TY - CHAP A1 - Démaris, Alise A1 - Grišić, Ana-Marija A1 - Huisinga, Wilhelm A1 - Walter, Reinisch A1 - Kloft, Charlotte T1 - Evaluation of dosing strategies of anti-TNF alpha monoclonal antibodies using pharmacokinetic modelling and simulation T2 - Journal of Crohn's and Colitis N2 - Background: Anti-TNFα monoclonal antibodies (mAbs) are a well-established treatment for patients with Crohn’s disease (CD). However, subtherapeutic concentrations of mAbs have been related to a loss of response during the first year of therapy1. Therefore, an appropriate dosing strategy is crucial to prevent the underexposure of mAbs for those patients. The aim of our study was to assess the impact of different dosing strategies (fixed dose or body size descriptor adapted) on drug exposure and the target concentration attainment for two different anti-TNFα mAbs: infliximab (IFX, body weight (BW)-based dosing) and certolizumab pegol (CZP, fixed dosing). For this purpose, a comprehensive pharmacokinetic (PK) simulation study was performed. Methods: A virtual population of 1000 clinically representative CD patients was generated based on the distribution of CD patient characteristics from an in-house clinical database (n = 116). Seven dosing regimens were investigated: fixed dose and per BW, lean BW (LBW), body surface area, height, body mass index and fat-free mass. The individual body size-adjusted doses were calculated from patient generated body size descriptor values. Then, using published PK models for IFX and CZP in CD patients2,3, for each patient, 1000 concentration–time profiles were simulated to consider the typical profile of a specific patient as well as the range of possible individual profiles due to unexplained PK variability across patients. For each dosing strategy, the variability in maximum and minimum mAb concentrations (Cmax and Cmin, respectively), area under the concentration-time curve (AUC) and the per cent of patients reaching target concentration were assessed during maintenance therapy. Results: For IFX and CZP, Cmin showed the highest variability between patients (CV ≈110% and CV ≈80%, respectively) with a similar extent across all dosing strategies. For IFX, the per cent of patients reaching the target (Cmin = 5 µg/ml) was similar across all dosing strategies (~15%). For CZP, the per cent of patients reaching the target average concentration of 17 µg/ml ranged substantially (52–71%), being the highest for LBW-adjusted dosing. Conclusion: By using a PK simulation approach, different dosing regimen of IFX and CZP revealed the highest variability for Cmin, the most commonly used PK parameter guiding treatment decisions, independent upon dosing regimen. Our results demonstrate similar target attainment with fixed dosing of IFX compared with currently recommended BW-based dosing. For CZP, the current fixed dosing strategy leads to comparable percentage of patients reaching target as the best performing body size-adjusted dosing (66% vs. 71%, respectively). KW - linical databases KW - crohn's disease KW - regimen KW - monoclonal antibodies KW - body surface area KW - infliximab KW - fat-free mass KW - certolizumab pegol KW - body mass index procedure Y1 - 2020 U6 - https://doi.org/10.1093/ecco-jcc/jjz203.201 SN - 1873-9946 SN - 1876-4479 VL - 14 IS - Supp. 1 SP - S171 EP - S172 PB - Oxford Univ. Press CY - Oxford ER - TY - JOUR A1 - Eshghi, Nasim A1 - Mach, Thomas A1 - Reichel, Lothar T1 - New matrix function approximations and quadrature rules based on the Arnoldi process JF - Journal of computational and applied mathematics N2 - The Arnoldi process can be applied to inexpensively approximate matrix functions of the form f (A)v and matrix functionals of the form v*(f (A))*g(A)v, where A is a large square non-Hermitian matrix, v is a vector, and the superscript * denotes transposition and complex conjugation. Here f and g are analytic functions that are defined in suitable regions in the complex plane. This paper reviews available approximation methods and describes new ones that provide higher accuracy for essentially the same computational effort by exploiting available, but generally not used, moment information. Numerical experiments show that in some cases the modifications of the Arnoldi decompositions proposed can improve the accuracy of v*(f (A))*g(A)v about as much as performing an additional step of the Arnoldi process. KW - Arnoldi process KW - Matrix function approximation KW - Quadrature rule Y1 - 2021 U6 - https://doi.org/10.1016/j.cam.2021.113442 SN - 0377-0427 SN - 1879-1778 VL - 391 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Pohle, Jennifer A1 - Adam, Timo A1 - Beumer, Larissa T1 - Flexible estimation of the state dwell-time distribution in hidden semi-Markov models JF - Computational statistics & data analysis N2 - Hidden semi-Markov models generalise hidden Markov models by explicitly modelling the time spent in a given state, the so-called dwell time, using some distribution defined on the natural numbers. While the (shifted) Poisson and negative binomial distribution provide natural choices for such distributions, in practice, parametric distributions can lack the flexibility to adequately model the dwell times. To overcome this problem, a penalised maximum likelihood approach is proposed that allows for a flexible and data-driven estimation of the dwell-time distributions without the need to make any distributional assumption. This approach is suitable for direct modelling purposes or as an exploratory tool to investigate the latent state dynamics. The feasibility and potential of the suggested approach is illustrated in a simulation study and by modelling muskox movements in northeast Greenland using GPS tracking data. The proposed method is implemented in the R-package PHSMM which is available on CRAN. KW - Penalized likelihood KW - Smoothing KW - Time series KW - Animal movement modeling Y1 - 2022 U6 - https://doi.org/10.1016/j.csda.2022.107479 SN - 0167-9473 SN - 1872-7352 VL - 172 PB - Elsevier CY - Amsterdam ER - TY - GEN A1 - Kolbe, Benedikt Maximilian A1 - Evans, Myfanwy E. T1 - Isotopic tiling theory for hyperbolic surfaces T2 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - In this paper, we develop the mathematical tools needed to explore isotopy classes of tilings on hyperbolic surfaces of finite genus, possibly nonorientable, with boundary, and punctured. More specifically, we generalize results on Delaney-Dress combinatorial tiling theory using an extension of mapping class groups to orbifolds, in turn using this to study tilings of covering spaces of orbifolds. Moreover, we study finite subgroups of these mapping class groups. Our results can be used to extend the Delaney-Dress combinatorial encoding of a tiling to yield a finite symbol encoding the complexity of an isotopy class of tilings. The results of this paper provide the basis for a complete and unambiguous enumeration of isotopically distinct tilings of hyperbolic surfaces. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1347 KW - isotopic tiling theory KW - Delaney–Dress tiling theory KW - mapping class groups KW - Orbifolds KW - maps on surfaces KW - hyperbolic tilings Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-544285 SN - 1866-8372 IS - 1 ER - TY - JOUR A1 - Pathiraja, Sahani Darschika A1 - Leeuwen, Peter Jan van T1 - Multiplicative Non-Gaussian model error estimation in data assimilation JF - Journal of advances in modeling earth systems : JAMES N2 - Model uncertainty quantification is an essential component of effective data assimilation. Model errors associated with sub-grid scale processes are often represented through stochastic parameterizations of the unresolved process. Many existing Stochastic Parameterization schemes are only applicable when knowledge of the true sub-grid scale process or full observations of the coarse scale process are available, which is typically not the case in real applications. We present a methodology for estimating the statistics of sub-grid scale processes for the more realistic case that only partial observations of the coarse scale process are available. Model error realizations are estimated over a training period by minimizing their conditional sum of squared deviations given some informative covariates (e.g., state of the system), constrained by available observations and assuming that the observation errors are smaller than the model errors. From these realizations a conditional probability distribution of additive model errors given these covariates is obtained, allowing for complex non-Gaussian error structures. Random draws from this density are then used in actual ensemble data assimilation experiments. We demonstrate the efficacy of the approach through numerical experiments with the multi-scale Lorenz 96 system using both small and large time scale separations between slow (coarse scale) and fast (fine scale) variables. The resulting error estimates and forecasts obtained with this new method are superior to those from two existing methods. KW - model uncertainty KW - non-Gaussian KW - data-driven KW - uncertainty KW - quantification KW - Lorenz 96 KW - sub-grid scale Y1 - 2022 U6 - https://doi.org/10.1029/2021MS002564 SN - 1942-2466 VL - 14 IS - 4 PB - American Geophysical Union CY - Washington ER - TY - GEN A1 - Keller, Matthias A1 - Pinchover, Yehuda A1 - Pogorzelski, Felix T1 - From hardy to rellich inequalities on graphs T2 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - We show how to deduce Rellich inequalities from Hardy inequalities on infinite graphs. Specifically, the obtained Rellich inequality gives an upper bound on a function by the Laplacian of the function in terms of weighted norms. These weights involve the Hardy weight and a function which satisfies an eikonal inequality. The results are proven first for Laplacians and are extended to Schrodinger operators afterwards. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1379 KW - 35R02 KW - 39A12 (primary) KW - 26D15 KW - 31C20 KW - 35B09 KW - 58E35 (secondary) Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-542140 SN - 1866-8372 IS - 3 ER - TY - GEN A1 - Mazzonetto, Sara A1 - Salimova, Diyora T1 - Existence, uniqueness, and numerical approximations for stochastic burgers equations T2 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - In this article, we propose an all-in-one statement which includes existence, uniqueness, regularity, and numerical approximations of mild solutions for a class of stochastic partial differential equations (SPDEs) with non-globally monotone nonlinearities. The proof of this result exploits the properties of an existing fully explicit space-time discrete approximation scheme, in particular the fact that it satisfies suitable a priori estimates. We also obtain almost sure and strong convergence of the approximation scheme to the mild solutions of the considered SPDEs. We conclude by applying the main result of the article to the stochastic Burgers equations with additive space-time white noise. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1393 KW - stochastic Burgers equations KW - SPDEs KW - mild solution KW - existence KW - numerical approximation Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-515796 SN - 1866-8372 IS - 4 ER - TY - JOUR A1 - Hethey, Christoph Philipp A1 - Hartung, Niklas A1 - Wangorsch, Gaby A1 - Weisser, Karin A1 - Huisinga, Wilhelm T1 - Physiology-based toxicokinetic modelling of aluminium in rat and man JF - Archives of toxicology : official journal of EUROTOX N2 - A sufficient quantitative understanding of aluminium (Al) toxicokinetics (TK) in man is still lacking, although highly desirable for risk assessment of Al exposure. Baseline exposure and the risk of contamination severely limit the feasibility of TK studies administering the naturally occurring isotope Al-27, both in animals and man. These limitations are absent in studies with Al-26 as a tracer, but tissue data are limited to animal studies. A TK model capable of inter-species translation to make valid predictions of Al levels in humans-especially in toxicological relevant tissues like bone and brain-is urgently needed. Here, we present: (i) a curated dataset which comprises all eligible studies with single doses of Al-26 tracer administered as citrate or chloride salts orally and/or intravenously to rats and humans, including ultra-long-term kinetic profiles for plasma, blood, liver, spleen, muscle, bone, brain, kidney, and urine up to 150 weeks; and (ii) the development of a physiology-based (PB) model for Al TK after intravenous and oral administration of aqueous Al citrate and Al chloride solutions in rats and humans. Based on the comprehensive curated Al-26 dataset, we estimated substance-dependent parameters within a non-linear mixed-effect modelling context. The model fitted the heterogeneous Al-26 data very well and was successfully validated against datasets in rats and humans. The presented PBTK model for Al, based on the most extensive and diverse dataset of Al exposure to date, constitutes a major advancement in the field, thereby paving the way towards a more quantitative risk assessment in humans. KW - PBTK KW - Toxicokinetics KW - Al-26 KW - Aluminium Y1 - 2021 U6 - https://doi.org/10.1007/s00204-021-03107-y SN - 0340-5761 SN - 1432-0738 VL - 95 IS - 9 SP - 2977 EP - 3000 PB - Springer CY - Berlin ; Heidelberg ER - TY - JOUR A1 - Lilienkamp, Henning A1 - von Specht, Sebastian A1 - Weatherill, Graeme A1 - Caire, Giuseppe A1 - Cotton, Fabrice T1 - Ground-Motion modeling as an image processing task BT - introducing a neural network based, fully data-driven, and nonergodic JF - Bulletin of the Seismological Society of America N2 - We construct and examine the prototype of a deep learning-based ground-motion model (GMM) that is both fully data driven and nonergodic. We formulate ground-motion modeling as an image processing task, in which a specific type of neural network, the U-Net, relates continuous, horizontal maps of earthquake predictive parameters to sparse observations of a ground-motion intensity measure (IM). The processing of map-shaped data allows the natural incorporation of absolute earthquake source and observation site coordinates, and is, therefore, well suited to include site-, source-, and path-specific amplification effects in a nonergodic GMM. Data-driven interpolation of the IM between observation points is an inherent feature of the U-Net and requires no a priori assumptions. We evaluate our model using both a synthetic dataset and a subset of observations from the KiK-net strong motion network in the Kanto basin in Japan. We find that the U-Net model is capable of learning the magnitude???distance scaling, as well as site-, source-, and path-specific amplification effects from a strong motion dataset. The interpolation scheme is evaluated using a fivefold cross validation and is found to provide on average unbiased predictions. The magnitude???distance scaling as well as the site amplification of response spectral acceleration at a period of 1 s obtained for the Kanto basin are comparable to previous regional studies. Y1 - 2022 U6 - https://doi.org/10.1785/0120220008 SN - 0037-1106 SN - 1943-3573 VL - 112 IS - 3 SP - 1565 EP - 1582 PB - Seismological Society of America CY - Albany ER - TY - JOUR A1 - Cvetković, Nada A1 - Conrad, Tim A1 - Lie, Han Cheng T1 - A convergent discretization method for transition path theory for diffusion processes JF - Multiscale modeling & simulation : a SIAM interdisciplinary journal N2 - Transition path theory (TPT) for diffusion processes is a framework for analyzing the transitions of multiscale ergodic diffusion processes between disjoint metastable subsets of state space. Most methods for applying TPT involve the construction of a Markov state model on a discretization of state space that approximates the underlying diffusion process. However, the assumption of Markovianity is difficult to verify in practice, and there are to date no known error bounds or convergence results for these methods. We propose a Monte Carlo method for approximating the forward committor, probability current, and streamlines from TPT for diffusion processes. Our method uses only sample trajectory data and partitions of state space based on Voronoi tessellations. It does not require the construction of a Markovian approximating process. We rigorously prove error bounds for the approximate TPT objects and use these bounds to show convergence to their exact counterparts in the limit of arbitrarily fine discretization. We illustrate some features of our method by application to a process that solves the Smoluchowski equation on a triple-well potential. KW - ergodic diffusion processes KW - transition paths KW - rare events KW - Monte Carlo KW - methods Y1 - 2021 U6 - https://doi.org/10.1137/20M1329354 SN - 1540-3459 SN - 1540-3467 VL - 19 IS - 1 SP - 242 EP - 266 PB - Society for Industrial and Applied Mathematics CY - Philadelphia ER - TY - JOUR A1 - Dube, Jonas A1 - Böckmann, Christine A1 - Ritter, Christoph T1 - Lidar-Derived Aerosol Properties from Ny-Ålesund, Svalbard during the MOSAiC Spring 2020 JF - Remote sensing / Molecular Diversity Preservation International (MDPI) N2 - In this work, we present Raman lidar data (from a Nd:YAG operating at 355 nm, 532 nm and 1064 nm) from the international research village Ny-Alesund for the time period of January to April 2020 during the Arctic haze season of the MOSAiC winter. We present values of the aerosol backscatter, the lidar ratio and the backscatter Angstrom exponent, though the latter depends on wavelength. The aerosol polarization was generally below 2%, indicating mostly spherical particles. We observed that events with high backscatter and high lidar ratio did not coincide. In fact, the highest lidar ratios (LR > 75 sr at 532 nm) were already found by January and may have been caused by hygroscopic growth, rather than by advection of more continental aerosol. Further, we performed an inversion of the lidar data to retrieve a refractive index and a size distribution of the aerosol. Our results suggest that in the free troposphere (above approximate to 2500 m) the aerosol size distribution is quite constant in time, with dominance of small particles with a modal radius well below 100 nm. On the contrary, below approximate to 2000 m in altitude, we frequently found gradients in aerosol backscatter and even size distribution, sometimes in accordance with gradients of wind speed, humidity or elevated temperature inversions, as if the aerosol was strongly modified by vertical displacement in what we call the "mechanical boundary layer". Finally, we present an indication that additional meteorological soundings during MOSAiC campaign did not necessarily improve the fidelity of air backtrajectories. KW - aerosol KW - Arctic haze KW - lidar KW - microphysical properties KW - backtrajectories; KW - Ny-Alesund KW - Svalbard KW - MOSAiC KW - aerosol-boundary layer interactions Y1 - 2022 U6 - https://doi.org/10.3390/rs14112578 SN - 2072-4292 VL - 14 IS - 11 PB - MDPI CY - Basel ER - TY - JOUR A1 - Kempton, Mark A1 - Münch, Florentin A1 - Yau, Shing-Tung T1 - A homology vanishing theorem for graphs with positive curvature JF - Communications in analysis and geometry N2 - We prove a homology vanishing theorem for graphs with positive Bakry-' Emery curvature, analogous to a classic result of Bochner on manifolds [3]. Specifically, we prove that if a graph has positive curvature at every vertex, then its first homology group is trivial, where the notion of homology that we use for graphs is the path homology developed by Grigor'yan, Lin, Muranov, and Yau [11]. We moreover prove that the fundamental group is finite for graphs with positive Bakry-' Emery curvature, analogous to a classic result of Myers on manifolds [22]. The proofs draw on several separate areas of graph theory, including graph coverings, gain graphs, and cycle spaces, in addition to the Bakry-Emery curvature, path homology, and graph homotopy. The main results follow as a consequence of several different relationships developed among these different areas. Specifically, we show that a graph with positive curvature cannot have a non-trivial infinite cover preserving 3-cycles and 4-cycles, and give a combinatorial interpretation of the first path homology in terms of the cycle space of a graph. Furthermore, we relate gain graphs to graph homotopy and the fundamental group developed by Grigor'yan, Lin, Muranov, and Yau [12], and obtain an alternative proof of their result that the abelianization of the fundamental group of a graph is isomorphic to the first path homology over the integers. Y1 - 2021 UR - https://www.intlpress.com/site/pub/files/_fulltext/journals/cag/2021/0029/0006/CAG-2021-0029-0006-a005.pdf U6 - https://doi.org/10.4310/CAG.2021.v29.n6.a5 SN - 1019-8385 SN - 1944-9992 VL - 29 IS - 6 SP - 1449 EP - 1473 PB - International Press of Boston CY - Somerville ER - TY - JOUR A1 - Dimitrova, Ilinka A1 - Koppitz, Jörg T1 - On relative ranks of the semigroup of orientation-preserving transformations on infinite chains JF - Asian-European journal of mathematics N2 - In this paper, we determine the relative rank of the semigroup OP(X) of all orientation-preserving transformations on infinite chains modulo the semigroup O(X) of all order-preserving transformations. KW - Transformation semigroups on infinite chains KW - order-preserving KW - transformations KW - orientation-preserving transformations KW - relative rank Y1 - 2020 U6 - https://doi.org/10.1142/S1793557121501461 SN - 1793-5571 SN - 1793-7183 VL - 14 IS - 08 PB - World Scientific CY - Singapore ER - TY - JOUR A1 - Malem-Shinitski, Noa A1 - Ojeda, Cesar A1 - Opper, Manfred T1 - Variational bayesian inference for nonlinear hawkes process with gaussian process self-effects JF - Entropy N2 - Traditionally, Hawkes processes are used to model time-continuous point processes with history dependence. Here, we propose an extended model where the self-effects are of both excitatory and inhibitory types and follow a Gaussian Process. Whereas previous work either relies on a less flexible parameterization of the model, or requires a large amount of data, our formulation allows for both a flexible model and learning when data are scarce. We continue the line of work of Bayesian inference for Hawkes processes, and derive an inference algorithm by performing inference on an aggregated sum of Gaussian Processes. Approximate Bayesian inference is achieved via data augmentation, and we describe a mean-field variational inference approach to learn the model parameters. To demonstrate the flexibility of the model we apply our methodology on data from different domains and compare it to previously reported results. KW - Bayesian inference KW - point process KW - Gaussian process Y1 - 2022 U6 - https://doi.org/10.3390/e24030356 SN - 1099-4300 VL - 24 IS - 3 PB - MDPI CY - Basel ER - TY - JOUR A1 - Ayanbayev, Birzhan A1 - Klebanov, Ilja A1 - Lie, Han Cheng A1 - Sullivan, Tim J. T1 - Gamma-convergence of Onsager-Machlup functionals BT - II. Infinite product measures on Banach spaces JF - Inverse problems : an international journal of inverse problems, inverse methods and computerised inversion of data N2 - We derive Onsager-Machlup functionals for countable product measures on weighted l(p) subspaces of the sequence space R-N. Each measure in the product is a shifted and scaled copy of a reference probability measure on R that admits a sufficiently regular Lebesgue density. We study the equicoercivity and Gamma-convergence of sequences of Onsager-Machlup functionals associated to convergent sequences of measures within this class. We use these results to establish analogous results for probability measures on separable Banach or Hilbert spaces, including Gaussian, Cauchy, and Besov measures with summability parameter 1 <= p <= 2. Together with part I of this paper, this provides a basis for analysis of the convergence of maximum a posteriori estimators in Bayesian inverse problems and most likely paths in transition path theory. KW - Bayesian inverse problems KW - Gamma-convergence KW - maximum a posteriori KW - estimation KW - Onsager-Machlup functional KW - small ball probabilities KW - transition path theory Y1 - 2021 U6 - https://doi.org/10.1088/1361-6420/ac3f82 SN - 0266-5611 SN - 1361-6420 VL - 38 IS - 2 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Bellingeri, Carlo A1 - Friz, Peter A1 - Paycha, Sylvie A1 - Preiß, Rosa Lili Dora T1 - Smooth rough paths, their geometry and algebraic renormalization JF - Vietnam journal of mathematics N2 - We introduce the class of "smooth rough paths" and study their main properties. Working in a smooth setting allows us to discard sewing arguments and focus on algebraic and geometric aspects. Specifically, a Maurer-Cartan perspective is the key to a purely algebraic form of Lyons' extension theorem, the renormalization of rough paths following up on [Bruned et al.: A rough path perspective on renormalization, J. Funct. Anal. 277(11), 2019], as well as a related notion of "sum of rough paths". We first develop our ideas in a geometric rough path setting, as this best resonates with recent works on signature varieties, as well as with the renormalization of geometric rough paths. We then explore extensions to the quasi-geometric and the more general Hopf algebraic setting. KW - Signatures KW - Rough paths KW - Cartan's development KW - Renormalization Y1 - 2022 U6 - https://doi.org/10.1007/s10013-022-00570-7 SN - 2305-221X SN - 2305-2228 VL - 50 IS - 3 SP - 719 EP - 761 PB - Springer CY - Singapore ER - TY - JOUR A1 - Ayanbayev, Birzhan A1 - Klebanov, Ilja A1 - Li, Han Cheng A1 - Sullivan, Tim J. T1 - Gamma-convergence of Onsager-Machlup functionals BT - I. With applications to maximum a posteriori estimation in Bayesian inverse problems JF - Inverse problems : an international journal of inverse problems, inverse methods and computerised inversion of data N2 - The Bayesian solution to a statistical inverse problem can be summarised by a mode of the posterior distribution, i.e. a maximum a posteriori (MAP) estimator. The MAP estimator essentially coincides with the (regularised) variational solution to the inverse problem, seen as minimisation of the Onsager-Machlup (OM) functional of the posterior measure. An open problem in the stability analysis of inverse problems is to establish a relationship between the convergence properties of solutions obtained by the variational approach and by the Bayesian approach. To address this problem, we propose a general convergence theory for modes that is based on the Gamma-convergence of OM functionals, and apply this theory to Bayesian inverse problems with Gaussian and edge-preserving Besov priors. Part II of this paper considers more general prior distributions. KW - Bayesian inverse problems KW - Gamma-convergence KW - maximum a posteriori KW - estimation KW - Onsager-Machlup functional KW - small ball probabilities; KW - transition path theory Y1 - 2021 U6 - https://doi.org/10.1088/1361-6420/ac3f81 SN - 0266-5611 SN - 1361-6420 VL - 38 IS - 2 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Dimitrova, Ilinka A1 - Koppitz, Jörg T1 - On relative ranks of the semigroup of orientation-preserving transformations on infinite chain with restricted range JF - Communications in algebra N2 - Let X be an infinite linearly ordered set and let Y be a nonempty subset of X. We calculate the relative rank of the semigroup OP(X,Y) of all orientation-preserving transformations on X with restricted range Y modulo the semigroup O(X,Y) of all order-preserving transformations on X with restricted range Y. For Y = X, we characterize the relative generating sets of minimal size. KW - Order-preserving transformations KW - orientation-preserving KW - transformations KW - relative rank KW - restricted range KW - transformation KW - semigroups on infinite chain Y1 - 2022 U6 - https://doi.org/10.1080/00927872.2021.2000998 SN - 0092-7872 SN - 1532-4125 VL - 50 IS - 5 SP - 2157 EP - 2168 PB - Taylor & Francis Group CY - Philadelphia ER - TY - JOUR A1 - Leung, Tsz Yan A1 - Leutbecher, Martin A1 - Reich, Sebastian A1 - Shepherd, Theodore G. T1 - Forecast verification BT - relating deterministic and probabilistic metrics JF - Quarterly journal of the Royal Meteorological Society N2 - The philosophy of forecast verification is rather different between deterministic and probabilistic verification metrics: generally speaking, deterministic metrics measure differences, whereas probabilistic metrics assess reliability and sharpness of predictive distributions. This article considers the root-mean-square error (RMSE), which can be seen as a deterministic metric, and the probabilistic metric Continuous Ranked Probability Score (CRPS), and demonstrates that under certain conditions, the CRPS can be mathematically expressed in terms of the RMSE when these metrics are aggregated. One of the required conditions is the normality of distributions. The other condition is that, while the forecast ensemble need not be calibrated, any bias or over/underdispersion cannot depend on the forecast distribution itself. Under these conditions, the CRPS is a fraction of the RMSE, and this fraction depends only on the heteroscedasticity of the ensemble spread and the measures of calibration. The derived CRPS-RMSE relationship for the case of perfect ensemble reliability is tested on simulations of idealised two-dimensional barotropic turbulence. Results suggest that the relationship holds approximately despite the normality condition not being met. KW - CRPS KW - ensembles KW - idealised turbulence KW - NWP KW - RMSE KW - verification Y1 - 2021 U6 - https://doi.org/10.1002/qj.4120 SN - 0035-9009 SN - 1477-870X VL - 147 IS - 739 SP - 3124 EP - 3134 PB - Wiley CY - Hoboken ER - TY - CHAP A1 - Rungrottheera, Wannarut A1 - Chang, Der-Chen A1 - Schulze, Bert-Wolfgang T1 - The edge calculus of singularity order >3 T2 - Journal of nonlinear and convex analysis : an international journal N2 - We study Mellin pseudo-differential algebras on singular straight cones and manifolds with singularity of order >= 3. Those are necessary to express parametrices of elliptic differential operators with a corresponding cornerdegenerate behavior, and we obtain regularity in weighted spaces. KW - Pseudo-differential algebras KW - symbols KW - singular manifolds KW - Mellin KW - operator calculus Y1 - 2020 SN - 1345-4773 SN - 1880-5221 VL - 21 IS - 2 SP - 387 EP - 401 PB - Yokohama Publishers CY - Yokohama ER - TY - JOUR A1 - Pornsawad, Pornsarp A1 - Sungcharoen, Parada A1 - Böckmann, Christine T1 - Convergence rate of the modified Landweber method for solving inverse potential problems JF - Mathematics : open access journal N2 - In this paper, we present the convergence rate analysis of the modified Landweber method under logarithmic source condition for nonlinear ill-posed problems. The regularization parameter is chosen according to the discrepancy principle. The reconstructions of the shape of an unknown domain for an inverse potential problem by using the modified Landweber method are exhibited. KW - nonlinear operator KW - regularization KW - modified Landweber method KW - discrepancy principle KW - logarithmic source condition Y1 - 2020 U6 - https://doi.org/10.3390/math8040608 SN - 2227-7390 VL - 8 IS - 4 PB - MDPI CY - Basel ER - TY - JOUR A1 - Kürschner, Patrick A1 - Freitag, Melina A. T1 - Inexact methods for the low rank solution to large scale Lyapunov equations JF - BIT : numerical mathematics ; the leading applied mathematics journal for all computational mathematicians N2 - The rational Krylov subspace method (RKSM) and the low-rank alternating directions implicit (LR-ADI) iteration are established numerical tools for computing low-rank solution factors of large-scale Lyapunov equations. In order to generate the basis vectors for the RKSM, or extend the low-rank factors within the LR-ADI method, the repeated solution to a shifted linear system of equations is necessary. For very large systems this solve is usually implemented using iterative methods, leading to inexact solves within this inner iteration (and therefore to "inexact methods"). We will show that one can terminate this inner iteration before full precision has been reached and still obtain very good accuracy in the final solution to the Lyapunov equation. In particular, for both the RKSM and the LR-ADI method we derive theory for a relaxation strategy (e.g. increasing the solve tolerance of the inner iteration, as the outer iteration proceeds) within the iterative methods for solving the large linear systems. These theoretical choices involve unknown quantities, therefore practical criteria for relaxing the solution tolerance within the inner linear system are then provided. The theory is supported by several numerical examples, which show that the total amount of work for solving Lyapunov equations can be reduced significantly. KW - Lyapunov equation KW - alternating direction implicit KW - rational Krylov KW - subspaces KW - low-rank approximations Y1 - 2019 U6 - https://doi.org/10.1007/s10543-020-00813-4 SN - 0006-3835 SN - 1572-9125 VL - 60 IS - 4 SP - 1221 EP - 1259 PB - Springer CY - Dordrecht ER - TY - JOUR A1 - Hartung, Niklas A1 - Wahl, Martin A1 - Rastogi, Abhishake A1 - Huisinga, Wilhelm T1 - Nonparametric goodness-of-fit testing for parametric covariate models in pharmacometric analyses JF - CPT: pharmacometrics & systems pharmacology N2 - The characterization of covariate effects on model parameters is a crucial step during pharmacokinetic/pharmacodynamic analyses. Although covariate selection criteria have been studied extensively, the choice of the functional relationship between covariates and parameters, however, has received much less attention. Often, a simple particular class of covariate-to-parameter relationships (linear, exponential, etc.) is chosen ad hoc or based on domain knowledge, and a statistical evaluation is limited to the comparison of a small number of such classes. Goodness-of-fit testing against a nonparametric alternative provides a more rigorous approach to covariate model evaluation, but no such test has been proposed so far. In this manuscript, we derive and evaluate nonparametric goodness-of-fit tests for parametric covariate models, the null hypothesis, against a kernelized Tikhonov regularized alternative, transferring concepts from statistical learning to the pharmacological setting. The approach is evaluated in a simulation study on the estimation of the age-dependent maturation effect on the clearance of a monoclonal antibody. Scenarios of varying data sparsity and residual error are considered. The goodness-of-fit test correctly identified misspecified parametric models with high power for relevant scenarios. The case study provides proof-of-concept of the feasibility of the proposed approach, which is envisioned to be beneficial for applications that lack well-founded covariate models. Y1 - 2021 U6 - https://doi.org/10.1002/psp4.12614 SN - 2163-8306 VL - 10 IS - 6 SP - 564 EP - 576 PB - Nature Publ. Group CY - London ER - TY - JOUR A1 - Jia, Weihan A1 - Anslan, Sten A1 - Chen, Fahu A1 - Cao, Xianyong A1 - Dong, Hailiang A1 - Dulias, Katharina A1 - Gu, Zhengquan A1 - Heinecke, Liv A1 - Jiang, Hongchen A1 - Kruse, Stefan A1 - Kang, Wengang A1 - Li, Kai A1 - Liu, Sisi A1 - Liu, Xingqi A1 - Liu, Ying A1 - Ni, Jian A1 - Schwalb, Antje A1 - Stoof-Leichsenring, Kathleen R. A1 - Shen, Wei A1 - Tian, Fang A1 - Wang, Jing A1 - Wang, Yongbo A1 - Wang, Yucheng A1 - Xu, Hai A1 - Yang, Xiaoyan A1 - Zhang, Dongju A1 - Herzschuh, Ulrike T1 - Sedimentary ancient DNA reveals past ecosystem and biodiversity changes on the Tibetan Plateau: overview and prospects JF - Quaternary science reviews : the international multidisciplinary research and review journal N2 - Alpine ecosystems on the Tibetan Plateau are being threatened by ongoing climate warming and intensified human activities. Ecological time-series obtained from sedimentary ancient DNA (sedaDNA) are essential for understanding past ecosystem and biodiversity dynamics on the Tibetan Plateau and their responses to climate change at a high taxonomic resolution. Hitherto only few but promising studies have been published on this topic. The potential and limitations of using sedaDNA on the Tibetan Plateau are not fully understood. Here, we (i) provide updated knowledge of and a brief introduction to the suitable archives, region-specific taphonomy, state-of-the-art methodologies, and research questions of sedaDNA on the Tibetan Plateau; (ii) review published and ongoing sedaDNA studies from the Tibetan Plateau; and (iii) give some recommendations for future sedaDNA study designs. Based on the current knowledge of taphonomy, we infer that deep glacial lakes with freshwater and high clay sediment input, such as those from the southern and southeastern Tibetan Plateau, may have a high potential for sedaDNA studies. Metabarcoding (for microorganisms and plants), metagenomics (for ecosystems), and hybridization capture (for prehistoric humans) are three primary sedaDNA approaches which have been successfully applied on the Tibetan Plateau, but their power is still limited by several technical issues, such as PCR bias and incompleteness of taxonomic reference databases. Setting up high-quality and open-access regional taxonomic reference databases for the Tibetan Plateau should be given priority in the future. To conclude, the archival, taphonomic, and methodological conditions of the Tibetan Plateau are favorable for performing sedaDNA studies. More research should be encouraged to address questions about long-term ecological dynamics at ecosystem scale and to bring the paleoecology of the Tibetan Plateau into a new era. KW - Sedimentary ancient DNA (sedaDNA) KW - Tibetan Plateau KW - Environmental DNA KW - Taphonomy KW - Ecosystem KW - Biodiversity KW - Paleoecology KW - Paleogeography Y1 - 2022 U6 - https://doi.org/10.1016/j.quascirev.2022.107703 SN - 0277-3791 SN - 1873-457X VL - 293 PB - Elsevier CY - Oxford ER - TY - JOUR A1 - Schanner, Maximilian A1 - Korte, Monika A1 - Holschneider, Matthias T1 - ArchKalmag14k: A kalman-filter based global geomagnetic model for the holocene JF - Journal of geophysical research : Solid earth N2 - We propose a global geomagnetic field model for the last 14 thousand years, based on thermoremanent records. We call the model ArchKalmag14k. ArchKalmag14k is constructed by modifying recently proposed algorithms, based on space-time correlations. Due to the amount of data and complexity of the model, the full Bayesian posterior is numerically intractable. To tackle this, we sequentialize the inversion by implementing a Kalman-filter with a fixed time step. Every step consists of a prediction, based on a degree dependent temporal covariance, and a correction via Gaussian process regression. Dating errors are treated via a noisy input formulation. Cross correlations are reintroduced by a smoothing algorithm and model parameters are inferred from the data. Due to the specific statistical nature of the proposed algorithms, the model comes with space and time-dependent uncertainty estimates. The new model ArchKalmag14k shows less variation in the large-scale degrees than comparable models. Local predictions represent the underlying data and agree with comparable models, if the location is sampled well. Uncertainties are bigger for earlier times and in regions of sparse data coverage. We also use ArchKalmag14k to analyze the appearance and evolution of the South Atlantic anomaly together with reverse flux patches at the core-mantle boundary, considering the model uncertainties. While we find good agreement with earlier models for recent times, our model suggests a different evolution of intensity minima prior to 1650 CE. In general, our results suggest that prior to 6000 BCE the data is not sufficient to support global models. Y1 - 2022 U6 - https://doi.org/10.1029/2021JB023166 SN - 2169-9313 SN - 2169-9356 VL - 127 IS - 2 PB - American Geophysical Union CY - Washington ER - TY - JOUR A1 - Hanisch, Florian A1 - Ludewig, Matthias T1 - A rigorous construction of the supersymmetric path integral associated to a compact spin manifold JF - Communications in mathematical physics N2 - We give a rigorous construction of the path integral in N = 1/2 supersymmetry as an integral map for differential forms on the loop space of a compact spin manifold. It is defined on the space of differential forms which can be represented by extended iterated integrals in the sense of Chen and Getzler-Jones-Petrack. Via the iterated integral map, we compare our path integral to the non-commutative loop space Chern character of Guneysu and the second author. Our theory provides a rigorous background to various formal proofs of the Atiyah-Singer index theorem for twisted Dirac operators using supersymmetric path integrals, as investigated by Alvarez-Gaume, Atiyah, Bismut and Witten. Y1 - 2022 U6 - https://doi.org/10.1007/s00220-022-04336-7 SN - 0010-3616 SN - 1432-0916 VL - 391 IS - 3 SP - 1209 EP - 1239 PB - Springer CY - Berlin ; Heidelberg ER - TY - JOUR A1 - De Oliveira Gomes, André A1 - Högele, Michael Anton T1 - The Kramers problem for SDEs driven by small, accelerated Lévy noise with exponentially light jumps JF - Stochastics and dynamics N2 - We establish Freidlin-Wentzell results for a nonlinear ordinary differential equation starting close to the stable state 0, say, subject to a perturbation by a stochastic integral which is driven by an epsilon-small and (1/epsilon)-accelerated Levy process with exponentially light jumps. For this purpose, we derive a large deviations principle for the stochastically perturbed system using the weak convergence approach developed by Budhiraja, Dupuis, Maroulas and collaborators in recent years. In the sequel, we solve the associated asymptotic first escape problem from the bounded neighborhood of 0 in the limit as epsilon -> 0 which is also known as the Kramers problem in the literature. KW - Freidlin-Wentzell theory KW - large deviations principle KW - accelerated small KW - noise Levy diffusions KW - first passage times KW - first exit location KW - strongly tempered stable Levy measure Y1 - 2021 U6 - https://doi.org/10.1142/S0219493721500192 SN - 0219-4937 SN - 1793-6799 VL - 21 IS - 04 PB - World Scientific CY - Singapore ER - TY - JOUR A1 - Lie, Han Cheng A1 - Stahn, Martin A1 - Sullivan, Tim J. T1 - Randomised one-step time integration methods for deterministic operator differential equations JF - Calcolo N2 - Uncertainty quantification plays an important role in problems that involve inferring a parameter of an initial value problem from observations of the solution. Conrad et al. (Stat Comput 27(4):1065-1082, 2017) proposed randomisation of deterministic time integration methods as a strategy for quantifying uncertainty due to the unknown time discretisation error. We consider this strategy for systems that are described by deterministic, possibly time-dependent operator differential equations defined on a Banach space or a Gelfand triple. Our main results are strong error bounds on the random trajectories measured in Orlicz norms, proven under a weaker assumption on the local truncation error of the underlying deterministic time integration method. Our analysis establishes the theoretical validity of randomised time integration for differential equations in infinite-dimensional settings. KW - Time integration KW - Operator differential equations KW - Randomisation KW - Uncertainty quantification Y1 - 2022 U6 - https://doi.org/10.1007/s10092-022-00457-6 SN - 0008-0624 SN - 1126-5434 VL - 59 IS - 1 PB - Springer CY - Milano ER - TY - JOUR A1 - Wiljes, Jana de A1 - Tong, Xin T. T1 - Analysis of a localised nonlinear ensemble Kalman Bucy filter with complete and accurate observations JF - Nonlinearity N2 - Concurrent observation technologies have made high-precision real-time data available in large quantities. Data assimilation (DA) is concerned with how to combine this data with physical models to produce accurate predictions. For spatial-temporal models, the ensemble Kalman filter with proper localisation techniques is considered to be a state-of-the-art DA methodology. This article proposes and investigates a localised ensemble Kalman Bucy filter for nonlinear models with short-range interactions. We derive dimension-independent and component-wise error bounds and show the long time path-wise error only has logarithmic dependence on the time range. The theoretical results are verified through some simple numerical tests. KW - data assimilation KW - stability and accuracy KW - dimension independent bound KW - localisation KW - high dimensional KW - filter KW - nonlinear Y1 - 2020 U6 - https://doi.org/10.1088/1361-6544/ab8d14 SN - 0951-7715 SN - 1361-6544 VL - 33 IS - 9 SP - 4752 EP - 4782 PB - IOP Publ. CY - Bristol ER - TY - JOUR A1 - Schick, Thomas A1 - Seyedhosseini, Mehran T1 - On an index theorem of Chang, Weinberger and Yu JF - Münster journal of mathematics N2 - In this paper we prove a strengthening of a theorem of Chang, Weinberger and Yu on obstructions to the existence of positive scalar curvature metrics on compact manifolds with boundary. They construct a relative index for the Dirac operator, which lives in a relative K-theory group, measuring the difference between the fundamental group of the boundary and of the full manifold. Whenever the Riemannian metric has product structure and positive scalar curvature near the boundary, one can define an absolute index of the Dirac operator taking value in the K-theory of the C*-algebra of fundamental group of the full manifold. This index depends on the metric near the boundary. We prove that (a slight variation of) the relative index of Chang, Weinberger and Yu is the image of this absolute index under the canonical map of K-theory groups. This has the immediate corollary that positive scalar curvature on the whole manifold implies vanishing of the relative index, giving a conceptual and direct proof of the vanishing theorem of Chang, Weinberger and Yu (rather: a slight variation). To take the fundamental groups of the manifold and its boundary into account requires working with maximal C*-completions of the involved *-algebras. A significant part of this paper is devoted to foundational results regarding these completions. On the other hand, we introduce and propose a more conceptual and more geometric completion, which still has all the required functoriality. Y1 - 2021 U6 - https://doi.org/10.17879/59019522628 SN - 1867-5778 SN - 1867-5786 VL - 14 IS - 1 SP - 123 EP - 154 PB - WWU, Fachbereich Mathematik und Informatik CY - Münster 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 - 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 - Hinz, Michael A1 - Schwarz, Michael T1 - A note on Neumann problems on graphs JF - Positivity N2 - We discuss Neumann problems for self-adjoint Laplacians on (possibly infinite) graphs. Under the assumption that the heat semigroup is ultracontractive we discuss the unique solvability for non-empty subgraphs with respect to the vertex boundary and provide analytic and probabilistic representations for Neumann solutions. A second result deals with Neumann problems on canonically compactifiable graphs with respect to the Royden boundary and provides conditions for unique solvability and analytic and probabilistic representations. KW - Graphs KW - Discrete Dirichlet forms KW - Neumann problem KW - Royden boundary Y1 - 2022 U6 - https://doi.org/10.1007/s11117-022-00930-0 SN - 1385-1292 SN - 1572-9281 VL - 26 IS - 4 PB - Springer CY - Dordrecht ER - TY - JOUR A1 - Mera, Azal Jaafar Musa A1 - Tarkhanov, Nikolai T1 - An elliptic equation of finite index in a domain JF - Boletin de la Sociedad Matemática Mexicana N2 - We give an example of first order elliptic equation for a complex-valued function in a plane domain which has a finite number of linearly independent solutions for any right-hand side. No boundary value conditions are thus required. KW - elliptic equation KW - Fredholm operator KW - index Y1 - 2022 U6 - https://doi.org/10.1007/s40590-022-00442-7 SN - 1405-213X SN - 2296-4495 VL - 28 IS - 2 PB - Springer International CY - New York [u.a.] ER - TY - JOUR A1 - Kortenkamp, Ulrich A1 - Kuzle, Ana A1 - Reitz-Koncebovski, Karen T1 - Fachdidaktisches Wissen aus dem Fachwissen generieren BT - Design Research zur Verknüpfung von Fachwissenschaft und Fachdidaktik in der Lehrkräftebildung Mathematik JF - PSI-Potsdam: Ergebnisbericht zu den Aktivitäten im Rahmen der Qualitätsoffensive Lehrerbildung (2019-2023) (Potsdamer Beiträge zur Lehrerbildung und Bildungsforschung ; 3) N2 - Das Mathematik-Teilprojekt SPIES-M zielt auf eine stärkere Professionsorientierung und die Verknüpfung von Fachwissenschaft und Fachdidaktik in der universitären Lehrkräftebildung. Zu allen großen Inhaltsgebieten der Mathematik wurden neue Lehrveranstaltungen konzipiert und in den Studienordnungen sämtlicher Lehrämter Mathematik an der Universität Potsdam implementiert. Für die Konzeption wurden theoriebasiert Gestaltungsprinzipien herausgearbeitet, die sowohl für das Design als auch für die Evaluation und Weiterentwicklung der Lehrveranstaltungen nach dem Design-Research-Ansatz genutzt werden können. Die Umsetzung der Gestaltungsprinzipien wird am Beispiel der Fundamentalen Idee der Proportionalität verdeutlicht und dabei aufgezeigt, wie Studierende dazu befähigt werden können, fachdidaktisches Wissen aus fachmathematischen Inhalten zu generieren. Die Entwicklung des Professionswissens der Studierenden wird mithilfe unterschiedlicher Instrumente untersucht, um Rückschlüsse auf die Wirksamkeit der neu konzipierten Lehrveranstaltungen zu ziehen. Für die Untersuchungen im Mixed-Methods-Design werden neben Beobachtungen in Lehrveranstaltungen eigens konzipierte Wissenstests, Gruppeninterviews, Unterrichtsentwürfe aus Praxisphasen und Lerntagebücher genutzt. Die Studierendenperspektive wird durch Befragungen zur wahrgenommenen (Berufs-)Relevanz der Lehrveranstaltungen erhoben. Weiteres wesentliches Element der Begleitforschung ist die kollegiale Supervision durch sogenannte „Spies“ (Spione), die die Veranstaltungen kriteriengeleitet beobachten und anschließend gemeinsam mit den Dozierenden reflektieren. Die bisherigen Ergebnisse werden hier präsentiert und hinsichtlich ihrer Implikationen diskutiert. Die im Projekt entwickelten Gestaltungsprinzipien als Werkzeug für Design und Evaluation sowie das Spies-Konzept der kollegialen Supervision werden für die Qualitätsentwicklung von Lehrveranstaltungen zum Transfer vorgeschlagen. N2 - The mathematics sub-project SPIES-M aims at a stronger professional orientation and the linking of subject-specific knowledge and subject-specific didactics in university teacher training. New courses were designed for all major mathematical content areas and implemented in the academic regulations of all mathematics teacher training programs at the University of Potsdam. For the course design, theory-based design principles were developed, which can be used both for the design, and for the evaluation and further development of the courses according to the design-research approach. The implementation of the design principles is exemplary illustrated for the fundamental idea of proportionality, by showing how students can be empowered to generate subject didactic knowledge from subject mathematical content. For this study, an explorative mixed-methods design was chosen, in which the development of the students’ professional knowledge was examined with the help of different instruments in order to draw conclusions about the effectiveness of the newly designed courses. In addition to course observations, specially designed knowledge tests, group interviews, lesson plans from practical phases, and learning diaries were used. The students’ perspective was examined through surveys on the perceived (professional) relevance of the courses. Another important element of the accompanying research was the collegial supervision by so-called „spies“, who observed the courses according to criteria and then reflected on them together with the course lecturers. Here, the current results are presented and discussed regarding their diverse implications. Lastly, the developed design principles as a tool for the design and evaluation of the mathematics courses as well as the spies concept of collegial supervision are proposed for transfer for the quality development of courses in general. KW - Lehrkräftebildung Mathematik KW - Professionswissen KW - Verknüpfung Fachwissenschaft und Fachdidaktik KW - Design Research KW - Gestaltungsprinzipien KW - kollegiale Supervision KW - teacher training mathematics KW - professional knowledge KW - linking of subject science and didactic KW - design research KW - design elements KW - collegial supervision Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-617602 SN - 978-3-86956-568-2 SN - 2626-3556 SN - 2626-4722 IS - 3 SP - 171 EP - 191 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Bär, Christian A1 - Bandara, Lashi T1 - Boundary value problems for general first-order elliptic differential operators JF - Journal of functional analysis N2 - We study boundary value problems for first-order elliptic differential operators on manifolds with compact boundary. The adapted boundary operator need not be selfadjoint and the boundary condition need not be pseudo-local.We show the equivalence of various characterisations of elliptic boundary conditions and demonstrate how the boundary conditions traditionally considered in the literature fit in our framework. The regularity of the solutions up to the boundary is proven. We show that imposing elliptic boundary conditions yields a Fredholm operator if the manifold is compact. We provide examples which are conveniently treated by our methods. KW - elliptic differential operators of firstorder KW - elliptic boundary KW - conditions KW - boundary regularity KW - Fredholm property KW - H-infinity-functional calculus KW - maximal regularity KW - Rarita-Schwinger KW - operator Y1 - 2022 U6 - https://doi.org/10.1016/j.jfa.2022.109445 SN - 0022-1236 SN - 1096-0783 VL - 282 IS - 12 PB - Elsevier CY - Amsterdam [u.a.] ER - TY - THES A1 - Malem-Shinitski, Noa T1 - Bayesian inference and modeling for point processes with applications from neuronal activity to scene viewing T1 - Bayessche Inferenz und Modellierung für Punktprozesse mit Anwendungen von neuronaler Aktivität bis Szenenbetrachtung N2 - Point processes are a common methodology to model sets of events. From earthquakes to social media posts, from the arrival times of neuronal spikes to the timing of crimes, from stock prices to disease spreading -- these phenomena can be reduced to the occurrences of events concentrated in points. Often, these events happen one after the other defining a time--series. Models of point processes can be used to deepen our understanding of such events and for classification and prediction. Such models include an underlying random process that generates the events. This work uses Bayesian methodology to infer the underlying generative process from observed data. Our contribution is twofold -- we develop new models and new inference methods for these processes. We propose a model that extends the family of point processes where the occurrence of an event depends on the previous events. This family is known as Hawkes processes. Whereas in most existing models of such processes, past events are assumed to have only an excitatory effect on future events, we focus on the newly developed nonlinear Hawkes process, where past events could have excitatory and inhibitory effects. After defining the model, we present its inference method and apply it to data from different fields, among others, to neuronal activity. The second model described in the thesis concerns a specific instance of point processes --- the decision process underlying human gaze control. This process results in a series of fixated locations in an image. We developed a new model to describe this process, motivated by the known Exploration--Exploitation dilemma. Alongside the model, we present a Bayesian inference algorithm to infer the model parameters. Remaining in the realm of human scene viewing, we identify the lack of best practices for Bayesian inference in this field. We survey four popular algorithms and compare their performances for parameter inference in two scan path models. The novel models and inference algorithms presented in this dissertation enrich the understanding of point process data and allow us to uncover meaningful insights. N2 - Punktprozesse sind eine gängige Methode zur Modellierung von Ereignismengen. Von Erdbeben bis zu Social-Media-Posts, von den neuronalen Spikes bis zum Zeitpunkt von Verbrechen, von Aktienkursen bis zur Ausbreitung von Krankheiten - diese Phänomene lassen sich auf das Auftreten von Ereignissen reduzieren, die in Punkten konzentriert sind. Häufig treten diese Ereignisse nacheinander auf und bilden eine Zeitreihe. Modelle von Punktprozessen können verwendet werden, um unser Verständnis solcher Ereignisse für Klassifizierung und Vorhersage zu vertiefen. Solche Modelle umfassen einen zugrunde liegenden Zufallsprozess, der die Ereignisse erzeugt. In dieser Arbeit wird die Bayes'sche Methodik verwendet, um den zugrunde liegenden generativen Prozess aus den beobachteten Daten abzuleiten. Wir leisten einen doppelten Beitrag: Wir entwickeln neue Modelle und neue Inferenzmethoden für diese Prozesse. Wir schlagen ein Modell vor, das die Familie der Punktprozesse erweitert, bei denen das Auftreten eines Ereignisses von den vorherigen Ereignissen abhängt. Diese Familie ist als Hawkes-Prozesse bekannt. Während in den meisten bestehenden Modellen solcher Prozesse davon ausgegangen wird, dass vergangene Ereignisse nur eine exzitatorische Wirkung auf zukünftige Ereignisse haben, konzentrieren wir uns auf den neu entwickelten nichtlinearen Hawkes-Prozess, bei dem vergangene Ereignisse exzitatorische und hemmende Wirkungen haben können. Nach der Definition des Modells stellen wir seine Inferenzmethode vor und wenden sie auf Daten aus verschiedenen Bereichen an, unter anderem auf die neuronale Aktivität. Das zweite Modell, das in dieser Arbeit beschrieben wird, betrifft einen speziellen Fall von Punktprozessen - den Entscheidungsprozess, der der menschlichen Blicksteuerung zugrunde liegt. Dieser Prozess führt zu einer Reihe von fixierten Positionen in einem Bild. Wir haben ein neues Modell entwickelt, um diesen Prozess zu beschreiben, motiviert durch das bekannte Exploration-Exploitation-Dilemma. Neben dem Modell stellen wir einen Bayes'schen Inferenzalgorithmus vor, um die Modellparameter abzuleiten. Wir bleiben auf dem Gebiet der menschlichen Szenenbetrachtung und stellen fest, dass es in diesem Bereich keine bewährten Verfahren für die Bayes'sche Inferenz gibt. Wir geben einen Überblick über vier gängige Algorithmen und vergleichen ihre Leistungen bei der Ableitung von Parametern für zwei Scanpfadmodelle. Die in dieser Dissertation vorgestellten neuen Modelle und Inferenzalgorithmen bereichern das Verständnis von Punktprozessdaten und ermöglichen es uns, sinnvolle Erkenntnisse zu gewinnen. KW - Bayesian inference KW - point process KW - statistical machine learning KW - sampling KW - modeling KW - Bayessche Inferenz KW - Modellierung KW - Punktprozess KW - Stichprobenentnahme aus einem statistischen Modell KW - statistisches maschinelles Lernen Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-614952 ER - TY - JOUR A1 - Reich, Sebastian A1 - Weissmann, Simon T1 - Fokker-Planck particle systems for Bayesian inference: computational approaches JF - SIAM ASA journal on uncertainty quantification N2 - Bayesian inference can be embedded into an appropriately defined dynamics in the space of probability measures. In this paper, we take Brownian motion and its associated Fokker-Planck equation as a starting point for such embeddings and explore several interacting particle approximations. More specifically, we consider both deterministic and stochastic interacting particle systems and combine them with the idea of preconditioning by the empirical covariance matrix. In addition to leading to affine invariant formulations which asymptotically speed up convergence, preconditioning allows for gradient-free implementations in the spirit of the ensemble Kalman filter. While such gradient-free implementations have been demonstrated to work well for posterior measures that are nearly Gaussian, we extend their scope of applicability to multimodal measures by introducing localized gradient-free approximations. Numerical results demonstrate the effectiveness of the considered methodologies. KW - Bayesian inverse problems KW - Fokker-Planck equation KW - gradient flow KW - affine KW - invariance KW - gradient-free sampling methods KW - localization Y1 - 2021 U6 - https://doi.org/10.1137/19M1303162 SN - 2166-2525 VL - 9 IS - 2 SP - 446 EP - 482 PB - Society for Industrial and Applied Mathematics CY - Philadelphia ER - TY - THES A1 - Schindler, Daniel T1 - Mathematical modeling and simulation of protrusion-driven cell dynamics T1 - Mathematische Modellierung und Simulation von amöboiden Zelldynamiken N2 - Amoeboid cell motility takes place in a variety of biomedical processes such as cancer metastasis, embryonic morphogenesis, and wound healing. In contrast to other forms of cell motility, it is mainly driven by substantial cell shape changes. Based on the interplay of explorative membrane protrusions at the front and a slower-acting membrane retraction at the rear, the cell moves in a crawling kind of way. Underlying these protrusions and retractions are multiple physiological processes resulting in changes of the cytoskeleton, a meshwork of different multi-functional proteins. The complexity and versatility of amoeboid cell motility raise the need for novel computational models based on a profound theoretical framework to analyze and simulate the dynamics of the cell shape. The objective of this thesis is the development of (i) a mathematical framework to describe contour dynamics in time and space, (ii) a computational model to infer expansion and retraction characteristics of individual cell tracks and to produce realistic contour dynamics, (iii) and a complementing Open Science approach to make the above methods fully accessible and easy to use. In this work, we mainly used single-cell recordings of the model organism Dictyostelium discoideum. Based on stacks of segmented microscopy images, we apply a Bayesian approach to obtain smooth representations of the cell membrane, so-called cell contours. We introduce a one-parameter family of regularized contour flows to track reference points on the contour (virtual markers) in time and space. This way, we define a coordinate system to visualize local geometric and dynamic quantities of individual contour dynamics in so-called kymograph plots. In particular, we introduce the local marker dispersion as a measure to identify membrane protrusions and retractions in a fully automated way. This mathematical framework is the basis of a novel contour dynamics model, which consists of three biophysiologically motivated components: one stochastic term, accounting for membrane protrusions, and two deterministic terms to control the shape and area of the contour, which account for membrane retractions. Our model provides a fully automated approach to infer protrusion and retraction characteristics from experimental cell tracks while being also capable of simulating realistic and qualitatively different contour dynamics. Furthermore, the model is used to classify two different locomotion types: the amoeboid and a so-called fan-shaped type. With the complementing Open Science approach, we ensure a high standard regarding the usability of our methods and the reproducibility of our research. In this context, we introduce our software publication named AmoePy, an open-source Python package to segment, analyze, and simulate amoeboid cell motility. Furthermore, we describe measures to improve its usability and extensibility, e.g., by detailed run instructions and an automatically generated source code documentation, and to ensure its functionality and stability, e.g., by automatic software tests, data validation, and a hierarchical package structure. The mathematical approaches of this work provide substantial improvements regarding the modeling and analysis of amoeboid cell motility. We deem the above methods, due to their generalized nature, to be of greater value for other scientific applications, e.g., varying organisms and experimental setups or the transition from unicellular to multicellular movement. Furthermore, we enable other researchers from different fields, i.e., mathematics, biophysics, and medicine, to apply our mathematical methods. By following Open Science standards, this work is of greater value for the cell migration community and a potential role model for other Open Science contributions. N2 - Amöboide Zellmotilität findet bei einer Vielzahl biomedizinischer Prozesse wie Krebsmetastasierung, embryonaler Morphogenese und Wundheilung statt. Im Gegensatz zu anderen Formen der Zellmotilität wird sie hauptsächlich durch erhebliche Formveränderungen der Zelle angetrieben. Sie beruht auf dem Zusammenspiel von explorativen Membranausstülpungen an der Vorderseite und einem langsamer wirkenden Membraneinzug an der Rückseite. Die Komplexität amöboider Zellmotilität machen neue Berechnungsmodelle erforderlich, um die Dynamik der Zellform mathematisch fundiert zu analysieren und zu simulieren. Ziel dieser Arbeit ist die Entwicklung (i) eines mathematischen Frameworks zur Beschreibung der Konturendynamik in Zeit und Raum, (ii) eines Computermodells, um Eigenschaften der Membranveränderungen von einzelnen Zellen zu inferieren und gleichzeitig realistische Konturdynamiken zu simulieren, (iii) und eines ergänzenden Open-Science-Ansatzes, um die oben genannten Methoden vollständig zugänglich und leicht anwendbar zu machen. Auf der Grundlage von aufeinander folgenden Mikroskopiebildern vom Modellorganismus Dictyostelium discoideum, wenden wir einen Bayesschen Ansatz an, um glatte Darstellungen der Zellmembran, sogenannte Zellkonturen, zu erhalten. Wir führen eine einparametrige Familie von regularisierten Konturflüssen ein, um Referenzpunkte auf der Kontur (virtuelle Marker) in Zeit und Raum zu verfolgen. Auf diese Weise definieren wir ein Koordinatensystem zur Visualisierung lokaler geometrischer und dynamischer Größen der individuellen Konturdynamiken in sogenannten Kymographen-Plots. Insbesondere führen wir die lokale Marker-Dispersion ein, mit der signifikante Membranveränderungen identifiziert werden können. Dieses mathematische Framework bildet die Grundlage für unser neues Modell zur Beschreibung von Konturendynamiken. Es besteht aus drei biophysiologisch motivierten Komponenten: einem stochastischen Term, der die Membranausstülpungen steuert, und zwei deterministischen Termen, die das Membraneinziehen, unter Berücksichtigung der Konturform und -fläche, steuern. Unser Modell bietet einen vollautomatisierten Ansatz zur Inferrenz der Charakteristiken von Membranveränderungen für experimentelle Zelldaten. Außerdem ermöglicht es die Simulation von realistischen und qualitativ unterschiedlichen Konturendynamiken. Mit dem ergänzenden Open-Science-Ansatz setzen wir einen hohen Standard hinsichtlich der Nutzbarkeit unserer Methoden und der Reproduzierbarkeit unserer Forschung. In diesem Kontext stellen wir die Softwarepublikation AmoePy vor, ein Open-Source-Pythonpaket zur Segmentierung, Analyse und Simulation von amöboider Zellmotilität. Darüber hinaus beschreiben wir Maßnahmen zur Verbesserung der Benutzerfreundlichkeit und Erweiterbarkeit, z. B. durch detaillierte Ausführanweisungen und eine automatisch generierte Quellcodedokumentation, und zur Gewährleistung der Funktionalität und Stabilität, z. B. durch automatische Softwaretests, Datenvalidierung und eine hierarchische Paketstruktur. Die mathematischen Methoden dieser Arbeit stellen wesentliche Verbesserungen in der Modellierung und Analyse der amöboiden Zellmotilität dar. Wir sind der Ansicht, dass die oben genannten Methoden aufgrund ihrer Verallgemeinerbarkeit von größerem Wert für andere wissenschaftliche Anwendungen sind und potentiell einsetzbar in verschiedenen Wissenschaftsfeldern sind, u. a. Mathematik, Biophysik und Medizin. Durch die Einhaltung von Open-Science-Standards ist diese Arbeit von größerem Wert und ein potenzielles Vorbild für andere Open-Science-Beiträge. KW - amöboide Bewegung KW - Zellmotilität KW - mathematische Modellierung KW - offene Wissenschaft KW - amoeboid motion KW - cell motility KW - mathematical modeling KW - open science Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-613275 ER - TY - JOUR A1 - Shlapunov, Alexander A1 - Tarchanov, Nikolaj Nikolaevič T1 - An open mapping theorem for the Navier-Stokes type equations associated with the de Rham complex over R-n JF - Siberian electronic mathematical reports = Sibirskie ėlektronnye matematičeskie izvestija N2 - We consider an initial problem for the Navier-Stokes type equations associated with the de Rham complex over R-n x[0, T], n >= 3, with a positive time T. We prove that the problem induces an open injective mappings on the scales of specially constructed function spaces of Bochner-Sobolev type. In particular, the corresponding statement on the intersection of these classes gives an open mapping theorem for smooth solutions to the Navier-Stokes equations. KW - Navier-Stokes equations KW - de Rham complex KW - open mapping theorem Y1 - 2021 U6 - https://doi.org/10.33048/semi.2021.18.108 SN - 1813-3304 VL - 18 IS - 2 SP - 1433 EP - 1466 PB - Institut Matematiki Imeni S. L. Soboleva CY - Novosibirsk ER - TY - JOUR A1 - Beckus, Siegfried A1 - Eliaz, Latif T1 - Eigenfunctions growth of R-limits on graphs JF - Journal of spectral theory / European Mathematical Society N2 - A characterization of the essential spectrum of Schrodinger operators on infinite graphs is derived involving the concept of R-limits. This concept, which was introduced previously for operators on N and Z(d) as "right-limits," captures the behaviour of the operator at infinity. For graphs with sub-exponential growth rate, we show that each point in sigma(ss)(H) corresponds to a bounded generalized eigenfunction of a corresponding R-limit of H. If, additionally, the graph is of uniform sub-exponential growth, also the converse inclusion holds. KW - Essential spectrum KW - Schrodinger operators KW - graphs KW - right limits KW - generalized eigenfunctions Y1 - 2021 U6 - https://doi.org/10.4171/JST/389 SN - 1664-039X SN - 1664-0403 VL - 11 IS - 4 SP - 1895 EP - 1933 PB - EMS Press, an imprint of the European Mathematical Society - EMS - Publishing House GmbH, Institut für Mathematik, Technische Universität CY - Berlin ER - TY - JOUR A1 - Ropp, Guillaume A1 - Lesur, Vincent A1 - Bärenzung, Julien A1 - Holschneider, Matthias T1 - Sequential modelling of the Earth’s core magnetic field JF - Earth, Planets and Space N2 - We describe a new, original approach to the modelling of the Earth's magnetic field. The overall objective of this study is to reliably render fast variations of the core field and its secular variation. This method combines a sequential modelling approach, a Kalman filter, and a correlation-based modelling step. Sources that most significantly contribute to the field measured at the surface of the Earth are modelled. Their separation is based on strong prior information on their spatial and temporal behaviours. We obtain a time series of model distributions which display behaviours similar to those of recent models based on more classic approaches, particularly at large temporal and spatial scales. Interesting new features and periodicities are visible in our models at smaller time and spatial scales. An important aspect of our method is to yield reliable error bars for all model parameters. These errors, however, are only as reliable as the description of the different sources and the prior information used are realistic. Finally, we used a slightly different version of our method to produce candidate models for the thirteenth edition of the International Geomagnetic Reference Field. KW - geomagnetic field KW - secular variation KW - Kalman filter KW - IGRF Y1 - 2020 U6 - https://doi.org/10.1186/s40623-020-01230-1 SN - 1880-5981 VL - 72 IS - 1 PB - Springer CY - New York ER - TY - JOUR A1 - Matzka, Jürgen A1 - Stolle, Claudia A1 - Yamazaki, Yosuke A1 - Bronkalla, Oliver A1 - Morschhauser, Achim T1 - The geomagnetic Kp index and derived indices of geomagnetic activity JF - Space weather : the international journal of research and applications N2 - The geomagnetic Kp index is one of the most extensively used indices of geomagnetic activity, both for scientific and operational purposes. This article reviews the properties of the Kp index and provides a reference for users of the Kp index and associated data products as derived and distributed by the GFZ German Research Centre for Geosciences. The near real-time production of the nowcast Kp index is of particular interest for space weather services and here we describe and evaluate its current setup. Y1 - 2021 U6 - https://doi.org/10.1029/2020SW002641 SN - 1542-7390 VL - 19 IS - 5 PB - Wiley CY - New York ER - TY - JOUR A1 - Pathiraja, Sahani Darschika A1 - Reich, Sebastian A1 - Stannat, Wilhelm T1 - McKean-Vlasov SDEs in nonlinear filtering JF - SIAM journal on control and optimization : a publication of the Society for Industrial and Applied Mathematics N2 - Various particle filters have been proposed over the last couple of decades with the common feature that the update step is governed by a type of control law. This feature makes them an attractive alternative to traditional sequential Monte Carlo which scales poorly with the state dimension due to weight degeneracy. This article proposes a unifying framework that allows us to systematically derive the McKean-Vlasov representations of these filters for the discrete time and continuous time observation case, taking inspiration from the smooth approximation of the data considered in [D. Crisan and J. Xiong, Stochastics, 82 (2010), pp. 53-68; J. M. Clark and D. Crisan, Probab. Theory Related Fields, 133 (2005), pp. 43-56]. We consider three filters that have been proposed in the literature and use this framework to derive Ito representations of their limiting forms as the approximation parameter delta -> 0. All filters require the solution of a Poisson equation defined on R-d, for which existence and uniqueness of solutions can be a nontrivial issue. We additionally establish conditions on the signal-observation system that ensures well-posedness of the weighted Poisson equation arising in one of the filters. KW - data assimilation KW - feedback particle filter KW - Poincare inequality KW - well-posedness KW - nonlinear filtering KW - McKean-Vlasov KW - mean-field equations Y1 - 2022 U6 - https://doi.org/10.1137/20M1355197 SN - 0363-0129 SN - 1095-7138 VL - 59 IS - 6 SP - 4188 EP - 4215 PB - Society for Industrial and Applied Mathematics CY - Philadelphia ER - TY - JOUR A1 - Garmendia, Alfonso A1 - Zambon, Marco T1 - Quotients of singular foliations and Lie 2-group actions JF - Journal of noncommutative geometry N2 - Androulidakis-Skandalis (2009) showed that every singular foliation has an associated topological groupoid, called holonomy groupoid. In this note, we exhibit some functorial properties of this assignment: if a foliated manifold (M, FM ) is the quotient of a foliated manifold (P, FP ) along a surjective submersion with connected fibers, then the same is true for the corresponding holonomy groupoids. For quotients by a Lie group action, an analogue statement holds under suitable assumptions, yielding a Lie 2-group action on the holonomy groupoid. KW - Lie groupoid KW - singular foliation KW - fibration Y1 - 2021 U6 - https://doi.org/10.4171/JNCG/434 SN - 1661-6952 SN - 1661-6960 VL - 15 IS - 4 SP - 1251 EP - 1283 PB - EMS Press, an imprint of the European Mathematical Society - EMS - Publishing House GmbH, Institut für Mathematik, Technische Universität Berlin CY - Berlin ER - TY - JOUR A1 - Ruchi, Sangeetika A1 - Dubinkina, Svetlana A1 - Wiljes, Jana de T1 - Fast hybrid tempered ensemble transform filter formulation for Bayesian elliptical problems via Sinkhorn approximation JF - Nonlinear processes in geophysics / European Geosciences Union ; American Geophysical Union N2 - Identification of unknown parameters on the basis of partial and noisy data is a challenging task, in particular in high dimensional and non-linear settings. Gaussian approximations to the problem, such as ensemble Kalman inversion, tend to be robust and computationally cheap and often produce astonishingly accurate estimations despite the simplifying underlying assumptions. Yet there is a lot of room for improvement, specifically regarding a correct approximation of a non-Gaussian posterior distribution. The tempered ensemble transform particle filter is an adaptive Sequential Monte Carlo (SMC) method, whereby resampling is based on optimal transport mapping. Unlike ensemble Kalman inversion, it does not require any assumptions regarding the posterior distribution and hence has shown to provide promising results for non-linear non-Gaussian inverse problems. However, the improved accuracy comes with the price of much higher computational complexity, and the method is not as robust as ensemble Kalman inversion in high dimensional problems. In this work, we add an entropy-inspired regularisation factor to the underlying optimal transport problem that allows the high computational cost to be considerably reduced via Sinkhorn iterations. Further, the robustness of the method is increased via an ensemble Kalman inversion proposal step before each update of the samples, which is also referred to as a hybrid approach. The promising performance of the introduced method is numerically verified by testing it on a steady-state single-phase Darcy flow model with two different permeability configurations. The results are compared to the output of ensemble Kalman inversion, and Markov chain Monte Carlo methods results are computed as a benchmark. Y1 - 2021 U6 - https://doi.org/10.5194/npg-28-23-2021 SN - 1023-5809 SN - 1607-7946 VL - 28 IS - 1 SP - 23 EP - 41 PB - Copernicus CY - Göttingen ER - TY - JOUR A1 - Schanner, Maximilian Arthus A1 - Mauerberger, Stefan A1 - Korte, Monika A1 - Holschneider, Matthias T1 - Correlation based time evolution of the archeomagnetic field JF - Journal of geophysical research : JGR ; an international quarterly. B, Solid earth N2 - In a previous study, a new snapshot modeling concept for the archeomagnetic field was introduced (Mauerberger et al., 2020, ). By assuming a Gaussian process for the geomagnetic potential, a correlation-based algorithm was presented, which incorporates a closed-form spatial correlation function. This work extends the suggested modeling strategy to the temporal domain. A space-time correlation kernel is constructed from the tensor product of the closed-form spatial correlation kernel with a squared exponential kernel in time. Dating uncertainties are incorporated into the modeling concept using a noisy input Gaussian process. All but one modeling hyperparameters are marginalized, to reduce their influence on the outcome and to translate their variability to the posterior variance. The resulting distribution incorporates uncertainties related to dating, measurement and modeling process. Results from application to archeomagnetic data show less variation in the dipole than comparable models, but are in general agreement with previous findings. Y1 - 2021 U6 - https://doi.org/10.1029/2020JB021548 SN - 2169-9313 SN - 2169-9356 VL - 126 IS - 7 PB - American Geophysical Union CY - Washington ER - TY - JOUR A1 - Démaris, Alix A1 - Widigson, Ella S. K. A1 - Ilvemark, Johan F. K. F. A1 - Steenholdt, Casper A1 - Seidelin, Jakob B. A1 - Huisinga, Wilhelm A1 - Michelet, Robin A1 - Aulin, Linda B. S. A1 - Kloft, Charlotte T1 - Ulcerative colitis and acute severe ulcerative colitis patients are overlooked in infliximab population pharmacokinetic models BT - results from a comprehensive review JF - Pharmaceutics / Molecular Diversity Preservation International N2 - Ulcerative colitis (UC) is part of the inflammatory bowels diseases, and moderate to severe UC patients can be treated with anti-tumour necrosis alpha monoclonal antibodies, including infliximab (IFX). Even though treatment of UC patients by IFX has been in place for over a decade, many gaps in modelling of IFX PK in this population remain. This is even more true for acute severe UC (ASUC) patients for which early prediction of IFX pharmacokinetic (PK) could highly improve treatment outcome. Thus, this review aims to compile and analyse published population PK models of IFX in UC and ASUC patients, and to assess the current knowledge on disease activity impact on IFX PK. For this, a semi-systematic literature search was conducted, from which 26 publications including a population PK model analysis of UC patients receiving IFX therapy were selected. Amongst those, only four developed a model specifically for UC patients, and only three populations included severe UC patients. Investigations of disease activity impact on PK were reported in only 4 of the 14 models selected. In addition, the lack of reported model codes and assessment of predictive performance make the use of published models in a clinical setting challenging. Thus, more comprehensive investigation of PK in UC and ASUC is needed as well as more adequate reports on developed models and their evaluation in order to apply them in a clinical setting. KW - infliximab KW - inflammatory bowel disease KW - ulcerative colitis KW - acute severe KW - disease activity KW - pharmacokinetic KW - pharmacometrics Y1 - 2022 U6 - https://doi.org/10.3390/pharmaceutics14102095 SN - 1999-4923 VL - 14 IS - 10 PB - MDPI CY - Basel ER - TY - JOUR A1 - Baerenzung, Julien A1 - Holschneider, Matthias A1 - Wicht, Johannes A1 - Lesur, Vincent A1 - Sanchez, Sabrina T1 - The Kalmag model as a candidate for IGRF-13 JF - Earth, planets and space N2 - We present a new model of the geomagnetic field spanning the last 20 years and called Kalmag. Deriving from the assimilation of CHAMP and Swarm vector field measurements, it separates the different contributions to the observable field through parameterized prior covariance matrices. To make the inverse problem numerically feasible, it has been sequentialized in time through the combination of a Kalman filter and a smoothing algorithm. The model provides reliable estimates of past, present and future mean fields and associated uncertainties. The version presented here is an update of our IGRF candidates; the amount of assimilated data has been doubled and the considered time window has been extended from [2000.5, 2019.74] to [2000.5, 2020.33]. KW - Geomagnetic field KW - Secular variation KW - Assimilation KW - Kalman filter KW - Machine learning Y1 - 2020 U6 - https://doi.org/10.1186/s40623-020-01295-y SN - 1880-5981 VL - 72 IS - 1 PB - Springer CY - New York ER - TY - JOUR A1 - Hastermann, Gottfried A1 - Reinhardt, Maria A1 - Klein, Rupert A1 - Reich, Sebastian T1 - Balanced data assimilation for highly oscillatory mechanical systems JF - Communications in applied mathematics and computational science : CAMCoS N2 - Data assimilation algorithms are used to estimate the states of a dynamical system using partial and noisy observations. The ensemble Kalman filter has become a popular data assimilation scheme due to its simplicity and robustness for a wide range of application areas. Nevertheless, this filter also has limitations due to its inherent assumptions of Gaussianity and linearity, which can manifest themselves in the form of dynamically inconsistent state estimates. This issue is investigated here for balanced, slowly evolving solutions to highly oscillatory Hamiltonian systems which are prototypical for applications in numerical weather prediction. It is demonstrated that the standard ensemble Kalman filter can lead to state estimates that do not satisfy the pertinent balance relations and ultimately lead to filter divergence. Two remedies are proposed, one in terms of blended asymptotically consistent time-stepping schemes, and one in terms of minimization-based postprocessing methods. The effects of these modifications to the standard ensemble Kalman filter are discussed and demonstrated numerically for balanced motions of two prototypical Hamiltonian reference systems. KW - data assimilation KW - ensemble Kalman filter KW - balanced dynamics KW - highly KW - oscillatory systems KW - Hamiltonian dynamics KW - geophysics Y1 - 2021 U6 - https://doi.org/10.2140/camcos.2021.16.119 SN - 1559-3940 SN - 2157-5452 VL - 16 IS - 1 SP - 119 EP - 154 PB - Mathematical Sciences Publishers CY - Berkeley ER -