@inproceedings{HaferKiy2013, author = {Hafer, J{\"o}rg and Kiy, Alexander}, title = {The university-wide introduction of an ePortfolio system as transdisciplinary task}, series = {Proceedings of the PLE Conference 2013: Learning and Diversity in the Cities of the Future}, booktitle = {Proceedings of the PLE Conference 2013: Learning and Diversity in the Cities of the Future}, editor = {Buchem, Ilona and Graham, Attwell and Tur, Gemma}, publisher = {Logos}, address = {Berlin}, pages = {363 -- 373}, year = {2013}, language = {en} } @article{KoppitzSupaporn2013, author = {Koppitz, J{\"o}rg and Supaporn, Worakrit}, title = {Categary equivalences of clones of operations preserving unaryoperations}, series = {COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES}, volume = {66}, journal = {COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES}, number = {2}, publisher = {Publ. House of the Bulgarian Acad. of Sciences}, address = {Sofia}, issn = {1310-1331}, pages = {177 -- 184}, year = {2013}, abstract = {Any clones on arbitrary set A can be written of the form Pol (A)Q for some set Q of relations on A. We consider clones of the form Pal (A)Q where Q is a set of unary relations on a finite set A. A clone Pol (A)Q is said to be a clone on a set of the smallest cardinality with respect to category equivalence if vertical bar A vertical bar <= vertical bar S vertical bar for all finite sets S and all clones C on S that category equivalent to Pol (A)Q. We characterize the clones on a set of the smallest cardinality with respect to category equivalent and show how we can find a clone on a set of the smallest cardinality that category equivalent to a given clone.}, language = {en} } @article{Reich2013, author = {Reich, Sebastian}, title = {A nonparametric ensemble transform method for bayesian inference}, series = {SIAM journal on scientific computing}, volume = {35}, journal = {SIAM journal on scientific computing}, number = {4}, publisher = {Society for Industrial and Applied Mathematics}, address = {Philadelphia}, issn = {1064-8275}, doi = {10.1137/130907367}, pages = {A2013 -- A2024}, year = {2013}, abstract = {Many applications, such as intermittent data assimilation, lead to a recursive application of Bayesian inference within a Monte Carlo context. Popular data assimilation algorithms include sequential Monte Carlo methods and ensemble Kalman filters (EnKFs). These methods differ in the way Bayesian inference is implemented. Sequential Monte Carlo methods rely on importance sampling combined with a resampling step, while EnKFs utilize a linear transformation of Monte Carlo samples based on the classic Kalman filter. While EnKFs have proven to be quite robust even for small ensemble sizes, they are not consistent since their derivation relies on a linear regression ansatz. In this paper, we propose another transform method, which does not rely on any a priori assumptions on the underlying prior and posterior distributions. The new method is based on solving an optimal transportation problem for discrete random variables.}, language = {en} } @article{DebusscheHoegeleImkeller2013, author = {Debussche, Arnaud and Hoegele, Michael and Imkeller, Peter}, title = {The source of stochastic models in conceptual climate dynamics}, series = {Lecture notes in mathematics : a collection of informal reports and seminars}, volume = {2085}, journal = {Lecture notes in mathematics : a collection of informal reports and seminars}, number = {3}, publisher = {Springer}, address = {Berlin}, isbn = {978-3-319-00828-8; 978-3-319-00827-1}, issn = {0075-8434}, doi = {10.1007/978-3-319-00828-8}, pages = {151 -- 157}, year = {2013}, language = {en} } @article{DebusscheHoegeleImkeller2013, author = {Debussche, Arnaud and H{\"o}gele, Michael and Imkeller, Peter}, title = {Localization and metastability}, series = {Lecture notes in mathematics : a collection of informal reports and seminars}, volume = {2085}, journal = {Lecture notes in mathematics : a collection of informal reports and seminars}, publisher = {Springer}, address = {Berlin}, isbn = {978-3-319-00828-8; 978-3-319-00827-1}, issn = {0075-8434}, doi = {10.1007/978-3-319-00828-8_7}, pages = {131 -- 149}, year = {2013}, abstract = {In this chapter, equipped with our previously obtained knowledge of exit and transition times in the limit of small noise amplitude ??0 , we shall investigate the global asymptotic behavior of our jump diffusion process in the time scale in which transitions occur, i.e. in the scale given by ?0(?)=?(1?Bc?(0)),?,?>0 . It turns out that in this time scale, the switching of the diffusion between neighborhoods of the stable solutions ? ± can be well described by a Markov chain jumping back and forth between two states with a characteristic Q-matrix determined by the quantities ?((D±0)c)?(Bc?(0)) as jumping rates.}, language = {en} } @article{DebusscheHoegeleImkeller2013, author = {Debussche, Arnaud and Hoegele, Michael and Imkeller, Peter}, title = {Asymptotic transition times}, series = {Lecture notes in mathematics : a collection of informal reports and seminars}, volume = {2085}, journal = {Lecture notes in mathematics : a collection of informal reports and seminars}, publisher = {Springer}, address = {Berlin}, isbn = {978-3-319-00828-8; 978-3-319-00827-1}, issn = {0075-8434}, doi = {10.1007/978-3-319-00828-8_6}, pages = {121 -- 130}, year = {2013}, language = {en} } @article{DebusscheHoegeleImkeller2013, author = {Debussche, Arnaud and Hoegele, Michael and Imkeller, Peter}, title = {Asymptotic exit times}, series = {Lecture notes in mathematics : a collection of informal reports and seminars}, volume = {2085}, journal = {Lecture notes in mathematics : a collection of informal reports and seminars}, publisher = {Springer}, address = {Berlin}, isbn = {978-3-319-00828-8; 978-3-319-00827-1}, issn = {0075-8434}, doi = {10.1007/978-3-319-00828-8_5}, pages = {87 -- 120}, year = {2013}, language = {en} } @article{DebusscheHoegeleImkeller2013, author = {Debussche, Arnaud and Hoegele, Michael and Imkeller, Peter}, title = {The small deviation of the small noise solution}, series = {Lecture notes in mathematics : a collection of informal reports and seminars}, volume = {2085}, journal = {Lecture notes in mathematics : a collection of informal reports and seminars}, publisher = {Springer}, address = {Berlin}, isbn = {978-3-319-00828-8; 978-3-319-00827-1}, issn = {0075-8434}, doi = {10.1007/978-3-319-00828-8_4}, pages = {69 -- 85}, year = {2013}, language = {en} } @article{DebusscheHoegeleImkeller2013, author = {Debussche, Arnaud and H{\"o}gele, Michael and Imkeller, Peter}, title = {The stochastic chafee-infante equation}, series = {Lecture notes in mathematics : a collection of informal reports and seminars}, volume = {2085}, journal = {Lecture notes in mathematics : a collection of informal reports and seminars}, publisher = {Springer}, address = {Berlin}, isbn = {978-3-319-00828-8; 978-3-319-00827-1}, issn = {0075-8434}, doi = {10.1007/978-3-319-00828-8_3}, pages = {45 -- 68}, year = {2013}, abstract = {In this preparatory chapter, the tools of stochastic analysis needed for the investigation of the asymptotic behavior of the stochastic Chafee-Infante equation are provided. In the first place, this encompasses a recollection of basic facts about L{\´e}vy processes with values in Hilbert spaces. Playing the role of the additive noise processes perturbing the deterministic Chafee-Infante equation in the systems the stochastic dynamics of which will be our main interest, symmetric ?-stable L{\´e}vy processes are in the focus of our investigation (Sect. 3.1).}, language = {en} } @article{DebusscheHoegeleImkeller2013, author = {Debussche, Arnaud and H{\"o}gele, Michael and Imkeller, Peter}, title = {The Fine Dynamics of the Chafee-Infante Equation}, series = {Lecture notes in mathematics : a collection of informal reports and seminars}, volume = {2085}, journal = {Lecture notes in mathematics : a collection of informal reports and seminars}, publisher = {Springer}, address = {Berlin}, isbn = {978-3-319-00828-8; 978-3-319-00827-1}, issn = {0075-8434}, doi = {10.1007/978-3-319-00828-8_2}, pages = {11 -- 43}, year = {2013}, abstract = {In this chapter, we introduce the deterministic Chafee-Infante equation. This equation has been the subject of intense research and is very well understood now. We recall some properties of its longtime dynamics and in particular the structure of its attractor. We then define reduced domains of attraction that will be fundamental in our study and give a result describing precisely the time that a solution starting form a reduced domain of attraction needs to reach a stable equilibrium. This result is then proved using the detailed knowledge of the attractor and classical tools such as the stable and unstable manifolds in a neighborhood of an equilibrium.}, language = {en} } @unpublished{DebusscheHoegeleImkeller2013, author = {Debussche, Arnaud and Hoegele, Michael and Imkeller, Peter}, title = {The dynamics of nonlinear reaction-diffusion equations with small levy noise preface}, series = {Lecture notes in mathematics : a collection of informal reports and seminars}, volume = {2085}, journal = {Lecture notes in mathematics : a collection of informal reports and seminars}, publisher = {Springer}, address = {Berlin}, isbn = {978-3-319-00828-8; 978-3-319-00827-1}, issn = {0075-8434}, pages = {V -- +}, year = {2013}, language = {en} } @unpublished{DebusscheHoegeleImkeller2013, author = {Debussche, Arnaud and H{\"o}gele, Michael and Imkeller, Peter}, title = {The dynamics of nonlinear reaction-diffusion equations with small levy noise}, series = {Lecture notes in mathematics : a collection of informal reports and seminars}, volume = {2085}, journal = {Lecture notes in mathematics : a collection of informal reports and seminars}, publisher = {Springer}, address = {Berlin}, isbn = {978-3-319-00828-8; 978-3-319-00827-1}, issn = {0075-8434}, doi = {10.1007/978-3-319-00828-8_1}, pages = {1 -- 10}, year = {2013}, abstract = {Our primary interest in this book lies in the study of dynamical properties of reaction-diffusion equations perturbed by L{\´e}vy noise of intensity ? in the small noise limit ??0 .}, language = {en} } @article{Schmidt2013, author = {Schmidt, Hans-J{\"u}rgen}, title = {The tetralogy of Birkhoff theorems}, series = {General relativity and gravitation}, volume = {45}, journal = {General relativity and gravitation}, number = {2}, publisher = {Springer}, address = {New York}, issn = {0001-7701}, doi = {10.1007/s10714-012-1478-5}, pages = {395 -- 410}, year = {2013}, abstract = {We classify the existent Birkhoff-type theorems into four classes: first, in field theory, the theorem states the absence of helicity 0- and spin 0-parts of the gravitational field. Second, in relativistic astrophysics, it is the statement that the gravitational far-field of a spherically symmetric star carries, apart from its mass, no information about the star; therefore, a radially oscillating star has a static gravitational far-field. Third, in mathematical physics, Birkhoff's theorem reads: up to singular exceptions of measure zero, the spherically symmetric solutions of Einstein's vacuum field equation with can be expressed by the Schwarzschild metric; for , it is the Schwarzschild-de Sitter metric instead. Fourth, in differential geometry, any statement of the type: every member of a family of pseudo-Riemannian space-times has more isometries than expected from the original metric ansatz, carries the name Birkhoff-type theorem. Within the fourth of these classes we present some new results with further values of dimension and signature of the related spaces; including them are some counterexamples: families of space-times where no Birkhoff-type theorem is valid. These counterexamples further confirm the conjecture, that the Birkhoff-type theorems have their origin in the property, that the two eigenvalues of the Ricci tensor of 2-D pseudo-Riemannian spaces always coincide, a property not having an analogy in higher dimensions. Hence, Birkhoff-type theorems exist only for those physical situations which are reducible to 2-D.}, language = {en} } @article{OsterlohBoeckmannNicolaeetal.2013, author = {Osterloh, Lukas and B{\"o}ckmann, Christine and Nicolae, Doina and Nemuc, Anca}, title = {Regularized inversion of microphysical atmospheric particle parameters - theory and application}, series = {Journal of computational physics}, volume = {237}, journal = {Journal of computational physics}, number = {11}, publisher = {Elsevier}, address = {San Diego}, issn = {0021-9991}, doi = {10.1016/j.jcp.2012.11.040}, pages = {79 -- 94}, year = {2013}, abstract = {Retrieving the distribution of aerosols in the atmosphere via remote sensing techniques is a highly complex task that requires dealing with a wide range of different problems stemming both from Physics and Mathematics. We focus on retrieving this distribution from multi-wavelength lidar data for aerosol ensembles consisting of spherical particles via an iterative regularization technique. The optical efficiencies for spherical scatterers are examined to account for the behavior of the underlying integral equation. The ill-posedness of the problem and the conditioning of the discretized problem are analyzed. Some critical points in the model, like the assumed wavelength-independence of the refractive index and the fixed grid of investigated refractive indices, are studied with regard to their expected impact on the regularized solution. A new Monte-Carlo type method is proposed for retrieval of the refractive index. To validate the results, the developed algorithm is applied to two measurement cases of burning biomass gained from multi-wavelength Raman lidar.}, language = {en} } @article{KarpuzCevikKoppitzetal.2013, author = {Karpuz, Eylem Guzel and Cevik, Ahmet Sinan and Koppitz, J{\"o}rg and Cangul, Ismail Naci}, title = {Some fixed-point results on (generalized) Bruck-Reilly *-extensions of monoids}, series = {Fixed point theory and applications}, journal = {Fixed point theory and applications}, number = {3}, publisher = {Springer}, address = {Cham}, issn = {1687-1812}, doi = {10.1186/1687-1812-2013-78}, pages = {9}, year = {2013}, abstract = {In this paper, we determine necessary and sufficient conditions for Bruck-Reilly and generalized Bruck-Reilly *-extensions of arbitrary monoids to be regular, coregular and strongly pi-inverse. These semigroup classes have applications in various field of mathematics, such as matrix theory, discrete mathematics and p-adic analysis (especially in operator theory). In addition, while regularity and coregularity have so many applications in the meaning of boundaries (again in operator theory), inverse monoids and Bruck-Reilly extensions contain a mixture fixed-point results of algebra, topology and geometry within the purposes of this journal.}, language = {en} } @article{ZoellerHolschneiderHainzl2013, author = {Z{\"o}ller, Gert and Holschneider, Matthias and Hainzl, Sebastian}, title = {The Maximum Earthquake Magnitude in a Time Horizon: Theory and Case Studies}, series = {Bulletin of the Seismological Society of America}, volume = {103}, journal = {Bulletin of the Seismological Society of America}, number = {2A}, publisher = {Seismological Society of America}, address = {Albany}, issn = {0037-1106}, doi = {10.1785/0120120013}, pages = {860 -- 875}, year = {2013}, abstract = {We show how the maximum magnitude within a predefined future time horizon may be estimated from an earthquake catalog within the context of Gutenberg-Richter statistics. The aim is to carry out a rigorous uncertainty assessment, and calculate precise confidence intervals based on an imposed level of confidence a. In detail, we present a model for the estimation of the maximum magnitude to occur in a time interval T-f in the future, given a complete earthquake catalog for a time period T in the past and, if available, paleoseismic events. For this goal, we solely assume that earthquakes follow a stationary Poisson process in time with unknown productivity Lambda and obey the Gutenberg-Richter law in magnitude domain with unknown b-value. The random variables. and b are estimated by means of Bayes theorem with noninformative prior distributions. Results based on synthetic catalogs and on retrospective calculations of historic catalogs from the highly active area of Japan and the low-seismicity, but high-risk region lower Rhine embayment (LRE) in Germany indicate that the estimated magnitudes are close to the true values. Finally, we discuss whether the techniques can be extended to meet the safety requirements for critical facilities such as nuclear power plants. For this aim, the maximum magnitude for all times has to be considered. In agreement with earlier work, we find that this parameter is not a useful quantity from the viewpoint of statistical inference.}, language = {en} } @article{SchmidtSingleton2013, author = {Schmidt, Hans-J{\"u}rgen and Singleton, Douglas}, title = {Exact radial solution in 2+1 gravity with a real scalar field}, series = {Physics letters : B}, volume = {721}, journal = {Physics letters : B}, number = {4-5}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0370-2693}, doi = {10.1016/j.physletb.2013.03.007}, pages = {294 -- 298}, year = {2013}, abstract = {In this Letter we give some general considerations about circularly symmetric, static space-times in 2 + 1 dimensions, focusing first on the surprising (at the time) existence of the BTZ black hole solution. We show that BTZ black holes and Schwarzschild black holes in 3 + 1 dimensions originate from different definitions of a black hole. There are two by-products of this general discussion: (i) we give a new and simple derivation of (2 + 1)-dimensional Anti-de Sitter (AdS) space-time; (ii) we present an exact solution to (2 + 1)-dimensional gravity coupled to a self-interacting real scalar field. The spatial part of the metric of this solution is flat but the temporal part behaves asymptotically like AdS space-time. The scalar field has logarithmic behavior as one would expect for a massless scalar field in flat space-time. The solution can be compared to gravitating scalar field solutions in 3 + 1 dimensions but with certain oddities connected with the (2 + 1)-dimensional character of the space-time. The solution is unique to 2 + 1 dimensions; it does not carry over to 3 + 1 dimensions.}, language = {en} } @article{CotroneiHolschneider2013, author = {Cotronei, Mariantonia and Holschneider, Matthias}, title = {Partial parameterization of orthogonal wavelet matrix filters}, series = {Journal of computational and applied mathematics}, volume = {243}, journal = {Journal of computational and applied mathematics}, number = {4}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0377-0427}, doi = {10.1016/j.cam.2012.11.016}, pages = {113 -- 125}, year = {2013}, abstract = {In this paper we propose a procedure which allows the construction of a large family of FIR d x d matrix wavelet filters by exploiting the one-to-one correspondence between QMF systems and orthogonal operators which commute with the shifts by two. A characterization of the class of filters of full rank type that can be obtained with such procedure is given. In particular, we restrict our attention to a special construction based on the representation of SO(2d) in terms of the elements of its Lie algebra. Explicit expressions for the filters in the case d = 2 are given, as a result of a local analysis of the parameterization obtained from perturbing the Haar system.}, language = {en} } @article{Murr2013, author = {Murr, R{\"u}diger}, title = {Characterization of infinite divisibility by duality formulas application to Levy processes and random measures}, series = {Stochastic processes and their application}, volume = {123}, journal = {Stochastic processes and their application}, number = {5}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0304-4149}, doi = {10.1016/j.spa.2012.12.012}, pages = {1729 -- 1749}, year = {2013}, abstract = {Processes with independent increments are proven to be the unique solutions of duality formulas. This result is based on a simple characterization of infinitely divisible random vectors by a functional equation in which a difference operator appears. This operator is constructed by a variational method and compared to approaches involving chaos decompositions. We also obtain a related characterization of infinitely divisible random measures.}, language = {en} } @article{EichmairMetzger2013, author = {Eichmair, Michael and Metzger, Jan}, title = {Large isoperimetric surfaces in initial data sets}, series = {Journal of differential geometry}, volume = {94}, journal = {Journal of differential geometry}, number = {1}, publisher = {International Press of Boston}, address = {Somerville}, issn = {0022-040X}, pages = {159 -- 186}, year = {2013}, abstract = {We study the isoperimetric structure of asymptotically flat Riemannian 3-manifolds (M, g) that are C-0-asymptotic to Schwarzschild of mass m > 0. Refining an argument due to H. Bray, we obtain an effective volume comparison theorem in Schwarzschild. We use it to show that isoperimetric regions exist in (M, g) for all sufficiently large volumes, and that they are close to centered coordinate spheres. This implies that the volume-preserving stable constant mean curvature spheres constructed by G. Huisken and S.-T. Yau as well as R. Ye as perturbations of large centered coordinate spheres minimize area among all competing surfaces that enclose the same volume. This confirms a conjecture of H. Bray. Our results are consistent with the uniqueness results for volume-preserving stable constant mean curvature surfaces in initial data sets obtained by G. Huisken and S.-T. Yau and strengthened by J. Qing and G. Tian. The additional hypotheses that the surfaces be spherical and far out in the asymptotic region in their results are not necessary in our work.}, language = {en} }