Poisson brackets symmetry from the pentagon-wheel cocycle in the graph complex

Kontsevich designed a scheme to generate infinitesimal symmetries $\dot{\mathcal{P}} = \mathcal{Q}(\mathcal{P})$ of Poisson brackets $\mathcal{P}$ on all affine manifolds $M^r$; every such deformation is encoded by oriented graphs on $n+2$ vertices and $2n$ edges. In particular, these symmetries can be obtained by orienting sums of non-oriented graphs $\gamma$ on $n$ vertices and $2n-2$ edges. The bi-vector flow $\dot{\mathcal{P}} = \text{Or}(\gamma)(\mathcal{P})$ preserves the space of Poisson structures if $\gamma$ is a cocycle with respect to the vertex-expanding differential in the graph complex. A class of such cocycles $\boldsymbol{\gamma}_{2\ell+1}$ is known to exist: marked by $\ell \in \mathbb{N}$, each of them contains a $(2\ell+1)$-gon wheel with a nonzero coefficient. At $\ell=1$ the tetrahedron $\boldsymbol{\gamma}_3$ itself is a cocycle; at $\ell=2$ the Kontsevich--Willwacher pentagon-wheel cocycle $\boldsymbol{\gamma}_5$ consists of two graphs. We reconstruct the symmetry $\mathcal{Q}_5(\mathcal{P}) = \text{Or}(\boldsymbol{\gamma}_5)(\mathcal{P})$ and verify that $\mathcal{Q}_5$ is a Poisson cocycle indeed: $[\![\mathcal{P},\mathcal{Q}_5(\mathcal{P})]\!]\doteq 0$ via $[\![\mathcal{P},\mathcal{P}]\!]=0$.Comment: Int. workshop "Supersymmetries and quantum symmetries -- SQS'17" (July 31 -- August 5, 2017 at JINR Dubna, Russia), 4+v pages, 2 figures, 1 tabl

A polymorphism in the 3' untranslated region of the gene encoding prostaglandin endoperoxide synthase 2 is not associated with an increase in breast cancer risk: a nested case-control study

INTRODUCTION: Prostaglandins are integral components in the cellular response to inflammation, promoting cellular proliferation and angiogenesis. The enzyme responsible for the conversion of arachidonic acid to prostaglandins in response to inflammation is prostaglandin endoperoxide synthase 2/cyclo-oxygenase 2 (PTGS2/COX2). Polymorphisms in the PTGS2 gene have been associated with various diseases, including inflammatory bowel disease and cancer of the lung, colorectum, and breast. METHODS: We genotyped the five most common polymorphisms (rs20417, rs5277, rs20432, rs5275, and rs4648298) in the Nurses' Health Study (1,270 cases, 1,762 controls) to test the hypothesis that polymorphisms in PTGS2 are associated with breast cancer risk, using logistic regression analyses. The Nurses' Health Study 2 (317 cases, 634 controls) and Harvard Women's Health Study (702 cases, 703 controls) were used to further examine putative associations. RESULTS: The rs5275 polymorphism in the 3' untranslated region of the PTGS2 gene was associated with a decrease in breast cancer risk. We therefore genotyped this single-nucleotide polymorphism in the Nurses' Health Study 2 and Harvard Women's Health Study. Similar results were observed in these subsequent analyses, with no statistically significant heterogeneity in risk estimates between studies. In pooled analyses, women homozygous for the T allele at rs5275 had a 20% lower risk of breast cancer than those homozygous for the C allele (odds ratio 0.80, 95% confidence interval 0.66 to 0.97). CONCLUSION: Although this polymorphism may be associated with a decrease in breast cancer risk among Caucasian women, we provide strong evidence that it is not associated with an increased risk of breast cancer

Migraine, vascular risk, and cardiovascular events in women: prospective cohort study

Objectives To evaluate whether the association between migraine with aura and increased risk of cardiovascular disease is modified by vascular risk groups as measured by the Framingham risk score for coronary heart disease

Awareness, Accuracy, and Predictive Validity of Self-reported Cholesterol in Women

Background: Although current guidelines emphasize the importance of cholesterol knowledge, little is known about accuracy of this knowledge, factors affecting accuracy, and the relationship of self-reported cholesterol with cardiovascular disease (CVD). Methods: The 39,876 female health professionals with no prior CVD in the Women’s Health Study were asked to provide self-reported and measured levels of total and high-density lipoprotein (HDL) cholesterol. Demographic and cardiovascular risk factors were considered as determinants of awareness and accuracy. Accuracy was evaluated by the difference between reported and measured cholesterol. In addition, we examined the relationship of self-reported cholesterol with incident CVD over 10 years. Results: Compared with women who were unaware of their cholesterol levels, aware women (84%) had higher levels of income, education, and exercise and were more likely to be married, normal in weight, treated for hypertension and hypercholesterolemia, nonsmokers, moderate drinkers, and users of hormone therapy. Women underestimated their total cholesterol by 9.7 mg/dL (95% CI: 9.2–10.2); covariates explained little of this difference (R$^2$ < .01). Higher levels of self-reported cholesterol were strongly associated with increased risk of CVD, which occurred in 741 women (hazard ratio 1.23/40 mg/dL cholesterol, 95% CI: 1.15–1.33). Women with elevated cholesterol who were unaware of their level had particularly increased risk (HR=1.88, P < .001) relative to aware women with normal measured cholesterol. Conclusion: Women with obesity, smoking, untreated hypertension, or sedentary lifestyle have decreased awareness of their cholesterol levels. Self-reported cholesterol underestimates measured values, but is strongly related to CVD. Lack of awareness of elevated cholesterol is associated with increased risk of CVD

Socioeconomic status, blood pressure progression, and incident hypertension in a prospective cohort of female health professionals

Aims The aim of this study was to examine the association between socioeconomic status, blood pressure (BP) progression, and incident hypertension. Methods and results We included 27 207 female health professionals free of hypertension and cardiovascular disease at baseline. Participants were classified into five education and six income categories. The main outcome variables were BP progression at 48 months of follow-up and incident hypertension during the entire study period. At 48 months, 48.1% of women had BP progression. The multivariable adjusted relative risks [95% confidence intervals (CIs)] for BP progression were 1.0 (referent), 0.96 (0.92-1.00), 0.92 (0.88-0.96), 0.90 (0.85-0.94), and 0.84 (0.78-0.91) (P for trend <0.0001) across increasing education categories and 1.0 (referent), 1.01 (0.94-1.08), 0.99 (0.93-1.06), 0.97 (0.91-1.04), 0.96 (0.90-1.03), and 0.89 (0.83-0.96) across increasing income categories (P for trend = 0.0001). During a median follow-up of 9.8 years, 8248 cases of incident hypertension occurred. Multivariable adjusted hazard ratios (95% CI) were 1.0 (referent), 0.92 (0.86-0.99), 0.85 (0.79-0.92), 0.87 (0.80-0.94), and 0.74 (0.65-0.84) (P for trend <0.0001) across increasing education categories and 1.0 (referent), 1.07 (0.95-1.21), 1.07 (0.95-1.20), 1.06 (0.94-1.18), 1.04 (0.93-1.16), and 0.93 (0.82-1.06) (P for trend 0.08) across increasing income categories. In joint analyses, education but not income remained associated with BP progression and incident hypertension. Conclusion Socioeconomic status, as determined by education but not by income, is a strong independent predictor of BP progression and incident hypertension in wome

Job Strain, Job Insecurity, and Incident Cardiovascular Disease in the Women’s Health Study: Results from a 10-Year Prospective Study

Objectives: Research about work-related stressors and cardiovascular disease (CVD) has produced mixed findings. Moreover, a paucity of data exists regarding the long-term associations between job strain and job insecurity and CVD among women. Methods We used Cox proportional hazard models to examine the relationship between job strain, job insecurity, and incident CVD over 10 years of follow-up among 22,086 participants in the Women’s Health Study (mean age 57±5 years). Results: During 10 years of follow-up there were 170 myocardial infarctions (MI), 163 ischemic strokes, 440 coronary revascularizations, and 52 CVD deaths. In models adjusted for age, race, education, and income, women with high job strain (high demand, low control) were 38% more likely to experience a CVD event than their counterparts who reported low job strain (low demand, high control; Rate Ratio (RR) = 1.38, 95% Confidence Interval (CI) = 1.08–1.77), and women with active jobs (high demand, high control) were 38% more likely to experience a CVD event relative to women who reported low job strain (95% CI = 1.07–1.77). Outcome-specific analyses revealed that high job strain predicted non-fatal myocardial infarction (RR = 1.67, CI = 1.04–2.70), and coronary revascularization (RR = 1.41, CI = 1.05–1.90). No evidence of an association between job insecurity and long-term CVD risk was observed. Conclusion: High strain and active jobs, but not job insecurity, were related to increased CVD risk among women. Both job strain and job insecurity were significantly related to CVD risk factors. With the increase of women in the workforce, these data emphasize the importance of addressing job strain in CVD prevention efforts among working women.African and African American Studie

Prospective Cohort Study of Type 2 Diabetes and the Risk of Parkinson's Disease

OBJECTIVE—To evaluate the association between type 2 diabetes and newly reported Parkinson's disease

The Mitochondrial A10398G Polymorphism, Interaction with Alcohol Consumption, and Breast Cancer Risk

Polymorphisms in the mitochondrial genome are hypothesized to be associated with risk of various diseases, including cancer. However, there has been conflicting evidence for associations between a common polymorphism in the mitochondrial genome (A10398G, G10398A in some prior reports) and breast cancer risk. Reactive oxygen species, a by-product of mitochondrial energy production, can lead to oxidative stress and DNA damage in both the mitochondria and their cells. Alcohol consumption, which may also lead to oxidative stress, is associated with breast cancer risk. Therefore, we hypothesized that polymorphisms in the mitochondrial genome interact with alcohol consumption to alter breast cancer risk. We genotyped the A10398G polymorphism in a case-control study nested within the Nurses' Health Study (NHS, 1,561 cases, 2,209 controls). We observed an interaction between alcohol consumption (yes/no) and A10398G on breast cancer risk (p-int = 0.03). The risk associated with alcohol consumption was limited to carriers of the 10398G allele (Odds Ratio 1.52, 95% Confidence Interval 1.10–2.08 comparing drinkers to non-drinkers). However, we were unable to replicate these findings in the Women's Health Study (WHS, 678 cases, 669 controls), although the power to detect this interaction in the WHS was low (power = 0.57). Further examination of this interaction, such as sufficiently powered epidemiological studies of cancer risk or associations with biomarkers of oxidative stress, may provide further evidence for GxE interactions between the A10398G mitochondrial polymorphism and alcohol consumption on breast cancer risk