Assessing mesh convergence in discrete-fracture simulations that use random meshes

A pervasive fracturing process is one in which a multitude of cracks are dynamically active, propagating in arbitrary directions, coalescing, and branching. Pervasive fracturing is a highly nonlinear process involving complex material constitutive behavior, postpeak material softening, localization, new surface generation, and ubiquitous contact. A popular computational method for modeling pervasive fracture processes is to only allow fractures to propagate along interelement edges within a predefined finite-element mesh. With this approach, to avoid nonobjectivity in the simulation results, it is necessary to use a random mesh that has no preferred orientation. To define mesh convergence, simulation results are viewed in a weak or probabilistic sense rather than at the level of a single realization. For random variables, there are a number of different modes in which convergence may be understood. These are almost sure convergence, convergence in probability, and convergence in distribution. Each mode of convergence may be stronger or weaker than another. Herein, the fracture convergence assessment is based on demonstrating empirically the mode of convergence in distribution. Specifically, a sequence of cumulative distribution functions is verified to converge in the L∞ norm. The effect of finite sample sizes is quantified using confidence levels from the Kolmogorov–Smirnov statistic. This statistical method and convergence assessment is independent of the underlying distribution

Essai sur le rôle respectif de la déduction et de l'induction dans les principaux systèmes d'interprétation du droit civil français : thèse pour le doctorat... présentée... / par Nguyen Huy Man,... ; Université de Paris, Faculté de droit

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Additional file 1: of Anthropometric and blood parameters for the prediction of NAFLD among overweight and obese adults

Electronic Supplementary Material: Figure S1. Histogram of MRI-derived liver fat content (%) values. Figure S2. Spearman’s correlations (ρ) between liver fat, anthropometric parameters and biomarkers. Table S1. Associations between individual predictors and the odds ratio of non-alcoholic fatty liver disease, sorted by decreasing area under the receiver operator characteristic curve (AUROC)*. (DOCX 123 kb

Additional file 2: of Obesity as risk factor for subtypes of breast cancer: results from a prospective cohort study

Table S1. Characteristics of breast cancer cases with and without available immunohistochemistry (IHC) markers; Table S2. Antibodies; Table S3. Frequency of histological tumor types; Table S4. Hazard ratios of breast cancer across tertiles of BMI by clusters of breast tumors from hierarchical clustering, after exclusion of situ tumors; Table S5. Hazard ratios of luminal A breast cancer across tertiles of BMI; Table S6. Hazard ratios of breast cancer subtypes across tertiles of BMI among postmenopausal non-users of hormone therapy; Table S7. Hazard ratios of breast cancer subtypes across tertiles of BMI among postmenopausal users of hormone therapy; Table S8. Hazard ratios of breast cancer subtypes across tertiles of BMI among pre- and perimenopausal women; Table S9. Hazard ratios of breast cancer subtypes across tertiles of BMI among postmenopausal non-users of hormone therapy, after exclusion of situ tumors; Table S10. Hazard ratios of breast cancer subtypes across tertiles of BMI among postmenopausal users of hormone therapy, after exclusion of situ tumors; Table S11. Hazard ratios of breast cancer subtypes across tertiles of BMI among pre- and perimenopausal women, after exclusion of situ tumors. (DOCX 84 kb

Additional file 1: of Obesity as risk factor for subtypes of breast cancer: results from a prospective cohort study

Figure S1. Flow Chart. (DOCX 29 kb

DataSheet1_Changes in aortic diameter induced by weight loss: The HELENA trial- whole-body MR imaging in a dietary intervention trial.docx

Obesity-related metabolic disorders such as hypertension, hyperlipidemia and chronic inflammation have been associated with aortic dilatation and resulting in aortic aneurysms in many cases. Whether weight loss may reduce the risk of aortic dilatation is not clear. In this study, the diameter of the descending thoracic aorta, infrarenal abdominal aorta and aortic bifurcation of 144 overweight or obese non-smoking adults were measured by MR-imaging, at baseline, and 12 and 50 weeks after weight loss by calorie restriction. Changes in aortic diameter, anthropometric measures and body composition and metabolic markers were evaluated using linear mixed models. The association of the aortic diameters with the aforementioned clinical parameters was analyzed using Spearman`s correlation. Weight loss was associated with a reduction in the thoracic and abdominal aortic diameters 12 weeks after weight loss (predicted relative differences for Quartile 4: 2.5% ± 0.5 and -2.2% ± 0.8, p < 0.031; respectively). Furthermore, there was a nominal reduction in aortic diameters during the 50-weeks follow-up period. Aortic diameters were positively associated with weight, visceral adipose tissue, glucose, HbA1c and with both systolic and diastolic blood pressure. Weight loss induced by calorie restriction may reduce aortic diameters. Future studies are needed to investigate, whether the reduction of aortic diameters via calorie restriction may help to prevent aortic aneurysms.</p

Additional file 6 of Buffy coat signatures of breast cancer risk in a prospective cohort study

Additional file 6. Supplementary Table 6. Top GO Biological Processes, GO Cellular Components, GO Molecular Functions, Reactome, and KEGG Pathways enriched from significantly differentially methylated regions (FDR 0.075) identified when overlapping DMRs identified in the main analysis with DMRs identified when samples were limited to participants aged 50 and above at recruitment

Additional file 10 of Buffy coat signatures of breast cancer risk in a prospective cohort study

Additional file 10: Fig. S3. ROC curves for the tested classifiers. Individual ROC curves are shown for each cross-validation fold. SVM: support vector machines; PLR: penalized logistic regression; NNET: neural network; RF: random forests; LogitBoost: boosted logistic regressison; KNN: k-nearest neighbours; PAM: Prediction Analysis for Microarrays; RPART: classification and regression tre

Additional file 7 of Buffy coat signatures of breast cancer risk in a prospective cohort study

Additional file 7: Fig. S2. Relative proportions of hypermethylated, hypomethylated and all regions of the dataset when annotated by Enhancer status as annotated in the FANTOM5 enhancer atlas for the GM12878 human lymphoblastoid cell line; andgenic annotations

Additional file 8 of Buffy coat signatures of breast cancer risk in a prospective cohort study

Additional file 8. Supplementary Table 7. Genomic regions in which DNA methylation is significantly correlated to length of time to diagnosis (days) by Kendall rank correlation (FDR < 0.05)