TY - JOUR A1 - Maier, Corinna Sabrina A1 - Wiljes, Jana de A1 - Hartung, Niklas A1 - Kloft, Charlotte A1 - Huisinga, Wilhelm T1 - A continued learning approach for model-informed precision dosing BT - Updating models in clinical practice JF - CPT: pharmacometrics & systems pharmacology N2 - Model-informed precision dosing (MIPD) is a quantitative dosing framework that combines prior knowledge on the drug-disease-patient system with patient data from therapeutic drug/ biomarker monitoring (TDM) to support individualized dosing in ongoing treatment. Structural models and prior parameter distributions used in MIPD approaches typically build on prior clinical trials that involve only a limited number of patients selected according to some exclusion/inclusion criteria. Compared to the prior clinical trial population, the patient population in clinical practice can be expected to also include altered behavior and/or increased interindividual variability, the extent of which, however, is typically unknown. Here, we address the question of how to adapt and refine models on the level of the model parameters to better reflect this real-world diversity. We propose an approach for continued learning across patients during MIPD using a sequential hierarchical Bayesian framework. The approach builds on two stages to separate the update of the individual patient parameters from updating the population parameters. Consequently, it enables continued learning across hospitals or study centers, because only summary patient data (on the level of model parameters) need to be shared, but no individual TDM data. We illustrate this continued learning approach with neutrophil-guided dosing of paclitaxel. The present study constitutes an important step toward building confidence in MIPD and eventually establishing MIPD increasingly in everyday therapeutic use. Y1 - 2021 U6 - https://doi.org/10.1002/psp4.12745 SN - 2163-8306 VL - 11 IS - 2 SP - 185 EP - 198 PB - London CY - Nature Publ. Group 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 - Zöller, Gert T1 - A note on the estimation of the maximum possible earthquake magnitude based on extreme value theory for the Groningen Gas Field JF - The bulletin of the Seismological Society of America : BSSA N2 - Extreme value statistics is a popular and frequently used tool to model the occurrence of large earthquakes. The problem of poor statistics arising from rare events is addressed by taking advantage of the validity of general statistical properties in asymptotic regimes. In this note, I argue that the use of extreme value statistics for the purpose of practically modeling the tail of the frequency-magnitude distribution of earthquakes can produce biased and thus misleading results because it is unknown to what degree the tail of the true distribution is sampled by data. Using synthetic data allows to quantify this bias in detail. The implicit assumption that the true M-max is close to the maximum observed magnitude M-max,M-observed restricts the class of the potential models a priori to those with M-max = M-max,M-observed + Delta M with an increment Delta M approximate to 0.5... 1.2. This corresponds to the simple heuristic method suggested by Wheeler (2009) and labeled :M-max equals M-obs plus an increment." The incomplete consideration of the entire model family for the frequency-magnitude distribution neglects, however, the scenario of a large so far unobserved earthquake. Y1 - 2022 U6 - https://doi.org/10.1785/0120210307 SN - 0037-1106 SN - 1943-3573 VL - 112 IS - 4 SP - 1825 EP - 1831 PB - Seismological Society of America CY - El Cerito, Calif. 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 - 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 - Houdebert, Pierre A1 - Zass, Alexander T1 - An explicit Dobrushin uniqueness region for Gibbs point processes with repulsive interactions JF - Journal of applied probability / Applied Probability Trust N2 - We present a uniqueness result for Gibbs point processes with interactions that come from a non-negative pair potential; in particular, we provide an explicit uniqueness region in terms of activity z and inverse temperature beta. The technique used relies on applying to the continuous setting the classical Dobrushin criterion. We also present a comparison to the two other uniqueness methods of cluster expansion and disagreement percolation, which can also be applied for this type of interaction. KW - Gibbs point process KW - DLR equations KW - uniqueness KW - Dobrushin criterion; KW - cluster expansion KW - disagreement percolation Y1 - 2022 U6 - https://doi.org/10.1017/jpr.2021.70 SN - 0021-9002 SN - 1475-6072 VL - 59 IS - 2 SP - 541 EP - 555 PB - Cambridge Univ. Press CY - Cambridge 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 - 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 - JOUR A1 - Kaya, Adem A1 - Freitag, Melina A. T1 - Conditioning analysis for discrete Helmholtz problems JF - Computers and mathematics with applications : an international journal N2 - In this paper, we examine conditioning of the discretization of the Helmholtz problem. Although the discrete Helmholtz problem has been studied from different perspectives, to the best of our knowledge, there is no conditioning analysis for it. We aim to fill this gap in the literature. We propose a novel method in 1D to observe the near-zero eigenvalues of a symmetric indefinite matrix. Standard classification of ill-conditioning based on the matrix condition number is not true for the discrete Helmholtz problem. We relate the ill-conditioning of the discretization of the Helmholtz problem with the condition number of the matrix. We carry out analytical conditioning analysis in 1D and extend our observations to 2D with numerical observations. We examine several discretizations. We find different regions in which the condition number of the problem shows different characteristics. We also explain the general behavior of the solutions in these regions. KW - Helmholtz problem KW - Condition number KW - Ill-conditioning KW - Indefinite KW - matrices Y1 - 2022 U6 - https://doi.org/10.1016/j.camwa.2022.05.016 SN - 0898-1221 SN - 1873-7668 VL - 118 SP - 171 EP - 182 PB - Elsevier Science CY - Amsterdam ER - TY - JOUR A1 - Engbert, Ralf A1 - Rabe, Maximilian Michael A1 - Schwetlick, Lisa A1 - Seelig, Stefan A. A1 - Reich, Sebastian A1 - Vasishth, Shravan T1 - Data assimilation in dynamical cognitive science JF - Trends in cognitive sciences N2 - Dynamical models make specific assumptions about cognitive processes that generate human behavior. In data assimilation, these models are tested against timeordered data. Recent progress on Bayesian data assimilation demonstrates that this approach combines the strengths of statistical modeling of individual differences with the those of dynamical cognitive models. Y1 - 2022 U6 - https://doi.org/10.1016/j.tics.2021.11.006 SN - 1364-6613 SN - 1879-307X VL - 26 IS - 2 SP - 99 EP - 102 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Kolbe, Benedikt Maximilian A1 - Evans, Myfanwy E. T1 - Enumerating isotopy classes of tilings guided by the symmetry of triply JF - Siam journal on applied algebra and geometry N2 - We present a technique for the enumeration of all isotopically distinct ways of tiling a hyperbolic surface of finite genus, possibly nonorientable and with punctures and boundary. This generalizes the enumeration using Delaney--Dress combinatorial tiling theory of combinatorial classes of tilings to isotopy classes of tilings. To accomplish this, we derive an action of the mapping class group of the orbifold associated to the symmetry group of a tiling on the set of tilings. We explicitly give descriptions and presentations of semipure mapping class groups and of tilings as decorations on orbifolds. We apply this enumerative result to generate an array of isotopically distinct tilings of the hyperbolic plane with symmetries generated by rotations that are commensurate with the threedimensional symmetries of the primitive, diamond, and gyroid triply periodic minimal surfaces, which have relevance to a variety of physical systems. KW - isotopic tiling theory KW - mapping class group KW - orbifolds KW - group KW - presentations KW - representations of groups as automorphism groups of KW - algebraic systems KW - triply periodic minimal surface KW - Delaney--Dress KW - tiling theory KW - hyperbolic tilings KW - two-dimensional topology Y1 - 2022 U6 - https://doi.org/10.1137/20M1358943 SN - 2470-6566 VL - 6 IS - 1 SP - 1 EP - 40 PB - Society for Industrial and Applied Mathematics CY - Philadelphia ER - TY - JOUR A1 - Stachanow, Viktoria A1 - Neumann, Uta A1 - Blankenstein, Oliver A1 - Bindellini, Davide A1 - Melin, Johanna A1 - Ross, Richard A1 - Whitaker, Martin J. J. A1 - Huisinga, Wilhelm A1 - Michelet, Robin A1 - Kloft, Charlotte T1 - Exploring dried blood spot cortisol concentrations as an alternative for monitoring pediatric adrenal insufficiency patients BT - a model-based analysis JF - Frontiers in pharmacology N2 - Congenital adrenal hyperplasia (CAH) is the most common form of adrenal insufficiency in childhood; it requires cortisol replacement therapy with hydrocortisone (HC, synthetic cortisol) from birth and therapy monitoring for successful treatment. In children, the less invasive dried blood spot (DBS) sampling with whole blood including red blood cells (RBCs) provides an advantageous alternative to plasma sampling. Potential differences in binding/association processes between plasma and DBS however need to be considered to correctly interpret DBS measurements for therapy monitoring. While capillary DBS samples would be used in clinical practice, venous cortisol DBS samples from children with adrenal insufficiency were analyzed due to data availability and to directly compare and thus understand potential differences between venous DBS and plasma. A previously published HC plasma pharmacokinetic (PK) model was extended by leveraging these DBS concentrations. In addition to previously characterized binding of cortisol to albumin (linear process) and corticosteroid-binding globulin (CBG; saturable process), DBS data enabled the characterization of a linear cortisol association with RBCs, and thereby providing a quantitative link between DBS and plasma cortisol concentrations. The ratio between the observed cortisol plasma and DBS concentrations varies highly from 2 to 8. Deterministic simulations of the different cortisol binding/association fractions demonstrated that with higher blood cortisol concentrations, saturation of cortisol binding to CBG was observed, leading to an increase in all other cortisol binding fractions. In conclusion, a mathematical PK model was developed which links DBS measurements to plasma exposure and thus allows for quantitative interpretation of measurements of DBS samples. KW - adrenal insufficiency KW - cortisol KW - dried blood spots KW - pediatrics KW - pharmacokinetics KW - binding KW - association KW - red blood cells Y1 - 2022 U6 - https://doi.org/10.3389/fphar.2022.819590 SN - 1663-9812 VL - 13 PB - Frontiers Media CY - Lausanne 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 - JOUR A1 - Molkenthin, Christian A1 - Donner, Christian A1 - Reich, Sebastian A1 - Zöller, Gert A1 - Hainzl, Sebastian A1 - Holschneider, Matthias A1 - Opper, Manfred T1 - GP-ETAS: semiparametric Bayesian inference for the spatio-temporal epidemic type aftershock sequence model JF - Statistics and Computing N2 - The spatio-temporal epidemic type aftershock sequence (ETAS) model is widely used to describe the self-exciting nature of earthquake occurrences. While traditional inference methods provide only point estimates of the model parameters, we aim at a fully Bayesian treatment of model inference, allowing naturally to incorporate prior knowledge and uncertainty quantification of the resulting estimates. Therefore, we introduce a highly flexible, non-parametric representation for the spatially varying ETAS background intensity through a Gaussian process (GP) prior. Combined with classical triggering functions this results in a new model formulation, namely the GP-ETAS model. We enable tractable and efficient Gibbs sampling by deriving an augmented form of the GP-ETAS inference problem. This novel sampling approach allows us to assess the posterior model variables conditioned on observed earthquake catalogues, i.e., the spatial background intensity and the parameters of the triggering function. Empirical results on two synthetic data sets indicate that GP-ETAS outperforms standard models and thus demonstrate the predictive power for observed earthquake catalogues including uncertainty quantification for the estimated parameters. Finally, a case study for the l'Aquila region, Italy, with the devastating event on 6 April 2009, is presented. KW - Self-exciting point process KW - Hawkes process KW - Spatio-temporal ETAS model KW - Bayesian inference KW - Sampling KW - Earthquake modeling KW - Gaussian process KW - Data augmentation Y1 - 2022 U6 - https://doi.org/10.1007/s11222-022-10085-3 SN - 0960-3174 SN - 1573-1375 VL - 32 IS - 2 PB - Springer CY - Dordrecht 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 - Lewandowski, Max T1 - Hadamard states for bosonic quantum field theory on globally hyperbolic spacetimes JF - Journal of mathematical physics N2 - According to Radzikowski’s celebrated results, bisolutions of a wave operator on a globally hyperbolic spacetime are of the Hadamard form iff they are given by a linear combination of distinguished parametrices i2(G˜aF−G˜F+G˜A−G˜R) in the sense of Duistermaat and Hörmander [Acta Math. 128, 183–269 (1972)] and Radzikowski [Commun. Math. Phys. 179, 529 (1996)]. Inspired by the construction of the corresponding advanced and retarded Green operator GA, GR as done by Bär, Ginoux, and Pfäffle {Wave Equations on Lorentzian Manifolds and Quantization [European Mathematical Society (EMS), Zürich, 2007]}, we construct the remaining two Green operators GF, GaF locally in terms of Hadamard series. Afterward, we provide the global construction of i2(G˜aF−G˜F), which relies on new techniques such as a well-posed Cauchy problem for bisolutions and a patching argument using Čech cohomology. This leads to global bisolutions of the Hadamard form, each of which can be chosen to be a Hadamard two-point-function, i.e., the smooth part can be adapted such that, additionally, the symmetry and the positivity condition are exactly satisfied. Y1 - 2022 U6 - https://doi.org/10.1063/5.0055753 SN - 0022-2488 SN - 1089-7658 VL - 63 IS - 1 PB - American Institute of Physics CY - Melville 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 - Bär, Christian A1 - Hanke, Bernhard T1 - Local flexibility for open partial differential relations JF - Communications on pure and applied mathematics / issued by the Courant Institute of Mathematical Sciences, New York Univ. N2 - We show that local deformations, near closed subsets, of solutions to open partial differential relations can be extended to global deformations, provided all but the highest derivatives stay constant along the subset. The applicability of this general result is illustrated by a number of examples, dealing with convex embeddings of hypersurfaces, differential forms, and lapse functions in Lorentzian geometry. The main application is a general approximation result by sections that have very restrictive local properties on open dense subsets. This shows, for instance, that given any K is an element of Double-struck capital R every manifold of dimension at least 2 carries a complete C-1,C- 1-metric which, on a dense open subset, is smooth with constant sectional curvature K. Of course, this is impossible for C-2-metrics in general. Y1 - 2021 U6 - https://doi.org/10.1002/cpa.21982 SN - 0010-3640 SN - 1097-0312 VL - 75 IS - 6 SP - 1377 EP - 1415 PB - Wiley CY - Hoboken 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 - 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 -