TY - JOUR A1 - Saposhnikov, V. V. A1 - Morosov, Andrej A1 - Saposhnikov, Vl. V. A1 - Gössel, Michael T1 - Design of self-checking unidirectional combinational circuits with low area overhead Y1 - 1997 ER - TY - JOUR A1 - Lilienkamp, Henning A1 - von Specht, Sebastian A1 - Weatherill, Graeme A1 - Caire, Giuseppe A1 - Cotton, Fabrice T1 - Ground-Motion modeling as an image processing task BT - introducing a neural network based, fully data-driven, and nonergodic JF - Bulletin of the Seismological Society of America N2 - We construct and examine the prototype of a deep learning-based ground-motion model (GMM) that is both fully data driven and nonergodic. We formulate ground-motion modeling as an image processing task, in which a specific type of neural network, the U-Net, relates continuous, horizontal maps of earthquake predictive parameters to sparse observations of a ground-motion intensity measure (IM). The processing of map-shaped data allows the natural incorporation of absolute earthquake source and observation site coordinates, and is, therefore, well suited to include site-, source-, and path-specific amplification effects in a nonergodic GMM. Data-driven interpolation of the IM between observation points is an inherent feature of the U-Net and requires no a priori assumptions. We evaluate our model using both a synthetic dataset and a subset of observations from the KiK-net strong motion network in the Kanto basin in Japan. We find that the U-Net model is capable of learning the magnitude???distance scaling, as well as site-, source-, and path-specific amplification effects from a strong motion dataset. The interpolation scheme is evaluated using a fivefold cross validation and is found to provide on average unbiased predictions. The magnitude???distance scaling as well as the site amplification of response spectral acceleration at a period of 1 s obtained for the Kanto basin are comparable to previous regional studies. Y1 - 2022 U6 - https://doi.org/10.1785/0120220008 SN - 0037-1106 SN - 1943-3573 VL - 112 IS - 3 SP - 1565 EP - 1582 PB - Seismological Society of America CY - Albany ER - TY - JOUR A1 - Zöller, Gert A1 - Ullah, Shahid A1 - Bindi, Dino A1 - Parolai, Stefano A1 - Mikhailova, Natalya T1 - The largest expected earthquake magnitudes in Central Asia BT - statistical inference from an earthquake catalogue with uncertain magnitudes JF - Seismicity, fault rupture and earthquake hazards in slowly deforming regions N2 - The knowledge of the largest expected earthquake magnitude in a region is one of the key issues in probabilistic seismic hazard calculations and the estimation of worst-case scenarios. Earthquake catalogues are the most informative source of information for the inference of earthquake magnitudes. We analysed the earthquake catalogue for Central Asia with respect to the largest expected magnitudes m(T) in a pre-defined time horizon T-f using a recently developed statistical methodology, extended by the explicit probabilistic consideration of magnitude errors. For this aim, we assumed broad error distributions for historical events, whereas the magnitudes of recently recorded instrumental earthquakes had smaller errors. The results indicate high probabilities for the occurrence of large events (M >= 8), even in short time intervals of a few decades. The expected magnitudes relative to the assumed maximum possible magnitude are generally higher for intermediate-depth earthquakes (51-300 km) than for shallow events (0-50 km). For long future time horizons, for example, a few hundred years, earthquakes with M >= 8.5 have to be taken into account, although, apart from the 1889 Chilik earthquake, it is probable that no such event occurred during the observation period of the catalogue. Y1 - 2017 SN - 978-1-86239-745-3 SN - 978-1-86239-964-8 U6 - https://doi.org/10.1144/SP432.3 SN - 0305-8719 VL - 432 SP - 29 EP - 40 PB - The Geological Society CY - London ER - TY - JOUR A1 - Harutjunjan, Gohar A1 - Schulze, Bert-Wolfgang T1 - Reduction of orders in boundary value problems without transmission property N2 - Given an algebra of pseudo-differential operators on a manifold, an elliptic element is said to be a reduction of orders, if it induces isomorphisms of Sobolev spaces with a corresponding shift of smoothness. Reductions of orders on a manifold with boundary refer to boundary value problems. We employ specific smooth symbols of arbitrary real orders and with parameters, and we show that the associated operators induce isomorphisms between Sobolev spaces on a given manifold with boundary. Such operators for integer orders have the transmission property and belong to the calculus of Boutet de Monvel [1], cf. also [9]. In general, they fit to the algebra of boundary value problems without the transmission property in the sense of [17] and [24]. Order reducing elements of the present kind are useful for constructing parametrices of mixed elliptic problems. We show that order reducing symbols have the Volterra property and are parabolic of anisotropy 1; analogous relations are formulated for arbitrary anisotropies. We then investigate parameter-dependent operators, apply a kernel cut-off construction with respect to the parameter and show that corresponding holomorphic operator-valued Mellin symbols reduce orders in weighted Sobolev spaces on a cone with boundary. We finally construct order reducing operators on a compact manifold with conical singularities and boundary Y1 - 2004 SN - 0025-5645 ER - TY - JOUR A1 - Harutjunjan, Gohar A1 - Schulze, Bert-Wolfgang T1 - Parametrices of mixed elliptic problems N2 - Mixed elliptic problems for differential operators A in a domain Q with smooth boundary Y are studied in the form Au = f in Omega, T+/-u = g+/- on Y+/-, where Y+/- subset of Y are manifolds with a common boundary Z, such that Y- boolean OR Y+ = Y and Y- boolean AND Y+ = z, with boundary conditions T+/- on Y+/- (with smooth coefficients up to Z from the respective side) satisfying the Shapiro-Lopatinskij condition. We consider such problems in standard Sobolev spaces and characterise natural extra conditions on the interface Z with an analogue of Shapiro-Lopatinskij ellipticity for an associated transmission problem on the boundary; then the extended operator is Fredholm. The transmission operators on the boundary with respect to Z belong to a complete pseudo-differential calculus, a modification of the algebra of boundary value problems without the transmission property. We construct parametrices of elliptic elements in that calculus, and we obtain parametrices of the original mixed problems under additional conditions on the interface. We consider the Zaremba problem and other mixed problems for the Laplace operator, determine the number of extra conditions and calculate the index of associated Fredholm operators. (C) 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim Y1 - 2004 SN - 0025-584X ER - TY - BOOK A1 - Nazajkinskij, Vladimir E. A1 - Savin, Anton A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - Elliptic theory on manifolds with nonisolated singularities : 5 Index formulas for elliptic problems on manifolds with edges T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2003 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Schulze, Bert-Wolfgang T1 - Toeplitz operators, and ellipticity of boundary value problems with global projection conditions T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2003 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Dines, Nicoleta A1 - Harutjunjan, Gohar A1 - Schulze, Bert-Wolfgang T1 - The Zaremba problem in edge sobolev spaces T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2003 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Dines, Nicoleta A1 - Schulze, Bert-Wolfgang T1 - Melin-edges representations of elliptic operators T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2003 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Schulze, Bert-Wolfgang T1 - Crack theory with singularities at the boundary T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2003 SN - 1437-739X PB - Univ. CY - Potsdam ER -