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 - JOUR A1 - Klein, Markus A1 - Rosenberger, Elke T1 - Tunneling for a class of difference operators JF - ANNALES HENRI POINCARE N2 - We analyze a general class of difference operators on where is a multi-well potential and is a small parameter. We decouple the wells by introducing certain Dirichlet operators on regions containing only one potential well, and we shall treat the eigenvalue problem for as a small perturbation of these comparison problems. We describe tunneling by a certain interaction matrix, similar to the analysis for the Schrodinger operator [see Helffer and Sjostrand in Commun Partial Differ Equ 9:337-408, 1984], and estimate the remainder, which is exponentially small and roughly quadratic compared with the interaction matrix. Y1 - 2012 U6 - https://doi.org/10.1007/s00023-011-0152-x SN - 1424-0637 VL - 13 IS - 5 SP - 1231 EP - 1269 PB - Springer CY - Basel ER - TY - INPR A1 - Klein, Markus A1 - Rosenberger, Elke T1 - Tunneling for a class of difference operators N2 - We analyze a general class of difference operators containing a multi-well potential and a small parameter. We decouple the wells by introducing certain Dirichlet operators on regions containing only one potential well, and we treat the eigenvalue problem as a small perturbation of these comparison problems. We describe tunneling by a certain interaction matrix similar to the analysis for the Schrödinger operator, and estimate the remainder, which is exponentially small and roughly quadratic compared with the interaction matrix. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 1 (2012) 5 KW - semi-classical difference operator KW - tunneling KW - interaction matrix Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-56989 ER - TY - JOUR A1 - Neidhardt, Hagen A1 - Zagrebnov, Valentin A. T1 - Trotter-Kato product formula and symmetrically-normed ideals Y1 - 1998 ER - TY - JOUR A1 - Neidhardt, Hagen A1 - Zagrebnov, Valentin A. T1 - Trotter-Kato product formula and operator-norm convergence Y1 - 1999 ER - TY - JOUR A1 - Zagrebnov, Valentin T1 - Trotter product formula on Hilbert and Banach spaces for operator-norm convergence JF - Lectures in pure and applied mathematics KW - random point processes KW - statistical mechanics KW - stochastic analysis Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-471971 SN - 978-3-86956-485-2 SN - 2199-4951 SN - 2199-496X SP - 23 EP - 34 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Brungs, Hans A1 - Gräter, Joachim T1 - Trees and Valuation Rings Y1 - 2000 ER - TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Pabhapote, Nittiya T1 - Tree-recognizers and tree-hyperrecognizers Y1 - 2001 ER - TY - JOUR A1 - Arworn, Srichan A1 - Denecke, Klaus-Dieter T1 - Tree Transformations defined by Hypersubstitutions Y1 - 2001 SN - 1509 - 9415 ER - TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Leeratanavalee, Sorasak T1 - Tree transformations defined by generalized hypersubstitutions Y1 - 2003 ER - TY - INPR A1 - Gairing, Jan A1 - Högele, Michael A1 - Kosenkova, Tetiana T1 - Transportation distances and noise sensitivity of multiplicative Lévy SDE with applications N2 - This article assesses the distance between the laws of stochastic differential equations with multiplicative Lévy noise on path space in terms of their characteristics. The notion of transportation distance on the set of Lévy kernels introduced by Kosenkova and Kulik yields a natural and statistically tractable upper bound on the noise sensitivity. This extends recent results for the additive case in terms of coupling distances to the multiplicative case. The strength of this notion is shown in a statistical implementation for simulations and the example of a benchmark time series in paleoclimate. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 5 (2016) 2 KW - stochastic differential equations KW - multiplicative Lévy noise KW - Lévy type processes KW - heavy-tailed distributions KW - model selection KW - Wasserstein distance KW - time series Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-86693 SN - 2193-6943 VL - 5 IS - 2 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Gairing, Jan A1 - Högele, Michael A1 - Kosenkova, Tetiana T1 - Transportation distances and noise sensitivity of multiplicative Levy SDE with applications JF - Stochastic processes and their application N2 - This article assesses the distance between the laws of stochastic differential equations with multiplicative Levy noise on path space in terms of their characteristics. The notion of transportation distance on the set of Levy kernels introduced by Kosenkova and Kulik yields a natural and statistically tractable upper bound on the noise sensitivity. This extends recent results for the additive case in terms of coupling distances to the multiplicative case. The strength of this notion is shown in a statistical implementation for simulations and the example of a benchmark time series in paleoclimate. KW - Stochastic differential equations KW - Multiplicative Levy noise KW - Levy type processes KW - Heavy-tailed distributions KW - Model selection KW - Wasserstein distance KW - Time series Y1 - 2017 U6 - https://doi.org/10.1016/j.spa.2017.09.003 SN - 0304-4149 SN - 1879-209X VL - 128 IS - 7 SP - 2153 EP - 2178 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Schulze, Bert-Wolfgang T1 - Transmission algebras on singular spaces with components of different dimensions Y1 - 1995 ER - TY - JOUR A1 - Wicha, Sebastian G. A1 - Huisinga, Wilhelm A1 - Kloft, Charlotte T1 - Translational pharmacometric evaluation of typical antibiotic broad-spectrum combination therapies against staphylococcus aureus exploiting in vitro information JF - CPT: pharmacometrics & systems pharmacology N2 - Broad-spectrum antibiotic combination therapy is frequently applied due to increasing resistance development of infective pathogens. The objective of the present study was to evaluate two common empiric broad-spectrum combination therapies consisting of either linezolid (LZD) or vancomycin (VAN) combined with meropenem (MER) against Staphylococcus aureus (S. aureus) as the most frequent causative pathogen of severe infections. A semimechanistic pharmacokinetic-pharmacodynamic (PK-PD) model mimicking a simplified bacterial life-cycle of S. aureus was developed upon time-kill curve data to describe the effects of LZD, VAN, and MER alone and in dual combinations. The PK-PD model was successfully (i) evaluated with external data from two clinical S. aureus isolates and further drug combinations and (ii) challenged to predict common clinical PK-PD indices and breakpoints. Finally, clinical trial simulations were performed that revealed that the combination of VAN-MER might be favorable over LZD-MER due to an unfavorable antagonistic interaction between LZD and MER. Y1 - 2017 U6 - https://doi.org/10.1002/psp4.12197 SN - 2163-8306 VL - 6 SP - 512 EP - 522 PB - Wiley CY - Hoboken ER - TY - JOUR A1 - Schrohe, Elmar T1 - Traces on the cone algebra with asymptotics Y1 - 1996 ER - TY - JOUR A1 - Grubb, G. A1 - Schrohe, Elmar T1 - Trace expansions and the noncommutative dresidue for manifolds with boundary Y1 - 2001 ER - TY - GEN A1 - Weisser, Karin A1 - Stübler, Sabine A1 - Matheis, Walter A1 - Huisinga, Wilhelm T1 - Towards toxicokinetic modelling of aluminium exposure from adjuvants in medicinal products T2 - Regulatory toxicology and pharmacology : official journal of the International Society for Regulatory Toxicology and Pharmacology N2 - As a potentially toxic agent on nervous system and bone, the safety of aluminium exposure from adjuvants in vaccines and subcutaneous immune therapy (SCIT) products has to be continuously reevaluated, especially regarding concomitant administrations. For this purpose, knowledge on absorption and disposition of aluminium in plasma and tissues is essential. Pharmacokinetic data after vaccination in humans, however, are not available, and for methodological and ethical reasons difficult to obtain. To overcome these limitations, we discuss the possibility of an in vitro-in silico approach combining a toxicokinetic model for aluminium disposition with biorelevant kinetic absorption parameters from adjuvants. We critically review available kinetic aluminium-26 data for model building and, on the basis of a reparameterized toxicokinetic model (Nolte et al., 2001), we identify main modelling gaps. The potential of in vitro dissolution experiments for the prediction of intramuscular absorption kinetics of aluminium after vaccination is explored. It becomes apparent that there is need for detailed in vitro dissolution and in vivo absorption data to establish an in vitro-in vivo correlation (IVIVC) for aluminium adjuvants. We conclude that a combination of new experimental data and further refinement of the Nolte model has the potential to fill a gap in aluminium risk assessment. (C) 2017 Elsevier Inc. All rights reserved. KW - Aluminium KW - Aluminium adjuvants KW - Absorption kinetics KW - Toxicokinetic modelling KW - In vitro dissolution Y1 - 2017 U6 - https://doi.org/10.1016/j.yrtph.2017.02.018 SN - 0273-2300 SN - 1096-0295 VL - 88 SP - 310 EP - 321 PB - Elsevier CY - San Diego ER - TY - JOUR A1 - Neidhardt, Hagen A1 - Zagrebnov, Valentin A. T1 - Towards the right Hamiltonians for singular perturbations via regularization and extension theory Y1 - 1996 ER - TY - JOUR A1 - Acevedo, Walter A1 - Reich, Sebastian A1 - Cubasch, Ulrich T1 - Towards the assimilation of tree-ring-width records using ensemble Kalman filtering techniques JF - Climate dynamics : observational, theoretical and computational research on the climate system N2 - This paper investigates the applicability of the Vaganov–Shashkin–Lite (VSL) forward model for tree-ring-width chronologies as observation operator within a proxy data assimilation (DA) setting. Based on the principle of limiting factors, VSL combines temperature and moisture time series in a nonlinear fashion to obtain simulated TRW chronologies. When used as observation operator, this modelling approach implies three compounding, challenging features: (1) time averaging, (2) “switching recording” of 2 variables and (3) bounded response windows leading to “thresholded response”. We generate pseudo-TRW observations from a chaotic 2-scale dynamical system, used as a cartoon of the atmosphere-land system, and attempt to assimilate them via ensemble Kalman filtering techniques. Results within our simplified setting reveal that VSL’s nonlinearities may lead to considerable loss of assimilation skill, as compared to the utilization of a time-averaged (TA) linear observation operator. In order to understand this undesired effect, we embed VSL’s formulation into the framework of fuzzy logic (FL) theory, which thereby exposes multiple representations of the principle of limiting factors. DA experiments employing three alternative growth rate functions disclose a strong link between the lack of smoothness of the growth rate function and the loss of optimality in the estimate of the TA state. Accordingly, VSL’s performance as observation operator can be enhanced by resorting to smoother FL representations of the principle of limiting factors. This finding fosters new interpretations of tree-ring-growth limitation processes. KW - Proxy forward modeling KW - Data assimilation KW - Fuzzy logic KW - Ensemble Kalman filter KW - Paleoclimate reconstruction Y1 - 2016 U6 - https://doi.org/10.1007/s00382-015-2683-1 SN - 0930-7575 SN - 1432-0894 VL - 46 SP - 1909 EP - 1920 PB - Springer CY - New York ER - TY - THES A1 - Reimann, Hans T1 - Towards robust inference for Bayesian filtering of linear Gaussian dynamical systems subject to additive change T1 - Hin zu einer robusten Inferenz für Bayes'sche Filterung linearer gaußscher dynamischer Systeme bei additiver Veränderung N2 - State space models enjoy wide popularity in mathematical and statistical modelling across disciplines and research fields. Frequent solutions to problems of estimation and forecasting of a latent signal such as the celebrated Kalman filter hereby rely on a set of strong assumptions such as linearity of system dynamics and Gaussianity of noise terms. We investigate fallacy in mis-specification of the noise terms, that is signal noise and observation noise, regarding heavy tailedness in that the true dynamic frequently produces observation outliers or abrupt jumps of the signal state due to realizations of these heavy tails not considered by the model. We propose a formalisation of observation noise mis-specification in terms of Huber’s ε-contamination as well as a computationally cheap solution via generalised Bayesian posteriors with a diffusion Stein divergence loss resulting in the diffusion score matching Kalman filter - a modified algorithm akin in complexity to the regular Kalman filter. For this new filter interpretations of novel terms, stability and an ensemble variant are discussed. Regarding signal noise mis-specification, we propose a formalisation in the frame work of change point detection and join ideas from the popular CUSUM algo- rithm with ideas from Bayesian online change point detection to combine frequent reliability constraints and online inference resulting in a Gaussian mixture model variant of multiple Kalman filters. We hereby exploit open-end sequential probability ratio tests on the evidence of Kalman filters on observation sub-sequences for aggregated inference under notions of plausibility. Both proposed methods are combined to investigate the double mis-specification problem and discussed regarding their capabilities in reliable and well-tuned uncertainty quantification. Each section provides an introduction to required terminology and tools as well as simulation experiments on the popular target tracking task and the non-linear, chaotic Lorenz-63 system to showcase practical performance of theoretical considerations. N2 - Modelle im Zustandsraum finden breite Anwendung in der mathematischen und statistischen Modellierung verschiedener Disziplinen und Forschungsgebiete. Häufige Lösung von Problemen der Schätzung und Vorhersage von latenten Signalen wie der populäre Kalman Filter benötigen hierbei eine Reihe von starken annahmen wie Linearität der Dynamiken des Systems und Normalität der Fehlerterme. Wir untersuchen Hürden in der Modellierung durch Mis-Spezifizierung der Fehlerterme, hier des Signalfehlers und des Beobachtungsfehlers, bezüglich schweren Rändern. Die wahre Dynamik produziert häufig Beobachtungsausreißer oder plötzliche Sprünge des Signals als Realisationen dieser schweren Ränder, diese werden aber nicht durch das Modell berücksichtigt. Wir schlagen eine Formalisierung der Mis-Spezifizierung des Beobachtungsfehlers im Sinne von Hubers Epsilon-Kontaminierung sowie eine rechnerisch kosteneffiziente Lösung vor. Diese Lösung durch generalisierte Bayes'sche a-posteriori Verteilungen mit einer Diffusion Stein Divergenz resultiert in dem Diffusion-Score-Matching Kalman Filter - ein modifizierter Algorithmus ähnlich dem regulären Kalman Filter in Komplexität. Für diesen neuen Filter diskutieren wir Interpretationen neuer Terme, der Langzeitstabilität und eine Ensemble Variante. Bezüglich der Mis-Spezifizierung des Signalfehlers schlagen wir eine Formalisierung durch Wechselpunktdetektierung vor und verknüpfen Ideen des populären CUSUM Algorithmus mit Ideen der Bayes'schen Online Wechselpunktdetektierung um Eigenschaften in Zuverlässigkeit und Online-Inferenz zu erhalten. Das Ergebnis ist eine Gaussian-Mixture-Model Variante aus mehreren Kalman Filtern. Hierbei nutzen wir explizit die Open-End sequentielle Probability-Ratio-Tests zwischen den verschiedenen Kalman Filtern, um Inferenzen unter Plausibiltätsargumenten zu aggregieren. Beide vorgeschlagenen Ansätze werden gemeinsam untersucht für den Fall der zweifachen Mis-Spezifizierung und die Ergebnisse werden diskutiert bezüglich ihrer Zuverlässigkeit und Unsicherheitsquantifizierung. Jedes Kapitel beinhaltet eine Einführung in die notwendige Terminologie und mathematischen Werkzeuge, sowie Simulationsexperimente für das populäre Beispiel des Target Trackings und das nicht-lineare, chaotische Lorenz-63 System, um die praktische Performance die Theorie zu veranschaulichen. KW - statistical model Mis-specification KW - robust filtering KW - state space change point detection KW - Bayesian filtering KW - Bayesian modelling KW - Bayes'sche Modellierung KW - robustes Filtern KW - Zustandsraum Wechselpunktdetektierung KW - Mis-Spezifizierung statistischer Modelle Y1 - 2024 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-649469 ER - TY - BOOK A1 - Schmidt, Hans-Jürgen A1 - Kluske, Sabine T1 - Towards a no hair theorem for higher order gravit Y1 - 1995 ER - TY - JOUR A1 - Kluske, Sabine A1 - Schmidt, Hans-Jürgen T1 - Towards a cosmic no hair theorem for higher-order gravity Y1 - 1996 ER - TY - JOUR A1 - Schmidt, Hans-Jürgen T1 - Topologische Aspekte in der Kosmologie Y1 - 2000 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 - BOOK A1 - Schulze, Bert-Wolfgang T1 - Toeplitz operators, and ellipticity of boundary value problems with global projection conditions T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2003 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - INPR A1 - Schulze, Bert-Wolfgang T1 - Toeplitz operators, and ellipticity of boundary value problems with global projection conditions N2 - Ellipticity of (pseudo-) differential operators A on a compact manifold X with boundary (or with edges) Y is connected with boundary (or edge) conditions of trace and potential type, formulated in terms of global projections on Y together with an additional symbolic structure. This gives rise to operator block matrices A with A in the upper left corner. We study an algebra of such operators, where ellipticity is equivalent to the Fredhom property in suitable scales of spaces: Sobolev spaces on X plus closed subspaces of Sobolev spaces on Y which are the range of corresponding pseudo-differential projections. Moreover, we express parametrices of elliptic elements within our algebra and discuss spectral boundary value problems for differential operators. T3 - Preprint - (2003) 03 Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26510 ER - TY - INPR A1 - Harutyunyan, Anahit V. T1 - Toeplitz operators and division theorems in anisotropic spaces of holomorphic functions in the polydisc N2 - This work is an introduction to anisotropic spaces, which have an ω-weight of analytic functions and are generalizations of Lipshitz classes in the polydisc. We prove that these classes form an algebra and are invariant with respect to monomial multiplication. These operators are bounded in these (Lipshitz and Djrbashian) spaces. As an application, we show a theorem about the division by good-inner functions in the mentioned classes is proved. T3 - Preprint - (2001) 28 KW - Toeplitz operators KW - anisotropic spaces KW - polydisc KW - good-inner function Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26110 ER - TY - BOOK A1 - Harutjunjan, A. V. T1 - Toeplitz operators and division theorems in anisotropic spaces of holomorphic functions in the polydisc T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2001 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Gavrilov, V. R. A1 - Kasper, Uwe A1 - Melnikov, V. N. A1 - Rainer, Martin T1 - Toda chains with type A(m) Lie algebra for multidimensional m-component perfect fluid cosmology Y1 - 1999 ER - TY - JOUR A1 - Gavrilov, V. R. A1 - Kasper, Uwe A1 - Melnikov, V. N. A1 - Rainer, Martin T1 - Toda chains with type A m Lie algebra for multidimensional m-component perfect fluid cosmology JF - Preprint / Universität Potsdam, Institut für Mathematik Y1 - 1998 VL - 1998, 02 PB - Univ. CY - Potsdam 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 - INPR A1 - Louis, Pierre-Yves A1 - Rouquier, Jean-Baptiste T1 - Time-to-Coalescence for interacting particle systems : parallel versus sequential updating N2 - Studying the influence of the updating scheme for MCMC algorithm on spatially extended models is a well known problem. For discrete-time interacting particle systems we study through simulations the effectiveness of a synchronous updating scheme versus the usual sequential one. We compare the speed of convergence of the associated Markov chains from the point of view of the time-to-coalescence arising in the coupling-from-the-past algorithm. Unlike the intuition, the synchronous updating scheme is not always the best one. The distribution of the time-to-coalescence for these spatially extended models is studied too. T3 - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2009, 03 Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49454 ER - TY - THES A1 - Angwenyi, David T1 - Time-continuous state and parameter estimation with application to hyperbolic SPDEs T1 - Zeitkontinuierliche Zustands- und Parameterschätzung bei Anwendung auf hyperbolische SPDEs N2 - Data assimilation has been an active area of research in recent years, owing to its wide utility. At the core of data assimilation are filtering, prediction, and smoothing procedures. Filtering entails incorporation of measurements' information into the model to gain more insight into a given state governed by a noisy state space model. Most natural laws are governed by time-continuous nonlinear models. For the most part, the knowledge available about a model is incomplete; and hence uncertainties are approximated by means of probabilities. Time-continuous filtering, therefore, holds promise for wider usefulness, for it offers a means of combining noisy measurements with imperfect model to provide more insight on a given state. The solution to time-continuous nonlinear Gaussian filtering problem is provided for by the Kushner-Stratonovich equation. Unfortunately, the Kushner-Stratonovich equation lacks a closed-form solution. Moreover, the numerical approximations based on Taylor expansion above third order are fraught with computational complications. For this reason, numerical methods based on Monte Carlo methods have been resorted to. Chief among these methods are sequential Monte-Carlo methods (or particle filters), for they allow for online assimilation of data. Particle filters are not without challenges: they suffer from particle degeneracy, sample impoverishment, and computational costs arising from resampling. The goal of this thesis is to:— i) Review the derivation of Kushner-Stratonovich equation from first principles and its extant numerical approximation methods, ii) Study the feedback particle filters as a way of avoiding resampling in particle filters, iii) Study joint state and parameter estimation in time-continuous settings, iv) Apply the notions studied to linear hyperbolic stochastic differential equations. The interconnection between Itô integrals and stochastic partial differential equations and those of Stratonovich is introduced in anticipation of feedback particle filters. With these ideas and motivated by the variants of ensemble Kalman-Bucy filters founded on the structure of the innovation process, a feedback particle filter with randomly perturbed innovation is proposed. Moreover, feedback particle filters based on coupling of prediction and analysis measures are proposed. They register a better performance than the bootstrap particle filter at lower ensemble sizes. We study joint state and parameter estimation, both by means of extended state spaces and by use of dual filters. Feedback particle filters seem to perform well in both cases. Finally, we apply joint state and parameter estimation in the advection and wave equation, whose velocity is spatially varying. Two methods are employed: Metropolis Hastings with filter likelihood and a dual filter comprising of Kalman-Bucy filter and ensemble Kalman-Bucy filter. The former performs better than the latter. N2 - Die Datenassimilation war in den letzten Jahren aufgrund ihres breiten Nutzens ein aktives Forschungsgebiet. Im Zentrum der Datenassimilation stehen Filter-, Vorhersage- und Glättungsverfahren. Die Filterung beinhaltet die Einbeziehung von Messinformationen in das Modell, um einen besseren Einblick in einen gegebenen Zustand zu erhalten, der durch ein verrauschtes Zustandsraummodell gesteuert wird. Die meisten Naturgesetze werden von zeitkontinuierlichen nichtlinearen Modellen bestimmt. Das verfügbare Wissen über ein Modell ist größtenteils unvollständig; und daher werden Unsicherheiten mittels Wahrscheinlichkeiten angenähert. Die zeitkontinuierliche Filterung verspricht daher eine größere Nützlichkeit, denn sie bietet die Möglichkeit, verrauschte Messungen mit einem unvollkommenen Modell zu kombinieren, um mehr Einblick in einen bestimmten Zustand zu erhalten. Das Problem der zeitkontinuierlichen nichtlinearen Gaußschen Filterung wird durch die Kushner-Stratonovich-Gleichung gelöst. Leider fehlt der Kushner-Stratonovich-Gleichung eine geschlossene Lösung. Darüber hinaus sind die numerischen Näherungen, die auf der Taylor-Erweiterung über der dritten Ordnung basieren, mit rechnerischen Komplikationen behaftet. Aus diesem Grund wurde auf numerische Methoden zurückgegriffen, die auf Monte-Carlo-Methoden basieren. Die wichtigsten dieser Methoden sind sequentielle Monte-Carlo-Methoden (oder Partikelfilter), da sie die Online-Assimilation von Daten ermöglichen. Partikelfilter sind nicht unproblematisch: Sie leiden unter Partikelentartung, Probenverarmung und Rechenkosten, die sich aus der Neuabtastung ergeben. Das Ziel dieser Arbeit ist es, i) die Ableitung der Kushner-Stratonovich-Gleichung aus den ersten Prinzipien und ihre vorhandenen numerischen Approximationsmethoden zu überprüfen, ii) die Rückkopplungs-Partikelfilter zu untersuchen, um eine Neuabtastung in Partikelfiltern zu vermeiden, iii) Studieren Sie die Zustands- und Parameterschätzung in zeitkontinuierlichen Einstellungen, iv) Wenden Sie die untersuchten Begriffe auf lineare hyperbolische stochastische Differentialgleichungen an. Die Verbindung zwischen Itô Integralen und stochastischen partiellen Differentialgleichungen und denen von Stratonovich wird in Erwartung von Rückkopplungs-Partikelfiltern eingeführt. Mit diesen Ideen und motiviert durch die Varianten von Kalman-Bucy-Filtern, die auf der Struktur des Innovationsprozesses gegründet, wird ein Feedback-Partikelfilter mit zufällig gestörter Innovation vorgeschlagen. Darüber hinaus werden Rückkopplungspartikelfilter basierend auf der Kopplung von Vorhersage- und Analysemaßnahmen vorgeschlagen. Diese Feedback-Partikelfiltern haben eine bessere Leistung als der Bootstrap-Partikelfilter bei niedrigeren Ensemble-Größen. Wir untersuchen gemeinsame Zustands- und Parameterschätzungen, sowohl durch erweiterte Zustandsräume als auch durch Verwendung von Doppelfiltern. Rückkopplungs-Partikelfilter scheinen in beiden Fällen gut zu funktionieren. Schließlich wenden wir eine gemeinsame Zustands- und Parameterschätzung in der Advektions-und Wellengleichung an, deren Geschwindigkeit räumlich variiert. Es werden zwei Verfahren verwendet: Metropolis-Hastings mit Filterwahrscheinlichkeit und ein Doppelfilter bestehend aus Kalman-Bucy-Filter und Ensemble-Kalman-Bucy-Filter. Ersteres schneidet besser ab als letzteres. KW - state estimation KW - filtering KW - parameter estimation KW - Zustandsschätzung KW - Filterung KW - Parameter Schätzung Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-436542 ER - TY - JOUR A1 - Klein, Markus A1 - Rama, Juliane T1 - Time asymptotics of e(-ith(kappa)) for analytic matrices and analytic perturbation theory JF - Asymptotic analysis N2 - In quantum mechanics the temporal decay of certain resonance states is associated with an effective time evolution e(-ith(kappa)), where h(.) is an analytic family of non-self-adjoint matrices. In general the corresponding resonance states do not decay exponentially in time. Using analytic perturbation theory, we derive asymptotic expansions for e(-ith(kappa)), simultaneously in the limits kappa -> 0 and t -> infinity, where the corrections with respect to pure exponential decay have uniform bounds in one complex variable kappa(2)t. In the Appendix we briefly review analytic perturbation theory, replacing the classical reference to the 1920 book of Knopp [Funktionentheorie II, Anwendungen und Weiterfuhrung der allgemeinen Theorie, Sammlung Goschen, Vereinigung wissenschaftlicher Verleger Walter de Gruyter, 1920] and its terminology by standard modern references. This might be of independent interest. KW - resonances KW - exponential decay KW - long-time corrections KW - Fermi golden rule KW - analytic perturbation theory Y1 - 2014 U6 - https://doi.org/10.3233/ASY-141226 SN - 0921-7134 SN - 1875-8576 VL - 89 IS - 3-4 SP - 189 EP - 233 PB - IOS Press CY - Amsterdam ER - TY - JOUR A1 - Rastogi, Abhishake T1 - Tikhonov regularization with oversmoothing penalty for nonlinear statistical inverse problems JF - Communications on Pure and Applied Analysis N2 - In this paper, we consider the nonlinear ill-posed inverse problem with noisy data in the statistical learning setting. The Tikhonov regularization scheme in Hilbert scales is considered to reconstruct the estimator from the random noisy data. In this statistical learning setting, we derive the rates of convergence for the regularized solution under certain assumptions on the nonlinear forward operator and the prior assumptions. We discuss estimates of the reconstruction error using the approach of reproducing kernel Hilbert spaces. KW - Statistical inverse problem KW - Tikhonov regularization KW - Hilbert Scales KW - reproducing kernel Hilbert space KW - minimax convergence rates Y1 - 2020 U6 - https://doi.org/10.3934/cpaa.2020183 SN - 1534-0392 SN - 1553-5258 VL - 19 IS - 8 SP - 4111 EP - 4126 PB - American Institute of Mathematical Sciences CY - Springfield ER - TY - JOUR A1 - Saynisch-Wagner, Jan A1 - Bärenzung, Julien A1 - Hornschild, Aaron A1 - Irrgang, Christopher A1 - Thomas, Maik T1 - Tide-induced magnetic signals and their errors derived from CHAMP and Swarm satellite magnetometer observations JF - Earth, planets and space : EPS N2 - Satellite-measured tidal magnetic signals are of growing importance. These fields are mainly used to infer Earth's mantle conductivity, but also to derive changes in the oceanic heat content. We present a new Kalman filter-based method to derive tidal magnetic fields from satellite magnetometers: KALMAG. The method's advantage is that it allows to study a precisely estimated posterior error covariance matrix. We present the results of a simultaneous estimation of the magnetic signals of 8 major tides from 17 years of Swarm and CHAMP data. For the first time, robustly derived posterior error distributions are reported along with the reported tidal magnetic fields. The results are compared to other estimates that are either based on numerical forward models or on satellite inversions of the same data. For all comparisons, maximal differences and the corresponding globally averaged RMSE are reported. We found that the inter-product differences are comparable with the KALMAG-based errors only in a global mean sense. Here, all approaches give values of the same order, e.g., 0.09 nT-0.14 nT for M2. Locally, the KALMAG posterior errors are up to one order smaller than the inter-product differences, e.g., 0.12 nT vs. 0.96 nT for M2. KW - Tides KW - Electromagnetic induction KW - Error covariance KW - Satellite magnetometer observations Y1 - 2021 U6 - https://doi.org/10.1186/s40623-021-01557-3 SN - 1880-5981 VL - 73 IS - 1 PB - Springer CY - Heidelberg ER - TY - JOUR A1 - Hamm, Maximilian A1 - Pelivan, Ivanka A1 - Grott, Matthias A1 - de Wiljes, Jana T1 - Thermophysical modelling and parameter estimation of small solar system bodies via data assimilation JF - Monthly notices of the Royal Astronomical Society N2 - Deriving thermophysical properties such as thermal inertia from thermal infrared observations provides useful insights into the structure of the surface material on planetary bodies. The estimation of these properties is usually done by fitting temperature variations calculated by thermophysical models to infrared observations. For multiple free model parameters, traditional methods such as least-squares fitting or Markov chain Monte Carlo methods become computationally too expensive. Consequently, the simultaneous estimation of several thermophysical parameters, together with their corresponding uncertainties and correlations, is often not computationally feasible and the analysis is usually reduced to fitting one or two parameters. Data assimilation (DA) methods have been shown to be robust while sufficiently accurate and computationally affordable even for a large number of parameters. This paper will introduce a standard sequential DA method, the ensemble square root filter, for thermophysical modelling of asteroid surfaces. This method is used to re-analyse infrared observations of the MARA instrument, which measured the diurnal temperature variation of a single boulder on the surface of near-Earth asteroid (162173) Ryugu. The thermal inertia is estimated to be 295 +/- 18 Jm(-2) K-1 s(-1/2), while all five free parameters of the initial analysis are varied and estimated simultaneously. Based on this thermal inertia estimate the thermal conductivity of the boulder is estimated to be between 0.07 and 0.12,Wm(-1) K-1 and the porosity to be between 0.30 and 0.52. For the first time in thermophysical parameter derivation, correlations and uncertainties of all free model parameters are incorporated in the estimation procedure that is more than 5000 times more efficient than a comparable parameter sweep. KW - radiation mechanisms: thermal KW - methods: data analysis KW - methods KW - statistical KW - minor planets, asteroids: individual: (162173) Ryugu Y1 - 2020 U6 - https://doi.org/10.1093/mnras/staa1755 SN - 0035-8711 SN - 1365-2966 VL - 496 IS - 3 SP - 2776 EP - 2785 PB - Oxford Univ. Press CY - Oxford ER - TY - JOUR A1 - Cozzoni, Barbara A1 - Maibaum, Michael A1 - Hamm, Maximilian T1 - Thermal analysis and constraints for the MASCOT landing site selection on the asteroid Ryugu JF - Planetary and space science N2 - In June 2018, after 4 years of cruise, the Japanese space probe Hayabusa2 [1-Watanabe S. et al.: Hayabusa2 Mission Overview. (2017)] reached the Near-Earth Asteroid (162173) Ryugu. Hayabusa2 carried a small Lander named MASCOT (Mobile Asteroid Surface Scout) [2-Ho T. M. et al.: MASCOT-The Mobile Asteroid Surface Scout onboard the Hayabusa2 mission. (2017)], jointly developed by the German Aerospace Center (DLR) and the French Space Agency (CNES), to investigate Ryugu's surface structure, composition and physical properties including its thermal behaviour and magnetization in-situ. The Microgravity User Support Centre (DLR-MUSC) in Cologne was in charge of providing all thermal conditions and constraints necessary for the selection of the final landing site and for the final operations of the Lander MASCOT on the surface of the asteroid Ryugu. This article provides a comprehensive assessment of these thermal conditions and constraints, based on predictions performed with the Thermal Mathematical Model (TMM) of MASCOT using different asteroid surface thermal models, ephemeris data for approach as well as descent and hopping trajectories, the related operation sequences and scenarios and the possible environmental conditions driven by the Hayabusa2 spacecraft. A comparison with the real telemetry data confirms the analysis and provides further information about the asteroid characteristics. KW - MASCOT KW - Thermal mathematical model KW - Landing site selection KW - Small KW - spacecraft operations Y1 - 2021 U6 - https://doi.org/10.1016/j.pss.2021.105286 SN - 0032-0633 SN - 1873-5088 VL - 205 PB - Elsevier CY - Oxford ER - TY - JOUR A1 - Mueller-Schoell, Anna A1 - Groenland, Stefanie L. A1 - Scherf-Clavel, Oliver A1 - van Dyk, Madele A1 - Huisinga, Wilhelm A1 - Michelet, Robin A1 - Jaehde, Ulrich A1 - Steeghs, Neeltje A1 - Huitema, Alwin D. R. A1 - Kloft, Charlotte T1 - Therapeutic drug monitoring of oral targeted antineoplastic drugs JF - European journal of clinical pharmacology N2 - Purpose This review provides an overview of the current challenges in oral targeted antineoplastic drug (OAD) dosing and outlines the unexploited value of therapeutic drug monitoring (TDM). Factors influencing the pharmacokinetic exposure in OAD therapy are depicted together with an overview of different TDM approaches. Finally, current evidence for TDM for all approved OADs is reviewed. Methods A comprehensive literature search (covering literature published until April 2020), including primary and secondary scientific literature on pharmacokinetics and dose individualisation strategies for OADs, together with US FDA Clinical Pharmacology and Biopharmaceutics Reviews and the Committee for Medicinal Products for Human Use European Public Assessment Reports was conducted. Results OADs are highly potent drugs, which have substantially changed treatment options for cancer patients. Nevertheless, high pharmacokinetic variability and low treatment adherence are risk factors for treatment failure. TDM is a powerful tool to individualise drug dosing, ensure drug concentrations within the therapeutic window and increase treatment success rates. After reviewing the literature for 71 approved OADs, we show that exposure-response and/or exposure-toxicity relationships have been established for the majority. Moreover, TDM has been proven to be feasible for individualised dosing of abiraterone, everolimus, imatinib, pazopanib, sunitinib and tamoxifen in prospective studies. There is a lack of experience in how to best implement TDM as part of clinical routine in OAD cancer therapy. Conclusion Sub-therapeutic concentrations and severe adverse events are current challenges in OAD treatment, which can both be addressed by the application of TDM-guided dosing, ensuring concentrations within the therapeutic window. KW - targeted antineoplastic drugs KW - tyrosine kinase inhibitors KW - therapeutic KW - drug monitoring KW - oral anticancer drugs KW - personalised medicine Y1 - 2020 U6 - https://doi.org/10.1007/s00228-020-03014-8 SN - 0031-6970 SN - 1432-1041 VL - 77 IS - 4 SP - 441 EP - 464 PB - Springer CY - Heidelberg ER - TY - INPR A1 - Harutjunjan, Gohar A1 - Schulze, Bert-Wolfgang T1 - The Zaremba problem with singular interfaces as a corner boundary value problem N2 - We study mixed boundary value problems for an elliptic operator A on a manifold X with boundary Y , i.e., Au = f in int X, T±u = g± on int Y±, where Y is subdivided into subsets Y± with an interface Z and boundary conditions T± on Y± that are Shapiro-Lopatinskij elliptic up to Z from the respective sides. We assume that Z ⊂ Y is a manifold with conical singularity v. As an example we consider the Zaremba problem, where A is the Laplacian and T− Dirichlet, T+ Neumann conditions. The problem is treated as a corner boundary value problem near v which is the new point and the main difficulty in this paper. Outside v the problem belongs to the edge calculus as is shown in [3]. With a mixed problem we associate Fredholm operators in weighted corner Sobolev spaces with double weights, under suitable edge conditions along Z \ {v} of trace and potential type. We construct parametrices within the calculus and establish the regularity of solutions. T3 - Preprint - (2004) 26 KW - Zaremba problem KW - corner Sobolev spaces with double weights KW - pseudodifferential boundary value problems Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26855 ER - TY - BOOK A1 - Harutjunjan, Gohar A1 - Schulze, Bert-Wolfgang T1 - The zaremba problem with singular interfaces as a corner boundary value problem T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2004 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Harutyunyan, Gohar A1 - Schulze, Bert-Wolfgang T1 - The Zaremba problem with singular interfaces as a corner boundary value problem JF - Potential analysis : an international journal devoted to the interactions between potential theory, probability theory, geometry and functional analysis N2 - We study mixed boundary value problems for an elliptic operator A on a manifold X with boundary Y, i.e., Au = f in int X, T (+/-) u = g(+/-) on int Y+/-, where Y is subdivided into subsets Y+/- with an interface Z and boundary conditions T+/- on Y+/- that are Shapiro-Lopatinskij elliptic up to Z from the respective sides. We assume that Z subset of Y is a manifold with conical singularity v. As an example we consider the Zaremba problem, where A is the Laplacian and T- Dirichlet, T+ Neumann conditions. The problem is treated as a corner boundary value problem near v which is the new point and the main difficulty in this paper. Outside v the problem belongs to the edge calculus as is shown in Bull. Sci. Math. ( to appear). With a mixed problem we associate Fredholm operators in weighted corner Sobolev spaces with double weights, under suitable edge conditions along Z {v} of trace and potential type. We construct parametrices within the calculus and establish the regularity of solutions. KW - Zaremba problem KW - corner Sobolev spaces with double weights KW - pseudo-differential boundary value problems Y1 - 2006 U6 - https://doi.org/10.1007/s11118-006-9020-6 SN - 0926-2601 VL - 25 SP - 327 EP - 369 PB - Springer CY - Dordrecht ER - TY - INPR A1 - Dines, Nicoleta A1 - Harutjunjan, Gohar A1 - Schulze, Bert-Wolfgang T1 - The Zaremba problem in edge Sobolev spaces N2 - Mixed elliptic boundary value problems are characterised by conditions which have a jump along an interface of codimension 1 on the boundary. We study such problems in weighted edge Sobolev spaces and show the Fredholm property and the existence of parametrices under additional conditions of trace and potential type on the interface. Our methods from the calculus of boundary value problems on a manifold with edges will be illustrated by the Zaremba problem and other mixed problems for the Laplace operator. T3 - Preprint - (2003) 13 Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26615 ER - TY - BOOK A1 - Dines, Nicoleta A1 - Harutjunjan, Gohar A1 - Schulze, Bert-Wolfgang T1 - The Zaremba problem in edge sobolev spaces T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2003 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Denecke, Klaus-Dieter A1 - Freiberg, L. T1 - The word problem for M-solid varieties of semigroups Y1 - 1998 SN - 981-3083-86-7 ER - TY - JOUR A1 - Schulze, Bert-Wolfgang T1 - The variable discrete asymptotics in pseudo-differential boundary value problems II Y1 - 1995 ER - TY - JOUR A1 - Schulze, Bert-Wolfgang T1 - The variable discrete asymptotics in pseudo-differential boundary value problems II Y1 - 1995 ER - TY - JOUR A1 - Schulze, Bert-Wolfgang T1 - The variable discrete asymptotics in pseudo-differential boundary value problems Y1 - 1994 ER - TY - CHAP A1 - Hafer, Jörg A1 - Kiy, Alexander ED - Buchem, Ilona ED - Graham, Attwell ED - Tur, Gemma T1 - The university-wide introduction of an ePortfolio system as transdisciplinary task BT - Results of an implementation process and perspectives on an optimized process model T2 - Proceedings of the PLE Conference 2013: Learning and Diversity in the Cities of the Future Y1 - 2013 SP - 363 EP - 373 PB - Logos CY - Berlin ER - TY - JOUR A1 - Klein, Markus A1 - Rosenberger, Elke T1 - The tunneling effect for Schrödinger operators on a vector bundle JF - Analysis and mathematical physics N2 - In the semiclassical limit (h) over bar -> 0, we analyze a class of self-adjoint Schrodinger operators H-(h) over bar = (h) over bar L-2 + (h) over barW + V center dot id(E) acting on sections of a vector bundle E over an oriented Riemannian manifold M where L is a Laplace type operator, W is an endomorphism field and the potential energy V has non-degenerate minima at a finite number of points m(1),... m(r) is an element of M, called potential wells. Using quasimodes of WKB-type near m(j) for eigenfunctions associated with the low lying eigenvalues of H-(h) over bar, we analyze the tunneling effect, i.e. the splitting between low lying eigenvalues, which e.g. arises in certain symmetric configurations. Technically, we treat the coupling between different potential wells by an interaction matrix and we consider the case of a single minimal geodesic (with respect to the associated Agmon metric) connecting two potential wells and the case of a submanifold of minimal geodesics of dimension l + 1. This dimension l determines the polynomial prefactor for exponentially small eigenvalue splitting. KW - Laplace-type operator KW - Vector bundle KW - WKB-expansion KW - Quasimodes KW - Tunneling KW - Spectral gap KW - Complete asymptotics Y1 - 2021 U6 - https://doi.org/10.1007/s13324-021-00485-5 SN - 1664-2368 SN - 1664-235X VL - 11 IS - 2 PB - Springer International Publishing AG CY - Cham (ZG) ER -