Multigrid methods and stationary subdivisions

Multigridmethods are fast iterative solvers for sparse large ill-conditioned linear systems of equations derived, for instance, via discretization of PDEs in fluid dynamics, electrostatics and continuummechanics problems. Subdivision schemes are simple iterative algorithms for generation of smooth curves and surfaces with applications in 3D computer graphics and animation industry. This thesis presents the first definition and analysis of subdivision based multigrid methods. The main goal is to improve the convergence rate and the computational cost of multigrid taking advantage of the reproduction and regularity properties of underlying subdivision. The analysis focuses on the grid transfer operators appearing at the coarse grid correction step in the multigrid procedure. The convergence of multigrid is expressed in terms of algebraic properties of the trigonometric polynomial associated to the grid transfer operator. We interpreter the coarse-to-fine grid transfer operator as one step of subdivision. We reformulate the algebraic properties ensuring multigrid convergence in terms of regularity and generation properties of subdivision. The theoretical analysis is supported by numerical experiments for both algebraic and geometric multigrid. The numerical tests with the bivariate anisotropic Laplacian ask for subdivision schemes with anisotropic dilation. We construct a family of interpolatory subdivision schemes with such dilation which are optimal in terms of the size of the support versus their polynomial generation properties. The numerical tests confirmthe validity of our theoretical analysis

The role of coffee consumption in breast and ovarian cancer risk: updated meta-analyses

Background: Coffee consumption in relation to female hormone-related cancers has been investigated but metaanalyses regarding breast and ovarian cancer include studies published up to 2012 with inconsistent results for ovarian cancer. Methods: We conducted two updated meta-analyses of studies published up to June 2016 to quantify the association of coffee intake with breast and ovarian cancer risk with random effects models. We used the dataset developed by the International Agency for Research on Cancer Working Group for Monograph 116 meeting (May 2016). We additionally performed a PubMed search in June 2016. Results: Summary relative risks (RRs) (95% confidence intervals (CI)) for the study-specific highest vs. lowest coffee consumption were for breast and ovarian cancer respectively: 0.97 (0.93–1.00, Ι2 5.5%, 40 studies, 76,728 cases) and 1.03 (0.93–1.14, Ι 2 31.9%, 31 studies, 13,111 cases). For decaffeinated coffee the corresponding RRs were: 1.00 (0.93-1.08, I2 32.2%, 13 studies) and 0.83 (0.71-0.96, I2 about 0%, 9 studies). The association of coffee with ovarian cancer risk was higher among publications before (RR=1.37, 1.12–1.69) compared to after 2000 (RR=0.96, 0.86-1.06). Conclusion: Our meta-analyses provide strong, quantitative evidence that coffee consumption is not related to breast cancer risk and appears to be unrelated to ovarian cancer risk

Intake of prebiotic fibers and the risk of laryngeal cancer: the PrebiotiCa study

Purpose To evaluate whether the intake of specific fibers with prebiotic activity, e.g., inulin-type fructans (ITFs), fructo-oligosaccharides (FOSs), and galacto-oligosaccharides (GOSs), is associated with laryngeal cancer risk. Methods Within the PrebiotiCa study, we used data from a case-control study (Italy, 1992-2009) with 689 incident, histologically confirmed laryngeal cancer cases and 1605 controls. Six prebiotic molecules (ITFs, nystose [FOS], kestose [FOS], 1F-beta-fructofuranosylnystose [FOS], raffinose [GOS] and stachyose [GOS]) were quantified in various foods via ad hoc conducted laboratory analyses. Subjects' prebiotic fiber intake was calculated by multiplying food frequency questionnaire intake by the prebiotic content of each food item. The odds ratios (OR) of laryngeal cancer for prebiotic fiber intake were calculated using logistic regression models, including, among others, terms for tobacco, alcohol, and total energy intake. Results The intakes of kestose, raffinose and stachyose were inversely associated with laryngeal cancer, with ORs for the highest versus the lowest quartile of 0.70 (95% confidence interval, CI 0.50-0.99) for kestose, 0.65 (95% CI 0.45-0.93) for raffinose and 0.61 (95% CI 0.45-0.83) for stachyose. ITFs, nystose and 1F-beta-fructofuranosylnystose were not associated with laryngeal cancer risk. Current smokers and heavy drinkers with medium-low intakes of such prebiotic fibers had, respectively, an over 15-fold increased risk versus never smokers with medium-high intakes and a five to sevenfold increased risk versus never/moderate drinkers with medium-high intakes. Conclusion Although disentangling the effects of the various components of fiber-rich foods is complex, our results support a favorable role of selected prebiotic fibers on laryngeal cancers risk

Association of prebiotic fiber intake with colorectal cancer risk: the PrebiotiCa study

Purpose. To evaluate the association between the intake of specific fibers with prebiotic activity, namely inulin-type fructans (ITFs), fructooligosaccharides (FOSs) and galactooligosaccharides (GOSs), and colorectal cancer risk. Methods. Within the PrebiotiCa study, we used data from a multicentric case–control study conducted in Italy and including 1953 incident, histologically confirmed, colorectal cancer patients and 4154 hospital controls. The amount of six prebiotic molecules [ITFs, nystose (FOS), kestose (FOS), 1F-β-fructofuranosylnystose (FOS), raffinose (GOS) and stachyose (GOS)] in a variety of foods was quantified via laboratory analyses. Subjects’ prebiotic fiber intake was estimated by multiplying food frequency questionnaire intake by the prebiotic content of each food item. The odds ratios (OR) of colorectal cancer for quintiles of intakes were derived from logistic regression models including terms for major confounders and total energy intake. Results. GOSs intake was inversely associated with colorectal cancer risk. The OR for the highest versus the lowest quintile of intake were 0.73 (95% confidence interval, CI 0.58–0.92) for raffinose and 0.64 (95% CI 0.53–0.77) for stachyose, with significant inverse trends across quintiles. No association was found with total ITFs and FOSs. The association with stachyose was stronger for colon (continuous OR = 0.74, 95% CI 0.66–0.83) than rectal cancer (OR = 0.89, 95% CI 0.79–1.02). Conclusion. Colorectal cancer risk was inversely associated with the intake of dietary GOSs, but not ITFs and FOSs

Multigrid methods and stationary subdivisions

Multigridmethods are fast iterative solvers for sparse large ill-conditioned linear systems of equations derived, for instance, via discretization of PDEs in fluid dynamics, electrostatics and continuummechanics problems. Subdivision schemes are simple iterative algorithms for generation of smooth curves and surfaces with applications in 3D computer graphics and animation industry. This thesis presents the first definition and analysis of subdivision based multigrid methods. The main goal is to improve the convergence rate and the computational cost of multigrid taking advantage of the reproduction and regularity properties of underlying subdivision. The analysis focuses on the grid transfer operators appearing at the coarse grid correction step in the multigrid procedure. The convergence of multigrid is expressed in terms of algebraic properties of the trigonometric polynomial associated to the grid transfer operator. We interpreter the coarse-to-fine grid transfer operator as one step of subdivision. We reformulate the algebraic properties ensuring multigrid convergence in terms of regularity and generation properties of subdivision. The theoretical analysis is supported by numerical experiments for both algebraic and geometric multigrid. The numerical tests with the bivariate anisotropic Laplacian ask for subdivision schemes with anisotropic dilation. We construct a family of interpolatory subdivision schemes with such dilation which are optimal in terms of the size of the support versus their polynomial generation properties. The numerical tests confirmthe validity of our theoretical analysis

Determinants and correlates of adipose tissue insulin resistance index in Japanese women without diabetes and obesity

Introduction Determinants and correlates of a novel index of adipose tissue insulin resistance (AT-IR) (the product of fasting insulin and free fatty acid concentrations) were investigated in Japanese women without diabetes and obesity.Research design and methods Cross-sectional associations of AT-IR with fat mass and distribution, and IR-related cardiometabolic variables were examined in 210 young and 148 middle-aged women whose average body mass index (BMI) was <23 kg/m2 and waist was <80 cm. Multivariate linear regression analyses were used to identify most important determinants of AT-IR.Results Young and middle-aged women did not differ in AT-IR (3.5±2.7 and 3.2±2.1, respectively). In both young and middle-aged women, AT-IR was positively associated with trunk/leg fat ratio, a sophisticated measure of abdominal fat accumulation, fasting plasma glucose (FPG), fasting triglycerides (FTG), serum alanine aminotransferase and γ-glutamyl-transpeptidase (all p<0.05). Furthermore, in middle-aged but not in young women, AT-IR showed positive associations with BMI, waist, fat mass index, low-density lipoprotein cholesterol, apolipoprotein B and systolic and diastolic blood pressure (BP) (all p<0.05). AT-IR showed no association with hemoglobin A1c, high-density lipoprotein (HDL) cholesterol and apolipoprotein A1 in two groups of women. On multivariate analysis including waist, FPG, FTG, HDL cholesterol and systolic BP as independent variables, FPG, FTG and HDL cholesterol emerged as independent determinants of AT-IR in young women (cumulative R2=0.141) and waist in middle-aged women (cumulative R2=0.056). In a model which included trunk/leg fat ratio instead of waist, trunk/leg fat ratio and systolic BP were determinants of AT-IR in middle-aged women (cumulative R2=0.093). Results did not alter in young women.Conclusions AT-IR may be a simple and useful surrogate index of adipose tissue insulin resistance even in populations without diabetes and obesity

PERsistent Sitagliptin treatment & Outcomes (PERS&O 2.0) study, long-term results: a real-world observation on DPP4-inhibitor effectiveness

Introduction Sitagliptin is a dipeptidyl peptidase 4 inhibitor for the treatment of type 2 diabetes (T2D). Limited real-world data on its effectiveness and safety are available from an Italian population.Research design and methods We evaluated long-term clinical data from the single-arm PERsistent Sitagliptin Treatment & Outcomes (PERS&O) study, which collected information on 440 patients with TD2 (275 men, 165 women; mean age 64.1 years; disease median duration: 12 years) treated with sitagliptin ‘add-on’. For each patient, we estimated the 10-year cardiovascular (CV) risk using the UK Prospective Diabetes Study (UKPDS) Risk Engine (RE). Drug survival was evaluated using Kaplan-Meier survival curves; repeated measures mixed effects models were used to evaluate the evolution of glycated hemoglobin (HbA1c) and CV risk during sitagliptin treatment.Results At baseline, most patients were overweight or obese (median body mass index (BMI) (kg/m2) 30.2); median HbA1c was 8.4%; median fasting plasma glucose: 172 mg/dL; median UKPDS RE score: 24.8%, being higher in men (median 30.2%) than in women (median 17.0%) as expected. Median follow-up from starting sitagliptin treatment was 5.6 years. From Kaplan-Meier curves, the estimated median drug survival was 32.8 months when considering discontinuation for any cause and 58.4 months when considering discontinuation for loss of efficacy. A significant improvement in HbA1c was evident during treatment with sitagliptin (p<0.01): the reduction was rapid (median HbA1c after 4–6 months: 7.5%) and continued at longer follow-up. When comparing patients treated with sitagliptin versus those stopping sitagliptin and switching to another antihyperglycemic drug, we detected a significant difference in the evolution of HbA1c in favor of patients who continued sitagliptin treatment. The UKPDS RE score at 10 years and the BMI significantly improved during treatment with sitagliptin (p<0.001). Adverse events were relatively uncommon.Conclusion Patients with T2D treated with sitagliptin achieved an improvement in metabolic control and a reduction in CV risk and did not experience relevant adverse events

Effect of alcohol consumption and the presence of fatty liver on the risk for incident type 2 diabetes: a population-based longitudinal study

Introduction Both fatty liver disease (FLD) and alcohol consumption have been reported to affect incident type 2 diabetes mellitus. The aim of this study was to evaluate the combined effect of FLD and alcohol consumption on incident type 2 diabetes.Research design and methods In this historical cohort study involving 9948 men, we investigated the influence of the presence of FLD and the grades of alcohol consumption on incident type 2 diabetes using Cox proportional hazards models. We categorized the participants into the following four groups: none or minimal alcohol consumption, <40 g/week; light, 40–140 g/week; moderate, 140–280 g/week; or heavy alcohol consumption, >280 g/week. FLD was diagnosed by abdominal ultrasonography.Results During the median 6.0-year follow-up, 568 participants developed type 2 diabetes. Heavy alcohol consumers with FLD showed a higher risk for developing type 2 diabetes compared with the other groups. Moderate alcohol consumers without FLD had a significantly higher risk for developing incident type 2 diabetes, compared with none or minimal and light alcohol consumers without FLD. In contrast, there was no apparent difference in the risk for incident type 2 diabetes between none or minimal, light, and moderate alcohol consumers with FLD. Furthermore, there was no statistically significant difference in the risk for incident type 2 diabetes between a moderate and heavy alcohol consumer without FLD and a none or minimal, light, and moderate alcohol consumer with FLD.Conclusions To prevent incident type 2 diabetes, we should acknowledge that the impact of alcohol consumption may vary in the presence of FLD