@unpublished{PfaeffleStephan2012, author = {Pf{\"a}ffle, Frank and Stephan, Christoph A.}, title = {Chiral asymmetry and the spectral action}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-60046}, year = {2012}, abstract = {We consider orthogonal connections with arbitrary torsion on compact Riemannian manifolds. For the induced Dirac operators, twisted Dirac operators and Dirac operators of Chamseddine-Connes type we compute the spectral action. In addition to the Einstein-Hilbert action and the bosonic part of the Standard Model Lagrangian we find the Holst term from Loop Quantum Gravity, a coupling of the Holst term to the scalar curvature and a prediction for the value of the Barbero-Immirzi parameter.}, language = {en} } @unpublished{BaerBallmann2012, author = {B{\"a}r, Christian and Ballmann, Werner}, title = {Boundary value problems for elliptic differential operators of first order}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-60023}, year = {2012}, abstract = {We study boundary value problems for linear elliptic differential operators of order one. The underlying manifold may be noncompact, but the boundary is assumed to be compact. We require a symmetry property of the principal symbol of the operator along the boundary. This is satisfied by Dirac type operators, for instance. We provide a selfcontained introduction to (nonlocal) elliptic boundary conditions, boundary regularity of solutions, and index theory. In particular, we simplify and generalize the traditional theory of elliptic boundary value problems for Dirac type operators. We also prove a related decomposition theorem, a general version of Gromov and Lawson's relative index theorem and a generalization of the cobordism theorem.}, language = {en} } @article{BettenbuehlRusconiEngbertetal.2012, author = {Bettenb{\"u}hl, Mario and Rusconi, Marco and Engbert, Ralf and Holschneider, Matthias}, title = {Bayesian selection of Markov Models for symbol sequences application to microsaccadic eye movements}, series = {PLoS one}, volume = {7}, journal = {PLoS one}, number = {9}, publisher = {PLoS}, address = {San Fransisco}, issn = {1932-6203}, doi = {10.1371/journal.pone.0043388}, pages = {10}, year = {2012}, abstract = {Complex biological dynamics often generate sequences of discrete events which can be described as a Markov process. The order of the underlying Markovian stochastic process is fundamental for characterizing statistical dependencies within sequences. As an example for this class of biological systems, we investigate the Markov order of sequences of microsaccadic eye movements from human observers. We calculate the integrated likelihood of a given sequence for various orders of the Markov process and use this in a Bayesian framework for statistical inference on the Markov order. Our analysis shows that data from most participants are best explained by a first-order Markov process. This is compatible with recent findings of a statistical coupling of subsequent microsaccade orientations. Our method might prove to be useful for a broad class of biological systems.}, language = {en} } @article{HolschneiderNarteauShebalinetal.2012, author = {Holschneider, Matthias and Narteau, C. and Shebalin, P. and Peng, Z. and Schorlemmer, Danijel}, title = {Bayesian analysis of the modified Omori law}, series = {Journal of geophysical research : Solid earth}, volume = {117}, journal = {Journal of geophysical research : Solid earth}, number = {6089}, publisher = {American Geophysical Union}, address = {Washington}, issn = {2169-9313}, doi = {10.1029/2011JB009054}, pages = {12}, year = {2012}, abstract = {In order to examine variations in aftershock decay rate, we propose a Bayesian framework to estimate the {K, c, p}-values of the modified Omori law (MOL), lambda(t) = K(c + t)(-p). The Bayesian setting allows not only to produce a point estimator of these three parameters but also to assess their uncertainties and posterior dependencies with respect to the observed aftershock sequences. Using a new parametrization of the MOL, we identify the trade-off between the c and p-value estimates and discuss its dependence on the number of aftershocks. Then, we analyze the influence of the catalog completeness interval [t(start), t(stop)] on the various estimates. To test this Bayesian approach on natural aftershock sequences, we use two independent and non-overlapping aftershock catalogs of the same earthquakes in Japan. Taking into account the posterior uncertainties, we show that both the handpicked (short times) and the instrumental (long times) catalogs predict the same ranges of parameter values. We therefore conclude that the same MOL may be valid over short and long times.}, language = {en} } @unpublished{AntonioukKiselevStepanenkoetal.2012, author = {Antoniouk, Alexandra Viktorivna and Kiselev, Oleg and Stepanenko, Vitaly and Tarkhanov, Nikolai Nikolaevich}, title = {Asymptotic solutions of the Dirichlet problem for the heat equation at a characteristic point}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-61987}, year = {2012}, abstract = {The Dirichlet problem for the heat equation in a bounded domain is characteristic, for there are boundary points at which the boundary touches a characteristic hyperplane t = c, c being a constant. It was I.G. Petrovskii (1934) who first found necessary and sufficient conditions on the boundary which guarantee that the solution is continuous up to the characteristic point, provided that the Dirichlet data are continuous. This paper initiated standing interest in studying general boundary value problems for parabolic equations in bounded domains. We contribute to the study by constructing a formal solution of the Dirichlet problem for the heat equation in a neighbourhood of a characteristic boundary point and showing its asymptotic character.}, language = {en} } @article{BergemannReich2012, author = {Bergemann, Kay and Reich, Sebastian}, title = {An ensemble Kalman-Bucy filter for continuous data assimilation}, series = {Meteorologische Zeitschrift}, volume = {21}, journal = {Meteorologische Zeitschrift}, number = {3}, publisher = {Schweizerbart}, address = {Stuttgart}, issn = {0941-2948}, doi = {10.1127/0941-2948/2012/0307}, pages = {213 -- 219}, year = {2012}, abstract = {The ensemble Kalman filter has emerged as a promising filter algorithm for nonlinear differential equations subject to intermittent observations. In this paper, we extend the well-known Kalman-Bucy filter for linear differential equations subject to continous observations to the ensemble setting and nonlinear differential equations. The proposed filter is called the ensemble Kalman-Bucy filter and its performance is demonstrated for a simple mechanical model (Langevin dynamics) subject to incremental observations of its velocity.}, language = {en} } @unpublished{KleinLeonardRosenberger2012, author = {Klein, Markus and L{\´e}onard, Christian and Rosenberger, Elke}, title = {Agmon-type estimates for a class of jump processes}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-56995}, year = {2012}, abstract = {In the limit we analyze the generators of families of reversible jump processes in the n-dimensional space associated with a class of symmetric non-local Dirichlet forms and show exponential decay of the eigenfunctions. The exponential rate function is a Finsler distance, given as solution of certain eikonal equation. Fine results are sensitive to the rate functions being twice differentiable or just Lipschitz. Our estimates are similar to the semiclassical Agmon estimates for differential operators of second order. They generalize and strengthen previous results on the lattice.}, language = {en} } @unpublished{Tarkhanov2012, author = {Tarkhanov, Nikolai Nikolaevich}, title = {A simple numerical approach to the Riemann hypothesis}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-57645}, year = {2012}, abstract = {The Riemann hypothesis is equivalent to the fact the the reciprocal function 1/zeta (s) extends from the interval (1/2,1) to an analytic function in the quarter-strip 1/2 < Re s < 1 and Im s > 0. Function theory allows one to rewrite the condition of analytic continuability in an elegant form amenable to numerical experiments.}, language = {en} } @article{NehringZessin2012, author = {Nehring, Benjamin and Zessin, Hans}, title = {A representation of the moment measures of the general ideal Boe gas}, series = {Mathematische Nachrichten}, volume = {285}, journal = {Mathematische Nachrichten}, number = {7}, publisher = {Wiley-VCH}, address = {Weinheim}, issn = {0025-584X}, doi = {10.1002/mana.201000111}, pages = {878 -- 888}, year = {2012}, abstract = {We reconsider the fundamental work of Fichtner 2 and exhibit the permanental structure of the ideal Bose gas again, using a new approach which combines a characterization of infinitely divisible random measures (due to Kerstan, Kummer and Matthes 4, 6 and Mecke 9, 10) with a decomposition of the moment measures into its factorial measures due to Krickeberg 5. To be more precise, we exhibit the moment measures of all orders of the general ideal Bose gas in terms of certain loop integrals. This representation can be considered as a point process analogue of the old idea of Symanzik 15 that local times and self-crossings of the Brownian motion can be used as a tool in quantum field theory. Behind the notion of a general ideal Bose gas there is a class of infinitely divisible point processes of all orders with a Levy-measure belonging to some large class of measures containing that of the classical ideal Bose gas considered by Fichtner. It is well-known that the calculation of moments of higher order of point processes is notoriously complicated. See for instance Krickebergs calculations for the Poisson or the Cox process in 5. Relations to the work of Shirai, Takahashi 12 and Soshnikov 14 on permanental and determinantal processes are outlined.}, language = {en} } @article{Reich2012, author = {Reich, Sebastian}, title = {A Gaussian-mixture ensemble transform filter}, series = {Quarterly journal of the Royal Meteorological Society}, volume = {138}, journal = {Quarterly journal of the Royal Meteorological Society}, number = {662}, publisher = {Wiley-Blackwell}, address = {Malden}, issn = {0035-9009}, doi = {10.1002/qj.898}, pages = {222 -- 233}, year = {2012}, abstract = {We generalize the popular ensemble Kalman filter to an ensemble transform filter, in which the prior distribution can take the form of a Gaussian mixture or a Gaussian kernel density estimator. The design of the filter is based on a continuous formulation of the Bayesian filter analysis step. We call the new filter algorithm the ensemble Gaussian-mixture filter (EGMF). The EGMF is implemented for three simple test problems (Brownian dynamics in one dimension, Langevin dynamics in two dimensions and the three-dimensional Lorenz-63 model). It is demonstrated that the EGMF is capable of tracking systems with non-Gaussian uni- and multimodal ensemble distributions.}, language = {en} }