@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;<f) be a fence, also called a zigzag poset. As usual, we denote by In the symmetric inverse semigroup on Xn. We say that a transformation α∈In is fence-preserving if x<fy implies that xα<fyα, for all x,y in the domain of α. In this paper, we study the semigroup PFIn of all partial fence-preserving injections of Xn and its subsemigroup IFn={α∈PFIn:α-1∈PFIn}. Clearly, IFn is an inverse semigroup and contains all regular elements of PFIn. We characterize the Green's relations for the semigroup IFn. Further, we prove that the semigroup IFn is generated by its elements with rank ≥n-2. Moreover, for n∈2N, we find the least generating set and calculate the rank of IFn.},
  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{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{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}
}
@misc{BeniniSchenkel2017,
  author    = {Benini, Marco and Schenkel, Alexander},
  title     = {Quantum field theories on categories fibered in groupoids},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  number    = {895},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-43154},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-431541},
  pages     = {48},
  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}
}
@inproceedings{AudinDucourtiouxOuedraogoetal.2017,
  author    = {Audin, Mich{\`e}le and Ducourtioux, Catherine and Ou{\´e}draogo, Fran{\c{c}}oise and Schulz, Ren{\´e} and Delgado, Julio and Ruzhansky, Michael and Lebeau, Gilles},
  title     = {Integral Fourier operators},
  editor    = {Paycha, Sylvie},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  isbn      = {978-3-86956-413-5},
  issn      = {2199-4951},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-402657},
  pages     = {xxi, 229},
  year      = {2017},
  abstract  = {This volume of contributions based on lectures delivered at a school on Fourier Integral Operators held in Ouagadougou, Burkina Faso, 14-26 September 2015, provides an introduction to Fourier Integral Operators (FIO) for a readership of Master and PhD students as well as any interested layperson. Considering the wide spectrum of their applications and the richness of the mathematical tools they involve, FIOs lie the cross-road of many a field. This volume offers the necessary background, whether analytic or geometric, to get acquainted with FIOs, complemented by more advanced material presenting various aspects of active research in that area.},
  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}
}
@misc{SerthPodlesnyBornsteinetal.2017,
  author    = {Serth, Sebastian and Podlesny, Nikolai and Bornstein, Marvin and Lindemann, Jan and Latt, Johanna and Selke, Jan and Schlosser, Rainer and Boissier, Martin and Uflacker, Matthias},
  title     = {An interactive platform to simulate dynamic pricing competition on online marketplaces},
  series = {2017 IEEE 21st International Enterprise Distributed Object Computing Conference (EDOC)},
  journal   = {2017 IEEE 21st International Enterprise Distributed Object Computing Conference (EDOC)},
  publisher = {Institute of Electrical and Electronics Engineers},
  address   = {New York},
  isbn      = {978-1-5090-3045-3},
  issn      = {2325-6354},
  doi       = {10.1109/EDOC.2017.17},
  pages     = {61 -- 66},
  year      = {2017},
  abstract  = {E-commerce marketplaces are highly dynamic with constant competition. While this competition is challenging for many merchants, it also provides plenty of opportunities, e.g., by allowing them to automatically adjust prices in order to react to changing market situations. For practitioners however, testing automated pricing strategies is time-consuming and potentially hazardously when done in production. Researchers, on the other side, struggle to study how pricing strategies interact under heavy competition. As a consequence, we built an open continuous time framework to simulate dynamic pricing competition called Price Wars. The microservice-based architecture provides a scalable platform for large competitions with dozens of merchants and a large random stream of consumers. Our platform stores each event in a distributed log. This allows to provide different performance measures enabling users to compare profit and revenue of various repricing strategies in real-time. For researchers, price trajectories are shown which ease evaluating mutual price reactions of competing strategies. Furthermore, merchants can access historical marketplace data and apply machine learning. By providing a set of customizable, artificial merchants, users can easily simulate both simple rule-based strategies as well as sophisticated data-driven strategies using demand learning to optimize their pricing strategies.},
  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{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}
}
@unpublished{FedchenkoTarkhanov2017,
  author    = {Fedchenko, Dmitry and Tarkhanov, Nikolai Nikolaevich},
  title     = {A Rad{\´o} Theorem for the Porous Medium Equation},
  series = {Preprints des Instituts f{\"u}r Mathematik der Universit{\"a}t Potsdam},
  volume    = {6},
  journal   = {Preprints des Instituts f{\"u}r Mathematik der Universit{\"a}t Potsdam},
  number    = {1},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-102735},
  pages     = {12},
  year      = {2017},
  abstract  = {We prove that each locally Lipschitz continuous function satisfying the porous medium equation away from the set of its zeroes is actually a weak solution of this equation in the whole domain.},
  language  = {en}
}
@unpublished{ShlapunovTarkhanov2017,
  author    = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich},
  title     = {Golusin-Krylov Formulas in Complex Analysis},
  series = {Preprints des Instituts f{\"u}r Mathematik der Universit{\"a}t Potsdam},
  volume    = {6},
  journal   = {Preprints des Instituts f{\"u}r Mathematik der Universit{\"a}t Potsdam},
  number    = {2},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-102774},
  pages     = {25},
  year      = {2017},
  abstract  = {This is a brief survey of a constructive technique of analytic continuation related to an explicit integral formula of Golusin and Krylov (1933). It goes far beyond complex analysis and applies to the Cauchy problem for elliptic partial differential equations as well. As started in the classical papers, the technique is elaborated in generalised Hardy spaces also called Hardy-Smirnov spaces.},
  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{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{HerzogEhlertFritz2017,
  author    = {Herzog, Moritz and Ehlert, Antje and Fritz, Annemarie},
  title     = {A Competency Model of Place Value Understanding in South African Primary School Pupils},
  series = {African Journal of Research in Mathematics, Science and Technology Education},
  volume    = {21},
  journal   = {African Journal of Research in Mathematics, Science and Technology Education},
  publisher = {Routledge, Taylor \& Francis Group},
  address   = {Abingdon},
  issn      = {1811-7295},
  doi       = {10.1080/18117295.2017.1279453},
  pages     = {37 -- 48},
  year      = {2017},
  abstract  = {Although the general development of mathematical abilities in primary school has been the focus of many researchers, the development of place value understanding has rarely been investigated to date. This is possibly due to the lack of conceptual approaches and empirical studies related to this topic. To fill this gap, a theory-driven and empirically validated model was developed that describes five sequential conceptual levels of place value understanding. The level sequence model gives us the ability to estimate general abilities and difficulties in primary school pupils in the development of a conceptual place value understanding. The level sequence model was tried and tested in Germany, and given that number words are very differently constructed in German and in the languages used in South African classrooms, this study aims to investigate whether this level sequence model can be transferred to South Africa. The findings based on the responses of 198 Grade 2-4 learners show that the English translation of the test items results in the same item level allocation as the original German test items, especially for the three basic levels. Educational implications are provided, in particular concrete suggestions on how place value might be taught according to the model and how to collect specific empirical data related to place value understanding.},
  language  = {en}
}
@misc{Paycha2017,
  author    = {Paycha, Sylvie},
  title     = {Interview with Pierre Cartier},
  series = {The mathematical intelligencer},
  volume    = {39},
  journal   = {The mathematical intelligencer},
  publisher = {Springer},
  address   = {New York},
  issn      = {0343-6993},
  doi       = {10.1007/s00283-016-9673-y},
  pages     = {15 -- 21},
  year      = {2017},
  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{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{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}
}
@misc{BeckerSchenkelSzabo2017,
  author    = {Becker, Christian and Schenkel, Alexander and Szabo, Richard J.},
  title     = {Differential cohomology and locally covariant quantum field theory},
  series = {Reviews in Mathematical Physics},
  volume    = {29},
  journal   = {Reviews in Mathematical Physics},
  number    = {1},
  publisher = {World Scientific},
  address   = {Singapore},
  issn      = {0129-055X},
  doi       = {10.1142/S0129055X17500039},
  pages     = {42},
  year      = {2017},
  abstract  = {We study differential cohomology on categories of globally hyperbolic Lorentzian manifolds. The Lorentzian metric allows us to define a natural transformation whose kernel generalizes Maxwell's equations and fits into a restriction of the fundamental exact sequences of differential cohomology. We consider smooth Pontryagin duals of differential cohomology groups, which are subgroups of the character groups. We prove that these groups fit into smooth duals of the fundamental exact sequences of differential cohomology and equip them with a natural presymplectic structure derived from a generalized Maxwell Lagrangian. The resulting presymplectic Abelian groups are quantized using the CCR-functor, which yields a covariant functor from our categories of globally hyperbolic Lorentzian manifolds to the category of C∗-algebras. We prove that this functor satisfies the causality and time-slice axioms of locally covariant quantum field theory, but that it violates the locality axiom. We show that this violation is precisely due to the fact that our functor has topological subfunctors describing the Pontryagin duals of certain singular cohomology groups. As a byproduct, we develop a Fr{\´e}chet-Lie group structure on differential cohomology groups.},
  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{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{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{ElinShoikhetTarkhanov2017,
  author    = {Elin, Mark and Shoikhet, David and Tarkhanov, Nikolai Nikolaevich},
  title     = {Analytic Semigroups of Holomorphic Mappings and Composition Operators},
  series = {Computational Methods and Function Theory},
  volume    = {18},
  journal   = {Computational Methods and Function Theory},
  number    = {2},
  publisher = {Springer},
  address   = {Heidelberg},
  issn      = {1617-9447},
  doi       = {10.1007/s40315-017-0227-x},
  pages     = {269 -- 294},
  year      = {2017},
  abstract  = {In this manuscript we provide a review on the classical and resent results related to the problem of analytic extension in parameter for a semigroup of holomorphic self-mappings of the unit ball in a complex Banach space and its relation to the linear continuous semigroup of composition operators.},
  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}
}
@misc{ShlapunovTarkhanov2017,
  author    = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich},
  title     = {Golusin-Krylov formulas in complex analysis},
  series = {Complex variables and elliptic equations},
  volume    = {63},
  journal   = {Complex variables and elliptic equations},
  number    = {7-8},
  publisher = {Routledge},
  address   = {Abingdon},
  issn      = {1747-6933},
  doi       = {10.1080/17476933.2017.1395872},
  pages     = {1142 -- 1167},
  year      = {2017},
  abstract  = {This is a brief survey of a constructive technique of analytic continuation related to an explicit integral formula of Golusin and Krylov (1933). It goes far beyond complex analysis and applies to the Cauchy problem for elliptic partial differential equations as well. As started in the classical papers, the technique is elaborated in generalised Hardy spaces also called Hardy-Smirnov spaces.},
  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{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{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{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}
}
@techreport{SultanowVolkovCox2017,
  author    = {Sultanow, Eldar and Volkov, Denis and Cox, Sean},
  title     = {Introducing a Finite State Machine for processing Collatz Sequences},
  edition   = {1st version},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-399223},
  year      = {2017},
  abstract  = {The present work will introduce a Finite State Machine (FSM) that processes any Collatz Sequence; further, we will endeavor to investigate its behavior in relationship to transformations of a special infinite input. Moreover, we will prove that the machine's word transformation is equivalent to the standard Collatz number transformation and subsequently discuss the possibilities for use of this approach at solving similar problems. The benefit of this approach is that the investigation of the word transformation performed by the Finite State Machine is less complicated than the traditional number-theoretical transformation.},
  language  = {en}
}
@incollection{Kortenkamp2017,
  author    = {Kortenkamp, Ulrich},
  title     = {Raum und Form},
  series = {Basiswissen Lehrerbildung: Mathematik unterrichten},
  booktitle = {Basiswissen Lehrerbildung: Mathematik unterrichten},
  editor    = {Abshagen, Maike and Barzel, B{\"a}rbel and Kramer, J{\"u}rg and Riecke-Baulecke, Thomas and R{\"o}sken-Winter, Bettina and Selter, Christoph},
  publisher = {Kallmeyer},
  address   = {Seelze},
  publisher      = {Universit{\"a}t Potsdam},
  pages     = {99 -- 112},
  year      = {2017},
  language  = {de}
}
@article{KocJanuchtaHoefflerThomaetal.2017,
  author    = {Koc-Januchta, Marta and H{\"o}ffler, Tim and Thoma, Gun-Brit and Prechtl, Helmut and Leutner, Detlev},
  title     = {Visualizers versus verbalizers},
  series = {Computers in human behavior},
  volume    = {68},
  journal   = {Computers in human behavior},
  publisher = {Elsevier},
  address   = {Oxford},
  issn      = {0747-5632},
  doi       = {10.1016/j.chb.2016.11.028},
  pages     = {170 -- 179},
  year      = {2017},
  abstract  = {This study was conducted in order to examine the differences between visualizers and verbalizers in the way they gaze at pictures and texts while learning. Using a collection of questionnaires, college students were classified according to their visual or verbal cognitive style and were asked to learn about two different, in terms of subject and type of knowledge, topics by means of text-picture combinations. Eye-tracking was used to investigate their gaze behavior. The results show that visualizers spent significantly more time inspecting pictures than verbalizers, while verbalizers spent more time inspecting texts. Results also suggest that both visualizers' and verbalizers' way of learning is active but mostly within areas providing the source of information in line with their cognitive style (pictures or text). Verbalizers tended to enter non-informative, irrelevant areas of pictures sooner than visualizers. The comparison of learning outcomes showed that the group of visualizers achieved better results than the group of verbalizers on a comprehension test.},
  language  = {en}
}
@misc{StraderSchneiderSchorlemmer2017,
  author    = {Strader, Anne and Schneider, Max and Schorlemmer, Danijel},
  title     = {Erratum zu: Strader, Anne; Schneider, Max; Schorlemmer, Danijel: Prospective and retrospective evaluation of five-year earthquake forecast models for California (Geophysical Journal International, 211 (2017) 1, S. 239 - 251, https://doi.org/10.1093/gji/ggx268)},
  series = {Geophysical journal international},
  volume    = {212},
  journal   = {Geophysical journal international},
  number    = {2},
  publisher = {Oxford Univ. Press},
  address   = {Oxford},
  issn      = {0956-540X},
  doi       = {10.1093/gji/ggx496},
  pages     = {1314 -- 1314},
  year      = {2017},
  abstract  = {S-test results for the USGS and RELM forecasts. The differences between the simulated log-likelihoods and the observed log-likelihood are labelled on the horizontal axes, with scaling adjustments for the 40year.retro experiment. The horizontal lines represent the confidence intervals, within the 0.05 significance level, for each forecast and experiment. If this range contains a log-likelihood difference of zero, the forecasted log-likelihoods are consistent with the observed, and the forecast passes the S-test (denoted by thin lines). If the minimum difference within this range does not contain zero, the forecast fails the S-test for that particular experiment, denoted by thick lines. Colours distinguish between experiments (see Table 2 for explanation of experiment durations). Due to anomalously large likelihood differences, S-test results for Wiemer-Schorlemmer.ALM during the 10year.retro and 40year.retro experiments are not displayed. The range of log-likelihoods for the Holliday-et-al.PI forecast is lower than for the other forecasts due to relatively homogeneous forecasted seismicity rates and use of a small fraction of the RELM testing region.},
  language  = {en}
}
@phdthesis{LindbladPetersen2017,
  author    = {Lindblad Petersen, Oliver},
  title     = {The Cauchy problem for the linearised Einstein equation and the Goursat problem for wave equations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-410216},
  school      = {Universit{\"a}t Potsdam},
  pages     = {108},
  year      = {2017},
  abstract  = {In this thesis, we study two initial value problems arising in general relativity. The first is the Cauchy problem for the linearised Einstein equation on general globally hyperbolic spacetimes, with smooth and distributional initial data. We extend well-known results by showing that given a solution to the linearised constraint equations of arbitrary real Sobolev regularity, there is a globally defined solution, which is unique up to addition of gauge solutions. Two solutions are considered equivalent if they differ by a gauge solution. Our main result is that the equivalence class of solutions depends continuously on the corre- sponding equivalence class of initial data. We also solve the linearised constraint equations in certain cases and show that there exist arbitrarily irregular (non-gauge) solutions to the linearised Einstein equation on Minkowski spacetime and Kasner spacetime. In the second part, we study the Goursat problem (the characteristic Cauchy problem) for wave equations. We specify initial data on a smooth compact Cauchy horizon, which is a lightlike hypersurface. This problem has not been studied much, since it is an initial value problem on a non-globally hyperbolic spacetime. Our main result is that given a smooth function on a non-empty, smooth, compact, totally geodesic and non-degenerate Cauchy horizon and a so called admissible linear wave equation, there exists a unique solution that is defined on the globally hyperbolic region and restricts to the given function on the Cauchy horizon. Moreover, the solution depends continuously on the initial data. A linear wave equation is called admissible if the first order part satisfies a certain condition on the Cauchy horizon, for example if it vanishes. Interestingly, both existence of solution and uniqueness are false for general wave equations, as examples show. If we drop the non-degeneracy assumption, examples show that existence of solution fails even for the simplest wave equation. The proof requires precise energy estimates for the wave equation close to the Cauchy horizon. In case the Ricci curvature vanishes on the Cauchy horizon, we show that the energy estimates are strong enough to prove local existence and uniqueness for a class of non-linear wave equations. Our results apply in particular to the Taub-NUT spacetime and the Misner spacetime. It has recently been shown that compact Cauchy horizons in spacetimes satisfying the null energy condition are necessarily smooth and totally geodesic. Our results therefore apply if the spacetime satisfies the null energy condition and the Cauchy horizon is compact and non-degenerate.},
  language  = {en}
}
@phdthesis{Pedeches2017,
  author    = {P{\´e}d{\`e}ches, Laure},
  title     = {Stochastic models for collective motions of populations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-405491},
  school      = {Universit{\"a}t Potsdam},
  pages     = {187},
  year      = {2017},
  abstract  = {Stochastisches Modell f{\"u}r kollektive Bewegung von Populationen In dieser Doktorarbeit befassen wir uns mit stochastischen Systemen, die eines der mysteri{\"o}sesten biologischen Ph{\"a}nomene als Modell darstellen: die kollektive Bewegung von Gemeinschaften. Diese werden bei V{\"o}gel- und Fischschw{\"a}rmen, aber auch bei manchen Bakterien, Viehherden oder gar bei Menschen beobachtet. Dieser Verhaltenstyp spielt ebenfalls in anderen Bereichen wie Finanzwesen, Linguistik oder auch Robotik eine Rolle. Wir nehmen uns der Dynamik einer Gruppe von N Individuen, insbesondere zweier asymptotischen Verhaltenstypen an. Einerseits befassen wir uns mit den Eigenschaften der Ergodizit{\"a}t in Langzeit: Existenz einer invarianten Wahrscheinlichkeitsverteilung durch Ljapunow-Funktionen, und Konvergenzrate der {\"U}bergangshalbgruppe gegen diese Wahrscheinlichkeit. Eine ebenfalls zentrale Thematik unserer Forschung ist der Begriff Flocking: es wird damit definiert, dass eine Gruppe von Individuen einen dynamischen Konsens ohne hierarchische Struktur erreichen kann; mathematisch gesehen entspricht dies der Aneinanderreihung der Geschwindigkeiten und dem Zusammenkommen des Schwarmes. Andererseits gehen wir das Ph{\"a}nomen der "Propagation of Chaos" an, wenn die Anzahl N der Teilchen ins Unendliche tendiert: die Bewegungen der jeweiligen Individuen werden asymptotisch unabh{\"a}ngig. Unser Ausgangspunkt ist das Cucker-Smale-Modell, ein deterministisches kinetisches Molekular-Modell f{\"u}r eine Gruppe ohne hierarchische Struktur. Die Wechselwirkung zwischen zwei Teilchen variiert gem{\"a}ß deren "Kommunikationsrate", die wiederum von deren relativen Entfernung abh{\"a}ngt und polynomisch abnimmt. Im ersten Kapitel adressieren wir das asymptotische Verhalten eines Cucker-Smale-Modells mit Rauschst{\"o}rung und dessen Varianten. Kapitel 2 stellt mehrere Definitionen des Flockings in einem Zufallsrahmen dar: diverse stochastische Systeme, die verschiedenen Rauschformen entsprechen (die eine gest{\"o}rte Umgebung, den "freien Willen" des jeweiligen Individuums oder eine unterbrochene {\"U}bertragung suggerieren) werden im Zusammenhang mit diesen Begriffen unter die Lupe genommen. Das dritte Kapitel basiert auf der "Cluster Expansion"-Methode aus der statistischen Mechanik. Wir beweisen die exponentielle Ergodizit{\"a}t von gewissen nicht-Markow-Prozessen mit nicht-glattem Drift und wenden diese Ergebnisse auf St{\"o}rungen des Ornstein-Uhlenbeck-Prozesses an. Im letzten Teil, nehmen wir uns der zweidimensionalen parabolisch-elliptischen Gleichung von Keller-Segel an. Wir beweisen die Existenz einer L{\"o}sung, welche in gewisser Hinsicht einzig ist, indem wir, mittels Vergleich mit Bessel-Prozessen und der Dirichlet Formtheorie, m{\"o}gliche Stoßtypen zwischen den Teilchen ermitteln.},
  language  = {en}
}
@phdthesis{Mera2017,
  author    = {Mera, Azal Jaafar Musa},
  title     = {The Navier-Stokes equations for elliptic quasicomplexes},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-398495},
  school      = {Universit{\"a}t Potsdam},
  pages     = {101},
  year      = {2017},
  abstract  = {The classical Navier-Stokes equations of hydrodynamics are usually written in terms of vector analysis. More promising is the formulation of these equations in the language of differential forms of degree one. In this way the study of Navier-Stokes equations includes the analysis of the de Rham complex. In particular, the Hodge theory for the de Rham complex enables one to eliminate the pressure from the equations. The Navier-Stokes equations constitute a parabolic system with a nonlinear term which makes sense only for one-forms. A simpler model of dynamics of incompressible viscous fluid is given by Burgers' equation. This work is aimed at the study of invariant structure of the Navier-Stokes equations which is closely related to the algebraic structure of the de Rham complex at step 1. To this end we introduce Navier-Stokes equations related to any elliptic quasicomplex of first order differential operators. These equations are quite similar to the classical Navier-Stokes equations including generalised velocity and pressure vectors. Elimination of the pressure from the generalised Navier-Stokes equations gives a good motivation for the study of the Neumann problem after Spencer for elliptic quasicomplexes. Such a study is also included in the work.We start this work by discussion of Lam{\´e} equations within the context of elliptic quasicomplexes on compact manifolds with boundary. The non-stationary Lam{\´e} equations form a hyperbolic system. However, the study of the first mixed problem for them gives a good experience to attack the linearised Navier-Stokes equations. On this base we describe a class of non-linear perturbations of the Navier-Stokes equations, for which the solvability results still hold.},
  language  = {en}
}
@inproceedings{VallerianiRoellyKulik2017,
  author    = {Valleriani, Angelo and Roelly, Sylvie and Kulik, Alexei Michajlovič},
  title     = {Stochastic processes with applications in the natural sciences},
  series = {Lectures in pure and applied mathematics},
  booktitle = {Lectures in pure and applied mathematics},
  number    = {4},
  editor    = {Roelly, Sylvie and H{\"o}gele, Michael and Rafler, Mathias},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  isbn      = {978-3-86956-414-2},
  issn      = {2199-4951},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-401802},
  pages     = {ix, 124},
  year      = {2017},
  abstract  = {The interdisciplinary workshop STOCHASTIC PROCESSES WITH APPLICATIONS IN THE NATURAL SCIENCES was held in Bogot{\´a}, at Universidad de los Andes from December 5 to December 9, 2016. It brought together researchers from Colombia, Germany, France, Italy, Ukraine, who communicated recent progress in the mathematical research related to stochastic processes with application in biophysics. The present volume collects three of the four courses held at this meeting by Angelo Valleriani, Sylvie Rœlly and Alexei Kulik. A particular aim of this collection is to inspire young scientists in setting up research goals within the wide scope of fields represented in this volume. Angelo Valleriani, PhD in high energy physics, is group leader of the team "Stochastic processes in complex and biological systems" from the Max-Planck-Institute of Colloids and Interfaces, Potsdam. Sylvie Rœlly, Docteur en Math{\´e}matiques, is the head of the chair of Probability at the University of Potsdam. Alexei Kulik, Doctor of Sciences, is a Leading researcher at the Institute of Mathematics of Ukrainian National Academy of Sciences.},
  language  = {en}
}
@phdthesis{Muecke2017,
  author    = {M{\"u}cke, Nicole},
  title     = {Direct and inverse problems in machine learning},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-403479},
  school      = {Universit{\"a}t Potsdam},
  pages     = {159},
  year      = {2017},
  abstract  = {We analyze an inverse noisy regression model under random design with the aim of estimating the unknown target function based on a given set of data, drawn according to some unknown probability distribution. Our estimators are all constructed by kernel methods, which depend on a Reproducing Kernel Hilbert Space structure using spectral regularization methods. A first main result establishes upper and lower bounds for the rate of convergence under a given source condition assumption, restricting the class of admissible distributions. But since kernel methods scale poorly when massive datasets are involved, we study one example for saving computation time and memory requirements in more detail. We show that Parallelizing spectral algorithms also leads to minimax optimal rates of convergence provided the number of machines is chosen appropriately. We emphasize that so far all estimators depend on the assumed a-priori smoothness of the target function and on the eigenvalue decay of the kernel covariance operator, which are in general unknown. To obtain good purely data driven estimators constitutes the problem of adaptivity which we handle for the single machine problem via a version of the Lepskii principle.},
  language  = {en}
}
@unpublished{PolkovnikovTarkhanov2017,
  author    = {Polkovnikov, Alexander and Tarkhanov, Nikolai Nikolaevich},
  title     = {A Riemann-Hilbert problem for the Moisil-Teodorescu system},
  volume    = {6},
  number    = {3},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-397036},
  pages     = {31},
  year      = {2017},
  abstract  = {In a bounded domain with smooth boundary in R^3 we consider the stationary Maxwell equations for a function u with values in R^3 subject to a nonhomogeneous condition (u,v)_x = u_0 on the boundary, where v is a given vector field and u_0 a function on the boundary. We specify this problem within the framework of the Riemann-Hilbert boundary value problems for the Moisil-Teodorescu system. This latter is proved to satisfy the Shapiro-Lopaniskij condition if an only if the vector v is at no point tangent to the boundary. The Riemann-Hilbert problem for the Moisil-Teodorescu system fails to possess an adjoint boundary value problem with respect to the Green formula, which satisfies the Shapiro-Lopatinskij condition. We develop the construction of Green formula to get a proper concept of adjoint boundary value problem.},
  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{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{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}
}
@phdthesis{Santilli2017,
  author    = {Santilli, Mario},
  title     = {Higher order rectifiability in Euclidean space},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-403632},
  school      = {Universit{\"a}t Potsdam},
  pages     = {45},
  year      = {2017},
  abstract  = {The first main goal of this thesis is to develop a concept of approximate differentiability of higher order for subsets of the Euclidean space that allows to characterize higher order rectifiable sets, extending somehow well known facts for functions. We emphasize that for every subset A of the Euclidean space and for every integer k ≥ 2 we introduce the approximate differential of order k of A and we prove it is a Borel map whose domain is a (possibly empty) Borel set. This concept could be helpful to deal with higher order rectifiable sets in applications. The other goal is to extend to general closed sets a well known theorem of Alberti on the second order rectifiability properties of the boundary of convex bodies. The Alberti theorem provides a stratification of second order rectifiable subsets of the boundary of a convex body based on the dimension of the (convex) normal cone. Considering a suitable generalization of this normal cone for general closed subsets of the Euclidean space and employing some results from the first part we can prove that the same stratification exists for every closed set.},
  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{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{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}
}
@phdthesis{Solms2017,
  author    = {Solms, Alexander Maximilian},
  title     = {Integrating nonlinear mixed effects and physiologically-based modeling approaches for the analysis of repeated measurement studies},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-397070},
  school      = {Universit{\"a}t Potsdam},
  pages     = {x, 141},
  year      = {2017},
  abstract  = {During the drug discovery \& development process, several phases encompassing a number of preclinical and clinical studies have to be successfully passed to demonstrate safety and efficacy of a new drug candidate. As part of these studies, the characterization of the drug's pharmacokinetics (PK) is an important aspect, since the PK is assumed to strongly impact safety and efficacy. To this end, drug concentrations are measured repeatedly over time in a study population. The objectives of such studies are to describe the typical PK time-course and the associated variability between subjects. Furthermore, underlying sources significantly contributing to this variability, e.g. the use of comedication, should be identified. The most commonly used statistical framework to analyse repeated measurement data is the nonlinear mixed effect (NLME) approach. At the same time, ample knowledge about the drug's properties already exists and has been accumulating during the discovery \& development process: Before any drug is tested in humans, detailed knowledge about the PK in different animal species has to be collected. This drug-specific knowledge and general knowledge about the species' physiology is exploited in mechanistic physiological based PK (PBPK) modeling approaches -it is, however, ignored in the classical NLME modeling approach. Mechanistic physiological based models aim to incorporate relevant and known physiological processes which contribute to the overlying process of interest. In comparison to data--driven models they are usually more complex from a mathematical perspective. For example, in many situations, the number of model parameters outrange the number of measurements and thus reliable parameter estimation becomes more complex and partly impossible. As a consequence, the integration of powerful mathematical estimation approaches like the NLME modeling approach -which is widely used in data-driven modeling -and the mechanistic modeling approach is not well established; the observed data is rather used as a confirming instead of a model informing and building input. Another aggravating circumstance of an integrated approach is the inaccessibility to the details of the NLME methodology so that these approaches can be adapted to the specifics and needs of mechanistic modeling. Despite the fact that the NLME modeling approach exists for several decades, details of the mathematical methodology is scattered around a wide range of literature and a comprehensive, rigorous derivation is lacking. Available literature usually only covers selected parts of the mathematical methodology. Sometimes, important steps are not described or are only heuristically motivated, e.g. the iterative algorithm to finally determine the parameter estimates. Thus, in the present thesis the mathematical methodology of NLME modeling is systemically described and complemented to a comprehensive description, comprising the common theme from ideas and motivation to the final parameter estimation. Therein, new insights for the interpretation of different approximation methods used in the context of the NLME modeling approach are given and illustrated; furthermore, similarities and differences between them are outlined. Based on these findings, an expectation-maximization (EM) algorithm to determine estimates of a NLME model is described. Using the EM algorithm and the lumping methodology by Pilari2010, a new approach on how PBPK and NLME modeling can be combined is presented and exemplified for the antibiotic levofloxacin. Therein, the lumping identifies which processes are informed by the available data and the respective model reduction improves the robustness in parameter estimation. Furthermore, it is shown how apriori known factors influencing the variability and apriori known unexplained variability is incorporated to further mechanistically drive the model development. Concludingly, correlation between parameters and between covariates is automatically accounted for due to the mechanistic derivation of the lumping and the covariate relationships. A useful feature of PBPK models compared to classical data-driven PK models is in the possibility to predict drug concentration within all organs and tissue in the body. Thus, the resulting PBPK model for levofloxacin is used to predict drug concentrations and their variability within soft tissues which are the site of action for levofloxacin. These predictions are compared with data of muscle and adipose tissue obtained by microdialysis, which is an invasive technique to measure a proportion of drug in the tissue, allowing to approximate the concentrations in the interstitial fluid of tissues. Because, so far, comparing human in vivo tissue PK and PBPK predictions are not established, a new conceptual framework is derived. The comparison of PBPK model predictions and microdialysis measurements shows an adequate agreement and reveals further strengths of the presented new approach. We demonstrated how mechanistic PBPK models, which are usually developed in the early stage of drug development, can be used as basis for model building in the analysis of later stages, i.e. in clinical studies. As a consequence, the extensively collected and accumulated knowledge about species and drug are utilized and updated with specific volunteer or patient data. The NLME approach combined with mechanistic modeling reveals new insights for the mechanistic model, for example identification and quantification of variability in mechanistic processes. This represents a further contribution to the learn \& confirm paradigm across different stages of drug development. Finally, the applicability of mechanism--driven model development is demonstrated on an example from the field of Quantitative Psycholinguistics to analyse repeated eye movement data. Our approach gives new insight into the interpretation of these experiments and the processes behind.},
  language  = {en}
}
@misc{WeisserStueblerMatheisetal.2017,
  author    = {Weisser, Karin and St{\"u}bler, Sabine and Matheis, Walter and Huisinga, Wilhelm},
  title     = {Towards toxicokinetic modelling of aluminium exposure from adjuvants in medicinal products},
  series = {Regulatory toxicology and pharmacology : official journal of the International Society for Regulatory Toxicology and Pharmacology},
  volume    = {88},
  journal   = {Regulatory toxicology and pharmacology : official journal of the International Society for Regulatory Toxicology and Pharmacology},
  publisher = {Elsevier},
  address   = {San Diego},
  issn      = {0273-2300},
  doi       = {10.1016/j.yrtph.2017.02.018},
  pages     = {310 -- 321},
  year      = {2017},
  abstract  = {As a potentially toxic agent on nervous system and bone, the safety of aluminium exposure from adjuvants in vaccines and subcutaneous immune therapy (SCIT) products has to be continuously reevaluated, especially regarding concomitant administrations. For this purpose, knowledge on absorption and disposition of aluminium in plasma and tissues is essential. Pharmacokinetic data after vaccination in humans, however, are not available, and for methodological and ethical reasons difficult to obtain. To overcome these limitations, we discuss the possibility of an in vitro-in silico approach combining a toxicokinetic model for aluminium disposition with biorelevant kinetic absorption parameters from adjuvants. We critically review available kinetic aluminium-26 data for model building and, on the basis of a reparameterized toxicokinetic model (Nolte et al., 2001), we identify main modelling gaps. The potential of in vitro dissolution experiments for the prediction of intramuscular absorption kinetics of aluminium after vaccination is explored. It becomes apparent that there is need for detailed in vitro dissolution and in vivo absorption data to establish an in vitro-in vivo correlation (IVIVC) for aluminium adjuvants. We conclude that a combination of new experimental data and further refinement of the Nolte model has the potential to fill a gap in aluminium risk assessment. (C) 2017 Elsevier Inc. All rights reserved.},
  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}
}