@article{HedayatMahmoudiSchulze2018, author = {Hedayat Mahmoudi, Mahdi and Schulze, Bert-Wolfgang}, title = {A new approach to the second order edge calculus}, series = {Journal of pseudo-differential operators and applications}, volume = {9}, journal = {Journal of pseudo-differential operators and applications}, number = {2}, publisher = {Springer}, address = {Basel}, issn = {1662-9981}, doi = {10.1007/s11868-017-0191-2}, pages = {265 -- 300}, year = {2018}, abstract = {We establish essential steps of an iterative approach to operator algebras, ellipticity and Fredholm property on stratified spaces with singularities of second order. We cover, in particular, corner-degenerate differential operators. Our constructions are focused on the case where no additional conditions of trace and potential type are posed, but this case works well and will be considered in a forthcoming paper as a conclusion of the present calculus.}, language = {en} } @article{Zoeller2018, author = {Z{\"o}ller, Gert}, title = {A statistical model for earthquake recurrence based on the assimilation of paleoseismicity, historic seismicity, and instrumental seismicity}, series = {Journal of geophysical research : Solid earth}, volume = {123}, journal = {Journal of geophysical research : Solid earth}, number = {6}, publisher = {American Geophysical Union}, address = {Washington}, issn = {2169-9313}, doi = {10.1029/2017JB015099}, pages = {4906 -- 4921}, year = {2018}, abstract = {Paleoearthquakes and historic earthquakes are the most important source of information for the estimation of long-term earthquake recurrence intervals in fault zones, because corresponding sequences cover more than one seismic cycle. However, these events are often rare, dating uncertainties are enormous, and missing or misinterpreted events lead to additional problems. In the present study, I assume that the time to the next major earthquake depends on the rate of small and intermediate events between the large ones in terms of a clock change model. Mathematically, this leads to a Brownian passage time distribution for recurrence intervals. I take advantage of an earlier finding that under certain assumptions the aperiodicity of this distribution can be related to the Gutenberg-Richter b value, which can be estimated easily from instrumental seismicity in the region under consideration. In this way, both parameters of the Brownian passage time distribution can be attributed with accessible seismological quantities. This allows to reduce the uncertainties in the estimation of the mean recurrence interval, especially for short paleoearthquake sequences and high dating errors. Using a Bayesian framework for parameter estimation results in a statistical model for earthquake recurrence intervals that assimilates in a simple way paleoearthquake sequences and instrumental data. I present illustrative case studies from Southern California and compare the method with the commonly used approach of exponentially distributed recurrence times based on a stationary Poisson process.}, language = {en} } @article{CarpentierKloppLoeffleretal.2018, author = {Carpentier, Alexandra and Klopp, Olga and L{\"o}ffler, Matthias and Nickl, Richard}, title = {Adaptive confidence sets for matrix completion}, series = {Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability}, volume = {24}, journal = {Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability}, number = {4A}, publisher = {International Statistical Institute}, address = {Voorburg}, issn = {1350-7265}, doi = {10.3150/17-BEJ933}, pages = {2429 -- 2460}, year = {2018}, abstract = {In the present paper, we study the problem of existence of honest and adaptive confidence sets for matrix completion. We consider two statistical models: the trace regression model and the Bernoulli model. In the trace regression model, we show that honest confidence sets that adapt to the unknown rank of the matrix exist even when the error variance is unknown. Contrary to this, we prove that in the Bernoulli model, honest and adaptive confidence sets exist only when the error variance is known a priori. In the course of our proofs, we obtain bounds for the minimax rates of certain composite hypothesis testing problems arising in low rank inference.}, language = {en} } @article{KellerPinchoverPogorzelski2018, author = {Keller, Matthias and Pinchover, Yehuda and Pogorzelski, Felix}, title = {An improved discrete hardy inequality}, series = {The American mathematical monthly : an official publication of the Mathematical Association of America}, volume = {125}, journal = {The American mathematical monthly : an official publication of the Mathematical Association of America}, number = {4}, publisher = {Taylor \& Francis Group}, address = {Philadelphia}, issn = {0002-9890}, doi = {10.1080/00029890.2018.1420995}, pages = {347 -- 350}, year = {2018}, abstract = {In this note, we prove an improvement of the classical discrete Hardy inequality. Our improved Hardy-type inequality holds with a weight w which is strictly greater than the classical Hardy weight w(H)(n) : 1/(2n)(2), where N.}, language = {en} } @article{CarpentierKim2018, author = {Carpentier, Alexandra and Kim, Arlene K. H.}, title = {An iterative hard thresholding estimator for low rank matrix recovery with explicit limiting distribution}, series = {Statistica Sinica}, volume = {28}, journal = {Statistica Sinica}, number = {3}, publisher = {Statistica Sinica, Institute of Statistical Science, Academia Sinica}, address = {Taipei}, issn = {1017-0405}, doi = {10.5705/ss.202016.0103}, pages = {1371 -- 1393}, year = {2018}, abstract = {We consider the problem of low rank matrix recovery in a stochastically noisy high-dimensional setting. We propose a new estimator for the low rank matrix, based on the iterative hard thresholding method, that is computationally efficient and simple. We prove that our estimator is optimal in terms of the Frobenius risk and in terms of the entry-wise risk uniformly over any change of orthonormal basis, allowing us to provide the limiting distribution of the estimator. When the design is Gaussian, we prove that the entry-wise bias of the limiting distribution of the estimator is small, which is of interest for constructing tests and confidence sets for low-dimensional subsets of entries of the low rank matrix.}, language = {en} } @article{LiuMuenchPeyerimhoff2018, author = {Liu, Shiping and M{\"u}nch, Florentin and Peyerimhoff, Norbert}, title = {Bakry-Emery curvature and diameter bounds on graphs}, series = {Calculus of variations and partial differential equations}, volume = {57}, journal = {Calculus of variations and partial differential equations}, number = {2}, publisher = {Springer}, address = {Heidelberg}, issn = {0944-2669}, doi = {10.1007/s00526-018-1334-x}, pages = {9}, year = {2018}, abstract = {We prove finiteness and diameter bounds for graphs having a positive Ricci-curvature bound in the Bakry-{\´E}mery sense. Our first result using only curvature and maximal vertex degree is sharp in the case of hypercubes. The second result depends on an additional dimension bound, but is independent of the vertex degree. In particular, the second result is the first Bonnet-Myers type theorem for unbounded graph Laplacians. Moreover, our results improve diameter bounds from Fathi and Shu (Bernoulli 24(1):672-698, 2018) and Horn et al. (J f{\"u}r die reine und angewandte Mathematik (Crelle's J), 2017, https://doi.org/10.1515/crelle-2017-0038) and solve a conjecture from Cushing et al. (Bakry-{\´E}mery curvature functions of graphs, 2016).}, language = {en} } @inproceedings{OPUS4-41526, title = {Beitr{\"a}ge zum Mathematikunterricht 2017}, editor = {Kortenkamp, Ulrich and Kuzle, Ana}, publisher = {WTM-Verlag}, address = {M{\"u}nster}, isbn = {978-3-95987-072-6}, year = {2018}, language = {de} } @phdthesis{Khalil2018, author = {Khalil, Sara}, title = {Boundary Value Problems on Manifolds with Singularities}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-419018}, school = {Universit{\"a}t Potsdam}, pages = {10, 160}, year = {2018}, abstract = {In the thesis there are constructed new quantizations for pseudo-differential boundary value problems (BVPs) on manifolds with edge. The shape of operators comes from Boutet de Monvel's calculus which exists on smooth manifolds with boundary. The singular case, here with edge and boundary, is much more complicated. The present approach simplifies the operator-valued symbolic structures by using suitable Mellin quantizations on infinite stretched model cones of wedges with boundary. The Mellin symbols themselves are, modulo smoothing ones, with asymptotics, holomorphic in the complex Mellin covariable. One of the main results is the construction of parametrices of elliptic elements in the corresponding operator algebra, including elliptic edge conditions.}, language = {en} } @article{KuehnSorgenfreiGiangrisostomietal.2018, author = {K{\"u}hn, Danilo and Sorgenfrei, Florian and Giangrisostomi, Erika and Jay, Raphael and Musazay, Abdurrahman and Ovsyannikov, Ruslan and Strahlman, Christian and Svensson, Svante and M{\aa}rtensson, Nils and F{\"o}hlisch, Alexander}, title = {Capabilities of angle resolved time of flight electron spectroscopy with the 60 degrees wide angle acceptance lens}, series = {Journal of electron spectroscopy and related phenomena : the international journal on theoretical and experimental aspects of electron spectroscopy}, volume = {224}, journal = {Journal of electron spectroscopy and related phenomena : the international journal on theoretical and experimental aspects of electron spectroscopy}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0368-2048}, doi = {10.1016/j.elspec.2017.06.008}, pages = {45 -- 50}, year = {2018}, abstract = {The simultaneous detection of energy, momentum and temporal information in electron spectroscopy is the key aspect to enhance the detection efficiency in order to broaden the range of scientific applications. Employing a novel 60 degrees wide angle acceptance lens system, based on an additional accelerating electron optical element, leads to a significant enhancement in transmission over the previously employed 30 degrees electron lenses. Due to the performance gain, optimized capabilities for time resolved electron spectroscopy and other high transmission applications with pulsed ionizing radiation have been obtained. The energy resolution and transmission have been determined experimentally utilizing BESSY II as a photon source. Four different and complementary lens modes have been characterized. (C) 2017 The Authors. Published by Elsevier B.V.}, language = {en} } @article{ZemellaThoringHoffmeisteretal.2018, author = {Zemella, Anne and Thoring, Lena and Hoffmeister, Christian and Samalikova, Maria and Ehren, Patricia and W{\"u}stenhagen, Doreen Anja and Kubick, Stefan}, title = {Cell-free protein synthesis as a novel tool for directed glycoengineering of active erythropoietin}, series = {Scientific reports}, volume = {8}, journal = {Scientific reports}, publisher = {Nature Publ. Group}, address = {London}, issn = {2045-2322}, doi = {10.1038/s41598-018-26936-x}, pages = {12}, year = {2018}, abstract = {As one of the most complex post-translational modification, glycosylation is widely involved in cell adhesion, cell proliferation and immune response. Nevertheless glycoproteins with an identical polypeptide backbone mostly differ in their glycosylation patterns. Due to this heterogeneity, the mapping of different glycosylation patterns to their associated function is nearly impossible. In the last years, glycoengineering tools including cell line engineering, chemoenzymatic remodeling and site-specific glycosylation have attracted increasing interest. The therapeutic hormone erythropoietin (EPO) has been investigated in particular by various groups to establish a production process resulting in a defined glycosylation pattern. However commercially available recombinant human EPO shows batch-to-batch variations in its glycoforms. Therefore we present an alternative method for the synthesis of active glycosylated EPO with an engineered O-glycosylation site by combining eukaryotic cell-free protein synthesis and site-directed incorporation of non-canonical amino acids with subsequent chemoselective modifications.}, language = {en} } @article{Gerlach2018, author = {Gerlach, Moritz Reinhardt}, title = {Convergence of dynamics and the Perron-Frobenius operator}, series = {Israel Journal of Mathematics}, volume = {225}, journal = {Israel Journal of Mathematics}, number = {1}, publisher = {Hebrew univ magnes press}, address = {Jerusalem}, issn = {0021-2172}, doi = {10.1007/s11856-018-1671-7}, pages = {451 -- 463}, year = {2018}, abstract = {We complete the picture how the asymptotic behavior of a dynamical system is reflected by properties of the associated Perron-Frobenius operator. Our main result states that strong convergence of the powers of the Perron-Frobenius operator is equivalent to setwise convergence of the underlying dynamic in the measure algebra. This situation is furthermore characterized by uniform mixing-like properties of the system.}, language = {en} } @article{ChangSchulze2018, author = {Chang, Der-Chen and Schulze, Bert-Wolfgang}, title = {Corner spaces and Mellin quantization}, series = {Journal of nonlinear and convex analysis : an international journal}, volume = {19}, journal = {Journal of nonlinear and convex analysis : an international journal}, number = {2}, publisher = {Yokohama Publishers}, address = {Yokohama}, issn = {1345-4773}, pages = {179 -- 195}, year = {2018}, abstract = {Manifolds with corners in the present investigation are non-smooth configurations - specific stratified spaces - with an incomplete metric such as cones, manifolds with edges, or corners of piecewise smooth domains in Euclidean space. We focus here on operators on such "corner manifolds" of singularity order <= 2, acting in weighted corner Sobolev spaces. The corresponding corner degenerate pseudo-differential operators are formulated via Mellin quantizations, and they also make sense on infinite singular cones.}, language = {en} } @misc{BlanchardScott2018, author = {Blanchard, Gilles and Scott, Clayton}, title = {Corrigendum to: Classification with asymmetric label noise}, series = {Electronic journal of statistics}, volume = {12}, journal = {Electronic journal of statistics}, number = {1}, publisher = {Institute of Mathematical Statistics}, address = {Cleveland}, issn = {1935-7524}, doi = {10.1214/18-EJS1422}, pages = {1779 -- 1781}, year = {2018}, abstract = {We point out a flaw in Lemma 15 of [1]. We also indicate how the main results of that section are still valid using a modified argument.}, language = {en} } @article{PathirajaMoradkhaniMarshalletal.2018, author = {Pathiraja, Sahani Darschika and Moradkhani, H. and Marshall, L. and Sharma, Ashish and Geenens, G.}, title = {Data-driven model uncertainty estimation in hydrologic data assimilation}, series = {Water resources research : WRR / American Geophysical Union}, volume = {54}, journal = {Water resources research : WRR / American Geophysical Union}, number = {2}, publisher = {American Geophysical Union}, address = {Washington}, issn = {0043-1397}, doi = {10.1002/2018WR022627}, pages = {1252 -- 1280}, year = {2018}, abstract = {The increasing availability of earth observations necessitates mathematical methods to optimally combine such data with hydrologic models. Several algorithms exist for such purposes, under the umbrella of data assimilation (DA). However, DA methods are often applied in a suboptimal fashion for complex real-world problems, due largely to several practical implementation issues. One such issue is error characterization, which is known to be critical for a successful assimilation. Mischaracterized errors lead to suboptimal forecasts, and in the worst case, to degraded estimates even compared to the no assimilation case. Model uncertainty characterization has received little attention relative to other aspects of DA science. Traditional methods rely on subjective, ad hoc tuning factors or parametric distribution assumptions that may not always be applicable. We propose a novel data-driven approach (named SDMU) to model uncertainty characterization for DA studies where (1) the system states are partially observed and (2) minimal prior knowledge of the model error processes is available, except that the errors display state dependence. It includes an approach for estimating the uncertainty in hidden model states, with the end goal of improving predictions of observed variables. The SDMU is therefore suited to DA studies where the observed variables are of primary interest. Its efficacy is demonstrated through a synthetic case study with low-dimensional chaotic dynamics and a real hydrologic experiment for one-day-ahead streamflow forecasting. In both experiments, the proposed method leads to substantial improvements in the hidden states and observed system outputs over a standard method involving perturbation with Gaussian noise.}, language = {en} } @article{HoferTemmelHoudebert2018, author = {Hofer-Temmel, Christoph and Houdebert, Pierre}, title = {Disagreement percolation for Gibbs ball models}, series = {Stochastic processes and their application}, volume = {129}, journal = {Stochastic processes and their application}, number = {10}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0304-4149}, doi = {10.1016/j.spa.2018.11.003}, pages = {3922 -- 3940}, year = {2018}, abstract = {We generalise disagreement percolation to Gibbs point processes of balls with varying radii. This allows to establish the uniqueness of the Gibbs measure and exponential decay of pair correlations in the low activity regime by comparison with a sub-critical Boolean model. Applications to the Continuum Random Cluster model and the Quermass-interaction model are presented. At the core of our proof lies an explicit dependent thinning from a Poisson point process to a dominated Gibbs point process. (C) 2018 Elsevier B.V. All rights reserved.}, language = {en} } @article{BlanchardHoffmannReiss2018, author = {Blanchard, Gilles and Hoffmann, Marc and Reiss, Markus}, title = {Early stopping for statistical inverse problems via truncated SVD estimation}, series = {Electronic journal of statistics}, volume = {12}, journal = {Electronic journal of statistics}, number = {2}, publisher = {Institute of Mathematical Statistics}, address = {Cleveland}, issn = {1935-7524}, doi = {10.1214/18-EJS1482}, pages = {3204 -- 3231}, year = {2018}, abstract = {We consider truncated SVD (or spectral cut-off, projection) estimators for a prototypical statistical inverse problem in dimension D. Since calculating the singular value decomposition (SVD) only for the largest singular values is much less costly than the full SVD, our aim is to select a data-driven truncation level (m) over cap is an element of {1, . . . , D} only based on the knowledge of the first (m) over cap singular values and vectors. We analyse in detail whether sequential early stopping rules of this type can preserve statistical optimality. Information-constrained lower bounds and matching upper bounds for a residual based stopping rule are provided, which give a clear picture in which situation optimal sequential adaptation is feasible. Finally, a hybrid two-step approach is proposed which allows for classical oracle inequalities while considerably reducing numerical complexity.}, language = {en} } @article{FladFladHarutyunyanSchulze2018, author = {Flad, Heinz-J{\"u}rgen and Flad-Harutyunyan, Gohar and Schulze, Bert-Wolfgang}, title = {Ellipticity of the quantum mechanical Hamiltonians}, series = {Journal of pseudo-differential operators and applications}, volume = {9}, journal = {Journal of pseudo-differential operators and applications}, number = {3}, publisher = {Springer}, address = {Basel}, issn = {1662-9981}, doi = {10.1007/s11868-017-0201-4}, pages = {451 -- 467}, year = {2018}, abstract = {In paper (Flad and Harutyunyan in Discrete Contin Dyn Syst 420-429, 2011) is shown that the Hamiltonian of the helium atom in the Born-Oppenheimer approximation, in the case if two particles coincide, is an edge-degenerate operator, which is elliptic in the corresponding edge calculus. The aim of this paper is an analogous investigation in the case if all three particles coincide. More precisely, we show that the Hamiltonian in the mentioned case is a corner-degenerate operator, which is elliptic as an operator in the corner analysis.}, language = {en} } @article{KaminskiSchlagenhaufRappetal.2018, author = {Kaminski, Jakob A. and Schlagenhauf, Florian and Rapp, Michael Armin and Awasthi, Swapnil and Ruggeri, Barbara and Deserno, Lorenz and Banaschewski, Tobias and Bokde, Arun L. W. and Bromberg, Uli and B{\"u}chel, Christian and Quinlan, Erin Burke and Desrivieres, Sylvane and Flor, Herta and Frouin, Vincent and Garavan, Hugh and Gowland, Penny and Ittermann, Bernd and Martinot, Jean-Luc and Martinot, Marie-Laure Paillere and Nees, Frauke and Orfanos, Dimitri Papadopoulos and Paus, Tomas and Poustka, Luise and Smolka, Michael N. and Fr{\"o}hner, Juliane H. and Walter, Henrik and Whelan, Robert and Ripke, Stephan and Schumann, Gunter and Heinz, Andreas}, title = {Epigenetic variance in dopamine D2 receptor}, series = {Translational Psychiatry}, volume = {8}, journal = {Translational Psychiatry}, publisher = {Nature Publ. Group}, address = {New York}, organization = {IMAGEN Consortium}, issn = {2158-3188}, doi = {10.1038/s41398-018-0222-7}, pages = {11}, year = {2018}, abstract = {Genetic and environmental factors both contribute to cognitive test performance. A substantial increase in average intelligence test results in the second half of the previous century within one generation is unlikely to be explained by genetic changes. One possible explanation for the strong malleability of cognitive performance measure is that environmental factors modify gene expression via epigenetic mechanisms. Epigenetic factors may help to understand the recent observations of an association between dopamine-dependent encoding of reward prediction errors and cognitive capacity, which was modulated by adverse life events. The possible manifestation of malleable biomarkers contributing to variance in cognitive test performance, and thus possibly contributing to the "missing heritability" between estimates from twin studies and variance explained by genetic markers, is still unclear. Here we show in 1475 healthy adolescents from the IMaging and GENetics (IMAGEN) sample that general IQ (gIQ) is associated with (1) polygenic scores for intelligence, (2) epigenetic modification of DRD2 gene, (3) gray matter density in striatum, and (4) functional striatal activation elicited by temporarily surprising reward-predicting cues. Comparing the relative importance for the prediction of gIQ in an overlapping subsample, our results demonstrate neurobiological correlates of the malleability of gIQ and point to equal importance of genetic variance, epigenetic modification of DRD2 receptor gene, as well as functional striatal activation, known to influence dopamine neurotransmission. Peripheral epigenetic markers are in need of confirmation in the central nervous system and should be tested in longitudinal settings specifically assessing individual and environmental factors that modify epigenetic structure.}, language = {en} } @article{AfshariMoeinSomogyvariValleyetal.2018, author = {Afshari Moein, Mohammad J. and Somogyv{\´a}ri, M{\´a}rk and Valley, Beno{\^i}t and Jalali, Mohammadreza and L{\"o}w, Simon and Bayer, Peter}, title = {Fracture network characterization using stress-based tomography}, series = {Journal of geophysical research : JGR}, volume = {123}, journal = {Journal of geophysical research : JGR}, number = {11}, publisher = {American Geophysical Union}, address = {Washington}, issn = {2169-9313}, doi = {10.1029/2018JB016438}, pages = {9324 -- 9340}, year = {2018}, abstract = {Information on structural features of a fracture network at early stages of Enhanced Geothermal System development is mostly restricted to borehole images and, if available, outcrop data. However, using this information to image discontinuities in deep reservoirs is difficult. Wellbore failure data provides only some information on components of the in situ stress state and its heterogeneity. Our working hypothesis is that slip on natural fractures primarily controls these stress heterogeneities. Based on this, we introduce stress-based tomography in a Bayesian framework to characterize the fracture network and its heterogeneity in potential Enhanced Geothermal System reservoirs. In this procedure, first a random initial discrete fracture network (DFN) realization is generated based on prior information about the network. The observations needed to calibrate the DFN are based on local variations of the orientation and magnitude of at least one principal stress component along boreholes. A Markov Chain Monte Carlo sequence is employed to update the DFN iteratively by a fracture translation within the domain. The Markov sequence compares the simulated stress profile with the observed stress profiles in the borehole, evaluates each iteration with Metropolis-Hastings acceptance criteria, and stores acceptable DFN realizations in an ensemble. Finally, this obtained ensemble is used to visualize the potential occurrence of fractures in a probability map, indicating possible fracture locations and lengths. We test this methodology to reconstruct simple synthetic and more complex outcrop-based fracture networks and successfully image the significant fractures in the domain.}, language = {en} } @article{LonnemannHasselhorn2018, author = {Lonnemann, Jan and Hasselhorn, Marcus}, title = {Fr{\"u}he mathematische Bildung}, series = {Fr{\"u}he Bildung}, volume = {7}, journal = {Fr{\"u}he Bildung}, number = {3}, publisher = {Hogrefe}, address = {G{\"o}ttingen}, issn = {2191-9186}, doi = {10.1026/2191-9186/a000379}, pages = {129 -- 134}, year = {2018}, abstract = {Im vorliegenden Beitrag werden aktuelle Forschungstrends im Bereich der fr{\"u}hen mathematischen Bildung im Kontext j{\"u}ngst formulierter Zieldimensionen f{\"u}r die fr{\"u}he mathematische Bildung (siehe Benz et al., 2017) dargestellt. Es wird auf spielbasierte F{\"o}rdermaßnahmen, Kompetenzen im Bereich „Raum und Form", den Einfluss sprachlicher Parameter auf die Entwicklung mathematischer Kompetenzen sowie auf mathematikbezogene Kompetenzen fr{\"u}hp{\"a}dagogischer Fachkr{\"a}fte eingegangen. Dar{\"u}ber hinaus werden die Ergebnisse einer aktuellen Feldstudie zur F{\"o}rderung fr{\"u}her mathematischer Kompetenzen (siehe Dillon, Kannan, Dean, Spelke \& Duflo, 2017) vorgestellt. Abschließend wird die Entwicklung und Implementierung anschlussf{\"a}higer Bildungskonzepte als eine der zentralen Herausforderungen zuk{\"u}nftiger Forschungs- und Bildungsbem{\"u}hungen diskutiert}, language = {de} }