@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{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{HartungBenaryWolfetal.2017, author = {Hartung, Niklas and Benary, Uwe and Wolf, Jana and Kofahl, Bente}, title = {Paracrine and autocrine regulation of gene expression by Wnt-inhibitor Dickkopf in wild-type and mutant hepatocytes}, series = {BMC systems biology}, volume = {11}, journal = {BMC systems biology}, publisher = {BioMed Central}, address = {London}, issn = {1752-0509}, doi = {10.1186/s12918-017-0470-9}, pages = {16}, year = {2017}, abstract = {Background: Cells are able to communicate and coordinate their function within tissues via secreted factors. Aberrant secretion by cancer cells can modulate this intercellular communication, in particular in highly organised tissues such as the liver. Hepatocytes, the major cell type of the liver, secrete Dickkopf (Dkk), which inhibits Wnt/beta-catenin signalling in an autocrine and paracrine manner. Consequently, Dkk modulates the expression of Wnt/beta-catenin target genes. We present a mathematical model that describes the autocrine and paracrine regulation of hepatic gene expression by Dkk under wild-type conditions as well as in the presence of mutant cells. Results: Our spatial model describes the competition of Dkk and Wnt at receptor level, intra-cellular Wnt/beta-catenin signalling, and the regulation of target gene expression for 21 individual hepatocytes. Autocrine and paracrine regulation is mediated through a feedback mechanism via Dkk and Dkk diffusion along the porto-central axis. Along this axis an APC concentration gradient is modelled as experimentally detected in liver. Simulations of mutant cells demonstrate that already a single mutant cell increases overall Dkk concentration. The influence of the mutant cell on gene expression of surrounding wild-type hepatocytes is limited in magnitude and restricted to hepatocytes in close proximity. To explore the underlying molecular mechanisms, we perform a comprehensive analysis of the model parameters such as diffusion coefficient, mutation strength and feedback strength. Conclusions: Our simulations show that Dkk concentration is elevated in the presence of a mutant cell. However, the impact of these elevated Dkk levels on wild-type hepatocytes is confined in space and magnitude. The combination of inter-and intracellular processes, such as Dkk feedback, diffusion and Wnt/beta-catenin signal transduction, allow wild-type hepatocytes to largely maintain their gene expression.}, language = {en} } @article{HartungHuynhGaudyMarquesteetal.2017, author = {Hartung, Niklas and Huynh, Cecilia T. -K. and Gaudy-Marqueste, Caroline and Flavian, Antonin and Malissen, Nausicaa and Richard-Lallemand, Marie-Aleth and Hubert, Florence and Grob, Jean-Jacques}, title = {Study of metastatic kinetics in metastatic melanoma treated with B-RAF inhibitors: Introducing mathematical modelling of kinetics into the therapeutic decision}, series = {PLoS one}, volume = {12}, journal = {PLoS one}, publisher = {PLoS}, address = {San Fransisco}, issn = {1932-6203}, doi = {10.1371/journal.pone.0176080}, pages = {11}, year = {2017}, abstract = {Background Evolution of metastatic melanoma (MM) under B-RAF inhibitors (BRAFi) is unpredictable, but anticipation is crucial for therapeutic decision. Kinetics changes in metastatic growth are driven by molecular and immune events, and thus we hypothesized that they convey relevant information for decision making. Patients and methods We used a retrospective cohort of 37 MM patients treated by BRAFi only with at least 2 close CT-scans available before BRAFi, as a model to study kinetics of metastatic growth before, under and after BRAFi. All metastases (mets) were individually measured at each CT-scan. From these measurements, different measures of growth kinetics of each met and total tumor volume were computed at different time points. A historical cohort permitted to build a reference model for the expected spontaneous disease kinetics without BRAFi. All variables were included in Cox and multistate regression models for survival, to select best candidates for predicting overall survival. Results Before starting BRAFi, fast kinetics and moreover a wide range of kinetics (fast and slow growing mets in a same patient) were pejorative markers. At the first assessment after BRAFi introduction, high heterogeneity of kinetics predicted short survival, and added independent information over RECIST progression in multivariate analysis. Metastatic growth rates after BRAFi discontinuation was usually not faster than before BRAFi introduction, but they were often more heterogeneous than before. Conclusions Monitoring kinetics of different mets before and under BRAFi by repeated CT-scan provides information for predictive mathematical modelling. Disease kinetics deserves more interest}, 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{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} } @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} } @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} } @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} }