline, patients randomly assigned to the invasive strategy had greater improvement in angina-related health status than those assigned to the conservative strategy. The modest mean differences favoring the invasive strategy in the overall group reflected minimal differences among asymptomatic patients and larger differences among patients who had had angina at baseline