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

GWAS analysis of handgrip and lower body strength in older adults in the CHARGE consortium

Decline in muscle strength with aging is an important predictor of health trajectory in the elderly. Several factors, including genetics, are proposed contributors to variability in muscle strength. To identify genetic contributors to muscle strength, a meta-analysis of genomewide association studies of handgrip was conducted. Grip strength was measured using a handheld dynamometer in 27 581 individuals of European descent over 65 years of age from 14 cohort studies. Genomewide association analysis was conducted on ~2.7 million imputed and genotyped variants (SNPs). Replication of the most significant findings was conducted using data from 6393 individuals from three cohorts. GWAS of lower body strength was also characterized in a subset of cohorts. Two genomewide significant (P-value< 5 × 10−8) and 39 suggestive (P-value< 5 × 10−5) associations were observed from meta-analysis of the discovery cohorts. After meta-analysis with replication cohorts, genomewide significant association was observed for rs752045 on chromosome 8 (β = 0.47, SE = 0.08, P-value = 5.20 × 10−10). This SNP is mapped to an intergenic region and is located within an accessible chromatin region (DNase hypersensitivity site) in skeletal muscle myotubes differentiated from the human skeletal muscle myoblasts cell line. This locus alters a binding motif of the CCAAT/enhancer-binding protein-β (CEBPB) that is implicated in muscle repair mechanisms. GWAS of lower body strength did not yield significant results. A common genetic variant in a chromosomal region that regulates myotube differentiation and muscle repair may contribute to variability in grip strength in the elderly. Further studies are needed to uncover the mechanisms that link this genetic variant with muscle strength

Acylcarnitine metabolomic profiles inform clinically-defined major depressive phenotypes.

Background: Acylcarnitines have important functions in mitochondrial energetics and beta-oxidation, and have been implicated to play a significant role in metabolic functions of the brain. This retrospective study examined whether plasma acylcarnitine profiles can help biochemically distinguish the three phenotypic subtypes of major depressive disorder (MDD): core depression (CD+), anxious depression (ANX+), and neurovegetative symptoms of melancholia (NVSM+).Methods: Depressed outpatients (n = 240) from the Mayo Clinic Pharmacogenomics Research Network were treated with citalopram or escitalopram for eight weeks. Plasma samples collected at baseline and after eight weeks of treatment with citalopram or escitalopram were profiled for short-, medium- and long-chain acylcarnitine levels using AbsoluteIDQ (R) p180-Kit and LC-MS. Linear mixed effects models were used to examine whether acylcarnitine levels discriminated the clinical phenotypes at baseline or eight weeks post-treatment, and whether temporal changes in acylcarnitine profiles differed between groups.Results: Compared to ANX+, CD+ and NVSM+ had significantly lower concentrations of short- and long-chain acylcarnitines at both baseline and week 8. In NVSM+, the medium- and long-chain acylcarnitines were also significantly lower in NVSM+ compared to ANX+. Short-chain acylcarnitine levels increased significantly from baseline to week 8 in CD+ and ANX+, whereas medium- and long-chain acylcarnitines significantly decreased in CD+ and NVSM+.Conclusions: In depressed patients treated with SSRIs, beta-oxidation and mitochondrial energetics as evaluated by levels and changes in acylcarnitines may provide the biochemical basis of the clinical heterogeneity of MDD, especially when combined with clinical characteristics