@article{MickelssonPaycha2010, author = {Mickelsson, Jouko and Paycha, Sylvie}, title = {The logarithmic residue density of a generalized Laplacian}, series = {Journal of the Australian Mathematical Society}, volume = {90}, journal = {Journal of the Australian Mathematical Society}, number = {1}, publisher = {Cambridge Univ. Press}, address = {Cambridge}, issn = {0263-6115}, doi = {10.1017/S144678871100108X}, pages = {53 -- 80}, year = {2010}, abstract = {We show that the residue density of the logarithm of a generalized Laplacian on a closed manifold definesan invariant polynomial-valued differential form. We express it in terms of a finite sum of residues ofclassical pseudodifferential symbols. In the case of the square of a Dirac operator, these formulas providea pedestrian proof of the Atiyah-Singer formula for a pure Dirac operator in four dimensions and for atwisted Dirac operator on a flat space of any dimension. These correspond to special cases of a moregeneral formula by Scott and Zagier. In our approach, which is of perturbative nature, we use either aCampbell-Hausdorff formula derived by Okikiolu or a noncommutative Taylor-type formula.}, language = {en} } @misc{MickelssonPaycha2011, author = {Mickelsson, Jouko and Paycha, Sylvie}, title = {The logarithmic residue density of a generalized Laplacian}, series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, number = {649}, issn = {1866-8372}, doi = {10.25932/publishup-41368}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-413680}, pages = {28}, year = {2011}, abstract = {We show that the residue density of the logarithm of a generalized Laplacian on a closed manifold defines an invariant polynomial-valued differential form. We express it in terms of a finite sum of residues of classical pseudodifferential symbols. In the case of the square of a Dirac operator, these formulas provide a pedestrian proof of the Atiyah-Singer formula for a pure Dirac operator in four dimensions and for a twisted Dirac operator on a flat space of any dimension. These correspond to special cases of a more general formula by Scott and Zagier. In our approach, which is of perturbative nature, we use either a Campbell-Hausdorff formula derived by Okikiolu or a noncommutative Taylor-type formula.}, language = {en} } @phdthesis{Kunze2013, author = {Kunze, Matthias}, title = {Searching business process models by example}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-68844}, school = {Universit{\"a}t Potsdam}, year = {2013}, abstract = {Business processes are fundamental to the operations of a company. Each product manufactured and every service provided is the result of a series of actions that constitute a business process. Business process management is an organizational principle that makes the processes of a company explicit and offers capabilities to implement procedures, control their execution, analyze their performance, and improve them. Therefore, business processes are documented as process models that capture these actions and their execution ordering, and make them accessible to stakeholders. As these models are an essential knowledge asset, they need to be managed effectively. In particular, the discovery and reuse of existing knowledge becomes challenging in the light of companies maintaining hundreds and thousands of process models. In practice, searching process models has been solved only superficially by means of free-text search of process names and their descriptions. Scientific contributions are limited in their scope, as they either present measures for process similarity or elaborate on query languages to search for particular aspects. However, they fall short in addressing efficient search, the presentation of search results, and the support to reuse discovered models. This thesis presents a novel search method, where a query is expressed by an exemplary business process model that describes the behavior of a possible answer. This method builds upon a formal framework that captures and compares the behavior of process models by the execution ordering of actions. The framework contributes a conceptual notion of behavioral distance that quantifies commonalities and differences of a pair of process models, and enables process model search. Based on behavioral distances, a set of measures is proposed that evaluate the quality of a particular search result to guide the user in assessing the returned matches. A projection of behavioral aspects to a process model enables highlighting relevant fragments that led to a match and facilitates its reuse. The thesis further elaborates on two search techniques that provide concrete behavioral distance functions as an instantiation of the formal framework. Querying enables search with a notion of behavioral inclusion with regard to the query. In contrast, similarity search obtains process models that are similar to a query, even if the query is not precisely matched. For both techniques, indexes are presented that enable efficient search. Methods to evaluate the quality and performance of process model search are introduced and applied to the techniques of this thesis. They show good results with regard to human assessment and scalability in a practical setting.}, 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} } @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{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{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} } @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{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} }