@article{SchulzeTarchanov1999, author = {Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.}, title = {Elliptic complexes of pseudodifferential operators on manifolds with edges}, year = {1999}, language = {en} } @article{SchulzeTarchanov1999, author = {Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.}, title = {Ellipticity and parametrices on manifolds with cuspidal edges}, year = {1999}, language = {en} } @article{SchulzeTarchanov1998, author = {Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.}, title = {Pseudodifferential calculus on manifolds with singular points}, issn = {1311- 0454}, year = {1998}, language = {en} } @article{SchulzeTarchanov1999, author = {Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.}, title = {The Riemann-Roch theorem for manifolds with conical singularities}, year = {1999}, language = {en} } @book{SchulzeTarchanov1998, author = {Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.}, title = {Elliptic complexes of pseudodifferential operators on manifolds with edges}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, volume = {1998, 14}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, publisher = {Univ.}, address = {Potsdam}, pages = {150 S.}, year = {1998}, language = {en} } @article{SchulzeTarchanov1998, author = {Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.}, title = {Green pseudodifferential operators on manifolds with edges}, year = {1998}, language = {en} } @book{SchulzeTarchanov1998, author = {Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.}, title = {Euler solutions of pseudodifferential equations}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, volume = {1998, 09}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, publisher = {Univ.}, address = {Potsdam}, pages = {32 S.}, year = {1998}, language = {en} } @unpublished{SchulzeTarkhanov1999, author = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {Ellipticity and parametrices on manifolds with caspidal edges}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25411}, year = {1999}, language = {en} } @book{SchulzeTarkhanov2005, author = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {New algebras of boundary value problems for elliptic pseudodifferential operators}, 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 = {80 S.}, year = {2005}, language = {en} } @unpublished{SchulzeTarkhanov1997, author = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {The Riemann-Roch theorem for manifolds with conical singularities}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25051}, year = {1997}, abstract = {The classical Riemann-Roch theorem is extended to solutions of elliptic equations on manifolds with conical points.}, language = {en} } @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} } @article{SharmaHainzlZoelleretal.2020, author = {Sharma, Shubham and Hainzl, Sebastian and Z{\"o}ller, Gert and Holschneider, Matthias}, title = {Is Coulomb stress the best choice for aftershock forecasting?}, series = {Journal of geophysical research : Solid earth}, volume = {125}, journal = {Journal of geophysical research : Solid earth}, number = {9}, publisher = {American Geophysical Union}, address = {Washington}, issn = {2169-9313}, doi = {10.1029/2020JB019553}, pages = {12}, year = {2020}, abstract = {The Coulomb failure stress (CFS) criterion is the most commonly used method for predicting spatial distributions of aftershocks following large earthquakes. However, large uncertainties are always associated with the calculation of Coulomb stress change. The uncertainties mainly arise due to nonunique slip inversions and unknown receiver faults; especially for the latter, results are highly dependent on the choice of the assumed receiver mechanism. Based on binary tests (aftershocks yes/no), recent studies suggest that alternative stress quantities, a distance-slip probabilistic model as well as deep neural network (DNN) approaches, all are superior to CFS with predefined receiver mechanism. To challenge this conclusion, which might have large implications, we use 289 slip inversions from SRCMOD database to calculate more realistic CFS values for a layered half-space and variable receiver mechanisms. We also analyze the effect of the magnitude cutoff, grid size variation, and aftershock duration to verify the use of receiver operating characteristic (ROC) analysis for the ranking of stress metrics. The observations suggest that introducing a layered half-space does not improve the stress maps and ROC curves. However, results significantly improve for larger aftershocks and shorter time periods but without changing the ranking. We also go beyond binary testing and apply alternative statistics to test the ability to estimate aftershock numbers, which confirm that simple stress metrics perform better than the classic Coulomb failure stress calculations and are also better than the distance-slip probabilistic model.}, language = {en} } @article{ShcherbakovZhuangZoelleretal.2019, author = {Shcherbakov, Robert and Zhuang, Jiancang and Z{\"o}ller, Gert and Ogata, Yosihiko}, title = {Forecasting the magnitude of the largest expected earthquake}, series = {Nature Communications}, volume = {10}, journal = {Nature Communications}, publisher = {Nature Publishing Group}, address = {London}, issn = {2041-1723}, doi = {10.1038/s41467-019-11958-4}, pages = {11}, year = {2019}, abstract = {The majority of earthquakes occur unexpectedly and can trigger subsequent sequences of events that can culminate in more powerful earthquakes. This self-exciting nature of seismicity generates complex clustering of earthquakes in space and time. Therefore, the problem of constraining the magnitude of the largest expected earthquake during a future time interval is of critical importance in mitigating earthquake hazard. We address this problem by developing a methodology to compute the probabilities for such extreme earthquakes to be above certain magnitudes. We combine the Bayesian methods with the extreme value theory and assume that the occurrence of earthquakes can be described by the Epidemic Type Aftershock Sequence process. We analyze in detail the application of this methodology to the 2016 Kumamoto, Japan, earthquake sequence. We are able to estimate retrospectively the probabilities of having large subsequent earthquakes during several stages of the evolution of this sequence.}, language = {en} } @article{ShebalinNarteauZecharetal.2014, author = {Shebalin, Peter N. and Narteau, Clement and Zechar, Jeremy Douglas and Holschneider, Matthias}, title = {Combining earthquake forecasts using differential probability gains}, series = {Earth, planets and space}, volume = {66}, journal = {Earth, planets and space}, publisher = {Springer}, address = {Heidelberg}, issn = {1880-5981}, doi = {10.1186/1880-5981-66-37}, pages = {14}, year = {2014}, abstract = {We describe an iterative method to combine seismicity forecasts. With this method, we produce the next generation of a starting forecast by incorporating predictive skill from one or more input forecasts. For a single iteration, we use the differential probability gain of an input forecast relative to the starting forecast. At each point in space and time, the rate in the next-generation forecast is the product of the starting rate and the local differential probability gain. The main advantage of this method is that it can produce high forecast rates using all types of numerical forecast models, even those that are not rate-based. Naturally, a limitation of this method is that the input forecast must have some information not already contained in the starting forecast. We illustrate this method using the Every Earthquake a Precursor According to Scale (EEPAS) and Early Aftershocks Statistics (EAST) models, which are currently being evaluated at the US testing center of the Collaboratory for the Study of Earthquake Predictability. During a testing period from July 2009 to December 2011 (with 19 target earthquakes), the combined model we produce has better predictive performance - in terms of Molchan diagrams and likelihood - than the starting model (EEPAS) and the input model (EAST). Many of the target earthquakes occur in regions where the combined model has high forecast rates. Most importantly, the rates in these regions are substantially higher than if we had simply averaged the models.}, language = {en} } @article{ShebalinNarteauHolschneider2012, author = {Shebalin, Peter and Narteau, Clement and Holschneider, Matthias}, title = {From alarm-based to rate-based earthquake forecast models}, series = {Bulletin of the Seismological Society of America}, volume = {102}, journal = {Bulletin of the Seismological Society of America}, number = {1}, publisher = {Seismological Society of America}, address = {Albany}, issn = {0037-1106}, doi = {10.1785/0120110126}, pages = {64 -- 72}, year = {2012}, abstract = {We propose a conversion method from alarm-based to rate-based earthquake forecast models. A differential probability gain g(alarm)(ref) is the absolute value of the local slope of the Molchan trajectory that evaluates the performance of the alarm-based model with respect to the chosen reference model. We consider that this differential probability gain is constant over time. Its value at each point of the testing region depends only on the alarm function value. The rate-based model is the product of the event rate of the reference model at this point multiplied by the corresponding differential probability gain. Thus, we increase or decrease the initial rates of the reference model according to the additional amount of information contained in the alarm-based model. Here, we apply this method to the Early Aftershock STatistics (EAST) model, an alarm-based model in which early aftershocks are used to identify space-time regions with a higher level of stress and, consequently, a higher seismogenic potential. The resulting rate-based model shows similar performance to the original alarm-based model for all ranges of earthquake magnitude in both retrospective and prospective tests. This conversion method offers the opportunity to perform all the standard evaluation tests of the earthquake testing centers on alarm-based models. In addition, we infer that it can also be used to consecutively combine independent forecast models and, with small modifications, seismic hazard maps with short- and medium-term forecasts.}, language = {en} } @article{ShinReichFrank2012, author = {Shin, Seoleun and Reich, Sebastian and Frank, Jason}, title = {Hydrostatic Hamiltonian particle-mesh (HPM) methods for atmospheric modelling}, series = {Quarterly journal of the Royal Meteorological Society}, volume = {138}, journal = {Quarterly journal of the Royal Meteorological Society}, number = {666}, publisher = {Wiley-Blackwell}, address = {Hoboken}, issn = {0035-9009}, doi = {10.1002/qj.982}, pages = {1388 -- 1399}, year = {2012}, abstract = {We develop a hydrostatic Hamiltonian particle-mesh (HPM) method for efficient long-term numerical integration of the atmosphere. In the HPM method, the hydrostatic approximation is interpreted as a holonomic constraint for the vertical position of particles. This can be viewed as defining a set of vertically buoyant horizontal meshes, with the altitude of each mesh point determined so as to satisfy the hydrostatic balance condition and with particles modelling horizontal advection between the moving meshes. We implement the method in a vertical-slice model and evaluate its performance for the simulation of idealized linear and nonlinear orographic flow in both dry and moist environments. The HPM method is able to capture the basic features of the gravity wave to a degree of accuracy comparable with that reported in the literature. The numerical solution in the moist experiment indicates that the influence of moisture on wave characteristics is represented reasonably well and the reduction of momentum flux is in good agreement with theoretical analysis.}, language = {en} } @article{ShinSommerReichetal.2010, author = {Shin, Seoleun and Sommer, Matthias and Reich, Sebastian and N{\´e}vir, Peter}, title = {Evaluation of three spatial discretization schemes with the Galewsky et al. test}, issn = {1530-261X}, doi = {10.1002/Asl.279}, year = {2010}, abstract = {We evaluate the Hamiltonian particle methods (HPM) and the Nambu discretization applied to shallow-water equations on the sphere using the test suggested by Galewsky et al. (2004). Both simulations show excellent conservation of energy and are stable in long-term simulation. We repeat the test also using the ICOSWP scheme to compare with the two conservative spatial discretization schemes. The HPM simulation captures the main features of the reference solution, but wave 5 pattern is dominant in the simulations applied on the ICON grid with relatively low spatial resolutions. Nevertheless, agreement in statistics between the three schemes indicates their qualitatively similar behaviors in the long-term integration.}, language = {en} } @article{ShinZoellerHolschneideretal.2011, author = {Shin, Seoleun and Z{\"o}ller, Gert and Holschneider, Matthias and Reich, Sebastian}, title = {A multigrid solver for modeling complex interseismic stress fields}, series = {Computers \& geosciences : an international journal devoted to the publication of papers on all aspects of geocomputation and to the distribution of computer programs and test data sets ; an official journal of the International Association for Mathematical Geology}, volume = {37}, journal = {Computers \& geosciences : an international journal devoted to the publication of papers on all aspects of geocomputation and to the distribution of computer programs and test data sets ; an official journal of the International Association for Mathematical Geology}, number = {8}, publisher = {Elsevier}, address = {Oxford}, issn = {0098-3004}, doi = {10.1016/j.cageo.2010.11.011}, pages = {1075 -- 1082}, year = {2011}, abstract = {We develop a multigrid, multiple time stepping scheme to reduce computational efforts for calculating complex stress interactions in a strike-slip 2D planar fault for the simulation of seismicity. The key elements of the multilevel solver are separation of length scale, grid-coarsening, and hierarchy. In this study the complex stress interactions are split into two parts: the first with a small contribution is computed on a coarse level, and the rest for strong interactions is on a fine level. This partition leads to a significant reduction of the number of computations. The reduction of complexity is even enhanced by combining the multigrid with multiple time stepping. Computational efficiency is enhanced by a factor of 10 while retaining a reasonable accuracy, compared to the original full matrix-vortex multiplication. The accuracy of solution and computational efficiency depend on a given cut-off radius that splits multiplications into the two parts. The multigrid scheme is constructed in such a way that it conserves stress in the entire half-space.}, language = {en} } @unpublished{Shlapunov2000, author = {Shlapunov, Alexander}, title = {On Iterations of double layer potentials}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25687}, year = {2000}, abstract = {We prove the existence of Hp(D)-limit of iterations of double layer potentials constructed with the use of Hodge parametrix on a smooth compact manifold X, D being an open connected subset of X. This limit gives us an orthogonal projection from Sobolev space Hp(D) to a closed subspace of Hp(D)-solutions of an elliptic operator P of order p ≥ 1. Using this result we obtain formulae for Sobolev solutions to the equation Pu = f in D whenever these solutions exist. This representation involves the sum of a series whose terms are iterations of double layer potentials. Similar regularization is constructed also for a P-Neumann problem in D.}, language = {en} } @book{Shlapunov1999, author = {Shlapunov, Alexander}, title = {Iterations of self-adjoint operators and their applications to elliptic systems}, 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 = {23 S.}, year = {1999}, language = {en} } @unpublished{Shlapunov1999, author = {Shlapunov, Alexander}, title = {Iterations of self-adjoint operators and their applications to elliptic systems}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25401}, year = {1999}, abstract = {Let Hsub(0), Hsub(1) be Hilbert spaces and L : Hsub(0) -> Hsub(1) be a linear bounded operator with ||L|| ≤ 1. Then L*L is a bounded linear self-adjoint non-negative operator in the Hilbert space Hsub(0) and one can use the Neumann series ∑∞sub(v=0)(I - L*L)v L*f in order to study solvability of the operator equation Lu = f. In particular, applying this method to the ill-posed Cauchy problem for solutions to an elliptic system Pu = 0 of linear PDE's of order p with smooth coefficients we obtain solvability conditions and representation formulae for solutions of the problem in Hardy spaces whenever these solutions exist. For the Cauchy-Riemann system in C the summands of the Neumann series are iterations of the Cauchy type integral. We also obtain similar results 1) for the equation Pu = f in Sobolev spaces, 2) for the Dirichlet problem and 3) for the Neumann problem related to operator P*P if P is a homogeneous first order operator and its coefficients are constant. In these cases the representations involve sums of series whose terms are iterations of integro-differential operators, while the solvability conditions consist of convergence of the series together with trivial necessary conditions.}, language = {en} } @article{ShlapunovTarchanov2021, author = {Shlapunov, Alexander and Tarchanov, Nikolaj Nikolaevič}, title = {An open mapping theorem for the Navier-Stokes type equations associated with the de Rham complex over R-n}, series = {Siberian electronic mathematical reports = Sibirskie ėlektronnye matematičeskie izvestija}, volume = {18}, journal = {Siberian electronic mathematical reports = Sibirskie ėlektronnye matematičeskie izvestija}, number = {2}, publisher = {Institut Matematiki Imeni S. L. Soboleva}, address = {Novosibirsk}, issn = {1813-3304}, doi = {10.33048/semi.2021.18.108}, pages = {1433 -- 1466}, year = {2021}, abstract = {We consider an initial problem for the Navier-Stokes type equations associated with the de Rham complex over R-n x[0, T], n >= 3, with a positive time T. We prove that the problem induces an open injective mappings on the scales of specially constructed function spaces of Bochner-Sobolev type. In particular, the corresponding statement on the intersection of these classes gives an open mapping theorem for smooth solutions to the Navier-Stokes equations.}, language = {en} } @unpublished{ShlapunovTarkhanov2016, author = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich}, title = {An open mapping theorem for the Navier-Stokes equations}, volume = {5}, number = {10}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-98687}, pages = {80}, year = {2016}, abstract = {We consider the Navier-Stokes equations in the layer R^n x [0,T] over R^n with finite T > 0. Using the standard fundamental solutions of the Laplace operator and the heat operator, we reduce the Navier-Stokes equations to a nonlinear Fredholm equation of the form (I+K) u = f, where K is a compact continuous operator in anisotropic normed H{\"o}lder spaces weighted at the point at infinity with respect to the space variables. Actually, the weight function is included to provide a finite energy estimate for solutions to the Navier-Stokes equations for all t in [0,T]. On using the particular properties of the de Rham complex we conclude that the Fr{\´e}chet derivative (I+K)' is continuously invertible at each point of the Banach space under consideration and the map I+K is open and injective in the space. In this way the Navier-Stokes equations prove to induce an open one-to-one mapping in the scale of H{\"o}lder spaces.}, language = {en} } @unpublished{ShlapunovTarkhanov2017, author = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich}, title = {Golusin-Krylov Formulas in Complex Analysis}, series = {Preprints des Instituts f{\"u}r Mathematik der Universit{\"a}t Potsdam}, volume = {6}, journal = {Preprints des Instituts f{\"u}r Mathematik der Universit{\"a}t Potsdam}, number = {2}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-102774}, pages = {25}, year = {2017}, abstract = {This is a brief survey of a constructive technique of analytic continuation related to an explicit integral formula of Golusin and Krylov (1933). It goes far beyond complex analysis and applies to the Cauchy problem for elliptic partial differential equations as well. As started in the classical papers, the technique is elaborated in generalised Hardy spaces also called Hardy-Smirnov spaces.}, language = {en} } @article{ShlapunovTarkhanov2007, author = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich}, title = {Formal poincare lemma}, 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 = {36 S.}, year = {2007}, language = {en} } @article{ShlapunovTarkhanov2005, author = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich}, title = {Mixed problems with parameter}, issn = {1061-9208}, year = {2005}, abstract = {Let X be a smooth n-dimensional manifold and D be an open connected set in X with smooth boundary OD. Perturbing the Cauchy problem for an elliptic system Au = f in D with data on a closed set Gamma subset of partial derivativeD, we obtain a family of mixed problems depending on a small parameter epsilon > 0. Although the mixed problems are subjected to a noncoercive boundary condition on partial derivativeDF in general, each of them is uniquely solvable in an appropriate Hilbert space D-T and the corresponding family {u(epsilon)} of solutions approximates the solution of the Cauchy problem in D-T whenever the solution exists. We also prove that the existence of a solution to the Cauchy problem in D-T is equivalent to the boundedness of the family {u(epsilon)}. We thus derive a solvability condition for the Cauchy problem and an effective method of constructing the solution. Examples for Dirac operators in the Euclidean space R-n are treated. In this case, we obtain a family of mixed boundary problems for the Helmholtz equation}, language = {en} } @book{ShlapunovTarkhanov2004, author = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich}, title = {Mixed problems with a parameter}, 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 = {28 S.}, year = {2004}, language = {en} } @unpublished{ShlapunovTarkhanov2004, author = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich}, title = {Mixed problems with a parameter}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26677}, year = {2004}, abstract = {Let X be a smooth n -dimensional manifold and D be an open connected set in X with smooth boundary ∂D. Perturbing the Cauchy problem for an elliptic system Au = f in D with data on a closed set Γ ⊂ ∂D we obtain a family of mixed problems depending on a small parameter ε > 0. Although the mixed problems are subject to a non-coercive boundary condition on ∂D\Γ in general, each of them is uniquely solvable in an appropriate Hilbert space DT and the corresponding family {uε} of solutions approximates the solution of the Cauchy problem in DT whenever the solution exists. We also prove that the existence of a solution to the Cauchy problem in DT is equivalent to the boundedness of the family {uε}. We thus derive a solvability condition for the Cauchy problem and an effective method of constructing its solution. Examples for Dirac operators in the Euclidean space Rn are considered. In the latter case we obtain a family of mixed boundary problems for the Helmholtz equation.}, language = {en} } @misc{ShlapunovTarkhanov2017, author = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich}, title = {Golusin-Krylov formulas in complex analysis}, series = {Complex variables and elliptic equations}, volume = {63}, journal = {Complex variables and elliptic equations}, number = {7-8}, publisher = {Routledge}, address = {Abingdon}, issn = {1747-6933}, doi = {10.1080/17476933.2017.1395872}, pages = {1142 -- 1167}, year = {2017}, abstract = {This is a brief survey of a constructive technique of analytic continuation related to an explicit integral formula of Golusin and Krylov (1933). It goes far beyond complex analysis and applies to the Cauchy problem for elliptic partial differential equations as well. As started in the classical papers, the technique is elaborated in generalised Hardy spaces also called Hardy-Smirnov spaces.}, language = {en} } @unpublished{ShlapunovTarkhanov2001, author = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich}, title = {Duality by reproducing kernels}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26095}, year = {2001}, abstract = {Let A be a determined or overdetermined elliptic differential operator on a smooth compact manifold X. Write Ssub(A)(D) for the space of solutions to thesystem Au = 0 in a domain D ⊂ X. Using reproducing kernels related to various Hilbert structures on subspaces of Ssub(A)(D) we show explicit identifications of the dual spaces. To prove the "regularity" of reproducing kernels up to the boundary of D we specify them as resolution operators of abstract Neumann problems. The matter thus reduces to a regularity theorem for the Neumann problem, a well-known example being the ∂-Neumann problem. The duality itself takes place only for those domains D which possess certain convexity properties with respect to A.}, language = {en} } @unpublished{ShlapunovTarkhanov2007, author = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich}, title = {Formal Poincar{\´e} lemma}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30231}, year = {2007}, abstract = {We show how the multiple application of the formal Cauchy-Kovalevskaya theorem leads to the main result of the formal theory of overdetermined systems of partial differential equations. Namely, any sufficiently regular system Au = f with smooth coefficients on an open set U ⊂ Rn admits a solution in smooth sections of a bundle of formal power series, provided that f satisfies a compatibility condition in U.}, language = {en} } @article{ShlapunovTarkhanov2013, author = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich}, title = {On completeness of root functions of Sturm-Liouville problems with discontinuous boundary operators}, series = {Journal of differential equations}, volume = {255}, journal = {Journal of differential equations}, number = {10}, publisher = {Elsevier}, address = {San Diego}, issn = {0022-0396}, doi = {10.1016/j.jde.2013.07.029}, pages = {3305 -- 3337}, year = {2013}, abstract = {We consider a Sturm-Liouville boundary value problem in a bounded domain D of R-n. By this is meant that the differential equation is given by a second order elliptic operator of divergent form in D and the boundary conditions are of Robin type on partial derivative D. The first order term of the boundary operator is the oblique derivative whose coefficients bear discontinuities of the first kind. Applying the method of weak perturbation of compact selfadjoint operators and the method of rays of minimal growth, we prove the completeness of root functions related to the boundary value problem in Lebesgue and Sobolev spaces of various types. (C) 2013 Elsevier Inc. All rights reserved.}, language = {en} } @book{ShlapunovTarkhanov2001, author = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich}, title = {Duality by reproducing kernels}, 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 = {78 S.}, year = {2001}, language = {en} } @unpublished{ShlapunovTarkhanov2013, author = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich}, title = {Sturm-Liouville problems in domains with non-smooth edges}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-67336}, year = {2013}, abstract = {We consider a (generally, non-coercive) mixed boundary value problem in a bounded domain for a second order elliptic differential operator A. The differential operator is assumed to be of divergent form and the boundary operator B is of Robin type. The boundary is assumed to be a Lipschitz surface. Besides, we distinguish a closed subset of the boundary and control the growth of solutions near this set. We prove that the pair (A,B) induces a Fredholm operator L in suitable weighted spaces of Sobolev type, the weight function being a power of the distance to the singular set. Moreover, we prove the completeness of root functions related to L.}, language = {en} } @unpublished{ShlapunovTarkhanov2012, author = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich}, title = {On completeness of root functions of Sturm-Liouville problems with discontinuous boundary operators}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-57759}, year = {2012}, abstract = {We consider a Sturm-Liouville boundary value problem in a bounded domain D of R^n. By this is meant that the differential equation is given by a second order elliptic operator of divergent form in D and the boundary conditions are of Robin type on bD. The first order term of the boundary operator is the oblique derivative whose coefficients bear discontinuities of the first kind. Applying the method of weak perturbation of compact self-adjoint operators and the method of rays of minimal growth, we prove the completeness of root functions related to the boundary value problem in Lebesgue and Sobolev spaces of various types.}, language = {en} } @article{ShojaeiFard2013, author = {Shojaei-Fard, Ali}, title = {A GEOMETRIC PERSPECTIVE ON COUNTERTERMS RELATED TO DYSON-SCHWINGER EQUATIONS}, series = {INTERNATIONAL JOURNAL OF MODERN PHYSICS A}, volume = {28}, journal = {INTERNATIONAL JOURNAL OF MODERN PHYSICS A}, number = {32}, publisher = {WORLD SCIENTIFIC PUBL CO PTE LTD}, address = {SINGAPORE}, issn = {0217-751X}, doi = {10.1142/S0217751X13501704}, pages = {15}, year = {2013}, abstract = {We study Dyson-Schwinger equations (DSEs) in terms of some groups of diffeographisms to provide a new geometric formulation for their corresponding counterterms on the basis of systems of ordinary differential equations.}, language = {en} } @article{ShojaeiFard2013, author = {Shojaei-Fard, Ali}, title = {The global beta-functions from solutions of dyson-schwinger equations}, series = {Modern physics letters : A, Particles and fields, gravitation, cosmology, nuclear physics}, volume = {28}, journal = {Modern physics letters : A, Particles and fields, gravitation, cosmology, nuclear physics}, number = {34}, publisher = {World Scientific}, address = {Singapore}, issn = {0217-7323}, doi = {10.1142/S0217732313501526}, pages = {12}, year = {2013}, abstract = {We apply the geometric interpretation of Dyson-Schwinger equations (DSEs) in terms of equi-singular flat connections to provide a process which relates beta-functions of a DSE under different regularization schemes.}, language = {en} } @article{ShojaeiFard2013, author = {Shojaei-Fard, Ali}, title = {Motivic Dyson-Schwinger equations}, series = {International journal of modern physics : A, Particles and fields, gravitation, cosmology, nuclear physics}, volume = {28}, journal = {International journal of modern physics : A, Particles and fields, gravitation, cosmology, nuclear physics}, number = {20}, publisher = {World Scientific}, address = {Singapore}, issn = {0217-751X}, doi = {10.1142/S0217751X13501029}, pages = {19}, year = {2013}, abstract = {We consider Dyson-Schwinger Equations (DSEs) in the context of Connes-Kreimer renormalization Hopf algebra of Feynman diagrams and Connes-Marcolli universal Tannakian formalism. This study leads us to formulate a family of Picard-Fuchs equations and a category of Feynman motivic sheaves with respect to each combinatorial DSE.}, language = {en} } @article{ShojaeiFard2014, author = {Shojaei-Fard, Ali}, title = {Counterterms in the context of the universal Hopf algebra of renormalization}, series = {International journal of modern physics : A, Particles and fields, gravitation, cosmology, nuclear physics}, volume = {29}, journal = {International journal of modern physics : A, Particles and fields, gravitation, cosmology, nuclear physics}, number = {8}, publisher = {World Scientific}, address = {Singapore}, issn = {0217-751X}, doi = {10.1142/S0217751X14500456}, pages = {15}, year = {2014}, abstract = {The manuscript discovers a new interpretation of counterterms of renormalizable Quantum Field Theories in terms of formal expansions of decorated rooted trees.}, language = {en} } @article{ShtrakovKoppitz2016, author = {Shtrakov, Slavcho and Koppitz, J{\"o}rg}, title = {Stable varieties of semigroups and groupoids}, series = {Algebra universalis}, volume = {75}, journal = {Algebra universalis}, publisher = {Springer}, address = {Basel}, issn = {0002-5240}, doi = {10.1007/s00012-015-0359-7}, pages = {85 -- 106}, year = {2016}, abstract = {The paper deals with Sigma-composition and Sigma-essential composition of terms which lead to stable and s-stable varieties of algebras. A full description of all stable varieties of semigroups, commutative and idempotent groupoids is obtained. We use an abstract reduction system which simplifies the presentations of terms of type tau - (2) to study the variety of idempotent groupoids and s-stable varieties of groupoids. S-stable varieties are a variation of stable varieties, used to highlight replacement of subterms of a term in a deductive system instead of the usual replacement of variables by terms.}, language = {en} } @article{SiddiquiMautePedatellaetal.2018, author = {Siddiqui, Tarique Adnan and Maute, Astrid and Pedatella, Nick and Yamazaki, Yosuke and L{\"u}hr, Hermann and Stolle, Claudia}, title = {On the variability of the semidiurnal solar and lunar tides of the equatorial electrojet during sudden stratospheric warmings}, series = {Annales geophysicae}, volume = {36}, journal = {Annales geophysicae}, number = {6}, publisher = {Copernicus}, address = {G{\"o}ttingen}, issn = {0992-7689}, doi = {10.5194/angeo-36-1545-2018}, pages = {1545 -- 1562}, year = {2018}, abstract = {The variabilities of the semidiurnal solar and lunar tides of the equatorial electrojet (EEJ) are investigated during the 2003, 2006, 2009 and 2013 major sudden stratospheric warming (SSW) events in this study. For this purpose, ground-magnetometer recordings at the equatorial observatories in Huancayo and Fuquene are utilized. Results show a major enhancement in the amplitude of the EEJ semidiurnal lunar tide in each of the four warming events. The EEJ semidiurnal solar tidal amplitude shows an amplification prior to the onset of warmings, a reduction during the deceleration of the zonal mean zonal wind at 60 degrees N and 10 hPa, and a second enhancement a few days after the peak reversal of the zonal mean zonal wind during all four SSWs. Results also reveal that the amplitude of the EEJ semidiurnal lunar tide becomes comparable or even greater than the amplitude of the EEJ semidiurnal solar tide during all these warming events. The present study also compares the EEJ semidiurnal solar and lunar tidal changes with the variability of the migrating semidiurnal solar (SW2) and lunar (M2) tides in neutral temperature and zonal wind obtained from numerical simulations at E-region heights. A better agreement between the enhancements of the EEJ semidiurnal lunar tide and the M2 tide is found in comparison with the enhancements of the EEJ semidiurnal solar tide and the SW2 tide in both the neutral temperature and zonal wind at the E-region altitudes.}, language = {en} } @unpublished{Siegert2010, author = {Siegert, Sabine}, title = {Das Sankt-Petersburg-Paradoxon}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49595}, year = {2010}, abstract = {Aus dem Inhalt: 1 Einleitung 2 Historische L{\"o}sungsans{\"a}tze 3 Martingal-Ansatz 4 Markovketten-Ansatz 5 Asymptotische Interpretationen 6 Bezug zur Praxis 7 R{\´e}sum{\´e} Anhang Literaturverzeichnis}, language = {de} } @article{SinclairBussideVilliersetal.2016, author = {Sinclair, Nathalie and Bussi, Maria G. Bartolini and de Villiers, Michael and Jones, Keith and Kortenkamp, Ulrich and Leung, Allen and Owens, Kay}, title = {Recent research on geometry education: an ICME-13 survey team report}, series = {ZDM : The International Journal on Mathematics Education}, volume = {48}, journal = {ZDM : The International Journal on Mathematics Education}, publisher = {Springer}, address = {Heidelberg}, issn = {1863-9690}, doi = {10.1007/s11858-016-0796-6}, pages = {691 -- 719}, year = {2016}, abstract = {This survey on the theme of Geometry Education (including new technologies) focuses chiefly on the time span since 2008. Based on our review of the research literature published during this time span (in refereed journal articles, conference proceedings and edited books), we have jointly identified seven major threads of contributions that span from the early years of learning (pre-school and primary school) through to post-compulsory education and to the issue of mathematics teacher education for geometry. These threads are as follows: developments and trends in the use of theories; advances in the understanding of visuo spatial reasoning; the use and role of diagrams and gestures; advances in the understanding of the role of digital technologies; advances in the understanding of the teaching and learning of definitions; advances in the understanding of the teaching and learning of the proving process; and, moving beyond traditional Euclidean approaches. Within each theme, we identify relevant research and also offer commentary on future directions.}, language = {en} } @article{SiskaJonesJeonetal.2017, author = {Siska, Veronika and Jones, Eppie Ruth and Jeon, Sungwon and Bhak, Youngjune and Kim, Hak-Min and Cho, Yun Sung and Kim, Hyunho and Lee, Kyusang and Veselovskaya, Elizaveta and Balueva, Tatiana and Gallego-Llorente, Marcos and Hofreiter, Michael and Bradley, Daniel G. and Eriksson, Anders and Pinhasi, Ron and Bhak, Jong and Manica, Andrea}, title = {Genome-wide data from two early Neolithic East Asian individuals dating to 7700 years ago}, series = {Science Advances}, volume = {3}, journal = {Science Advances}, number = {2}, publisher = {American Assoc. for the Advancement of Science}, address = {Washington}, issn = {2375-2548}, doi = {10.1126/sciadv.1601877}, pages = {10}, year = {2017}, abstract = {Ancient genomes have revolutionized our understanding of Holocene prehistory and, particularly, the Neolithic transition in western Eurasia. In contrast, East Asia has so far received little attention, despite representing a core region at which the Neolithic transition took place independently ~3 millennia after its onset in the Near East. We report genome-wide data from two hunter-gatherers from Devil's Gate, an early Neolithic cave site (dated to ~7.7 thousand years ago) located in East Asia, on the border between Russia and Korea. Both of these individuals are genetically most similar to geographically close modern populations from the Amur Basin, all speaking Tungusic languages, and, in particular, to the Ulchi. The similarity to nearby modern populations and the low levels of additional genetic material in the Ulchi imply a high level of genetic continuity in this region during the Holocene, a pattern that markedly contrasts with that reported for Europe.}, language = {en} } @article{SkeelReich2011, author = {Skeel, R. D. and Reich, Sebastian}, title = {Corrected potential energy functions for constrained molecular dynamics}, series = {European physical journal special topics}, volume = {200}, journal = {European physical journal special topics}, number = {1}, publisher = {Springer}, address = {Heidelberg}, issn = {1951-6355}, doi = {10.1140/epjst/e2011-01518-8}, pages = {55 -- 72}, year = {2011}, abstract = {Atomic oscillations present in classical molecular dynamics restrict the step size that can be used. Multiple time stepping schemes offer only modest improvements, and implicit integrators are costly and inaccurate. The best approach may be to actually remove the highest frequency oscillations by constraining bond lengths and bond angles, thus permitting perhaps a 4-fold increase in the step size. However, omitting degrees of freedom produces errors in statistical averages, and rigid angles do not bend for strong excluded volume forces. These difficulties can be addressed by an enhanced treatment of holonomic constrained dynamics using ideas from papers of Fixman (1974) and Reich (1995, 1999). In particular, the 1995 paper proposes the use of "flexible" constraints, and the 1999 paper uses a modified potential energy function with rigid constraints to emulate flexible constraints. Presented here is a more direct and rigorous derivation of the latter approach, together with justification for the use of constraints in molecular modeling. With rigor comes limitations, so practical compromises are proposed: simplifications of the equations and their judicious application when assumptions are violated. Included are suggestions for new approaches.}, language = {en} } @phdthesis{Solms2017, author = {Solms, Alexander Maximilian}, title = {Integrating nonlinear mixed effects and physiologically-based modeling approaches for the analysis of repeated measurement studies}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-397070}, school = {Universit{\"a}t Potsdam}, pages = {x, 141}, year = {2017}, abstract = {During the drug discovery \& development process, several phases encompassing a number of preclinical and clinical studies have to be successfully passed to demonstrate safety and efficacy of a new drug candidate. As part of these studies, the characterization of the drug's pharmacokinetics (PK) is an important aspect, since the PK is assumed to strongly impact safety and efficacy. To this end, drug concentrations are measured repeatedly over time in a study population. The objectives of such studies are to describe the typical PK time-course and the associated variability between subjects. Furthermore, underlying sources significantly contributing to this variability, e.g. the use of comedication, should be identified. The most commonly used statistical framework to analyse repeated measurement data is the nonlinear mixed effect (NLME) approach. At the same time, ample knowledge about the drug's properties already exists and has been accumulating during the discovery \& development process: Before any drug is tested in humans, detailed knowledge about the PK in different animal species has to be collected. This drug-specific knowledge and general knowledge about the species' physiology is exploited in mechanistic physiological based PK (PBPK) modeling approaches -it is, however, ignored in the classical NLME modeling approach. Mechanistic physiological based models aim to incorporate relevant and known physiological processes which contribute to the overlying process of interest. In comparison to data--driven models they are usually more complex from a mathematical perspective. For example, in many situations, the number of model parameters outrange the number of measurements and thus reliable parameter estimation becomes more complex and partly impossible. As a consequence, the integration of powerful mathematical estimation approaches like the NLME modeling approach -which is widely used in data-driven modeling -and the mechanistic modeling approach is not well established; the observed data is rather used as a confirming instead of a model informing and building input. Another aggravating circumstance of an integrated approach is the inaccessibility to the details of the NLME methodology so that these approaches can be adapted to the specifics and needs of mechanistic modeling. Despite the fact that the NLME modeling approach exists for several decades, details of the mathematical methodology is scattered around a wide range of literature and a comprehensive, rigorous derivation is lacking. Available literature usually only covers selected parts of the mathematical methodology. Sometimes, important steps are not described or are only heuristically motivated, e.g. the iterative algorithm to finally determine the parameter estimates. Thus, in the present thesis the mathematical methodology of NLME modeling is systemically described and complemented to a comprehensive description, comprising the common theme from ideas and motivation to the final parameter estimation. Therein, new insights for the interpretation of different approximation methods used in the context of the NLME modeling approach are given and illustrated; furthermore, similarities and differences between them are outlined. Based on these findings, an expectation-maximization (EM) algorithm to determine estimates of a NLME model is described. Using the EM algorithm and the lumping methodology by Pilari2010, a new approach on how PBPK and NLME modeling can be combined is presented and exemplified for the antibiotic levofloxacin. Therein, the lumping identifies which processes are informed by the available data and the respective model reduction improves the robustness in parameter estimation. Furthermore, it is shown how apriori known factors influencing the variability and apriori known unexplained variability is incorporated to further mechanistically drive the model development. Concludingly, correlation between parameters and between covariates is automatically accounted for due to the mechanistic derivation of the lumping and the covariate relationships. A useful feature of PBPK models compared to classical data-driven PK models is in the possibility to predict drug concentration within all organs and tissue in the body. Thus, the resulting PBPK model for levofloxacin is used to predict drug concentrations and their variability within soft tissues which are the site of action for levofloxacin. These predictions are compared with data of muscle and adipose tissue obtained by microdialysis, which is an invasive technique to measure a proportion of drug in the tissue, allowing to approximate the concentrations in the interstitial fluid of tissues. Because, so far, comparing human in vivo tissue PK and PBPK predictions are not established, a new conceptual framework is derived. The comparison of PBPK model predictions and microdialysis measurements shows an adequate agreement and reveals further strengths of the presented new approach. We demonstrated how mechanistic PBPK models, which are usually developed in the early stage of drug development, can be used as basis for model building in the analysis of later stages, i.e. in clinical studies. As a consequence, the extensively collected and accumulated knowledge about species and drug are utilized and updated with specific volunteer or patient data. The NLME approach combined with mechanistic modeling reveals new insights for the mechanistic model, for example identification and quantification of variability in mechanistic processes. This represents a further contribution to the learn \& confirm paradigm across different stages of drug development. Finally, the applicability of mechanism--driven model development is demonstrated on an example from the field of Quantitative Psycholinguistics to analyse repeated eye movement data. Our approach gives new insight into the interpretation of these experiments and the processes behind.}, language = {en} } @article{SomogyvariReich2020, author = {Somogyv{\´a}ri, M{\´a}rk and Reich, Sebastian}, title = {Convergence tests for transdimensional Markov chains in geoscience imaging}, series = {Mathematical geosciences : the official journal of the International Association for Mathematical Geosciences}, volume = {52}, journal = {Mathematical geosciences : the official journal of the International Association for Mathematical Geosciences}, number = {5}, publisher = {Springer}, address = {Heidelberg}, issn = {1874-8961}, doi = {10.1007/s11004-019-09811-x}, pages = {651 -- 668}, year = {2020}, abstract = {Classic inversion methods adjust a model with a predefined number of parameters to the observed data. With transdimensional inversion algorithms such as the reversible-jump Markov chain Monte Carlo (rjMCMC), it is possible to vary this number during the inversion and to interpret the observations in a more flexible way. Geoscience imaging applications use this behaviour to automatically adjust model resolution to the inhomogeneities of the investigated system, while keeping the model parameters on an optimal level. The rjMCMC algorithm produces an ensemble as result, a set of model realizations, which together represent the posterior probability distribution of the investigated problem. The realizations are evolved via sequential updates from a randomly chosen initial solution and converge toward the target posterior distribution of the inverse problem. Up to a point in the chain, the realizations may be strongly biased by the initial model, and must be discarded from the final ensemble. With convergence assessment techniques, this point in the chain can be identified. Transdimensional MCMC methods produce ensembles that are not suitable for classic convergence assessment techniques because of the changes in parameter numbers. To overcome this hurdle, three solutions are introduced to convert model realizations to a common dimensionality while maintaining the statistical characteristics of the ensemble. A scalar, a vector and a matrix representation for models is presented, inferred from tomographic subsurface investigations, and three classic convergence assessment techniques are applied on them. It is shown that appropriately chosen scalar conversions of the models could retain similar statistical ensemble properties as geologic projections created by rasterization.}, language = {en} } @phdthesis{Srithus2008, author = {Srithus, Ratana}, title = {Algebras derived by hypersubstitutions}, pages = {XIII, 87 Bl.}, year = {2008}, language = {en} } @article{StachanowNeumannBlankensteinetal.2022, author = {Stachanow, Viktoria and Neumann, Uta and Blankenstein, Oliver and Bindellini, Davide and Melin, Johanna and Ross, Richard and Whitaker, Martin J. J. and Huisinga, Wilhelm and Michelet, Robin and Kloft, Charlotte}, title = {Exploring dried blood spot cortisol concentrations as an alternative for monitoring pediatric adrenal insufficiency patients}, series = {Frontiers in pharmacology}, volume = {13}, journal = {Frontiers in pharmacology}, publisher = {Frontiers Media}, address = {Lausanne}, issn = {1663-9812}, doi = {10.3389/fphar.2022.819590}, pages = {8}, year = {2022}, abstract = {Congenital adrenal hyperplasia (CAH) is the most common form of adrenal insufficiency in childhood; it requires cortisol replacement therapy with hydrocortisone (HC, synthetic cortisol) from birth and therapy monitoring for successful treatment. In children, the less invasive dried blood spot (DBS) sampling with whole blood including red blood cells (RBCs) provides an advantageous alternative to plasma sampling. Potential differences in binding/association processes between plasma and DBS however need to be considered to correctly interpret DBS measurements for therapy monitoring. While capillary DBS samples would be used in clinical practice, venous cortisol DBS samples from children with adrenal insufficiency were analyzed due to data availability and to directly compare and thus understand potential differences between venous DBS and plasma. A previously published HC plasma pharmacokinetic (PK) model was extended by leveraging these DBS concentrations. In addition to previously characterized binding of cortisol to albumin (linear process) and corticosteroid-binding globulin (CBG; saturable process), DBS data enabled the characterization of a linear cortisol association with RBCs, and thereby providing a quantitative link between DBS and plasma cortisol concentrations. The ratio between the observed cortisol plasma and DBS concentrations varies highly from 2 to 8. Deterministic simulations of the different cortisol binding/association fractions demonstrated that with higher blood cortisol concentrations, saturation of cortisol binding to CBG was observed, leading to an increase in all other cortisol binding fractions. In conclusion, a mathematical PK model was developed which links DBS measurements to plasma exposure and thus allows for quantitative interpretation of measurements of DBS samples.}, language = {en} } @article{StaniforthWoodReich2006, author = {Staniforth, Andrew and Wood, Nigel and Reich, Sebastian}, title = {A time-staggered semi-Lagrangian discretization of the rotating shallow-water equations}, series = {Quarterly journal of the Royal Meteorological Society}, volume = {132}, journal = {Quarterly journal of the Royal Meteorological Society}, number = {621C}, publisher = {Wiley}, address = {Weinheim}, issn = {0035-9009}, doi = {10.1256/qj.06.30}, pages = {3107 -- 3116}, year = {2006}, abstract = {A time-staggered semi-Lagrangian discretization of the rotating shallow-water equations is proposed and analysed. Application of regularization to the geopotential field used in the momentum equations leads to an unconditionally stable scheme. The analysis, together with a fully nonlinear example application, suggests that this approach is a promising, efficient, and accurate alternative to traditional schemes.}, language = {en} } @inproceedings{SteenholdtEdlundAinsworthetal.2015, author = {Steenholdt, Casper and Edlund, Helena and Ainsworth, Mark A. and Brynskov, Jorn and Thomsen, Ole Ostergaard and Huisinga, Wilhelm and Kloft, Charlotte}, title = {Relationship between measures of infliximab exposure and clinical outcome of infliximab intensification at therapeutic failure in Crohn's disease}, series = {JOURNAL OF CROHNS \& COLITIS}, volume = {9}, booktitle = {JOURNAL OF CROHNS \& COLITIS}, publisher = {Oxford Univ. Press}, address = {Oxford}, issn = {1873-9946}, pages = {S330 -- S330}, year = {2015}, language = {en} } @article{StepanenkoTarkhanov2010, author = {Stepanenko, Victor and Tarkhanov, Nikolai Nikolaevich}, title = {The Cauchy problem for Chaplygin's system}, issn = {1747-6933}, doi = {10.1080/17476930903394978}, year = {2010}, abstract = {We discuss the Cauchy problem for the so-called Chaplygin system which often appears in gas, aero- and hydrodynamics. This system can be thought of as a nonlinear analogue of the Cauchy-Riemann system in the plane. We pose Cauchy data on a part of the boundary and apply variational approach to construct a solution to this ill-posed problem. The problem actually gives insight to fundamental questions related to instable problems for nonlinear equations.}, language = {en} } @article{Stephan2009, author = {Stephan, Christoph A.}, title = {Inverse seesaw mechanism in noncommutative geometry}, issn = {1550-7998}, doi = {10.1103/Physrevd.80.065007}, year = {2009}, abstract = {In this paper we will implement the inverse seesaw mechanism into the noncommutative framework on the basis of the AC extension of the standard model. The main difference from the classical AC model is the chiral nature of the AC fermions with respect to a U(1)(X) extension of the standard model gauge group. It is this extension which allows us to couple the right-handed neutrinos via a gauge invariant mass term to left-handed A particles. The natural scale of these gauge invariant masses is of the order of 10(17) GeV while the Dirac masses of the neutrino and the AC particles are generated dynamically and are therefore much smaller (similar to 1 to similar to 10(6) GeV). From this configuration, a working inverse seesaw mechanism for the neutrinos is obtained.}, language = {en} } @article{Stephan2009, author = {Stephan, Christoph A.}, title = {Krajewski diagrams and the standard model}, issn = {0022-2488}, doi = {10.1063/1.3112622}, year = {2009}, abstract = {This paper provides a complete list of Krajewski diagrams representing the standard model of particle physics. We will give the possible representations of the algebra and the anomaly free lifts which provide the representation of the standard model gauge group on the fermionic Hilbert space. The algebra representations following from the Krajewski diagrams are not complete in the sense that the corresponding spectral triples do not necessarily obey to the axiom of Poincare duality. This defect may be repaired by adding new particles to the model, i.e., by building models beyond the standard model. The aim of this list of finite spectral triples (up to Poincare duality) is therefore to provide a basis for model building beyond the standard model.}, language = {en} } @article{Stephan2009, author = {Stephan, Christoph A.}, title = {New scalar fields in noncommutative geometry}, issn = {1550-7998}, doi = {10.1103/Physrevd.79.065013}, year = {2009}, abstract = {In this publication we present an extension of the standard model within the framework of Connes' noncommutative geometry. The model presented here is based on a minimal spectral triple which contains the standard model particles, new vectorlike fermions, and a new U(1) gauge subgroup. Additionally a new complex scalar field appears that couples to the right-handed neutrino, the new fermions, and the standard Higgs particle. The bosonic part of the action is given by the spectral action which also determines relations among the gauge couplings, the quartic scalar couplings, and the Yukawa couplings at a cutoff energy of similar to 10(17) GeV. We investigate the renormalization group flow of these relations. The low energy behavior allows to constrain the Higgs mass, the mass of the new scalar, and the mixing between these two scalar fields.}, language = {en} } @article{StolleMichaelisRauberg2016, author = {Stolle, Claudia and Michaelis, Ingo and Rauberg, Jan}, title = {The role of high-resolution geomagnetic field models for investigating ionospheric currents at low Earth orbit satellites}, series = {Earth, planets and space}, volume = {68}, journal = {Earth, planets and space}, publisher = {Springer}, address = {Heidelberg}, issn = {1880-5981}, doi = {10.1186/s40623-016-0494-1}, pages = {10}, year = {2016}, abstract = {Low Earth orbiting geomagnetic satellite missions, such as the Swarm satellite mission, are the only means to monitor and investigate ionospheric currents on a global scale and to make in situ measurements of F region currents. High-precision geomagnetic satellite missions are also able to detect ionospheric currents during quiet-time geomagnetic conditions that only have few nanotesla amplitudes in the magnetic field. An efficient method to isolate the ionospheric signals from satellite magnetic field measurements has been the use of residuals between the observations and predictions from empirical geomagnetic models for other geomagnetic sources, such as the core and lithospheric field or signals from the quiet-time magnetospheric currents. This study aims at highlighting the importance of high-resolution magnetic field models that are able to predict the lithospheric field and that consider the quiet-time magnetosphere for reliably isolating signatures from ionospheric currents during geomagnetically quiet times. The effects on the detection of ionospheric currents arising from neglecting the lithospheric and magnetospheric sources are discussed on the example of four Swarm orbits during very quiet times. The respective orbits show a broad range of typical scenarios, such as strong and weak ionospheric signal (during day- and nighttime, respectively) superimposed over strong and weak lithospheric signals. If predictions from the lithosphere or magnetosphere are not properly considered, the amplitude of the ionospheric currents, such as the midlatitude Sq currents or the equatorial electrojet (EEJ), is modulated by 10-15 \% in the examples shown. An analysis from several orbits above the African sector, where the lithospheric field is significant, showed that the peak value of the signatures of the EEJ is in error by 5 \% in average when lithospheric contributions are not considered, which is in the range of uncertainties of present empirical models of the EEJ.}, language = {en} } @article{StraderSchneiderSchorlemmer2017, author = {Strader, Anne and Schneider, Max and Schorlemmer, Danijel}, title = {Prospective and retrospective evaluation of five-year earthquake forecast models for California}, series = {Geophysical journal international}, volume = {211}, journal = {Geophysical journal international}, publisher = {Oxford Univ. Press}, address = {Oxford}, issn = {0956-540X}, doi = {10.1093/gji/ggx268}, pages = {239 -- 251}, year = {2017}, language = {en} } @misc{StraderSchneiderSchorlemmer2017, author = {Strader, Anne and Schneider, Max and Schorlemmer, Danijel}, title = {Erratum zu: Strader, Anne; Schneider, Max; Schorlemmer, Danijel: Prospective and retrospective evaluation of five-year earthquake forecast models for California (Geophysical Journal International, 211 (2017) 1, S. 239 - 251, https://doi.org/10.1093/gji/ggx268)}, series = {Geophysical journal international}, volume = {212}, journal = {Geophysical journal international}, number = {2}, publisher = {Oxford Univ. Press}, address = {Oxford}, issn = {0956-540X}, doi = {10.1093/gji/ggx496}, pages = {1314 -- 1314}, year = {2017}, abstract = {S-test results for the USGS and RELM forecasts. The differences between the simulated log-likelihoods and the observed log-likelihood are labelled on the horizontal axes, with scaling adjustments for the 40year.retro experiment. The horizontal lines represent the confidence intervals, within the 0.05 significance level, for each forecast and experiment. If this range contains a log-likelihood difference of zero, the forecasted log-likelihoods are consistent with the observed, and the forecast passes the S-test (denoted by thin lines). If the minimum difference within this range does not contain zero, the forecast fails the S-test for that particular experiment, denoted by thick lines. Colours distinguish between experiments (see Table 2 for explanation of experiment durations). Due to anomalously large likelihood differences, S-test results for Wiemer-Schorlemmer.ALM during the 10year.retro and 40year.retro experiments are not displayed. The range of log-likelihoods for the Holliday-et-al.PI forecast is lower than for the other forecasts due to relatively homogeneous forecasted seismicity rates and use of a small fraction of the RELM testing region.}, language = {en} } @article{StrieweKramer2018, author = {Striewe, Michael and Kramer, Matthias}, title = {Empirische Untersuchungen von L{\"u}ckentext-Items zur Beherrschung der Syntax einer Programmiersprache}, 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-opus4-416353}, pages = {101 -- 115}, year = {2018}, abstract = {L{\"u}ckentext-Items auf der Basis von Programmcode k{\"o}nnen eingesetzt werden, um Kenntnisse in der Syntax einer Programmiersprache zu pr{\"u}fen, ohne dazu komplexe Programmieraufgaben zu stellen, deren Bearbeitung weitere Kompetenzen erfordert. Der vorliegende Beitrag dokumentiert den Einsatz von insgesamt zehn derartigen Items in einer universit{\"a}ren Erstsemestervorlesung zur Programmierung mit Java. Es werden sowohl Erfahrungen mit der Konstruktion der Items als auch empirische Daten aus dem Einsatz diskutiert. Der Beitrag zeigt dadurch insbesondere die Herausforderungen bei der Konstruktion valider Instrumente zur Kompetenzmessung in der Programmierausbildung auf. Die begrenzten und teilweise vorl{\"a}ufigen Ergebnisse zur Qualit{\"a}t der erzeugten Items legen trotzdem nahe, dass Erstellung und Einsatz entsprechender Items m{\"o}glich ist und einen Beitrag zur Kompetenzmessung leisten kann.}, language = {de} } @article{StueblerKloftHuisinga2023, author = {St{\"u}bler, Sabine and Kloft, Charlotte and Huisinga, Wilhelm}, title = {Cell-level systems biology model to study inflammatory bowel diseases and their treatment options}, series = {CPT: pharmacometrics \& systems pharmacology}, volume = {12}, journal = {CPT: pharmacometrics \& systems pharmacology}, number = {5}, publisher = {Nature Publ. Group}, address = {London}, issn = {2163-8306}, doi = {10.1002/psp4.12932}, pages = {690 -- 705}, year = {2023}, abstract = {To help understand the complex and therapeutically challenging inflammatory bowel diseases (IBDs), we developed a systems biology model of the intestinal immune system that is able to describe main aspects of IBD and different treatment modalities thereof. The model, including key cell types and processes of the mucosal immune response, compiles a large amount of isolated experimental findings from literature into a larger context and allows for simulations of different inflammation scenarios based on the underlying data and assumptions. In the context of a large and diverse virtual IBD population, we characterized the patients based on their phenotype (in contrast to healthy individuals, they developed persistent inflammation after a trigger event) rather than on a priori assumptions on parameter differences to a healthy individual. This allowed to reproduce the enormous diversity of predispositions known to lead to IBD. Analyzing different treatment effects, the model provides insight into characteristics of individual drug therapy. We illustrate for anti-TNF-alpha therapy, how the model can be used (i) to decide for alternative treatments with best prospects in the case of nonresponse, and (ii) to identify promising combination therapies with other available treatment options.}, language = {en} } @article{SukiasyanMelkonyan2020, author = {Sukiasyan, Hayk and Melkonyan, Tatev}, title = {Semi-recursive algorithm of piecewise linear approximation of two-dimensional function by the method of worst segment dividing}, series = {Lectures in pure and applied mathematics}, journal = {Lectures in pure and applied mathematics}, number = {6}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, isbn = {978-3-86956-485-2}, issn = {2199-4951}, doi = {10.25932/publishup-47198}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-471982}, pages = {35 -- 44}, year = {2020}, language = {en} } @unpublished{SultanovKalyakinTarkhanov2014, author = {Sultanov, Oskar and Kalyakin, Leonid and Tarkhanov, Nikolai Nikolaevich}, title = {Elliptic perturbations of dynamical systems with a proper node}, volume = {3}, number = {4}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-70460}, pages = {12}, year = {2014}, abstract = {The paper is devoted to asymptotic analysis of the Dirichlet problem for a second order partial differential equation containing a small parameter multiplying the highest order derivatives. It corresponds to a small perturbation of a dynamical system having a stationary solution in the domain. We focus on the case where the trajectories of the system go into the domain and the stationary solution is a proper node.}, language = {en} } @phdthesis{Supaporn2014, author = {Supaporn, Worakrit}, title = {Categorical equivalence of clones}, pages = {89}, year = {2014}, language = {en} } @phdthesis{Susanti2013, author = {Susanti, Yeni}, title = {On Particular n-Clones}, address = {Potsdam}, pages = {108 S.}, year = {2013}, language = {en} } @article{TaghvaeideWiljesMehtaetal.2017, author = {Taghvaei, Amirhossein and de Wiljes, Jana and Mehta, Prashant G. and Reich, Sebastian}, title = {Kalman filter and its modern extensions for the continuous-time nonlinear filtering problem}, series = {Journal of dynamic systems measurement and control}, volume = {140}, journal = {Journal of dynamic systems measurement and control}, number = {3}, publisher = {ASME}, address = {New York}, issn = {0022-0434}, doi = {10.1115/1.4037780}, pages = {11}, year = {2017}, abstract = {This paper is concerned with the filtering problem in continuous time. Three algorithmic solution approaches for this problem are reviewed: (i) the classical Kalman-Bucy filter, which provides an exact solution for the linear Gaussian problem; (ii) the ensemble Kalman-Bucy filter (EnKBF), which is an approximate filter and represents an extension of the Kalman-Bucy filter to nonlinear problems; and (iii) the feedback particle filter (FPF), which represents an extension of the EnKBF and furthermore provides for a consistent solution in the general nonlinear, non-Gaussian case. The common feature of the three algorithms is the gain times error formula to implement the update step (to account for conditioning due to the observations) in the filter. In contrast to the commonly used sequential Monte Carlo methods, the EnKBF and FPF avoid the resampling of the particles in the importance sampling update step. Moreover, the feedback control structure provides for error correction potentially leading to smaller simulation variance and improved stability properties. The paper also discusses the issue of nonuniqueness of the filter update formula and formulates a novel approximation algorithm based on ideas from optimal transport and coupling of measures. Performance of this and other algorithms is illustrated for a numerical example.}, language = {en} } @article{Tarkhanov2008, author = {Tarkhanov, Nikolai Nikolaevich}, title = {Cancellation of a Publication}, 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 = {2 S.}, year = {2008}, language = {en} } @book{Tarkhanov2006, author = {Tarkhanov, Nikolai Nikolaevich}, title = {Euler characteristic of Fredholm quasicomplexes}, 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 = {8 S.}, year = {2006}, language = {en} } @book{Tarkhanov2005, author = {Tarkhanov, Nikolai Nikolaevich}, title = {Unitary solutions of paratial differential equations}, 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 = {35 S.}, year = {2005}, language = {en} } @book{Tarkhanov2005, author = {Tarkhanov, Nikolai Nikolaevich}, title = {Operator algebras related to the Bochner-Matinelli integral}, 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 = {15 S.}, year = {2005}, language = {en} } @book{Tarkhanov2005, author = {Tarkhanov, Nikolai Nikolaevich}, title = {Root functions of elliptic boundary problems in domains with conic points on the boundary}, 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 = {20 S.}, year = {2005}, language = {en} } @article{Tarkhanov2004, author = {Tarkhanov, Nikolai Nikolaevich}, title = {Fixed point formula for holomorphic functions}, issn = {0002-9939}, year = {2004}, abstract = {We show a Lefschetz fixed point formula for holomorphic functions in a bounded domain D with smooth boundary in the complex plane. To introduce the Lefschetz number for a holomorphic map of D, we make use of the Bergman kernel of this domain. The Lefschetz number is proved to be the sum of the usual contributions of fixed points of the map in D and contributions of boundary fixed points, these latter being different for attracting and repulsing fixed points}, language = {en} } @book{Tarkhanov2003, author = {Tarkhanov, Nikolai Nikolaevich}, title = {A fixed point formula in one complex variable}, 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 = {14 S.}, year = {2003}, language = {en} } @book{Tarkhanov2002, author = {Tarkhanov, Nikolai Nikolaevich}, title = {Anisotropic edge problems}, 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 = {43 S.}, year = {2002}, language = {en} } @unpublished{Tarkhanov2015, author = {Tarkhanov, Nikolai Nikolaevich}, title = {A spectral theorem for deformation quantisation}, volume = {4}, number = {4}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-72425}, pages = {8}, year = {2015}, abstract = {We present a construction of the eigenstate at a noncritical level of the Hamiltonian function. Moreover, we evaluate the contributions of Morse critical points to the spectral decomposition.}, language = {en} } @unpublished{Tarkhanov2002, author = {Tarkhanov, Nikolai Nikolaevich}, title = {Anisotropic edge problems}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26280}, year = {2002}, abstract = {We investigate elliptic pseudodifferential operators which degenerate in an anisotropic way on a submanifold of arbitrary codimension. To find Fredholm problems for such operators we adjoint to them boundary and coboundary conditions on the submanifold.The algebra obtained this way is a far reaching generalisation of Boutet de Monvel's algebra of boundary value problems with transmission property. We construct left and right regularisers and prove theorems on hypoellipticity and local solvability.}, language = {en} } @unpublished{Tarkhanov2004, author = {Tarkhanov, Nikolai Nikolaevich}, title = {Harmonic integrals on domains with edges}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26800}, year = {2004}, abstract = {We study the Neumann problem for the de Rham complex in a bounded domain of Rn with singularities on the boundary. The singularities may be general enough, varying from Lipschitz domains to domains with cuspidal edges on the boundary. Following Lopatinskii we reduce the Neumann problem to a singular integral equation of the boundary. The Fredholm solvability of this equation is then equivalent to the Fredholm property of the Neumann problem in suitable function spaces. The boundary integral equation is explicitly written and may be treated in diverse methods. This way we obtain, in particular, asymptotic expansions of harmonic forms near singularities of the boundary.}, language = {en} } @unpublished{Tarkhanov2006, author = {Tarkhanov, Nikolai Nikolaevich}, title = {Euler characteristic of Fredholm quasicomplexes}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30117}, year = {2006}, abstract = {By quasicomplexes are usually meant perturbations of complexes small in some sense. Of interest are not only perturbations within the category of complexes but also those going beyond this category. A sequence perturbed in this way is no longer a complex, and so it bears no cohomology. We show how to introduce Euler characteristic for small perturbations of Fredholm complexes. The paper is to appear in Funct. Anal. and its Appl., 2006.}, language = {en} } @unpublished{Tarkhanov2005, author = {Tarkhanov, Nikolai Nikolaevich}, title = {Root functions of elliptic boundary problems in domains with conic points of the boundary}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29812}, year = {2005}, abstract = {We prove the completeness of the system of eigen and associated functions (i.e., root functions) of an elliptic boundary value problem in a domain whose boundary is a smooth surface away from a finite number of points, each of them possesses a neighbourhood where the boundary is a conical surface.}, language = {en} } @unpublished{Tarkhanov2005, author = {Tarkhanov, Nikolai Nikolaevich}, title = {Operator algebras related to the Bochner-Martinelli Integral}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29789}, year = {2005}, abstract = {We describe a general method of computing the square of the singular integral of Bochner-Martinelli. Any explicit formula for the square applies in a familiar way to describe the C*-algebra generated by this integral.}, language = {en} } @article{Tarkhanov2011, author = {Tarkhanov, Nikolai Nikolaevich}, title = {The dirichlet to Neumann operator for elliptic complexes}, series = {Transactions of the American Mathematical Society}, volume = {363}, journal = {Transactions of the American Mathematical Society}, number = {12}, publisher = {American Mathematical Soc.}, address = {Providence}, issn = {0002-9947}, pages = {6421 -- 6437}, year = {2011}, abstract = {We define the Dirichlet to Neumann operator for an elliptic complex of first order differential operators on a compact Riemannian manifold with boundary. Under reasonable conditions the Betti numbers of the complex prove to be completely determined by the Dirichlet to Neumann operator on the boundary.}, language = {en} } @unpublished{Tarkhanov2012, author = {Tarkhanov, Nikolai Nikolaevich}, title = {A simple numerical approach to the Riemann hypothesis}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-57645}, year = {2012}, abstract = {The Riemann hypothesis is equivalent to the fact the the reciprocal function 1/zeta (s) extends from the interval (1/2,1) to an analytic function in the quarter-strip 1/2 < Re s < 1 and Im s > 0. Function theory allows one to rewrite the condition of analytic continuability in an elegant form amenable to numerical experiments.}, language = {en} }