The classical theory of calculus of variations for generalized functions

We present an extension of the classical theory of calculus of variations to generalized functions. The framework is the category of generalized smooth functions, which includes Schwartz distributions, while sharing many nonlinear properties with ordinary smooth functions. We prove full connections between extremals and Euler-Lagrange equations, classical necessary and sufficient conditions to have a minimizer, the necessary Legendre condition, Jacobi's theorem on conjugate points and Noether's theorem. We close with an application to low regularity Riemannian geometry

Association between global leukocyte DNA methylation and cardiovascular risk in postmenopausal women

BACKGROUND: Genetic studies to date have not provided satisfactory evidence regarding risk polymorphisms for cardiovascular disease (CVD). Conversely, epigenetic mechanisms, including DNA methylation, seem to influence the risk of CVD and related conditions. Because postmenopausal women experience an increase in CVD, we set out to determine whether global DNA methylation was associated with cardiovascular risk in this population. METHODS: In this cross sectional study carried out in a university hospital, 90 postmenopausal women without prior CVD diagnosis (55.5 ± 4.9 years, 5.8 [3.0–10.0] years since menopause) were enrolled. DNA was extracted from peripheral leukocytes and global DNA methylation levels were obtained with an ELISA kit. Cardiovascular risk was estimated by the Framingham General Cardiovascular Risk Score (10-year risk) (FRS). Clinical and laboratory variables were assessed. Patients were stratified into two CVD risk groups: low (FRS: <10 %, n = 69) and intermediate/high risk (FRS ≥10 %, n = 21). RESULTS: Age, time since menopause, blood pressure, total cholesterol, and LDL-c levels were higher in FRS ≥10 % group vs. FRS <10 % group. BMI, triglycerides, HDL-c, HOMA-IR, glucose and hsC-reactive protein levels were similar in the two groups. Global DNA methylation (% 5mC) in the overall sample was 26.5 % (23.6–36.9). The FRS ≥10 % group presented lower global methylation levels compared with the FRS <10 % group: 23.9 % (20.6–29.1) vs. 28.8 % (24.3–39.6), p = 0.02. This analysis remained significant even after adjustment for time since menopause (p = 0.02). CONCLUSIONS: Our results indicate that lower global DNA methylation is associated with higher cardiovascular risk in postmenopausal women

SHORT COMMUNICATION - Perspective of a New Diagnostic for Human Trichomonosis

Several diagnostic techniques have been employed for the detection of Trichomonas vaginalis . Microtubules constitute the cytoskeleton in eukaryotic cells and are sensitive to antimitotic drugs, such as Taxol (paclitaxel). We used FLUTAX a fluorescent taxoid - to analyze the microtubule distribution in living trophozoites of T. vaginalis in urine and in vaginal discharge. A high intensity of fluorescence was observed in living T. vaginalis , epithelial cells and leukocytes present in urine and vaginal discharge. Our preliminary results show the perspective of a new diagnostic technique for trichomonosis and will contribute to the understanding of the cytoskeleton of T. vaginalis