Mathematics of Gravitational Lensing: Multiple Imaging and Magnification

The mathematical theory of gravitational lensing has revealed many generic and global properties. Beginning with multiple imaging, we review Morse-theoretic image counting formulas and lower bound results, and complex-algebraic upper bounds in the case of single and multiple lens planes. We discuss recent advances in the mathematics of stochastic lensing, discussing a general formula for the global expected number of minimum lensed images as well as asymptotic formulas for the probability densities of the microlensing random time delay functions, random lensing maps, and random shear, and an asymptotic expression for the global expected number of micro-minima. Multiple imaging in optical geometry and a spacetime setting are treated. We review global magnification relation results for model-dependent scenarios and cover recent developments on universal local magnification relations for higher order caustics.Comment: 25 pages, 4 figures. Invited review submitted for special issue of General Relativity and Gravitatio

A standardized, evidence-based protocol to assess clinical actionability of genetic disorders associated with genomic variation

Genome and exome sequencing can identify variants unrelated to the primary goal of sequencing. Detecting pathogenic variants associated with an increased risk of a medical disorder enables clinical interventions to improve future health outcomes in patients and their at-risk relatives. The Clinical Genome Resource, or ClinGen, aims to assess clinical actionability of genes and associated disorders as part of a larger effort to build a central resource of information regarding the clinical relevance of genomic variation for use in precision medicine and research

Neutralino Gamma-ray Signals from Accreting Halo Dark Matter

There is mounting evidence that a self-consistent model for particle cold dark matter has to take into consideration spatial inhomogeneities on sub-galactic scales seen, for instance, in high-resolution N-body simulations of structure formation. Also in more idealized, analytic models, there appear density enhancements in certain regions of the halo. We use the results from a recent N-body simulation of the Milky Way halo and investigate the gamma-ray flux which would be produced when a specific dark matter candidate, the neutralino, annihilates in regions of enhanced density. The clumpiness found on all scales in the simulation results in very strong gamma-ray signals which seem to already rule out some regions of the supersymmetric parameter space, and would be further probed by upcoming experiments, such as the GLAST gamma-ray satellite. As an orthogonal model of structure formation, we also consider Sikivie's simple infall model of dark matter which predicts that there should exist continuous regions of enhanced density, caustic rings, in the dark matter halo of the Milky Way. We find, however, that the gamma-ray signal from caustic rings is generally too small to be detectable.Comment: 15 pages, 11 figure

Pooled analysis of prospective cohort studies on height, weight, and breast cancer risk

The association between anthropometric indices and the risk of breast cancer was analyzed using pooled data from seven prospective cohort studies. Together, these cohorts comprise 337,819 women and 4,385 incident invasive breast cancer cases. In multivariate analyses controlling for reproductive, dietary, and other risk factors, the pooled relative risk (RR) of breast cancer per height increment of 5 cm was 1.02 (95% confidence interval (Cl): 0.96, 1.10) in premenopausal women and 1.07 (95% Cl: 1.03, 1.12) in postmenopausal women. Body mass index (BMI) showed significant inverse and positive associations with breast cancer among pre- and postmenopausal women, respectively; these associations were nonlinear. Compared with premenopausal women with a BMI of less than 21 kg/m2, women with a BMI exceeding 31 kg/m2 had an RR of 0.54 (95% Cl: 0.34, 0.85). In postmenopausal women, the RRs did not increase further when BMI exceeded 28 kg/m2; the RR for these women was 1.26 (95% Cl: 1.09, 1.46). The authors found little evidence for interaction with other breast cancer risk factors. Their data indicate that height is an independent risk factor for postmenopausal breast cancer; in premenopausal women, this relation is less clear. The association between BMI and breast cancer varies by menopausal status. Weight control may reduce the risk among postmenopausal women

Dietary fat and risk of lung cancer in a pooled analysis of prospective studies

Harvard School of Public Health, Department of Nutrition, Boston, Massachusetts 02115, USA. Lung cancer rates are highest in countries with the greatest fat intakes. In several case-control studies, positive associations have been observed between lung cancer and intakes of total and saturated fat, particularly among nonsmokers. We analyzed the association between fat and cholesterol intakes and lung cancer risk in eight prospective cohort studies that met predefined criteria. Among the 280,419 female and 149,862 male participants who were followed for up to 6-16 years, 3,188 lung cancer cases were documented. Using the Cox proportional hazards model, we calculated study-specific relative risks that were adjusted for smoking history and other potential risk factors. Pooled relative risks were computed using a random effects model. Fat intake was not associated with lung cancer risk. For an increment of 5% of energy from fat, the pooled multivariate relative risks were 1.01 [95% confidence interval (CI), 0.98-1.05] for total, 1.03 (95% CI, 0.96-1.11) for saturated, 1.01 (95% CI, 0.93-1.10) for monounsaturated, and 0.99 (95% CI, 0.90-1.10) for polyunsaturated fat. No associations were observed between intakes of total or specific types of fat and lung cancer risk among never, past, or current smokers. Dietary cholesterol was not associated with lung cancer incidence [for a 100-mg/day increment, the pooled multivariate relative risk was 1.01 (95% CI, 0.97-1.05)]. There was no statistically significant heterogeneity among studies or by sex. These data do not support an important relation between fat or cholesterol intakes and lung cancer risk. The means to prevent this important disease remains avoidance of smoking

Intake of fruits and vegetables and risk of breast cancer: a pooled analysis of cohort studies.

Context: Some epidemiologic studies suggest that elevated fruit and vegetable consumption is associated with a reduced risk of breast cancer. However, most have been case-control studies in which recall and selection bias may influence the results. Additionally, publication bias may have influenced the literature on associations for specific fruit and vegetable subgroups. Objective: To examine the association between breast cancer and total and specific fruit and vegetable group intakes using standardized exposure definitions. Data Sources/Study Selection: Eight prospective studies that had at least 200 incident breast cancer cases, assessed usual dietary intake, and completed a validation study of the diet assessment method or a closely related instrument were included in these analyses. Data Extraction: Using the primary data from each of the studies, we calculated study-specific relative risks (RRs) that were combined using a random-effects model. Data Synthesis: The studies included 7377 incident invasive breast cancer cases occurring among 351825 women whose diet was analyzed at baseline. For comparisons of the highest vs lowest quartiles of intake, weak, nonsignificant associations were observed for total fruits (pooled multivariate RR, 0.93; 95% confidence interval [CI], 0.86-1.00; P for trend = .08), total vegetables (RR, 0.96; 95% CI, 0.89-1.04; P for trend = .54), and total fruits and vegetables (RR, 0.93; 95% CI, 0.86-1.00; P for trend = .12). No additional benefit was apparent in comparisons of the highest and lowest deciles of intake. No associations were observed for green leafy vegetables, 8 botanical groups, and 17 specific fruits and vegetables. Conclusion: These results suggest that fruit and vegetable consumption during adulthood is not significantly associated with reduced breast cancer risk

Genomewide meta-analysis identifies loci associated with IGF-I and IGFBP-3 levels with impact on age-related traits

The growth hormone/insulin-like growth factor (IGF) axis can be manipulated in animal models to promote longevity, and IGF-related proteins including IGF-I and IGF-binding protein-3 (IGFBP-3) have also been implicated in risk of human diseases including cardiovascular diseases, diabetes, and cancer. Throug