@article{WangHainzlZoelleretal.2012,
  author    = {Wang, Lifeng and Hainzl, Sebastian and Z{\"o}ller, Gert and Holschneider, Matthias},
  title     = {Stress- and aftershock-constrained joint inversions for coseismic and postseismic slip applied to the 2004 M6.0 Parkfield earthquake},
  series = {Journal of geophysical research : Solid earth},
  volume    = {117},
  journal   = {Journal of geophysical research : Solid earth},
  publisher = {American Geophysical Union},
  address   = {Washington},
  issn      = {2169-9313},
  doi       = {10.1029/2011JB009017},
  pages     = {18},
  year      = {2012},
  abstract  = {Both aftershocks and geodetically measured postseismic displacements are important markers of the stress relaxation process following large earthquakes. Postseismic displacements can be related to creep-like relaxation in the vicinity of the coseismic rupture by means of inversion methods. However, the results of slip inversions are typically non-unique and subject to large uncertainties. Therefore, we explore the possibility to improve inversions by mechanical constraints. In particular, we take into account the physical understanding that postseismic deformation is stress-driven, and occurs in the coseismically stressed zone. We do joint inversions for coseismic and postseismic slip in a Bayesian framework in the case of the 2004 M6.0 Parkfield earthquake. We perform a number of inversions with different constraints, and calculate their statistical significance. According to information criteria, the best result is preferably related to a physically reasonable model constrained by the stress-condition (namely postseismic creep is driven by coseismic stress) and the condition that coseismic slip and large aftershocks are disjunct. This model explains 97\% of the coseismic displacements and 91\% of the postseismic displacements during day 1-5 following the Parkfield event, respectively. It indicates that the major postseismic deformation can be generally explained by a stress relaxation process for the Parkfield case. This result also indicates that the data to constrain the coseismic slip model could be enriched postseismically. For the 2004 Parkfield event, we additionally observe asymmetric relaxation process at the two sides of the fault, which can be explained by material contrast ratio across the fault of similar to 1.15 in seismic velocity.},
  language  = {en}
}
@article{Wallenta2012,
  author    = {Wallenta, D.},
  title     = {Elliptic quasicomplexes on compact closed manifolds},
  series = {Integral equations and operator theor},
  volume    = {73},
  journal   = {Integral equations and operator theor},
  number    = {4},
  publisher = {Springer},
  address   = {Basel},
  issn      = {0378-620X},
  doi       = {10.1007/s00020-012-1983-7},
  pages     = {517 -- 536},
  year      = {2012},
  abstract  = {We consider quasicomplexes of pseudodifferential operators on a smooth compact manifold without boundary. To each quasicomplex we associate a complex of symbols. The quasicomplex is elliptic if this symbol complex is exact away from the zero section. We prove that elliptic quasicomplexes are Fredholm. Moreover, we introduce the Euler characteristic for elliptic quasicomplexes and prove a generalisation of the Atiyah-Singer index theorem.},
  language  = {en}
}
@article{KellerValleriani2012,
  author    = {Keller, Peter and Valleriani, Angelo},
  title     = {Single-molecule stochastic times in a reversible bimolecular reaction},
  series = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr},
  volume    = {137},
  journal   = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr},
  number    = {8},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {0021-9606},
  doi       = {10.1063/1.4747337},
  pages     = {7},
  year      = {2012},
  abstract  = {In this work, we consider the reversible reaction between reactants of species A and B to form the product C. We consider this reaction as a prototype of many pseudobiomolecular reactions in biology, such as for instance molecular motors. We derive the exact probability density for the stochastic waiting time that a molecule of species A needs until the reaction with a molecule of species B takes place. We perform this computation taking fully into account the stochastic fluctuations in the number of molecules of species B. We show that at low numbers of participating molecules, the exact probability density differs from the exponential density derived by assuming the law of mass action. Finally, we discuss the condition of detailed balance in the exact stochastic and in the approximate treatment.},
  language  = {en}
}
@article{KurtenbachEickerMayerGuerretal.2012,
  author    = {Kurtenbach, E. and Eicker, A. and Mayer-Guerr, T. and Holschneider, Matthias and Hayn, M. and Fuhrmann, M. and Kusche, J.},
  title     = {Improved daily GRACE gravity field solutions using a Kalman smoother},
  series = {Journal of geodynamics},
  volume    = {59},
  journal   = {Journal of geodynamics},
  number    = {3},
  publisher = {Elsevier},
  address   = {Oxford},
  issn      = {0264-3707},
  doi       = {10.1016/j.jog.2012.02.006},
  pages     = {39 -- 48},
  year      = {2012},
  abstract  = {Different GRACE data analysis centers provide temporal variations of the Earth's gravity field as monthly, 10-daily or weekly solutions. These temporal mean fields cannot model the variations occurring during the respective time span. The aim of our approach is to extract as much temporal information as possible out of the given GRACE data. Therefore the temporal resolution shall be increased with the goal to derive daily snapshots. Yet, such an increase in temporal resolution is accompanied by a loss of redundancy and therefore in a reduced accuracy if the daily solutions are calculated individually. The approach presented here therefore introduces spatial and temporal correlations of the expected gravity field signal derived from geophysical models in addition to the daily observations, thus effectively constraining the spatial and temporal evolution of the GRACE solution. The GRACE data processing is then performed within the framework of a Kalman filter and smoother estimation procedure. The approach is at first investigated in a closed-loop simulation scenario and then applied to the original GRACE observations (level-1B data) to calculate daily solutions as part of the gravity field model ITG-Grace2010. Finally, the daily models are compared to vertical GPS station displacements and ocean bottom pressure observations. From these comparisons it can be concluded that particular in higher latitudes the daily solutions contain high-frequent temporal gravity field information and represent an improvement to existing geophysical models.},
  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{IochumLevyVassilevich2012,
  author    = {Iochum, B. and Levy, C. and Vassilevich, D. V.},
  title     = {Global and local aspects of spectral actions},
  series = {Journal of physics : A, Mathematical and theoretical},
  volume    = {45},
  journal   = {Journal of physics : A, Mathematical and theoretical},
  number    = {37},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1751-8113},
  doi       = {10.1088/1751-8113/45/37/374020},
  pages     = {19},
  year      = {2012},
  abstract  = {The principal object in noncommutative geometry is the spectral triple consisting of an algebra A, a Hilbert space H and a Dirac operator D. Field theories are incorporated in this approach by the spectral action principle, which sets the field theory action to Tr f (D-2/Lambda(2)), where f is a real function such that the trace exists and Lambda is a cutoff scale. In the low-energy (weak-field) limit, the spectral action reproduces reasonably well the known physics including the standard model. However, not much is known about the spectral action beyond the low-energy approximation. In this paper, after an extensive introduction to spectral triples and spectral actions, we study various expansions of the spectral actions (exemplified by the heat kernel). We derive the convergence criteria. For a commutative spectral triple, we compute the heat kernel on the torus up to the second order in gauge connection and consider limiting cases. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker's 75th birthday devoted to 'Applications of zeta functions and other spectral functions in mathematics and physics'.},
  language  = {en}
}
@article{BlanchardMathe2012,
  author    = {Blanchard, Gilles and Mathe, Peter},
  title     = {Discrepancy principle for statistical inverse problems with application to conjugate gradient iteration},
  series = {Inverse problems : an international journal of inverse problems, inverse methods and computerised inversion of data},
  volume    = {28},
  journal   = {Inverse problems : an international journal of inverse problems, inverse methods and computerised inversion of data},
  number    = {11},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {0266-5611},
  doi       = {10.1088/0266-5611/28/11/115011},
  pages     = {23},
  year      = {2012},
  abstract  = {The authors discuss the use of the discrepancy principle for statistical inverse problems, when the underlying operator is of trace class. Under this assumption the discrepancy principle is well defined, however a plain use of it may occasionally fail and it will yield sub-optimal rates. Therefore, a modification of the discrepancy is introduced, which corrects both of the above deficiencies. For a variety of linear regularization schemes as well as for conjugate gradient iteration it is shown to yield order optimal a priori error bounds under general smoothness assumptions. A posteriori error control is also possible, however at a sub-optimal rate, in general. This study uses and complements previous results for bounded deterministic noise.},
  language  = {en}
}
@article{SchachtschneiderHolschneiderMandea2012,
  author    = {Schachtschneider, R. and Holschneider, Matthias and Mandea, M.},
  title     = {Error distribution in regional modelling of the geomagnetic field},
  series = {Geophysical journal international},
  volume    = {191},
  journal   = {Geophysical journal international},
  number    = {3},
  publisher = {Wiley-Blackwell},
  address   = {Hoboken},
  issn      = {0956-540X},
  doi       = {10.1111/j.1365-246X.2012.05675.x},
  pages     = {1015 -- 1024},
  year      = {2012},
  abstract  = {In this study we analyse the error distribution in regional models of the geomagnetic field. Our main focus is to investigate the distribution of errors when combining two regional patches to obtain a global field from regional ones. To simulate errors in overlapping patches we choose two different data region shapes that resemble that scenario. First, we investigate the errors in elliptical regions and secondly we choose a region obtained from two overlapping circular spherical caps. We conduct a Monte-Carlo simulation using synthetic data to obtain the expected mean errors. For the elliptical regions the results are similar to the ones obtained for circular spherical caps: the maximum error at the boundary decreases towards the centre of the region. A new result emerges as errors at the boundary vary with azimuth, being largest in the major axis direction and minimal in the minor axis direction. Inside the region there is an error decay towards a minimum at the centre at a rate similar to the one in circular regions. In the case of two combined circular regions there is also an error decay from the boundary towards the centre. The minimum error occurs at the centre of the combined regions. The maximum error at the boundary occurs on the line containing the two cap centres, the minimum in the perpendicular direction where the two circular cap boundaries meet. The large errors at the boundary are eliminated by combining regional patches. We propose an algorithm for finding the boundary region that is applicable to irregularly shaped model regions.},
  language  = {en}
}
@article{Baumgaertel2012,
  author    = {Baumg{\"a}rtel, Hellmut},
  title     = {On a critical radiation density in the Friedmann equation},
  series = {Journal of mathematical physics},
  volume    = {53},
  journal   = {Journal of mathematical physics},
  number    = {12},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {0022-2488},
  doi       = {10.1063/1.4771668},
  pages     = {9},
  year      = {2012},
  abstract  = {The paper presents a classification of the basic types of admissible solutions of the general Friedmann equation with non-vanishing cosmological constant and for the case that radiation and matter do not couple. There are four distinct types. The classification uses first the discriminant of a polynomial of the third degree, closely related to the right hand side of the Friedmann equation. The decisive term is then a critical radiation density which can be calculated explicitly.},
  language  = {en}
}
@phdthesis{Keller2012,
  author    = {Keller, Peter},
  title     = {Mathematical modeling of molecular motors},
  address   = {Potsdam},
  pages     = {116 S.},
  year      = {2012},
  language  = {en}
}