On the stability of some isoperimetric inequalities for the fundamental tones of free plates

We provide a quantitative version of the isoperimetric inequality for the fundamental tone of a biharmonic Neumann problem. Such an inequality has been recently established by Chasman adapting Weinberger's argument for the corresponding second order problem. Following a scheme introduced by Brasco and Pratelli for the second order case, we prove that a similar quantitative inequality holds also for the biharmonic operator. We also prove the sharpness of both such an inequality and the corresponding one for the biharmonic Steklov problem

On a classical spectral optimization problem in linear elasticity

We consider a classical shape optimization problem for the eigenvalues of elliptic operators with homogeneous boundary conditions on domains in the $N$-dimensional Euclidean space. We survey recent results concerning the analytic dependence of the elementary symmetric functions of the eigenvalues upon domain perturbation and the role of balls as critical points of such functions subject to volume constraint. Our discussion concerns Dirichlet and buckling-type problems for polyharmonic operators, the Neumann and the intermediate problems for the biharmonic operator, the Lam\'{e} and the Reissner-Mindlin systems.Comment: To appear in the proceedings of the workshop `New Trends in Shape Optimization', Friedrich-Alexander Universit\"{a}t Erlangen-Nuremberg, 23-27 September 201

Spectral analysis of the biharmonic operator subject to Neumann boundary conditions on dumbbell domains

We consider the biharmonic operator subject to homogeneous boundary conditions of Neumann type on a planar dumbbell domain which consists of two disjoint domains connected by a thin channel. We analyse the spectral behaviour of the operator, characterizing the limit of the eigenvalues and of the eigenprojections as the thickness of the channel goes to zero. In applications to linear elasticity, the fourth order operator under consideration is related to the deformation of a free elastic plate, a part of which shrinks to a segment. In contrast to what happens with the classical second order case, it turns out that the limiting equation is here distorted by a strange factor depending on a parameter which plays the role of the Poisson coefficient of the represented plate.Comment: To appear in "Integral Equations and Operator Theory

Analyticity and criticality results for the eigenvalues of the biharmonic operator

We consider the eigenvalues of the biharmonic operator subject to several homogeneous boundary conditions (Dirichlet, Neumann, Navier, Steklov). We show that simple eigenvalues and elementary symmetric functions of multiple eigenvalues are real analytic, and provide Hadamard-type formulas for the corresponding shape derivatives. After recalling the known results in shape optimization, we prove that balls are always critical domains under volume constraint.Comment: To appear on the proceedings of the conference "Geometric Properties for Parabolic and Elliptic PDE's - 4th Italian-Japanese Workshop" held in Palinuro (Italy), May 25-29, 201

Rare coding SNP in DZIP1 gene associated with late-onset sporadic Parkinson's disease

We present the first application of the hypothesis-rich mathematical theory to genome-wide association data. The Hamza et al. late-onset sporadic Parkinson's disease genome-wide association study dataset was analyzed. We found a rare, coding, non-synonymous SNP variant in the gene DZIP1 that confers increased susceptibility to Parkinson's disease. The association of DZIP1 with Parkinson's disease is consistent with a Parkinson's disease stem-cell ageing theory.Comment: 14 page

A comprehensive 1000 Genomes-based genome-wide association meta-analysis of coronary artery disease

Existing knowledge of genetic variants affecting risk of coronary artery disease (CAD) is largely based on genome-wide association studies (GWAS) analysis of common SNPs. Leveraging phased haplotypes from the 1000 Genomes Project, we report a GWAS meta-analysis of 185 thousand CAD cases and controls, interrogating 6.7 million common (MAF>0.05) as well as 2.7 million low frequency (0.005<MAF<0.05) variants. In addition to confirmation of most known CAD loci, we identified 10 novel loci, eight additive and two recessive, that contain candidate genes that newly implicate biological processes in vessel walls. We observed intra-locus allelic heterogeneity but little evidence of low frequency variants with larger effects and no evidence of synthetic association. Our analysis provides a comprehensive survey of the fine genetic architecture of CAD showing that genetic susceptibility to this common disease is largely determined by common SNPs of small effect siz

Genome-wide association meta-analysis of fish and EPA+DHA consumption in 17 US and European cohorts

BackgroundRegular fish and omega-3 consumption may have several health benefits and are recommended by major dietary guidelines. Yet, their intakes remain remarkably variable both within and across populations, which could partly owe to genetic influences.ObjectiveTo identify common genetic variants that influence fish and dietary eicosapentaenoic acid plus docosahexaenoic acid (EPA+DHA) consumption.DesignWe conducted genome-wide association (GWA) meta-analysis of fish (n = 86,467) and EPA+DHA (n = 62,265) consumption in 17 cohorts of European descent from the CHARGE (Cohorts for Heart and Aging Research in Genomic Epidemiology) Consortium Nutrition Working Group. Results from cohort-specific GWA analyses (additive model) for fish and EPA+DHA consumption were adjusted for age, sex, energy intake, and population stratification, and meta-analyzed separately using fixed-effect meta-analysis with inverse variance weights (METAL software). Additionally, heritability was estimated in 2 cohorts.ResultsHeritability estimates for fish and EPA+DHA consumption ranged from 0.13–0.24 and 0.12–0.22, respectively. A significant GWA for fish intake was observed for rs9502823 on chromosome 6: each copy of the minor allele (FreqA = 0.015) was associated with 0.029 servings/day (~1 serving/month) lower fish consumption (P = 1.96x10-8). No significant association was observed for EPA+DHA, although rs7206790 in the obesity-associated FTO gene was among top hits (P = 8.18x10-7). Post-hoc calculations demonstrated 95% statistical power to detect a genetic variant associated with effect size of 0.05% for fish and 0.08% for EPA+DHA.ConclusionsThese novel findings suggest that non-genetic personal and environmental factors are principal determinants of the remarkable variation in fish consumption, representing modifiable targets for increasing intakes among all individuals. Genes underlying the signal at rs72838923 and mechanisms for the association warrant further investigation.</div

Genome-Wide Study of Gene Variants Associated with Differential Cardiovascular Event Reduction by Pravastatin Therapy

Statin therapy reduces the risk of coronary heart disease (CHD), however, the person-to-person variability in response to statin therapy is not well understood. We have investigated the effect of genetic variation on the reduction of CHD events by pravastatin. First, we conducted a genome-wide association study of 682 CHD cases from the Cholesterol and Recurrent Events (CARE) trial and 383 CHD cases from the West of Scotland Coronary Prevention Study (WOSCOPS), two randomized, placebo-controlled studies of pravastatin. In a combined case-only analysis, 79 single nucleotide polymorphisms (SNPs) were associated with differential CHD event reduction by pravastatin according to genotype (P<0.0001), and these SNPs were analyzed in a second stage that included cases as well as non-cases from CARE and WOSCOPS and patients from the PROspective Study of Pravastatin in the Elderly at Risk/PHArmacogenomic study of Statins in the Elderly at risk for cardiovascular disease (PROSPER/PHASE), a randomized placebo controlled study of pravastatin in the elderly. We found that one of these SNPs (rs13279522) was associated with differential CHD event reduction by pravastatin therapy in all 3 studies: P = 0.002 in CARE, P = 0.01 in WOSCOPS, P = 0.002 in PROSPER/PHASE. In a combined analysis of CARE, WOSCOPS, and PROSPER/PHASE, the hazard ratio for CHD when comparing pravastatin with placebo decreased by a factor of 0.63 (95% CI: 0.52 to 0.75) for each extra copy of the minor allele (P = 4.8×10−7). This SNP is located in DnaJ homolog subfamily C member 5B (DNAJC5B) and merits investigation in additional randomized studies of pravastatin and other statins

Prediction of LDL cholesterol response to statin using transcriptomic and genetic variation

BACKGROUND: Statins are widely prescribed for lowering LDL-cholesterol (LDLC) levels and risk of cardiovascular disease. There is, however, substantial inter-individual variation in the magnitude of statin-induced LDLC reduction. To date, analysis of individual DNA sequence variants has explained only a small proportion of this variability. The present study was aimed at assessing whether transcriptomic analyses could be used to identify additional genetic contributions to inter-individual differences in statin efficacy. RESULTS: Using expression array data from immortalized lymphoblastoid cell lines derived from 372 participants of the Cholesterol and Pharmacogenetics clinical trial, we identify 100 signature genes differentiating high versus low statin responders. A radial-basis support vector machine prediction model of these signature genes explains 12.3% of the variance in statin-mediated LDLC change. Addition of SNPs either associated with expression levels of the signature genes (eQTLs) or previously reported to be associated with statin response in genome-wide association studies results in a combined model that predicts 15.0% of the variance. Notably, a model of the signature gene associated eQTLs alone explains up to 17.2% of the variance in the tails of a separate subset of the Cholesterol and Pharmacogenetics population. Furthermore, using a support vector machine classification model, we classify the most extreme 15% of high and low responders with high accuracy. CONCLUSIONS: These results demonstrate that transcriptomic information can explain a substantial proportion of the variance in LDLC response to statin treatment, and suggest that this may provide a framework for identifying novel pathways that influence cholesterol metabolism. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s13059-014-0460-9) contains supplementary material, which is available to authorized users