@article{PornsawadBoeckmannPanitsupakamon2022, author = {Pornsawad, Pornsarp and B{\"o}ckmann, Christine and Panitsupakamon, Wannapa}, title = {The Levenberg-Marquardt regularization for the backward heat equation with fractional derivative}, series = {Electronic transactions on numerical analysis - ETNA}, volume = {57}, journal = {Electronic transactions on numerical analysis - ETNA}, publisher = {Kent State University}, address = {Kent}, isbn = {978-3-7001-8258-0}, issn = {1068-9613}, doi = {10.1553/etna_vol57s67}, pages = {67 -- 79}, year = {2022}, abstract = {The backward heat problem with time-fractional derivative in Caputo's sense is studied. The inverse problem is severely ill-posed in the case when the fractional order is close to unity. A Levenberg-Marquardt method with a new a posteriori stopping rule is investigated. We show that optimal order can be obtained for the proposed method under a H{\"o}lder-type source condition. Numerical examples for one and two dimensions are provided.}, language = {en} } @article{StachanowNeumannBlankensteinetal.2022, author = {Stachanow, Viktoria and Neumann, Uta and Blankenstein, Oliver and Bindellini, Davide and Melin, Johanna and Ross, Richard and Whitaker, Martin J. J. and Huisinga, Wilhelm and Michelet, Robin and Kloft, Charlotte}, title = {Exploring dried blood spot cortisol concentrations as an alternative for monitoring pediatric adrenal insufficiency patients}, series = {Frontiers in pharmacology}, volume = {13}, journal = {Frontiers in pharmacology}, publisher = {Frontiers Media}, address = {Lausanne}, issn = {1663-9812}, doi = {10.3389/fphar.2022.819590}, pages = {8}, year = {2022}, abstract = {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.}, language = {en} } @article{YenvonSpechtLinetal.2022, author = {Yen, Ming-Hsuan and von Specht, Sebastian and Lin, Yen-Yu and Cotton, Fabrice and Ma, Kuo-Fong}, title = {Within- and between-event variabilities of strong-velocity pulses of moderate earthquakes within dense seismic arrays}, series = {Bulletin of the Seismological Society of America}, volume = {112}, journal = {Bulletin of the Seismological Society of America}, number = {1}, publisher = {Seismological Society of America}, address = {El Cerito, Calif.}, issn = {0037-1106}, doi = {10.1785/0120200376}, pages = {361 -- 380}, year = {2022}, abstract = {Ground motion with strong-velocity pulses can cause significant damage to buildings and structures at certain periods; hence, knowing the period and velocity amplitude of such pulses is critical for earthquake structural engineering. However, the physical factors relating the scaling of pulse periods with magnitude are poorly understood. In this study, we investigate moderate but damaging earthquakes (M-w 6-7) and characterize ground- motion pulses using the method of Shahi and Baker (2014) while considering the potential static-offset effects. We confirm that the within-event variability of the pulses is large. The identified pulses in this study are mostly from strike-slip-like earthquakes. We further perform simulations using the freq uency-wavenumber algorithm to investigate the causes of the variability of the pulse periods within and between events for moderate strike-slip earthquakes. We test the effect of fault dips, and the impact of the asperity locations and sizes. The simulations reveal that the asperity properties have a high impact on the pulse periods and amplitudes at nearby stations. Our results emphasize the importance of asperity characteristics, in addition to earthquake magnitudes for the occurrence and properties of pulses produced by the forward directivity effect. We finally quantify and discuss within- and between-event variabilities of pulse properties at short distances.}, language = {en} } @article{PohleAdamBeumer2022, author = {Pohle, Jennifer and Adam, Timo and Beumer, Larissa}, title = {Flexible estimation of the state dwell-time distribution in hidden semi-Markov models}, series = {Computational statistics \& data analysis}, volume = {172}, journal = {Computational statistics \& data analysis}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0167-9473}, doi = {10.1016/j.csda.2022.107479}, pages = {15}, year = {2022}, abstract = {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.}, language = {en} } @article{PathirajaLeeuwen2022, author = {Pathiraja, Sahani Darschika and Leeuwen, Peter Jan van}, title = {Multiplicative Non-Gaussian model error estimation in data assimilation}, series = {Journal of advances in modeling earth systems : JAMES}, volume = {14}, journal = {Journal of advances in modeling earth systems : JAMES}, number = {4}, publisher = {American Geophysical Union}, address = {Washington}, issn = {1942-2466}, doi = {10.1029/2021MS002564}, pages = {23}, year = {2022}, abstract = {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.}, language = {en} } @article{LilienkampvonSpechtWeatherilletal.2022, author = {Lilienkamp, Henning and von Specht, Sebastian and Weatherill, Graeme and Caire, Giuseppe and Cotton, Fabrice}, title = {Ground-Motion modeling as an image processing task}, series = {Bulletin of the Seismological Society of America}, volume = {112}, journal = {Bulletin of the Seismological Society of America}, number = {3}, publisher = {Seismological Society of America}, address = {Albany}, issn = {0037-1106}, doi = {10.1785/0120220008}, pages = {1565 -- 1582}, year = {2022}, abstract = {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.}, language = {en} } @article{DubeBoeckmannRitter2022, author = {Dube, Jonas and B{\"o}ckmann, Christine and Ritter, Christoph}, title = {Lidar-Derived Aerosol Properties from Ny-{\AA}lesund, Svalbard during the MOSAiC Spring 2020}, series = {Remote sensing / Molecular Diversity Preservation International (MDPI)}, volume = {14}, journal = {Remote sensing / Molecular Diversity Preservation International (MDPI)}, number = {11}, publisher = {MDPI}, address = {Basel}, issn = {2072-4292}, doi = {10.3390/rs14112578}, pages = {17}, year = {2022}, abstract = {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.}, language = {en} } @article{MalemShinitskiOjedaOpper2022, author = {Malem-Shinitski, Noa and Ojeda, Cesar and Opper, Manfred}, title = {Variational bayesian inference for nonlinear hawkes process with gaussian process self-effects}, series = {Entropy}, volume = {24}, journal = {Entropy}, number = {3}, publisher = {MDPI}, address = {Basel}, issn = {1099-4300}, doi = {10.3390/e24030356}, pages = {22}, year = {2022}, abstract = {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.}, language = {en} } @article{BellingeriFrizPaychaetal.2022, author = {Bellingeri, Carlo and Friz, Peter and Paycha, Sylvie and Preiß, Rosa Lili Dora}, title = {Smooth rough paths, their geometry and algebraic renormalization}, series = {Vietnam journal of mathematics}, volume = {50}, journal = {Vietnam journal of mathematics}, number = {3}, publisher = {Springer}, address = {Singapore}, issn = {2305-221X}, doi = {10.1007/s10013-022-00570-7}, pages = {719 -- 761}, year = {2022}, abstract = {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.}, language = {en} } @article{DimitrovaKoppitz2022, author = {Dimitrova, Ilinka and Koppitz, J{\"o}rg}, title = {On relative ranks of the semigroup of orientation-preserving transformations on infinite chain with restricted range}, series = {Communications in algebra}, volume = {50}, journal = {Communications in algebra}, number = {5}, publisher = {Taylor \& Francis Group}, address = {Philadelphia}, issn = {0092-7872}, doi = {10.1080/00927872.2021.2000998}, pages = {2157 -- 2168}, year = {2022}, abstract = {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.}, language = {en} } @article{JiaAnslanChenetal.2022, author = {Jia, Weihan and Anslan, Sten and Chen, Fahu and Cao, Xianyong and Dong, Hailiang and Dulias, Katharina and Gu, Zhengquan and Heinecke, Liv and Jiang, Hongchen and Kruse, Stefan and Kang, Wengang and Li, Kai and Liu, Sisi and Liu, Xingqi and Liu, Ying and Ni, Jian and Schwalb, Antje and Stoof-Leichsenring, Kathleen R. and Shen, Wei and Tian, Fang and Wang, Jing and Wang, Yongbo and Wang, Yucheng and Xu, Hai and Yang, Xiaoyan and Zhang, Dongju and Herzschuh, Ulrike}, title = {Sedimentary ancient DNA reveals past ecosystem and biodiversity changes on the Tibetan Plateau: overview and prospects}, series = {Quaternary science reviews : the international multidisciplinary research and review journal}, volume = {293}, journal = {Quaternary science reviews : the international multidisciplinary research and review journal}, publisher = {Elsevier}, address = {Oxford}, issn = {0277-3791}, doi = {10.1016/j.quascirev.2022.107703}, pages = {14}, year = {2022}, abstract = {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.}, language = {en} } @article{SchannerKorteHolschneider2022, author = {Schanner, Maximilian and Korte, Monika and Holschneider, Matthias}, title = {ArchKalmag14k: A kalman-filter based global geomagnetic model for the holocene}, series = {Journal of geophysical research : Solid earth}, volume = {127}, journal = {Journal of geophysical research : Solid earth}, number = {2}, publisher = {American Geophysical Union}, address = {Washington}, issn = {2169-9313}, doi = {10.1029/2021JB023166}, pages = {17}, year = {2022}, abstract = {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.}, language = {en} } @article{HanischLudewig2022, author = {Hanisch, Florian and Ludewig, Matthias}, title = {A rigorous construction of the supersymmetric path integral associated to a compact spin manifold}, series = {Communications in mathematical physics}, volume = {391}, journal = {Communications in mathematical physics}, number = {3}, publisher = {Springer}, address = {Berlin ; Heidelberg}, issn = {0010-3616}, doi = {10.1007/s00220-022-04336-7}, pages = {1209 -- 1239}, year = {2022}, abstract = {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.}, language = {en} } @article{LieStahnSullivan2022, author = {Lie, Han Cheng and Stahn, Martin and Sullivan, Tim J.}, title = {Randomised one-step time integration methods for deterministic operator differential equations}, series = {Calcolo}, volume = {59}, journal = {Calcolo}, number = {1}, publisher = {Springer}, address = {Milano}, issn = {0008-0624}, doi = {10.1007/s10092-022-00457-6}, pages = {33}, year = {2022}, abstract = {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.}, language = {en} } @article{HinzSchwarz2022, author = {Hinz, Michael and Schwarz, Michael}, title = {A note on Neumann problems on graphs}, series = {Positivity}, volume = {26}, journal = {Positivity}, number = {4}, publisher = {Springer}, address = {Dordrecht}, issn = {1385-1292}, doi = {10.1007/s11117-022-00930-0}, pages = {23}, year = {2022}, abstract = {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.}, language = {en} } @article{MeraTarkhanov2022, author = {Mera, Azal Jaafar Musa and Tarkhanov, Nikolai}, title = {An elliptic equation of finite index in a domain}, series = {Boletin de la Sociedad Matem{\´a}tica Mexicana}, volume = {28}, journal = {Boletin de la Sociedad Matem{\´a}tica Mexicana}, number = {2}, publisher = {Springer International}, address = {New York [u.a.]}, issn = {1405-213X}, doi = {10.1007/s40590-022-00442-7}, pages = {10}, year = {2022}, abstract = {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.}, language = {en} } @article{BaerBandara2022, author = {B{\"a}r, Christian and Bandara, Lashi}, title = {Boundary value problems for general first-order elliptic differential operators}, series = {Journal of functional analysis}, volume = {282}, journal = {Journal of functional analysis}, number = {12}, publisher = {Elsevier}, address = {Amsterdam [u.a.]}, issn = {0022-1236}, doi = {10.1016/j.jfa.2022.109445}, pages = {69}, year = {2022}, abstract = {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.}, language = {en} } @article{DemarisWidigsonIlvemarketal.2022, author = {D{\´e}maris, Alix and Widigson, Ella S. K. and Ilvemark, Johan F. K. F. and Steenholdt, Casper and Seidelin, Jakob B. and Huisinga, Wilhelm and Michelet, Robin and Aulin, Linda B. S. and Kloft, Charlotte}, title = {Ulcerative colitis and acute severe ulcerative colitis patients are overlooked in infliximab population pharmacokinetic models}, series = {Pharmaceutics / Molecular Diversity Preservation International}, volume = {14}, journal = {Pharmaceutics / Molecular Diversity Preservation International}, number = {10}, publisher = {MDPI}, address = {Basel}, issn = {1999-4923}, doi = {10.3390/pharmaceutics14102095}, pages = {32}, year = {2022}, abstract = {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.}, language = {en} } @article{NassarHohmannMicheletetal.2022, author = {Nassar, Yomna M. and Hohmann, Nicolas and Michelet, Robin and Gottwalt, Katharina and Meid, Andreas D. and Burhenne, J{\"u}rgen and Huisinga, Wilhelm and Haefeli, Walter E. and Mikus, Gerd and Kloft, Charlotte}, title = {Quantification of the Time Course of CYP3A Inhibition, Activation, and Induction Using a Population Pharmacokinetic Model of Microdosed Midazolam Continuous Infusion}, series = {Clinical Pharmacokinetics}, volume = {61}, journal = {Clinical Pharmacokinetics}, number = {11}, publisher = {Springer}, address = {Northcote}, issn = {0312-5963}, doi = {10.1007/s40262-022-01175-6}, pages = {1595 -- 1607}, year = {2022}, abstract = {Background Cytochrome P450 (CYP) 3A contributes to the metabolism of many approved drugs. CYP3A perpetrator drugs can profoundly alter the exposure of CYP3A substrates. However, effects of such drug-drug interactions are usually reported as maximum effects rather than studied as time-dependent processes. Identification of the time course of CYP3A modulation can provide insight into when significant changes to CYP3A activity occurs, help better design drug-drug interaction studies, and manage drug-drug interactions in clinical practice. Objective We aimed to quantify the time course and extent of the in vivo modulation of different CYP3A perpetrator drugs on hepatic CYP3A activity and distinguish different modulatory mechanisms by their time of onset, using pharmacologically inactive intravenous microgram doses of the CYP3A-specific substrate midazolam, as a marker of CYP3A activity. Methods Twenty-four healthy individuals received an intravenous midazolam bolus followed by a continuous infusion for 10 or 36 h. Individuals were randomized into four arms: within each arm, two individuals served as a placebo control and, 2 h after start of the midazolam infusion, four individuals received the CYP3A perpetrator drug: voriconazole (inhibitor, orally or intravenously), rifampicin (inducer, orally), or efavirenz (activator, orally). After midazolam bolus administration, blood samples were taken every hour (rifampicin arm) or every 15 min (remaining study arms) until the end of midazolam infusion. A total of 1858 concentrations were equally divided between midazolam and its metabolite, 1'-hydroxymidazolam. A nonlinear mixed-effects population pharmacokinetic model of both compounds was developed using NONMEM (R). CYP3A activity modulation was quantified over time, as the relative change of midazolam clearance encountered by the perpetrator drug, compared to the corresponding clearance value in the placebo arm. Results Time course of CYP3A modulation and magnitude of maximum effect were identified for each perpetrator drug. While efavirenz CYP3A activation was relatively fast and short, reaching a maximum after approximately 2-3 h, the induction effect of rifampicin could only be observed after 22 h, with a maximum after approximately 28-30 h followed by a steep drop to almost baseline within 1-2 h. In contrast, the inhibitory impact of both oral and intravenous voriconazole was prolonged with a steady inhibition of CYP3A activity followed by a gradual increase in the inhibitory effect until the end of sampling at 8 h. Relative maximum clearance changes were +59.1\%, +46.7\%, -70.6\%, and -61.1\% for efavirenz, rifampicin, oral voriconazole, and intravenous voriconazole, respectively. Conclusions We could distinguish between different mechanisms of CYP3A modulation by the time of onset. Identification of the time at which clearance significantly changes, per perpetrator drug, can guide the design of an optimal sampling schedule for future drug-drug interaction studies. The impact of a short-term combination of different perpetrator drugs on the paradigm CYP3A substrate midazolam was characterized and can define combination intervals in which no relevant interaction is to be expected.}, language = {en} } @article{BaerHanke2022, author = {B{\"a}r, Christian and Hanke, Bernhard}, title = {Local flexibility for open partial differential relations}, series = {Communications on pure and applied mathematics / issued by the Courant Institute of Mathematical Sciences, New York Univ.}, volume = {75}, journal = {Communications on pure and applied mathematics / issued by the Courant Institute of Mathematical Sciences, New York Univ.}, number = {6}, publisher = {Wiley}, address = {Hoboken}, issn = {0010-3640}, doi = {10.1002/cpa.21982}, pages = {1377 -- 1415}, year = {2022}, abstract = {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.}, language = {en} } @article{MaierWiljesHartungetal.2022, author = {Maier, Corinna Sabrina and Wiljes, Jana de and Hartung, Niklas and Kloft, Charlotte and Huisinga, Wilhelm}, title = {A continued learning approach for model-informed precision dosing}, series = {CPT: pharmacometrics \& systems pharmacology}, volume = {11}, journal = {CPT: pharmacometrics \& systems pharmacology}, number = {2}, publisher = {London}, address = {Nature Publ. Group}, issn = {2163-8306}, doi = {10.1002/psp4.12745}, pages = {185 -- 198}, year = {2022}, abstract = {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.}, language = {en} } @article{HydeEvans2022, author = {Hyde, Stephen T. and Evans, Myfanwy E.}, title = {Symmetric tangled Platonic polyhedra}, series = {Proceedings of the National Academy of Sciences of the United States of America}, volume = {119}, journal = {Proceedings of the National Academy of Sciences of the United States of America}, number = {1}, publisher = {National Acad. of Sciences}, address = {Washington}, issn = {0027-8424}, doi = {10.1073/pnas.2110345118}, pages = {10}, year = {2022}, abstract = {Conventional embeddings of the edge-graphs of Platonic polyhedra, {f,z}, where f,z denote the number of edges in each face and the edge-valence at each vertex, respectively, are untangled in that they can be placed on a sphere (S-2) such that distinct edges do not intersect, analogous to unknotted loops, which allow crossing-free drawings of S-1 on the sphere. The most symmetric (flag-transitive) realizations of those polyhedral graphs are those of the classical Platonic polyhedra, whose symmetries are *2fz, according to Conway's two-dimensional (2D) orbifold notation (equivalent to Schonflies symbols I-h, O-h, and T-d). Tangled Platonic {f,z} polyhedra-which cannot lie on the sphere without edge-crossings-are constructed as windings of helices with three, five, seven,... strands on multigenus surfaces formed by tubifying the edges of conventional Platonic polyhedra, have (chiral) symmetries 2fz (I, O, and T), whose vertices, edges, and faces are symmetrically identical, realized with two flags. The analysis extends to the "theta(z)" polyhedra, {2,z}. The vertices of these symmetric tangled polyhedra overlap with those of the Platonic polyhedra; however, their helicity requires curvilinear (or kinked) edges in all but one case. We show that these 2fz polyhedral tangles are maximally symmetric; more symmetric embeddings are necessarily untangled. On one hand, their topologies are very constrained: They are either self-entangled graphs (analogous to knots) or mutually catenated entangled compound polyhedra (analogous to links). On the other hand, an endless variety of entanglements can be realized for each topology. Simpler examples resemble patterns observed in synthetic organometallic materials and clathrin coats in vivo.}, language = {en} } @article{KolbeEvans2022, author = {Kolbe, Benedikt Maximilian and Evans, Myfanwy E.}, title = {Enumerating isotopy classes of tilings guided by the symmetry of triply}, series = {Siam journal on applied algebra and geometry}, volume = {6}, journal = {Siam journal on applied algebra and geometry}, number = {1}, publisher = {Society for Industrial and Applied Mathematics}, address = {Philadelphia}, issn = {2470-6566}, doi = {10.1137/20M1358943}, pages = {1 -- 40}, year = {2022}, abstract = {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.}, language = {en} } @article{HoudebertZass2022, author = {Houdebert, Pierre and Zass, Alexander}, title = {An explicit Dobrushin uniqueness region for Gibbs point processes with repulsive interactions}, series = {Journal of applied probability / Applied Probability Trust}, volume = {59}, journal = {Journal of applied probability / Applied Probability Trust}, number = {2}, publisher = {Cambridge Univ. Press}, address = {Cambridge}, issn = {0021-9002}, doi = {10.1017/jpr.2021.70}, pages = {541 -- 555}, year = {2022}, abstract = {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.}, language = {en} } @article{KayaFreitag2022, author = {Kaya, Adem and Freitag, Melina A.}, title = {Conditioning analysis for discrete Helmholtz problems}, series = {Computers and mathematics with applications : an international journal}, volume = {118}, journal = {Computers and mathematics with applications : an international journal}, publisher = {Elsevier Science}, address = {Amsterdam}, issn = {0898-1221}, doi = {10.1016/j.camwa.2022.05.016}, pages = {171 -- 182}, year = {2022}, abstract = {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.}, language = {en} } @article{Lewandowski2022, author = {Lewandowski, Max}, title = {Hadamard states for bosonic quantum field theory on globally hyperbolic spacetimes}, series = {Journal of mathematical physics}, volume = {63}, journal = {Journal of mathematical physics}, number = {1}, publisher = {American Institute of Physics}, address = {Melville}, issn = {0022-2488}, doi = {10.1063/5.0055753}, pages = {34}, year = {2022}, abstract = {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 H{\"o}rmander [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 B{\"a}r, Ginoux, and Pf{\"a}ffle {Wave Equations on Lorentzian Manifolds and Quantization [European Mathematical Society (EMS), Z{\"u}rich, 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.}, language = {en} } @article{Zoeller2022, author = {Z{\"o}ller, Gert}, title = {A note on the estimation of the maximum possible earthquake magnitude based on extreme value theory for the Groningen Gas Field}, series = {The bulletin of the Seismological Society of America : BSSA}, volume = {112}, journal = {The bulletin of the Seismological Society of America : BSSA}, number = {4}, publisher = {Seismological Society of America}, address = {El Cerito, Calif.}, issn = {0037-1106}, doi = {10.1785/0120210307}, pages = {1825 -- 1831}, year = {2022}, abstract = {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.}, language = {en} } @article{EngbertRabeSchwetlicketal.2022, author = {Engbert, Ralf and Rabe, Maximilian Michael and Schwetlick, Lisa and Seelig, Stefan A. and Reich, Sebastian and Vasishth, Shravan}, title = {Data assimilation in dynamical cognitive science}, series = {Trends in cognitive sciences}, volume = {26}, journal = {Trends in cognitive sciences}, number = {2}, publisher = {Elsevier}, address = {Amsterdam}, issn = {1364-6613}, doi = {10.1016/j.tics.2021.11.006}, pages = {99 -- 102}, year = {2022}, abstract = {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.}, language = {en} } @article{EvansHyde2022, author = {Evans, Myfanwy E. and Hyde, Stephen T.}, title = {Symmetric Tangling of Honeycomb Networks}, series = {Symmetry}, volume = {14}, journal = {Symmetry}, edition = {9}, publisher = {MDPI}, address = {Basel, Schweiz}, issn = {2073-8994}, doi = {10.3390/sym14091805}, pages = {1 -- 13}, year = {2022}, abstract = {Symmetric, elegantly entangled structures are a curious mathematical construction that has found their way into the heart of the chemistry lab and the toolbox of constructive geometry. Of particular interest are those structures—knots, links and weavings—which are composed locally of simple twisted strands and are globally symmetric. This paper considers the symmetric tangling of multiple 2-periodic honeycomb networks. We do this using a constructive methodology borrowing elements of graph theory, low-dimensional topology and geometry. The result is a wide-ranging enumeration of symmetric tangled honeycomb networks, providing a foundation for their exploration in both the chemistry lab and the geometers toolbox.}, language = {en} }