@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} } @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} } @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} } @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} } @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} } @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} } @unpublished{Zessin2010, author = {Zessin, Hans}, title = {Classical Symmetric Point Processes : Lectures held at ICIMAF, La Habana, Cuba, 2010}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49619}, year = {2010}, abstract = {The aim of these lectures is a reformulation and generalization of the fundamental investigations of Alexander Bach [2, 3] on the concept of probability in the work of Boltzmann [6] in the language of modern point process theory. The dominating point of view here is its subordination under the disintegration theory of Krickeberg [14]. This enables us to make Bach's consideration much more transparent. Moreover the point process formulation turns out to be the natural framework for the applications to quantum mechanical models.}, 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} } @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} } @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} } @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{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} } @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{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{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{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} } @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{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} } @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} } @book{OPUS4-28852, title = {General algebra and applications}, series = {Research and exposition in mathematics}, volume = {20}, journal = {Research and exposition in mathematics}, editor = {Denecke, Klaus-Dieter}, publisher = {Heldermann}, address = {Berlin}, isbn = {3-88538-220-2}, pages = {237 S. : Ill.}, year = {1993}, language = {en} } @book{OPUS4-23744, title = {General algebra and applications in discrete mathematics : proceedings of "Conference on General Algebra and Discrete Mathematics"}, series = {Berichte aus der Mathematik}, journal = {Berichte aus der Mathematik}, editor = {Denecke, Klaus-Dieter}, publisher = {Shaker}, address = {Aachen}, isbn = {3-8265-2431-4}, pages = {217 S. : graph. Darst.}, year = {1997}, language = {en} } @book{OPUS4-19362, title = {General algebra and applications : proceedings of the 59th Workshop on General Algebra ; 15th Conference for Young Algebraists, Potsdam 2000}, series = {Berichte aus der Mathematik}, journal = {Berichte aus der Mathematik}, editor = {Denecke, Klaus-Dieter and Vogel, Hans-J{\"u}rgen}, publisher = {Shaker}, address = {Aachen}, isbn = {3-8265-7983-6}, pages = {VI, 202 S. : graph. Darst.}, year = {2000}, language = {en} } @book{OPUS4-11733, title = {Mathematik : Lehrbuch f{\"u}r die Klasse 7 ; Gymnasium Brandenburg}, editor = {Br{\"u}ckner, Axel}, publisher = {Paetec}, address = {Berlin}, isbn = {3-89818-124-3}, pages = {240 S.}, year = {2006}, language = {de} } @book{OPUS4-13368, title = {Mathematik : Lehrbuch f{\"u}r die Klasse 10 ; Gymnasium Brandenburg}, editor = {Br{\"u}ckner, Axel}, publisher = {Paetec}, address = {Berlin}, isbn = {3-89818-142-1}, pages = {248 S.}, year = {2005}, language = {de} } @book{OPUS4-12339, title = {Pisa und Co : Kritik eines Programm}, editor = {Jahnke, Thomas and Meyerh{\"o}fer, Wolfram}, publisher = {Franzbecker}, address = {Hildesheim}, isbn = {3-88120-428-8}, pages = {349 S.}, year = {2006}, language = {de} } @book{OPUS4-12576, title = {Approaches to singular analysis : a volume of advances in partial differential equations}, series = {Operator theory : advances and applications}, volume = {125}, journal = {Operator theory : advances and applications}, editor = {Gil, Juan and Grieser, Daniel and Lesch, Matthias}, publisher = {Birkh{\"a}user Basel}, address = {Basel}, isbn = {3-7643-6518-8}, doi = {10.1007/978-3-0348-8253-8}, pages = {256 S.}, year = {2001}, language = {en} } @book{OPUS4-14127, title = {Aspects of Boundary Problems in Analysis and Geometry : advances in partial differential equations}, series = {Operator Theory : Advances and Applications}, volume = {151}, journal = {Operator Theory : Advances and Applications}, editor = {Gil, Juan and Krainer, Thomas and Witt, Ingo}, publisher = {Birkh{\"a}user}, address = {Basel}, isbn = {3-7643-7069-6}, pages = {XII, 560 S.}, year = {2004}, language = {en} } @book{OPUS4-14776, title = {Mathematik : Lehrbuch f{\"u}r die Klasse 9 ; Brandenburg ; Gymnasium}, editor = {Br{\"u}ckner, Axel}, publisher = {Paetec}, address = {Berlin}, isbn = {3-89818-138-3}, pages = {240 S.}, year = {2004}, language = {de} } @book{OPUS4-14781, title = {Mathematik : Lehrbuch f{\"u}r die Klasse 8 ; Gymnasium Brandenburg}, editor = {Br{\"u}ckner, Axel}, publisher = {Paetec}, address = {Berlin}, isbn = {3-89818-130-8}, pages = {240 S.}, year = {2004}, language = {de} } @book{OPUS4-41720, title = {Mathematik mit digitalen Medien - konkret}, series = {Lernen, Lehren und Forschen mit digitalen Medien in der Primarstufe ; 4}, journal = {Lernen, Lehren und Forschen mit digitalen Medien in der Primarstufe ; 4}, editor = {Ladel, Silke and Kortenkamp, Ulrich and Etzold, Heiko}, publisher = {WTM-Verlag}, address = {M{\"u}nster}, isbn = {978-3-95987-078-8}, publisher = {Universit{\"a}t Potsdam}, year = {2018}, abstract = {Neue Medien" war {\"u}ber viele Jahre hinweg das Codewort f{\"u}r Computer, die den Einzug in den Schulunterricht schaffen sollten - wenn es nach den Bef{\"u}rwortern ging. Die Widerst{\"a}nde, gerade in der Grundschule, waren groß und vielf{\"a}ltig. Es ist verst{\"a}ndlich, dass kurz nach der spielerischen Heranf{\"u}hrung an Bildung im Kindergarten, in einer Zeit, in der die Sch{\"u}lerinnen und Sch{\"u}ler auch das soziale Miteinander ein{\"u}ben m{\"u}ssen und auch fein- und grobmotorische F{\"a}higkeiten erwerben sollen, das vereinzelnde Sitzen vor einem Bildschirm nicht zu den obersten Priorit{\"a}ten geh{\"o}rt - und auch unserer Meinung nach nicht geh{\"o}ren sollte. In den letzten Jahren hat sich der Begriff der neuen Medien aber ver{\"a}ndert, und das, was bisher damit verbunden wurde, ist mit der „Digitalisierung" nicht nur des Schulunterrichts, sondern des ganzen Lebens, zu einem Dreh- und Angelpunkt der Bildung geworden. Statt klobigen Computern mit Bildschirmen, die das Miteinander schon {\"u}ber die Ausstattung der Computerr{\"a}ume in die falsche Bahn lenken, haben mobile Ger{\"a}te in der Hand der Sch{\"u}lerinnen und Sch{\"u}ler {\"u}bernommen. Diese k{\"o}nnen nun gemeinsam an einem Ger{\"a}t arbeiten, sie k{\"o}nnen direkt mit den Bildschirminhalten interagieren, sie k{\"o}nnen die Kameras, Mikrophone und Sensoren nutzen, um authentische Daten zu erfassen und zu verarbeiten, sie k{\"o}nnen auch außerhalb des Klassenraums oder der Schule damit arbeiten und haben inzwischen fast jederzeit das ganze Wissen des Internets mit dabei. Schwerpunkt dieses Bandes ist daher der Umgang mit Tablets und den darauf laufenden „Apps" im Mathematikunterricht. In f{\"u}nf Beitr{\"a}gen werden konkrete Unterrichtsvorschl{\"a}ge gemacht, die als Blaupausen f{\"u}r App-gest{\"u}tzten Unterricht dienen k{\"o}nnen. Erg{\"a}nzt wird dieser Band durch einen allgemeinen Leitfaden zur Beurteilung von Apps f{\"u}r den Mathematikunterricht samt Beispielen.}, language = {de} } @book{OPUS4-27145, title = {Bruchrechnung verstehen}, editor = {Jahnke, Thomas}, year = {1995}, language = {de} } @book{OPUS4-33496, title = {Surveys in stochastic processes}, editor = {Blath, Jochen and Imkeller, Peter and Roelly, Sylvie}, publisher = {European Mathematical Society}, address = {Z{\"u}rich}, isbn = {978-3-03719-072-2}, pages = {XIII, 248 S.}, year = {2011}, language = {en} } @book{OPUS4-26873, title = {General Relativity and Gravitation}, editor = {Schmidt, Hans-J{\"u}rgen}, publisher = {Kluwer}, address = {Dordrecht}, issn = {0001-7701}, year = {1995}, abstract = {General Relativity and Gravitation is a journal of studies in general relativity and related topics, published under the auspices of the International Committee on General Relativity and Gravitation. The journal publishes original, high-quality research papers on the theoretical and experimental aspects of general relativity and related topics; surveys and review articles on current research in general relativity and gravitation; news regarding conferences and other enterprises of interest to scientists in this field; and book reviews. All manuscripts and editorial correspondence, as well as books for review, should be submitted to the Editor, and authors may propose who among the Associate Editors will deal with their paper. All submitted articles are acknowledged and refereed.}, language = {en} } @book{OPUS4-27555, title = {Stoffdynamik in Geosystemen}, editor = {Schachtzabel, Hartmut and Blumenstein, Oswald}, publisher = {Loche}, address = {Berlin}, year = {1995}, abstract = {Die Reihe 'Stoffdynamik in Geosystemen' hat ihre Wurzeln in der interdisziplin{\"a}ren Projektarbeit der gleichnamigen Arbeitsgruppe. Im ersten Band'Wenn Abwasser die Landschaft ver{\"a}ndert...' wurden am Beispiel der Abwasserbodenbehandlung die Probleme diskutiert und dokumentiert, welche aus der {\"U}berpr{\"a}gung von Naturr{\"a}umen durch die T{\"a}tigkeit des Menschen resultieren. Im Band 2 'Neue Cocktails nur mit bew{\"a}hrten Rezepten?' wurde {\"u}ber die Weiter-entwicklung der theoretischen und methodischen Ans{\"a}tze berichtet. Mathematische bzw. geophysikalische Methoden zur Aufkl{\"a}rung von Dynamik bzw. Struktur der Geosysteme bildeten den Gegenstand der 1999 und 2000 erschienen beiden B{\"a}nde 'Nichtlineare Methoden zur Datenanalyse' bzw. 'Geophysik f{\"u}r Landwirtschaft und Bodenkunde'}, language = {de} } @book{OPUS4-28616, title = {Statistics : a journal of theoretical and applied statistics}, editor = {L{\"a}uter, Henning}, publisher = {Gordon \& Breach Science Publ.}, address = {Reading Berkshire [u.a.]}, issn = {0233-1888}, year = {1994}, language = {en} } @book{OPUS4-17629, title = {Mathematik : Lehrbuch f{\"u}r die Klasse 7 ; Gymnasium Brandenburg}, editor = {Br{\"u}ckner, Axel}, publisher = {Paetec}, address = {Frankfurt am Main}, isbn = {3-89818-124-3}, pages = {240 S.}, year = {2002}, language = {de} } @article{OPUS4-18293, title = {Mathematik : Analysis ; Gymnasiale Oberstufe, NRW [Sch{\"u}lerbuch]}, editor = {Jahnke, Thomas and Wuttke, Hans}, publisher = {Cornelsen}, address = {Berlin}, isbn = {3-464-57211-0}, pages = {319 S.}, year = {2001}, language = {de} } @inproceedings{OPUS4-41526, title = {Beitr{\"a}ge zum Mathematikunterricht 2017}, editor = {Kortenkamp, Ulrich and Kuzle, Ana}, publisher = {WTM-Verlag}, address = {M{\"u}nster}, isbn = {978-3-95987-072-6}, year = {2018}, language = {de} } @book{OPUS4-20831, title = {Evolution equations, Feshbach resonances, singular Hodge theory}, series = {Mathematical topics}, volume = {16}, journal = {Mathematical topics}, editor = {Demuth, Michael and Schrohe, Elmar and Schulze, Bert-Wolfgang and Sj{\"o}strand, J.}, publisher = {Wiley-VCH}, address = {Berlin}, isbn = {3-527-40233-0}, pages = {431 S.}, year = {1999}, language = {en} } @book{OPUS4-23966, title = {Spectral theory, microlocal analysis, singular manifolds}, series = {Mathematical topics}, volume = {14}, journal = {Mathematical topics}, editor = {Demuth, Michael and Schrohe, Elmar and Schulze, Bert-Wolfgang and Sj{\"o}strand, J.}, publisher = {Akad.-Verl.}, address = {Berlin}, isbn = {3-05-501776-5}, pages = {366 S.}, year = {1997}, language = {en} } @book{OPUS4-27563, title = {Boundary value problems, Schr{\"o}dinger operators, deformation quantization}, series = {Mathematical topics}, volume = {8}, journal = {Mathematical topics}, editor = {Demuth, Michael and Schrohe, Elmar and Schulze, Bert-Wolfgang}, publisher = {Akad.-Verl.}, address = {Berlin}, isbn = {3-05-501699-8}, pages = {353 S.}, year = {1995}, language = {en} } @book{OPUS4-43561, title = {Implementation research on problem solving in school settings}, series = {Ars inveniendi et dejudicandi ; 13}, journal = {Ars inveniendi et dejudicandi ; 13}, editor = {Kuzle, Ana and Rott, Benjamin and Gebel, Inga}, publisher = {WTM-Verlag}, address = {M{\"u}nster}, isbn = {978-3-95987-116-7}, pages = {IV, 220}, year = {2019}, language = {en} }