@article{NitzeGrosseJonesetal.2018, author = {Nitze, Ingmar and Grosse, Guido and Jones, Benjamin M. and Romanovsky, Vladimir E. and Boike, Julia}, title = {Remote sensing quantifies widespread abundance of permafrost region disturbances across the Arctic and Subarctic}, series = {Nature Communications}, volume = {9}, journal = {Nature Communications}, publisher = {Nature Publ. Group}, address = {London}, issn = {2041-1723}, doi = {10.1038/s41467-018-07663-3}, pages = {11}, year = {2018}, abstract = {Local observations indicate that climate change and shifting disturbance regimes are causing permafrost degradation. However, the occurrence and distribution of permafrost region disturbances (PRDs) remain poorly resolved across the Arctic and Subarctic. Here we quantify the abundance and distribution of three primary PRDs using time-series analysis of 30-m resolution Landsat imagery from 1999 to 2014. Our dataset spans four continental-scale transects in North America and Eurasia, covering similar to 10\% of the permafrost region. Lake area loss (-1.45\%) dominated the study domain with enhanced losses occurring at the boundary between discontinuous and continuous permafrost regions. Fires were the most extensive PRD across boreal regions (6.59\%), but in tundra regions (0.63\%) limited to Alaska. Retrogressive thaw slumps were abundant but highly localized (< 10(-5)\%). Our analysis synergizes the global-scale importance of PRDs. The findings highlight the need to include PRDs in next-generation land surface models to project the permafrost carbon feedback.}, language = {en} } @article{Roos2019, author = {Roos, Saskia}, title = {The Dirac operator under collapse to a smooth limit space}, series = {Annals of global analysis and geometry}, volume = {57}, journal = {Annals of global analysis and geometry}, number = {1}, publisher = {Springer}, address = {Dordrecht}, issn = {0232-704X}, doi = {10.1007/s10455-019-09691-8}, pages = {121 -- 151}, year = {2019}, abstract = {Let (M-i, g(i))(i is an element of N) be a sequence of spin manifolds with uniform bounded curvature and diameter that converges to a lower-dimensional Riemannian manifold (B, h) in the Gromov-Hausdorff topology. Then, it happens that the spectrum of the Dirac operator converges to the spectrum of a certain first-order elliptic differential operator D-B on B. We give an explicit description of D-B and characterize the special case where D-B equals the Dirac operator on B.}, language = {en} } @article{GueneysuKeller2018, author = {G{\"u}neysu, Batu and Keller, Matthias}, title = {Scattering the Geometry of Weighted Graphs}, series = {Mathematical physics, analysis and geometry : an international journal devoted to the theory and applications of analysis and geometry to physics}, volume = {21}, journal = {Mathematical physics, analysis and geometry : an international journal devoted to the theory and applications of analysis and geometry to physics}, number = {3}, publisher = {Springer}, address = {Dordrecht}, issn = {1385-0172}, doi = {10.1007/s11040-018-9285-1}, pages = {15}, year = {2018}, abstract = {Given two weighted graphs (X, b(k), m(k)), k = 1, 2 with b(1) similar to b(2) and m(1) similar to m(2), we prove a weighted L-1-criterion for the existence and completeness of the wave operators W-+/- (H-2, H-1, I-1,I-2), where H-k denotes the natural Laplacian in l(2)(X, m(k)) w.r.t. (X, b(k), m(k)) and I-1,I-2 the trivial identification of l(2)(X, m(1)) with l(2) (X, m(2)). In particular, this entails a general criterion for the absolutely continuous spectra of H-1 and H-2 to be equal.}, language = {en} } @article{FedchenkoTarkhanov2017, author = {Fedchenko, Dmitry and Tarkhanov, Nikolai Nikolaevich}, title = {A Rado theorem for the porous medium equation}, series = {Boletin de la Sociedad Matem{\´a}tica Mexicana}, volume = {24}, journal = {Boletin de la Sociedad Matem{\´a}tica Mexicana}, number = {2}, publisher = {Springer}, address = {Cham}, issn = {1405-213X}, doi = {10.1007/s40590-017-0169-3}, pages = {427 -- 437}, year = {2017}, abstract = {We prove that if u is a locally Lipschitz continuous function on an open set chi subset of Rn + 1 satisfying the nonlinear heat equation partial derivative(t)u = Delta(vertical bar u vertical bar(p-1) u), p > 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{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; infinity. In this article we generalize and improve this result in several respects. First, we give a new and very simple proof for the fact that the same conclusion also holds if the semigroup is merely assumed to be bounded instead of Markov. As a main result, we then prove a version of this theorem for semigroups which only admit certain individual lower bounds. Moreover, we generalize a theorem of Ding on semigroups of Frobenius-Perron operators. We also demonstrate how our results can be adapted to the setting of general Banach lattices and we give some counterexamples to show optimality of our results. Our methods combine some rather concrete estimates and approximation arguments with abstract functional analytical tools. One of these tools is a theorem which relates the convergence of a time-continuous operator semigroup to the convergence of embedded discrete semigroups.}, language = {en} } @article{LeungLeutbecherReichetal.2019, author = {Leung, Tsz Yan and Leutbecher, Martin and Reich, Sebastian and Shepherd, Theodore G.}, title = {Atmospheric Predictability: Revisiting the Inherent Finite-Time Barrier}, series = {Journal of the atmospheric sciences}, volume = {76}, journal = {Journal of the atmospheric sciences}, number = {12}, publisher = {American Meteorological Soc.}, address = {Boston}, issn = {0022-4928}, doi = {10.1175/JAS-D-19-0057.1}, pages = {3883 -- 3892}, year = {2019}, abstract = {The accepted idea that there exists an inherent finite-time barrier in deterministically predicting atmospheric flows originates from Edward N. Lorenz's 1969 work based on two-dimensional (2D) turbulence. Yet, known analytic results on the 2D Navier-Stokes (N-S) equations suggest that one can skillfully predict the 2D N-S system indefinitely far ahead should the initial-condition error become sufficiently small, thereby presenting a potential conflict with Lorenz's theory. Aided by numerical simulations, the present work reexamines Lorenz's model and reviews both sides of the argument, paying particular attention to the roles played by the slope of the kinetic energy spectrum. It is found that when this slope is shallower than -3, the Lipschitz continuity of analytic solutions (with respect to initial conditions) breaks down as the model resolution increases, unless the viscous range of the real system is resolved—which remains practically impossible. This breakdown leads to the inherent finite-time limit. If, on the other hand, the spectral slope is steeper than -3, then the breakdown does not occur. In this way, the apparent contradiction between the analytic results and Lorenz's theory is reconciled.}, language = {en} } @misc{BeckusBellissardDeNittis2019, author = {Beckus, Siegfried and Bellissard, Jean and De Nittis, Giuseppe}, title = {Corrigendum to: Spectral continuity for aperiodic quantum systems I. General theory. - [Journal of functional analysis. - 275 (2018), 11, S. 2917 - 2977]}, series = {Journal of functional analysis}, volume = {277}, journal = {Journal of functional analysis}, number = {9}, publisher = {Elsevier}, address = {San Diego}, issn = {0022-1236}, doi = {10.1016/j.jfa.2019.06.001}, pages = {3351 -- 3353}, year = {2019}, abstract = {A correct statement of Theorem 4 in [1] is provided. The change does not affect the main results.}, language = {en} } @article{FernandesKoppitzMusunthia2019, author = {Fernandes, Vitor H. and Koppitz, J{\"o}rg and Musunthia, Tiwadee}, title = {The Rank of the Semigroup of All Order-Preserving Transformations on a Finite Fence}, series = {Bulletin of the Malaysian Mathematical Sciences Society volume}, volume = {42}, journal = {Bulletin of the Malaysian Mathematical Sciences Society volume}, number = {5}, publisher = {Malaysian mathematical sciences sciences soc}, address = {Pulau Punang}, issn = {0126-6705}, doi = {10.1007/s40840-017-0598-1}, pages = {2191 -- 2211}, year = {2019}, abstract = {A zig-zag (or fence) order is a special partial order on a (finite) set. In this paper, we consider the semigroup TFn of all order-preserving transformations on an n-element zig-zag-ordered set. We determine the rank of TFn and provide a minimal generating set for TFn. Moreover, a formula for the number of idempotents in TFn is given.}, 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{ShcherbakovZhuangZoelleretal.2019, author = {Shcherbakov, Robert and Zhuang, Jiancang and Z{\"o}ller, Gert and Ogata, Yosihiko}, title = {Forecasting the magnitude of the largest expected earthquake}, series = {Nature Communications}, volume = {10}, journal = {Nature Communications}, publisher = {Nature Publishing Group}, address = {London}, issn = {2041-1723}, doi = {10.1038/s41467-019-11958-4}, pages = {11}, year = {2019}, abstract = {The majority of earthquakes occur unexpectedly and can trigger subsequent sequences of events that can culminate in more powerful earthquakes. This self-exciting nature of seismicity generates complex clustering of earthquakes in space and time. Therefore, the problem of constraining the magnitude of the largest expected earthquake during a future time interval is of critical importance in mitigating earthquake hazard. We address this problem by developing a methodology to compute the probabilities for such extreme earthquakes to be above certain magnitudes. We combine the Bayesian methods with the extreme value theory and assume that the occurrence of earthquakes can be described by the Epidemic Type Aftershock Sequence process. We analyze in detail the application of this methodology to the 2016 Kumamoto, Japan, earthquake sequence. We are able to estimate retrospectively the probabilities of having large subsequent earthquakes during several stages of the evolution of this sequence.}, language = {en} } @article{ConfortiKosenkovaRoelly2019, author = {Conforti, Giovanni and Kosenkova, Tetiana and Roelly, Sylvie}, title = {Conditioned Point Processes with Application to Levy Bridges}, series = {Journal of theoretical probability}, volume = {32}, journal = {Journal of theoretical probability}, number = {4}, publisher = {Springer}, address = {New York}, issn = {0894-9840}, doi = {10.1007/s10959-018-0863-8}, pages = {2111 -- 2134}, year = {2019}, abstract = {Our first result concerns a characterization by means of a functional equation of Poisson point processes conditioned by the value of their first moment. It leads to a generalized version of Mecke's formula. En passant, it also allows us to gain quantitative results about stochastic domination for Poisson point processes under linear constraints. Since bridges of a pure jump L{\´e}vy process in Rd with a height a can be interpreted as a Poisson point process on space-time conditioned by pinning its first moment to a, our approach allows us to characterize bridges of L{\´e}vy processes by means of a functional equation. The latter result has two direct applications: First, we obtain a constructive and simple way to sample L{\´e}vy bridge dynamics; second, it allows us to estimate the number of jumps for such bridges. We finally show that our method remains valid for linearly perturbed L{\´e}vy processes like periodic Ornstein-Uhlenbeck processes driven by L{\´e}vy noise.}, language = {en} } @article{SalamatZoellerAmini2019, author = {Salamat, Mona and Z{\"o}ller, Gert and Amini, Morteza}, title = {Prediction of the Maximum Expected Earthquake Magnitude in Iran:}, series = {Pure and applied geophysics}, volume = {176}, journal = {Pure and applied geophysics}, number = {8}, publisher = {Springer}, address = {Basel}, issn = {0033-4553}, doi = {10.1007/s00024-019-02141-3}, pages = {3425 -- 3438}, year = {2019}, abstract = {This paper concerns the problem of predicting the maximum expected earthquake magnitude μ in a future time interval Tf given a catalog covering a time period T in the past. Different studies show the divergence of the confidence interval of the maximum possible earthquake magnitude m_{ max } for high levels of confidence (Salamat et al. 2017). Therefore, m_{ max } should be better replaced by μ (Holschneider et al. 2011). In a previous study (Salamat et al. 2018), μ is estimated for an instrumental earthquake catalog of Iran from 1900 onwards with a constant level of completeness ( {m0 = 5.5} ). In the current study, the Bayesian methodology developed by Z{\"o}ller et al. (2014, 2015) is applied for the purpose of predicting μ based on the catalog consisting of both historical and instrumental parts. The catalog is first subdivided into six subcatalogs corresponding to six seismotectonic zones, and each of those zone catalogs is subsequently subdivided according to changes in completeness level and magnitude uncertainty. For this, broad and small error distributions are considered for historical and instrumental earthquakes, respectively. We assume that earthquakes follow a Poisson process in time and Gutenberg-Richter law in the magnitude domain with a priori unknown a and b values which are first estimated by Bayes' theorem and subsequently used to estimate μ. Imposing different values of m_{ max } for different seismotectonic zones namely Alborz, Azerbaijan, Central Iran, Zagros, Kopet Dagh and Makran, the results show considerable probabilities for the occurrence of earthquakes with Mw ≥ 7.5 in short Tf , whereas for long Tf, μ is almost equal to m_{ max }}, language = {en} } @article{StaniforthWoodReich2006, author = {Staniforth, Andrew and Wood, Nigel and Reich, Sebastian}, title = {A time-staggered semi-Lagrangian discretization of the rotating shallow-water equations}, series = {Quarterly journal of the Royal Meteorological Society}, volume = {132}, journal = {Quarterly journal of the Royal Meteorological Society}, number = {621C}, publisher = {Wiley}, address = {Weinheim}, issn = {0035-9009}, doi = {10.1256/qj.06.30}, pages = {3107 -- 3116}, year = {2006}, abstract = {A time-staggered semi-Lagrangian discretization of the rotating shallow-water equations is proposed and analysed. Application of regularization to the geopotential field used in the momentum equations leads to an unconditionally stable scheme. The analysis, together with a fully nonlinear example application, suggests that this approach is a promising, efficient, and accurate alternative to traditional schemes.}, language = {en} } @article{KirscheBoeckmann2006, author = {Kirsche, Andreas and B{\"o}ckmann, Christine}, title = {Pade iteration method for regularization}, series = {Applied mathematics and computation}, volume = {180}, journal = {Applied mathematics and computation}, number = {2}, publisher = {Elsevier}, address = {New York}, issn = {0096-3003}, doi = {10.1016/j.amc.2006.01.011}, pages = {648 -- 663}, year = {2006}, abstract = {In this study we present iterative regularization methods using rational approximations, in particular, Pade approximants, which work well for ill-posed problems. We prove that the (k,j)-Pade method is a convergent and order optimal iterative regularization method in using the discrepancy principle of Morozov. Furthermore, we present a hybrid Pade method, compare it with other well-known methods and found that it is faster than the Landweber method. It is worth mentioning that this study is a completion of the paper [A. Kirsche, C. Bockmann, Rational approximations for ill-conditioned equation systems, Appl. Math. Comput. 171 (2005) 385-397] where this method was treated to solve ill-conditioned equation systems. (c) 2006 Elsevier Inc. All rights reserved.}, language = {en} } @article{Junek2020, author = {Junek, Heinz}, title = {Zyklizit{\"a}t in Raum, zeit und geist : {\"u}ber Pflasterungen, Rollkurven, Dezimalbr{\"u}che, Schwingungen, Wellen, Iteration und Neuronale Netze}, series = {Zyklizit{\"a}t \& Rhythmik: eine multidisziplin{\"a}re Vorlesungsreihe}, journal = {Zyklizit{\"a}t \& Rhythmik: eine multidisziplin{\"a}re Vorlesungsreihe}, publisher = {trafo}, address = {Berlin}, isbn = {978-3-86464-169-5}, pages = {85 -- 103}, year = {2020}, language = {de} } @article{Reich2006, author = {Reich, Sebastian}, title = {Linearly implicit time stepping methods for numerical weather prediction}, series = {BIT : numerical mathematics ; the leading applied mathematics journal for all computational mathematicians}, volume = {46}, journal = {BIT : numerical mathematics ; the leading applied mathematics journal for all computational mathematicians}, publisher = {Springer}, address = {Dordrecht}, issn = {0006-3835}, doi = {10.1007/s10543-006-0065-0}, pages = {607 -- 616}, year = {2006}, abstract = {The efficient time integration of the dynamic core equations for numerical weather prediction (NWP) remains a key challenge. One of the most popular methods is currently provided by implementations of the semi-implicit semi-Lagrangian (SISL) method, originally proposed by Robert (J. Meteorol. Soc. Jpn., 1982). Practical implementations of the SISL method are, however, not without certain shortcomings with regard to accuracy, conservation properties and stability. Based on recent work by Gottwald, Frank and Reich (LNCSE, Springer, 2002), Frank, Reich, Staniforth, White and Wood (Atm. Sci. Lett., 2005) and Wood, Staniforth and Reich (Atm. Sci. Lett., 2006) we propose an alternative semi-Lagrangian implementation based on a set of regularized equations and the popular Stormer-Verlet time stepping method in the context of the shallow-water equations (SWEs). Ultimately, the goal is to develop practical implementations for the 3D Euler equations that overcome some or all shortcomings of current SISL implementations.}, language = {en} }