@article{ZoellerUllahBindietal.2017, author = {Z{\"o}ller, Gert and Ullah, Shahid and Bindi, Dino and Parolai, Stefano and Mikhailova, Natalya}, title = {The largest expected earthquake magnitudes in Central Asia}, series = {Seismicity, fault rupture and earthquake hazards in slowly deforming regions}, volume = {432}, journal = {Seismicity, fault rupture and earthquake hazards in slowly deforming regions}, publisher = {The Geological Society}, address = {London}, isbn = {978-1-86239-745-3}, issn = {0305-8719}, doi = {10.1144/SP432.3}, pages = {29 -- 40}, year = {2017}, abstract = {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.}, language = {en} } @article{ZoellerHolschneiderHainzl2013, author = {Z{\"o}ller, Gert and Holschneider, Matthias and Hainzl, Sebastian}, title = {The Maximum Earthquake Magnitude in a Time Horizon: Theory and Case Studies}, series = {Bulletin of the Seismological Society of America}, volume = {103}, journal = {Bulletin of the Seismological Society of America}, number = {2A}, publisher = {Seismological Society of America}, address = {Albany}, issn = {0037-1106}, doi = {10.1785/0120120013}, pages = {860 -- 875}, year = {2013}, abstract = {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.}, language = {en} } @misc{ZoellerHolschneider2018, author = {Z{\"o}ller, Gert and Holschneider, Matthias}, title = {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 Z{\"o}ller and Matthias Holschneider" by Mathias Raschke}, series = {Bulletin of the Seismological Society of America}, volume = {108}, journal = {Bulletin of the Seismological Society of America}, number = {2}, publisher = {Seismological Society of America}, address = {Albany}, issn = {0037-1106}, doi = {10.1785/0120170131}, pages = {1029 -- 1030}, year = {2018}, language = {en} } @article{ZoellerHolschneider2014, author = {Z{\"o}ller, Gert and Holschneider, Matthias}, title = {Induced seismicity: What is the size of the largest expected earthquake?}, series = {The bulletin of the Seismological Society of America}, volume = {104}, journal = {The bulletin of the Seismological Society of America}, number = {6}, publisher = {Seismological Society of America}, address = {Albany}, issn = {0037-1106}, doi = {10.1785/0120140195}, pages = {3153 -- 3158}, year = {2014}, abstract = {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.}, language = {en} } @article{ZoellerHolschneider2016, author = {Z{\"o}ller, Gert and Holschneider, Matthias}, title = {The Maximum Possible and the Maximum Expected Earthquake Magnitude for Production-Induced Earthquakes at the Gas Field in Groningen, The Netherlands}, series = {Bulletin of the Seismological Society of America}, volume = {106}, journal = {Bulletin of the Seismological Society of America}, publisher = {Seismological Society of America}, address = {Albany}, issn = {0037-1106}, doi = {10.1785/0120160220}, pages = {2917 -- 2921}, year = {2016}, abstract = {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.}, language = {en} } @article{ZoellerHolschneider2016, author = {Z{\"o}ller, Gert and Holschneider, Matthias}, title = {The Earthquake History in a Fault Zone Tells Us Almost Nothing about m(max)}, series = {Seismological research letters}, volume = {87}, journal = {Seismological research letters}, publisher = {Seismological Society of America}, address = {Albany}, issn = {0895-0695}, doi = {10.1785/0220150176}, pages = {132 -- 137}, year = {2016}, abstract = {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.}, language = {en} } @article{ZoellerHainzlTilmannetal.2020, author = {Z{\"o}ller, Gert and Hainzl, Sebastian and Tilmann, Frederik and Woith, Heiko and Dahm, Torsten}, title = {Comment on: Wikelski, Martin; M{\"u}ller, 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}, series = {Ethology}, volume = {127}, journal = {Ethology}, number = {3}, publisher = {Wiley}, address = {Hoboken}, issn = {0179-1613}, doi = {10.1111/eth.13105}, pages = {302 -- 306}, year = {2020}, abstract = {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.}, language = {en} } @article{ZoellerBenZion2014, author = {Z{\"o}ller, Gert and Ben-Zion, Yehuda}, title = {Large earthquake hazard of the San Jacinto fault zone, CA, from long record of simulated seismicity assimilating the available instrumental and paleoseismic data}, series = {Pure and applied geophysics}, volume = {171}, journal = {Pure and applied geophysics}, number = {11}, publisher = {Springer}, address = {Basel}, issn = {0033-4553}, doi = {10.1007/s00024-014-0783-1}, pages = {2955 -- 2965}, year = {2014}, abstract = {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.}, language = {en} } @article{Zoeller2022, author = {Z{\"o}ller, Gert}, title = {A note on the estimation of the maximum possible earthquake magnitude based on extreme value theory for the Groningen Gas Field}, series = {The bulletin of the Seismological Society of America : BSSA}, volume = {112}, journal = {The bulletin of the Seismological Society of America : BSSA}, number = {4}, publisher = {Seismological Society of America}, address = {El Cerito, Calif.}, issn = {0037-1106}, doi = {10.1785/0120210307}, pages = {1825 -- 1831}, year = {2022}, abstract = {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.}, language = {en} } @article{Zoeller2018, author = {Z{\"o}ller, Gert}, title = {A statistical model for earthquake recurrence based on the assimilation of paleoseismicity, historic seismicity, and instrumental seismicity}, series = {Journal of geophysical research : Solid earth}, volume = {123}, journal = {Journal of geophysical research : Solid earth}, number = {6}, publisher = {American Geophysical Union}, address = {Washington}, issn = {2169-9313}, doi = {10.1029/2017JB015099}, pages = {4906 -- 4921}, year = {2018}, abstract = {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.}, language = {en} } @article{Zoeller2013, author = {Z{\"o}ller, Gert}, title = {Convergence of the frequency-magnitude distribution of global earthquakes - maybe in 200 years}, series = {Geophysical research letters}, volume = {40}, journal = {Geophysical research letters}, number = {15}, publisher = {American Geophysical Union}, address = {Washington}, issn = {0094-8276}, doi = {10.1002/grl.50779}, pages = {3873 -- 3877}, year = {2013}, abstract = {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.}, language = {en} } @article{Zaehle2005, author = {Z{\"a}hle, Henryk}, title = {Space-time regularity of catalytic super-Brownian motion}, year = {2005}, abstract = {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.}, language = {en} } @article{Zaehle2004, author = {Z{\"a}hle, Henryk}, title = {Heat equation with strongly inhomogeneous noise}, year = {2004}, abstract = {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.}, language = {en} } @article{ZolotovProkhorovNamgaladzeetal.2011, author = {Zolotov, O. V. and Prokhorov, Boris E. and Namgaladze, Alexander A. and Martynenko, O. V.}, title = {Variations in the total electron content of the ionosphere during preparation of earthquakes}, series = {Russian journal of physical chemistry : B, Focus on physics}, volume = {5}, journal = {Russian journal of physical chemistry : B, Focus on physics}, number = {3}, publisher = {Pleiades Publ.}, address = {New York}, issn = {1990-7931}, doi = {10.1134/S1990793111030146}, pages = {435 -- 438}, year = {2011}, abstract = {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.}, language = {en} } @phdthesis{Ziese2014, author = {Ziese, Ramona}, title = {Geometric electroelasticity}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-72504}, school = {Universit{\"a}t Potsdam}, pages = {vi, 113}, year = {2014}, abstract = {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.}, language = {en} } @article{ZieheLaskovNolteetal.2004, author = {Ziehe, Andreas and Laskov, Pavel and Nolte, G and M{\"u}ller, Klaus-Robert}, title = {A fast algorithm for joint diagonalization with non-orthogonal transformations and its application to blind source separation}, year = {2004}, abstract = {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}, language = {en} } @article{ZhukGunther2004, author = {Zhuk, Alexandre and Gunther, U.}, title = {Massive scalar fields in the early universe}, issn = {0218-2718}, year = {2004}, abstract = {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}, language = {en} } @book{Zhuchok2018, author = {Zhuchok, Anatolii V.}, title = {Relatively free doppelsemigroups}, number = {5}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, isbn = {978-3-86956-427-2}, issn = {2199-4951}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-407719}, publisher = {Universit{\"a}t Potsdam}, pages = {vii, 78}, year = {2018}, abstract = {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.}, language = {en} } @book{Zendler1998, author = {Zendler, Andreas}, title = {Poweranalytische Versuchsplanung zur Kontrolle statistischer und softwaretechnischer Relevanz}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Informatik}, volume = {1998, 07}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Informatik}, publisher = {Univ.}, address = {Potsdam}, issn = {0946-7580}, pages = {14 S.}, year = {1998}, language = {de} } @book{Zendler1999, author = {Zendler, Andreas}, title = {Einzelfallanalytische Versuchspl{\"a}ne der Biometrie zur Durchf{\"u}hrung software-technischer Experimente mit N=1}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Informatik}, volume = {1999, 10}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Informatik}, publisher = {Univ.}, address = {Potsdam}, issn = {0946-7580}, pages = {36 S.}, year = {1999}, language = {de} } @article{ZemellaThoringHoffmeisteretal.2018, author = {Zemella, Anne and Thoring, Lena and Hoffmeister, Christian and Samalikova, Maria and Ehren, Patricia and W{\"u}stenhagen, Doreen Anja and Kubick, Stefan}, title = {Cell-free protein synthesis as a novel tool for directed glycoengineering of active erythropoietin}, series = {Scientific reports}, volume = {8}, journal = {Scientific reports}, publisher = {Nature Publ. Group}, address = {London}, issn = {2045-2322}, doi = {10.1038/s41598-018-26936-x}, pages = {12}, year = {2018}, abstract = {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.}, language = {en} } @unpublished{Zehmisch2008, author = {Zehmisch, Ren{\´e}}, title = {{\"U}ber Waldidentit{\"a}ten der Brownschen Bewegung}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49469}, year = {2008}, abstract = {Aus dem Inhalt: 1 Abraham Wald (1902-1950) 2 Einf{\"u}hrung 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 {\"U}berschreitungszeit der Brown- schen Bewegung 2.9 Waldidentit{\"a}ten f{\"u}r die {\"U}berschreitungszeiten der Brownschen Bewegung 3 Erste Waldidentit{\"a}t 3.1 Burkholder, Gundy und Davis Ungleichungen der gestoppten Brown- schen Bewegung 3.2 Erste Waldidentit{\"a}t f{\"u}r die Brownsche Bewegung 3.3 Verfeinerungen der ersten Waldidentit{\"a}t 3.4 St{\"a}rkere Verfeinerung der ersten Waldidentit{\"a}t f{\"u}r die Brown- schen Bewegung 3.5 Verfeinerung der ersten Waldidentit{\"a}t f{\"u}r spezielle Stoppzeiten der Brownschen Bewegung 3.6 Beispiele f{\"u}r lokale Martingale f{\"u}r die Verfeinerung der ersten Waldidentit{\"a}t 3.7 {\"U}berschreitungszeiten der Brownschen Bewegung f{\"u}r nichtlineare Schranken 4 Zweite Waldidentit{\"a}t 4.1 Zweite Waldidentit{\"a}t f{\"u}r die Brownsche Bewegung 4.2 Anwendungen der ersten und zweitenWaldidentit{\"a}t f{\"u}r die Brown- schen Bewegung 5 Dritte Waldidentit{\"a}t 5.1 Dritte Waldidentit{\"a}t f{\"u}r die Brownsche Bewegung 5.2 Verfeinerung der dritten Waldidentit{\"a}t 5.3 Eine wichtige Voraussetzung f{\"u}r die Verfeinerung der drittenWal- didentit{\"a}t 5.4 Verfeinerung der dritten Waldidentit{\"a}t f{\"u}r spezielle Stoppzeiten der Brownschen Bewegung 6 Waldidentit{\"a}ten im Mehrdimensionalen 6.1 Erste Waldidentit{\"a}t im Mehrdimensionalen 6.2 Zweite Waldidentit{\"a}t im Mehrdimensionalen 6.3 Dritte Waldidentit{\"a}t im Mehrdimensionalen 7 Appendix}, language = {de} } @book{ZassZagrebnovSukiasyanetal.2020, author = {Zass, Alexander and Zagrebnov, Valentin and Sukiasyan, Hayk and Melkonyan, Tatev and Rafler, Mathias and Poghosyan, Suren and Zessin, Hans and Piatnitski, Andrey and Zhizhina, Elena and Pechersky, Eugeny and Pirogov, Sergei and Yambartsev, Anatoly and Mazzonetto, Sara and Lykov, Alexander and Malyshev, Vadim and Khachatryan, Linda and Nahapetian, Boris and Jursenas, Rytis and Jansen, Sabine and Tsagkarogiannis, Dimitrios and Kuna, Tobias and Kolesnikov, Leonid and Hryniv, Ostap and Wallace, Clare and Houdebert, Pierre and Figari, Rodolfo and Teta, Alessandro and Boldrighini, Carlo and Frigio, Sandro and Maponi, Pierluigi and Pellegrinotti, Alessandro and Sinai, Yakov G.}, title = {Proceedings of the XI international conference stochastic and analytic methods in mathematical physics}, number = {6}, editor = {Roelly, Sylvie and Rafler, Mathias and Poghosyan, Suren}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, isbn = {978-3-86956-485-2}, issn = {2199-4951}, doi = {10.25932/publishup-45919}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-459192}, publisher = {Universit{\"a}t Potsdam}, pages = {xiv, 194}, year = {2020}, abstract = {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.}, language = {en} } @article{Zass2020, author = {Zass, Alexander}, title = {A Gibbs point process of diffusions: Existence and uniqueness}, series = {Lectures in pure and applied mathematics}, journal = {Lectures in pure and applied mathematics}, number = {6}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, isbn = {978-3-86956-485-2}, issn = {2199-4951}, doi = {10.25932/publishup-47195}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-471951}, pages = {13 -- 22}, year = {2020}, language = {en} } @phdthesis{Zass2021, author = {Zass, Alexander}, title = {A multifaceted study of marked Gibbs point processes}, doi = {10.25932/publishup-51277}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-512775}, school = {Universit{\"a}t Potsdam}, pages = {vii, 104}, year = {2021}, abstract = {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.}, language = {en} } @article{Zass2021, author = {Zass, Alexander}, title = {Gibbs point processes on path space}, series = {Markov processes and related fields}, volume = {28}, journal = {Markov processes and related fields}, number = {3}, publisher = {Polymat}, address = {Moscow}, issn = {1024-2953}, pages = {329 -- 364}, year = {2021}, abstract = {We present general existence and uniqueness results for marked models with pair interactions, exemplified through Gibbs point processes on path space. More precisely, we study a class of infinite-dimensional diffusions under Gibbsian interactions, in the context of marked point configurations: the starting points belong to R-d, and the marks are the paths of Langevin diffusions. We use the entropy method to prove existence of an infinite-volume Gibbs point process and use cluster expansion tools to provide an explicit activity domain in which uniqueness holds.}, language = {en} } @article{ZaourarHamoudiHolschneideretal.2013, author = {Zaourar, Naima and Hamoudi, Mohamed and Holschneider, Matthias and Mandea, Mioara}, title = {Fractal dynamics of geomagnetic storms}, series = {Arabian journal of geosciences}, volume = {6}, journal = {Arabian journal of geosciences}, number = {6}, publisher = {Springer}, address = {Heidelberg}, issn = {1866-7511}, doi = {10.1007/s12517-011-0487-0}, pages = {1693 -- 1702}, year = {2013}, abstract = {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.}, language = {en} } @phdthesis{Zadorozhnyi2021, author = {Zadorozhnyi, Oleksandr}, title = {Contributions to the theoretical analysis of the algorithms with adversarial and dependent data}, school = {Universit{\"a}t Potsdam}, pages = {144}, year = {2021}, abstract = {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).}, language = {en} } @book{YinHuaWeian1998, author = {Yin, Yang and Hua, Chen and Weian, Liu}, title = {On solutions of the chemotaxis equations}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, volume = {1998, 06}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, publisher = {Univ.}, address = {Potsdam}, pages = {14 S.}, year = {1998}, language = {en} } @misc{YinHua2007, author = {Yin, Yang and Hua, Chen}, title = {On chemotaxis systems with saturation growth}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {25 S.}, year = {2007}, language = {en} } @book{YinWitt2002, author = {Yin, Huicheng and Witt, Ingo}, title = {Global singularity structure of weak solutions to 3-D semilinear dispersive wave equaions with discontinuous initial data}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {13 S.}, year = {2002}, language = {en} } @article{YinWitt2004, author = {Yin, H. C. and Witt, Ingo}, title = {Global singularity structure of weak solutions to 3-D semilinear dispersive wave equations with discontinuous initial data}, issn = {0022-0396}, year = {2004}, abstract = {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}, language = {en} } @article{YenvonSpechtLinetal.2022, author = {Yen, Ming-Hsuan and von Specht, Sebastian and Lin, Yen-Yu and Cotton, Fabrice and Ma, Kuo-Fong}, title = {Within- and between-event variabilities of strong-velocity pulses of moderate earthquakes within dense seismic arrays}, series = {Bulletin of the Seismological Society of America}, volume = {112}, journal = {Bulletin of the Seismological Society of America}, number = {1}, publisher = {Seismological Society of America}, address = {El Cerito, Calif.}, issn = {0037-1106}, doi = {10.1785/0120200376}, pages = {361 -- 380}, year = {2022}, abstract = {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.}, language = {en} } @book{YagdjianGalstian2007, author = {Yagdjian, Karen and Galstian, Anahit}, title = {Fundamental solutions for Wave Equation in de Sitter Model of Universe}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {36 S.}, year = {2007}, language = {en} } @book{Yagdjian2001, author = {Yagdjian, Karen}, title = {Geometric optics for the nonlinear hyperbolic systems of kirchhoff-type}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {42 S.}, year = {2001}, language = {en} } @article{XiongStolleAlkenetal.2020, author = {Xiong, Chao and Stolle, Claudia and Alken, Patrick and Rauberg, Jan}, title = {Relationship between large-scale ionospheric field-aligned currents and electron/ion precipitations}, series = {Earth, planets and space}, volume = {72}, journal = {Earth, planets and space}, number = {1}, publisher = {Springer}, address = {New York}, issn = {1880-5981}, doi = {10.1186/s40623-020-01286-z}, pages = {22}, year = {2020}, abstract = {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.}, language = {en} } @article{WormellReich2021, author = {Wormell, Caroline L. and Reich, Sebastian}, title = {Spectral convergence of diffusion maps}, series = {SIAM journal on numerical analysis / Society for Industrial and Applied Mathematics}, volume = {59}, journal = {SIAM journal on numerical analysis / Society for Industrial and Applied Mathematics}, number = {3}, publisher = {Society for Industrial and Applied Mathematics}, address = {Philadelphia}, issn = {0036-1429}, doi = {10.1137/20M1344093}, pages = {1687 -- 1734}, year = {2021}, abstract = {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.}, language = {en} } @book{Wollenberg1994, author = {Wollenberg, Manfred}, title = {On an inverse problem in modular theory}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, volume = {1994, 07}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, publisher = {Univ.}, address = {Potsdam}, pages = {14 S.}, year = {1994}, language = {en} } @article{Witt2004, author = {Witt, Ingo}, title = {Local asymptotic types}, issn = {0025-2611}, year = {2004}, abstract = {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}, language = {en} } @book{Witt2003, author = {Witt, Ingo}, title = {Green formulae for cone differential operators}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {25 S.}, year = {2003}, language = {en} } @phdthesis{Witt2003, author = {Witt, Ingo}, title = {Beitr{\"a}ge zur Theorie singul{\"a}rer hyperbolischer Differentialoperatoren}, address = {Potsdam}, pages = {121 S.}, year = {2003}, language = {de} } @book{Witt2002, author = {Witt, Ingo}, title = {A calculus for a class of finitely degenerate pseudodifferential operators}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {27 S.}, year = {2002}, language = {en} } @book{Witt2002, author = {Witt, Ingo}, title = {Local asymptotic types}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {21 S.}, year = {2002}, language = {en} } @book{Witt2001, author = {Witt, Ingo}, title = {Asymptotic algebras}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {13 S.}, year = {2001}, language = {en} } @book{Witt1999, author = {Witt, Ingo}, title = {On the factorization of meromorphic mellin symbols}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {30 S.}, year = {1999}, language = {en} } @book{Witt1999, author = {Witt, Ingo}, title = {Explicit algebras with the Leibniz-Mellin translation product}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {12 S.}, year = {1999}, language = {en} } @article{WismathKoppitzDenecke1997, author = {Wismath, Shelly and Koppitz, J{\"o}rg and Denecke, Klaus-Dieter}, title = {Maps between M-solid varieties of emigroups}, year = {1997}, language = {en} } @misc{WiljesTong2020, author = {Wiljes, Jana de and Tong, Xin T.}, title = {Analysis of a localised nonlinear ensemble Kalman Bucy filter with complete and accurate observations}, series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, volume = {33}, journal = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, number = {9}, publisher = {IOP Publ.}, address = {Bristol}, issn = {1866-8372}, doi = {10.25932/publishup-54041}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-540417}, pages = {4752 -- 4782}, year = {2020}, abstract = {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.}, language = {en} } @article{WiljesTong2020, author = {Wiljes, Jana de and Tong, Xin T.}, title = {Analysis of a localised nonlinear ensemble Kalman Bucy filter with complete and accurate observations}, series = {Nonlinearity}, volume = {33}, journal = {Nonlinearity}, number = {9}, publisher = {IOP Publ.}, address = {Bristol}, issn = {0951-7715}, doi = {10.1088/1361-6544/ab8d14}, pages = {4752 -- 4782}, year = {2020}, abstract = {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.}, language = {en} } @article{WiegnerBoesenbergBoeckmannetal.1999, author = {Wiegner, Matthias and B{\"o}senberg, Jens and B{\"o}ckmann, Christine and Eixmann, Ronald and Freudenthaler, Volker and Mattis, Ina and Trickl, Thomas}, title = {Lidar Network to Establish an Aerosol Climatology}, year = {1999}, language = {en} } @article{WichitsaNguanLaeuterLiero2016, author = {Wichitsa-Nguan, Korakot and L{\"a}uter, Henning and Liero, Hannelore}, title = {Estimability in Cox models}, series = {Statistical Papers}, volume = {57}, journal = {Statistical Papers}, publisher = {Springer}, address = {New York}, issn = {0932-5026}, doi = {10.1007/s00362-016-0755-x}, pages = {1121 -- 1140}, year = {2016}, abstract = {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.}, language = {en} } @phdthesis{Wichitsanguan2016, author = {Wichitsa-nguan, Korakot}, title = {Modifications and extensions of the logistic regression and Cox model}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-90033}, school = {Universit{\"a}t Potsdam}, pages = {x, 131}, year = {2016}, abstract = {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.}, language = {en} } @misc{WichaKeesSolmsetal.2015, author = {Wicha, Sebastian G. and Kees, Martin G. and Solms, Alexander Maximilian and Minichmayr, Iris K. and Kratzer, Alexander and Kloft, Charlotte}, title = {TDMx: A novel web-based open-access support tool for optimising antimicrobial dosing regimens in clinical routine}, series = {International journal of antimicrobial agents}, volume = {45}, journal = {International journal of antimicrobial agents}, number = {4}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0924-8579}, doi = {10.1016/j.ijantimicag.2014.12.010}, pages = {442 -- 444}, year = {2015}, language = {en} } @article{WichaHuisingaKloft2017, author = {Wicha, Sebastian G. and Huisinga, Wilhelm and Kloft, Charlotte}, title = {Translational pharmacometric evaluation of typical antibiotic broad-spectrum combination therapies against staphylococcus aureus exploiting in vitro information}, series = {CPT: pharmacometrics \& systems pharmacology}, volume = {6}, journal = {CPT: pharmacometrics \& systems pharmacology}, publisher = {Wiley}, address = {Hoboken}, issn = {2163-8306}, doi = {10.1002/psp4.12197}, pages = {512 -- 522}, year = {2017}, abstract = {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.}, language = {en} } @article{Westphal1996, author = {Westphal, Anke}, title = {Zur Wertorientierung in der instrumentalen Leistungsmotivation : glechtsspezifische Aspkte ; eine Studie an Brandenburger Musikschulen}, year = {1996}, language = {de} } @article{Wessel1995, author = {Wessel, Walter}, title = {Are all complete plane multimaps but one bounded by Euler only?}, year = {1995}, language = {en} } @unpublished{WeskeRinderleMaToumanietal.2013, author = {Weske, Mathias and Rinderle-Ma, Stefanie and Toumani, Farouk and Wolf, Karsten}, title = {Special section on BPM 2011 conference. - Special Issue}, series = {Information systems}, volume = {38}, journal = {Information systems}, number = {4}, publisher = {Elsevier}, address = {Oxford}, issn = {0306-4379}, doi = {10.1016/j.is.2013.01.003}, pages = {545 -- 546}, year = {2013}, language = {en} } @book{WenyiTianbo2005, author = {Wenyi, Chen and Tianbo, Wang}, title = {The hypoellipticity of differential forms on closed manifolds}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {11 S.}, year = {2005}, language = {en} } @book{Wendland1996, author = {Wendland, Horst}, title = {Schwach-diskrete Bewegungsgruppen im Raum}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, volume = {1996, 18}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, publisher = {Univ.}, address = {Potsdam}, pages = {10 Bl.}, year = {1996}, language = {de} } @phdthesis{Welke1996, author = {Welke, Dirk}, title = {Hyperidentit{\"a}ten partieller Algebren}, pages = {104 S.}, year = {1996}, language = {de} } @article{WeisseMiddletonHuisinga2010, author = {Weiße, Andrea Y. and Middleton, Richard H. and Huisinga, Wilhelm}, title = {Quantifying uncertainty, variability and likelihood for ordinary differential equation models}, issn = {1752-0509}, doi = {10.1186/1752-0509-4-144}, year = {2010}, abstract = {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.}, language = {en} } @misc{WeisserStueblerMatheisetal.2017, author = {Weisser, Karin and St{\"u}bler, Sabine and Matheis, Walter and Huisinga, Wilhelm}, title = {Towards toxicokinetic modelling of aluminium exposure from adjuvants in medicinal products}, series = {Regulatory toxicology and pharmacology : official journal of the International Society for Regulatory Toxicology and Pharmacology}, volume = {88}, journal = {Regulatory toxicology and pharmacology : official journal of the International Society for Regulatory Toxicology and Pharmacology}, publisher = {Elsevier}, address = {San Diego}, issn = {0273-2300}, doi = {10.1016/j.yrtph.2017.02.018}, pages = {310 -- 321}, year = {2017}, abstract = {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.}, language = {en} } @article{WeissHuisinga2011, author = {Weiss, Andrea Y. and Huisinga, Wilhelm}, title = {Error-controlled global sensitivity analysis of ordinary differential equations}, series = {Journal of computational physics}, volume = {230}, journal = {Journal of computational physics}, number = {17}, publisher = {Elsevier}, address = {San Diego}, issn = {0021-9991}, doi = {10.1016/j.jcp.2011.05.011}, pages = {6824 -- 6842}, year = {2011}, abstract = {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.}, language = {en} } @article{WeineltStegemannTheloeetal.2022, author = {Weinelt, Ferdinand Anton and Stegemann, Miriam Songa and Theloe, Anja and Pf{\"a}fflin, Frieder and Achterberg, Stephan and Weber, Franz and D{\"u}bel, Lucas and Mikolajewska, Agata and Uhrig, Alexander and Kiessling, Peggy and Huisinga, Wilhelm and Michelet, Robin and Hennig, Stefanie and Kloft, Charlotte}, title = {Evaluation of a meropenem and piperacillin monitoring program in intensive care unit patients calls for the regular assessment of empirical targets and easy-to-use dosing decision tools}, series = {Antibiotics : open access journal}, volume = {11}, journal = {Antibiotics : open access journal}, number = {6}, publisher = {MDPI}, address = {Basel}, issn = {2079-6382}, doi = {10.3390/antibiotics11060758}, pages = {17}, year = {2022}, abstract = {The drug concentrations targeted in meropenem and piperacillin/tazobactam therapy also depend on the susceptibility of the pathogen. Yet, the pathogen is often unknown, and antibiotic therapy is guided by empirical targets. To reliably achieve the targeted concentrations, dosing needs to be adjusted for renal function. We aimed to evaluate a meropenem and piperacillin/tazobactam monitoring program in intensive care unit (ICU) patients by assessing (i) the adequacy of locally selected empirical targets, (ii) if dosing is adequately adjusted for renal function and individual target, and (iii) if dosing is adjusted in target attainment (TA) failure. In a prospective, observational clinical trial of drug concentrations, relevant patient characteristics and microbiological data (pathogen, minimum inhibitory concentration (MIC)) for patients receiving meropenem or piperacillin/tazobactam treatment were collected. If the MIC value was available, a target range of 1-5 x MIC was selected for minimum drug concentrations of both drugs. If the MIC value was not available, 8-40 mg/L and 16-80 mg/L were selected as empirical target ranges for meropenem and piperacillin, respectively. A total of 356 meropenem and 216 piperacillin samples were collected from 108 and 96 ICU patients, respectively. The vast majority of observed MIC values was lower than the empirical target (meropenem: 90.0\%, piperacillin: 93.9\%), suggesting empirical target value reductions. TA was found to be low (meropenem: 35.7\%, piperacillin 50.5\%) with the lowest TA for severely impaired renal function (meropenem: 13.9\%, piperacillin: 29.2\%), and observed drug concentrations did not significantly differ between patients with different targets, indicating dosing was not adequately adjusted for renal function or target. Dosing adjustments were rare for both drugs (meropenem: 6.13\%, piperacillin: 4.78\%) and for meropenem irrespective of TA, revealing that concentration monitoring alone was insufficient to guide dosing adjustment. Empirical targets should regularly be assessed and adjusted based on local susceptibility data. To improve TA, scientific knowledge should be translated into easy-to-use dosing strategies guiding antibiotic dosing.}, language = {en} } @book{Weian2002, author = {Weian, Liu}, title = {Viscosity Solutions of Fully Nonlinea Parabolic Systems}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {31 S.}, year = {2002}, language = {en} } @phdthesis{Wei2008, author = {Wei, Yawei}, title = {Operators on manifolds with edge and boundary with singular trace conditions}, address = {Potsdam}, pages = {128 S.: graph. Darst.}, year = {2008}, language = {en} } @phdthesis{Wei2008, author = {Wei, Yawei}, title = {Operators on Manifolds with Edge and Boundary with Singular Trace Conditions}, address = {Potsdam}, pages = {127 S., : graph. Darst.}, year = {2008}, language = {en} } @article{WangZoellerHainzl2015, author = {Wang, Lifeng and Z{\"o}ller, Gert and Hainzl, Sebastian}, title = {Joint Determination of Slip and Stress Drop in a Bayesian Inversion Approach: A Case Study for the 2010 M8.8 Maule Earthquake}, series = {Pure and applied geophysics}, volume = {172}, journal = {Pure and applied geophysics}, number = {2}, publisher = {Springer}, address = {Basel}, issn = {0033-4553}, doi = {10.1007/s00024-014-0868-x}, pages = {375 -- 388}, year = {2015}, abstract = {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.}, language = {en} } @article{WangHainzlZoelleretal.2012, author = {Wang, Lifeng and Hainzl, Sebastian and Z{\"o}ller, Gert and Holschneider, Matthias}, title = {Stress- and aftershock-constrained joint inversions for coseismic and postseismic slip applied to the 2004 M6.0 Parkfield earthquake}, series = {Journal of geophysical research : Solid earth}, volume = {117}, journal = {Journal of geophysical research : Solid earth}, publisher = {American Geophysical Union}, address = {Washington}, issn = {2169-9313}, doi = {10.1029/2011JB009017}, pages = {18}, year = {2012}, abstract = {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.}, language = {en} } @article{WangLiZhangetal.2018, author = {Wang, Guang and Li, Pei-zhi and Zhang, Shi-yao and Zhong, Shan and Chu, Chang and Zeng, Shufei and Yan, Yu and Cheng, Xin and Chuai, Manli and Hocher, Berthold and Yang, Xuesong}, title = {Lipopolysaccharides (LPS) Induced Angiogenesis During Chicken Embryogenesis is Abolished by Combined ETA/ETB Receptor Blockade}, series = {Cellular physiology and biochemistry : international journal of experimental cellular physiology, biochemistry and pharmacology}, volume = {48}, journal = {Cellular physiology and biochemistry : international journal of experimental cellular physiology, biochemistry and pharmacology}, number = {5}, publisher = {Karger}, address = {Basel}, issn = {1015-8987}, doi = {10.1159/000492547}, pages = {2084 -- 2090}, year = {2018}, abstract = {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.}, language = {en} } @phdthesis{Waltz1994, author = {Waltz, Christine}, title = {Adjungierte Polynomideale und duale Typen auf Banachr{\"a}umen und ihre Anwendung}, pages = {109 Bl.}, year = {1994}, language = {de} } @book{Waltz1992, author = {Waltz, Christine}, title = {Interpolation von holomorphen Typen}, series = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik}, volume = {1992, 01}, journal = {Preprint / Universit{\"a}t Potsdam, Fachbereich Mathematik}, publisher = {Univ.}, address = {Potsdam}, pages = {23 Bl.}, year = {1992}, language = {de} } @article{Wallenta2014, author = {Wallenta, Daniel}, title = {A Lefschetz fixed point formula for elliptic quasicomplexes}, series = {Integral equations and operator theor}, volume = {78}, journal = {Integral equations and operator theor}, number = {4}, publisher = {Springer}, address = {Basel}, issn = {0378-620X}, doi = {10.1007/s00020-014-2122-4}, pages = {577 -- 587}, year = {2014}, abstract = {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.}, language = {en} } @phdthesis{Wallenta2015, author = {Wallenta, Daniel}, title = {Sequences of compact curvature}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-87489}, school = {Universit{\"a}t Potsdam}, pages = {viii, 73}, year = {2015}, abstract = {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.}, language = {en} } @unpublished{Wallenta2013, author = {Wallenta, Daniel}, title = {A Lefschetz fixed point formula for elliptic quasicomplexes}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-67016}, year = {2013}, abstract = {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.}, language = {en} } @article{Wallenta2012, author = {Wallenta, D.}, title = {Elliptic quasicomplexes on compact closed manifolds}, series = {Integral equations and operator theor}, volume = {73}, journal = {Integral equations and operator theor}, number = {4}, publisher = {Springer}, address = {Basel}, issn = {0378-620X}, doi = {10.1007/s00020-012-1983-7}, pages = {517 -- 536}, year = {2012}, abstract = {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.}, language = {en} } @phdthesis{Vu2014, author = {Vu, Dinh Phuong}, title = {Using video study to investigate eighth-grade mathematics classrooms in Vietnam}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-72464}, school = {Universit{\"a}t Potsdam}, pages = {273}, year = {2014}, abstract = {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.}, language = {en} } @unpublished{Voss2010, author = {Voss, Carola Regine}, title = {Harness-Prozesse}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49651}, year = {2010}, abstract = {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 ausgef{\"u}hrt, die bisher nur skizziert waren. Ziel dessen ist die Existenz einer Zerlegung von Harness-Prozessen {\"u}ber Z beziehungsweise R+ nachzuweisen.}, language = {de} } @article{vonKleistMenzStockeretal.2011, author = {von Kleist, Max and Menz, Stephan and Stocker, Hartmut and Arasteh, Keikawus and Schuette, Christof and Huisinga, Wilhelm}, title = {HIV quasispecies dynamics during pro-active treatment switching impact on multi-drug resistance and resistance archiving in latent reservoirs}, series = {PLoS one}, volume = {6}, journal = {PLoS one}, number = {3}, publisher = {PLoS}, address = {San Fransisco}, issn = {1932-6203}, doi = {10.1371/journal.pone.0018204}, pages = {12}, year = {2011}, abstract = {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.}, language = {en} } @article{VogelMarkiPoeschel1996, author = {Vogel, Hans-J{\"u}rgen and Marki, Laszlo and P{\"o}schel, Reinhard}, title = {Contributions to general algebra and categories}, year = {1996}, language = {en} } @article{Vogel1997, author = {Vogel, Hans-J{\"u}rgen}, title = {Relations as morphisms of a certain monoidal category}, year = {1997}, language = {en} } @article{Vogel1998, author = {Vogel, Hans-J{\"u}rgen}, title = {On functors between certain monoidal categories}, year = {1998}, language = {en} } @article{Vogel1995, author = {Vogel, Hans-J{\"u}rgen}, title = {On quasivarieties generated by - algebras}, year = {1995}, language = {en} } @book{Vogel1998, author = {Vogel, Hans-J{\"u}rgen}, title = {On morphisms between partial algebras}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, volume = {1998, 13}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, publisher = {Univ.}, address = {Potsdam}, pages = {27 Bl.}, year = {1998}, language = {en} } @article{Vogel1999, author = {Vogel, Hans-J{\"u}rgen}, title = {On morphisms between partial algebras}, year = {1999}, language = {en} } @article{Vogel1999, author = {Vogel, Hans-J{\"u}rgen}, title = {Halfdiagonal-halfterminal-symmetric monoidal categories with inversions}, year = {1999}, language = {en} } @article{Vogel1999, author = {Vogel, Hans-J{\"u}rgen}, title = {On properties of dht -symmetric categories}, year = {1999}, language = {en} } @article{VidalGarciaBandaraKeogh2018, author = {Vidal-Garcia, Marta and Bandara, Lashi and Keogh, J. Scott}, title = {ShapeRotator}, series = {Ecology and evolution}, volume = {8}, journal = {Ecology and evolution}, number = {9}, publisher = {Wiley}, address = {Hoboken}, issn = {2045-7758}, doi = {10.1002/ece3.4018}, pages = {4669 -- 4675}, year = {2018}, abstract = {The quantification of complex morphological patterns typically involves comprehensive shape and size analyses, usually obtained by gathering morphological data from all the structures that capture the phenotypic diversity of an organism or object. Articulated structures are a critical component of overall phenotypic diversity, but data gathered from these structures are difficult to incorporate into modern analyses because of the complexities associated with jointly quantifying 3D shape in multiple structures. While there are existing methods for analyzing shape variation in articulated structures in two-dimensional (2D) space, these methods do not work in 3D, a rapidly growing area of capability and research. Here, we describe a simple geometric rigid rotation approach that removes the effect of random translation and rotation, enabling the morphological analysis of 3D articulated structures. Our method is based on Cartesian coordinates in 3D space, so it can be applied to any morphometric problem that also uses 3D coordinates (e.g., spherical harmonics). We demonstrate the method by applying it to a landmark-based dataset for analyzing shape variation using geometric morphometrics. We have developed an R tool (ShapeRotator) so that the method can be easily implemented in the commonly used R package geomorph and MorphoJ software. This method will be a valuable tool for 3D morphological analyses in articulated structures by allowing an exhaustive examination of shape and size diversity.}, language = {en} } @unpublished{VasilievTarkhanov2016, author = {Vasiliev, Serguei and Tarkhanov, Nikolai Nikolaevich}, title = {Construction of series of perfect lattices by layer superposition}, volume = {5}, number = {11}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-100591}, pages = {11}, year = {2016}, abstract = {We construct a new series of perfect lattices in n dimensions by the layer superposition method of Delaunay-Barnes.}, language = {en} } @article{VasilievTarchanov2017, author = {Vasiliev, Sergey B. and Tarchanov, Nikolaj Nikolaevič}, title = {Construction of series of perfect lattices by layer superposition}, series = {Journal of Siberian Federal University : Mathematics \& physics}, volume = {10}, journal = {Journal of Siberian Federal University : Mathematics \& physics}, number = {3}, publisher = {Sibirskij Federalʹnyj Universitet}, address = {Krasnojarsk}, issn = {1997-1397}, doi = {10.17516/1997-1397-2017-10-3-353-361}, pages = {353 -- 361}, year = {2017}, abstract = {We construct a new series of perfect lattices in n dimensions by the layer superposition method of Delaunay-Barnes.}, language = {en} } @misc{vanLeeuwenKunschNergeretal.2019, author = {van Leeuwen, Peter Jan and Kunsch, Hans R. and Nerger, Lars and Potthast, Roland and Reich, Sebastian}, title = {Particle filters for high-dimensional geoscience applications: A review}, series = {Quarterly journal of the Royal Meteorological Society}, volume = {145}, journal = {Quarterly journal of the Royal Meteorological Society}, number = {723}, publisher = {Wiley}, address = {Hoboken}, issn = {0035-9009}, doi = {10.1002/qj.3551}, pages = {2335 -- 2365}, year = {2019}, abstract = {Particle filters contain the promise of fully nonlinear data assimilation. They have been applied in numerous science areas, including the geosciences, but their application to high-dimensional geoscience systems has been limited due to their inefficiency in high-dimensional systems in standard settings. However, huge progress has been made, and this limitation is disappearing fast due to recent developments in proposal densities, the use of ideas from (optimal) transportation, the use of localization and intelligent adaptive resampling strategies. Furthermore, powerful hybrids between particle filters and ensemble Kalman filters and variational methods have been developed. We present a state-of-the-art discussion of present efforts of developing particle filters for high-dimensional nonlinear geoscience state-estimation problems, with an emphasis on atmospheric and oceanic applications, including many new ideas, derivations and unifications, highlighting hidden connections, including pseudo-code, and generating a valuable tool and guide for the community. Initial experiments show that particle filters can be competitive with present-day methods for numerical weather prediction, suggesting that they will become mainstream soon.}, language = {en} } @book{VanLeeuwenChengReich2015, author = {Van Leeuwen, Peter Jan and Cheng, Yuan and Reich, Sebastian}, title = {Nonlinear data assimilation}, series = {Frontiers in applied dynamical systems: reviews and tutorials ; 2}, journal = {Frontiers in applied dynamical systems: reviews and tutorials ; 2}, publisher = {Springer}, address = {Cham}, isbn = {978-3-319-18346-6}, doi = {10.1007/978-3-319-18347-3}, pages = {xii, 118}, year = {2015}, abstract = {This book contains two review articles on nonlinear data assimilation that deal with closely related topics but were written and can be read independently. Both contributions focus on so-called particle filters. The first contribution by Jan van Leeuwen focuses on the potential of proposal densities. It discusses the issues with present-day particle filters and explorers new ideas for proposal densities to solve them, converging to particle filters that work well in systems of any dimension, closing the contribution with a high-dimensional example. The second contribution by Cheng and Reich discusses a unified framework for ensemble-transform particle filters. This allows one to bridge successful ensemble Kalman filters with fully nonlinear particle filters, and allows a proper introduction of localization in particle filters, which has been lacking up to now.}, language = {en} } @inproceedings{VallerianiRoellyKulik2017, author = {Valleriani, Angelo and Roelly, Sylvie and Kulik, Alexei Michajlovič}, title = {Stochastic processes with applications in the natural sciences}, series = {Lectures in pure and applied mathematics}, booktitle = {Lectures in pure and applied mathematics}, number = {4}, editor = {Roelly, Sylvie and H{\"o}gele, Michael and Rafler, Mathias}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, isbn = {978-3-86956-414-2}, issn = {2199-4951}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-401802}, pages = {ix, 124}, year = {2017}, abstract = {The interdisciplinary workshop STOCHASTIC PROCESSES WITH APPLICATIONS IN THE NATURAL SCIENCES was held in Bogot{\´a}, at Universidad de los Andes from December 5 to December 9, 2016. It brought together researchers from Colombia, Germany, France, Italy, Ukraine, who communicated recent progress in the mathematical research related to stochastic processes with application in biophysics. The present volume collects three of the four courses held at this meeting by Angelo Valleriani, Sylvie Rœlly and Alexei Kulik. A particular aim of this collection is to inspire young scientists in setting up research goals within the wide scope of fields represented in this volume. Angelo Valleriani, PhD in high energy physics, is group leader of the team "Stochastic processes in complex and biological systems" from the Max-Planck-Institute of Colloids and Interfaces, Potsdam. Sylvie Rœlly, Docteur en Math{\´e}matiques, is the head of the chair of Probability at the University of Potsdam. Alexei Kulik, Doctor of Sciences, is a Leading researcher at the Institute of Mathematics of Ukrainian National Academy of Sciences.}, language = {en} } @article{TyFangGonzalezetal.2019, author = {Ty, Alexander J. A. and Fang, Zheng and Gonzalez, Rivver A. and Rozdeba, Paul J. and Abarbanel, Henry D.}, title = {Machine learning of time series using time-delay embedding and precision annealing}, series = {Neural Computation}, volume = {31}, journal = {Neural Computation}, number = {10}, publisher = {MIT Press}, address = {Cambridge}, issn = {0899-7667}, doi = {10.1162/neco_a_01224}, pages = {2004 -- 2024}, year = {2019}, abstract = {Tasking machine learning to predict segments of a time series requires estimating the parameters of a ML model with input/output pairs from the time series. We borrow two techniques used in statistical data assimilation in order to accomplish this task: time-delay embedding to prepare our input data and precision annealing as a training method. The precision annealing approach identifies the global minimum of the action (-log[P]). In this way, we are able to identify the number of training pairs required to produce good generalizations (predictions) for the time series. We proceed from a scalar time series s(tn);tn=t0+n Delta t and, using methods of nonlinear time series analysis, show how to produce a DE>1-dimensional time-delay embedding space in which the time series has no false neighbors as does the observed s(tn) time series. In that DE-dimensional space, we explore the use of feedforward multilayer perceptrons as network models operating on DE-dimensional input and producing DE-dimensional outputs.}, language = {en} } @misc{Tschisgale2020, type = {Master Thesis}, author = {Tschisgale, Paul}, title = {Introduction to the Glauber dynamics for the Curie-Weiss Potts model}, doi = {10.25932/publishup-48676}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-486769}, school = {Universit{\"a}t Potsdam}, pages = {104}, year = {2020}, abstract = {This thesis aims at presenting in an organized fashion the required basics to understand the Glauber dynamics as a way of simulating configurations according to the Gibbs distribution of the Curie-Weiss Potts model. Therefore, essential aspects of discrete-time Markov chains on a finite state space are examined, especially their convergence behavior and related mixing times. Furthermore, special emphasis is placed on a consistent and comprehensive presentation of the Curie-Weiss Potts model and its analysis. Finally, the Glauber dynamics is studied in general and applied afterwards in an exemplary way to the Curie-Weiss model as well as the Curie-Weiss Potts model. The associated considerations are supplemented with two computer simulations aiming to show the cutoff phenomenon and the temperature dependence of the convergence behavior.}, language = {en} } @phdthesis{Trump2015, author = {Trump, Stephanie Sonja}, title = {Mathematik in der Physik der Sekundarstufe II!?}, school = {Universit{\"a}t Potsdam}, pages = {214}, year = {2015}, language = {de} } @phdthesis{Trappmann2007, author = {Trappmann, Henryk}, title = {Arborescent numbers : higher arithmetic operations and division trees}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-15247}, school = {Universit{\"a}t Potsdam}, year = {2007}, abstract = {The overall program "arborescent numbers" is to similarly perform the constructions from the natural numbers (N) to the positive fractional numbers (Q+) to positive real numbers (R+) beginning with (specific) binary trees instead of natural numbers. N can be regarded as the associative binary trees. The binary trees B and the left-commutative binary trees P allow the hassle-free definition of arbitrary high arithmetic operations (hyper ... hyperpowers). To construct the division trees the algebraic structure "coppice" is introduced which is a group with an addition over which the multiplication is right-distributive. Q+ is the initial associative coppice. The present work accomplishes one step in the program "arborescent numbers". That is the construction of the arborescent equivalent(s) of the positive fractional numbers. These equivalents are the "division binary trees" and the "fractional trees". A representation with decidable word problem for each of them is given. The set of functions f:R1->R1 generated from identity by taking powers is isomorphic to P and can be embedded into a coppice by taking inverses.}, language = {en} } @article{TinpunKoppitz2016, author = {Tinpun, Kittisak and Koppitz, J{\"o}rg}, title = {Generating sets of infinite full transformation semigroups with restricted range}, series = {Acta scientiarum mathematicarum}, volume = {82}, journal = {Acta scientiarum mathematicarum}, publisher = {Institutum Bolyaianum Universitatis Szegediensis}, address = {Szeged}, issn = {0001-6969}, doi = {10.14232/actasm-015-502-4}, pages = {55 -- 63}, year = {2016}, abstract = {In the present paper, we consider minimal generating sets of infinite full transformation semigroups with restricted range modulo specific subsets. In particular, we determine relative ranks.}, language = {en} } @phdthesis{Tinpun2019, author = {Tinpun, Kittisak}, title = {Relative rank of infinite full transformation semigroups with restricted range}, school = {Universit{\"a}t Potsdam}, year = {2019}, language = {en} } @article{Thiem1996, author = {Thiem, Wolfgang}, title = {Didaktik der Erziehungswissenschaft (P{\"a}dagogik) - ein weites Feld?}, year = {1996}, language = {de} }