TY - INPR A1 - Fedosov, Boris A1 - Schulze, Bert-Wolfgang A1 - Tarkhanov, Nikolai Nikolaevich T1 - A remark on the index of symmetric operators N2 - 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. T3 - Preprint - (1998) 04 KW - manifolds with singularities KW - differential operators KW - index KW - 'eta' invariant Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25169 ER - TY - JOUR A1 - Birukov, Anna A1 - Cuadrat, Rafael R. C. A1 - Polemiti, Elli A1 - Eichelmann, Fabian A1 - Schulze, Matthias Bernd T1 - Advanced glycation end-products, measured as skin autofluorescence, associate with vascular stiffness in diabetic, pre-diabetic and normoglycemic individuals BT - a cross-sectional study JF - Cardiovascular diabetology N2 - 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. KW - Advanced glycation end-products KW - AGE KW - Ankle-brachial index KW - Augmentation KW - index KW - Prediabetes KW - Glycemia KW - Pulse wave velocity KW - Skin KW - autofluorescence KW - Vascular stiffness Y1 - 2021 U6 - https://doi.org/10.1186/s12933-021-01296-5 SN - 1475-2840 VL - 20 IS - 1 PB - BioMed Central CY - London ER - TY - JOUR A1 - Mera, Azal Jaafar Musa A1 - Tarkhanov, Nikolai T1 - An elliptic equation of finite index in a domain JF - Boletin de la Sociedad Matemática Mexicana N2 - 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. KW - elliptic equation KW - Fredholm operator KW - index Y1 - 2022 U6 - https://doi.org/10.1007/s40590-022-00442-7 SN - 1405-213X SN - 2296-4495 VL - 28 IS - 2 PB - Springer International CY - New York [u.a.] ER - TY - INPR A1 - Fedchenko, Dmitry A1 - Tarkhanov, Nikolai Nikolaevich T1 - An index formula for Toeplitz operators N2 - 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. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 3(2014)12 KW - Toeplitz operators KW - Fredholm property KW - index Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-72499 SN - 2193-6943 VL - 3 IS - 12 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Fedchenko, Dmitri A1 - Tarkhanov, Nikolai Nikolaevich T1 - An index formula for Toeplitz operators JF - Complex variables and elliptic equations N2 - 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. KW - Toeplitz operators KW - Fredholm property KW - index KW - Primary: 47B35 KW - Secondary: 47L80 Y1 - 2015 U6 - https://doi.org/10.1080/17476933.2015.1050007 SN - 1747-6933 SN - 1747-6941 VL - 60 IS - 12 SP - 1764 EP - 1787 PB - Routledge, Taylor & Francis Group CY - Abingdon ER - TY - THES A1 - Weißhuhn, Peter T1 - Assessing biotope vulnerability to landscape changes T1 - Bewertung der Vulnerabilität von Biotopen gegenüber Landschaftsveränderungen N2 - 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. N2 - Weltweit wurden in den vergangenen Jahrzehnten massive Veränderungen in der Landnutzung vorgenommen. Diese gingen meistens mit dem Verlust natürlicher Habitate einher. Um die Folgen auf die verbliebenen naturnahen Biotope zu bewerten, sind Analyseinstrumente notwendig, die neben einzelnen Flächen auch kumulative Effekte auf der Landschaftsebene einbeziehen. Das interdisziplinäre Konzept der Vulnerabilität kann einem solchen Analyseinstrument den Rahmen bieten. Bisher wurde es kaum für die Bewertung ökologischer Systeme herangezogen. Dabei kann eine flächendeckende Biotop-Vulnerabilitätsanalyse jene Gebiete identifizieren, die vom Landschaftswandel am stärksten betroffen sind und die gleichzeitig die geringsten Erholungsaussichten aufweisen. Dazu wurde eine Reihe ökologischer Indikatoren gesichtet und entwickelt, um die drei Vulnerabilitätsgrößen Exposition, Sensitivität und Anpassungskapazität abzudecken. Dabei wurden die Lagebeziehungen einzelner Biotope sowie die Eigenschaften der jeweils ansässigen Artengemeinschaft ausgewertet. Der errechnete Index kombiniert sieben voneinander weitestgehend unabhängige Indikatoren und stellt eine Übersicht der Biotop-Vulnerabilität dar. Liegt eine flächendeckende Vulnerabilitätsbewertung vor, können räumliche Häufungen von hohen Werten sowie die Verteilung der besonders hohen und besonders niedrigen Werte über die Biotoptypen hinweg analysiert werden. Dies erscheint besonders sinnvoll für Flächengrößen mit Relevanz für die Raumplanung und die Verteilung der Naturschutzflächen. Es stellte sich heraus, dass in der Planungsregion Brandenburg vor allem die Biotope mit hoher Abhängigkeit von der Wasserverfügbarkeit, sowie die Gehölze enthaltenden Offenlandbiotope (z.B. Streuobstwiesen) besonders vulnerabel gegenüber Landschaftsveränderungen sind. Im Gegensatz dazu erscheint die Mehrheit der Waldbiotope weniger verwundbar zu sein. Trotz der Möglichkeit zur Ableitung solcher verallgemeinerten Aussagen für einige Biotoptypen legt die Werteverteilung nahe, Naturschutzmaßnahmen mehrheitlich spezifisch für einzelne Flächen zu entwerfen. Größe, Form und räumlicher Kontext einzelner Biotopflächen üben zusammengenommen häufig einen dominanten Einfluss auf die Vulnerabilität gegenüber Landschaftsveränderungen aus. Die Demonstration der Biotop-Vulnerabilitätsanalyse auf regionaler Ebene zeigt, dass mit Methoden der Geoinformatik auch große Biotop-Datensätze detailliert ausgewertet werden können. Die damit erzielte naturschutzfachliche Analyse basiert auf transparent berechneten qualitativen und quantitativen Indikatoren und ist damit vollständig nachvollziehbar. Sie bietet gleichzeitig einen großräumigen Überblick sowie Informationen zu den einzelnen Biotopflächen. Mit der Vulnerabilitätsanalyse von Biotopen wird die vorausschauende Abwägung zwischen verschiedenen Landnutzungen erleichtert. Dies kann dazu beitragen, dass der Habitatverlust in Zukunft auf ein nachhaltigeres Maß gebremst wird. Auch kann eine solche Biotopbewertung in die Planung von Renaturierungsmaßnahmen einfließen, um ökologische Schäden zunächst dort zu beheben, wo große Synergieeffekte im Biotopverbund und mit anderen Naturschutzzielen zu erwarten sind. Die Biotop-Vulnerabilitätsanalyse konnte im Einklang mit wichtigen ökologischen Konzepten wie Resilienz und Anpassungsfähigkeit entwickelt werden. Sie erweitert damit den ohnehin breiten thematischen Anwendungsbereich des Vulnerabilitätskonzepts. Somit kann Vulnerabilität zunehmend als Brückenkonzept dienen und der zur Lösung der großen gesellschaftlichen Herausforderungen notwendigen interdisziplinären Forschung einen gemeinsamen Rahmen geben. KW - vulnerability KW - biotope KW - habitat KW - index KW - landscape KW - spatial ecology KW - landscape ecology KW - Vulnerabilität KW - Biotop KW - Habitat KW - Index KW - Landschaft KW - raumbezogene Ökologie KW - Landschaftsökologie Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-442777 ER - TY - INPR A1 - Fedchenko, Dmitry A1 - Tarkhanov, Nikolai Nikolaevich T1 - Boundary value problems for elliptic complexes N2 - 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. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 5 (2016) 3 KW - elliptic complexes KW - Fredholm property KW - index Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-86705 SN - 2193-6943 VL - 5 IS - 3 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Blume, Theresa A1 - Schneider, Lisa A1 - Güntner, Andreas T1 - Comparative analysis of throughfall observations in six different forest stands BT - Influence of seasons, rainfall- and stand characteristics JF - Hydrological processes N2 - 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. KW - forest hydrology KW - forest stand characteristics KW - interception KW - leaf area KW - index KW - rainfall characteristics KW - seasonal effects KW - stratified event KW - analysis KW - throughfall KW - tree species effects Y1 - 2021 U6 - https://doi.org/10.1002/hyp.14461 SN - 0885-6087 SN - 1099-1085 VL - 36 IS - 3 PB - Wiley CY - Hoboken ER - TY - INPR A1 - Fedosov, Boris A1 - Tarkhanov, Nikolai Nikolaevich T1 - Deformation quantisation and boundary value problems N2 - 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. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 4 (2015) 5 KW - symplectic manifold KW - star product KW - trace KW - index Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-77150 SN - 2193-6943 VL - 4 IS - 5 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Tarkhanov, Nikolai Nikolaevich T1 - Deformation quantization and boundary value problems JF - International journal of geometric methods in modern physics : differential geometery, algebraic geometery, global analysis & topology N2 - 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. KW - Symplectic manifold KW - star product KW - trace KW - index Y1 - 2016 U6 - https://doi.org/10.1142/S0219887816500079 SN - 0219-8878 SN - 1793-6977 VL - 13 SP - 176 EP - 195 PB - World Scientific CY - Singapore ER - TY - INPR A1 - Savin, Anton A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - Elliptic operators in subspaces N2 - We construct elliptic theory in the subspaces, determined by pseudodifferential projections. The finiteness theorem as well as index formula are obtained for elliptic operators acting in the subspaces. Topological (K-theoretic) aspects of the theory are studied in detail. T3 - Preprint - (2000) 04 KW - pseudodifferential subspaces KW - elliptic operators in subspaces KW - Fredholm property KW - index KW - K-theory KW - problem of classification Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25701 ER - TY - INPR A1 - Savin, Anton A1 - Sternin, Boris T1 - Index defects in the theory of nonlocal boundary value problems and the η-invariant N2 - The paper deals with elliptic theory on manifolds with boundary represented as a covering space. We compute the index for a class of nonlocal boundary value problems. For a nontrivial covering, the index defect of the Atiyah-Patodi-Singer boundary value problem is computed. We obtain the Poincaré duality in the K-theory of the corresponding manifolds with singularities. T3 - Preprint - (2001) 31 KW - elliptic operator KW - boundary value problem KW - finiteness theorem KW - nonlocal problem KW - covering KW - relative η-invariant KW - index KW - modn-index Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26146 ER - TY - INPR A1 - Fedosov, Boris A1 - Schulze, Bert-Wolfgang A1 - Tarkhanov, Nikolai Nikolaevich T1 - On the index formula for singular surfaces N2 - 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. T3 - Preprint - (1997) 31 KW - manifolds with singularities KW - differential operators KW - index KW - 'eta' invariant KW - monodromy matrix Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25116 ER - TY - INPR A1 - Savin, Anton A1 - Sternin, Boris T1 - Pseudodifferential subspaces and their applications in elliptic theory N2 - The aim of this paper is to explain the notion of subspace defined by means of pseudodifferential projection and give its applications in elliptic theory. Such subspaces are indispensable in the theory of well-posed boundary value problems for an arbitrary elliptic operator, including the Dirac operator, which has no classical boundary value problems. Pseudodifferential subspaces can be used to compute the fractional part of the spectral Atiyah–Patodi–Singer eta invariant, when it defines a homotopy invariant (Gilkey’s problem). Finally, we explain how pseudodifferential subspaces can be used to give an analytic realization of the topological K-group with finite coefficients in terms of elliptic operators. It turns out that all three applications are based on a theory of elliptic operators on closed manifolds acting in subspaces. T3 - Preprint - (2005) 17 KW - elliptic operator KW - boundary value problem KW - pseudodifferential subspace KW - dimension functional KW - η-invariant KW - index KW - modn-index KW - parity condition Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-29937 ER - TY - INPR A1 - Nazaikinskii, Vladimir A1 - Sternin, Boris T1 - Relative elliptic theory N2 - This paper is a survey of relative elliptic theory (i.e. elliptic theory in the category of smooth embeddings), closely related to the Sobolev problem, first studied by Sternin in the 1960s. We consider both analytic aspects to the theory (the structure of the algebra of morphismus, ellipticity, Fredholm property) and topological aspects (index formulas and Riemann-Roch theorems). We also study the algebra of Green operators arising as a subalgebra of the algebra of morphisms. T3 - Preprint - (2002) 23 KW - Sobolev problem KW - elliptic morphism KW - (co)boundary operator KW - Green operator KW - index KW - Riemann-Roch theorem Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26400 ER - TY - THES A1 - Kunze, Matthias T1 - Searching business process models by example T1 - Prozessmodellsuche mittels Beispielmodellen N2 - 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. N2 - Geschäftsprozesse bilden die Grundlage eines jeden Unternehmens, da jedes Produkt und jede Dienstleistung das Ergebnis einer Reihe von Arbeitsschritten sind, deren Ablauf einen Geschäftsprozess darstellen. Das Geschäftsprozessmanagement rückt diese Prozesse ins Zentrum der Betrachtung und stellt Methoden bereit, um Prozesse umzusetzen, abzuwickeln und, basierend auf einer Auswertung ihrer Ausführung, zu verbessern. Zu diesem Zweck werden Geschäftsprozesse in Form von Prozessmodellen dokumentiert, welche die auszuführenden Arbeitsschritte und ihre Ausführungsbeziehungen erfassen und damit eine wesentliche Grundlage des Geschäftsprozessmanagements bilden. Um dieses Wissen verwerten zu können, muss es gut organisiert und leicht auffindbar sein – eine schwierige Aufgabe angesichts hunderter bzw. tausender Prozessmodelle, welche moderne Unternehmen unterhalten. In der Praxis haben sich bisher lediglich einfache Suchmethoden etabliert, zum Beispiel Freitextsuche in Prozessbeschreibungen. Wissenschaftliche Ansätze hingegen betrachten Ähnlichkeitsmaße und Anfragesprachen für Prozessmodelle, vernachlässigen dabei aber Maßnahmen zur effizienten Suche, sowie die verständliche Wiedergabe eines Suchergebnisses und Hilfestellungen für dessen Verwendung. Diese Dissertation stellt einen neuen Ansatz für die Prozessmodellsuche vor, wobei statt einer Anfragesprache Prozessmodelle zur Formulierung einer Anfrage verwendet werden, welche exemplarisch das Verhalten der gesuchten Prozesse beschreiben. Dieser Ansatz fußt auf einem formalen Framework, welches ein konzeptionelles Distanzmaß zur Bewertung gemeinsamen Verhaltens zweier Geschäftsprozesse definiert und die Grundlage zur Suche bildet. Darauf aufbauend werden Qualitätsmaße vorgestellt, die einem Benutzer bei der Bewertung von Suchergebnissen behilflich sind. Verhaltensausschnitte, die zur Aufnahme in das Suchergebnis geführt haben, können im Prozessmodell hervorgehoben werden. Die Arbeit führt zwei Suchtechniken ein, die konkrete Distanzmaße einsetzen, um Prozesse zu suchen, die das Verhalten einer Anfrage exakt enthalten (Querying), oder diesem in Bezug auf das Verhalten ähnlich sind (Similarity Search). Für beide Techniken werden Indexstrukturen vorgestellt, die effizientes Suchen ermöglichen. Abschließend werden allgemeine Methoden zur Evaluierung von Prozessmodellsuchansätzen vorgestellt, mit welchen die genannten Suchtechniken überprüft werden. Im Ergebnis zeigen diese eine hohe Qualität der Suchergebnisse hinsichtlich einer Vergleichsstudie mit Prozessexperten, sowie gute Skalierbarkeit für große Prozessmodellsammlungen. KW - Prozessmodellsuche KW - Ähnlichkeit KW - Query KW - Index KW - Präsentation KW - process model search KW - similarity KW - querying KW - index KW - presentation Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-68844 ER - TY - INPR A1 - Fedosov, Boris A1 - Schulze, Bert-Wolfgang A1 - Tarkhanov, Nikolai Nikolaevich T1 - The index of elliptic operators on manifolds with conical points N2 - 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. T3 - Preprint - (1997) 24 KW - manifolds with singularities KW - pseudodifferential operators KW - elliptic operators KW - index Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25096 ER - TY - INPR A1 - Fedosov, Boris A1 - Schulze, Bert-Wolfgang A1 - Tarkhanov, Nikolai Nikolaevich T1 - The index of higher order operators on singular surfaces N2 - 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. T3 - Preprint - (1998) 03 KW - manifolds with singularities KW - differential operators KW - index KW - 'eta' invariant KW - monodromy matrix Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25127 ER - TY - JOUR A1 - Mickelsson, Jouko A1 - Paycha, Sylvie T1 - The logarithmic residue density of a generalized Laplacian JF - Journal of the Australian Mathematical Society N2 - 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. KW - residue KW - index KW - Dirac operators Y1 - 2011 U6 - https://doi.org/10.1017/S144678871100108X SN - 0263-6115 SN - 1446-8107 VL - 90 IS - 1 SP - 53 EP - 80 PB - Cambridge Univ. Press CY - Cambridge ER - TY - GEN A1 - Mickelsson, Jouko A1 - Paycha, Sylvie T1 - The logarithmic residue density of a generalized Laplacian T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - 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. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 649 KW - residue KW - index KW - Dirac operators Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-413680 SN - 1866-8372 IS - 649 ER -