TY - JOUR A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris Ju. A1 - Satalov, Viktor E. T1 - An operator algebra on manifolds with cusp type singularities Y1 - 1998 ER - TY - JOUR A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris Ju. A1 - Satalov, Viktor E. T1 - On general boundary value problems for elliptic equations Y1 - 1998 ER - TY - JOUR A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris Ju. A1 - Satalov, Viktor E. T1 - On some global aspects of the theory of partial differential equations on manifolds with singularities Y1 - 1998 ER - TY - JOUR A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris Ju. A1 - Satalov, Viktor E. T1 - Differential equations on manifolds with singularities in classes of resurgent functions Y1 - 1998 ER - TY - INPR A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris A1 - Savin, Anton T1 - The homotopy classification and the index of boundary value problems for general elliptic operators N2 - We give the homotopy classification and compute the index of boundary value problems for elliptic equations. The classical case of operators that satisfy the Atiyah-Bott condition is studied first. We also consider the general case of boundary value problems for operators that do not necessarily satisfy the Atiyah-Bott condition. T3 - Preprint - (1999) 20 KW - elliptic boundary value problems KW - Atiyah-Bott condition KW - index theory KW - K-theory KW - homotopy classification Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25568 ER - TY - INPR A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris A1 - Shatalov, Victor T1 - Operator algebras on singular manifolds. I T3 - Preprint - (1997) 16 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25011 ER - TY - INPR A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris A1 - Shatalov, Victor T1 - On the index of differential operators on manifolds with conical singularities N2 - The paper contains the proof of the index formula for manifolds with conical points. For operators subject to an additional condition of spectral symmetry, the index is expressed as the sum of multiplicities of spectral points of the conormal symbol (indicial family) and the integral from the Atiyah-Singer form over the smooth part of the manifold. The obtained formula is illustrated by the example of the Euler operator on a two-dimensional manifold with conical singular point. T3 - Preprint - (1997) 10 KW - conical singularities KW - Mellin transform KW - pseudodiferential operators KW - ellipticity KW - Fredholm operators KW - regularizers KW - analytic index Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-24965 ER - TY - INPR A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris A1 - Shatalov, Victor T1 - Nonstationary problems for equations of Borel-Fuchs type N2 - In the paper, the nonstationary problems for equations of Borel-Fuchs type are investigated. The asymptotic expansion are obtained for different orders of degeneration of operators in question. The approach to nonstationary problems based on the asymptotic theory on abstract algebras is worked out. T3 - Preprint - (1997) 11 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-24973 ER - TY - INPR A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris A1 - Shatalov, Victor T1 - Operator algebras on singular manifolds. IV, V T3 - Preprint - (1997) 19 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25062 ER - TY - INPR A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris A1 - Shatalov, Victor T1 - On general boundary value problems for elliptic equations N2 - We construct a theory of general boundary value problems for differential operators whose symbols do not necessarily satisfy the Atiyah-Bott condition [3] of vanishing of the corresponding obstruction. A condition for these problems to be Fredholm is introduced and the corresponding finiteness theorems are proved. T3 - Preprint - (1997) 35 KW - elliptic boundary value problems KW - Atiyah-Bott condition KW - Calderón projections KW - Cauchy Riemann operator KW - Euler operator Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25138 ER - TY - BOOK A1 - Schulze, Bert-Wolfgang A1 - Tarchanov, Nikolaj N. T1 - Lefschetz theory on manifolds with edges : introduction T3 - Preprint / Universität Potsdam, Institut für Mathematik Y1 - 1997 VL - 1997, 08 PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Schulze, Bert-Wolfgang A1 - Tarchanov, Nikolaj N. T1 - Asymtotics of solutions to elliptic equations on manifolds with corners T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2000 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Schulze, Bert-Wolfgang A1 - Tarchanov, Nikolaj N. T1 - Ellipticity and parametrices on manifolds with cuspidal edges T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 1999 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Schulze, Bert-Wolfgang A1 - Tarchanov, Nikolaj N. T1 - Pseudodifferential operators on manifolds with corners T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2000 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Schulze, Bert-Wolfgang A1 - Tarchanov, Nikolaj N. T1 - The Rieman-Roch theorem for manifolds with conical singularities T3 - Preprint / Universität Potsdam, Institut für Mathematik Y1 - 1997 VL - 1997, 18 PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Schulze, Bert-Wolfgang A1 - Tarchanov, Nikolaj N. T1 - The index of elliptic operators on manifolds with cups Y1 - 1997 ER - TY - JOUR A1 - Schulze, Bert-Wolfgang A1 - Tarchanov, Nikolaj N. T1 - Coordinate invariance of the wedge Sobolev spaces = Wedge Sobelev spaces BT - Wedge Sobolev spaces Y1 - 1996 ER - TY - JOUR A1 - Schulze, Bert-Wolfgang A1 - Tarchanov, Nikolaj N. T1 - Elliptic complexes of pseudodifferential operators on manifolds with edges Y1 - 1999 ER - TY - JOUR A1 - Schulze, Bert-Wolfgang A1 - Tarchanov, Nikolaj N. T1 - Ellipticity and parametrices on manifolds with cuspidal edges Y1 - 1999 ER - TY - JOUR A1 - Schulze, Bert-Wolfgang A1 - Tarchanov, Nikolaj N. T1 - Pseudodifferential calculus on manifolds with singular points Y1 - 1998 SN - 1311- 0454 ER - TY - JOUR A1 - Schulze, Bert-Wolfgang A1 - Tarchanov, Nikolaj N. T1 - The Riemann-Roch theorem for manifolds with conical singularities Y1 - 1999 ER - TY - BOOK A1 - Schulze, Bert-Wolfgang A1 - Tarchanov, Nikolaj N. T1 - Elliptic complexes of pseudodifferential operators on manifolds with edges T3 - Preprint / Universität Potsdam, Institut für Mathematik Y1 - 1998 VL - 1998, 14 PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Schulze, Bert-Wolfgang A1 - Tarchanov, Nikolaj N. T1 - Green pseudodifferential operators on manifolds with edges Y1 - 1998 ER - TY - BOOK A1 - Schulze, Bert-Wolfgang A1 - Tarchanov, Nikolaj N. T1 - Euler solutions of pseudodifferential equations T3 - Preprint / Universität Potsdam, Institut für Mathematik Y1 - 1998 VL - 1998, 09 PB - Univ. CY - Potsdam ER - TY - INPR A1 - Schulze, Bert-Wolfgang A1 - Tarkhanov, Nikolai Nikolaevich T1 - Ellipticity and parametrices on manifolds with caspidal edges T3 - Preprint - (1999) 04 Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25411 ER - TY - BOOK A1 - Schulze, Bert-Wolfgang A1 - Tarkhanov, Nikolai Nikolaevich T1 - New algebras of boundary value problems for elliptic pseudodifferential operators T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2005 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - INPR A1 - Schulze, Bert-Wolfgang A1 - Tarkhanov, Nikolai Nikolaevich T1 - The Riemann-Roch theorem for manifolds with conical singularities N2 - The classical Riemann-Roch theorem is extended to solutions of elliptic equations on manifolds with conical points. T3 - Preprint - (1997) 18 KW - manifolds with singularities KW - elliptic operators KW - divisors Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25051 ER - TY - INPR A1 - Schulze, Bert-Wolfgang A1 - Tarkhanov, Nikolai Nikolaevich T1 - Elliptic complexes of pseudodifferential operators on manifolds with edges N2 - 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 Fréchet 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. T3 - Preprint - (1998) 14 KW - manifolds with singularities KW - pseudodifferential operators KW - elliptic complexes KW - Hodge theory Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25257 ER - TY - INPR A1 - Schulze, Bert-Wolfgang A1 - Tarkhanov, Nikolai Nikolaevich T1 - Pseudodifferential operators on manifolds with corners N2 - We describe an algebra of pseudodifferential operators on a manifold with corners. T3 - Preprint - (2000) 13 Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25783 ER - TY - INPR A1 - Schulze, Bert-Wolfgang A1 - Tarkhanov, Nikolai Nikolaevich T1 - Boundary value problems with Toeplitz conditions N2 - 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. T3 - Preprint - (2005) 08 KW - Pseudodifferential operators KW - boundary values problems KW - Toeplitz operators Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-29837 ER - TY - INPR A1 - Schulze, Bert-Wolfgang A1 - Tarkhanov, Nikolai Nikolaevich T1 - Euler solutions of pseudodifferential equations N2 - 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. T3 - Preprint - (1998) 09 KW - pseudodifferential operator KW - meromorphic family KW - residue Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25211 ER - TY - INPR A1 - Schulze, Bert-Wolfgang A1 - Tarkhanov, Nikolai Nikolaevich T1 - Lefschetz theory on manifolds with edges : introduction N2 - 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. N2 - Ziel des Buches ist es, die Lefschetz-Theorie der Fixpunkte für elliptische Komplexe von Pseudodifferentialoperatoren auf Mannigfaltigkeiten mit Kanten zu gewinnen. Die allgemeine Lefschetz-Theorie enthält die Index-Theorie als Spezialfall, aber der Fall, den wir analysieren werden, ist viel leichter als das Index-Problem. Ergebnisse in dieser Richtung sind wünschenswert, einerseits aus innermathematischen Gründen, aber auch im Hinblick auf Anwendungen in den Naturwissenschaften. T3 - Preprint - (1997) 08 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-24948 ER - TY - INPR A1 - Schulze, Bert-Wolfgang A1 - Tarkhanov, Nikolai Nikolaevich T1 - A Lefschetz fixed point formula in the relative elliptic theory N2 - 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. T3 - Preprint - (1998) 01 KW - elliptic complexes KW - relative cohomology KW - Lefschetz number Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25159 ER - TY - BOOK A1 - Schulze, Bert-Wolfgang A1 - Tarkhanov, Nikolai Nikolaevich T1 - Symbol algebra for manifolds with cuspidal singularities T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2003 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - INPR A1 - Schulze, Bert-Wolfgang A1 - Tarkhanov, Nikolai Nikolaevich T1 - Asymptotics of solutions to elliptic equatons on manifolds with corners N2 - 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. T3 - Preprint - (2000) 05 Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25716 ER - TY - INPR A1 - Schulze, Bert-Wolfgang A1 - Volpato, A. T1 - Green operators in the edge calculus N2 - 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. T3 - Preprint - (2004) 25 KW - operators on manifolds with edges KW - weighted spaces with asymptotics KW - Green and Mellin edge operators Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26846 ER - TY - BOOK A1 - Schulze, Bert-Wolfgang A1 - Volpato, A. T1 - Green operators in the edge calculus T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2004 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - INPR A1 - Schulze, Bert-Wolfgang A1 - Wei, Y. T1 - Edge-boundary problems with singular trace conditions N2 - 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. T3 - Preprint - (2008) 04 Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30317 ER - TY - JOUR A1 - Schulze, Bert-Wolfgang A1 - Wei, Y. T1 - The Mellin-edge quantisation for corner operators JF - Complex analysis and operator theory N2 - 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. Y1 - 2014 U6 - https://doi.org/10.1007/s11785-013-0289-3 SN - 1661-8254 SN - 1661-8262 VL - 8 IS - 4 SP - 803 EP - 841 PB - Springer CY - Basel ER - TY - BOOK A1 - Schulze, Bert-Wolfgang A1 - Wei, Ya-wei T1 - Edge-boundary problems with singular trace conditions T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2008 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Schulze, Bert-Wolfgang A1 - Wei, Ya-wei T1 - Edge-boundary problems with singular trace conditions N2 - 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. Y1 - 2009 UR - http://www.springerlink.com/content/100233 U6 - https://doi.org/10.1007/s10455-008-9143-7 SN - 0232-704X ER - TY - THES A1 - Schwarz, Michael T1 - Nodal domains and boundary representation for Dirichlet forms Y1 - 2020 ER - TY - JOUR A1 - Seelig, Stefan A. A1 - Rabe, Maximilian Michael A1 - Malem-Shinitski, Noa A1 - Risse, Sarah A1 - Reich, Sebastian A1 - Engbert, Ralf T1 - Bayesian parameter estimation for the SWIFT model of eye-movement control during reading JF - Journal of mathematical psychology N2 - 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. KW - dynamical models KW - reading KW - eye movements KW - saccades KW - likelihood function KW - Bayesian inference KW - MCMC KW - interindividual differences Y1 - 2020 U6 - https://doi.org/10.1016/j.jmp.2019.102313 SN - 0022-2496 SN - 1096-0880 VL - 95 PB - Elsevier CY - San Diego ER - TY - THES A1 - Seiler, Jörg T1 - Pseudodifferential Calculus on Manifolds with Non-Compact Edges Y1 - 1997 CY - Potsdam ER - TY - JOUR A1 - Seyedhosseini, Mehran T1 - A variant of Roe algebras for spaces with cylindrical ends with applications in relative higher index theory JF - Journal of noncommutative geometry N2 - In this paper, we define a variant of Roe algebras for spaces with cylindrical ends and use this to study questions regarding existence and classification of metrics of positive scalar curvature on such manifolds which are collared on the cylindrical end. We discuss how our constructions are related to relative higher index theory as developed by Chang, Weinberger, and Yu and use this relationship to define higher rho-invariants for positive scalar curvature metrics on manifolds with boundary. This paves the way for the classification of these metrics. Finally, we use the machinery developed here to give a concise proof of a result of Schick and the author, which relates the relative higher index with indices defined in the presence of positive scalar curvature on the boundary. KW - positive scalar curvature KW - higher index theory KW - rho-invariants KW - Roe algebras KW - manifolds with cylindrical ends KW - manifolds with boundary Y1 - 2022 U6 - https://doi.org/10.4171/JNCG/457 SN - 1661-6952 SN - 1661-6960 VL - 16 IS - 2 SP - 595 EP - 624 PB - European Mathematical Society CY - Zurich ER - TY - JOUR A1 - Shaki, Samuel A1 - Pinhas, Michal A1 - Fischer, Martin H. T1 - Heuristics and biases in mental arithmetic BT - revisiting and reversing operational momentum JF - Thinking & Reasoning N2 - 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. KW - Heuristics KW - mental arithmetic KW - mental number line KW - operational momentum KW - problem-solving Y1 - 2017 U6 - https://doi.org/10.1080/13546783.2017.1348987 SN - 1354-6783 SN - 1464-0708 VL - 24 IS - 2 SP - 138 EP - 156 PB - Routledge, Taylor & Francis Group CY - Abingdon ER - TY - JOUR A1 - Sharma, Shubham A1 - Hainzl, Sebastian A1 - Zöller, Gert T1 - Seismicity parameters dependence on main shock-induced co-seismic stress JF - Geophysical journal international N2 - 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. KW - earthquake hazards KW - earthquake interaction KW - forecasting and prediction KW - statistical seismology KW - b-value Y1 - 2023 U6 - https://doi.org/10.1093/gji/ggad201 SN - 0956-540X SN - 1365-246X VL - 235 IS - 1 SP - 509 EP - 517 PB - Oxford Univ. Press CY - Oxford ER - TY - JOUR A1 - Sharma, Shubham A1 - Hainzl, Sebastian A1 - Zöller, Gert A1 - Holschneider, Matthias T1 - Is Coulomb stress the best choice for aftershock forecasting? JF - Journal of geophysical research : Solid earth N2 - 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. Y1 - 2020 U6 - https://doi.org/10.1029/2020JB019553 SN - 2169-9313 SN - 2169-9356 VL - 125 IS - 9 PB - American Geophysical Union CY - Washington ER - TY - JOUR A1 - Shcherbakov, Robert A1 - Zhuang, Jiancang A1 - Zöller, Gert A1 - Ogata, Yosihiko T1 - Forecasting the magnitude of the largest expected earthquake JF - Nature Communications N2 - 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. Y1 - 2019 U6 - https://doi.org/10.1038/s41467-019-11958-4 SN - 2041-1723 VL - 10 PB - Nature Publishing Group CY - London ER - TY - JOUR A1 - Shebalin, Peter N. A1 - Narteau, Clement A1 - Zechar, Jeremy Douglas A1 - Holschneider, Matthias T1 - Combining earthquake forecasts using differential probability gains JF - Earth, planets and space N2 - 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. KW - Probabilistic forecasting KW - Earthquake interaction KW - Forecasting and prediction KW - Statistical seismology Y1 - 2014 U6 - https://doi.org/10.1186/1880-5981-66-37 SN - 1880-5981 VL - 66 PB - Springer CY - Heidelberg ER - TY - JOUR A1 - Shebalin, Peter A1 - Narteau, Clement A1 - Holschneider, Matthias T1 - From alarm-based to rate-based earthquake forecast models JF - Bulletin of the Seismological Society of America N2 - 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. Y1 - 2012 U6 - https://doi.org/10.1785/0120110126 SN - 0037-1106 VL - 102 IS - 1 SP - 64 EP - 72 PB - Seismological Society of America CY - Albany ER - TY - JOUR A1 - Shin, Seoleun A1 - Reich, Sebastian A1 - Frank, Jason T1 - Hydrostatic Hamiltonian particle-mesh (HPM) methods for atmospheric modelling JF - Quarterly journal of the Royal Meteorological Society N2 - 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. KW - conservative discretization KW - Lagrangian modeling KW - holonomic constraints KW - fluid mechanics Y1 - 2012 U6 - https://doi.org/10.1002/qj.982 SN - 0035-9009 VL - 138 IS - 666 SP - 1388 EP - 1399 PB - Wiley-Blackwell CY - Hoboken ER - TY - JOUR A1 - Shin, Seoleun A1 - Sommer, Matthias A1 - Reich, Sebastian A1 - Névir, Peter T1 - Evaluation of three spatial discretization schemes with the Galewsky et al. test N2 - 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. Y1 - 2010 UR - http://www3.interscience.wiley.com/cgi-bin/jhome/106562719 U6 - https://doi.org/10.1002/Asl.279 SN - 1530-261X ER - TY - JOUR A1 - Shin, Seoleun A1 - Zöller, Gert A1 - Holschneider, Matthias A1 - Reich, Sebastian T1 - A multigrid solver for modeling complex interseismic stress fields JF - 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 N2 - 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. KW - Multigrid KW - Multiple time stepping KW - Strike-slip fault model Y1 - 2011 U6 - https://doi.org/10.1016/j.cageo.2010.11.011 SN - 0098-3004 VL - 37 IS - 8 SP - 1075 EP - 1082 PB - Elsevier CY - Oxford ER - TY - INPR A1 - Shlapunov, Alexander T1 - On Iterations of double layer potentials N2 - 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. T3 - Preprint - (2000) 02 Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25687 ER - TY - BOOK A1 - Shlapunov, Alexander T1 - Iterations of self-adjoint operators and their applications to elliptic systems T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 1999 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - INPR A1 - Shlapunov, Alexander T1 - Iterations of self-adjoint operators and their applications to elliptic systems N2 - 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. T3 - Preprint - (1999) 03 Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25401 ER - TY - JOUR A1 - Shlapunov, Alexander A. A1 - Tarchanov, Nikolaj Nikolaevič T1 - Inverse image of precompact sets and regular solutions to the Navier-Stokes equations JF - Vestnik Udmurtskogo Universiteta. Matematika, mechanika, kompʹjuternye nauki N2 - We consider the initial value problem for the Navier-Stokes equations over R-3 x [0, T] with time T > 0 in the spatially periodic setting. We prove that it induces open injective mappings A(s): B-1(s) -> B-2(s-1) where B-1(s), B-2(s-1) are elements from scales of specially constructed function spaces of Bochner-Sobolev typeparametrized with the smoothness index s is an element of N. Finally, we prove that a map Asis surjective if and only if the inverse image A(s)(- 1) (K) of any pre compact set K from the range of the map Asis bounded in the Bochner space L-s([0, T], L-r(T-3))with the Ladyzhenskaya-Prodi-Serrin numbers s, r. KW - Navier-Stokes equations KW - regular solutions Y1 - 2022 U6 - https://doi.org/10.35634/vm220208 SN - 1994-9197 SN - 2076-5959 VL - 32 IS - 2 SP - 278 EP - 297 PB - Udmurtskij gosudarstvennyj universitet CY - Iževsk ER - TY - JOUR A1 - Shlapunov, Alexander A1 - Tarchanov, Nikolaj Nikolaevič T1 - An open mapping theorem for the Navier-Stokes type equations associated with the de Rham complex over R-n JF - Siberian electronic mathematical reports = Sibirskie ėlektronnye matematičeskie izvestija N2 - 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. KW - Navier-Stokes equations KW - de Rham complex KW - open mapping theorem Y1 - 2021 U6 - https://doi.org/10.33048/semi.2021.18.108 SN - 1813-3304 VL - 18 IS - 2 SP - 1433 EP - 1466 PB - Institut Matematiki Imeni S. L. Soboleva CY - Novosibirsk ER - TY - INPR A1 - Shlapunov, Alexander A1 - Tarkhanov, Nikolai Nikolaevich T1 - An open mapping theorem for the Navier-Stokes equations N2 - 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 Hölder 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 Fréchet 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 Hölder spaces. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 5 (2016)10 KW - Navier-Stokes equations KW - weighted Hölder spaces KW - integral representation method Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-98687 SN - 2193-6943 VL - 5 IS - 10 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - INPR A1 - Shlapunov, Alexander A1 - Tarkhanov, Nikolai Nikolaevich T1 - Golusin-Krylov Formulas in Complex Analysis T2 - Preprints des Instituts für Mathematik der Universität Potsdam N2 - 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. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 6 (2017) 2 KW - analytic continuation KW - integral formulas KW - Cauchy problem Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-102774 VL - 6 IS - 2 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Shlapunov, Alexander A1 - Tarkhanov, Nikolai Nikolaevich T1 - Formal poincare lemma JF - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2007 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Shlapunov, Alexander A1 - Tarkhanov, Nikolai Nikolaevich T1 - Mixed problems with parameter N2 - 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 Y1 - 2005 SN - 1061-9208 ER - TY - BOOK A1 - Shlapunov, Alexander A1 - Tarkhanov, Nikolai Nikolaevich T1 - Mixed problems with a parameter T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2004 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - INPR A1 - Shlapunov, Alexander A1 - Tarkhanov, Nikolai Nikolaevich T1 - Mixed problems with a parameter N2 - 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. T3 - Preprint - (2004) 02 Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26677 ER - TY - JOUR A1 - Shlapunov, Alexander A1 - Tarkhanov, Nikolai Nikolaevich T1 - Golusin-Krylov formulas in complex analysis JF - Complex variables and elliptic equations N2 - 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. KW - Analytic continuation KW - inegral formulas KW - Cauchy problem Y1 - 2017 U6 - https://doi.org/10.1080/17476933.2017.1395872 SN - 1747-6933 SN - 1747-6941 VL - 63 IS - 7-8 SP - 1142 EP - 1167 PB - Routledge CY - Abingdon ER - TY - INPR A1 - Shlapunov, Alexander A1 - Tarkhanov, Nikolai Nikolaevich T1 - Duality by reproducing kernels N2 - 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. T3 - Preprint - (2001) 26 Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26095 ER - TY - INPR A1 - Shlapunov, Alexander A1 - Tarkhanov, Nikolai Nikolaevich T1 - Formal Poincaré lemma N2 - 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. T3 - Preprint - (2007) 02 Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30231 ER - TY - JOUR A1 - Shlapunov, Alexander A1 - Tarkhanov, Nikolai Nikolaevich T1 - On completeness of root functions of Sturm-Liouville problems with discontinuous boundary operators JF - Journal of differential equations N2 - 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. KW - Sturm-Liouville problem KW - Discontinuous Robin condition KW - Root function KW - Lipschitz domain KW - Non-coercive problem Y1 - 2013 U6 - https://doi.org/10.1016/j.jde.2013.07.029 SN - 0022-0396 SN - 1090-2732 VL - 255 IS - 10 SP - 3305 EP - 3337 PB - Elsevier CY - San Diego ER - TY - BOOK A1 - Shlapunov, Alexander A1 - Tarkhanov, Nikolai Nikolaevich T1 - Duality by reproducing kernels T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2001 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - INPR A1 - Shlapunov, Alexander A1 - Tarkhanov, Nikolai Nikolaevich T1 - Sturm-Liouville problems in domains with non-smooth edges N2 - 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. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 2(2013)13 KW - Second order elliptic equations KW - non-coercive boundary conditions KW - root functions KW - weighted spaces Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-67336 ER - TY - INPR A1 - Shlapunov, Alexander A1 - Tarkhanov, Nikolai Nikolaevich T1 - On completeness of root functions of Sturm-Liouville problems with discontinuous boundary operators N2 - 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. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)11 KW - Sturm-Liouville problems KW - discontinuous Robin condition KW - root functions KW - Lipschitz domains Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-57759 SN - 2193-6943 ER - TY - JOUR A1 - Shojaei-Fard, Ali T1 - A GEOMETRIC PERSPECTIVE ON COUNTERTERMS RELATED TO DYSON-SCHWINGER EQUATIONS JF - INTERNATIONAL JOURNAL OF MODERN PHYSICS A N2 - 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. KW - Dyson-Schwinger equations KW - Hopf algebra of Feynman diagrams KW - counterterms KW - Picard-Fuchs equations KW - equi-singular connections Y1 - 2013 U6 - https://doi.org/10.1142/S0217751X13501704 SN - 0217-751X SN - 1793-656X VL - 28 IS - 32 PB - WORLD SCIENTIFIC PUBL CO PTE LTD CY - SINGAPORE ER - TY - JOUR A1 - Shojaei-Fard, Ali T1 - The global beta-functions from solutions of dyson-schwinger equations JF - Modern physics letters : A, Particles and fields, gravitation, cosmology, nuclear physics N2 - 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. KW - Dyson-Schwinger equations KW - beta-functions KW - renormalization Hopf algebra KW - equi-singular connections Y1 - 2013 U6 - https://doi.org/10.1142/S0217732313501526 SN - 0217-7323 SN - 1793-6632 VL - 28 IS - 34 PB - World Scientific CY - Singapore ER - TY - JOUR A1 - Shojaei-Fard, Ali T1 - Motivic Dyson-Schwinger equations JF - International journal of modern physics : A, Particles and fields, gravitation, cosmology, nuclear physics N2 - 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. KW - Connes-Kreimer Hopf algebra KW - Dyson-Schwinger equations KW - equi-singular connections KW - motivic Feynman rules KW - Picard-Fuchs equations KW - universal Hopf algebra of renormalization Y1 - 2013 U6 - https://doi.org/10.1142/S0217751X13501029 SN - 0217-751X VL - 28 IS - 20 PB - World Scientific CY - Singapore ER - TY - JOUR A1 - Shojaei-Fard, Ali T1 - Counterterms in the context of the universal Hopf algebra of renormalization JF - International journal of modern physics : A, Particles and fields, gravitation, cosmology, nuclear physics N2 - The manuscript discovers a new interpretation of counterterms of renormalizable Quantum Field Theories in terms of formal expansions of decorated rooted trees. KW - Perturbative renormalization KW - renormalization Hopf algebra KW - counterterms KW - rooted trees Y1 - 2014 U6 - https://doi.org/10.1142/S0217751X14500456 SN - 0217-751X SN - 1793-656X VL - 29 IS - 8 PB - World Scientific CY - Singapore ER - TY - JOUR A1 - Shtrakov, Slavcho A1 - Koppitz, Jörg T1 - Stable varieties of semigroups and groupoids JF - Algebra universalis N2 - 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. KW - composition of terms KW - essential position in terms KW - stable variety Y1 - 2016 U6 - https://doi.org/10.1007/s00012-015-0359-7 SN - 0002-5240 SN - 1420-8911 VL - 75 SP - 85 EP - 106 PB - Springer CY - Basel ER - TY - JOUR A1 - Siddiqui, Tarique Adnan A1 - Maute, Astrid A1 - Pedatella, Nick A1 - Yamazaki, Yosuke A1 - Lühr, Hermann A1 - Stolle, Claudia T1 - On the variability of the semidiurnal solar and lunar tides of the equatorial electrojet during sudden stratospheric warmings JF - Annales geophysicae N2 - 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. Y1 - 2018 U6 - https://doi.org/10.5194/angeo-36-1545-2018 SN - 0992-7689 SN - 1432-0576 VL - 36 IS - 6 SP - 1545 EP - 1562 PB - Copernicus CY - Göttingen ER - TY - JOUR A1 - Sinclair, Nathalie A1 - Bussi, Maria G. Bartolini A1 - de Villiers, Michael A1 - Jones, Keith A1 - Kortenkamp, Ulrich A1 - Leung, Allen A1 - Owens, Kay T1 - Recent research on geometry education: an ICME-13 survey team report JF - ZDM : The International Journal on Mathematics Education N2 - 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. KW - Geometry KW - Technology KW - Diagrams KW - Definitions KW - Gestures KW - Proving KW - Digital technology KW - Visuospatial reasoning Y1 - 2016 U6 - https://doi.org/10.1007/s11858-016-0796-6 SN - 1863-9690 SN - 1863-9704 VL - 48 SP - 691 EP - 719 PB - Springer CY - Heidelberg ER - TY - JOUR A1 - Siska, Veronika A1 - Jones, Eppie Ruth A1 - Jeon, Sungwon A1 - Bhak, Youngjune A1 - Kim, Hak-Min A1 - Cho, Yun Sung A1 - Kim, Hyunho A1 - Lee, Kyusang A1 - Veselovskaya, Elizaveta A1 - Balueva, Tatiana A1 - Gallego-Llorente, Marcos A1 - Hofreiter, Michael A1 - Bradley, Daniel G. A1 - Eriksson, Anders A1 - Pinhasi, Ron A1 - Bhak, Jong A1 - Manica, Andrea T1 - Genome-wide data from two early Neolithic East Asian individuals dating to 7700 years ago JF - Science Advances N2 - 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. Y1 - 2017 U6 - https://doi.org/10.1126/sciadv.1601877 SN - 2375-2548 VL - 3 IS - 2 PB - American Assoc. for the Advancement of Science CY - Washington ER - TY - JOUR A1 - Skeel, R. D. A1 - Reich, Sebastian T1 - Corrected potential energy functions for constrained molecular dynamics JF - European physical journal special topics N2 - 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. Y1 - 2011 U6 - https://doi.org/10.1140/epjst/e2011-01518-8 SN - 1951-6355 VL - 200 IS - 1 SP - 55 EP - 72 PB - Springer CY - Heidelberg ER - TY - THES A1 - Solms, Alexander Maximilian T1 - Integrating nonlinear mixed effects and physiologically–based modeling approaches for the analysis of repeated measurement studies T1 - Integration nicht-linearer gemischter Modelle und physiologie-basierte Modellierung Ansätze in die Auswertung longitudinaler Studien BT - with applications in quantitative pharmacology and quantitative psycholinguistics N2 - 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. N2 - Für die Erforschung und Entwicklung eines neuen Arzneistoffes wird die sichere und wirksame Anwendung in präklinischen und klinischen Studien systematisch untersucht. Ein wichtiger Bestandteil dieser Studien ist die Bestimmung der Pharmakokinetik (PK), da über diese das Wirkungs- und Nebenwirkungsprofil maßgeblich mitbestimmt wird. Um die PK zu bestimmen wird in der Studienpopulation die Wirkstoffkonzentration im Blut wiederholt über die Zeit gemessen. Damit kann sowohl der Konzentrations-Zeit-Verlauf als auch die dazugehörige Variabilität in der Studienpopulation bestimmt werden. Darüber hinaus ist ein weiteres Ziel, die Ursachen dieser Variabilität zu identifizieren. Fär die Auswertung der Daten werden nichtlineare, gemischte Effektmodelle (NLME) eingesetzt. Im Vorfeld der klinischen Studien sind bereits viele Eigenschaften des Wirkstoffes bekannt, da der Wirkstoff-Testung am Menschen die Bestimmung der PK an verschiedenen Tierspezies voraus geht. Auf Basis dieser wirkstoffspezifischen Daten und des Wissens um die spezifische humane Physiologie können mittels mechanistisch physiologiebasierter Modelle Vorhersagen für die humane PK getroffen werden. Bei der Analyse von PK Daten mittels NLME Modellen wird dieses vorhandene Wissen jedoch nicht verwertet. In physiologiebasierten Modellen werden physiologische Prozesse, die die PK bestimmen und beeinflussen können, ber+cksichtigt. Aus mathematischer Sicht sind solche mechanistischen Modelle im Allgemeinen deutlich komplexer als empirisch motivierte Modelle. In der Anwendung kommt es deswegen häufig zu Situationen, in denen die Anzahl der Modellparameter die Anzahl der zugrunde liegenden Beobachtungen übertrifft. Daraus folgt unter anderem, dass die Parameterschätzung, wie sie in empirisch motivierten Modellen genutzt wird, in der Regel unzuverlässig bzw. nicht möglich ist. In Folge dessen werden klinische Daten in der mechanistischen Modellierung meist nur zur Modellqualifizierung genutzt und nicht in die Modell(weiter)entwicklung integriert. Ein weiterer erschwerender Umstand, NLME und PBPK Modelle in der Anwendung zu kombinieren, beruht auch auf der Komplexität des NLME Ansatzes. Obwohl diese Methode seit Jahrzehnten existiert, sind in der Literatur nur ausgewählte Teilstücke der zugrunde liegenden Mathematik beschrieben und hergeleitet; eine lückenlose Beschreibung fehlt. Aus diesem Grund werden in der vorliegenden Arbeit systematisch die Methodik und mathematischen Zusammenhänge des NLME Ansatzes, von der ursprüngliche Idee und Motivation bis zur Parameterschätzung beschrieben. In diesem Kontext werden neue Interpretationen der unterschiedlichen Methoden, die im Rahmen der NLME Modellierung verwendet werden, vorgestellt; zudem werden Gemeinsamkeiten und Unterschiede zwischen diesen herausgearbeitet. Mittels dieser Erkenntnisse wird ein Expectation-Maximization (EM) Algorithmus zur Parameterschätzung in einer NLME Analyse beschrieben. Mittels des neuen EM Algorithmus, kombiniert mit dem Lumping-Ansatz von Pilari und Huisinga (S. Pilari, W. Huisinga, JPKPD Vol. 37(4), 2010.) wird anhand des Antibiotikums Levofloxacin ein neuer konzeptioneller Ansatz entwickelt, der PBPK- und NLME-Modellierung zur Datenanalyse integriert. Die Lumping-Methode definiert hierbei, welche Prozesse von den verfügbaren Daten informiert werden, sie verbessert somit die Robustheit der Parameterschätzung. Weiterhin wird gezeigt, wie a-priori Wissen über Variabilität und Faktoren, die diese beeinflussen, sowie unerklärte Variabilität in das Modell integriert werden können. Ein elementarer Vorteil von PBPK Modellen gegenüber empirisch motivieren PK Modellen besteht in der Möglichkeit, Wirkstoffkonzentrationen innerhalb von Organen und Gewebe im Körper vorherzusagen. So kann das PBPK-Modell für Levofloxacin genutzt werden, um Wirkstoffkonzentrationen innerhalb der Gewebe vorherzusagen, in denen typischerweise Infektionen auftreten. Für Muskel- und Fettgewebe werden die PBPK-Vorhersagen mit Mikrodialyse Gewebemessungen verglichen. Die gute übereinstimmung von PBPK-Modell und Mikrodialyse stellt eine noch nicht vorhanden Validierung des PBPK-Gewebemodells im Menschen dar. In dieser Dissertation wird gezeigt, wie mechanistische PBPK Modelle, die in der Regel in der frühen Phase der Arzneimittelentwicklung entwickelt werden, erfolgreich zur Analyse von klinischen Studien eingesetzt werden können. Das bestehende Wissen über den neuen Wirkstoff wird somit gezielt genutzt und mit klinischen Daten von Probanden oder Patienten aktualisiert. Im Fall von Levofloxacin konnte Variabilität in mechanistischen Prozessen identifiziert und quantifiziert werden. Dieses Vorgehen liefert einen weiteren Beitrag zum learn & confirm Paradigma im Forschungs- und Entwicklungsprozess eines neuen Wirkstoffes. Abschließend wird anhand eines weiteren real world-Beispieles aus dem Bereich der quantitativen Psycholinguistik die Anwendbarkeit und der Nutzen des vorgestellten integrierten Ansatz aus mechanistischer und NLME Modellierung in der Analyse von Blickbewegungsdaten gezeigt. Mittels eines mechanistisch motivierten Modells wird die Komplexität des Experimentes und der Daten abgebildet, wodurch sich neue Interpretationsmöglichkeiten ergeben. KW - NLME KW - PBPK KW - EM KW - lumping KW - popPBPK KW - mechanistic modeling KW - population analysis KW - popPK KW - microdialysis KW - nicht-lineare gemischte Modelle (NLME) KW - physiologie-basierte Pharmacokinetic (PBPK) KW - EM KW - Lumping KW - popPBPK KW - popPK KW - mechanistische Modellierung KW - Populations Analyse KW - Microdialyse Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-397070 ER - TY - JOUR A1 - Somogyvári, Márk A1 - Reich, Sebastian T1 - Convergence tests for transdimensional Markov chains in geoscience imaging JF - Mathematical geosciences : the official journal of the International Association for Mathematical Geosciences N2 - 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. KW - transdimensional inversion KW - MCMC modelling KW - convergence assessment Y1 - 2019 U6 - https://doi.org/10.1007/s11004-019-09811-x SN - 1874-8961 SN - 1874-8953 VL - 52 IS - 5 SP - 651 EP - 668 PB - Springer CY - Heidelberg ER - TY - THES A1 - Srithus, Ratana T1 - Algebras derived by hypersubstitutions Y1 - 2008 ER - TY - JOUR A1 - Stachanow, Viktoria A1 - Neumann, Uta A1 - Blankenstein, Oliver A1 - Bindellini, Davide A1 - Melin, Johanna A1 - Ross, Richard A1 - Whitaker, Martin J. J. A1 - Huisinga, Wilhelm A1 - Michelet, Robin A1 - Kloft, Charlotte T1 - Exploring dried blood spot cortisol concentrations as an alternative for monitoring pediatric adrenal insufficiency patients BT - a model-based analysis JF - Frontiers in pharmacology N2 - 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. KW - adrenal insufficiency KW - cortisol KW - dried blood spots KW - pediatrics KW - pharmacokinetics KW - binding KW - association KW - red blood cells Y1 - 2022 U6 - https://doi.org/10.3389/fphar.2022.819590 SN - 1663-9812 VL - 13 PB - Frontiers Media CY - Lausanne ER - TY - JOUR A1 - Staniforth, Andrew A1 - Wood, Nigel A1 - Reich, Sebastian T1 - A time-staggered semi-Lagrangian discretization of the rotating shallow-water equations JF - Quarterly journal of the Royal Meteorological Society N2 - 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. KW - regularization KW - temporal discretization Y1 - 2006 U6 - https://doi.org/10.1256/qj.06.30 SN - 0035-9009 VL - 132 IS - 621C SP - 3107 EP - 3116 PB - Wiley CY - Weinheim ER - TY - CHAP A1 - Steenholdt, Casper A1 - Edlund, Helena A1 - Ainsworth, Mark A. A1 - Brynskov, Jorn A1 - Thomsen, Ole Ostergaard A1 - Huisinga, Wilhelm A1 - Kloft, Charlotte T1 - Relationship between measures of infliximab exposure and clinical outcome of infliximab intensification at therapeutic failure in Crohn's disease T2 - JOURNAL OF CROHNS & COLITIS Y1 - 2015 SN - 1873-9946 SN - 1876-4479 VL - 9 SP - S330 EP - S330 PB - Oxford Univ. Press CY - Oxford ER - TY - JOUR A1 - Stepanenko, Victor A1 - Tarkhanov, Nikolai Nikolaevich T1 - The Cauchy problem for Chaplygin's system N2 - 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. Y1 - 2010 UR - http://www.informaworld.com/openurl?genre=journal&issn=1747-6933 U6 - https://doi.org/10.1080/17476930903394978 SN - 1747-6933 ER - TY - JOUR A1 - Stephan, Christoph A. T1 - Inverse seesaw mechanism in noncommutative geometry N2 - 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. Y1 - 2009 UR - http://prd.aps.org/ U6 - https://doi.org/10.1103/Physrevd.80.065007 SN - 1550-7998 ER - TY - JOUR A1 - Stephan, Christoph A. T1 - Krajewski diagrams and the standard model N2 - 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. Y1 - 2009 UR - http://jmp.aip.org/ U6 - https://doi.org/10.1063/1.3112622 SN - 0022-2488 ER - TY - JOUR A1 - Stephan, Christoph A. T1 - New scalar fields in noncommutative geometry N2 - 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. Y1 - 2009 UR - http://prd.aps.org/ U6 - https://doi.org/10.1103/Physrevd.79.065013 SN - 1550-7998 ER - TY - JOUR A1 - Stolle, Claudia A1 - Michaelis, Ingo A1 - Rauberg, Jan T1 - The role of high-resolution geomagnetic field models for investigating ionospheric currents at low Earth orbit satellites JF - Earth, planets and space N2 - 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. KW - Geomagnetic field KW - Ionospheric current KW - Geomagnetic models Y1 - 2016 U6 - https://doi.org/10.1186/s40623-016-0494-1 SN - 1880-5981 VL - 68 PB - Springer CY - Heidelberg ER - TY - JOUR A1 - Strader, Anne A1 - Schneider, Max A1 - Schorlemmer, Danijel T1 - Prospective and retrospective evaluation of five-year earthquake forecast models for California JF - Geophysical journal international KW - Probabilistic forecasting KW - Statistical methods KW - Earthquake interaction KW - fore-casting KW - and prediction KW - Statistical seismology Y1 - 2017 U6 - https://doi.org/10.1093/gji/ggx268 SN - 0956-540X SN - 1365-246X VL - 211 SP - 239 EP - 251 PB - Oxford Univ. Press CY - Oxford ER - TY - GEN A1 - Strader, Anne A1 - Schneider, Max A1 - Schorlemmer, Danijel T1 - 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) T2 - Geophysical journal international N2 - 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. Y1 - 2017 U6 - https://doi.org/10.1093/gji/ggx496 SN - 0956-540X SN - 1365-246X VL - 212 IS - 2 SP - 1314 EP - 1314 PB - Oxford Univ. Press CY - Oxford ER - TY - JOUR A1 - Stübler, Sabine A1 - Kloft, Charlotte A1 - Huisinga, Wilhelm T1 - Cell-level systems biology model to study inflammatory bowel diseases and their treatment options JF - CPT: pharmacometrics & systems pharmacology N2 - 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. Y1 - 2023 U6 - https://doi.org/10.1002/psp4.12932 SN - 2163-8306 VL - 12 IS - 5 SP - 690 EP - 705 PB - Nature Publ. Group CY - London ER - TY - JOUR A1 - Sukiasyan, Hayk A1 - Melkonyan, Tatev T1 - Semi-recursive algorithm of piecewise linear approximation of two-dimensional function by the method of worst segment dividing JF - Lectures in pure and applied mathematics KW - random point processes KW - statistical mechanics KW - stochastic analysis Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-471982 SN - 978-3-86956-485-2 SN - 2199-4951 SN - 2199-496X IS - 6 SP - 35 EP - 44 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - INPR A1 - Sultanov, Oskar A1 - Kalyakin, Leonid A1 - Tarkhanov, Nikolai Nikolaevich T1 - Elliptic perturbations of dynamical systems with a proper node N2 - 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. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 3 (2014) 4 KW - dynamical system KW - singular perturbation KW - asymptotic methods Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-70460 SN - 2193-6943 VL - 3 IS - 4 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - THES A1 - Supaporn, Worakrit T1 - Categorical equivalence of clones Y1 - 2014 ER - TY - THES A1 - Susanti, Yeni T1 - On Particular n-Clones Y1 - 2013 CY - Potsdam ER - TY - JOUR A1 - Taghvaei, Amirhossein A1 - de Wiljes, Jana A1 - Mehta, Prashant G. A1 - Reich, Sebastian T1 - Kalman filter and its modern extensions for the continuous-time nonlinear filtering problem JF - Journal of dynamic systems measurement and control N2 - 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. Y1 - 2017 U6 - https://doi.org/10.1115/1.4037780 SN - 0022-0434 SN - 1528-9028 VL - 140 IS - 3 PB - ASME CY - New York ER -