@unpublished{SchulzeTarkhanov1998, author = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {Elliptic complexes of pseudodifferential operators on manifolds with edges}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25257}, year = {1998}, abstract = {On a compact closed manifold with edges live pseudodifferential operators which are block matrices of operators with additional edge conditions like boundary conditions in boundary value problems. They include Green, trace and potential operators along the edges, act in a kind of Sobolev spaces and form an algebra with a wealthy symbolic structure. We consider complexes of Fr{\´e}chet spaces whose differentials are given by operators in this algebra. Since the algebra in question is a microlocalization of the Lie algebra of typical vector fields on a manifold with edges, such complexes are of great geometric interest. In particular, the de Rham and Dolbeault complexes on manifolds with edges fit into this framework. To each complex there correspond two sequences of symbols, one of the two controls the interior ellipticity while the other sequence controls the ellipticity at the edges. The elliptic complexes prove to be Fredholm, i.e., have a finite-dimensional cohomology. Using specific tools in the algebra of pseudodifferential operators we develop a Hodge theory for elliptic complexes and outline a few applications thereof.}, language = {en} } @unpublished{SchulzeTarkhanov2000, author = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {Pseudodifferential operators on manifolds with corners}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25783}, year = {2000}, abstract = {We describe an algebra of pseudodifferential operators on a manifold with corners.}, language = {en} } @unpublished{SchulzeTarkhanov2005, author = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {Boundary value problems with Toeplitz conditions}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29837}, year = {2005}, abstract = {We describe a new algebra of boundary value problems which contains Lopatinskii elliptic as well as Toeplitz type conditions. These latter are necessary, if an analogue of the Atiyah-Bott obstruction does not vanish. Every elliptic operator is proved to admit up to a stabilisation elliptic conditions of such a kind. Corresponding boundary value problems are then Fredholm in adequate scales of spaces. The crucial novelty consists of the new type of weighted Sobolev spaces which serve as domains of pseudodifferential operators and which fit well to the nature of operators.}, language = {en} } @unpublished{SchulzeTarkhanov1998, author = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {Euler solutions of pseudodifferential equations}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25211}, year = {1998}, abstract = {We consider a homogeneous pseudodifferential equation on a cylinder C = IR x X over a smooth compact closed manifold X whose symbol extends to a meromorphic function on the complex plane with values in the algebra of pseudodifferential operators over X. When assuming the symbol to be independent on the variable t element IR, we show an explicit formula for solutions of the equation. Namely, to each non-bijectivity point of the symbol in the complex plane there corresponds a finite-dimensional space of solutions, every solution being the residue of a meromorphic form manufactured from the inverse symbol. In particular, for differential equations we recover Euler's theorem on the exponential solutions. Our setting is model for the analysis on manifolds with conical points since C can be thought of as a 'stretched' manifold with conical points at t = -infinite and t = infinite.}, language = {en} } @unpublished{SchulzeTarkhanov1997, author = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {Lefschetz theory on manifolds with edges : introduction}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-24948}, year = {1997}, abstract = {The aim of this book is to develop the Lefschetz fixed point theory for elliptic complexes of pseudodifferential operators on manifolds with edges. The general Lefschetz theory contains the index theory as a special case, while the case to be studied is much more easier than the index problem. The main topics are: - The calculus of pseudodifferential operators on manifolds with edges, especially symbol structures (inner as well as edge symbols). - The concept of ellipticity, parametrix constructions, elliptic regularity in Sobolev spaces. - Hodge theory for elliptic complexes of pseudodifferential operators on manifolds with edges. - Development of the algebraic constructions for these complexes, such as homotopy, tensor products, duality. - A generalization of the fixed point formula of Atiyah and Bott for the case of simple fixed points. - Development of the fixed point formula also in the case of non-simple fixed points, provided that the complex consists of diferential operarators only. - Investigation of geometric complexes (such as, for instance, the de Rham complex and the Dolbeault complex). Results in this direction are desirable because of both purely mathe matical reasons and applications in natural sciences.}, language = {en} } @unpublished{SchulzeTarkhanov1998, author = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {A Lefschetz fixed point formula in the relative elliptic theory}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25159}, year = {1998}, abstract = {A version of the classical Lefschetz fixed point formula is proved for the cohomology of the cone of a cochain mapping of elliptic complexes. As a particular case we show a Lefschetz formula for the relative de Rham cohomology.}, language = {en} } @book{SchulzeTarkhanov2003, author = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {Symbol algebra for manifolds with cuspidal singularities}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {37 S.}, year = {2003}, language = {en} } @unpublished{SchulzeTarkhanov2000, author = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {Asymptotics of solutions to elliptic equatons on manifolds with corners}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25716}, year = {2000}, abstract = {We show an explicit link between the nature of a singular point and behaviour of the coefficients of the equation, under which formal asymptotic expansions are still available.}, language = {en} } @unpublished{SchulzeVolpato2004, author = {Schulze, Bert-Wolfgang and Volpato, A.}, title = {Green operators in the edge calculus}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26846}, year = {2004}, abstract = {Green operators on manifolds with edges are known to be an ingredient of parametrices of elliptic (edge-degenerate) operators. They play a similar role as corresponding operators in boundary value problems. Close to edge singularities the Green operators have a very complex asymptotic behaviour. We give a new characterisation of Green edge symbols in terms of kernels with discrete and continuous asymptotics in the axial variable of local model cones.}, language = {en} } @book{SchulzeVolpato2004, author = {Schulze, Bert-Wolfgang and Volpato, A.}, title = {Green operators in the edge calculus}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {24 S.}, year = {2004}, language = {en} } @unpublished{SchulzeWei2008, author = {Schulze, Bert-Wolfgang and Wei, Y.}, title = {Edge-boundary problems with singular trace conditions}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30317}, year = {2008}, abstract = {The ellipticity of boundary value problems on a smooth manifold with boundary relies on a two-component principal symbolic structure (σψ; σ∂), consisting of interior and boundary symbols. In the case of a smooth edge on manifolds with boundary we have a third symbolic component, namely the edge symbol σ∧, referring to extra conditions on the edge, analogously as boundary conditions. Apart from such conditions in integral form' there may exist singular trace conditions, investigated in [6] on closed' manifolds with edge. Here we concentrate on the phenomena in combination with boundary conditions and edge problem.}, language = {en} } @article{SchulzeWei2014, author = {Schulze, Bert-Wolfgang and Wei, Y.}, title = {The Mellin-edge quantisation for corner operators}, series = {Complex analysis and operator theory}, volume = {8}, journal = {Complex analysis and operator theory}, number = {4}, publisher = {Springer}, address = {Basel}, issn = {1661-8254}, doi = {10.1007/s11785-013-0289-3}, pages = {803 -- 841}, year = {2014}, abstract = {We establish a quantisation of corner-degenerate symbols, here called Mellin-edge quantisation, on a manifold with second order singularities. The typical ingredients come from the "most singular" stratum of which is a second order edge where the infinite transversal cone has a base that is itself a manifold with smooth edge. The resulting operator-valued amplitude functions on the second order edge are formulated purely in terms of Mellin symbols taking values in the edge algebra over . In this respect our result is formally analogous to a quantisation rule of (Osaka J. Math. 37:221-260, 2000) for the simpler case of edge-degenerate symbols that corresponds to the singularity order 1. However, from the singularity order 2 on there appear new substantial difficulties for the first time, partly caused by the edge singularities of the cone over that tend to infinity.}, language = {en} } @book{SchulzeWei2008, author = {Schulze, Bert-Wolfgang and Wei, Ya-wei}, title = {Edge-boundary problems with singular trace conditions}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {21 S.}, year = {2008}, language = {en} } @article{SchulzeWei2009, author = {Schulze, Bert-Wolfgang and Wei, Ya-wei}, title = {Edge-boundary problems with singular trace conditions}, issn = {0232-704X}, doi = {10.1007/s10455-008-9143-7}, year = {2009}, abstract = {The ellipticity of boundary value problems on a smooth manifold with boundary relies on a two-component principal symbolic structure (sigma(psi), sigma(partial derivative)), consisting of interior and boundary symbols. In the case of a smooth edge on manifolds with boundary, we have a third symbolic component, namely, the edge symbol sigma(boolean AND), referring to extra conditions on the edge, analogously as boundary conditions. Apart from such conditions 'in integral form' there may exist singular trace conditions, investigated in Kapanadze et al., Internal Equations and Operator Theory, 61, 241-279, 2008 on 'closed' manifolds with edge. Here, we concentrate on the phenomena in combination with boundary conditions and edge problem.}, language = {en} } @phdthesis{Schwarz2020, author = {Schwarz, Michael}, title = {Nodal domains and boundary representation for Dirichlet forms}, school = {Universit{\"a}t Potsdam}, pages = {164}, year = {2020}, language = {en} } @article{SeegererRomeike2018, author = {Seegerer, Stefan and Romeike, Ralf}, title = {Was jeder {\"u}ber Informatik lernen sollte}, series = {Commentarii informaticae didacticae}, journal = {Commentarii informaticae didacticae}, number = {12}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-416298}, pages = {13 -- 28}, year = {2018}, abstract = {Um f{\"u}r ein Leben in der digitalen Gesellschaft vorbereitet zu sein, braucht jeder heute in verschiedenen Situationen umfangreiche informatische Grundlagen. Die Bedeutung von Informatik nimmt nicht nur in immer mehr Bereichen unseres t{\"a}glichen Lebens zu, sondern auch in immer mehr Ausbildungsrichtungen. Um junge Menschen auf ihr zuk{\"u}nftiges Leben und/oder ihre zuk{\"u}nftige berufliche T{\"a}tigkeit vorzubereiten, bieten verschiedene Hochschulen Informatikmodule f{\"u}r Studierende anderer Fachrichtungen an. Die Materialien jener Kurse bilden einen umfangreichen Datenpool, um die f{\"u}r Studierende anderer F{\"a}cher bedeutenden Aspekte der Informatik mithilfe eines empirischen Ansatzes zu identifizieren. Im Folgenden werden 70 Module zu informatischer Bildung f{\"u}r Studierende anderer Fachrichtungen analysiert. Die Materialien - Publikationen, Syllabi und Stundentafeln - werden zun{\"a}chst mit einer qualitativen Inhaltsanalyse nach Mayring untersucht und anschließend quantitativ ausgewertet. Basierend auf der Analyse werden Ziele, zentrale Themen und Typen eingesetzter Werkzeuge identifiziert.}, language = {de} } @article{SeeligRabeMalemShinitskietal.2020, author = {Seelig, Stefan A. and Rabe, Maximilian Michael and Malem-Shinitski, Noa and Risse, Sarah and Reich, Sebastian and Engbert, Ralf}, title = {Bayesian parameter estimation for the SWIFT model of eye-movement control during reading}, series = {Journal of mathematical psychology}, volume = {95}, journal = {Journal of mathematical psychology}, publisher = {Elsevier}, address = {San Diego}, issn = {0022-2496}, doi = {10.1016/j.jmp.2019.102313}, pages = {32}, year = {2020}, abstract = {Process-oriented theories of cognition must be evaluated against time-ordered observations. Here we present a representative example for data assimilation of the SWIFT model, a dynamical model of the control of fixation positions and fixation durations during natural reading of single sentences. First, we develop and test an approximate likelihood function of the model, which is a combination of a spatial, pseudo-marginal likelihood and a temporal likelihood obtained by probability density approximation Second, we implement a Bayesian approach to parameter inference using an adaptive Markov chain Monte Carlo procedure. Our results indicate that model parameters can be estimated reliably for individual subjects. We conclude that approximative Bayesian inference represents a considerable step forward for computational models of eye-movement control, where modeling of individual data on the basis of process-based dynamic models has not been possible so far.}, language = {en} } @phdthesis{Seiler1997, author = {Seiler, J{\"o}rg}, title = {Pseudodifferential Calculus on Manifolds with Non-Compact Edges}, address = {Potsdam}, pages = {161 S.}, year = {1997}, language = {en} } @article{ShakiPinhasFischer2017, author = {Shaki, Samuel and Pinhas, Michal and Fischer, Martin H.}, title = {Heuristics and biases in mental arithmetic}, series = {Thinking \& Reasoning}, volume = {24}, journal = {Thinking \& Reasoning}, number = {2}, publisher = {Routledge, Taylor \& Francis Group}, address = {Abingdon}, issn = {1354-6783}, doi = {10.1080/13546783.2017.1348987}, pages = {138 -- 156}, year = {2017}, abstract = {Mental arithmetic is characterised by a tendency to overestimate addition and to underestimate subtraction results: the operational momentum (OM) effect. Here, motivated by contentious explanations of this effect, we developed and tested an arithmetic heuristics and biases model that predicts reverse OM due to cognitive anchoring effects. Participants produced bi-directional lines with lengths corresponding to the results of arithmetic problems. In two experiments, we found regular OM with zero problems (e.g., 3+0, 3-0) but reverse OM with non-zero problems (e.g., 2+1, 4-1). In a third experiment, we tested the prediction of our model. Our results suggest the presence of at least three competing biases in mental arithmetic: a more-or-less heuristic, a sign-space association and an anchoring bias. We conclude that mental arithmetic exhibits shortcuts for decision-making similar to traditional domains of reasoning and problem-solving.}, language = {en} } @article{SharmaHainzlZoeller2023, author = {Sharma, Shubham and Hainzl, Sebastian and Z{\"o}ller, Gert}, title = {Seismicity parameters dependence on main shock-induced co-seismic stress}, series = {Geophysical journal international}, volume = {235}, journal = {Geophysical journal international}, number = {1}, publisher = {Oxford Univ. Press}, address = {Oxford}, issn = {0956-540X}, doi = {10.1093/gji/ggad201}, pages = {509 -- 517}, year = {2023}, abstract = {The Gutenberg-Richter (GR) and the Omori-Utsu (OU) law describe the earthquakes' energy release and temporal clustering and are thus of great importance for seismic hazard assessment. Motivated by experimental results, which indicate stress-dependent parameters, we consider a combined global data set of 127 main shock-aftershock sequences and perform a systematic study of the relationship between main shock-induced stress changes and associated seismicity patterns. For this purpose, we calculate space-dependent Coulomb Stress (\& UDelta;CFS) and alternative receiver-independent stress metrics in the surrounding of the main shocks. Our results indicate a clear positive correlation between the GR b-value and the induced stress, contrasting expectations from laboratory experiments and suggesting a crucial role of structural heterogeneity and strength variations. Furthermore, we demonstrate that the aftershock productivity increases nonlinearly with stress, while the OU parameters c and p systematically decrease for increasing stress changes. Our partly unexpected findings can have an important impact on future estimations of the aftershock hazard.}, language = {en} }