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 - Zöller, Gert A1 - Holschneider, Matthias A1 - Hainzl, Sebastian T1 - The Maximum Earthquake Magnitude in a Time Horizon: Theory and Case Studies JF - Bulletin of the Seismological Society of America N2 - We show how the maximum magnitude within a predefined future time horizon may be estimated from an earthquake catalog within the context of Gutenberg-Richter statistics. The aim is to carry out a rigorous uncertainty assessment, and calculate precise confidence intervals based on an imposed level of confidence a. In detail, we present a model for the estimation of the maximum magnitude to occur in a time interval T-f in the future, given a complete earthquake catalog for a time period T in the past and, if available, paleoseismic events. For this goal, we solely assume that earthquakes follow a stationary Poisson process in time with unknown productivity Lambda and obey the Gutenberg-Richter law in magnitude domain with unknown b-value. The random variables. and b are estimated by means of Bayes theorem with noninformative prior distributions. Results based on synthetic catalogs and on retrospective calculations of historic catalogs from the highly active area of Japan and the low-seismicity, but high-risk region lower Rhine embayment (LRE) in Germany indicate that the estimated magnitudes are close to the true values. Finally, we discuss whether the techniques can be extended to meet the safety requirements for critical facilities such as nuclear power plants. For this aim, the maximum magnitude for all times has to be considered. In agreement with earlier work, we find that this parameter is not a useful quantity from the viewpoint of statistical inference. Y1 - 2013 U6 - https://doi.org/10.1785/0120120013 SN - 0037-1106 VL - 103 IS - 2A SP - 860 EP - 875 PB - Seismological Society of America CY - Albany ER - TY - GEN A1 - Zöller, Gert A1 - Holschneider, Matthias T1 - Reply to “Comment on ‘The Maximum Possible and the Maximum Expected Earthquake Magnitude for Production‐Induced Earthquakes at the Gas Field in Groningen, The Netherlands’ by Gert Zöller and Matthias Holschneider” by Mathias Raschke T2 - Bulletin of the Seismological Society of America Y1 - 2018 U6 - https://doi.org/10.1785/0120170131 SN - 0037-1106 SN - 1943-3573 VL - 108 IS - 2 SP - 1029 EP - 1030 PB - Seismological Society of America CY - Albany ER - TY - JOUR A1 - Zöller, Gert A1 - Holschneider, Matthias T1 - Induced seismicity: What is the size of the largest expected earthquake? JF - The bulletin of the Seismological Society of America N2 - The injection of fluids is a well-known origin for the triggering of earthquake sequences. The growing number of projects related to enhanced geothermal systems, fracking, and others has led to the question, which maximum earthquake magnitude can be expected as a consequence of fluid injection? This question is addressed from the perspective of statistical analysis. Using basic empirical laws of earthquake statistics, we estimate the magnitude M-T of the maximum expected earthquake in a predefined future time window T-f. A case study of the fluid injection site at Paradox Valley, Colorado, demonstrates that the magnitude m 4.3 of the largest observed earthquake on 27 May 2000 lies very well within the expectation from past seismicity without adjusting any parameters. Vice versa, for a given maximum tolerable earthquake at an injection site, we can constrain the corresponding amount of injected fluids that must not be exceeded within predefined confidence bounds. Y1 - 2014 U6 - https://doi.org/10.1785/0120140195 SN - 0037-1106 SN - 1943-3573 VL - 104 IS - 6 SP - 3153 EP - 3158 PB - Seismological Society of America CY - Albany ER - TY - JOUR A1 - Zöller, Gert A1 - Holschneider, Matthias T1 - The Maximum Possible and the Maximum Expected Earthquake Magnitude for Production-Induced Earthquakes at the Gas Field in Groningen, The Netherlands JF - Bulletin of the Seismological Society of America N2 - The Groningen gas field serves as a natural laboratory for production-induced earthquakes, because no earthquakes were observed before the beginning of gas production. Increasing gas production rates resulted in growing earthquake activity and eventually in the occurrence of the 2012M(w) 3.6 Huizinge earthquake. At least since this event, a detailed seismic hazard and risk assessment including estimation of the maximum earthquake magnitude is considered to be necessary to decide on the future gas production. In this short note, we first apply state-of-the-art methods of mathematical statistics to derive confidence intervals for the maximum possible earthquake magnitude m(max). Second, we calculate the maximum expected magnitude M-T in the time between 2016 and 2024 for three assumed gas-production scenarios. Using broadly accepted physical assumptions and 90% confidence level, we suggest a value of m(max) 4.4, whereas M-T varies between 3.9 and 4.3, depending on the production scenario. Y1 - 2016 U6 - https://doi.org/10.1785/0120160220 SN - 0037-1106 SN - 1943-3573 VL - 106 SP - 2917 EP - 2921 PB - Seismological Society of America CY - Albany ER - TY - JOUR A1 - Zöller, Gert A1 - Holschneider, Matthias T1 - The Earthquake History in a Fault Zone Tells Us Almost Nothing about m(max) JF - Seismological research letters N2 - In the present study, we summarize and evaluate the endeavors from recent years to estimate the maximum possible earthquake magnitude m(max) from observed data. In particular, we use basic and physically motivated assumptions to identify best cases and worst cases in terms of lowest and highest degree of uncertainty of m(max). In a general framework, we demonstrate that earthquake data and earthquake proxy data recorded in a fault zone provide almost no information about m(max) unless reliable and homogeneous data of a long time interval, including several earthquakes with magnitude close to m(max), are available. Even if detailed earthquake information from some centuries including historic and paleoearthquakes are given, only very few, namely the largest events, will contribute at all to the estimation of m(max), and this results in unacceptably high uncertainties. As a consequence, estimators of m(max) in a fault zone, which are based solely on earthquake-related information from this region, have to be dismissed. Y1 - 2016 U6 - https://doi.org/10.1785/0220150176 SN - 0895-0695 SN - 1938-2057 VL - 87 SP - 132 EP - 137 PB - Seismological Society of America CY - Albany ER - TY - JOUR A1 - Zöller, Gert A1 - Hainzl, Sebastian A1 - Tilmann, Frederik A1 - Woith, Heiko A1 - Dahm, Torsten T1 - Comment on: Wikelski, Martin; Müller, Uschi; Scocco, Paola; Catorci, Andrea; Desinov, Lev V.; Belyaev, Mikhail Y.; Keim, Daniel A.; Pohlmeier, Winfried; Fechteler, Gerhard; Mai, Martin P. : Potential short-term earthquake forecasting by farm animal monitoring. - Ethology. - 126 (2020), 9. - S. 931 - 941. -ISSN 0179-1613. - eISSN 1439-0310. - doi 10.1111/eth.13078 JF - Ethology N2 - Based on an analysis of continuous monitoring of farm animal behavior in the region of the 2016 M6.6 Norcia earthquake in Italy, Wikelski et al., 2020; (Seismol Res Lett, 89, 2020, 1238) conclude that animal activity can be anticipated with subsequent seismic activity and that this finding might help to design a "short-term earthquake forecasting method." We show that this result is based on an incomplete analysis and misleading interpretations. Applying state-of-the-art methods of statistics, we demonstrate that the proposed anticipatory patterns cannot be distinguished from random patterns, and consequently, the observed anomalies in animal activity do not have any forecasting power. KW - animal behavior KW - earthquake precursor KW - error diagram KW - prediction KW - randomness KW - statistics Y1 - 2020 U6 - https://doi.org/10.1111/eth.13105 SN - 0179-1613 SN - 1439-0310 VL - 127 IS - 3 SP - 302 EP - 306 PB - Wiley CY - Hoboken ER - TY - JOUR A1 - Zöller, Gert A1 - Ben-Zion, Yehuda T1 - Large earthquake hazard of the San Jacinto fault zone, CA, from long record of simulated seismicity assimilating the available instrumental and paleoseismic data JF - Pure and applied geophysics N2 - We investigate spatio-temporal properties of earthquake patterns in the San Jacinto fault zone (SJFZ), California, between Cajon Pass and the Superstition Hill Fault, using a long record of simulated seismicity constrained by available seismological and geological data. The model provides an effective realization of a large segmented strike-slip fault zone in a 3D elastic half-space, with heterogeneous distribution of static friction chosen to represent several clear step-overs at the surface. The simulated synthetic catalog reproduces well the basic statistical features of the instrumental seismicity recorded at the SJFZ area since 1981. The model also produces events larger than those included in the short instrumental record, consistent with paleo-earthquakes documented at sites along the SJFZ for the last 1,400 years. The general agreement between the synthetic and observed data allows us to address with the long-simulated seismicity questions related to large earthquakes and expected seismic hazard. The interaction between m a parts per thousand yen 7 events on different sections of the SJFZ is found to be close to random. The hazard associated with m a parts per thousand yen 7 events on the SJFZ increases significantly if the long record of simulated seismicity is taken into account. The model simulations indicate that the recent increased number of observed intermediate SJFZ earthquakes is a robust statistical feature heralding the occurrence of m a parts per thousand yen 7 earthquakes. The hypocenters of the m a parts per thousand yen 5 events in the simulation results move progressively towards the hypocenter of the upcoming m a parts per thousand yen 7 earthquake. KW - Earthquake dynamics KW - Earthquake interaction KW - forecasting KW - prediction KW - Statistical seismology KW - Seismicity and tectonics Y1 - 2014 U6 - https://doi.org/10.1007/s00024-014-0783-1 SN - 0033-4553 SN - 1420-9136 VL - 171 IS - 11 SP - 2955 EP - 2965 PB - Springer CY - Basel ER - TY - JOUR A1 - Zöller, Gert T1 - A note on the estimation of the maximum possible earthquake magnitude based on extreme value theory for the Groningen Gas Field JF - The bulletin of the Seismological Society of America : BSSA N2 - Extreme value statistics is a popular and frequently used tool to model the occurrence of large earthquakes. The problem of poor statistics arising from rare events is addressed by taking advantage of the validity of general statistical properties in asymptotic regimes. In this note, I argue that the use of extreme value statistics for the purpose of practically modeling the tail of the frequency-magnitude distribution of earthquakes can produce biased and thus misleading results because it is unknown to what degree the tail of the true distribution is sampled by data. Using synthetic data allows to quantify this bias in detail. The implicit assumption that the true M-max is close to the maximum observed magnitude M-max,M-observed restricts the class of the potential models a priori to those with M-max = M-max,M-observed + Delta M with an increment Delta M approximate to 0.5... 1.2. This corresponds to the simple heuristic method suggested by Wheeler (2009) and labeled :M-max equals M-obs plus an increment." The incomplete consideration of the entire model family for the frequency-magnitude distribution neglects, however, the scenario of a large so far unobserved earthquake. Y1 - 2022 U6 - https://doi.org/10.1785/0120210307 SN - 0037-1106 SN - 1943-3573 VL - 112 IS - 4 SP - 1825 EP - 1831 PB - Seismological Society of America CY - El Cerito, Calif. ER - TY - JOUR A1 - Zöller, Gert T1 - A statistical model for earthquake recurrence based on the assimilation of paleoseismicity, historic seismicity, and instrumental seismicity JF - Journal of geophysical research : Solid earth N2 - Paleoearthquakes and historic earthquakes are the most important source of information for the estimation of long-term earthquake recurrence intervals in fault zones, because corresponding sequences cover more than one seismic cycle. However, these events are often rare, dating uncertainties are enormous, and missing or misinterpreted events lead to additional problems. In the present study, I assume that the time to the next major earthquake depends on the rate of small and intermediate events between the large ones in terms of a clock change model. Mathematically, this leads to a Brownian passage time distribution for recurrence intervals. I take advantage of an earlier finding that under certain assumptions the aperiodicity of this distribution can be related to the Gutenberg-Richter b value, which can be estimated easily from instrumental seismicity in the region under consideration. In this way, both parameters of the Brownian passage time distribution can be attributed with accessible seismological quantities. This allows to reduce the uncertainties in the estimation of the mean recurrence interval, especially for short paleoearthquake sequences and high dating errors. Using a Bayesian framework for parameter estimation results in a statistical model for earthquake recurrence intervals that assimilates in a simple way paleoearthquake sequences and instrumental data. I present illustrative case studies from Southern California and compare the method with the commonly used approach of exponentially distributed recurrence times based on a stationary Poisson process. KW - statistical seismology KW - paleoearthquakes KW - stochastic models KW - seismic hazard Y1 - 2018 U6 - https://doi.org/10.1029/2017JB015099 SN - 2169-9313 SN - 2169-9356 VL - 123 IS - 6 SP - 4906 EP - 4921 PB - American Geophysical Union CY - Washington ER - TY - JOUR A1 - Zöller, Gert T1 - Convergence of the frequency-magnitude distribution of global earthquakes - maybe in 200 years JF - Geophysical research letters N2 - I study the ability to estimate the tail of the frequency-magnitude distribution of global earthquakes. While power-law scaling for small earthquakes is accepted by support of data, the tail remains speculative. In a recent study, Bell et al. (2013) claim that the frequency-magnitude distribution of global earthquakes converges to a tapered Pareto distribution. I show that this finding results from data fitting errors, namely from the biased maximum likelihood estimation of the corner magnitude theta in strongly undersampled models. In particular, the estimation of theta depends solely on the few largest events in the catalog. Taking this into account, I compare various state-of-the-art models for the global frequency-magnitude distribution. After discarding undersampled models, the remaining ones, including the unbounded Gutenberg-Richter distribution, perform all equally well and are, therefore, indistinguishable. Convergence to a specific distribution, if it ever takes place, requires about 200 years homogeneous recording of global seismicity, at least. KW - statistical seismology Y1 - 2013 U6 - https://doi.org/10.1002/grl.50779 SN - 0094-8276 SN - 1944-8007 VL - 40 IS - 15 SP - 3873 EP - 3877 PB - American Geophysical Union CY - Washington ER - TY - JOUR A1 - Zähle, Henryk T1 - Space-time regularity of catalytic super-Brownian motion N2 - The paper studies catalytic super-Brownian motion on the real line, where the branching rate is controlled by a catalyst. D. A. Dawson, K. Fleischmann and S. Roelly showed, for a broad class of catalysts, that, as for constant branching, the processes are absolutely continuous measures. This paper considers a class of catalysts, called moderate, which must satisfy a uniform boundedness condition and a condition controlling the degree of singularity---essentially that the mass of catalyst in small balls should (uniformly) be of order r^a, where a>0. The main result of this paper shows that for this class of catalysts there is a continuous density field for the process. Moreover the density is the unique solution (in law) of an appropriate SPDE. Y1 - 2005 UR - http://www.interscience.wiley.com/jpages/0025-584X/ ER - TY - JOUR A1 - Zähle, Henryk T1 - Heat equation with strongly inhomogeneous noise N2 - The author considers the heat equation in dimension one with singular drift and inhomogeneous space-time white noise. In particular, the quadratic variation measure of the white noise is not required to be absolutely continuous w.r.t. the Lebesgue measure, neither in space nor in time. Under some assumptions the author gives statements on strong and weak existence as well as strong and weak uniqueness of continuous solutions. Y1 - 2004 UR - http://www.sciencedirect.com/science/journal/03044149 ER - TY - JOUR A1 - Zolotov, O. V. A1 - Prokhorov, Boris E. A1 - Namgaladze, Alexander A. A1 - Martynenko, O. V. T1 - Variations in the total electron content of the ionosphere during preparation of earthquakes JF - Russian journal of physical chemistry : B, Focus on physics N2 - The morphological features in the deviations of the total electron content (TEC) of the ionosphere from the background undisturbed state as possible precursors of the earthquake of January 12, 2010 (21:53 UT (16:53 LT), 18.46A degrees N, 72.5A degrees W, 7.0 M) in Haiti are analyzed. To identify these features, global and regional differential TEC maps based on global 2-h TEC maps provided by NASA in the IONEX format were plotted. For the considered earthquake, long-lived disturbances, presumably of seismic origin, were localized in the near-epicenter area and were accompanied by similar effects in the magnetoconjugate region. Both decreases and increases in the local TEC over the period from 22 UT of January 10 to 08 UT of January 12, 2010 were observed. The horizontal dimensions of the anomalies were similar to 40A degrees in longitude and similar to 20A degrees in latitude, with the magnitude of TEC disturbances reaching similar to 40% relative to the background near the epicenter and more than 50% in the magnetoconjugate area. No significant geomagnetic disturbances within January 1-12, 2010 were observed, i.e., the detected TEC anomalies were manifestations of interplay between processes in the lithosphere-atmosphere-ionosphere system. KW - TEC KW - ionospheric precursors of earthquakes KW - GPS Y1 - 2011 U6 - https://doi.org/10.1134/S1990793111030146 SN - 1990-7931 VL - 5 IS - 3 SP - 435 EP - 438 PB - Pleiades Publ. CY - New York ER - TY - THES A1 - Ziese, Ramona T1 - Geometric electroelasticity T1 - Geometrische Elektroelastizität N2 - In this work a diffential geometric formulation of the theory of electroelasticity is developed which also includes thermal and magnetic influences. We study the motion of bodies consisting of an elastic material that are deformed by the influence of mechanical forces, heat and an external electromagnetic field. To this end physical balance laws (conservation of mass, balance of momentum, angular momentum and energy) are established. These provide an equation that describes the motion of the body during the deformation. Here the body and the surrounding space are modeled as Riemannian manifolds, and we allow that the body has a lower dimension than the surrounding space. In this way one is not (as usual) restricted to the description of the deformation of three-dimensional bodies in a three-dimensional space, but one can also describe the deformation of membranes and the deformation in a curved space. Moreover, we formulate so-called constitutive relations that encode the properties of the used material. Balance of energy as a scalar law can easily be formulated on a Riemannian manifold. The remaining balance laws are then obtained by demanding that balance of energy is invariant under the action of arbitrary diffeomorphisms on the surrounding space. This generalizes a result by Marsden and Hughes that pertains to bodies that have the same dimension as the surrounding space and does not allow the presence of electromagnetic fields. Usually, in works on electroelasticity the entropy inequality is used to decide which otherwise allowed deformations are physically admissible and which are not. It is alsoemployed to derive restrictions to the possible forms of constitutive relations describing the material. Unfortunately, the opinions on the physically correct statement of the entropy inequality diverge when electromagnetic fields are present. Moreover, it is unclear how to formulate the entropy inequality in the case of a membrane that is subjected to an electromagnetic field. Thus, we show that one can replace the use of the entropy inequality by the demand that for a given process balance of energy is invariant under the action of arbitrary diffeomorphisms on the surrounding space and under linear rescalings of the temperature. On the one hand, this demand also yields the desired restrictions to the form of the constitutive relations. On the other hand, it needs much weaker assumptions than the arguments in physics literature that are employing the entropy inequality. Again, our result generalizes a theorem of Marsden and Hughes. This time, our result is, like theirs, only valid for bodies that have the same dimension as the surrounding space. N2 - In der vorliegenden Arbeit wird eine diffentialgeometrische Formulierung der Elektroelastizitätstheorie entwickelt, die auch thermische und magnetische Einflüsse berücksichtigt. Hierbei wird die Bewegung von Körpern untersucht, die aus einem elastischen Material bestehen und sich durch mechanische Kräfte, Wärmezufuhr und den Einfluss eines äußeren elektromagnetischen Feldes verformen. Dazu werden physikalische Bilanzgleichungen (Massenerhaltung, Impuls-, Drehimpuls- und Energiebilanz) aufgestellt, um mit deren Hilfe eine Gleichung zu formulieren, die die Bewegung des Körpers während der Deformation beschreibt. Dabei werden sowohl der Körper als auch der umgebende Raum als Riemannsche Mannigfaltigkeiten modelliert, wobei zugelassen ist, dass der Körper eine geringere Dimension hat als der ihn umgebende Raum. Auf diese Weise kann man nicht nur - wie sonst üblich - die Deformation dreidimensionaler Körper im dreidimensionalen euklidischen Raum beschreiben, sondern auch die Deformation von Membranen und die Deformation innerhalb eines gekrümmten Raums. Weiterhin werden sogenannte konstitutive Gleichungen formuliert, die die Eigenschaften des verwendeten Materials kodieren. Die Energiebilanz ist eine skalare Gleichung und kann daher leicht auf Riemannschen Mannigfaltigkeiten formuliert werden. Es wird gezeigt, dass die Forderung der Invarianz der Energiebilanz unter der Wirkung von beliebigen Diffeomorphismen auf den umgebenden Raum bereits die restlichen Bilanzgleichungen impliziert. Das verallgemeinert ein Resultat von Marsden und Hughes, das nur für Körper anwendbar ist, die die selbe Dimension wie der umgebende Raum haben und keine elektromagnetischen Felder berücksichtigt. Üblicherweise wird in Arbeiten über Elektroelastizität die Entropieungleichung verwendet, um zu entscheiden, welche Deformationen physikalisch zulässig sind und welche nicht. Sie wird außerdem verwendet, um Einschränkungen für die möglichen Formen von konstitutiven Gleichungen, die das Material beschreiben, herzuleiten. Leider gehen die Meinungen über die physikalisch korrekte Formulierung der Entropieungleichung auseinander sobald elektromagnetische Felder beteiligt sind. Weiterhin ist unklar, wie die Entropieungleichung für den Fall einer Membran, die einem elektromagnetischen Feld ausgesetzt ist, formuliert werden muss. Daher zeigen wir, dass die Benutzung der Entropieungleichung ersetzt werden kann durch die Forderung, dass für einen gegebenen Prozess die Energiebilanz invariant ist unter der Wirkung eines beliebigen Diffeomorphimus' auf den umgebenden Raum und der linearen Reskalierung der Temperatur. Zum einen liefert diese Forderung die gewünschten Einschränkungen für die Form der konstitutiven Gleichungen, zum anderen benoetigt sie viel schwächere Annahmen als die übliche Argumentation mit der Entropieungleichung, die man in der Physikliteratur findet. Unser Resultat ist dabei wieder eine Verallgemeinerung eines Theorems von Marsden und Hughes, wobei es, so wie deren Resultat, nur für Körper gilt, die als offene Teilmengen des dreidimensionalen euklidischen Raums modelliert werden können. KW - Elastizität KW - Elektrodynamik KW - Mannigfaltigkeit KW - konstitutive Gleichungen KW - Bewegungsgleichung KW - elasticity KW - electrodynamics KW - manifold KW - constitutive relations KW - equation of motion Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-72504 ER - TY - JOUR A1 - Ziehe, Andreas A1 - Laskov, Pavel A1 - Nolte, G A1 - Müller, Klaus-Robert T1 - A fast algorithm for joint diagonalization with non-orthogonal transformations and its application to blind source separation N2 - A new efficient algorithm is presented for joint diagonalization of several matrices. The algorithm is based on the Frobenius-norm formulation of the joint diagonalization problem, and addresses diagonalization with a general, non- orthogonal transformation. The iterative scheme of the algorithm is based on a multiplicative update which ensures the invertibility of the diagonalizer. The algorithm's efficiency stems from the special approximation of the cost function resulting in a sparse, block-diagonal Hessian to be used in the computation of the quasi-Newton update step. Extensive numerical simulations illustrate the performance of the algorithm and provide a comparison to other leading diagonalization methods. The results of such comparison demonstrate that the proposed algorithm is a viable alternative to existing state-of-the-art joint diagonalization algorithms. The practical use of our algorithm is shown for blind source separation problems Y1 - 2004 ER - TY - JOUR A1 - Zhuk, Alexandre A1 - Gunther, U. T1 - Massive scalar fields in the early universe N2 - We discuss the role of gravitational excitons/radions in different cosmological scenarios. Gravitational excitons are massive moduli fields which describe conformal excitations of the internal spaces and which, due to their Planck-scale suppressed coupling to matter fields, are WIMPs. It is demonstrated that, depending on the concrete scenario, observational cosmological data set strong restrictions on the allowed masses and initial oscillation amplitudes of these particles Y1 - 2004 SN - 0218-2718 ER - TY - BOOK A1 - Zhuchok, Anatolii V. T1 - Relatively free doppelsemigroups N2 - A doppelalgebra is an algebra defined on a vector space with two binary linear associative operations. Doppelalgebras play a prominent role in algebraic K-theory. We consider doppelsemigroups, that is, sets with two binary associative operations satisfying the axioms of a doppelalgebra. Doppelsemigroups are a generalization of semigroups and they have relationships with such algebraic structures as interassociative semigroups, restrictive bisemigroups, dimonoids, and trioids. In the lecture notes numerous examples of doppelsemigroups and of strong doppelsemigroups are given. The independence of axioms of a strong doppelsemigroup is established. A free product in the variety of doppelsemigroups is presented. We also construct a free (strong) doppelsemigroup, a free commutative (strong) doppelsemigroup, a free n-nilpotent (strong) doppelsemigroup, a free n-dinilpotent (strong) doppelsemigroup, and a free left n-dinilpotent doppelsemigroup. Moreover, the least commutative congruence, the least n-nilpotent congruence, the least n-dinilpotent congruence on a free (strong) doppelsemigroup and the least left n-dinilpotent congruence on a free doppelsemigroup are characterized. The book addresses graduate students, post-graduate students, researchers in algebra and interested readers. N2 - Eine Doppelalgebra ist eine auf einem Vektorraum definierte Algebra mit zwei binären linearen assoziativen Operationen. Doppelalgebren spielen eine herausragende Rolle in der algebraischen K-Theorie. Wir betrachten Doppelhalbgruppen, d.h Mengen mit zwei binären assoziativen Operationen, welche die Axiome der Doppelhalbgruppe erfüllen. Doppelhalbgruppen sind Veralgemeinerungen von Halbgruppen und sie stehen in Beziehung zu solchen algebraischen Strukturen wie interassoziative Halbgruppen, restriktive Bihalbgruppen, Dimonoiden und Trioden. In dieser Lecture Notes werden eine Vielzahl von Beispielen für Doppelhalbgruppen und strong Doppelhalbgruppen gegeben. Die Unabhängigkeit der Axiome für Doppelhalbgruppen wird nachgewiesen. Ein freies Produkt in der Varietät der Doppelhalbgruppen wird vorgestellt. Wir konstruieren auch eine freie (kommutative) strong Doppelhalbgruppe, eine freie n-dinilpotent (strong) Doppelhalbgruppe und eine freie Links n-dinilpotent Doppelhalbgruppe. Darüber hinaus werden die kleinste n-nilpotente Kogruenz, die kleinste n-dinilpotente Kongruenz auf der freien (strong) Doppelhalbgruppe und die kleinste n-dinilpotente Kongruenz auf einer freien Doppelhalbgruppe charakterisiert. Das Buch richtet sich an Graduierte, Doktoranden, Forscher in Algebra und interessierte Leser. T3 - Lectures in pure and applied mathematics - 5 KW - doppelsemigroup KW - interassociativity KW - free algebra KW - semigroup KW - congruence Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-407719 SN - 978-3-86956-427-2 SN - 2199-4951 SN - 2199-496X IS - 5 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - INPR A1 - Zessin, Hans T1 - Classical Symmetric Point Processes : Lectures held at ICIMAF, La Habana, Cuba, 2010 N2 - The aim of these lectures is a reformulation and generalization of the fundamental investigations of Alexander Bach [2, 3] on the concept of probability in the work of Boltzmann [6] in the language of modern point process theory. The dominating point of view here is its subordination under the disintegration theory of Krickeberg [14]. This enables us to make Bach's consideration much more transparent. Moreover the point process formulation turns out to be the natural framework for the applications to quantum mechanical models. T3 - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2010, 06 Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49619 ER - TY - BOOK A1 - Zendler, Andreas T1 - Poweranalytische Versuchsplanung zur Kontrolle statistischer und softwaretechnischer Relevanz T3 - Preprint / Universität Potsdam, Institut für Informatik Y1 - 1998 SN - 0946-7580 VL - 1998, 07 PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Zendler, Andreas T1 - Einzelfallanalytische Versuchspläne der Biometrie zur Durchführung software-technischer Experimente mit N=1 T3 - Preprint / Universität Potsdam, Institut für Informatik Y1 - 1999 SN - 0946-7580 VL - 1999, 10 PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Zemella, Anne A1 - Thoring, Lena A1 - Hoffmeister, Christian A1 - Samalikova, Maria A1 - Ehren, Patricia A1 - Wüstenhagen, Doreen Anja A1 - Kubick, Stefan T1 - Cell-free protein synthesis as a novel tool for directed glycoengineering of active erythropoietin JF - Scientific reports N2 - As one of the most complex post-translational modification, glycosylation is widely involved in cell adhesion, cell proliferation and immune response. Nevertheless glycoproteins with an identical polypeptide backbone mostly differ in their glycosylation patterns. Due to this heterogeneity, the mapping of different glycosylation patterns to their associated function is nearly impossible. In the last years, glycoengineering tools including cell line engineering, chemoenzymatic remodeling and site-specific glycosylation have attracted increasing interest. The therapeutic hormone erythropoietin (EPO) has been investigated in particular by various groups to establish a production process resulting in a defined glycosylation pattern. However commercially available recombinant human EPO shows batch-to-batch variations in its glycoforms. Therefore we present an alternative method for the synthesis of active glycosylated EPO with an engineered O-glycosylation site by combining eukaryotic cell-free protein synthesis and site-directed incorporation of non-canonical amino acids with subsequent chemoselective modifications. Y1 - 2018 U6 - https://doi.org/10.1038/s41598-018-26936-x SN - 2045-2322 VL - 8 PB - Nature Publ. Group CY - London ER - TY - INPR A1 - Zehmisch, René T1 - Über Waldidentitäten der Brownschen Bewegung N2 - Aus dem Inhalt: 1 Abraham Wald (1902-1950) 2 Einführung der Grundbegriffe. Einige technische bekannte Ergebnisse 2.1 Martingal und Doob-Ungleichung 2.2 Brownsche Bewegung und spezielle Martingale 2.3 Gleichgradige Integrierbarkeit von Prozessen 2.4 Gestopptes Martingal 2.5 Optionaler Stoppsatz von Doob 2.6 Lokales Martingal 2.7 Quadratische Variation 2.8 Die Dichte der ersten einseitigen Überschreitungszeit der Brown- schen Bewegung 2.9 Waldidentitäten für die Überschreitungszeiten der Brownschen Bewegung 3 Erste Waldidentität 3.1 Burkholder, Gundy und Davis Ungleichungen der gestoppten Brown- schen Bewegung 3.2 Erste Waldidentität für die Brownsche Bewegung 3.3 Verfeinerungen der ersten Waldidentität 3.4 Stärkere Verfeinerung der ersten Waldidentität für die Brown- schen Bewegung 3.5 Verfeinerung der ersten Waldidentität für spezielle Stoppzeiten der Brownschen Bewegung 3.6 Beispiele für lokale Martingale für die Verfeinerung der ersten Waldidentität 3.7 Überschreitungszeiten der Brownschen Bewegung für nichtlineare Schranken 4 Zweite Waldidentität 4.1 Zweite Waldidentität für die Brownsche Bewegung 4.2 Anwendungen der ersten und zweitenWaldidentität für die Brown- schen Bewegung 5 Dritte Waldidentität 5.1 Dritte Waldidentität für die Brownsche Bewegung 5.2 Verfeinerung der dritten Waldidentität 5.3 Eine wichtige Voraussetzung für die Verfeinerung der drittenWal- didentität 5.4 Verfeinerung der dritten Waldidentität für spezielle Stoppzeiten der Brownschen Bewegung 6 Waldidentitäten im Mehrdimensionalen 6.1 Erste Waldidentität im Mehrdimensionalen 6.2 Zweite Waldidentität im Mehrdimensionalen 6.3 Dritte Waldidentität im Mehrdimensionalen 7 Appendix T3 - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2008, 04 Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49469 ER - TY - BOOK A1 - Zass, Alexander A1 - Zagrebnov, Valentin A1 - Sukiasyan, Hayk A1 - Melkonyan, Tatev A1 - Rafler, Mathias A1 - Poghosyan, Suren A1 - Zessin, Hans A1 - Piatnitski, Andrey A1 - Zhizhina, Elena A1 - Pechersky, Eugeny A1 - Pirogov, Sergei A1 - Yambartsev, Anatoly A1 - Mazzonetto, Sara A1 - Lykov, Alexander A1 - Malyshev, Vadim A1 - Khachatryan, Linda A1 - Nahapetian, Boris A1 - Jursenas, Rytis A1 - Jansen, Sabine A1 - Tsagkarogiannis, Dimitrios A1 - Kuna, Tobias A1 - Kolesnikov, Leonid A1 - Hryniv, Ostap A1 - Wallace, Clare A1 - Houdebert, Pierre A1 - Figari, Rodolfo A1 - Teta, Alessandro A1 - Boldrighini, Carlo A1 - Frigio, Sandro A1 - Maponi, Pierluigi A1 - Pellegrinotti, Alessandro A1 - Sinai, Yakov G. ED - Roelly, Sylvie ED - Rafler, Mathias ED - Poghosyan, Suren T1 - Proceedings of the XI international conference stochastic and analytic methods in mathematical physics N2 - The XI international conference Stochastic and Analytic Methods in Mathematical Physics was held in Yerevan 2 – 7 September 2019 and was dedicated to the memory of the great mathematician Robert Adol’fovich Minlos, who passed away in January 2018. The present volume collects a large majority of the contributions presented at the conference on the following domains of contemporary interest: classical and quantum statistical physics, mathematical methods in quantum mechanics, stochastic analysis, applications of point processes in statistical mechanics. The authors are specialists from Armenia, Czech Republic, Denmark, France, Germany, Italy, Japan, Lithuania, Russia, UK and Uzbekistan. A particular aim of this volume is to offer young scientists basic material in order to inspire their future research in the wide fields presented here. T3 - Lectures in pure and applied mathematics - 6 KW - statistical mechanics KW - random point processes KW - stochastic analysis Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-459192 SN - 978-3-86956-485-2 SN - 2199-4951 SN - 2199-496X IS - 6 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Zass, Alexander T1 - A Gibbs point process of diffusions: Existence and uniqueness 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-opus4-471951 SN - 978-3-86956-485-2 SN - 2199-4951 SN - 2199-496X IS - 6 SP - 13 EP - 22 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - THES A1 - Zass, Alexander T1 - A multifaceted study of marked Gibbs point processes T1 - Facetten von markierten Gibbsschen Punktprozessen N2 - This thesis focuses on the study of marked Gibbs point processes, in particular presenting some results on their existence and uniqueness, with ideas and techniques drawn from different areas of statistical mechanics: the entropy method from large deviations theory, cluster expansion and the Kirkwood--Salsburg equations, the Dobrushin contraction principle and disagreement percolation. We first present an existence result for infinite-volume marked Gibbs point processes. More precisely, we use the so-called entropy method (and large-deviation tools) to construct marked Gibbs point processes in R^d under quite general assumptions. In particular, the random marks belong to a general normed space S and are not bounded. Moreover, we allow for interaction functionals that may be unbounded and whose range is finite but random. The entropy method relies on showing that a family of finite-volume Gibbs point processes belongs to sequentially compact entropy level sets, and is therefore tight. We then present infinite-dimensional Langevin diffusions, that we put in interaction via a Gibbsian description. In this setting, we are able to adapt the general result above to show the existence of the associated infinite-volume measure. We also study its correlation functions via cluster expansion techniques, and obtain the uniqueness of the Gibbs process for all inverse temperatures β and activities z below a certain threshold. This method relies in first showing that the correlation functions of the process satisfy a so-called Ruelle bound, and then using it to solve a fixed point problem in an appropriate Banach space. The uniqueness domain we obtain consists then of the model parameters z and β for which such a problem has exactly one solution. Finally, we explore further the question of uniqueness of infinite-volume Gibbs point processes on R^d, in the unmarked setting. We present, in the context of repulsive interactions with a hard-core component, a novel approach to uniqueness by applying the discrete Dobrushin criterion to the continuum framework. We first fix a discretisation parameter a>0 and then study the behaviour of the uniqueness domain as a goes to 0. With this technique we are able to obtain explicit thresholds for the parameters z and β, which we then compare to existing results coming from the different methods of cluster expansion and disagreement percolation. Throughout this thesis, we illustrate our theoretical results with various examples both from classical statistical mechanics and stochastic geometry. N2 - Diese Arbeit konzentriert sich auf die Untersuchung von markierten Gibbs-Punkt-Prozessen und stellt insbesondere einige Ergebnisse zu deren Existenz und Eindeutigkeit vor. Dabei werden Ideen und Techniken aus verschiedenen Bereichen der statistischen Mechanik verwendet: die Entropie-Methode aus der Theorie der großen Abweichungen, die Cluster-Expansion und die Kirkwood-Salsburg-Gleichungen, das Dobrushin-Kontraktionsprinzip und die Disagreement-Perkolation. Wir präsentieren zunächst ein Existenzergebnis für unendlich-volumige markierte Gibbs-Punkt-Prozesse. Genauer gesagt verwenden wir die sogenannte Entropie-Methode (und Werkzeuge der großen Abweichung), um markierte Gibbs-Punkt-Prozesse in R^d unter möglichst allgemeinen Annahmen zu konstruieren. Insbesondere gehören die zufälligen Markierungen zu einem allgemeinen normierten Raum und sind nicht beschränkt. Außerdem lassen wir Interaktionsfunktionale zu, die unbeschränkt sein können und deren Reichweite endlich, aber zufällig ist. Die Entropie-Methode beruht darauf, zu zeigen, dass eine Familie von endlich-volumigen Gibbs-Punkt-Prozessen zu sequentiell kompakten Entropie-Niveau-Mengen gehört, und daher dicht ist. Wir stellen dann unendlich-dimensionale Langevin-Diffusionen vor, die wir über eine Gibbssche Beschreibung in Wechselwirkung setzen. In dieser Umgebung sind wir in der Lage, das vorangehend vorgestellte allgemeine Ergebnis anzupassen, um die Existenz des zugehörigen unendlich-dimensionalen Maßes zu zeigen. Wir untersuchen auch seine Korrelationsfunktionen über Cluster-Expansions Techniken und erhalten die Eindeutigkeit des Gibbs-Prozesses für alle inversen Temperaturen β und Aktivitäten z unterhalb einer bestimmten Schwelle. Diese Methode beruht darauf, zunächst zu zeigen, dass die Korrelationsfunktionen des Prozesses eine so genannte Ruelle-Schranke erfüllen, um diese dann zur Lösung eines Fixpunktproblems in einem geeigneten Banach-Raum zu verwenden. Der Eindeutigkeitsbereich, den wir erhalten, wird dann aus den Modellparametern z und β definiert, für die ein solches Problem genau eine Lösung hat. Schließlich untersuchen wir die Frage nach der Eindeutigkeit von unendlich-volumigen Gibbs-Punkt-Prozessen auf R^d im unmarkierten Fall weiter. Im Zusammenhang mit repulsiven Wechselwirkungen basierend auf einer Hartkernkomponente stellen wir einen neuen Ansatz zur Eindeutigkeit vor, indem wir das diskrete Dobrushin-Kriterium im kontinuierlichen Rahmen anwenden. Wir legen zunächst einen Diskretisierungsparameter a>0 fest und untersuchen dann das Verhalten des Bereichs der Eindeutigkeit, wenn a gegen 0 geht. Mit dieser Technik sind wir in der Lage, explizite Schwellenwerte für die Parameter z und β zu erhalten, die wir dann mit bestehenden Ergebnissen aus den verschiedenen Methoden der Cluster-Expansion und der Disagreement-Perkolation vergleichen. In dieser Arbeit illustrieren wir unsere theoretischen Ergebnisse mit verschiedenen Beispielen sowohl aus der klassischen statistischen Mechanik als auch aus der stochastischen Geometrie. KW - marked Gibbs point processes KW - Langevin diffusions KW - Dobrushin criterion KW - Entropy method KW - Cluster expansion KW - Kirkwood--Salsburg equations KW - DLR equations KW - Markierte Gibbs-Punkt-Prozesse KW - Entropiemethode KW - Cluster-Expansion KW - DLR-Gleichungen KW - Dobrushin-Kriterium KW - Kirkwood-Salsburg-Gleichungen KW - Langevin-Diffusions Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-512775 ER - TY - JOUR A1 - Zaourar, Naima A1 - Hamoudi, Mohamed A1 - Holschneider, Matthias A1 - Mandea, Mioara T1 - Fractal dynamics of geomagnetic storms JF - Arabian journal of geosciences N2 - We explore fluctuations of the horizontal component of the Earth's magnetic field to identify scaling behaviour of the temporal variability in geomagnetic data recorded by the Intermagnet observatories during the solar cycle 23 (years 1996 to 2005). In this work, we use the remarkable ability of scaling wavelet exponents to highlight the singularities associated with discontinuities present in the magnetograms obtained at two magnetic observatories for six intense magnetic storms, including the sudden storm commencements of 14 July 2000, 29-31 October and 20-21 November 2003. In the active intervals that occurred during geomagnetic storms, we observe a rapid and unidirectional change in the spectral scaling exponent at the time of storm onset. The corresponding fractal features suggest that the dynamics of the whole time series is similar to that of a fractional Brownian motion. Our findings point to an evident relatively sudden change related to the emergence of persistency of the fractal power exponent fluctuations precedes an intense magnetic storm. These first results could be useful in the framework of extreme events prediction studies. KW - Geomagnetic field KW - Magnetosphere KW - Geomagnetic storm KW - Multiscale analysis KW - Spectral exponent Y1 - 2013 U6 - https://doi.org/10.1007/s12517-011-0487-0 SN - 1866-7511 VL - 6 IS - 6 SP - 1693 EP - 1702 PB - Springer CY - Heidelberg ER - TY - JOUR A1 - Zagrebnov, Valentin T1 - Trotter product formula on Hilbert and Banach spaces for operator-norm convergence 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-opus4-471971 SN - 978-3-86956-485-2 SN - 2199-4951 SN - 2199-496X SP - 23 EP - 34 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - THES A1 - Zadorozhnyi, Oleksandr T1 - Contributions to the theoretical analysis of the algorithms with adversarial and dependent data N2 - In this work I present the concentration inequalities of Bernstein's type for the norms of Banach-valued random sums under a general functional weak-dependency assumption (the so-called $\cC-$mixing). The latter is then used to prove, in the asymptotic framework, excess risk upper bounds of the regularised Hilbert valued statistical learning rules under the τ-mixing assumption on the underlying training sample. These results (of the batch statistical setting) are then supplemented with the regret analysis over the classes of Sobolev balls of the type of kernel ridge regression algorithm in the setting of online nonparametric regression with arbitrary data sequences. Here, in particular, a question of robustness of the kernel-based forecaster is investigated. Afterwards, in the framework of sequential learning, the multi-armed bandit problem under $\cC-$mixing assumption on the arm's outputs is considered and the complete regret analysis of a version of Improved UCB algorithm is given. Lastly, probabilistic inequalities of the first part are extended to the case of deviations (both of Azuma-Hoeffding's and of Burkholder's type) to the partial sums of real-valued weakly dependent random fields (under the type of projective dependence condition). KW - Machine learning KW - nonparametric regression KW - kernel methods KW - regularisation KW - concentration inequalities KW - learning rates KW - sequential learning KW - multi-armed bandits KW - Sobolev spaces Y1 - 2021 ER - TY - BOOK A1 - Yin, Yang A1 - Hua, Chen A1 - Weian, Liu T1 - On solutions of the chemotaxis equations T3 - Preprint / Universität Potsdam, Institut für Mathematik Y1 - 1998 VL - 1998, 06 PB - Univ. CY - Potsdam ER - TY - GEN A1 - Yin, Yang A1 - Hua, Chen T1 - On chemotaxis systems with saturation growth T2 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2007 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - INPR A1 - Yin, Yang A1 - Hua, Chen T1 - On chemotaxis systems with saturation growth N2 - In this paper, we discuss the global existence of solutions for Chemotaxis models with saturation growth. If the coe±cients of the equations are all positive smooth T-periodic functions, then the problem has a positive T-periodic solution, and meanwhile we discuss here the stability problems for the T-periodic solutions. T3 - Preprint - (2007) 04 KW - Saturation model KW - Chemotaxis KW - global solution KW - asymptotic stable Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30254 ER - TY - BOOK A1 - Yin, Huicheng A1 - Witt, Ingo T1 - Global singularity structure of weak solutions to 3-D semilinear dispersive wave equaions with discontinuous initial data T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2002 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - INPR A1 - Yin, Huicheng T1 - Formation and construction of a shock wave for 3-D compressible Euler equations with spherical initial data N2 - In this paper, the problem on formation and construction of a shock wave for three dimensional compressible Euler equations with the small perturbed spherical initial data is studied. If the given smooth initial data satisfies certain nondegenerate condition, then from the results in [20], we know that there exists a unique blowup point at the blowup time such that the first order derivates of smooth solution blow up meanwhile the solution itself is still continuous at the blowup point. From the blowup point, we construct a weak entropy solution which is not uniformly Lipschitz continuous on two sides of shock curve, moreover the strength of the constructed shock is zero at the blowup point and then gradually increases. Additionally, some detailed and precise estimates on the solution are obtained in the neighbourhood of the blowup point. T3 - Preprint - (2002) 07 KW - compressible Euler equations KW - lifespan KW - nondegenerate condition KW - shock wave Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26263 ER - TY - INPR A1 - Yin, Huicheng T1 - Global existence of a shock for the supersonic flow past a curved wedge N2 - This note is devoted to the study on the global existence of a shock wave for the supersonic flow past a curved wedge. When the curved wedge is a small perturbation of a straight wedge and the angle of the wedge is less than some critical value, wwe show that a shock attached at the wedge will exist globally. T3 - Preprint - (2002) 08 Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26272 ER - TY - JOUR A1 - Yin, H. C. A1 - Witt, Ingo T1 - Global singularity structure of weak solutions to 3-D semilinear dispersive wave equations with discontinuous initial data N2 - We study the global singularity structure of solutions to 3-D semilinear wave equations with discontinuous initial data. More precisely, using Strichartz' inequality we show that the solutions stay conormal after nonlinear interaction if the Cauchy data are conormal along a circle. (C) 2003 Elsevier Inc. All rights reserved Y1 - 2004 SN - 0022-0396 ER - TY - INPR A1 - Yihong, Du A1 - Li, Ma T1 - Some remarks related to De Giorgi's conjecture N2 - For several classes of functions including the special case f(u) = u − u³, we obtain boundedness and symmetry results for solutions of the problem −Δu = f(u) defined on R up(n). Our results complement a number of recent results related to a conjecture of De Giorgi. T3 - Preprint - (2001) 18 Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26027 ER - TY - JOUR A1 - Yen, Ming-Hsuan A1 - von Specht, Sebastian A1 - Lin, Yen-Yu A1 - Cotton, Fabrice A1 - Ma, Kuo-Fong T1 - Within- and between-event variabilities of strong-velocity pulses of moderate earthquakes within dense seismic arrays JF - Bulletin of the Seismological Society of America N2 - Ground motion with strong-velocity pulses can cause significant damage to buildings and structures at certain periods; hence, knowing the period and velocity amplitude of such pulses is critical for earthquake structural engineering. However, the physical factors relating the scaling of pulse periods with magnitude are poorly understood. In this study, we investigate moderate but damaging earthquakes (M-w 6-7) and characterize ground- motion pulses using the method of Shahi and Baker (2014) while considering the potential static-offset effects. We confirm that the within-event variability of the pulses is large. The identified pulses in this study are mostly from strike-slip-like earthquakes. We further perform simulations using the freq uency-wavenumber algorithm to investigate the causes of the variability of the pulse periods within and between events for moderate strike-slip earthquakes. We test the effect of fault dips, and the impact of the asperity locations and sizes. The simulations reveal that the asperity properties have a high impact on the pulse periods and amplitudes at nearby stations. Our results emphasize the importance of asperity characteristics, in addition to earthquake magnitudes for the occurrence and properties of pulses produced by the forward directivity effect. We finally quantify and discuss within- and between-event variabilities of pulse properties at short distances. Y1 - 2021 U6 - https://doi.org/10.1785/0120200376 SN - 0037-1106 SN - 1943-3573 VL - 112 IS - 1 SP - 361 EP - 380 PB - Seismological Society of America CY - El Cerito, Calif. ER - TY - BOOK A1 - Yagdjian, Karen A1 - Galstian, Anahit T1 - Fundamental solutions for Wave Equation in de Sitter Model of Universe T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2007 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - INPR A1 - Yagdjian, Karen A1 - Galstian, Anahit T1 - Fundamental solutions for wave equation in de Sitter model of universe N2 - In this article we construct the fundamental solutions for the wave equation arising in the de Sitter model of the universe. We use the fundamental solutions to represent solutions of the Cauchy problem and to prove the Lp − Lq-decay estimates for the solutions of the equation with and without a source term. T3 - Preprint - (2007) 06 KW - de Sitter model ; Fundamental solutions ; Decay estimates Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30271 ER - TY - BOOK A1 - Yagdjian, Karen T1 - Geometric optics for the nonlinear hyperbolic systems of kirchhoff-type T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2001 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - INPR A1 - Yagdjian, Karen T1 - Geometric optics for the nonlinear hyperbolic systems of Kirchhoff-type N2 - Contents: 1 Introduction 2 Main result 3 Construction of the asymptotic solutions 3.1 Derivation of the equations for the profiles 3.2 Exsistence of the principal profile 3.3 Determination of Usub(2) and the remaining profiles 4 Stability of the samll global solutions. Justification of One Phase Nonlinear Geometric Optics for the Kirchhoff-type equations 4.1 Stability of the global solutions to the Kirchhoff-type symmetric hyperbolic systems 4.2 The nonlinear system of ordinary differential equations with the parameter 4.3 Some energies estimates 4.4 The dependence of the solution W(t, ξ) on the function s(t) 4.5 The oscillatory integrals of the bilinear forms of the solutions 4.6 Estimates for the basic bilinear form Γsub(s)(t) 4.7 Contraction mapping 4.8 Stability of the global solution 4.9 Justification of One Phase Nonlinear Geometric Optics for the Kirchhoff-type equations T3 - Preprint - (2001) 22 Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26059 ER - TY - JOUR A1 - Xiong, Chao A1 - Stolle, Claudia A1 - Alken, Patrick A1 - Rauberg, Jan T1 - Relationship between large-scale ionospheric field-aligned currents and electron/ion precipitations BT - DMSP observations JF - Earth, planets and space N2 - In this study, we have derived field-aligned currents (FACs) from magnetometers onboard the Defense Meteorological Satellite Project (DMSP) satellites. The magnetic latitude versus local time distribution of FACs from DMSP shows comparable dependences with previous findings on the intensity and orientation of interplanetary magnetic field (IMF)B(y)andB(z)components, which confirms the reliability of DMSP FAC data set. With simultaneous measurements of precipitating particles from DMSP, we further investigate the relation between large-scale FACs and precipitating particles. Our result shows that precipitation electron and ion fluxes both increase in magnitude and extend to lower latitude for enhanced southward IMFBz, which is similar to the behavior of FACs. Under weak northward and southwardB(z)conditions, the locations of the R2 current maxima, at both dusk and dawn sides and in both hemispheres, are found to be close to the maxima of the particle energy fluxes; while for the same IMF conditions, R1 currents are displaced further to the respective particle flux peaks. Largest displacement (about 3.5 degrees) is found between the downward R1 current and ion flux peak at the dawn side. Our results suggest that there exists systematic differences in locations of electron/ion precipitation and large-scale upward/downward FACs. As outlined by the statistical mean of these two parameters, the FAC peaks enclose the particle energy flux peaks in an auroral band at both dusk and dawn sides. Our comparisons also found that particle precipitation at dawn and dusk and in both hemispheres maximizes near the mean R2 current peaks. The particle precipitation flux maxima closer to the R1 current peaks are lower in magnitude. This is opposite to the known feature that R1 currents are on average stronger than R2 currents. KW - field-aligned currents KW - aurora KW - particle precipitation KW - DMSP Y1 - 2020 U6 - https://doi.org/10.1186/s40623-020-01286-z SN - 1880-5981 VL - 72 IS - 1 PB - Springer CY - New York ER - TY - INPR A1 - Xiaochun, Liu A1 - Witt, Ingo T1 - Pseudodifferential calculi on the half-line respecting prescribed asymptotic types N2 - Contents: 1. Introduction 2. Preliminaries 3. Basic Elements of the Calculus 4. Further Elements of the Calculus T3 - Preprint - (2002) 06 Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26255 ER - TY - INPR A1 - Xiaochun, Liu A1 - Witt, Ingo T1 - Asymptotic expansions for bounded solutions to semilinear Fuchsian equations N2 - It is shown that bounded solutions to semilinear elliptic Fuchsian equations obey complete asymptoic expansions in terms of powers and logarithms in the distance to the boundary. For that purpose, Schuze's notion of asymptotic type for conormal asymptotics close to a conical point is refined. This in turn allows to perform explicit calculations on asymptotic types - modulo the resolution of the spectral problem for determining the singular exponents in the asmptotic expansions. T3 - Preprint - (2001) 01 KW - Calculus of conormal symbols KW - conormal asymptotic expansions KW - discrete saymptotic types KW - weighted Sobolev spaces with discrete saymptotics Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25912 ER - TY - INPR A1 - Xiaochun, Liu A1 - Schulze, Bert-Wolfgang T1 - Boundary value problems in edge representation N2 - Edge representations of operators on closed manifolds are known to induce large classes of operators that are elliptic on specific manifolds with edges, cf. [9]. We apply this idea to the case of boundary value problems. We establish a correspondence between standard ellipticity and ellipticity with respect to the principal symbolic hierarchy of the edge algebra of boundary value problems, where an embedded submanifold on the boundary plays the role of an edge. We first consider the case that the weight is equal to the smoothness and calculate the dimensions of kernels and cokernels of the associated principal edge symbols. Then we pass to elliptic edge operators for arbitrary weights and construct the additional edge conditions by applying relative index results for conormal symbols. T3 - Preprint - (2004) 14 KW - Boundary value problems KW - edge singularities KW - ellipticity in the edge calculus Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26746 ER - TY - JOUR A1 - Wormell, Caroline L. A1 - Reich, Sebastian T1 - Spectral convergence of diffusion maps BT - Improved error bounds and an alternative normalization JF - SIAM journal on numerical analysis / Society for Industrial and Applied Mathematics N2 - Diffusion maps is a manifold learning algorithm widely used for dimensionality reduction. Using a sample from a distribution, it approximates the eigenvalues and eigenfunctions of associated Laplace-Beltrami operators. Theoretical bounds on the approximation error are, however, generally much weaker than the rates that are seen in practice. This paper uses new approaches to improve the error bounds in the model case where the distribution is supported on a hypertorus. For the data sampling (variance) component of the error we make spatially localized compact embedding estimates on certain Hardy spaces; we study the deterministic (bias) component as a perturbation of the Laplace-Beltrami operator's associated PDE and apply relevant spectral stability results. Using these approaches, we match long-standing pointwise error bounds for both the spectral data and the norm convergence of the operator discretization. We also introduce an alternative normalization for diffusion maps based on Sinkhorn weights. This normalization approximates a Langevin diffusion on the sample and yields a symmetric operator approximation. We prove that it has better convergence compared with the standard normalization on flat domains, and we present a highly efficient rigorous algorithm to compute the Sinkhorn weights. KW - diffusion maps KW - graph Laplacian KW - Sinkhorn problem KW - kernel methods Y1 - 2021 U6 - https://doi.org/10.1137/20M1344093 SN - 0036-1429 SN - 1095-7170 VL - 59 IS - 3 SP - 1687 EP - 1734 PB - Society for Industrial and Applied Mathematics CY - Philadelphia ER - TY - BOOK A1 - Wollenberg, Manfred T1 - On an inverse problem in modular theory T3 - Preprint / Universität Potsdam, Institut für Mathematik Y1 - 1994 VL - 1994, 07 PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Witt, Ingo T1 - Local asymptotic types N2 - The local theory of asymptotic types is elaborated. It appears as coordinate-free version of part of GOHBERG- SIGAL'S theory of the inversion of finitely meromorphic, operator-valued functions at a point Y1 - 2004 SN - 0025-2611 ER - TY - BOOK A1 - Witt, Ingo T1 - Green formulae for cone differential operators T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2003 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - THES A1 - Witt, Ingo T1 - Beiträge zur Theorie singulärer hyperbolischer Differentialoperatoren Y1 - 2003 CY - Potsdam ER - TY - BOOK A1 - Witt, Ingo T1 - A calculus for a class of finitely degenerate pseudodifferential operators T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2002 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Witt, Ingo T1 - Local asymptotic types T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2002 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - INPR A1 - Witt, Ingo T1 - Green formulae for cone differential operators N2 - Green formulae for elliptic cone differential operators are established. This is achieved by an accurate description of the maximal domain of an elliptic cone differential operator and its formal adjoint; thereby utilizing the concept of a discrete asymptotic type. From this description, the singular coefficients replacing the boundary traces in classical Green formulas are deduced. T3 - Preprint - (2003) 20 Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26633 ER - TY - BOOK A1 - Witt, Ingo T1 - Asymptotic algebras T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2001 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Witt, Ingo T1 - On the factorization of meromorphic mellin symbols T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 1999 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Witt, Ingo T1 - Explicit algebras with the Leibniz-Mellin translation product T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 1999 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - INPR A1 - Witt, Ingo T1 - Local asymptotic types N2 - The local theory of asymptotic types is elaborated. It appears as coordinate-free version of part of GOHBERG-SIGAL's theory of the inversion of finitely meromorphic, operator-valued functions at a point. T3 - Preprint - (2002) 16 Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26346 ER - TY - INPR A1 - Witt, Ingo T1 - A calculus for a class of finitely degenerate pseudodifferential operators N2 - For a class of degenerate pseudodifferential operators, local parametrices are constructed. This is done in the framework of a pseudodifferential calculus upon adding conditions of trace and potential type, respectively, along the boundary on which the operators degenerate. T3 - Preprint - (2002) 05 Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26246 ER - TY - INPR A1 - Witt, Ingo T1 - Asymptotic algebras N2 - The concept of asymptotic type that primarily appears in singular and asymptotic analysis is developed. Especially, asymptotic algebras are introduced. T3 - Preprint - (2001) 23 Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26069 ER - TY - INPR A1 - Witt, Ingo T1 - On the factorization of meromorphic Mellin symbols N2 - It is prooved that mermorphic, parameter-dependet elliptic Mellin symbols can be factorized in a particular way. The proof depends on the availability of logarithms of pseudodifferential operators. As a byproduct, we obtain a characterization of the group generated by pseudodifferential operators admitting a logarithm. The factorization has applications to the theory os pseudodifferential operators on spaces with conical singularities, e.g., to the index theory and the construction of various sub-calculi of the cone calculus. T3 - Preprint - (1999) 05 Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25427 ER - TY - JOUR A1 - Wismath, Shelly A1 - Koppitz, Jörg A1 - Denecke, Klaus-Dieter T1 - Maps between M-solid varieties of emigroups Y1 - 1997 ER - TY - GEN A1 - Wiljes, Jana de A1 - Tong, Xin T. T1 - Analysis of a localised nonlinear ensemble Kalman Bucy filter with complete and accurate observations T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - Concurrent observation technologies have made high-precision real-time data available in large quantities. Data assimilation (DA) is concerned with how to combine this data with physical models to produce accurate predictions. For spatial-temporal models, the ensemble Kalman filter with proper localisation techniques is considered to be a state-of-the-art DA methodology. This article proposes and investigates a localised ensemble Kalman Bucy filter for nonlinear models with short-range interactions. We derive dimension-independent and component-wise error bounds and show the long time path-wise error only has logarithmic dependence on the time range. The theoretical results are verified through some simple numerical tests. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1221 KW - data assimilation KW - stability and accuracy KW - dimension independent bound KW - localisation KW - high dimensional KW - filter KW - nonlinear Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-540417 SN - 1866-8372 VL - 33 IS - 9 SP - 4752 EP - 4782 PB - IOP Publ. CY - Bristol ER - TY - JOUR A1 - Wiljes, Jana de A1 - Tong, Xin T. T1 - Analysis of a localised nonlinear ensemble Kalman Bucy filter with complete and accurate observations JF - Nonlinearity N2 - Concurrent observation technologies have made high-precision real-time data available in large quantities. Data assimilation (DA) is concerned with how to combine this data with physical models to produce accurate predictions. For spatial-temporal models, the ensemble Kalman filter with proper localisation techniques is considered to be a state-of-the-art DA methodology. This article proposes and investigates a localised ensemble Kalman Bucy filter for nonlinear models with short-range interactions. We derive dimension-independent and component-wise error bounds and show the long time path-wise error only has logarithmic dependence on the time range. The theoretical results are verified through some simple numerical tests. KW - data assimilation KW - stability and accuracy KW - dimension independent bound KW - localisation KW - high dimensional KW - filter KW - nonlinear Y1 - 2020 U6 - https://doi.org/10.1088/1361-6544/ab8d14 SN - 0951-7715 SN - 1361-6544 VL - 33 IS - 9 SP - 4752 EP - 4782 PB - IOP Publ. CY - Bristol ER - TY - JOUR A1 - Wiegner, Matthias A1 - Bösenberg, Jens A1 - Böckmann, Christine A1 - Eixmann, Ronald A1 - Freudenthaler, Volker A1 - Mattis, Ina A1 - Trickl, Thomas T1 - Lidar Network to Establish an Aerosol Climatology Y1 - 1999 ER - TY - JOUR A1 - Wichitsa-Nguan, Korakot A1 - Läuter, Henning A1 - Liero, Hannelore T1 - Estimability in Cox models JF - Statistical Papers N2 - Our procedure of estimating is the maximum partial likelihood estimate (MPLE) which is the appropriate estimate in the Cox model with a general censoring distribution, covariates and an unknown baseline hazard rate . We find conditions for estimability and asymptotic estimability. The asymptotic variance matrix of the MPLE is represented and properties are discussed. KW - Cox model KW - Estimability KW - Asymptotic variance of maximum partial likelihood estimate Y1 - 2016 U6 - https://doi.org/10.1007/s00362-016-0755-x SN - 0932-5026 SN - 1613-9798 VL - 57 SP - 1121 EP - 1140 PB - Springer CY - New York ER - TY - THES A1 - Wichitsa-nguan, Korakot T1 - Modifications and extensions of the logistic regression and Cox model T1 - Modifikationen und Erweiterungen des logistischen Regressionsmodells und des Cox-Modells N2 - In many statistical applications, the aim is to model the relationship between covariates and some outcomes. A choice of the appropriate model depends on the outcome and the research objectives, such as linear models for continuous outcomes, logistic models for binary outcomes and the Cox model for time-to-event data. In epidemiological, medical, biological, societal and economic studies, the logistic regression is widely used to describe the relationship between a response variable as binary outcome and explanatory variables as a set of covariates. However, epidemiologic cohort studies are quite expensive regarding data management since following up a large number of individuals takes long time. Therefore, the case-cohort design is applied to reduce cost and time for data collection. The case-cohort sampling collects a small random sample from the entire cohort, which is called subcohort. The advantage of this design is that the covariate and follow-up data are recorded only on the subcohort and all cases (all members of the cohort who develop the event of interest during the follow-up process). In this thesis, we investigate the estimation in the logistic model for case-cohort design. First, a model with a binary response and a binary covariate is considered. The maximum likelihood estimator (MLE) is described and its asymptotic properties are established. An estimator for the asymptotic variance of the estimator based on the maximum likelihood approach is proposed; this estimator differs slightly from the estimator introduced by Prentice (1986). Simulation results for several proportions of the subcohort show that the proposed estimator gives lower empirical bias and empirical variance than Prentice's estimator. Then the MLE in the logistic regression with discrete covariate under case-cohort design is studied. Here the approach of the binary covariate model is extended. Proving asymptotic normality of estimators, standard errors for the estimators can be derived. The simulation study demonstrates the estimation procedure of the logistic regression model with a one-dimensional discrete covariate. Simulation results for several proportions of the subcohort and different choices of the underlying parameters indicate that the estimator developed here performs reasonably well. Moreover, the comparison between theoretical values and simulation results of the asymptotic variance of estimator is presented. Clearly, the logistic regression is sufficient for the binary outcome refers to be available for all subjects and for a fixed time interval. Nevertheless, in practice, the observations in clinical trials are frequently collected for different time periods and subjects may drop out or relapse from other causes during follow-up. Hence, the logistic regression is not appropriate for incomplete follow-up data; for example, an individual drops out of the study before the end of data collection or an individual has not occurred the event of interest for the duration of the study. These observations are called censored observations. The survival analysis is necessary to solve these problems. Moreover, the time to the occurence of the event of interest is taken into account. The Cox model has been widely used in survival analysis, which can effectively handle the censored data. Cox (1972) proposed the model which is focused on the hazard function. The Cox model is assumed to be λ(t|x) = λ0(t) exp(β^Tx) where λ0(t) is an unspecified baseline hazard at time t and X is the vector of covariates, β is a p-dimensional vector of coefficient. In this thesis, the Cox model is considered under the view point of experimental design. The estimability of the parameter β0 in the Cox model, where β0 denotes the true value of β, and the choice of optimal covariates are investigated. We give new representations of the observed information matrix In(β) and extend results for the Cox model of Andersen and Gill (1982). In this way conditions for the estimability of β0 are formulated. Under some regularity conditions, ∑ is the inverse of the asymptotic variance matrix of the MPLE of β0 in the Cox model and then some properties of the asymptotic variance matrix of the MPLE are highlighted. Based on the results of asymptotic estimability, the calculation of local optimal covariates is considered and shown in examples. In a sensitivity analysis, the efficiency of given covariates is calculated. For neighborhoods of the exponential models, the efficiencies have then been found. It is appeared that for fixed parameters β0, the efficiencies do not change very much for different baseline hazard functions. Some proposals for applicable optimal covariates and a calculation procedure for finding optimal covariates are discussed. Furthermore, the extension of the Cox model where time-dependent coefficient are allowed, is investigated. In this situation, the maximum local partial likelihood estimator for estimating the coefficient function β(·) is described. Based on this estimator, we formulate a new test procedure for testing, whether a one-dimensional coefficient function β(·) has a prespecified parametric form, say β(·; ϑ). The score function derived from the local constant partial likelihood function at d distinct grid points is considered. It is shown that the distribution of the properly standardized quadratic form of this d-dimensional vector under the null hypothesis tends to a Chi-squared distribution. Moreover, the limit statement remains true when replacing the unknown ϑ0 by the MPLE in the hypothetical model and an asymptotic α-test is given by the quantiles or p-values of the limiting Chi-squared distribution. Finally, we propose a bootstrap version of this test. The bootstrap test is only defined for the special case of testing whether the coefficient function is constant. A simulation study illustrates the behavior of the bootstrap test under the null hypothesis and a special alternative. It gives quite good results for the chosen underlying model. References P. K. Andersen and R. D. Gill. Cox's regression model for counting processes: a large samplestudy. Ann. Statist., 10(4):1100{1120, 1982. D. R. Cox. Regression models and life-tables. J. Roy. Statist. Soc. Ser. B, 34:187{220, 1972. R. L. Prentice. A case-cohort design for epidemiologic cohort studies and disease prevention trials. Biometrika, 73(1):1{11, 1986. N2 - In vielen statistischen Anwendungen besteht die Aufgabe darin, die Beziehung zwischen Einflussgrößen und einer Zielgröße zu modellieren. Die Wahl eines geeigneten Modells hängt vom Typ der Zielgröße und vom Ziel der Untersuchung ab - während lineare Modelle für die Beschreibung des Zusammenhanges stetiger Outputs und Einflussgrößen genutzt werden, dienen logistische Regressionsmodelle zur Modellierung binärer Zielgrößen und das Cox-Modell zur Modellierung von Lebendauer-Daten. In epidemiologischen, medizinischen, biologischen, sozialen und ökonomischen Studien wird oftmals die logistische Regression angewendet, um den Zusammenhang zwischen einer binären Zielgröße und den erklärenden Variablen, den Kovariaten, zu modellieren. In epidemiologischen Studien muss häufig eine große Anzahl von Individuen für eine lange Zeit beobachtet werden. Um hierbei Kosten zu reduzieren, wird ein "Case-Cohort-Design" angewendet. Hierbei werden die Einflussgrößen nur für die Individuen erfasst, für die das interessierende Ereignis eintritt, und für eine zufällig gewählte kleine Teilmenge von Individuen, die Subkohorte. In der vorliegenden Arbeit wird das Schätzen im logistischen Regressionsmodell unter Case-Cohort-Design betrachtet. Für den Fall, dass auch die Kovariate binär ist, wurde bereits von Prentice (1986) die asymptotische Normalität des Maximum-Likelihood-Schätzers für den Logarithmus des "odds ratio", einen Parameter, der den Effekt der Kovariate charakterisiert, angegeben. In dieser Arbeit wird über einen Maximum-Likelihood-Zugang ein Schätzer für die Varianz der Grenzverteilung hergeleitet, für den durch empirische Untersuchungen gezeigt wird, dass er dem von Prentice überlegen ist. Ausgehend von dem binärem Kovariate-Modell werden Maximum-Likelihood-Schätzer für logistische Regressionsmodelle mit diskreten Kovariaten unter Case-Cohort-Design hergeleitet. Die asymptotische Normalität wird gezeigt; darauf aufbauend können Formeln für die Standardfehler angegeben werden. Simulationsstudien ergänzen diesen Abschnitt. Sie zeigen den Einfluss des Umfanges der Subkohorte auf die Varianz der Schätzer. Logistische Regression ist geeignet, wenn man das interessierende Ereignis für alle Individuen beobachten kann und wenn man ein festes Zeitintervall betrachtet. Will man die Zeit bis zum Eintreten eines Ereignisses bei der Untersuchung der Wirkung der Kovariate berücksichtigen, so sind Lebensdauermodelle angemessen. Hierbei können auch zensierte Daten behandelt werden. Ein sehr häufig angewendetes Regressionsmodell ist das von Cox (1972) vorgeschlagene, bei dem die Hazardrate durch λ(t|x) = λ0(t) exp(β^Tx) definiert ist. Hierbei ist λ0(t) eine unspezifizierte Baseline-Hazardrate und X ist ein Kovariat-Vektor, β ist ein p-dimensionaler Koeffizientenvektor. Nachdem ein Überblick über das Schätzen und Testen im Cox-Modell und seinen Erweiterungen gegeben wird, werden Aussagen zur Schätzbarkeit des Parameters β durch die "partiallikelihood"- Methode hergeleitet. Grundlage hierzu sind neue Darstellungen der beobachteten Fisher-Information, die die Ergebnisse von Andersen and Gill (1982) erweitern. Unter Regularitätsbedingungen ist der Schätzer asymptotisch normal; die Inverse der Grenzmatrix der Fisher-Information ist die Varianzmatrix der Grenzverteilung. Bedingungen für die Nichtsingularität dieser Grenzmatrix führen zum Begriff der asymptotischen Schätzbarkeit, der in der vorliegenden Arbeit ausführlich untersucht wird. Darüber hinaus ist diese Matrix Grundlage für die Herleitung lokal optimaler Kovariate. In einer Sensitivitätsanalyse wird die Effizienz gewählter Kovariate berechnet. Die Berechnungen zeigen, dass die Baseline-Verteilung nur wenig Einfluss auf die Effizienz hat. Entscheidend ist die Wahl der Kovariate. Es werden einige Vorschläge für anwendbare optimale Kovariate und Berechnungsverfahren für das Auffinden optimaler Kovariate diskutiert. Eine Erweiterung des Cox-Modells besteht darin, zeitabhängige Koeffizienten zuzulassen. Da diese Koeffizientenfunktionen nicht näher spezifiziert sind, werden sie nichtparametrisch geschätzt. Eine mögliche Methode ist die "local-linear-partial-likelihood"-Methode, deren Eigenschaften beispielsweise in der Arbeit von Cai and Sun (2003) untersucht wurden. In der vorliegenden Arbeit werden Simulationen zu dieser Methode durchgeführt. Hauptaspekt ist das Testen der Koeffizientenfunktion. Getestet wird, ob diese Funktion eine bestimmte parametrische Form besitzt. Betrachtet wird der Score-Vektor, der von der "localconstant-partial-likelihood"-Funktion abgeleitet wird. Ausgehend von der asymptotischen Normalität dieses Vektors an verschiedenen Gitterpunkten kann gezeigt werden, dass die Verteilung der geeignet standardisierten quadratischen Form unter der Nullhypothese gegen eine Chi-Quadrat-Verteilung konvergiert. Die Eigenschaften des auf dieser Grenzverteilungsaussage aufbauenden Tests hängen nicht nur vom Stichprobenumfang, sondern auch vom verwendeten Glättungsparameter ab. Deshalb ist es sinnvoll, auch einen Bootstrap-Test zu betrachten. In der vorliegenden Arbeit wird ein Bootstrap-Test zum Testen der Hypothese, dass die Koeffizienten-Funktion konstant ist, d.h. dass das klassische Cox-Modell vorliegt, vorgeschlagen. Der Algorithmus wird angegeben. Simulationen zum Verhalten dieses Tests unter der Nullhypothese und einer speziellen Alternative werden durchgeführt. Literatur P. K. Andersen and R. D. Gill. Cox's regression model for counting processes: a large sample study. Ann. Statist., 10(4):1100{1120, 1982. Z. Cai and Y. Sun. Local linear estimation for time-dependent coefficients in Cox's regression models. Scand. J. Statist., 30(1):93-111, 2003. D. R. Cox. Regression models and life-tables. J. Roy. Statist. Soc. Ser. B, 34:187-220, 1972. R. L. Prentice. A case-cohort design for epidemiologic cohort studies and disease prevention trials. Biometrika, 73(1):1-11, 1986. KW - survival analysis KW - Cox model KW - logistic regression analysis KW - logistische Regression KW - Case-Cohort-Design KW - Cox-Modell Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-90033 ER - TY - GEN A1 - Wicha, Sebastian G. A1 - Kees, Martin G. A1 - Solms, Alexander Maximilian A1 - Minichmayr, Iris K. A1 - Kratzer, Alexander A1 - Kloft, Charlotte T1 - TDMx: A novel web-based open-access support tool for optimising antimicrobial dosing regimens in clinical routine T2 - International journal of antimicrobial agents Y1 - 2015 U6 - https://doi.org/10.1016/j.ijantimicag.2014.12.010 SN - 0924-8579 SN - 1872-7913 VL - 45 IS - 4 SP - 442 EP - 444 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Wicha, Sebastian G. A1 - Huisinga, Wilhelm A1 - Kloft, Charlotte T1 - Translational pharmacometric evaluation of typical antibiotic broad-spectrum combination therapies against staphylococcus aureus exploiting in vitro information JF - CPT: pharmacometrics & systems pharmacology N2 - Broad-spectrum antibiotic combination therapy is frequently applied due to increasing resistance development of infective pathogens. The objective of the present study was to evaluate two common empiric broad-spectrum combination therapies consisting of either linezolid (LZD) or vancomycin (VAN) combined with meropenem (MER) against Staphylococcus aureus (S. aureus) as the most frequent causative pathogen of severe infections. A semimechanistic pharmacokinetic-pharmacodynamic (PK-PD) model mimicking a simplified bacterial life-cycle of S. aureus was developed upon time-kill curve data to describe the effects of LZD, VAN, and MER alone and in dual combinations. The PK-PD model was successfully (i) evaluated with external data from two clinical S. aureus isolates and further drug combinations and (ii) challenged to predict common clinical PK-PD indices and breakpoints. Finally, clinical trial simulations were performed that revealed that the combination of VAN-MER might be favorable over LZD-MER due to an unfavorable antagonistic interaction between LZD and MER. Y1 - 2017 U6 - https://doi.org/10.1002/psp4.12197 SN - 2163-8306 VL - 6 SP - 512 EP - 522 PB - Wiley CY - Hoboken ER - TY - JOUR A1 - Westphal, Anke T1 - Zur Wertorientierung in der instrumentalen Leistungsmotivation : glechtsspezifische Aspkte ; eine Studie an Brandenburger Musikschulen Y1 - 1996 ER - TY - JOUR A1 - Wessel, Walter T1 - Are all complete plane multimaps but one bounded by Euler only? Y1 - 1995 ER - TY - INPR A1 - Weske, Mathias A1 - Rinderle-Ma, Stefanie A1 - Toumani, Farouk A1 - Wolf, Karsten T1 - Special section on BPM 2011 conference. - Special Issue T2 - Information systems Y1 - 2013 U6 - https://doi.org/10.1016/j.is.2013.01.003 SN - 0306-4379 VL - 38 IS - 4 SP - 545 EP - 546 PB - Elsevier CY - Oxford ER - TY - BOOK A1 - Wenyi, Chen A1 - Tianbo, Wang T1 - The hypoellipticity of differential forms on closed manifolds T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2005 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - INPR A1 - Wenyi, Chen A1 - Tianbo, Wang T1 - The hypoellipticity of differential forms on closed manifolds N2 - In this paper we consider the hypo-ellipticity of differential forms on a closed manifold.The main results show that there are some topological obstruct for the existence of the differential forms with hypoellipticity. T3 - Preprint - (2005) 06 KW - Hypoellipticity KW - Form KW - Integrability KW - Diophantine Approximation Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-29803 ER - TY - BOOK A1 - Wendland, Horst T1 - Schwach-diskrete Bewegungsgruppen im Raum T3 - Preprint / Universität Potsdam, Institut für Mathematik Y1 - 1996 VL - 1996, 18 PB - Univ. CY - Potsdam ER - TY - THES A1 - Welke, Dirk T1 - Hyperidentitäten partieller Algebren Y1 - 1996 ER - TY - JOUR A1 - Weiße, Andrea Y. A1 - Middleton, Richard H. A1 - Huisinga, Wilhelm T1 - Quantifying uncertainty, variability and likelihood for ordinary differential equation models N2 - Background: In many applications, ordinary differential equation (ODE) models are subject to uncertainty or variability in initial conditions and parameters. Both, uncertainty and variability can be quantified in terms of a probability density function on the state and parameter space. Results: The partial differential equation that describes the evolution of this probability density function has a form that is particularly amenable to application of the well- known method of characteristics. The value of the density at some point in time is directly accessible by the solution of the original ODE extended by a single extra dimension (for the value of the density). This leads to simple methods for studying uncertainty, variability and likelihood, with significant advantages over more traditional Monte Carlo and related approaches especially when studying regions with low probability. Conclusions: While such approaches based on the method of characteristics are common practice in other disciplines, their advantages for the study of biological systems have so far remained unrecognized. Several examples illustrate performance and accuracy of the approach and its limitations. Y1 - 2010 UR - http://www.biomedcentral.com/1752-0509/ U6 - https://doi.org/10.1186/1752-0509-4-144 SN - 1752-0509 ER - TY - GEN A1 - Weisser, Karin A1 - Stübler, Sabine A1 - Matheis, Walter A1 - Huisinga, Wilhelm T1 - Towards toxicokinetic modelling of aluminium exposure from adjuvants in medicinal products T2 - Regulatory toxicology and pharmacology : official journal of the International Society for Regulatory Toxicology and Pharmacology N2 - As a potentially toxic agent on nervous system and bone, the safety of aluminium exposure from adjuvants in vaccines and subcutaneous immune therapy (SCIT) products has to be continuously reevaluated, especially regarding concomitant administrations. For this purpose, knowledge on absorption and disposition of aluminium in plasma and tissues is essential. Pharmacokinetic data after vaccination in humans, however, are not available, and for methodological and ethical reasons difficult to obtain. To overcome these limitations, we discuss the possibility of an in vitro-in silico approach combining a toxicokinetic model for aluminium disposition with biorelevant kinetic absorption parameters from adjuvants. We critically review available kinetic aluminium-26 data for model building and, on the basis of a reparameterized toxicokinetic model (Nolte et al., 2001), we identify main modelling gaps. The potential of in vitro dissolution experiments for the prediction of intramuscular absorption kinetics of aluminium after vaccination is explored. It becomes apparent that there is need for detailed in vitro dissolution and in vivo absorption data to establish an in vitro-in vivo correlation (IVIVC) for aluminium adjuvants. We conclude that a combination of new experimental data and further refinement of the Nolte model has the potential to fill a gap in aluminium risk assessment. (C) 2017 Elsevier Inc. All rights reserved. KW - Aluminium KW - Aluminium adjuvants KW - Absorption kinetics KW - Toxicokinetic modelling KW - In vitro dissolution Y1 - 2017 U6 - https://doi.org/10.1016/j.yrtph.2017.02.018 SN - 0273-2300 SN - 1096-0295 VL - 88 SP - 310 EP - 321 PB - Elsevier CY - San Diego ER - TY - JOUR A1 - Weiss, Andrea Y. A1 - Huisinga, Wilhelm T1 - Error-controlled global sensitivity analysis of ordinary differential equations JF - Journal of computational physics N2 - We propose a novel strategy for global sensitivity analysis of ordinary differential equations. It is based on an error-controlled solution of the partial differential equation (PDE) that describes the evolution of the probability density function associated with the input uncertainty/variability. The density yields a more accurate estimate of the output uncertainty/variability, where not only some observables (such as mean and variance) but also structural properties (e.g., skewness, heavy tails, bi-modality) can be resolved up to a selected accuracy. For the adaptive solution of the PDE Cauchy problem we use the Rothe method with multiplicative error correction, which was originally developed for the solution of parabolic PDEs. We show that, unlike in parabolic problems, conservation properties necessitate a coupling of temporal and spatial accuracy to avoid accumulation of spatial approximation errors over time. We provide convergence conditions for the numerical scheme and suggest an implementation using approximate approximations for spatial discretization to efficiently resolve the coupling of temporal and spatial accuracy. The performance of the method is studied by means of low-dimensional case studies. The favorable properties of the spatial discretization technique suggest that this may be the starting point for an error-controlled sensitivity analysis in higher dimensions. KW - ODE with random initial conditions KW - Global sensitivity analysis KW - Cauchy problem KW - Error control/adaptivity KW - Rothe method KW - Approximate approximations Y1 - 2011 U6 - https://doi.org/10.1016/j.jcp.2011.05.011 SN - 0021-9991 VL - 230 IS - 17 SP - 6824 EP - 6842 PB - Elsevier CY - San Diego ER - TY - JOUR A1 - Weicker, Karsten T1 - Vorlesungs-Pflege BT - Maßnahmen zur Runderneuerung degenerierender Informatikvorlesungen JF - Commentarii informaticae didacticae N2 - Ähnlich zu Alterungsprozessen bei Software degenerieren auch Vorlesungen, wenn sie nicht hinreichend gepflegt werden. Die Gründe hierfür werden ebenso beleuchtet wie mögliche Indikatoren und Maßnahmen – der Blick ist dabei immer der eines Informatikers. An drei Vorlesungen wird erläutert, wie der Degeneration von Lehrveranstaltungen gegengewirkt werden kann. Mangels hinreichend großer empirischer Daten liefert das Paper keine unumstößlichen Wahrheiten. Ein Ziel ist es vielmehr Kollegen, die ähnliche Phänomene beobachten, einen ersten Anker für einen inneren Diskurs zu bieten. Ein langfristiges Ziel ist die Sammlung eines Katalogs an Maßnahmen zur Pflege von Informatikvorlesungen. KW - Wartung von Lehrveranstaltungen KW - Re-Engineering KW - Strukturverbesserung KW - Lehrevaluation KW - Degenerationsprozesse Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-416315 IS - 12 SP - 47 EP - 59 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - BOOK A1 - Weian, Liu T1 - Viscosity Solutions of Fully Nonlinea Parabolic Systems T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2002 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - THES A1 - Wei, Yawei T1 - Operators on manifolds with edge and boundary with singular trace conditions Y1 - 2008 CY - Potsdam ER - TY - THES A1 - Wei, Yawei T1 - Operators on Manifolds with Edge and Boundary with Singular Trace Conditions Y1 - 2008 CY - Potsdam ER - TY - JOUR A1 - Wang, Lifeng A1 - Zöller, Gert A1 - Hainzl, Sebastian T1 - Joint Determination of Slip and Stress Drop in a Bayesian Inversion Approach: A Case Study for the 2010 M8.8 Maule Earthquake JF - Pure and applied geophysics N2 - Stress drop is a key factor in earthquake mechanics and engineering seismology. However, stress drop calculations based on fault slip can be significantly biased, particularly due to subjectively determined smoothing conditions in the traditional least-square slip inversion. In this study, we introduce a mechanically constrained Bayesian approach to simultaneously invert for fault slip and stress drop based on geodetic measurements. A Gaussian distribution for stress drop is implemented in the inversion as a prior. We have done several synthetic tests to evaluate the stability and reliability of the inversion approach, considering different fault discretization, fault geometries, utilized datasets, and variability of the slip direction, respectively. We finally apply the approach to the 2010 M8.8 Maule earthquake and invert for the coseismic slip and stress drop simultaneously. Two fault geometries from the literature are tested. Our results indicate that the derived slip models based on both fault geometries are similar, showing major slip north of the hypocenter and relatively weak slip in the south, as indicated in the slip models of other studies. The derived mean stress drop is 5-6 MPa, which is close to the stress drop of similar to 7 MPa that was independently determined according to force balance in this region Luttrell et al. (J Geophys Res, 2011). These findings indicate that stress drop values can be consistently extracted from geodetic data. KW - Stress drop KW - Fault slip KW - Bayesian KW - Geodetic measurements Y1 - 2015 U6 - https://doi.org/10.1007/s00024-014-0868-x SN - 0033-4553 SN - 1420-9136 VL - 172 IS - 2 SP - 375 EP - 388 PB - Springer CY - Basel ER - TY - JOUR A1 - Wang, Lifeng A1 - Hainzl, Sebastian A1 - Zöller, Gert A1 - Holschneider, Matthias T1 - Stress- and aftershock-constrained joint inversions for coseismic and postseismic slip applied to the 2004 M6.0 Parkfield earthquake JF - Journal of geophysical research : Solid earth N2 - Both aftershocks and geodetically measured postseismic displacements are important markers of the stress relaxation process following large earthquakes. Postseismic displacements can be related to creep-like relaxation in the vicinity of the coseismic rupture by means of inversion methods. However, the results of slip inversions are typically non-unique and subject to large uncertainties. Therefore, we explore the possibility to improve inversions by mechanical constraints. In particular, we take into account the physical understanding that postseismic deformation is stress-driven, and occurs in the coseismically stressed zone. We do joint inversions for coseismic and postseismic slip in a Bayesian framework in the case of the 2004 M6.0 Parkfield earthquake. We perform a number of inversions with different constraints, and calculate their statistical significance. According to information criteria, the best result is preferably related to a physically reasonable model constrained by the stress-condition (namely postseismic creep is driven by coseismic stress) and the condition that coseismic slip and large aftershocks are disjunct. This model explains 97% of the coseismic displacements and 91% of the postseismic displacements during day 1-5 following the Parkfield event, respectively. It indicates that the major postseismic deformation can be generally explained by a stress relaxation process for the Parkfield case. This result also indicates that the data to constrain the coseismic slip model could be enriched postseismically. For the 2004 Parkfield event, we additionally observe asymmetric relaxation process at the two sides of the fault, which can be explained by material contrast ratio across the fault of similar to 1.15 in seismic velocity. Y1 - 2012 U6 - https://doi.org/10.1029/2011JB009017 SN - 2169-9313 SN - 2169-9356 VL - 117 PB - American Geophysical Union CY - Washington ER - TY - JOUR A1 - Wang, Guang A1 - Li, Pei-zhi A1 - Zhang, Shi-yao A1 - Zhong, Shan A1 - Chu, Chang A1 - Zeng, Shufei A1 - Yan, Yu A1 - Cheng, Xin A1 - Chuai, Manli A1 - Hocher, Berthold A1 - Yang, Xuesong T1 - Lipopolysaccharides (LPS) Induced Angiogenesis During Chicken Embryogenesis is Abolished by Combined ETA/ETB Receptor Blockade JF - Cellular physiology and biochemistry : international journal of experimental cellular physiology, biochemistry and pharmacology N2 - Background/Aims: Angiogenesis plays a key role during embryonic development. The vascular endothelin (ET) system is involved in the regulation of angiogenesis. Lipopolysaccharides (LPS) could induce angiogenesis. The effects of ET blockers on baseline and LPS-stimulated angiogenesis during embryonic development remain unknown so far. Methods: The blood vessel density (BVD) of chorioallantoic membranes (CAMs), which were treated with saline (control), LPS, and/or BQ123 and the ETB blocker BQ788, were quantified and analyzed using an IPP 6.0 image analysis program. Moreover, the expressions of ET-1, ET-2, ET3, ET receptor A (ETRA), ET receptor B (ETRB) and VEGFR2 mRNA during embryogenesis were analyzed by semi-quantitative RT-PCR. Results: All components of the ET system are detectable during chicken embryogenesis. LPS increased angiogenesis substantially. This process was completely blocked by the treatment of a combination of the ETA receptor blockers-BQ123 and the ETB receptor blocker BQ788. This effect was accompanied by a decrease in ETRA, ETRB, and VEGFR2 gene expression. However, the baseline angiogenesis was not affected by combined ETA/ETB receptor blockade. Conclusion: During chicken embryogenesis, the LPS-stimulated angiogenesis, but not baseline angiogenesis, is sensitive to combined ETA/ETB receptor blockade. KW - Lipopolysaccharides (LPS) KW - Angiogenesis KW - Chicken chorioallantoic membrane (CAM) KW - Endothelin (ET) Y1 - 2018 U6 - https://doi.org/10.1159/000492547 SN - 1015-8987 SN - 1421-9778 VL - 48 IS - 5 SP - 2084 EP - 2090 PB - Karger CY - Basel ER - TY - THES A1 - Waltz, Christine T1 - Adjungierte Polynomideale und duale Typen auf Banachräumen und ihre Anwendung Y1 - 1994 ER - TY - BOOK A1 - Waltz, Christine T1 - Interpolation von holomorphen Typen T3 - Preprint / Universität Potsdam, Fachbereich Mathematik Y1 - 1992 VL - 1992, 01 PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Wallenta, Daniel T1 - A Lefschetz fixed point formula for elliptic quasicomplexes JF - Integral equations and operator theor N2 - In a recent paper, the Lefschetz number for endomorphisms (modulo trace class operators) of sequences of trace class curvature was introduced. We show that this is a well defined, canonical extension of the classical Lefschetz number and establish the homotopy invariance of this number. Moreover, we apply the results to show that the Lefschetz fixed point formula holds for geometric quasiendomorphisms of elliptic quasicomplexes. KW - Elliptic complexes KW - Fredholm complexes KW - Lefschetz number Y1 - 2014 U6 - https://doi.org/10.1007/s00020-014-2122-4 SN - 0378-620X SN - 1420-8989 VL - 78 IS - 4 SP - 577 EP - 587 PB - Springer CY - Basel ER - TY - THES A1 - Wallenta, Daniel T1 - Sequences of compact curvature T1 - Sequenzen mit kompakter Krümmung N2 - By perturbing the differential of a (cochain-)complex by "small" operators, one obtains what is referred to as quasicomplexes, i.e. a sequence whose curvature is not equal to zero in general. In this situation the cohomology is no longer defined. Note that it depends on the structure of the underlying spaces whether or not an operator is "small." This leads to a magical mix of perturbation and regularisation theory. In the general setting of Hilbert spaces compact operators are "small." In order to develop this theory, many elements of diverse mathematical disciplines, such as functional analysis, differential geometry, partial differential equation, homological algebra and topology have to be combined. All essential basics are summarised in the first chapter of this thesis. This contains classical elements of index theory, such as Fredholm operators, elliptic pseudodifferential operators and characteristic classes. Moreover we study the de Rham complex and introduce Sobolev spaces of arbitrary order as well as the concept of operator ideals. In the second chapter, the abstract theory of (Fredholm) quasicomplexes of Hilbert spaces will be developed. From the very beginning we will consider quasicomplexes with curvature in an ideal class. We introduce the Euler characteristic, the cone of a quasiendomorphism and the Lefschetz number. In particular, we generalise Euler's identity, which will allow us to develop the Lefschetz theory on nonseparable Hilbert spaces. Finally, in the third chapter the abstract theory will be applied to elliptic quasicomplexes with pseudodifferential operators of arbitrary order. We will show that the Atiyah-Singer index formula holds true for those objects and, as an example, we will compute the Euler characteristic of the connection quasicomplex. In addition to this we introduce geometric quasiendomorphisms and prove a generalisation of the Lefschetz fixed point theorem of Atiyah and Bott. N2 - Die Theorie der Sequenzen mit kompakter Krümmung, sogenannter Quasikomplexe, ist eine Verallgemeinerung der Theorie der Fredholm Komplexe. Um ein Verständnis für (Quasi-)Komplexe zu gewinnen, müssen Inhalte aus verschiedenen Teilgebieten der Mathematik kombiniert werden. Alle hierfür wesentlichen Grundlagen sind im ersten Kapitel dieser Dissertation zusammengefasst. Dies betrifft unter anderem gewisse Elemente der Funktionalanalysis und der Differentialgeometrie, sowie die Theorie der klassischen Pseudodifferentialoperatoren. Im zweiten Kapitel wird anschließend die abstrakte Theorie der Quasikomplexe und zugehöriger Quasimorphismen im Kontext der Funktionalanalysis entwickelt. Dabei werden verschiedene Typen von Quasikomplexen und Quasimorphismen klassifiziert, deren Eigenschaften analysiert und Beispiele betrachtet. Ein zentraler Punkt hierbei ist die Lösung des Problems, für welche dieser Objekte sich eine besondere charakteristische Zahl, die sogenannte Lefschetz-Zahl, definieren lässt. Die dargestellten Resultate zeigen, dass die in dieser Arbeit gegebene Definition eine natürliche Erweiterung der klassischen Lefschetz-Zahl darstellt. Abschließend wird die entwickelte Theorie im dritten Kapitel auf elliptische Quasikomplexe von Pseudodifferentialoperatoren angewendet. Dabei werden insbesondere Verallgemeinerungen der berühmten Atiyah-Singer-Index-Formel und des Lefschetz-Fixpunkt-Theorems von Atiyah and Bott bewiesen. KW - Index Theorie KW - Fredholm Komplexe KW - Elliptische Komplexe KW - Index theory KW - Elliptic complexes KW - Fredholm complexes Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-87489 ER - TY - INPR A1 - Wallenta, Daniel T1 - A Lefschetz fixed point formula for elliptic quasicomplexes N2 - In a recent paper with N. Tarkhanov, the Lefschetz number for endomorphisms (modulo trace class operators) of sequences of trace class curvature was introduced. We show that this is a well defined, canonical extension of the classical Lefschetz number and establish the homotopy invariance of this number. Moreover, we apply the results to show that the Lefschetz fixed point formula holds for geometric quasiendomorphisms of elliptic quasicomplexes. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 2(2013)12 KW - Perturbed complexes KW - curvature KW - Lefschetz number KW - fixed point formula Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-67016 ER - TY - JOUR A1 - Wallenta, D. T1 - Elliptic quasicomplexes on compact closed manifolds JF - Integral equations and operator theor N2 - We consider quasicomplexes of pseudodifferential operators on a smooth compact manifold without boundary. To each quasicomplex we associate a complex of symbols. The quasicomplex is elliptic if this symbol complex is exact away from the zero section. We prove that elliptic quasicomplexes are Fredholm. Moreover, we introduce the Euler characteristic for elliptic quasicomplexes and prove a generalisation of the Atiyah-Singer index theorem. KW - Elliptic complexes KW - Fredholm complexes KW - Index theory Y1 - 2012 U6 - https://doi.org/10.1007/s00020-012-1983-7 SN - 0378-620X VL - 73 IS - 4 SP - 517 EP - 536 PB - Springer CY - Basel ER - TY - THES A1 - Vu, Dinh Phuong T1 - Using video study to investigate eighth-grade mathematics classrooms in Vietnam T1 - Die Nutzung von Videostudien zur Untersuchung des Mathematikunterrichts in der 8. Klasse in Vietnam N2 - The International Project for the Evaluation of Educational Achievement (IEA) was formed in the 1950s (Postlethwaite, 1967). Since that time, the IEA has conducted many studies in the area of mathematics, such as the First International Mathematics Study (FIMS) in 1964, the Second International Mathematics Study (SIMS) in 1980-1982, and a series of studies beginning with the Third International Mathematics and Science Study (TIMSS) which has been conducted every 4 years since 1995. According to Stigler et al. (1999), in the FIMS and the SIMS, U.S. students achieved low scores in comparison with students in other countries (p. 1). The TIMSS 1995 “Videotape Classroom Study” was therefore a complement to the earlier studies conducted to learn “more about the instructional and cultural processes that are associated with achievement” (Stigler et al., 1999, p. 1). The TIMSS Videotape Classroom Study is known today as the TIMSS Video Study. From the findings of the TIMSS 1995 Video Study, Stigler and Hiebert (1999) likened teaching to “mountain ranges poking above the surface of the water,” whereby they implied that we might see the mountaintops, but we do not see the hidden parts underneath these mountain ranges (pp. 73-78). By watching the videotaped lessons from Germany, Japan, and the United States again and again, they discovered that “the systems of teaching within each country look similar from lesson to lesson. At least, there are certain recurring features [or patterns] that typify many of the lessons within a country and distinguish the lessons among countries” (pp. 77-78). They also discovered that “teaching is a cultural activity,” so the systems of teaching “must be understood in relation to the cultural beliefs and assumptions that surround them” (pp. 85, 88). From this viewpoint, one of the purposes of this dissertation was to study some cultural aspects of mathematics teaching and relate the results to mathematics teaching and learning in Vietnam. Another research purpose was to carry out a video study in Vietnam to find out the characteristics of Vietnamese mathematics teaching and compare these characteristics with those of other countries. In particular, this dissertation carried out the following research tasks: - Studying the characteristics of teaching and learning in different cultures and relating the results to mathematics teaching and learning in Vietnam - Introducing the TIMSS, the TIMSS Video Study and the advantages of using video study in investigating mathematics teaching and learning - Carrying out the video study in Vietnam to identify the image, scripts and patterns, and the lesson signature of eighth-grade mathematics teaching in Vietnam - Comparing some aspects of mathematics teaching in Vietnam and other countries and identifying the similarities and differences across countries - Studying the demands and challenges of innovating mathematics teaching methods in Vietnam – lessons from the video studies Hopefully, this dissertation will be a useful reference material for pre-service teachers at education universities to understand the nature of teaching and develop their teaching career. N2 - Das International Project for the Evaluation of Educational Achievement (IEA) wurde in den 1950er Jahren gegründet. Seitdem führte das IEA viele Studien in Bereich mathematischer Bildung durch, insbesondere die First International Mathematics Study (FIMS) im Jahre 1964, die Second International Mathematics Study (SIMS) in den Jahren 1980–1982 und eine Reihe von Studien, die mit der Third International Mathematics and Science Study (TIMSS) begann und seit 1995 alle vier Jahre durchgeführt wird. Nach Stigler et al. (1999) erreichten US-amerikanische Studenten bei FIMS und SIMS niedrigere Ergebnisse als Schüler anderer Länder (S. 1). Daher wurde TIMSS 1995 erweitert um eine ‘Videotape Classroom Study’ mit dem Ziel, „mehr über die unterrichtlichen und kulturellen Prozesse, die mit Leistung zusammenhängen“, zu erfahren (S. 1; Übersetzung vom engl. Original). Von den Ergebnissen der TIMMS 1995 Video Study ausgehend verglichen Stigler und Hiebert (1999) Unterricht mit „Gebirgszügen, die die Wasseroberfläche durchstoßen“, womit sie ausdrücken sollten, was die Bergspitzen sichtbar, große Teile des Gebirges aber unter dem Wasser verborgen sind (S. 73–78; Übersetzung vom engl. Original). Durch die wiederholte Analyse videographierter Unterrichtsstunden aus Deutschland, Japan und den USA entdeckten sie, dass „die Arten des Unterrichts innerhalb jedes Landes von Stunde zu Stunde ähnlich sind. Zumindest gibt es bestimmte wiederkehrende Aspekte [oder Skripte], welche für viele Stunden eines Landes typisch sind und die Stunden gegenüber anderen Ländern abgrenzen“ (S. 77f.). Sie entdeckten außerdem, dass Unterricht eine „kulturelle Aktivität“ ist, Unterrichtsarten also „verstanden werden müssen in Relation zu den kulturellen Überzeugungen und Annahmen, die sie umgeben“ (S. 85, 88). Hierauf aufbauend war es ein Ziel der Dissertation, kulturelle Aspekte des Mathematikunterricht zu untersuchen und die Ergebnisse mit Mathematikunterricht in Vietnam zu vergleichen. Ein weiteres Ziel war die Erhebung der Charakteristika vietnamesischen Mathematikunterricht durch eine Videostudie in Vietnam und der anschließende Vergleich dieser Charakteristika mit denen anderer Länder. Im Einzelnen befasste sich diese Dissertation mit den folgenden Forschungszielen: - Untersuchung der Charakteristika von Lehren und Lernen in unterschiedlichen Kulturen und vorläufiger Vergleich der Resultate mit dem Lehren und Lernen von Mathematik in Vietnam - Einführung der TIMSS und der TIMSS Video Study und der methodologischen Vorteile von Videostudien für die Untersuchung von Mathematikunterricht in Vietnam - Durchführung der Videostudie in Vietnam, um Unterrichtsskripte des Mathematikunterrichts in 8. Klassen in Vietnam zu identifizieren - Vergleich ausgewählter Aspekte des Mathematikunterrichts in Vietnam mit denen anderer Länder auf der Grundlage der Videostudie in Vietnam und Diskussion von Ähnlichkeiten und Unterschieden zwischen Ländern - Untersuchung der Herausforderungen für eine Innovation der Unterrichtsmethoden im Mathematikunterricht Vietnams Diese Dissertation entstand in der Hoffnung, dass sie eine nützliche Referenz für Lehramtsstudenten zum Verständnis der Natur des Unterrichts und zur Entwicklung der eigenen Lehrerpersönlichkeit darstellen möge. KW - Videostudie KW - Mathematikunterricht KW - Unterrichtsmethode KW - TIMSS KW - Kulturelle Aktivität KW - video study KW - mathematics education KW - teaching methods KW - TIMSS KW - Vietnam Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-72464 ER - TY - INPR A1 - Voss, Carola Regine T1 - Harness-Prozesse N2 - Harness-Prozesse finden in der Forschung immer mehr Anwendung. Vor allem gewinnen Harness-Prozesse in stetiger Zeit an Bedeutung. Grundlegende Literatur zu diesem Thema ist allerdings wenig vorhanden. In der vorliegenden Arbeit wird die vorhandene Grundlagenliteratur zu Harness-Prozessen in diskreter und stetiger Zeit aufgearbeitet und Beweise ausgeführt, die bisher nur skizziert waren. Ziel dessen ist die Existenz einer Zerlegung von Harness-Prozessen über Z beziehungsweise R+ nachzuweisen. T3 - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2010, 13 Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49651 ER - TY - JOUR A1 - von Kleist, Max A1 - Menz, Stephan A1 - Stocker, Hartmut A1 - Arasteh, Keikawus A1 - Schuette, Christof A1 - Huisinga, Wilhelm T1 - HIV quasispecies dynamics during pro-active treatment switching impact on multi-drug resistance and resistance archiving in latent reservoirs JF - PLoS one N2 - The human immunodeficiency virus (HIV) can be suppressed by highly active anti-retroviral therapy (HAART) in the majority of infected patients. Nevertheless, treatment interruptions inevitably result in viral rebounds from persistent, latently infected cells, necessitating lifelong treatment. Virological failure due to resistance development is a frequent event and the major threat to treatment success. Currently, it is recommended to change treatment after the confirmation of virological failure. However, at the moment virological failure is detected, drug resistant mutants already replicate in great numbers. They infect numerous cells, many of which will turn into latently infected cells. This pool of cells represents an archive of resistance, which has the potential of limiting future treatment options. The objective of this study was to design a treatment strategy for treatment-naive patients that decreases the likelihood of early treatment failure and preserves future treatment options. We propose to apply a single, pro-active treatment switch, following a period of treatment with an induction regimen. The main goal of the induction regimen is to decrease the abundance of randomly generated mutants that confer resistance to the maintenance regimen, thereby increasing subsequent treatment success. Treatment is switched before the overgrowth and archiving of mutant strains that carry resistance against the induction regimen and would limit its future re-use. In silico modelling shows that an optimal trade-off is achieved by switching treatment at & 80 days after the initiation of antiviral therapy. Evaluation of the proposed treatment strategy demonstrated significant improvements in terms of resistance archiving and virological response, as compared to conventional HAART. While continuous pro-active treatment alternation improved the clinical outcome in a randomized trial, our results indicate that a similar improvement might also be reached after a single pro-active treatment switch. The clinical validity of this finding, however, remains to be shown by a corresponding trial. Y1 - 2011 U6 - https://doi.org/10.1371/journal.pone.0018204 SN - 1932-6203 VL - 6 IS - 3 PB - PLoS CY - San Fransisco ER - TY - JOUR A1 - Vogel, Hans-Jürgen A1 - Marki, Laszlo A1 - Pöschel, Reinhard T1 - Contributions to general algebra and categories Y1 - 1996 ER - TY - JOUR A1 - Vogel, Hans-Jürgen T1 - Relations as morphisms of a certain monoidal category Y1 - 1997 ER - TY - JOUR A1 - Vogel, Hans-Jürgen T1 - On functors between certain monoidal categories Y1 - 1998 ER - TY - JOUR A1 - Vogel, Hans-Jürgen T1 - On quasivarieties generated by - algebras Y1 - 1995 ER - TY - BOOK A1 - Vogel, Hans-Jürgen T1 - On morphisms between partial algebras T3 - Preprint / Universität Potsdam, Institut für Mathematik Y1 - 1998 VL - 1998, 13 PB - Univ. CY - Potsdam ER -