TY - GEN A1 - Zöller, Gert A1 - Holschneider, Matthias T1 - Reply to “Comment on ‘The Maximum Possible and the Maximum Expected Earthquake Magnitude for Production‐Induced Earthquakes at the Gas Field in Groningen, The Netherlands’ by Gert Zöller and Matthias Holschneider” by Mathias Raschke T2 - Bulletin of the Seismological Society of America Y1 - 2018 U6 - https://doi.org/10.1785/0120170131 SN - 0037-1106 SN - 1943-3573 VL - 108 IS - 2 SP - 1029 EP - 1030 PB - Seismological Society of America CY - Albany ER - TY - JOUR A1 - Zöller, Gert T1 - A statistical model for earthquake recurrence based on the assimilation of paleoseismicity, historic seismicity, and instrumental seismicity JF - Journal of geophysical research : Solid earth N2 - 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. KW - statistical seismology KW - paleoearthquakes KW - stochastic models KW - seismic hazard Y1 - 2018 U6 - https://doi.org/10.1029/2017JB015099 SN - 2169-9313 SN - 2169-9356 VL - 123 IS - 6 SP - 4906 EP - 4921 PB - American Geophysical Union CY - Washington ER - TY - BOOK A1 - Zhuchok, Anatolii V. T1 - Relatively free doppelsemigroups N2 - A doppelalgebra is an algebra defined on a vector space with two binary linear associative operations. Doppelalgebras play a prominent role in algebraic K-theory. We consider doppelsemigroups, that is, sets with two binary associative operations satisfying the axioms of a doppelalgebra. Doppelsemigroups are a generalization of semigroups and they have relationships with such algebraic structures as interassociative semigroups, restrictive bisemigroups, dimonoids, and trioids. In the lecture notes numerous examples of doppelsemigroups and of strong doppelsemigroups are given. The independence of axioms of a strong doppelsemigroup is established. A free product in the variety of doppelsemigroups is presented. We also construct a free (strong) doppelsemigroup, a free commutative (strong) doppelsemigroup, a free n-nilpotent (strong) doppelsemigroup, a free n-dinilpotent (strong) doppelsemigroup, and a free left n-dinilpotent doppelsemigroup. Moreover, the least commutative congruence, the least n-nilpotent congruence, the least n-dinilpotent congruence on a free (strong) doppelsemigroup and the least left n-dinilpotent congruence on a free doppelsemigroup are characterized. The book addresses graduate students, post-graduate students, researchers in algebra and interested readers. N2 - Eine Doppelalgebra ist eine auf einem Vektorraum definierte Algebra mit zwei binären linearen assoziativen Operationen. Doppelalgebren spielen eine herausragende Rolle in der algebraischen K-Theorie. Wir betrachten Doppelhalbgruppen, d.h Mengen mit zwei binären assoziativen Operationen, welche die Axiome der Doppelhalbgruppe erfüllen. Doppelhalbgruppen sind Veralgemeinerungen von Halbgruppen und sie stehen in Beziehung zu solchen algebraischen Strukturen wie interassoziative Halbgruppen, restriktive Bihalbgruppen, Dimonoiden und Trioden. In dieser Lecture Notes werden eine Vielzahl von Beispielen für Doppelhalbgruppen und strong Doppelhalbgruppen gegeben. Die Unabhängigkeit der Axiome für Doppelhalbgruppen wird nachgewiesen. Ein freies Produkt in der Varietät der Doppelhalbgruppen wird vorgestellt. Wir konstruieren auch eine freie (kommutative) strong Doppelhalbgruppe, eine freie n-dinilpotent (strong) Doppelhalbgruppe und eine freie Links n-dinilpotent Doppelhalbgruppe. Darüber hinaus werden die kleinste n-nilpotente Kogruenz, die kleinste n-dinilpotente Kongruenz auf der freien (strong) Doppelhalbgruppe und die kleinste n-dinilpotente Kongruenz auf einer freien Doppelhalbgruppe charakterisiert. Das Buch richtet sich an Graduierte, Doktoranden, Forscher in Algebra und interessierte Leser. T3 - Lectures in pure and applied mathematics - 5 KW - doppelsemigroup KW - interassociativity KW - free algebra KW - semigroup KW - congruence Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-407719 SN - 978-3-86956-427-2 SN - 2199-4951 SN - 2199-496X IS - 5 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Zemella, Anne A1 - Thoring, Lena A1 - Hoffmeister, Christian A1 - Samalikova, Maria A1 - Ehren, Patricia A1 - Wüstenhagen, Doreen Anja A1 - Kubick, Stefan T1 - Cell-free protein synthesis as a novel tool for directed glycoengineering of active erythropoietin JF - Scientific reports N2 - 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. Y1 - 2018 U6 - https://doi.org/10.1038/s41598-018-26936-x SN - 2045-2322 VL - 8 PB - Nature Publ. Group CY - London ER - TY - JOUR A1 - Wang, Guang A1 - Li, Pei-zhi A1 - Zhang, Shi-yao A1 - Zhong, Shan A1 - Chu, Chang A1 - Zeng, Shufei A1 - Yan, Yu A1 - Cheng, Xin A1 - Chuai, Manli A1 - Hocher, Berthold A1 - Yang, Xuesong T1 - Lipopolysaccharides (LPS) Induced Angiogenesis During Chicken Embryogenesis is Abolished by Combined ETA/ETB Receptor Blockade JF - Cellular physiology and biochemistry : international journal of experimental cellular physiology, biochemistry and pharmacology N2 - Background/Aims: Angiogenesis plays a key role during embryonic development. The vascular endothelin (ET) system is involved in the regulation of angiogenesis. Lipopolysaccharides (LPS) could induce angiogenesis. The effects of ET blockers on baseline and LPS-stimulated angiogenesis during embryonic development remain unknown so far. Methods: The blood vessel density (BVD) of chorioallantoic membranes (CAMs), which were treated with saline (control), LPS, and/or BQ123 and the ETB blocker BQ788, were quantified and analyzed using an IPP 6.0 image analysis program. Moreover, the expressions of ET-1, ET-2, ET3, ET receptor A (ETRA), ET receptor B (ETRB) and VEGFR2 mRNA during embryogenesis were analyzed by semi-quantitative RT-PCR. Results: All components of the ET system are detectable during chicken embryogenesis. LPS increased angiogenesis substantially. This process was completely blocked by the treatment of a combination of the ETA receptor blockers-BQ123 and the ETB receptor blocker BQ788. This effect was accompanied by a decrease in ETRA, ETRB, and VEGFR2 gene expression. However, the baseline angiogenesis was not affected by combined ETA/ETB receptor blockade. Conclusion: During chicken embryogenesis, the LPS-stimulated angiogenesis, but not baseline angiogenesis, is sensitive to combined ETA/ETB receptor blockade. KW - Lipopolysaccharides (LPS) KW - Angiogenesis KW - Chicken chorioallantoic membrane (CAM) KW - Endothelin (ET) Y1 - 2018 U6 - https://doi.org/10.1159/000492547 SN - 1015-8987 SN - 1421-9778 VL - 48 IS - 5 SP - 2084 EP - 2090 PB - Karger CY - Basel ER - TY - JOUR A1 - Vidal-Garcia, Marta A1 - Bandara, Lashi A1 - Keogh, J. Scott T1 - ShapeRotator BT - an R tool for standardized rigid rotations of articulated three-dimensional structures with application for geometric morphometrics JF - Ecology and evolution N2 - The quantification of complex morphological patterns typically involves comprehensive shape and size analyses, usually obtained by gathering morphological data from all the structures that capture the phenotypic diversity of an organism or object. Articulated structures are a critical component of overall phenotypic diversity, but data gathered from these structures are difficult to incorporate into modern analyses because of the complexities associated with jointly quantifying 3D shape in multiple structures. While there are existing methods for analyzing shape variation in articulated structures in two-dimensional (2D) space, these methods do not work in 3D, a rapidly growing area of capability and research. Here, we describe a simple geometric rigid rotation approach that removes the effect of random translation and rotation, enabling the morphological analysis of 3D articulated structures. Our method is based on Cartesian coordinates in 3D space, so it can be applied to any morphometric problem that also uses 3D coordinates (e.g., spherical harmonics). We demonstrate the method by applying it to a landmark-based dataset for analyzing shape variation using geometric morphometrics. We have developed an R tool (ShapeRotator) so that the method can be easily implemented in the commonly used R package geomorph and MorphoJ software. This method will be a valuable tool for 3D morphological analyses in articulated structures by allowing an exhaustive examination of shape and size diversity. KW - articulation KW - morphology KW - motion correction KW - multi-modular morphology Y1 - 2018 U6 - https://doi.org/10.1002/ece3.4018 SN - 2045-7758 VL - 8 IS - 9 SP - 4669 EP - 4675 PB - Wiley CY - Hoboken ER - TY - JOUR A1 - Siddiqui, Tarique Adnan A1 - Maute, Astrid A1 - Pedatella, Nick A1 - Yamazaki, Yosuke A1 - Lühr, Hermann A1 - Stolle, Claudia T1 - On the variability of the semidiurnal solar and lunar tides of the equatorial electrojet during sudden stratospheric warmings JF - Annales geophysicae N2 - The variabilities of the semidiurnal solar and lunar tides of the equatorial electrojet (EEJ) are investigated during the 2003, 2006, 2009 and 2013 major sudden stratospheric warming (SSW) events in this study. For this purpose, ground-magnetometer recordings at the equatorial observatories in Huancayo and Fuquene are utilized. Results show a major enhancement in the amplitude of the EEJ semidiurnal lunar tide in each of the four warming events. The EEJ semidiurnal solar tidal amplitude shows an amplification prior to the onset of warmings, a reduction during the deceleration of the zonal mean zonal wind at 60 degrees N and 10 hPa, and a second enhancement a few days after the peak reversal of the zonal mean zonal wind during all four SSWs. Results also reveal that the amplitude of the EEJ semidiurnal lunar tide becomes comparable or even greater than the amplitude of the EEJ semidiurnal solar tide during all these warming events. The present study also compares the EEJ semidiurnal solar and lunar tidal changes with the variability of the migrating semidiurnal solar (SW2) and lunar (M2) tides in neutral temperature and zonal wind obtained from numerical simulations at E-region heights. A better agreement between the enhancements of the EEJ semidiurnal lunar tide and the M2 tide is found in comparison with the enhancements of the EEJ semidiurnal solar tide and the SW2 tide in both the neutral temperature and zonal wind at the E-region altitudes. Y1 - 2018 U6 - https://doi.org/10.5194/angeo-36-1545-2018 SN - 0992-7689 SN - 1432-0576 VL - 36 IS - 6 SP - 1545 EP - 1562 PB - Copernicus CY - Göttingen ER - TY - JOUR A1 - Salamat, Mona A1 - Zöller, Gert A1 - Zare, Mehdi A1 - Amini, Mortaza T1 - The maximum expected earthquake magnitudes in different future time intervals of six seismotectonic zones of Iran and its surroundings JF - Journal of seismology N2 - One of the crucial components in seismic hazard analysis is the estimation of the maximum earthquake magnitude and associated uncertainty. In the present study, the uncertainty related to the maximum expected magnitude mu is determined in terms of confidence intervals for an imposed level of confidence. Previous work by Salamat et al. (Pure Appl Geophys 174:763-777, 2017) shows the divergence of the confidence interval of the maximum possible magnitude m(max) for high levels of confidence in six seismotectonic zones of Iran. In this work, the maximum expected earthquake magnitude mu is calculated in a predefined finite time interval and imposed level of confidence. For this, we use a conceptual model based on a doubly truncated Gutenberg-Richter law for magnitudes with constant b-value and calculate the posterior distribution of mu for the time interval T-f in future. We assume a stationary Poisson process in time and a Gutenberg-Richter relation for magnitudes. The upper bound of the magnitude confidence interval is calculated for different time intervals of 30, 50, and 100 years and imposed levels of confidence alpha = 0.5, 0.1, 0.05, and 0.01. The posterior distribution of waiting times T-f to the next earthquake with a given magnitude equal to 6.5, 7.0, and7.5 are calculated in each zone. In order to find the influence of declustering, we use the original and declustered version of the catalog. The earthquake catalog of the territory of Iran and surroundings are subdivided into six seismotectonic zones Alborz, Azerbaijan, Central Iran, Zagros, Kopet Dagh, and Makran. We assume the maximum possible magnitude m(max) = 8.5 and calculate the upper bound of the confidence interval of mu in each zone. The results indicate that for short time intervals equal to 30 and 50 years and imposed levels of confidence 1 - alpha = 0.95 and 0.90, the probability distribution of mu is around mu = 7.16-8.23 in all seismic zones. KW - Maximum expected earthquake magnitude KW - Future time interval KW - Level of confidence KW - Iran Y1 - 2018 U6 - https://doi.org/10.1007/s10950-018-9780-7 SN - 1383-4649 SN - 1573-157X VL - 22 IS - 6 SP - 1485 EP - 1498 PB - Springer CY - Dordrecht ER - TY - JOUR A1 - Rungrottheera, Wannarut A1 - Lyu, Xiaojing A1 - Schulze, Bert-Wolfgang T1 - Parameter-dependent edge calculus and corner parametrices JF - Journal of nonlinear and convex analysis : an international journal N2 - Let B be a compact manifold with smooth edge of dimension > 0. We study the interplay between parameter-dependent edge algebra algebra on B and operator families belonging to the corner calculus, and we characterize parametrices in the corner case. KW - Edge calculus KW - corner parametrices Y1 - 2018 SN - 1345-4773 SN - 1880-5221 VL - 19 IS - 12 SP - 2021 EP - 2051 PB - Yokohama Publishers CY - Yokohama ER - TY - JOUR A1 - Paycha, Sylvie T1 - When the market wins over research and higher education JF - Sustainable Futures for Higher Education : the Making of Knowledge Makers N2 - In this chapter, an overview of systematic eradication of basic science foci in European universities in the last two decades is given. This happens under the slogan of optimisation of the university education to the needs and demands of the society. It is pointed out that reliance on “market demands” brings with it long-term deficiencies in the maintenance of basic and advanced knowledge construction in societies necessary for long-term future technological advances. University policies that claim improvement of higher education towards more immediate efficiency may end up with the opposite effect of affecting its quality and long term expected positive impact on society. Y1 - 2018 SN - 978-3-319-96035-7 SN - 978-3-319-96034-0 U6 - https://doi.org/10.1007/978-3-319-96035-7_2 SN - 2364-6799 VL - 7 SP - 23 EP - 28 PB - Springer CY - Cham ER - TY - JOUR A1 - Pathiraja, Sahani Darschika A1 - Moradkhani, H. A1 - Marshall, L. A1 - Sharma, Ashish A1 - Geenens, G. T1 - Data-driven model uncertainty estimation in hydrologic data assimilation JF - Water resources research : WRR / American Geophysical Union N2 - 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. KW - data assimilation KW - model error KW - uncertainty quantification KW - particle filter KW - nonparametric statistics Y1 - 2018 U6 - https://doi.org/10.1002/2018WR022627 SN - 0043-1397 SN - 1944-7973 VL - 54 IS - 2 SP - 1252 EP - 1280 PB - American Geophysical Union CY - Washington ER - TY - JOUR A1 - Pathiraja, Sahani Darschika A1 - Anghileri, Daniela A1 - Burlando, Paolo A1 - Sharma, Ashish A1 - Marshall, Lucy A1 - Moradkhani, Hamid T1 - Time-varying parameter models for catchments with land use change BT - the importance of model structure JF - Hydrology and earth system sciences : HESS N2 - Rapid population and economic growth in Southeast Asia has been accompanied by extensive land use change with consequent impacts on catchment hydrology. Modeling methodologies capable of handling changing land use conditions are therefore becoming ever more important and are receiving increasing attention from hydrologists. A recently developed data-assimilation-based framework that allows model parameters to vary through time in response to signals of change in observations is considered for a medium-sized catchment (2880 km(2)) in northern Vietnam experiencing substantial but gradual land cover change. We investigate the efficacy of the method as well as the importance of the chosen model structure in ensuring the success of a time-varying parameter method. The method was used with two lumped daily conceptual models (HBV and HyMOD) that gave good-quality streamflow predictions during pre-change conditions. Although both time-varying parameter models gave improved streamflow predictions under changed conditions compared to the time-invariant parameter model, persistent biases for low flows were apparent in the HyMOD case. It was found that HyMOD was not suited to representing the modified baseflow conditions, resulting in extreme and unrealistic time-varying parameter estimates. This work shows that the chosen model can be critical for ensuring the time-varying parameter framework successfully models streamflow under changing land cover conditions. It can also be used to determine whether land cover changes (and not just meteorological factors) contribute to the observed hydrologic changes in retrospective studies where the lack of a paired control catchment precludes such an assessment. Y1 - 2018 U6 - https://doi.org/10.5194/hess-22-2903-2018 SN - 1027-5606 SN - 1607-7938 VL - 22 IS - 5 SP - 2903 EP - 2919 PB - Copernicus CY - Göttingen ER - TY - JOUR A1 - Omori, Toshihiro A1 - Winter, Katja A1 - Shinohara, Kyosuke A1 - Hamada, Hiroshi A1 - Ishikawa, Takuji T1 - Simulation of the nodal flow of mutant embryos with a small number of cilia BT - comparison of mechanosensing and vesicle transport hypotheses JF - Royal Society Open Science N2 - Left-right (L-R) asymmetry in the body plan is determined by nodal flow in vertebrate embryos. Shinohara et al. (Shinohara K et al. 2012 Nat. Commun. 3, 622 (doi:10.1038/ncomms1624)) used Dpcd and Rfx3 mutant mouse embryos and showed that only a few cilia were sufficient to achieve L-R asymmetry. However, the mechanism underlying the breaking of symmetry by such weak ciliary flow is unclear. Flow-mediated signals associated with the L-R asymmetric organogenesis have not been clarified, and two different hypotheses-vesicle transport and mechanosensing-are now debated in the research field of developmental biology. In this study, we developed a computational model of the node system reported by Shinohara et al. and examined the feasibilities of the two hypotheses with a small number of cilia. With the small number of rotating cilia, flow was induced locally and global strong flow was not observed in the node. Particles were then effectively transported only when they were close to the cilia, and particle transport was strongly dependent on the ciliary positions. Although the maximum wall shear rate was also influenced by ciliary position, the mean wall shear rate at the perinodal wall increased monotonically with the number of cilia. We also investigated the membrane tension of immotile cilia, which is relevant to the regulation of mechanotransduction. The results indicated that tension of about 0.1 mu Nm(-1) was exerted at the base even when the fluid shear rate was applied at about 0.1 s(-1). The area of high tension was also localized at the upstream side, and negative tension appeared at the downstream side. Such localization may be useful to sense the flow direction at the periphery, as time-averaged anticlockwise circulation was induced in the node by rotation of a few cilia. Our numerical results support the mechanosensing hypothesis, and we expect that our study will stimulate further experimental investigations of mechanotransduction in the near future. KW - nodal flow KW - left-right asymmetry KW - boundary element method KW - fluid-structure interaction Y1 - 2018 U6 - https://doi.org/10.1098/rsos.180601 SN - 2054-5703 VL - 5 IS - 8 PB - Royal Society CY - London ER - TY - JOUR A1 - Nitze, Ingmar A1 - Grosse, Guido A1 - Jones, Benjamin M. A1 - Romanovsky, Vladimir E. A1 - Boike, Julia T1 - Remote sensing quantifies widespread abundance of permafrost region disturbances across the Arctic and Subarctic JF - Nature Communications N2 - Local observations indicate that climate change and shifting disturbance regimes are causing permafrost degradation. However, the occurrence and distribution of permafrost region disturbances (PRDs) remain poorly resolved across the Arctic and Subarctic. Here we quantify the abundance and distribution of three primary PRDs using time-series analysis of 30-m resolution Landsat imagery from 1999 to 2014. Our dataset spans four continental-scale transects in North America and Eurasia, covering similar to 10% of the permafrost region. Lake area loss (-1.45%) dominated the study domain with enhanced losses occurring at the boundary between discontinuous and continuous permafrost regions. Fires were the most extensive PRD across boreal regions (6.59%), but in tundra regions (0.63%) limited to Alaska. Retrogressive thaw slumps were abundant but highly localized (< 10(-5)%). Our analysis synergizes the global-scale importance of PRDs. The findings highlight the need to include PRDs in next-generation land surface models to project the permafrost carbon feedback. Y1 - 2018 U6 - https://doi.org/10.1038/s41467-018-07663-3 SN - 2041-1723 VL - 9 PB - Nature Publ. Group CY - London ER - TY - JOUR A1 - Mücke, Nicole A1 - Blanchard, Gilles T1 - Parallelizing spectrally regularized kernel algorithms JF - Journal of machine learning research N2 - We consider a distributed learning approach in supervised learning for a large class of spectral regularization methods in an reproducing kernel Hilbert space (RKHS) framework. The data set of size n is partitioned into m = O (n(alpha)), alpha < 1/2, disjoint subsamples. On each subsample, some spectral regularization method (belonging to a large class, including in particular Kernel Ridge Regression, L-2-boosting and spectral cut-off) is applied. The regression function f is then estimated via simple averaging, leading to a substantial reduction in computation time. We show that minimax optimal rates of convergence are preserved if m grows sufficiently slowly (corresponding to an upper bound for alpha) as n -> infinity, depending on the smoothness assumptions on f and the intrinsic dimensionality. In spirit, the analysis relies on a classical bias/stochastic error analysis. KW - Distributed Learning KW - Spectral Regularization KW - Minimax Optimality Y1 - 2018 SN - 1532-4435 VL - 19 PB - Microtome Publishing CY - Cambridge, Mass. ER - TY - JOUR A1 - Mera, Azal A1 - Stepanenko, Vitaly A. A1 - Tarkhanov, Nikolai Nikolaevich T1 - Successive approximation for the inhomogeneous burgers equation JF - Journal of Siberian Federal University : Mathematics & Physics N2 - The inhomogeneous Burgers equation is a simple form of the Navier-Stokes equations. From the analytical point of view, the inhomogeneous form is poorly studied, the complete analytical solution depending closely on the form of the nonhomogeneous term. KW - Navier-Stokes equations KW - classical solution Y1 - 2018 U6 - https://doi.org/10.17516/1997-1397-2018-11-4-519-531 SN - 1997-1397 SN - 2313-6022 VL - 11 IS - 4 SP - 519 EP - 531 PB - Siberian Federal University CY - Krasnoyarsk ER - TY - JOUR A1 - Melin, Johanna A1 - Parra-Guillen, Zinnia Patricia A1 - Hartung, Niklas A1 - Huisinga, Wilhelm A1 - Ross, Richard J. A1 - Whitaker, Martin J. A1 - Kloft, Charlotte T1 - Predicting Cortisol Exposure from Paediatric Hydrocortisone Formulation Using a Semi-Mechanistic Pharmacokinetic Model Established in Healthy Adults JF - Clinical Pharmacokinetics N2 - Background and objective Optimisation of hydrocortisone replacement therapy in children is challenging as there is currently no licensed formulation and dose in Europe for children under 6 years of age. In addition, hydrocortisone has non-linear pharmacokinetics caused by saturable plasma protein binding. A paediatric hydrocortisone formulation, Infacort (R) oral hydrocortisone granules with taste masking, has therefore been developed. The objective of this study was to establish a population pharmacokinetic model based on studies in healthy adult volunteers to predict hydrocortisone exposure in paediatric patients with adrenal insufficiency. Methods Cortisol and binding protein concentrations were evaluated in the absence and presence of dexamethasone in healthy volunteers (n = 30). Dexamethasone was used to suppress endogenous cortisol concentrations prior to and after single doses of 0.5, 2, 5 and 10 mg of Infacort (R) or 20 mg of Infacort (R)/hydrocortisone tablet/hydrocortisone intravenously. A plasma protein binding model was established using unbound and total cortisol concentrations, and sequentially integrated into the pharmacokinetic model. Results Both specific (non-linear) and non-specific (linear) protein binding were included in the cortisol binding model. A two-compartment disposition model with saturable absorption and constant endogenous cortisol baseline (Baseline (cort),15.5 nmol/L) described the data accurately. The predicted cortisol exposure for a given dose varied considerably within a small body weight range in individuals weighing < 20 kg. Conclusions Our semi-mechanistic population pharmacokinetic model for hydrocortisone captures the complex pharmacokinetics of hydrocortisone in a simplified but comprehensive framework. The predicted cortisol exposure indicated the importance of defining an accurate hydrocortisone dose to mimic physiological concentrations for neonates and infants weighing < 20 kg. Y1 - 2018 U6 - https://doi.org/10.1007/s40262-017-0575-8 SN - 0312-5963 SN - 1179-1926 VL - 57 IS - 4 SP - 515 EP - 527 PB - Springer CY - Northcote ER - TY - JOUR A1 - Lonnemann, Jan A1 - Hasselhorn, Marcus T1 - Frühe mathematische Bildung T1 - Early Mathematics Education BT - Aktuelle Forschungstrends und Perspektiven BT - Current Research Trends and Perspectives JF - Frühe Bildung N2 - Im vorliegenden Beitrag werden aktuelle Forschungstrends im Bereich der frühen mathematischen Bildung im Kontext jüngst formulierter Zieldimensionen für die frühe mathematische Bildung (siehe Benz et al., 2017) dargestellt. Es wird auf spielbasierte Fördermaßnahmen, Kompetenzen im Bereich „Raum und Form“, den Einfluss sprachlicher Parameter auf die Entwicklung mathematischer Kompetenzen sowie auf mathematikbezogene Kompetenzen frühpädagogischer Fachkräfte eingegangen. Darüber hinaus werden die Ergebnisse einer aktuellen Feldstudie zur Förderung früher mathematischer Kompetenzen (siehe Dillon, Kannan, Dean, Spelke & Duflo, 2017) vorgestellt. Abschließend wird die Entwicklung und Implementierung anschlussfähiger Bildungskonzepte als eine der zentralen Herausforderungen zukünftiger Forschungs- und Bildungsbemühungen diskutiert N2 - Current research trends in the field of early mathematical education are presented in the context of recently formulated target dimensions of early mathematical education (see Benz et al., 2017). Game-based approaches, competencies in the field of “space and form”, the influence of language skills on the development of mathematical competencies, as well as mathematics-related competencies of early childhood educators are discussed. In addition, the results of a recent field study on a preschool intervention intended to enhance children's early mathematical skills (see Dillon, Kannan, Dean, Spelke, & Duflo, 2017) are presented. Finally, we discuss the development and implementation of aligned educational concepts as one of the central challenges of future research and educational activities. KW - early mathematical education KW - target dimensions KW - conditions of success KW - alignment Y1 - 2018 U6 - https://doi.org/10.1026/2191-9186/a000379 SN - 2191-9186 SN - 2191-9194 VL - 7 IS - 3 SP - 129 EP - 134 PB - Hogrefe CY - Göttingen ER - TY - JOUR A1 - Liu, Shiping A1 - Münch, Florentin A1 - Peyerimhoff, Norbert T1 - Bakry-Emery curvature and diameter bounds on graphs JF - Calculus of variations and partial differential equations N2 - We prove finiteness and diameter bounds for graphs having a positive Ricci-curvature bound in the Bakry–Émery 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 für 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–Émery curvature functions of graphs, 2016). Y1 - 2018 U6 - https://doi.org/10.1007/s00526-018-1334-x SN - 0944-2669 SN - 1432-0835 VL - 57 IS - 2 PB - Springer CY - Heidelberg ER - TY - JOUR A1 - Kühn, Danilo A1 - Sorgenfrei, Florian A1 - Giangrisostomi, Erika A1 - Jay, Raphael A1 - Musazay, Abdurrahman A1 - Ovsyannikov, Ruslan A1 - Strahlman, Christian A1 - Svensson, Svante A1 - Mårtensson, Nils A1 - Föhlisch, Alexander T1 - Capabilities of angle resolved time of flight electron spectroscopy with the 60 degrees wide angle acceptance lens JF - Journal of electron spectroscopy and related phenomena : the international journal on theoretical and experimental aspects of electron spectroscopy N2 - 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. KW - Artof KW - Electron spectroscopy KW - Wide angle KW - Time of flight KW - Energy resolution KW - Synchrotron Y1 - 2018 U6 - https://doi.org/10.1016/j.elspec.2017.06.008 SN - 0368-2048 SN - 1873-2526 VL - 224 SP - 45 EP - 50 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Kubin, Markus A1 - Guo, Meiyuan A1 - Kroll, Thomas A1 - Loechel, Heike A1 - Kallman, Erik A1 - Baker, Michael L. A1 - Mitzner, Rolf A1 - Gul, Sheraz A1 - Kern, Jan A1 - Föhlisch, Alexander A1 - Erko, Alexei A1 - Bergmann, Uwe A1 - Yachandra, Vittal A1 - Yano, Junko A1 - Lundberg, Marcus A1 - Wernet, Philippe T1 - Probing the oxidation state of transition metal complexes BT - a case study on how charge and spin densities determine Mn L-edge X-ray absorption energies JF - Chemical science N2 - Transition metals in inorganic systems and metalloproteins can occur in different oxidation states, which makes them ideal redox-active catalysts. To gain a mechanistic understanding of the catalytic reactions, knowledge of the oxidation state of the active metals, ideally in operando, is therefore critical. L-edge X-ray absorption spectroscopy (XAS) is a powerful technique that is frequently used to infer the oxidation state via a distinct blue shift of L-edge absorption energies with increasing oxidation state. A unified description accounting for quantum-chemical notions whereupon oxidation does not occur locally on the metal but on the whole molecule and the basic understanding that L-edge XAS probes the electronic structure locally at the metal has been missing to date. Here we quantify how charge and spin densities change at the metal and throughout the molecule for both redox and core-excitation processes. We explain the origin of the L-edge XAS shift between the high-spin complexes Mn-II(acac)(2) and Mn-III(acac)(3) as representative model systems and use ab initio theory to uncouple effects of oxidation-state changes from geometric effects. The shift reflects an increased electron affinity of Mn-III in the core-excited states compared to the ground state due to a contraction of the Mn 3d shell upon core-excitation with accompanied changes in the classical Coulomb interactions. This new picture quantifies how the metal-centered core hole probes changes in formal oxidation state and encloses and substantiates earlier explanations. The approach is broadly applicable to mechanistic studies of redox-catalytic reactions in molecular systems where charge and spin localization/delocalization determine reaction pathways. Y1 - 2018 U6 - https://doi.org/10.1039/c8sc00550h SN - 2041-6520 SN - 2041-6539 VL - 9 IS - 33 SP - 6813 EP - 6829 PB - Royal Society of Chemistry CY - Cambridge ER - TY - JOUR A1 - Kong, Xiang-Zhao A1 - Deuber, Claudia A. A1 - Kittilä, Anniina A1 - Somogyvári, Márk A1 - Mikutis, Gediminas A1 - Bayer, Peter A1 - Stark, Wendelin J. A1 - Saar, Martin O. T1 - Tomographic Reservoir Imaging with DNA-Labeled Silica Nanotracers: The First Field Validation JF - Environmental science & technology N2 - This study presents the first field validation of using DNA-labeled silica nanoparticles as tracers to image subsurface reservoirs by travel time based tomography. During a field campaign in Switzerland, we performed short-pulse tracer tests under a forced hydraulic head gradient to conduct a multisource-multireceiver tracer test and tomographic inversion, determining the two-dimensional hydraulic conductivity field between two vertical wells. Together with three traditional solute dye tracers, we injected spherical silica nanotracers, encoded with synthetic DNA molecules, which are protected by a silica layer against damage due to chemicals, microorganisms, and enzymes. Temporal moment analyses of the recorded tracer concentration breakthrough curves (BTCs) indicate higher mass recovery, less mean residence time, and smaller dispersion of the DNA-labeled nanotracers, compared to solute dye tracers. Importantly, travel time based tomography, using nanotracer BTCs, yields a satisfactory hydraulic conductivity tomogram, validated by the dye tracer results and previous field investigations. These advantages of DNA-labeled nanotracers, in comparison to traditional solute dye tracers, make them well-suited for tomographic reservoir characterizations in fields such as hydrogeology, petroleum engineering, and geothermal energy, particularly with respect to resolving preferential flow paths or the heterogeneity of contact surfaces or by enabling source zone characterizations of dense nonaqueous phase liquids. Y1 - 2018 U6 - https://doi.org/10.1021/acs.est.8b04367 SN - 0013-936X SN - 1520-5851 VL - 52 IS - 23 SP - 13681 EP - 13689 PB - American Chemical Society CY - Washington ER - TY - JOUR A1 - Knöchel, Jane A1 - Kloft, Charlotte A1 - Huisinga, Wilhelm T1 - Understanding and reducing complex systems pharmacology models based on a novel input-response index JF - Journal of pharmacokinetics and pharmacodynamics N2 - A growing understanding of complex processes in biology has led to large-scale mechanistic models of pharmacologically relevant processes. These models are increasingly used to study the response of the system to a given input or stimulus, e.g., after drug administration. Understanding the input–response relationship, however, is often a challenging task due to the complexity of the interactions between its constituents as well as the size of the models. An approach that quantifies the importance of the different constituents for a given input–output relationship and allows to reduce the dynamics to its essential features is therefore highly desirable. In this article, we present a novel state- and time-dependent quantity called the input–response index that quantifies the importance of state variables for a given input–response relationship at a particular time. It is based on the concept of time-bounded controllability and observability, and defined with respect to a reference dynamics. In application to the brown snake venom–fibrinogen (Fg) network, the input–response indices give insight into the coordinated action of specific coagulation factors and about those factors that contribute only little to the response. We demonstrate how the indices can be used to reduce large-scale models in a two-step procedure: (i) elimination of states whose dynamics have only minor impact on the input–response relationship, and (ii) proper lumping of the remaining (lower order) model. In application to the brown snake venom–fibrinogen network, this resulted in a reduction from 62 to 8 state variables in the first step, and a further reduction to 5 state variables in the second step. We further illustrate that the sequence, in which a recursive algorithm eliminates and/or lumps state variables, has an impact on the final reduced model. The input–response indices are particularly suited to determine an informed sequence, since they are based on the dynamics of the original system. In summary, the novel measure of importance provides a powerful tool for analysing the complex dynamics of large-scale systems and a means for very efficient model order reduction of nonlinear systems. KW - Control theory KW - Model order reduction KW - Blood coagulation network KW - Nonlinear systems Y1 - 2017 U6 - https://doi.org/10.1007/s10928-017-9561-x SN - 1567-567X SN - 1573-8744 VL - 45 IS - 1 SP - 139 EP - 157 PB - Springer Science + Business Media B.V. CY - New York ER - TY - JOUR A1 - Klein, Markus A1 - Rosenberger, Elke T1 - The tunneling effect for a class of difference operators JF - Reviews in Mathematical Physics N2 - We analyze a general class of self-adjoint difference operators H-epsilon = T-epsilon + V-epsilon on l(2)((epsilon Z)(d)), where V-epsilon is a multi-well potential and v(epsilon) is a small parameter. We give a coherent review of our results on tunneling up to new sharp results on the level of complete asymptotic expansions (see [30-35]). Our emphasis is on general ideas and strategy, possibly of interest for a broader range of readers, and less on detailed mathematical proofs. The wells are decoupled by introducing certain Dirichlet operators on regions containing only one potential well. Then the eigenvalue problem for the Hamiltonian H-epsilon is treated as a small perturbation of these comparison problems. After constructing a Finslerian distance d induced by H-epsilon, we show that Dirichlet eigenfunctions decay exponentially with a rate controlled by this distance to the well. It follows with microlocal techniques that the first n eigenvalues of H-epsilon converge to the first n eigenvalues of the direct sum of harmonic oscillators on R-d located at several wells. In a neighborhood of one well, we construct formal asymptotic expansions of WKB-type for eigenfunctions associated with the low-lying eigenvalues of H-epsilon. These are obtained from eigenfunctions or quasimodes for the operator H-epsilon acting on L-2(R-d), via restriction to the lattice (epsilon Z)(d). Tunneling is then described by a certain interaction matrix, similar to the analysis for the Schrodinger operator (see [22]), the remainder is exponentially small and roughly quadratic compared with the interaction matrix. We give weighted l(2)-estimates for the difference of eigenfunctions of Dirichlet-operators in neighborhoods of the different wells and the associated WKB-expansions at the wells. In the last step, we derive full asymptotic expansions for interactions between two "wells" (minima) of the potential energy, in particular for the discrete tunneling effect. Here we essentially use analysis on phase space, complexified in the momentum variable. These results are as sharp as the classical results for the Schrodinger operator in [22]. KW - Semiclassical difference operator KW - tunneling KW - interaction matrix KW - asymptotic expansion KW - multi-well potential KW - Finsler distance KW - Agmon estimates Y1 - 2018 U6 - https://doi.org/10.1142/S0129055X18300029 SN - 0129-055X SN - 1793-6659 VL - 30 IS - 4 PB - World Scientific CY - Singapore ER - TY - JOUR A1 - Klein, Markus A1 - Rosenberger, Elke T1 - Tunneling for a class of difference operators BT - Complete asymptotics JF - Annales Henri Poincaré : a journal of theoretical and mathematical physics N2 - We analyze a general class of difference operators Hε=Tε+Vε on ℓ2((εZ)d), where Vε is a multi-well potential and ε is a small parameter. We derive full asymptotic expansions of the prefactor of the exponentially small eigenvalue splitting due to interactions between two “wells” (minima) of the potential energy, i.e., for the discrete tunneling effect. We treat both the case where there is a single minimal geodesic (with respect to the natural Finsler metric induced by the leading symbol h0(x,ξ) of Hε) connecting the two minima and the case where the minimal geodesics form an ℓ+1 dimensional manifold, ℓ≥1. These results on the tunneling problem are as sharp as the classical results for the Schrödinger operator in Helffer and Sjöstrand (Commun PDE 9:337–408, 1984). Technically, our approach is pseudo-differential and we adapt techniques from Helffer and Sjöstrand [Analyse semi-classique pour l’équation de Harper (avec application à l’équation de Schrödinger avec champ magnétique), Mémoires de la S.M.F., 2 series, tome 34, pp 1–113, 1988)] and Helffer and Parisse (Ann Inst Henri Poincaré 60(2):147–187, 1994) to our discrete setting. Y1 - 2018 U6 - https://doi.org/10.1007/s00023-018-0732-0 SN - 1424-0637 SN - 1424-0661 VL - 19 IS - 11 SP - 3511 EP - 3559 PB - Springer International Publishing CY - Cham ER - TY - THES A1 - Khalil, Sara T1 - Boundary Value Problems on Manifolds with Singularities T1 - Randwertprobleme auf Mannigfaltigkeiten mit Singularitäten N2 - 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. N2 - In der Dissertation wurden neue Quantisierungen konstruiert für pseudo-differentielle Randwertprobleme auf Mannigfaltigkeiten mit Kanten-Singularitäten. Die Gestalt der hier behandelten Operatoren ist motiviert durch Boutet de Monvels Kalkül, der auf glatten Mannigfaltigkeiten mit Rand bekannt ist. Der singuläre Fall, hier mit Kanten und Rand, ist weitaus komplizierter. Der gegenwärtige Zugang vereinfacht die operatarwertigen Symbolstrukturen unter Verwendung geeigneter Mellin-Quantisierungen auf unendlichen gestreckten Modell- Kegeln, die entsprechenden Keilen mit Rand zugeordnet sind. Die Mellin-Symbole selbst sind holomorph in der komplexen Mellin Kovariablen bis auf glättende Restglieder mit Asymptotiken. Zu den Hauptresultaten gehört die Konstruktion von Parametrices elliptischer Elemente in der erzeugten Operator-Algebra, einschließlich elliptischer Kanten-Bedingungen. KW - manifolds with singularities KW - boundary value problems KW - pseudo-differential equation KW - manifolds with edge KW - Boutet de Monvel's calculus KW - edge boundary value problems KW - Mannigfaltigkeiten mit Singularitäten KW - Randwertprobleme KW - pseudo-differentielle Gleichungen KW - Mannigfaltigkeiten mit Kante KW - Boutet de Monvels Kalkül KW - Kanten-Randwertprobleme Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-419018 ER - TY - JOUR A1 - Keller, Matthias A1 - Schwarz, Michael T1 - The Kazdan-Warner equation on canonically compactifiable graphs JF - Calculus of variations and partial differential equations N2 - We study the Kazdan-Warner equation on canonically compactifiable graphs. These graphs are distinguished as analytic properties of Laplacians on these graphs carry a strong resemblance to Laplacians on open pre-compact manifolds. Y1 - 2018 U6 - https://doi.org/10.1007/s00526-018-1329-7 SN - 0944-2669 SN - 1432-0835 VL - 57 IS - 2 PB - Springer CY - Heidelberg ER - TY - JOUR A1 - Keller, Matthias A1 - Pinchover, Yehuda A1 - Pogorzelski, Felix T1 - Optimal Hardy inequalities for Schrodinger operators on graphs JF - Communications in mathematical physics N2 - For a given subcritical discrete Schrodinger operator H on a weighted infinite graph X, we construct a Hardy-weight w which is optimal in the following sense. The operator H - lambda w is subcritical in X for all lambda < 1, null-critical in X for lambda = 1, and supercritical near any neighborhood of infinity in X for any lambda > 1. Our results rely on a criticality theory for Schrodinger operators on general weighted graphs. Y1 - 2018 U6 - https://doi.org/10.1007/s00220-018-3107-y SN - 0010-3616 SN - 1432-0916 VL - 358 IS - 2 SP - 767 EP - 790 PB - Springer CY - New York ER - TY - JOUR A1 - Keller, Matthias A1 - Pinchover, Yehuda A1 - Pogorzelski, Felix T1 - An improved discrete hardy inequality JF - The American mathematical monthly : an official publication of the Mathematical Association of America N2 - 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. KW - Primary 26D15 Y1 - 2018 U6 - https://doi.org/10.1080/00029890.2018.1420995 SN - 0002-9890 SN - 1930-0972 VL - 125 IS - 4 SP - 347 EP - 350 PB - Taylor & Francis Group CY - Philadelphia ER - TY - JOUR A1 - Kaminski, Jakob A. A1 - Schlagenhauf, Florian A1 - Rapp, Michael Armin A1 - Awasthi, Swapnil A1 - Ruggeri, Barbara A1 - Deserno, Lorenz A1 - Banaschewski, Tobias A1 - Bokde, Arun L. W. A1 - Bromberg, Uli A1 - Büchel, Christian A1 - Quinlan, Erin Burke A1 - Desrivieres, Sylvane A1 - Flor, Herta A1 - Frouin, Vincent A1 - Garavan, Hugh A1 - Gowland, Penny A1 - Ittermann, Bernd A1 - Martinot, Jean-Luc A1 - Martinot, Marie-Laure Paillere A1 - Nees, Frauke A1 - Orfanos, Dimitri Papadopoulos A1 - Paus, Tomas A1 - Poustka, Luise A1 - Smolka, Michael N. A1 - Fröhner, Juliane H. A1 - Walter, Henrik A1 - Whelan, Robert A1 - Ripke, Stephan A1 - Schumann, Gunter A1 - Heinz, Andreas T1 - Epigenetic variance in dopamine D2 receptor BT - a marker of IQ malleability? JF - Translational Psychiatry N2 - 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. Y1 - 2018 U6 - https://doi.org/10.1038/s41398-018-0222-7 SN - 2158-3188 VL - 8 PB - Nature Publ. Group CY - New York ER - TY - THES A1 - Jende, Alexander T1 - On the characterization of particular orthogroups by disjunctions of identities N2 - In this thesis, we discuss the characterization of orthogroups by so-called disjunctions of identities. The orthogroups are a subclass of the class of completely regular semigroups, a generalization of the concept of a group. Thus there is for all elements of an orthogroup some kind of an inverse element such that both elements commute. Based on a fundamental result by A.H. Clifford, every completely regular semigroup is a semilattice of completely simple semigroups. This allows the description the gross structure of such semigroup. In particular every orthogroup is a semilattice of rectangular groups which are isomorphic to direct products of rectangular bands and groups. Semilattices of rectangular groups coming from various classes are characterized using the concept of an alternative variety, a generalization of the classical idea of a variety by Birkhoff. After starting with some fundamental definitions and results concerning semigroups, we introduce the concept of disjunctions of identities and summarize some necessary properties. In particular we present some disjunction of identities which is sufficient for a semigroup for being completely regular. Furthermore we derive from this identity some statements concerning Rees matrix semigroups, a possible representation of completely simple semigroups. A main result of this thesis is the general description of disjunctions of identities such that a completely regular semigroup satisfying the described identity is a semilattice of left groups (right groups / groups). In this case the completely regular semigroup is an orthogroup. Furthermore we define various classes of rectangular groups such that there is an exponent taken from a set of pairwise coprime positive integers. An important result is the characterization of the class of all semilattices of particular rectangular groups (taken from the classes defined before) using a set-theoretic minimal set of disjunctions of identities. Additionally we investigate semilattices of groups (so-called Clifford semigroups). For this purpose we consider abelian groups of particular exponents and prove some well-known results from the theory of Clifford semigroups in an alternative way applying the concept of disjunctions of identities. As a practical application of the results concerning semilattices of left zero semigroups and right zero semigroups we identify a particular transformation semigroup. For more detailed information about the product of two arbitrary elements of a semilattice of semigroups we introduce the concept of strong semilattices of semigroups. It is well-known that a semilattice of groups is a strong semilattice of groups. So we can characterize a strong semilattice of groups of particular pairwise coprime exponents by disjunctions of identities. Additionally we describe the class of all strong semilattices of left zero semigroups and right zero semigroups with the help of such kind of identity, and we relate this statement to the theory of normal bands. A possible extension of the already described semilattices of rectangular groups can be achieved by an auxiliary total order (in terms of chains of semigroups). To this end we present a corresponding characterization due to disjunctions of identities which is obviously minimal. A list of open questions which have arisen during the research for this thesis, but left crude, is attached. N2 - In dieser Dissertation wird die Charakterisierung von Orthogruppen durch sogenannte Alternatividentitäten diskutiert. Die Orthogruppen bilden eine Unterklasse der Klasse der vollständig regulären Halbgruppen, einer Verallgemeinerung des Konzeptes einer Gruppe. Somit besitzen alle Elemente einer Orthogruppe eine Art inverses Element, mit welchem sie sogar kommutieren. Nach einem elementaren Ergebnis von A.H. Clifford lässt sich jede vollständig reguläre Halbgruppe als Halbverband von vollständig einfachen Halbgruppen darstellen. Dies erlaubt eine grobe Beschreibung der Struktur einer solchen Halbgruppe. Insbesondere lässt sich jede Orthogruppe als Halbverband von rektangulären Gruppen, welche isomorph zu direkten Produkten von rektangulären Bändern und Gruppen sind, beschreiben. Halbverbände rektangulärer Gruppen verschiedener Klassen werden unter Verwendung des Konzeptes der Alternativvarietät, einer Verallgemeinerung des klassischen Begriffs der Varietät nach Birkhoff, charakterisiert. Nach grundlegenden Definitionen und Aussagen zu Halbgruppen, werden die Alternatividentitäten eingeführt und notwendige theoretische Aspekte erläutert. Insbesondere wird eine Alternatividentität angegeben, welche eine hinreichende Bedingung dafür ist, dass eine Halbgruppe vollständig regulär ist. Weiterhin werden in diesem Kontext Aussagen zu Rees-Matrix-Halbgruppen, einer möglichen Darstellung der vollständig einfachen Halbgruppen, hergeleitet. Ein Hauptresultat der Dissertation ist die allgemeine Beschreibung von Alternatividentitäten, sodass eine vollständig reguläre Halbgruppe ein Halbverband von Linksgruppen (Rechtsgruppen / Gruppen) ist. In diesem Fall ist die vollständig reguläre Halbgruppe sogar eine Orthogruppe. Weiterhin werden verschiedene Klassen von rektangulären Gruppen definiert, die einen bestimmten Exponenten aus einer gegebenen Menge von paarweise teilerfremden natürlichen Zahlen besitzen. Ein wichtiges Ergebnis ist die Charakterisierung der Klasse aller Halbverbände von bestimmten rektangulären Gruppen (aus den vorher definierten Klassen) mittels einer mengentheoretisch minimalen Menge von Alternatividentitäten. Es werden außerdem Halbverbände von Gruppen (sogenannte Clifford-Halbgruppen) näher untersucht. Hierfür werden abelsche Gruppen mit bestimmtem Exponenten betrachtet und teilweise bekannte Resultate aus der Theorie der Clifford-Halbgruppen mittels des Konzeptes der Alternatividentitäten auf alternativem Weg bewiesen. Als konkrete Anwendung der Ergebnisse über Halbverbände von Linksnullhalbgruppen und Rechtsnullhalbgruppen wird die Identifizierung einer speziellen Transformationshalbgruppe dargelegt. Um detailliertere Aussagen über das Produkt zweier beliebiger Elemente eines Halbverbandes von Halbgruppen zu erhalten, wird das Konzept der starken Halbverbände von Halbgruppen eingeführt. Hierbei ist bekannt, dass jeder Halbverband von Gruppen ein starker Halbverband von Gruppen ist. Somit lässt sich ein starker Halbverband von Gruppen mit bestimmten, paarweise teilerfremden Exponenten durch Alternatividentitäten charakterisieren. Zusätzlich wird die Klasse aller starken Halbverbände von Linksnullhalbgruppen und Rechtsnullhalbgruppen durch diese Art von Identitäten beschrieben und in die Theorie der normalen Bänder eingeordnet. Eine mögliche Ergänzung der beschriebenen Halbverbände von rektangulären Gruppen erfolgt durch die zusätzliche Forderung einer totalen Ordnung (im Sinne von Ketten von Halbgruppen). Hierfür wird ebenfalls eine entsprechende Charakterisierung durch Alternatividentitäten präsentiert, welche offensichtlich minimal ist. Eine Auflistung offener Fragen, welche während der Arbeit an der Dissertation entstanden sind, jedoch unbearbeitet bleiben mussten, ist beigefügt. KW - Halbgruppentheorie KW - Orthogruppen KW - Alternatividentitäten KW - Alternativvarietäten KW - Clifford-Halbgruppen KW - starker Halbverband von Halbgruppen KW - Kette von Halbgruppen KW - semigroup theory KW - orthogroup KW - disjunction of identities KW - alternative variety KW - Clifford semigroup KW - strong semilattice of semigroups KW - chain of semigroups Y1 - 2018 ER - TY - JOUR A1 - Hofer-Temmel, Christoph A1 - Houdebert, Pierre T1 - Disagreement percolation for Gibbs ball models JF - Stochastic processes and their application N2 - 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. KW - Continuum random cluster model KW - Disagreement percolation KW - Dependent thinning KW - Boolean model KW - Stochastic domination KW - Phase transition KW - Unique Gibbs state KW - Exponential decay of pair correlation Y1 - 2019 U6 - https://doi.org/10.1016/j.spa.2018.11.003 SN - 0304-4149 SN - 1879-209X VL - 129 IS - 10 SP - 3922 EP - 3940 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Hlawenka, Peter A1 - Siemensmeyer, Konrad A1 - Weschke, Eugen A1 - Varykhalov, Andrei A1 - Sanchez-Barriga, Jaime A1 - Shitsevalova, Natalya Y. A1 - Dukhnenko, A. V. A1 - Filipov, V. B. A1 - Gabani, Slavomir A1 - Flachbart, Karol A1 - Rader, Oliver A1 - Rienks, Emile D. L. T1 - Samarium hexaboride is a trivial surface conductor JF - Nature Communications N2 - SmB6 is predicted to be the first member of the intersection of topological insulators and Kondo insulators, strongly correlated materials in which the Fermi level lies in the gap of a many-body resonance that forms by hybridization between localized and itinerant states. While robust, surface-only conductivity at low temperature and the observation of surface states at the expected high symmetry points appear to confirm this prediction, we find both surface states at the (100) surface to be topologically trivial. We find the (Gamma) over bar state to appear Rashba split and explain the prominent (X) over bar state by a surface shift of the many-body resonance. We propose that the latter mechanism, which applies to several crystal terminations, can explain the unusual surface conductivity. While additional, as yet unobserved topological surface states cannot be excluded, our results show that a firm connection between the two material classes is still outstanding. Y1 - 2018 U6 - https://doi.org/10.1038/s41467-018-02908-7 SN - 2041-1723 VL - 9 PB - Nature Publ. Group CY - London ER - TY - JOUR A1 - Hedayat Mahmoudi, Mahdi A1 - Schulze, Bert-Wolfgang T1 - A new approach to the second order edge calculus JF - Journal of pseudo-differential operators and applications N2 - 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. KW - Operators on singular manifolds KW - Mellin transform KW - Stratified spaces KW - Ellipticity and parametrices Y1 - 2018 U6 - https://doi.org/10.1007/s11868-017-0191-2 SN - 1662-9981 SN - 1662-999X VL - 9 IS - 2 SP - 265 EP - 300 PB - Springer CY - Basel ER - TY - JOUR A1 - Güneysu, Batu A1 - Keller, Matthias T1 - Scattering the Geometry of Weighted Graphs JF - Mathematical physics, analysis and geometry : an international journal devoted to the theory and applications of analysis and geometry to physics N2 - Given two weighted graphs (X, b(k), m(k)), k = 1, 2 with b(1) similar to b(2) and m(1) similar to m(2), we prove a weighted L-1-criterion for the existence and completeness of the wave operators W-+/- (H-2, H-1, I-1,I-2), where H-k denotes the natural Laplacian in l(2)(X, m(k)) w.r.t. (X, b(k), m(k)) and I-1,I-2 the trivial identification of l(2)(X, m(1)) with l(2) (X, m(2)). In particular, this entails a general criterion for the absolutely continuous spectra of H-1 and H-2 to be equal. KW - Graphs KW - Laplacian KW - Scattering theory Y1 - 2018 U6 - https://doi.org/10.1007/s11040-018-9285-1 SN - 1385-0172 SN - 1572-9656 VL - 21 IS - 3 PB - Springer CY - Dordrecht ER - TY - JOUR A1 - Gomez, Christophe A1 - Hartung, Niklas T1 - Stochastic and deterministic models for the metastatic emission process BT - Formalisms and Crosslinks JF - Cancer Systems Biology N2 - Although the detection of metastases radically changes prognosis of and treatment decisions for a cancer patient, clinically undetectable micrometastases hamper a consistent classification into localized or metastatic disease. This chapter discusses mathematical modeling efforts that could help to estimate the metastatic risk in such a situation. We focus on two approaches: (1) a stochastic framework describing metastatic emission events at random times, formalized via Poisson processes, and (2) a deterministic framework describing the micrometastatic state through a size-structured density function in a partial differential equation model. Three aspects are addressed in this chapter. First, a motivation for the Poisson process framework is presented and modeling hypotheses and mechanisms are introduced. Second, we extend the Poisson model to account for secondary metastatic emission. Third, we highlight an inherent crosslink between the stochastic and deterministic frameworks and discuss its implications. For increased accessibility the chapter is split into an informal presentation of the results using a minimum of mathematical formalism and a rigorous mathematical treatment for more theoretically interested readers. KW - Poisson process KW - Structured population equation KW - Metastasis KW - Mathematical modeling Y1 - 2018 SN - 978-1-4939-7493-1 SN - 978-1-4939-7492-4 U6 - https://doi.org/10.1007/978-1-4939-7493-1_10 SN - 1064-3745 SN - 1940-6029 VL - 1711 SP - 193 EP - 224 PB - Humana Press Inc. CY - Totowa ER - TY - JOUR A1 - Gerlach, Moritz Reinhardt A1 - Glück, Jochen T1 - Lower bounds and the asymptotic behaviour of positive operator semigroups JF - Ergodic theory and dynamical systems N2 - If (T-t) is a semigroup of Markov operators on an L-1-space that admits a nontrivial lower bound, then a well-known theorem of Lasota and Yorke asserts that the semigroup is strongly convergent as t -> infinity. In this article we generalize and improve this result in several respects. First, we give a new and very simple proof for the fact that the same conclusion also holds if the semigroup is merely assumed to be bounded instead of Markov. As a main result, we then prove a version of this theorem for semigroups which only admit certain individual lower bounds. Moreover, we generalize a theorem of Ding on semigroups of Frobenius-Perron operators. We also demonstrate how our results can be adapted to the setting of general Banach lattices and we give some counterexamples to show optimality of our results. Our methods combine some rather concrete estimates and approximation arguments with abstract functional analytical tools. One of these tools is a theorem which relates the convergence of a time-continuous operator semigroup to the convergence of embedded discrete semigroups. Y1 - 2017 U6 - https://doi.org/10.1017/etds.2017.9 SN - 0143-3857 SN - 1469-4417 VL - 38 SP - 3012 EP - 3041 PB - Cambridge Univ. Press CY - New York ER - TY - JOUR A1 - Gerlach, Moritz Reinhardt T1 - Convergence of dynamics and the Perron-Frobenius operator JF - Israel Journal of Mathematics N2 - 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. Y1 - 2018 U6 - https://doi.org/10.1007/s11856-018-1671-7 SN - 0021-2172 SN - 1565-8511 VL - 225 IS - 1 SP - 451 EP - 463 PB - Hebrew univ magnes press CY - Jerusalem ER - TY - JOUR A1 - Flad, Heinz-Jürgen A1 - Flad-Harutyunyan, Gohar A1 - Schulze, Bert-Wolfgang T1 - Ellipticity of the quantum mechanical Hamiltonians BT - corner singularity of the helium atom JF - Journal of pseudo-differential operators and applications N2 - 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. Y1 - 2018 U6 - https://doi.org/10.1007/s11868-017-0201-4 SN - 1662-9981 SN - 1662-999X VL - 9 IS - 3 SP - 451 EP - 467 PB - Springer CY - Basel ER - TY - JOUR A1 - Fiedler, Bernhard A1 - Zöller, Gert A1 - Holschneider, Matthias A1 - Hainzl, Sebastian T1 - Multiple Change-Point Detection in Spatiotemporal Seismicity Data JF - Bulletin of the Seismological Society of America N2 - Earthquake rates are driven by tectonic stress buildup, earthquake-induced stress changes, and transient aseismic processes. Although the origin of the first two sources is known, transient aseismic processes are more difficult to detect. However, the knowledge of the associated changes of the earthquake activity is of great interest, because it might help identify natural aseismic deformation patterns such as slow-slip events, as well as the occurrence of induced seismicity related to human activities. For this goal, we develop a Bayesian approach to identify change-points in seismicity data automatically. Using the Bayes factor, we select a suitable model, estimate possible change-points, and we additionally use a likelihood ratio test to calculate the significance of the change of the intensity. The approach is extended to spatiotemporal data to detect the area in which the changes occur. The method is first applied to synthetic data showing its capability to detect real change-points. Finally, we apply this approach to observational data from Oklahoma and observe statistical significant changes of seismicity in space and time. Y1 - 2018 U6 - https://doi.org/10.1785/0120170236 SN - 0037-1106 SN - 1943-3573 VL - 108 IS - 3A SP - 1147 EP - 1159 PB - Seismological Society of America CY - Albany ER - TY - JOUR A1 - Dereudre, David A1 - Houdebert, Pierre T1 - Sharp phase transition for the continuum Widom-Rowlinson model JF - Annales de l'Institut Henri Poincaré. B, Probability and statistics N2 - The Widom-Rowlinson model (or the Area-interaction model) is a Gibbs point process in R-d with the formal Hamiltonian defined as the volume of Ux epsilon omega B1(x), where. is a locally finite configuration of points and B-1(x) denotes the unit closed ball centred at x. The model is also tuned by two other parameters: the activity z > 0 related to the intensity of the process and the inverse temperature beta >= 0 related to the strength of the interaction. In the present paper we investigate the phase transition of the model in the point of view of percolation theory and the liquid-gas transition. First, considering the graph connecting points with distance smaller than 2r > 0, we show that for any beta >= 0, there exists 0 <(similar to a)(zc) (beta, r) < +infinity such that an exponential decay of connectivity at distance n occurs in the subcritical phase (i.e. z <(similar to a)(zc) (beta, r)) and a linear lower bound of the connection at infinity holds in the supercritical case (i.e. z >(similar to a)(zc) (beta, r)). These results are in the spirit of recent works using the theory of randomised tree algorithms (Probab. Theory Related Fields 173 (2019) 479-490, Ann. of Math. 189 (2019) 75-99, Duminil-Copin, Raoufi and Tassion (2018)). Secondly we study a standard liquid-gas phase transition related to the uniqueness/non-uniqueness of Gibbs states depending on the parameters z, beta. Old results (Phys. Rev. Lett. 27 (1971) 1040-1041, J. Chem. Phys. 52 (1970) 1670-1684) claim that a non-uniqueness regime occurs for z = beta large enough and it is conjectured that the uniqueness should hold outside such an half line ( z = beta >= beta(c) > 0). We solve partially this conjecture in any dimension by showing that for beta large enough the non-uniqueness holds if and only if z = beta. We show also that this critical value z = beta corresponds to the percolation threshold (similar to a)(zc) (beta, r) = beta for beta large enough, providing a straight connection between these two notions of phase transition. KW - Gibbs point process KW - DLR equations KW - Boolean model KW - Continuum KW - percolation KW - Random cluster model KW - Fortuin-Kasteleyn representation KW - Randomised tree algorithm KW - OSSS inequality Y1 - 2018 U6 - https://doi.org/10.1214/20-AIHP1082 SN - 0246-0203 SN - 1778-7017 VL - 57 IS - 1 SP - 387 EP - 407 PB - Association des Publications de l'Institut Henri Poincaré CY - Bethesda, Md. ER - TY - JOUR A1 - de Wiljes, Jana A1 - Reich, Sebastian A1 - Stannat, Wilhelm T1 - Long-Time stability and accuracy of the ensemble Kalman-Bucy Filter for fully observed processes and small measurement noise JF - SIAM Journal on Applied Dynamical Systems N2 - The ensemble Kalman filter has become a popular data assimilation technique in the geosciences. However, little is known theoretically about its long term stability and accuracy. In this paper, we investigate the behavior of an ensemble Kalman-Bucy filter applied to continuous-time filtering problems. We derive mean field limiting equations as the ensemble size goes to infinity as well as uniform-in-time accuracy and stability results for finite ensemble sizes. The later results require that the process is fully observed and that the measurement noise is small. We also demonstrate that our ensemble Kalman-Bucy filter is consistent with the classic Kalman-Bucy filter for linear systems and Gaussian processes. We finally verify our theoretical findings for the Lorenz-63 system. KW - data assimilation KW - Kalman Bucy filter KW - ensemble Kalman filter KW - stability KW - accuracy KW - asymptotic behavior Y1 - 2018 U6 - https://doi.org/10.1137/17M1119056 SN - 1536-0040 VL - 17 IS - 2 SP - 1152 EP - 1181 PB - Society for Industrial and Applied Mathematics CY - Philadelphia ER - TY - JOUR A1 - Chang, Der-Chen A1 - Schulze, Bert-Wolfgang T1 - Corner spaces and Mellin quantization JF - Journal of nonlinear and convex analysis : an international journal N2 - 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. KW - Mellin quantizations KW - operator-valued symbols KW - weighted edge and corner spaces Y1 - 2018 SN - 1345-4773 SN - 1880-5221 VL - 19 IS - 2 SP - 179 EP - 195 PB - Yokohama Publishers CY - Yokohama ER - TY - JOUR A1 - Chang, Der-Chen A1 - Mahmoudi, Mahdi Hedayat A1 - Schulze, Bert-Wolfgang T1 - Volterra operators in the edge-calculus JF - Analysis and Mathematical Physics N2 - We study the Volterra property of a class of anisotropic pseudo-differential operators on R x B for a manifold B with edge Y and time-variable t. This exposition belongs to a program for studying parabolicity in such a situation. In the present consideration we establish non-smoothing elements in a subalgebra with anisotropic operator-valued symbols of Mellin type with holomorphic symbols in the complex Mellin covariable from the cone theory, where the covariable t of t extends to symbolswith respect to t to the lower complex v half-plane. The resulting space ofVolterra operators enlarges an approach of Buchholz (Parabolische Pseudodifferentialoperatoren mit operatorwertigen Symbolen. Ph. D. thesis, Universitat Potsdam, 1996) by necessary elements to a new operator algebra containing Volterra parametrices under an appropriate condition of anisotropic ellipticity. Our approach avoids some difficulty in choosing Volterra quantizations in the edge case by generalizing specific achievements from the isotropic edge-calculus, obtained by Seiler (Pseudodifferential calculus on manifolds with non-compact edges, Ph. D. thesis, University of Potsdam, 1997), see also Gil et al. (in: Demuth et al (eds) Mathematical research, vol 100. Akademic Verlag, Berlin, pp 113-137, 1997; Osaka J Math 37: 221-260, 2000). KW - Volterra operator KW - Anisotropic pseudo-differential operators KW - Edge calculus KW - Operator-valued symbols of Mellin type Y1 - 2018 U6 - https://doi.org/10.1007/s13324-018-0238-4 SN - 1664-2368 SN - 1664-235X VL - 8 IS - 4 SP - 551 EP - 570 PB - Springer CY - Basel ER - TY - JOUR A1 - Carpentier, Alexandra A1 - Klopp, Olga A1 - Löffler, Matthias A1 - Nickl, Richard T1 - Adaptive confidence sets for matrix completion JF - Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability N2 - 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. KW - adaptivity KW - confidence sets KW - low rank recovery KW - matrix completion KW - minimax hypothesis testing KW - unknown variance Y1 - 2018 U6 - https://doi.org/10.3150/17-BEJ933 SN - 1350-7265 SN - 1573-9759 VL - 24 IS - 4A SP - 2429 EP - 2460 PB - International Statistical Institute CY - Voorburg ER - TY - JOUR A1 - Carpentier, Alexandra A1 - Kim, Arlene K. H. T1 - An iterative hard thresholding estimator for low rank matrix recovery with explicit limiting distribution JF - Statistica Sinica N2 - 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. KW - High dimensional statistical inference KW - inverse problem KW - limiting distribution KW - low rank matrix recovery KW - numerical methods KW - uncertainty quantification Y1 - 2018 U6 - https://doi.org/10.5705/ss.202016.0103 SN - 1017-0405 SN - 1996-8507 VL - 28 IS - 3 SP - 1371 EP - 1393 PB - Statistica Sinica, Institute of Statistical Science, Academia Sinica CY - Taipei ER - TY - GEN A1 - Böckmann, Christine A1 - Ritter, Christoph A1 - Cappelletti, David T1 - Mathematical tool for a closure study of aerosol microphysical property retrieval using lidar and photometer data T2 - IGARSS 2018 - 2018 IEEE International Geoscience and Remote Sensing Symposium N2 - We present a project combining lidar, photometer and particle counter data with a regularization software tool for a closure study of aerosol microphysical property retrieval. In a first step only lidar data are used to retrieve the particle size distribution (PSD). Secondly, photometer data are added, which results in a good consistency of the retrieved PSDs. Finally, those retrieved PSDs may be compared with the measured PSD from a particle counter. The data here were taken in Ny Alesund, Svalbard, as an example. KW - Aerosol KW - Raman lidar KW - photometer KW - inversion KW - regularization KW - particle microphysics Y1 - 2018 SN - 978-1-5386-7150-4 U6 - https://doi.org/10.1109/IGARSS.2018.8518674 SN - 2153-6996 SP - 5575 EP - 5578 PB - IEEE CY - New York ER - TY - JOUR A1 - Bourne, D. P. A1 - Cushing, D. A1 - Liu, S. A1 - Münch, Florentin A1 - Peyerimhoff, Norbert T1 - Ollivier-Ricci idleness functions of graphs JF - SIAM Journal on Discrete Mathematics N2 - We study the Ollivier-Ricci curvature of graphs as a function of the chosen idleness. We show that this idleness function is concave and piecewise linear with at most three linear parts, and at most two linear parts in the case of a regular graph. We then apply our result to show that the idleness function of the Cartesian product of two regular graphs is completely determined by the idleness functions of the factors. KW - Ollivier-Ricci KW - idleness KW - optimal transport Y1 - 2018 U6 - https://doi.org/10.1137/17M1134469 SN - 0895-4801 SN - 1095-7146 VL - 32 IS - 2 SP - 1408 EP - 1424 PB - Society for Industrial and Applied Mathematics CY - Philadelphia ER - TY - GEN A1 - Blanchard, Gilles A1 - Scott, Clayton T1 - Corrigendum to: Classification with asymmetric label noise BT - Consistency and maximal denoising T2 - Electronic journal of statistics N2 - 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. Y1 - 2018 U6 - https://doi.org/10.1214/18-EJS1422 SN - 1935-7524 VL - 12 IS - 1 SP - 1779 EP - 1781 PB - Institute of Mathematical Statistics CY - Cleveland ER - TY - JOUR A1 - Blanchard, Gilles A1 - Mücke, Nicole T1 - Optimal rates for regularization of statistical inverse learning problems JF - Foundations of Computational Mathematics N2 - We consider a statistical inverse learning (also called inverse regression) problem, where we observe the image of a function f through a linear operator A at i.i.d. random design points X-i , superposed with an additive noise. The distribution of the design points is unknown and can be very general. We analyze simultaneously the direct (estimation of Af) and the inverse (estimation of f) learning problems. In this general framework, we obtain strong and weak minimax optimal rates of convergence (as the number of observations n grows large) for a large class of spectral regularization methods over regularity classes defined through appropriate source conditions. This improves on or completes previous results obtained in related settings. The optimality of the obtained rates is shown not only in the exponent in n but also in the explicit dependency of the constant factor in the variance of the noise and the radius of the source condition set. KW - Reproducing kernel Hilbert space KW - Spectral regularization KW - Inverse problem KW - Statistical learning KW - Minimax convergence rates Y1 - 2018 U6 - https://doi.org/10.1007/s10208-017-9359-7 SN - 1615-3375 SN - 1615-3383 VL - 18 IS - 4 SP - 971 EP - 1013 PB - Springer CY - New York ER -