@article{AcevedoDeWiljesReich2017, author = {Acevedo, Walter and De Wiljes, Jana and Reich, Sebastian}, title = {Second-order accurate ensemble transform particle filters}, series = {SIAM journal on scientific computing}, volume = {39}, journal = {SIAM journal on scientific computing}, number = {5}, publisher = {Society for Industrial and Applied Mathematics}, address = {Philadelphia}, issn = {1064-8275}, doi = {10.1137/16M1095184}, pages = {A1834 -- A1850}, year = {2017}, abstract = {Particle filters (also called sequential Monte Carlo methods) are widely used for state and parameter estimation problems in the context of nonlinear evolution equations. The recently proposed ensemble transform particle filter (ETPF) [S. Reich, SIAM T. Sci. Comput., 35, (2013), pp. A2013-A2014[ replaces the resampling step of a standard particle filter by a linear transformation which allows for a hybridization of particle filters with ensemble Kalman filters and renders the resulting hybrid filters applicable to spatially extended systems. However, the linear transformation step is computationally expensive and leads to an underestimation of the ensemble spread for small and moderate ensemble sizes. Here we address both of these shortcomings by developing second order accurate extensions of the ETPF. These extensions allow one in particular to replace the exact solution of a linear transport problem by its Sinkhorn approximation. It is also demonstrated that the nonlinear ensemble transform filter arises as a special case of our general framework. We illustrate the performance of the second-order accurate filters for the chaotic Lorenz-63 and Lorenz-96 models and a dynamic scene-viewing model. The numerical results for the Lorenz-63 and Lorenz-96 models demonstrate that significant accuracy improvements can be achieved in comparison to a standard ensemble Kalman filter and the ETPF for small to moderate ensemble sizes. The numerical results for the scene-viewing model reveal, on the other hand, that second-order corrections can lead to statistically inconsistent samples from the posterior parameter distribution.}, language = {en} } @article{AcevedoFallahReichetal.2017, author = {Acevedo, Walter and Fallah, Bijan and Reich, Sebastian and Cubasch, Ulrich}, title = {Assimilation of pseudo-tree-ring-width observations into an atmospheric general circulation model}, series = {Climate of the past : an interactive open access journal of the European Geosciences Union}, volume = {13}, journal = {Climate of the past : an interactive open access journal of the European Geosciences Union}, publisher = {Copernicus}, address = {G{\"o}ttingen}, issn = {1814-9324}, doi = {10.5194/cp-13-545-2017}, pages = {545 -- 557}, year = {2017}, abstract = {Paleoclimate data assimilation (DA) is a promising technique to systematically combine the information from climate model simulations and proxy records. Here, we investigate the assimilation of tree-ring-width (TRW) chronologies into an atmospheric global climate model using ensemble Kalman filter (EnKF) techniques and a process-based tree-growth forward model as an observation operator. Our results, within a perfect-model experiment setting, indicate that the "online DA" approach did not outperform the "off-line" one, despite its considerable additional implementation complexity. On the other hand, it was observed that the nonlinear response of tree growth to surface temperature and soil moisture does deteriorate the operation of the time-averaged EnKF methodology. Moreover, for the first time we show that this skill loss appears significantly sensitive to the structure of the growth rate function, used to represent the principle of limiting factors (PLF) within the forward model. In general, our experiments showed that the error reduction achieved by assimilating pseudo-TRW chronologies is modulated by the magnitude of the yearly internal variability in themodel. This result might help the dendrochronology community to optimize their sampling efforts.}, language = {en} } @article{BandaraMcIntoshRosen2017, author = {Bandara, Lashi and McIntosh, Alan and Rosen, Andreas}, title = {Riesz continuity of the Atiyah}, series = {Mathematische Annalen}, volume = {370}, journal = {Mathematische Annalen}, number = {1-2}, publisher = {Springer}, address = {Heidelberg}, issn = {0025-5831}, doi = {10.1007/s00208-017-1610-7}, pages = {863 -- 915}, year = {2017}, abstract = {We prove that the Atiyah-Singer Dirac operator in L2 depends Riesz continuously on L∞ perturbations of complete metrics g on a smooth manifold. The Lipschitz bound for the map depends on bounds on Ricci curvature and its first derivatives as well as a lower bound on injectivity radius. Our proof uses harmonic analysis techniques related to Calder{\´o}n's first commutator and the Kato square root problem. We also show perturbation results for more general functions of general Dirac-type operators on vector bundles.}, language = {en} } @article{BeniniCapoferriDappiaggi2017, author = {Benini, Marco and Capoferri, Matteo and Dappiaggi, Claudio}, title = {Hadamard States for Quantum Abelian Duality}, series = {Annales de l'Institut Henri Poincar{\´e}}, volume = {18}, journal = {Annales de l'Institut Henri Poincar{\´e}}, publisher = {Springer}, address = {Basel}, issn = {1424-0637}, doi = {10.1007/s00023-017-0593-y}, pages = {3325 -- 3370}, year = {2017}, abstract = {Abelian duality is realized naturally by combining differential cohomology and locally covariant quantum field theory. This leads to a -algebra of observables, which encompasses the simultaneous discretization of both magnetic and electric fluxes. We discuss the assignment of physically well-behaved states on this algebra and the properties of the associated GNS triple. We show that the algebra of observables factorizes as a suitable tensor product of three -algebras: the first factor encodes dynamical information, while the other two capture topological data corresponding to electric and magnetic fluxes. On the former factor and in the case of ultra-static globally hyperbolic spacetimes with compact Cauchy surfaces, we exhibit a state whose two-point correlation function has the same singular structure of a Hadamard state. Specifying suitable counterparts also on the topological factors, we obtain a state for the full theory, ultimately implementing Abelian duality transformations as Hilbert space isomorphisms.}, language = {en} } @article{BeniniSchenkel2017, author = {Benini, Marco and Schenkel, Alexander}, title = {Quantum Field Theories on Categories Fibered in Groupoids}, series = {Communications in mathematical physics}, volume = {356}, journal = {Communications in mathematical physics}, publisher = {Springer}, address = {New York}, issn = {0010-3616}, doi = {10.1007/s00220-017-2986-7}, pages = {19 -- 64}, year = {2017}, abstract = {We introduce an abstract concept of quantum field theory on categories fibered in groupoids over the category of spacetimes. This provides us with a general and flexible framework to study quantum field theories defined on spacetimes with extra geometric structures such as bundles, connections and spin structures. Using right Kan extensions, we can assign to any such theory an ordinary quantum field theory defined on the category of spacetimes and we shall clarify under which conditions it satisfies the axioms of locally covariant quantum field theory. The same constructions can be performed in a homotopy theoretic framework by using homotopy right Kan extensions, which allows us to obtain first toy-models of homotopical quantum field theories resembling some aspects of gauge theories.}, language = {en} } @article{BeniniSchenkel2017, author = {Benini, Marco and Schenkel, Alexander}, title = {Poisson Algebras for Non-Linear Field Theories in the Cahiers Topos}, series = {Annales de l'Institut Henri Poincar{\´e}}, volume = {18}, journal = {Annales de l'Institut Henri Poincar{\´e}}, publisher = {Springer}, address = {Basel}, issn = {1424-0637}, doi = {10.1007/s00023-016-0533-2}, pages = {1435 -- 1464}, year = {2017}, language = {en} } @article{BrungsGraeter2017, author = {Brungs, Hans H. and Gr{\"a}ter, Joachim}, title = {On central extensions of SL(2, F) admitting left-orderings}, series = {Journal of Algebra}, volume = {486}, journal = {Journal of Algebra}, publisher = {Elsevier}, address = {San Diego}, issn = {0021-8693}, doi = {10.1016/j.jalgebra.2017.05.025}, pages = {288 -- 327}, year = {2017}, abstract = {For an arbitrary euclidean field F we introduce a central extension (G(F), Phi) of SL(2, F) admitting a left-ordering and study its algebraic properties. The elements of G(F) are order preserving bijections of the convex hull of Q in F. If F = R then G(F) is isomorphic to the classical universal covering group of the Lie group SL(2, R). Among other results we show that G(F) is a perfect group which possesses a rank 1 cone of exceptional type. We also prove that its centre is an infinite cyclic group and investigate its normal subgroups.}, language = {en} } @article{ChangSchulze2017, author = {Chang, D. -C. and Schulze, Bert-Wolfgang}, title = {Calculus on spaces with higher singularities}, series = {Journal of pseudo-differential operators and applications}, volume = {8}, journal = {Journal of pseudo-differential operators and applications}, publisher = {Springer}, address = {Basel}, issn = {1662-9981}, doi = {10.1007/s11868-016-0180-x}, pages = {585 -- 622}, year = {2017}, abstract = {We establish extensions of the standard pseudo-differential calculus to specific classes of operators with operator-valued symbols occurring in symbolic hierarchies motivated by manifolds with higher singularities or stratified spaces.}, language = {en} } @article{ChangHedayatMahmoudiSchulze2017, author = {Chang, Der-Chen and Hedayat Mahmoudi, Mahdi and Schulze, Bert-Wolfgang}, title = {Singular degenerate operators}, series = {Applicable analysis : an international journal}, volume = {96}, journal = {Applicable analysis : an international journal}, number = {14}, publisher = {Routledge, Taylor \& Francis Group}, address = {Abingdon}, issn = {0003-6811}, doi = {10.1080/00036811.2017.1336546}, pages = {2434 -- 2456}, year = {2017}, abstract = {We outline some simplified and more general method for constructing parametrices on higher singular spaces. We also outline basic ideas on operators on manifolds with conical or edge singularities.}, language = {en} } @article{ChangSchulze2017, author = {Chang, Der-Chen and Schulze, Bert-Wolfgang}, title = {Ellipticity on spaces with higher singularities}, series = {Science China Mathematics}, volume = {60}, journal = {Science China Mathematics}, number = {11}, publisher = {Science China Press}, address = {Beijing}, issn = {1674-7283}, doi = {10.1007/s11425-016-0519-9}, pages = {2053 -- 2076}, year = {2017}, abstract = {We study corner-degenerate pseudo-differential operators of any singularity order and develop ellipticity based on the principal symbolic hierarchy, associated with the stratification of the underlying space. We construct parametrices within the calculus and discuss the aspect of additional trace and potential conditions along lower-dimensional strata.}, language = {en} } @article{ConfortiRoelly2017, author = {Conforti, Giovanni and Roelly, Sylvie}, title = {Bridge mixtures of random walks on an Abelian group}, series = {Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability}, volume = {23}, journal = {Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability}, publisher = {International Statistical Institute}, address = {Voorburg}, issn = {1350-7265}, doi = {10.3150/15-BEJ783}, pages = {1518 -- 1537}, year = {2017}, language = {en} } @article{CotroneiDiSalvoHolschneideretal.2017, author = {Cotronei, Mariantonia and Di Salvo, Rosa and Holschneider, Matthias and Puccio, Luigia}, title = {Interpolation in reproducing kernel Hilbert spaces based on random subdivision schemes}, series = {Journal of computational and applied mathematics}, volume = {311}, journal = {Journal of computational and applied mathematics}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0377-0427}, doi = {10.1016/j.cam.2016.08.002}, pages = {342 -- 353}, year = {2017}, abstract = {In this paper we present a Bayesian framework for interpolating data in a reproducing kernel Hilbert space associated with a random subdivision scheme, where not only approximations of the values of a function at some missing points can be obtained, but also uncertainty estimates for such predicted values. This random scheme generalizes the usual subdivision by taking into account, at each level, some uncertainty given in terms of suitably scaled noise sequences of i.i.d. Gaussian random variables with zero mean and given variance, and generating, in the limit, a Gaussian process whose correlation structure is characterized and used for computing realizations of the conditional posterior distribution. The hierarchical nature of the procedure may be exploited to reduce the computational cost compared to standard techniques in the case where many prediction points need to be considered.}, language = {en} } @article{DereudreMazzonettoRoelly2017, author = {Dereudre, David and Mazzonetto, Sara and Roelly, Sylvie}, title = {Exact simulation of Brownian diffusions with drift admitting jumps}, series = {SIAM journal on scientific computing}, volume = {39}, journal = {SIAM journal on scientific computing}, number = {3}, publisher = {Society for Industrial and Applied Mathematics}, address = {Philadelphia}, issn = {1064-8275}, doi = {10.1137/16M107699X}, pages = {A711 -- A740}, year = {2017}, abstract = {In this paper, using an algorithm based on the retrospective rejection sampling scheme introduced in [A. Beskos, O. Papaspiliopoulos, and G. O. Roberts,Methodol. Comput. Appl. Probab., 10 (2008), pp. 85-104] and [P. Etore and M. Martinez, ESAIM Probab.Stat., 18 (2014), pp. 686-702], we propose an exact simulation of a Brownian di ff usion whose drift admits several jumps. We treat explicitly and extensively the case of two jumps, providing numerical simulations. Our main contribution is to manage the technical di ffi culty due to the presence of t w o jumps thanks to a new explicit expression of the transition density of the skew Brownian motion with two semipermeable barriers and a constant drift.}, language = {en} } @article{DereudreRoelly2017, author = {Dereudre, David and Roelly, Sylvie}, title = {Path-dependent infinite-dimensional SDE with non-regular drift}, series = {Annales de l'Institut Henri Poincar{\´e} : B, Probability and statistics}, volume = {53}, journal = {Annales de l'Institut Henri Poincar{\´e} : B, Probability and statistics}, number = {2}, publisher = {Inst. of Mathematical Statistics}, address = {Bethesda}, issn = {0246-0203}, doi = {10.1214/15-AIHP728}, pages = {641 -- 657}, year = {2017}, abstract = {We establish in this paper the existence of weak solutions of infinite-dimensional shift invariant stochastic differential equations driven by a Brownian term. The drift function is very general, in the sense that it is supposed to be neither bounded or continuous, nor Markov. On the initial law we only assume that it admits a finite specific entropy and a finite second moment. The originality of our method leads in the use of the specific entropy as a tightness tool and in the description of such infinite-dimensional stochastic process as solution of a variational problem on the path space. Our result clearly improves previous ones obtained for free dynamics with bounded drift.}, language = {en} } @article{DimitrovaFernandesKoppitz2017, author = {Dimitrova, Ilinka and Fernandes, Vitor H. and Koppitz, J{\"o}rg}, title = {A note on generators of the endomorphism semigroup of an infinite countable chain}, series = {Journal of Algebra and its Applications}, volume = {16}, journal = {Journal of Algebra and its Applications}, number = {2}, publisher = {World Scientific}, address = {Singapore}, issn = {0219-4988}, doi = {10.1142/S0219498817500311}, pages = {9}, year = {2017}, abstract = {In this note, we consider the semigroup O(X) of all order endomorphisms of an infinite chain X and the subset J of O(X) of all transformations alpha such that vertical bar Im(alpha)vertical bar = vertical bar X vertical bar. For an infinite countable chain X, we give a necessary and sufficient condition on X for O(X) = < J > to hold. We also present a sufficient condition on X for O(X) = < J > to hold, for an arbitrary infinite chain X.}, language = {en} } @article{DimitrovaKoppitz2017, author = {Dimitrova, Ilinka and Koppitz, J{\"o}rg}, title = {On the semigroup of all partial fence-preserving injections on a finite set}, series = {Journal of Algebra and Its Applications}, volume = {16}, journal = {Journal of Algebra and Its Applications}, number = {12}, publisher = {World Scientific}, address = {Singapore}, issn = {0219-4988}, doi = {10.1142/S0219498817502231}, pages = {14}, year = {2017}, abstract = {For n∈N , let Xn={a1,a2,…,an} be an n-element set and let F=(Xn; 1, weakly away from the zero set u(-1) (0) in chi, then u is a weak solution to this equation in all of chi.}, language = {en} } @article{GairingHoegeleKosenkova2017, author = {Gairing, Jan and H{\"o}gele, Michael and Kosenkova, Tetiana}, title = {Transportation distances and noise sensitivity of multiplicative Levy SDE with applications}, series = {Stochastic processes and their application}, volume = {128}, journal = {Stochastic processes and their application}, number = {7}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0304-4149}, doi = {10.1016/j.spa.2017.09.003}, pages = {2153 -- 2178}, year = {2017}, abstract = {This article assesses the distance between the laws of stochastic differential equations with multiplicative Levy noise on path space in terms of their characteristics. The notion of transportation distance on the set of Levy kernels introduced by Kosenkova and Kulik yields a natural and statistically tractable upper bound on the noise sensitivity. This extends recent results for the additive case in terms of coupling distances to the multiplicative case. The strength of this notion is shown in a statistical implementation for simulations and the example of a benchmark time series in paleoclimate.}, language = {en} } @article{GairingHogeleKosenkovaetal.2017, author = {Gairing, Jan M. and Hogele, Michael A. and Kosenkova, Tania and Monahan, Adam H.}, title = {How close are time series to power tail Levy diffusions?}, series = {Chaos : an interdisciplinary journal of nonlinear science}, volume = {27}, journal = {Chaos : an interdisciplinary journal of nonlinear science}, publisher = {American Institute of Physics}, address = {Melville}, issn = {1054-1500}, doi = {10.1063/1.4986496}, pages = {20}, year = {2017}, abstract = {This article presents a new and easily implementable method to quantify the so-called coupling distance between the law of a time series and the law of a differential equation driven by Markovian additive jump noise with heavy-tailed jumps, such as a-stable Levy flights. Coupling distances measure the proximity of the empirical law of the tails of the jump increments and a given power law distribution. In particular, they yield an upper bound for the distance of the respective laws on path space. We prove rates of convergence comparable to the rates of the central limit theorem which are confirmed by numerical simulations. Our method applied to a paleoclimate time series of glacial climate variability confirms its heavy tail behavior. In addition, this approach gives evidence for heavy tails in datasets of precipitable water vapor of the Western Tropical Pacific. Published by AIP Publishing.}, language = {en} } @article{GerlachGlueck2017, author = {Gerlach, Moritz Reinhardt and Gl{\"u}ck, Jochen}, title = {On a convergence theorem for semigroups of positive integral operators}, series = {Comptes Rendus Mathematique}, volume = {355}, journal = {Comptes Rendus Mathematique}, publisher = {Elsevier}, address = {Paris}, issn = {1631-073X}, doi = {10.1016/j.crma.2017.07.017}, pages = {973 -- 976}, year = {2017}, abstract = {We give a new and very short proof of a theorem of Greiner asserting that a positive and contractive -semigroup on an -space is strongly convergent in case it has a strictly positive fixed point and contains an integral operator. Our proof is a streamlined version of a much more general approach to the asymptotic theory of positive semigroups developed recently by the authors. Under the assumptions of Greiner's theorem, this approach becomes particularly elegant and simple. We also give an outlook on several generalisations of this result.}, language = {en} } @article{GroschwitzSzabo2017, author = {Groschwitz, Jonas and Szabo, Tibor}, title = {Sharp Thresholds for Half-Random Games II}, series = {GRAPHS AND COMBINATORICS}, volume = {33}, journal = {GRAPHS AND COMBINATORICS}, publisher = {Springer}, address = {Tokyo}, issn = {0911-0119}, doi = {10.1007/s00373-016-1753-4}, pages = {387 -- 401}, year = {2017}, abstract = {We study biased Maker-Breaker positional games between two players, one of whom is playing randomly against an opponent with an optimal strategy. In this work we focus on the case of Breaker playing randomly and Maker being "clever". The reverse scenario is treated in a separate paper. We determine the sharp threshold bias of classical games played on the edge set of the complete graph , such as connectivity, perfect matching, Hamiltonicity, and minimum degree-1 and -2. In all of these games, the threshold is equal to the trivial upper bound implied by the number of edges needed for Maker to occupy a winning set. Moreover, we show that CleverMaker can not only win against asymptotically optimal bias, but can do so very fast, wasting only logarithmically many moves (while the winning set sizes are linear in n).}, language = {en} } @article{GuoPaychaZhang2017, author = {Guo, Li and Paycha, Sylvie and Zhang, Bin}, title = {Algebraic Birkhoff factorization and the Euler-Maclaurin formula on cones}, series = {Duke mathematical journal}, volume = {166}, journal = {Duke mathematical journal}, number = {3}, publisher = {Duke Univ. Press}, address = {Durham}, issn = {0012-7094}, doi = {10.1215/00127094-3715303}, pages = {537 -- 571}, year = {2017}, abstract = {We equip the space of lattice cones with a coproduct which makes it a cograded, coaugmented, connnected coalgebra. The exponential generating sum and exponential generating integral on lattice cones can be viewed as linear maps on this space with values in the space of meromorphic germs with linear poles at zero. We investigate the subdivision properties-reminiscent of the inclusion-exclusion principle for the cardinal on finite sets-of such linear maps and show that these properties are compatible with the convolution quotient of maps on the coalgebra. Implementing the algebraic Birkhoff factorization procedure on the linear maps under consideration, we factorize the exponential generating sum as a convolution quotient of two maps, with each of the maps in the factorization satisfying a subdivision property. A direct computation shows that the polar decomposition of the exponential generating sum on a smooth lattice cone yields an Euler-Maclaurin formula. The compatibility with subdivisions of the convolution quotient arising in the algebraic Birkhoff factorization then yields the Euler-Maclaurin formula for any lattice cone. This provides a simple formula for the interpolating factor by means of a projection formula.}, language = {en} } @article{HartungBenaryWolfetal.2017, author = {Hartung, Niklas and Benary, Uwe and Wolf, Jana and Kofahl, Bente}, title = {Paracrine and autocrine regulation of gene expression by Wnt-inhibitor Dickkopf in wild-type and mutant hepatocytes}, series = {BMC systems biology}, volume = {11}, journal = {BMC systems biology}, publisher = {BioMed Central}, address = {London}, issn = {1752-0509}, doi = {10.1186/s12918-017-0470-9}, pages = {16}, year = {2017}, abstract = {Background: Cells are able to communicate and coordinate their function within tissues via secreted factors. Aberrant secretion by cancer cells can modulate this intercellular communication, in particular in highly organised tissues such as the liver. Hepatocytes, the major cell type of the liver, secrete Dickkopf (Dkk), which inhibits Wnt/beta-catenin signalling in an autocrine and paracrine manner. Consequently, Dkk modulates the expression of Wnt/beta-catenin target genes. We present a mathematical model that describes the autocrine and paracrine regulation of hepatic gene expression by Dkk under wild-type conditions as well as in the presence of mutant cells. Results: Our spatial model describes the competition of Dkk and Wnt at receptor level, intra-cellular Wnt/beta-catenin signalling, and the regulation of target gene expression for 21 individual hepatocytes. Autocrine and paracrine regulation is mediated through a feedback mechanism via Dkk and Dkk diffusion along the porto-central axis. Along this axis an APC concentration gradient is modelled as experimentally detected in liver. Simulations of mutant cells demonstrate that already a single mutant cell increases overall Dkk concentration. The influence of the mutant cell on gene expression of surrounding wild-type hepatocytes is limited in magnitude and restricted to hepatocytes in close proximity. To explore the underlying molecular mechanisms, we perform a comprehensive analysis of the model parameters such as diffusion coefficient, mutation strength and feedback strength. Conclusions: Our simulations show that Dkk concentration is elevated in the presence of a mutant cell. However, the impact of these elevated Dkk levels on wild-type hepatocytes is confined in space and magnitude. The combination of inter-and intracellular processes, such as Dkk feedback, diffusion and Wnt/beta-catenin signal transduction, allow wild-type hepatocytes to largely maintain their gene expression.}, language = {en} } @article{HartungHuynhGaudyMarquesteetal.2017, author = {Hartung, Niklas and Huynh, Cecilia T. -K. and Gaudy-Marqueste, Caroline and Flavian, Antonin and Malissen, Nausicaa and Richard-Lallemand, Marie-Aleth and Hubert, Florence and Grob, Jean-Jacques}, title = {Study of metastatic kinetics in metastatic melanoma treated with B-RAF inhibitors: Introducing mathematical modelling of kinetics into the therapeutic decision}, series = {PLoS one}, volume = {12}, journal = {PLoS one}, publisher = {PLoS}, address = {San Fransisco}, issn = {1932-6203}, doi = {10.1371/journal.pone.0176080}, pages = {11}, year = {2017}, abstract = {Background Evolution of metastatic melanoma (MM) under B-RAF inhibitors (BRAFi) is unpredictable, but anticipation is crucial for therapeutic decision. Kinetics changes in metastatic growth are driven by molecular and immune events, and thus we hypothesized that they convey relevant information for decision making. Patients and methods We used a retrospective cohort of 37 MM patients treated by BRAFi only with at least 2 close CT-scans available before BRAFi, as a model to study kinetics of metastatic growth before, under and after BRAFi. All metastases (mets) were individually measured at each CT-scan. From these measurements, different measures of growth kinetics of each met and total tumor volume were computed at different time points. A historical cohort permitted to build a reference model for the expected spontaneous disease kinetics without BRAFi. All variables were included in Cox and multistate regression models for survival, to select best candidates for predicting overall survival. Results Before starting BRAFi, fast kinetics and moreover a wide range of kinetics (fast and slow growing mets in a same patient) were pejorative markers. At the first assessment after BRAFi introduction, high heterogeneity of kinetics predicted short survival, and added independent information over RECIST progression in multivariate analysis. Metastatic growth rates after BRAFi discontinuation was usually not faster than before BRAFi introduction, but they were often more heterogeneous than before. Conclusions Monitoring kinetics of different mets before and under BRAFi by repeated CT-scan provides information for predictive mathematical modelling. Disease kinetics deserves more interest}, language = {en} } @article{KhalilSchulze2017, author = {Khalil, Sara and Schulze, Bert-Wolfgang}, title = {Boundary problems on a manifold with edge}, series = {Asian-European Journal of Mathematics}, volume = {10}, journal = {Asian-European Journal of Mathematics}, number = {2}, publisher = {World Scientific}, address = {Singapore}, issn = {1793-5571}, doi = {10.1142/S1793557117500875}, pages = {43}, year = {2017}, abstract = {We establish a calculus of boundary value problems (BVPs) on a manifold N with boundary and edge, based on Boutet de Monvel's theory of BVPs in the case of a smooth boundary and on the edge calculus, where in the present case the model cone has a base which is a compact manifold with boundary. The corresponding calculus with boundary and edge is a unification of both structures and controls different operator-valued symbolic structures, in order to obtain ellipticity and parametrices.}, language = {en} } @article{KolasinskiMenne2017, author = {Kolasinski, Slawomir and Menne, Ulrich}, title = {Decay rates for the quadratic and super-quadratic tilt-excess of integral varifolds}, series = {Nonlinear Differential Equations and Applications NoDEA}, volume = {24}, journal = {Nonlinear Differential Equations and Applications NoDEA}, publisher = {Springer}, address = {Basel}, issn = {1021-9722}, doi = {10.1007/s00030-017-0436-z}, pages = {56}, year = {2017}, abstract = {This paper concerns integral varifolds of arbitrary dimension in an open subset of Euclidean space satisfying integrability conditions on their first variation. Firstly, the study of pointwise power decay rates almost everywhere of the quadratic tilt-excess is completed by establishing the precise decay rate for two-dimensional integral varifolds of locally bounded first variation. In order to obtain the exact decay rate, a coercive estimate involving a height-excess quantity measured in Orlicz spaces is established. Moreover, counter-examples to pointwise power decay rates almost everywhere of the super-quadratic tilt-excess are obtained. These examples are optimal in terms of the dimension of the varifold and the exponent of the integrability condition in most cases, for example if the varifold is not two-dimensional. These examples also demonstrate that within the scale of Lebesgue spaces no local higher integrability of the second fundamental form, of an at least two-dimensional curvature varifold, may be deduced from boundedness of its generalised mean curvature vector. Amongst the tools are Cartesian products of curvature varifolds.}, language = {en} } @article{Kollosche2017, author = {Kollosche, David}, title = {Entdeckendes Lernen}, series = {Journal f{\"u}r Mathematik-Didaktik}, volume = {38}, journal = {Journal f{\"u}r Mathematik-Didaktik}, publisher = {Springer}, address = {Heidelberg}, issn = {0173-5322}, doi = {10.1007/s13138-017-0116-x}, pages = {209 -- 237}, year = {2017}, abstract = {Trotz der nachweislichen Popularit{\"a}t des Entdeckenden Lernens in der deutschsprachigen Mathematikdidaktik finden sich aktuell keine kritischen Beitr{\"a}ge, die dazu beitragen k{\"o}nnten, dieses grundlegende Unterrichtskonzept zu hinterfragen und auszusch{\"a}rfen. In diesem Diskussionsbeitrag werden zun{\"a}chst die Theorie und einige Umsetzungsbeispiele des Entdeckenden Lernens herausgearbeitet, um aufzuzeigen, dass das Entdeckende Lernen einem vagen Sammelbegriff gleicht, unter dem oft fragw{\"u}rdige Unterrichtsumgebungen legitimiert werden. Anschließend werden an Hand erkenntnistheoretischer, lerntheoretischer, didaktischer und soziokultureller Betrachtungen Probleme des Entdeckenden Lernens im Mathematikunterricht und M{\"o}glichkeiten ihrer {\"U}berwindung thematisiert. Dabei zeigt sich, dass die Konzeption des Entdeckenden Lernens hinter dem aktuellen mathematikdidaktischen Erkenntnisstand zur{\"u}ckf{\"a}llt und Lehrer sowie Sch{\"u}ler mit unm{\"o}glichen Forderungen konfrontiert, dass lerntheoretische Vorteile des Entdeckenden Lernens oft nicht nachweisbar sind, dass die Idee des Entdeckens auf einem problematischen platonistischen Verst{\"a}ndnis von Erkenntnis beruht und dass Entdeckendes Lernen bildungsferne Sch{\"u}ler zu benachteiligen droht. Abschließend werden Forschungsdesiderata abgeleitet, deren Bearbeitung dazu beitragen k{\"o}nnte, die aufgezeigten Problemfelder zu {\"u}berwinden.}, language = {de} } @article{LazaridesRubach2017, author = {Lazarides, Rebecca and Rubach, Charlott}, title = {Instructional characteristics in mathematics classrooms}, series = {Mathematics Education Research Journal}, volume = {29}, journal = {Mathematics Education Research Journal}, publisher = {Springer}, address = {Dordrecht}, issn = {1033-2170}, doi = {10.1007/s13394-017-0196-4}, pages = {201 -- 217}, year = {2017}, abstract = {This longitudinal study examined relationships between student-perceived teaching for meaning, support for autonomy, and competence in mathematic classrooms (Time 1), and students' achievement goal orientations and engagement in mathematics 6 months later (Time 2). We tested whether student-perceived instructional characteristics at Time 1 indirectly related to student engagement at Time 2, via their achievement goal orientations (Time 2), and, whether student gender moderated these relationships. Participants were ninth and tenth graders (55.2\% girls) from 46 classrooms in ten secondary schools in Berlin, Germany. Only data from students who participated at both timepoints were included (N = 746 out of total at Time 1 1118; dropout 33.27\%). Longitudinal structural equation modeling showed that student-perceived teaching for meaning and support for competence indirectly predicted intrinsic motivation and effort, via students' mastery goal orientation. These paths were equivalent for girls and boys. The findings are significant for mathematics education, in identifying motivational processes that partly explain the relationships between student-perceived teaching for meaning and competence support and intrinsic motivation and effort in mathematics.}, language = {en} } @article{LesurWardinskiBaerenzungetal.2017, author = {Lesur, Vincent and Wardinski, Ingo and B{\"a}renzung, Julien and Holschneider, Matthias}, title = {On the frequency spectra of the core magnetic field Gauss coefficients}, series = {Physics of the earth and planetary interiors}, volume = {276}, journal = {Physics of the earth and planetary interiors}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0031-9201}, doi = {10.1016/j.pepi.2017.05.017}, pages = {145 -- 158}, year = {2017}, abstract = {From monthly mean observatory data spanning 1957-2014, geomagnetic field secular variation values were calculated by annual differences. Estimates of the spherical harmonic Gauss coefficients of the core field secular variation were then derived by applying a correlation based modelling. Finally, a Fourier transform was applied to the time series of the Gauss coefficients. This process led to reliable temporal spectra of the Gauss coefficients up to spherical harmonic degree 5 or 6, and down to periods as short as 1 or 2 years depending on the coefficient. We observed that a k(-2) slope, where k is the frequency, is an acceptable approximation for these spectra, with possibly an exception for the dipole field. The monthly estimates of the core field secular variation at the observatory sites also show that large and rapid variations of the latter happen. This is an indication that geomagnetic jerks are frequent phenomena and that significant secular variation signals at short time scales - i.e. less than 2 years, could still be extracted from data to reveal an unexplored part of the core dynamics.}, language = {en} } @article{MakhmudovMakhmudovTarkhanov2017, author = {Makhmudov, K. O. and Makhmudov, O. I. and Tarkhanov, Nikolai Nikolaevich}, title = {A nonstandard Cauchy problem for the heat equation}, series = {Mathematical Notes}, volume = {102}, journal = {Mathematical Notes}, publisher = {Pleiades Publ.}, address = {New York}, issn = {0001-4346}, doi = {10.1134/S0001434617070264}, pages = {250 -- 260}, year = {2017}, abstract = {We consider the Cauchy problem for the heat equation in a cylinder C (T) = X x (0, T) over a domain X in R (n) , with data on a strip lying on the lateral surface. The strip is of the form S x (0, T), where S is an open subset of the boundary of X. The problem is ill-posed. Under natural restrictions on the configuration of S, we derive an explicit formula for solutions of this problem.}, language = {en} } @article{MakhmudovTarchanov2017, author = {Makhmudov, O. I. and Tarchanov, Nikolaj Nikolaevič}, title = {The first mixed problem for the nonstationary Lam{\´e} system}, series = {The Rocky Mountain journal of mathematics}, volume = {47}, journal = {The Rocky Mountain journal of mathematics}, number = {8}, publisher = {Rocky Mountain Mathematics Consortium}, address = {Tempe}, issn = {0035-7596}, doi = {10.1216/RMJ-2017-47-8-2731}, pages = {2731 -- 2756}, year = {2017}, abstract = {We find an adequate interpretation of the stationary Lam'{e} operator within the framework of elliptic complexes and study the first mixed problem for the nonstationary Lam'{e} system.}, language = {en} } @article{MeraTarchanov2017, author = {Mera, Azal Jaafar Musa and Tarchanov, Nikolaj Nikolaevič}, title = {The Neumann Problem after Spencer}, series = {Žurnal Sibirskogo Federalʹnogo Universiteta = Journal of Siberian Federal University : Matematika i fizika = Mathematics \& physics}, volume = {10}, journal = {Žurnal Sibirskogo Federalʹnogo Universiteta = Journal of Siberian Federal University : Matematika i fizika = Mathematics \& physics}, publisher = {Sibirskij Federalʹnyj Universitet}, address = {Krasnojarsk}, issn = {1997-1397}, doi = {10.17516/1997-1397-2017-10-4-474-493}, pages = {474 -- 493}, year = {2017}, abstract = {When trying to extend the Hodge theory for elliptic complexes on compact closed manifolds to the case of compact manifolds with boundary one is led to a boundary value problem for the Laplacian of the complex which is usually referred to as Neumann problem. We study the Neumann problem for a larger class of sequences of differential operators on a compact manifold with boundary. These are sequences of small curvature, i.e., bearing the property that the composition of any two neighbouring operators has order less than two.}, language = {en} } @article{MusunthiaKoppitz2017, author = {Musunthia, Tiwadee and Koppitz, J{\"o}rg}, title = {Maximal subsemigroups of some semigroups of order-preserving mappings on a countably infinite set}, series = {Forum mathematicum}, volume = {29}, journal = {Forum mathematicum}, publisher = {De Gruyter}, address = {Berlin}, issn = {0933-7741}, doi = {10.1515/forum-2015-0093}, pages = {971 -- 984}, year = {2017}, abstract = {In this paper, we study the maximal subsemigroups of several semigroups of order-preserving transformations on the natural numbers and the integers, respectively. We determine all maximal subsemigroups of the monoid of all order-preserving injections on the set of natural numbers as well as on the set of integers. Further, we give all maximal subsemigroups of the monoid of all bijections on the integers. For the monoid of all order-preserving transformations on the natural numbers, we classify also all its maximal subsemigroups, containing a particular set of transformations.}, language = {en} } @article{Muench2017, author = {M{\"u}nch, Florentin}, title = {Remarks on curvature dimension conditions on graphs}, series = {Calculus of variations and partial differential equations}, volume = {56}, journal = {Calculus of variations and partial differential equations}, publisher = {Springer}, address = {Heidelberg}, issn = {0944-2669}, doi = {10.1007/s00526-016-1104-6}, pages = {8}, year = {2017}, abstract = {We show a connection between the CDE′ inequality introduced in Horn et al. (Volume doubling, Poincar{\´e} inequality and Gaussian heat kernel estimate for nonnegative curvature graphs. arXiv:1411.5087v2, 2014) and the CDψ inequality established in M{\"u}nch (Li-Yau inequality on finite graphs via non-linear curvature dimension conditions. arXiv:1412.3340v1, 2014). In particular, we introduce a CDφψ inequality as a slight generalization of CDψ which turns out to be equivalent to CDE′ with appropriate choices of φ and ψ. We use this to prove that the CDE′ inequality implies the classical CD inequality on graphs, and that the CDE′ inequality with curvature bound zero holds on Ricci-flat graphs.}, language = {en} } @article{ParkLuehrKervalishvilietal.2017, author = {Park, Jaeheung and L{\"u}hr, Hermann and Kervalishvili, Guram and Rauberg, Jan and Stolle, Claudia and Kwak, Young-Sil and Lee, Woo Kyoung}, title = {Morphology of high-latitude plasma density perturbations as deduced from the total electron content measurements onboard the Swarm constellation}, series = {Journal of geophysical research : A, Space physics}, volume = {122}, journal = {Journal of geophysical research : A, Space physics}, number = {1}, publisher = {American Geophysical Union}, address = {Washington}, issn = {2169-9380}, doi = {10.1002/2016JA023086}, pages = {1338 -- 1359}, year = {2017}, abstract = {In this study, we investigate the climatology of high-latitude total electron content (TEC) variations as observed by the dual-frequency Global Navigation Satellite Systems (GNSS) receivers onboard the Swarm satellite constellation. The distribution of TEC perturbations as a function of geographic/magnetic coordinates and seasons reasonably agrees with that of the Challenging Minisatellite Payload observations published earlier. Categorizing the high-latitude TEC perturbations according to line-of-sight directions between Swarm and GNSS satellites, we can deduce their morphology with respect to the geomagnetic field lines. In the Northern Hemisphere, the perturbation shapes are mostly aligned with the L shell surface, and this anisotropy is strongest in the nightside auroral (substorm) and subauroral regions and weakest in the central polar cap. The results are consistent with the well-known two-cell plasma convection pattern of the high-latitude ionosphere, which is approximately aligned with L shells at auroral regions and crossing different L shells for a significant part of the polar cap. In the Southern Hemisphere, the perturbation structures exhibit noticeable misalignment to the local L shells. Here the direction toward the Sun has an additional influence on the plasma structure, which we attribute to photoionization effects. The larger offset between geographic and geomagnetic poles in the south than in the north is responsible for the hemispheric difference.}, language = {en} } @article{PathirajaAnghileriBurlandoetal.2017, author = {Pathiraja, Sahani Darschika and Anghileri, Daniela and Burlando, P. and Sharma, A. and Marshall, L. and Moradkhani, H.}, title = {Insights on the impact of systematic model errors on data assimilation performance in changing catchments}, series = {Advances in water resources}, volume = {113}, journal = {Advances in water resources}, publisher = {Elsevier}, address = {Oxford}, issn = {0309-1708}, doi = {10.1016/j.advwatres.2017.12.006}, pages = {202 -- 222}, year = {2017}, abstract = {The global prevalence of rapid and extensive land use change necessitates hydrologic modelling methodologies capable of handling non-stationarity. This is particularly true in the context of Hydrologic Forecasting using Data Assimilation. Data Assimilation has been shown to dramatically improve forecast skill in hydrologic and meteorological applications, although such improvements are conditional on using bias-free observations and model simulations. A hydrologic model calibrated to a particular set of land cover conditions has the potential to produce biased simulations when the catchment is disturbed. This paper sheds new light on the impacts of bias or systematic errors in hydrologic data assimilation, in the context of forecasting in catchments with changing land surface conditions and a model calibrated to pre-change conditions. We posit that in such cases, the impact of systematic model errors on assimilation or forecast quality is dependent on the inherent prediction uncertainty that persists even in pre-change conditions. Through experiments on a range of catchments, we develop a conceptual relationship between total prediction uncertainty and the impacts of land cover changes on the hydrologic regime to demonstrate how forecast quality is affected when using state estimation Data Assimilation with no modifications to account for land cover changes. This work shows that systematic model errors as a result of changing or changed catchment conditions do not always necessitate adjustments to the modelling or assimilation methodology, for instance through re-calibration of the hydrologic model, time varying model parameters or revised offline/online bias estimation.}, language = {en} } @article{ShakiPinhasFischer2017, author = {Shaki, Samuel and Pinhas, Michal and Fischer, Martin H.}, title = {Heuristics and biases in mental arithmetic}, series = {Thinking \& Reasoning}, volume = {24}, journal = {Thinking \& Reasoning}, number = {2}, publisher = {Routledge, Taylor \& Francis Group}, address = {Abingdon}, issn = {1354-6783}, doi = {10.1080/13546783.2017.1348987}, pages = {138 -- 156}, year = {2017}, abstract = {Mental arithmetic is characterised by a tendency to overestimate addition and to underestimate subtraction results: the operational momentum (OM) effect. Here, motivated by contentious explanations of this effect, we developed and tested an arithmetic heuristics and biases model that predicts reverse OM due to cognitive anchoring effects. Participants produced bi-directional lines with lengths corresponding to the results of arithmetic problems. In two experiments, we found regular OM with zero problems (e.g., 3+0, 3-0) but reverse OM with non-zero problems (e.g., 2+1, 4-1). In a third experiment, we tested the prediction of our model. Our results suggest the presence of at least three competing biases in mental arithmetic: a more-or-less heuristic, a sign-space association and an anchoring bias. We conclude that mental arithmetic exhibits shortcuts for decision-making similar to traditional domains of reasoning and problem-solving.}, language = {en} } @article{SiskaJonesJeonetal.2017, author = {Siska, Veronika and Jones, Eppie Ruth and Jeon, Sungwon and Bhak, Youngjune and Kim, Hak-Min and Cho, Yun Sung and Kim, Hyunho and Lee, Kyusang and Veselovskaya, Elizaveta and Balueva, Tatiana and Gallego-Llorente, Marcos and Hofreiter, Michael and Bradley, Daniel G. and Eriksson, Anders and Pinhasi, Ron and Bhak, Jong and Manica, Andrea}, title = {Genome-wide data from two early Neolithic East Asian individuals dating to 7700 years ago}, series = {Science Advances}, volume = {3}, journal = {Science Advances}, number = {2}, publisher = {American Assoc. for the Advancement of Science}, address = {Washington}, issn = {2375-2548}, doi = {10.1126/sciadv.1601877}, pages = {10}, year = {2017}, abstract = {Ancient genomes have revolutionized our understanding of Holocene prehistory and, particularly, the Neolithic transition in western Eurasia. In contrast, East Asia has so far received little attention, despite representing a core region at which the Neolithic transition took place independently ~3 millennia after its onset in the Near East. We report genome-wide data from two hunter-gatherers from Devil's Gate, an early Neolithic cave site (dated to ~7.7 thousand years ago) located in East Asia, on the border between Russia and Korea. Both of these individuals are genetically most similar to geographically close modern populations from the Amur Basin, all speaking Tungusic languages, and, in particular, to the Ulchi. The similarity to nearby modern populations and the low levels of additional genetic material in the Ulchi imply a high level of genetic continuity in this region during the Holocene, a pattern that markedly contrasts with that reported for Europe.}, language = {en} } @article{StraderSchneiderSchorlemmer2017, author = {Strader, Anne and Schneider, Max and Schorlemmer, Danijel}, title = {Prospective and retrospective evaluation of five-year earthquake forecast models for California}, series = {Geophysical journal international}, volume = {211}, journal = {Geophysical journal international}, publisher = {Oxford Univ. Press}, address = {Oxford}, issn = {0956-540X}, doi = {10.1093/gji/ggx268}, pages = {239 -- 251}, year = {2017}, language = {en} } @article{TaghvaeideWiljesMehtaetal.2017, author = {Taghvaei, Amirhossein and de Wiljes, Jana and Mehta, Prashant G. and Reich, Sebastian}, title = {Kalman filter and its modern extensions for the continuous-time nonlinear filtering problem}, series = {Journal of dynamic systems measurement and control}, volume = {140}, journal = {Journal of dynamic systems measurement and control}, number = {3}, publisher = {ASME}, address = {New York}, issn = {0022-0434}, doi = {10.1115/1.4037780}, pages = {11}, year = {2017}, abstract = {This paper is concerned with the filtering problem in continuous time. Three algorithmic solution approaches for this problem are reviewed: (i) the classical Kalman-Bucy filter, which provides an exact solution for the linear Gaussian problem; (ii) the ensemble Kalman-Bucy filter (EnKBF), which is an approximate filter and represents an extension of the Kalman-Bucy filter to nonlinear problems; and (iii) the feedback particle filter (FPF), which represents an extension of the EnKBF and furthermore provides for a consistent solution in the general nonlinear, non-Gaussian case. The common feature of the three algorithms is the gain times error formula to implement the update step (to account for conditioning due to the observations) in the filter. In contrast to the commonly used sequential Monte Carlo methods, the EnKBF and FPF avoid the resampling of the particles in the importance sampling update step. Moreover, the feedback control structure provides for error correction potentially leading to smaller simulation variance and improved stability properties. The paper also discusses the issue of nonuniqueness of the filter update formula and formulates a novel approximation algorithm based on ideas from optimal transport and coupling of measures. Performance of this and other algorithms is illustrated for a numerical example.}, 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} } @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{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} }