@unpublished{FedosovSchulzeTarkhanov1998, author = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {A remark on the index of symmetric operators}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25169}, year = {1998}, abstract = {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.}, language = {en} } @article{BirukovCuadratPolemitietal.2021, author = {Birukov, Anna and Cuadrat, Rafael R. C. and Polemiti, Elli and Eichelmann, Fabian and Schulze, Matthias Bernd}, title = {Advanced glycation end-products, measured as skin autofluorescence, associate with vascular stiffness in diabetic, pre-diabetic and normoglycemic individuals}, series = {Cardiovascular diabetology}, volume = {20}, journal = {Cardiovascular diabetology}, number = {1}, publisher = {BioMed Central}, address = {London}, issn = {1475-2840}, doi = {10.1186/s12933-021-01296-5}, pages = {11}, year = {2021}, abstract = {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.}, language = {en} } @article{MeraTarkhanov2022, author = {Mera, Azal Jaafar Musa and Tarkhanov, Nikolai}, title = {An elliptic equation of finite index in a domain}, series = {Boletin de la Sociedad Matem{\´a}tica Mexicana}, volume = {28}, journal = {Boletin de la Sociedad Matem{\´a}tica Mexicana}, number = {2}, publisher = {Springer International}, address = {New York [u.a.]}, issn = {1405-213X}, doi = {10.1007/s40590-022-00442-7}, pages = {10}, year = {2022}, abstract = {We give an example of first order elliptic equation for a complex-valued function in a plane domain which has a finite number of linearly independent solutions for any right-hand side. No boundary value conditions are thus required.}, language = {en} } @unpublished{FedchenkoTarkhanov2014, author = {Fedchenko, Dmitry and Tarkhanov, Nikolai Nikolaevich}, title = {An index formula for Toeplitz operators}, volume = {3}, number = {12}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-72499}, pages = {24}, year = {2014}, abstract = {We prove a Fedosov index formula for the index of Toeplitz operators connected with the Hardy space of solutions to an elliptic system of first order partial differential equations in a bounded domain of Euclidean space with infinitely differentiable boundary.}, language = {en} } @article{FedchenkoTarkhanov2015, author = {Fedchenko, Dmitri and Tarkhanov, Nikolai Nikolaevich}, title = {An index formula for Toeplitz operators}, series = {Complex variables and elliptic equations}, volume = {60}, journal = {Complex variables and elliptic equations}, number = {12}, publisher = {Routledge, Taylor \& Francis Group}, address = {Abingdon}, issn = {1747-6933}, doi = {10.1080/17476933.2015.1050007}, pages = {1764 -- 1787}, year = {2015}, abstract = {We prove a Fedosov index formula for the index of Toeplitz operators connected with the Hardy space of solutions to an elliptic system of first-order partial differential equations in a bounded domain in R-n with smooth boundary.}, language = {en} } @phdthesis{Weisshuhn2020, author = {Weißhuhn, Peter}, title = {Assessing biotope vulnerability to landscape changes}, doi = {10.25932/publishup-44277}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-442777}, school = {Universit{\"a}t Potsdam}, pages = {v, 134}, year = {2020}, abstract = {Largescale patterns of global land use change are very frequently accompanied by natural habitat loss. To assess the consequences of habitat loss for the remaining natural and semi-natural biotopes, inclusion of cumulative effects at the landscape level is required. The interdisciplinary concept of vulnerability constitutes an appropriate assessment framework at the landscape level, though with few examples of its application for ecological assessments. A comprehensive biotope vulnerability analysis allows identification of areas most affected by landscape change and at the same time with the lowest chances of regeneration. To this end, a series of ecological indicators were reviewed and developed. They measured spatial attributes of individual biotopes as well as some ecological and conservation characteristics of the respective resident species community. The final vulnerability index combined seven largely independent indicators, which covered exposure, sensitivity and adaptive capacity of biotopes to landscape changes. Results for biotope vulnerability were provided at the regional level. This seems to be an appropriate extent with relevance for spatial planning and designing the distribution of nature reserves. Using the vulnerability scores calculated for the German federal state of Brandenburg, hot spots and clusters within and across the distinguished types of biotopes were analysed. Biotope types with high dependence on water availability, as well as biotopes of the open landscape containing woody plants (e.g., orchard meadows) are particularly vulnerable to landscape changes. In contrast, the majority of forest biotopes appear to be less vulnerable. Despite the appeal of such generalised statements for some biotope types, the distribution of values suggests that conservation measures for the majority of biotopes should be designed specifically for individual sites. Taken together, size, shape and spatial context of individual biotopes often had a dominant influence on the vulnerability score. The implementation of biotope vulnerability analysis at the regional level indicated that large biotope datasets can be evaluated with high level of detail using geoinformatics. Drawing on previous work in landscape spatial analysis, the reproducible approach relies on transparent calculations of quantitative and qualitative indicators. At the same time, it provides a synoptic overview and information on the individual biotopes. It is expected to be most useful for nature conservation in combination with an understanding of population, species, and community attributes known for specific sites. The biotope vulnerability analysis facilitates a foresighted assessment of different land uses, aiding in identifying options to slow habitat loss to sustainable levels. It can also be incorporated into planning of restoration measures, guiding efforts to remedy ecological damage. Restoration of any specific site could yield synergies with the conservation objectives of other sites, through enhancing the habitat network or buffering against future landscape change. Biotope vulnerability analysis could be developed in line with other important ecological concepts, such as resilience and adaptability, further extending the broad thematic scope of the vulnerability concept. Vulnerability can increasingly serve as a common framework for the interdisciplinary research necessary to solve major societal challenges.}, language = {en} } @unpublished{FedchenkoTarkhanov2016, author = {Fedchenko, Dmitry and Tarkhanov, Nikolai Nikolaevich}, title = {Boundary value problems for elliptic complexes}, volume = {5}, number = {3}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-86705}, pages = {12}, year = {2016}, abstract = {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.}, language = {en} } @article{BlumeSchneiderGuentner2021, author = {Blume, Theresa and Schneider, Lisa and G{\"u}ntner, Andreas}, title = {Comparative analysis of throughfall observations in six different forest stands}, series = {Hydrological processes}, volume = {36}, journal = {Hydrological processes}, number = {3}, publisher = {Wiley}, address = {Hoboken}, issn = {0885-6087}, doi = {10.1002/hyp.14461}, pages = {21}, year = {2021}, abstract = {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.}, language = {en} } @unpublished{FedosovTarkhanov2015, author = {Fedosov, Boris and Tarkhanov, Nikolai Nikolaevich}, title = {Deformation quantisation and boundary value problems}, volume = {4}, number = {5}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-77150}, pages = {27}, year = {2015}, abstract = {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.}, language = {en} } @article{Tarkhanov2016, author = {Tarkhanov, Nikolai Nikolaevich}, title = {Deformation quantization and boundary value problems}, series = {International journal of geometric methods in modern physics : differential geometery, algebraic geometery, global analysis \& topology}, volume = {13}, journal = {International journal of geometric methods in modern physics : differential geometery, algebraic geometery, global analysis \& topology}, publisher = {World Scientific}, address = {Singapore}, issn = {0219-8878}, doi = {10.1142/S0219887816500079}, pages = {176 -- 195}, year = {2016}, abstract = {We describe a natural construction of deformation quantization 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.}, language = {en} }