Manifold-Based B-Splines on Unstructured Meshes

We introduce new manifold-based splines that are able to exactly reproduce B-splines on unstructured surface meshes. Such splines can be used in isogeometric analysis (IGA) to represent smooth surfaces of arbitrary topology. Since prevalent computer-aided design (CAD) models are composed of tensor-product B-spline patches, any IGA suitable construction should be able to reproduce B-splines. To achieve this goal, we focus on univariate manifold-based constructions that can reproduce B-splines. The manifold-based splines are constructed by smoothly blending together polynomial interpolants defined on overlapping charts. The proposed constructions automatically reproduce B-splines in regular parts of the mesh, with no extraordinary vertices, and polynomial basis functions in the remaining parts of the mesh. We study and compare analytically and numerically the finite element convergence of several univariate constructions. The obtained results directly carry over to the tensor-product case

Warum können Patientinnen mit Anorexia nervosa depressiv und trotzdem leistungsfähig sein? Die mögliche Bedeutung von emotionaler Suppression im Rahmen eines leistungsbetonten Experiments

BACKGROUND: Inappropriate aldosterone and parathyroid hormone (PTH) secretion is associated with increased cardiovascular risk. Accumulating evidence suggests bidirectional interplay between aldosterone and PTH. METHODS: We evaluated the cross-sectional relationship between plasma aldosterone concentration (PAC), aldosterone to renin ratio (ARR) and PTH and subsequently tested whether the interaction between PAC and PTH modified the risk of cardiovascular death. PAC [78.0 (48.0-123.0) pg/mL], ARR [6.4 (2.9-12.9) pg/mL/pg/mL] and PTH concentration [median: 29.0 (22.0-40.0) pg/mL] were measured in 3074 patients (mean age: 62.5 ± 10.6 years; 30.3% women) referred to coronary angiography in a tertiary care center in Southwest Germany. RESULTS: Using multiple linear regression analysis, PAC and ARR emerged as an independent predictor of higher PTH concentrations (β=0.12 and 0.21, P<0.001 for both) irrespective of intake of antihypertensive treatment, 25(OH)D, kidney function, serum calcium, phosphate, magnesium, cortisol, NT-pro-BNP, soluble α-klotho and FGF-23 concentration. After a median follow-up of 9.9 years, 512 (16.7%) participants had died due to fatal cardiovascular events. Multivariate Cox proportional hazard analysis revealed that both PAC and PTH were independently associated with cardiovascular mortality, with a potential synergistic interaction (P=0.028). PAC and PTH are exclusively associated with cardiovascular death in subjects with PTH and PAC concentrations above the median, respectively (PAC: HR per log SD: 1.14; 95% CI 1.02-1.29; P=0.026; PTH: HR per log SD: 1.18; 95% CI 1.02-1.37; P=0.031). CONCLUSIONS: Higher PAC and ARR were independently associated with PTH. PAC was independently related to incident cardiovascular mortality exclusively in patients with elevated PTH and vice versa