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Background Advanced glycation end-products are proteins that become glycated after contact with sugars and are implicated in endothelial dysfunction and arterial stiffening. We aimed to investigate the relationships between advanced glycation end-products, measured as skin autofluorescence, and vascular stiffness in various glycemic strata. Methods We performed a cross-sectional analysis within the European Prospective Investigation into Cancer and Nutrition (EPIC)-Potsdam cohort, comprising n = 3535 participants (median age 67 years, 60% women). Advanced glycation end-products were measured as skin autofluorescence with AGE-Reader (TM), vascular stiffness was measured as pulse wave velocity, augmentation index and ankle-brachial index with Vascular Explorer (TM). A subset of 1348 participants underwent an oral glucose tolerance test. Participants were sub-phenotyped into normoglycemic, prediabetes and diabetes groups. Associations between skin autofluorescence and various indices of vascular stiffness were assessed by multivariable regression analyses and were adjusted for age, sex, measures of adiposity and lifestyle, blood pressure, prevalent conditions, medication use and blood biomarkers. Results Skin autofluorescence associated with pulse wave velocity, augmentation index and ankle-brachial index, adjusted beta coefficients (95% CI) per unit skin autofluorescence increase: 0.38 (0.21; 0.55) for carotid-femoral pulse wave velocity, 0.25 (0.14; 0.37) for aortic pulse wave velocity, 1.00 (0.29; 1.70) for aortic augmentation index, 4.12 (2.24; 6.00) for brachial augmentation index and - 0.04 (- 0.05; - 0.02) for ankle-brachial index. The associations were strongest in men, younger individuals and were consistent across all glycemic strata: for carotid-femoral pulse wave velocity 0.36 (0.12; 0.60) in normoglycemic, 0.33 (- 0.01; 0.67) in prediabetes and 0.45 (0.09; 0.80) in diabetes groups; with similar estimates for aortic pulse wave velocity. Augmentation index was associated with skin autofluorescence only in normoglycemic and diabetes groups. Ankle-brachial index inversely associated with skin autofluorescence across all sex, age and glycemic strata. Conclusions Our findings indicate that advanced glycation end-products measured as skin autofluorescence might be involved in vascular stiffening independent of age and other cardiometabolic risk factors not only in individuals with diabetes but also in normoglycemic and prediabetic conditions. Skin autofluorescence might prove as a rapid and non-invasive method for assessment of macrovascular disease progression across all glycemic strata.
Throughfall, that is, the fraction of rainfall that passes through the forest canopy, is strongly influenced by rainfall and forest stand characteristics which are in turn both subject to seasonal dynamics. Disentangling the complex interplay of these controls is challenging, and only possible with long-term monitoring and a large number of throughfall events measured in parallel at different forest stands. We therefore based our analysis on 346 rainfall events across six different forest stands at the long-term terrestrial environmental observatory TERENO Northeast Germany. These forest stands included pure stands of beech, pine and young pine, and mixed stands of oak-beech, pine-beech and pine-oak-beech. Throughfall was overall relatively low, with 54-68% of incident rainfall in summer. Based on the large number of events it was possible to not only investigate mean or cumulative throughfall but also its statistical distribution. The distributions of throughfall fractions show distinct differences between the three types of forest stands (deciduous, mixed and pine). The distributions of the deciduous stands have a pronounced peak at low throughfall fractions and a secondary peak at high fractions in summer, as well as a pronounced peak at higher throughfall fractions in winter. Interestingly, the mixed stands behave like deciduous stands in summer and like pine stands in winter: their summer distributions are similar to the deciduous stands but the winter peak at high throughfall fractions is much less pronounced. The seasonal comparison further revealed that the wooden components and the leaves behaved differently in their throughfall response to incident rainfall, especially at higher rainfall intensities. These results are of interest for estimating forest water budgets and in the context of hydrological and land surface modelling where poor simulation of throughfall would adversely impact estimates of evaporative recycling and water availability for vegetation and runoff.
The aim of this paper is to bring together two areas which are of great importance for the study of overdetermined boundary value problems. The first area is homological algebra which is the main tool in constructing the formal theory of overdetermined problems. And the second area is the global calculus of pseudodifferential operators which allows one to develop explicit analysis.
We introduce a natural symmetry condition for a pseudodifferential operator on a manifold with cylindrical ends ensuring that the operator admits a doubling across the boundary. For such operators we prove an explicit index formula containing, apart from the Atiyah-Singer integral, a finite number of residues of the logarithmic derivative of the conormal symbol.
For general elliptic pseudodifferential operators on manifolds with singular points, we prove an algebraic index formula. In this formula the symbolic contributions from the interior and from the singular points are explicitly singled out. For two-dimensional manifolds, the interior contribution is reduced to the Atiyah-Singer integral over the cosphere bundle while two additional terms arise. The first of the two is one half of the 'eta' invariant associated to the conormal symbol of the operator at singular points. The second term is also completely determined by the conormal symbol. The example of the Cauchy-Riemann operator on the complex plane shows that all the three terms may be non-zero.
The index formula for elliptic pseudodifferential operators on a two-dimensional manifold with conical points contains the Atiyah-Singer integral as well as two additional terms. One of the two is the 'eta' invariant defined by the conormal symbol, and the other term is explicitly expressed via the principal and subprincipal symbols of the operator at conical points. In the preceding paper we clarified the meaning of the additional terms for first-order differential operators. The aim of this paper is an explicit description of the contribution of a conical point for higher-order differential operators. We show that changing the origin in the complex plane reduces the entire contribution of the conical point to the shifted 'eta' invariant. In turn this latter is expressed in terms of the monodromy matrix for an ordinary differential equation defined by the conormal symbol.
In the preceding paper we proved an explicit index formula for elliptic pseudodifferential operators on a two-dimensional manifold with conical points. Apart from the Atiyah-Singer integral, it contains two additional terms, one of the two being the 'eta' invariant defined by the conormal symbol. In this paper we clarify the meaning of the additional terms for differential operators.
We describe a natural construction of deformation quantisation on a compact symplectic manifold with boundary. On the algebra of quantum observables a trace functional is defined which as usual annihilates the commutators. This gives rise to an index as the trace of the unity element. We formulate the index theorem as a conjecture and examine it by the classical harmonic oscillator.