@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{KellerLiuPeyerimhoff2021, author = {Keller, Matthias and Liu, Shiping and Peyerimhoff, Norbert}, title = {A note on eigenvalue bounds for non-compact manifolds}, series = {Mathematische Nachrichten}, volume = {294}, journal = {Mathematische Nachrichten}, number = {6}, publisher = {Wiley-VCH}, address = {Weinheim}, issn = {0025-584X}, doi = {10.1002/mana.201900209}, pages = {1134 -- 1139}, year = {2021}, abstract = {In this article we prove upper bounds for the Laplace eigenvalues lambda(k) below the essential spectrum for strictly negatively curved Cartan-Hadamard manifolds. Our bound is given in terms of k(2) and specific geometric data of the manifold. This applies also to the particular case of non-compact manifolds whose sectional curvature tends to -infinity, where no essential spectrum is present due to a theorem of Donnelly/Li. The result stands in clear contrast to Laplacians on graphs where such a bound fails to be true in general.}, language = {en} } @article{SaynischWagnerBaerenzungHornschildetal.2021, author = {Saynisch-Wagner, Jan and B{\"a}renzung, Julien and Hornschild, Aaron and Irrgang, Christopher and Thomas, Maik}, title = {Tide-induced magnetic signals and their errors derived from CHAMP and Swarm satellite magnetometer observations}, series = {Earth, planets and space : EPS}, volume = {73}, journal = {Earth, planets and space : EPS}, number = {1}, publisher = {Springer}, address = {Heidelberg}, issn = {1880-5981}, doi = {10.1186/s40623-021-01557-3}, pages = {11}, year = {2021}, abstract = {Satellite-measured tidal magnetic signals are of growing importance. These fields are mainly used to infer Earth's mantle conductivity, but also to derive changes in the oceanic heat content. We present a new Kalman filter-based method to derive tidal magnetic fields from satellite magnetometers: KALMAG. The method's advantage is that it allows to study a precisely estimated posterior error covariance matrix. We present the results of a simultaneous estimation of the magnetic signals of 8 major tides from 17 years of Swarm and CHAMP data. For the first time, robustly derived posterior error distributions are reported along with the reported tidal magnetic fields. The results are compared to other estimates that are either based on numerical forward models or on satellite inversions of the same data. For all comparisons, maximal differences and the corresponding globally averaged RMSE are reported. We found that the inter-product differences are comparable with the KALMAG-based errors only in a global mean sense. Here, all approaches give values of the same order, e.g., 0.09 nT-0.14 nT for M2. Locally, the KALMAG posterior errors are up to one order smaller than the inter-product differences, e.g., 0.12 nT vs. 0.96 nT for M2.}, language = {en} } @article{WormellReich2021, author = {Wormell, Caroline L. and Reich, Sebastian}, title = {Spectral convergence of diffusion maps}, series = {SIAM journal on numerical analysis / Society for Industrial and Applied Mathematics}, volume = {59}, journal = {SIAM journal on numerical analysis / Society for Industrial and Applied Mathematics}, number = {3}, publisher = {Society for Industrial and Applied Mathematics}, address = {Philadelphia}, issn = {0036-1429}, doi = {10.1137/20M1344093}, pages = {1687 -- 1734}, year = {2021}, abstract = {Diffusion maps is a manifold learning algorithm widely used for dimensionality reduction. Using a sample from a distribution, it approximates the eigenvalues and eigenfunctions of associated Laplace-Beltrami operators. Theoretical bounds on the approximation error are, however, generally much weaker than the rates that are seen in practice. This paper uses new approaches to improve the error bounds in the model case where the distribution is supported on a hypertorus. For the data sampling (variance) component of the error we make spatially localized compact embedding estimates on certain Hardy spaces; we study the deterministic (bias) component as a perturbation of the Laplace-Beltrami operator's associated PDE and apply relevant spectral stability results. Using these approaches, we match long-standing pointwise error bounds for both the spectral data and the norm convergence of the operator discretization. We also introduce an alternative normalization for diffusion maps based on Sinkhorn weights. This normalization approximates a Langevin diffusion on the sample and yields a symmetric operator approximation. We prove that it has better convergence compared with the standard normalization on flat domains, and we present a highly efficient rigorous algorithm to compute the Sinkhorn weights.}, language = {en} } @article{ChangKhalilSchulze2021, author = {Chang, Der-Chen and Khalil, Sara and Schulze, Bert-Wolfgang}, title = {Analysis on regular corner spaces}, series = {The journal of geometric analysis}, volume = {31}, journal = {The journal of geometric analysis}, number = {9}, publisher = {Springer}, address = {New York}, issn = {1050-6926}, doi = {10.1007/s12220-021-00614-3}, pages = {9199 -- 9240}, year = {2021}, abstract = {We establish a new approach of treating elliptic boundary value problems (BVPs) on manifolds with boundary and regular corners, up to singularity order 2. Ellipticity and parametrices are obtained in terms of symbols taking values in algebras of BVPs on manifolds of corresponding lower singularity orders. Those refer to Boutet de Monvel's calculus of operators with the transmission property, see Boutet de Monvel (Acta Math 126:11-51, 1971) for the case of smooth boundary. On corner configuration operators act in spaces with multiple weights. We mainly study the case of upper left entries in the respective 2 x 2 operator block-matrices of such a calculus. Green operators in the sense of Boutet de Monvel (Acta Math 126:11-51, 1971) analogously appear in singular cases, and they are complemented by contributions of Mellin type. We formulate a result on ellipticity and the Fredholm property in weighted corner spaces, with parametrices of analogous kind.}, 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{RodriguezZuluagaStolleYamazakietal.2021, author = {Rodr{\´i}guez Zuluaga, Juan and Stolle, Claudia and Yamazaki, Yosuke and Xiong, Chao and England, Scott L.}, title = {A synoptic-scale wavelike structure in the nighttime equatorial ionization anomaly}, series = {Earth and Space Science : ESS}, volume = {8}, journal = {Earth and Space Science : ESS}, number = {2}, publisher = {American Geophysical Union}, address = {Malden, Mass.}, issn = {2333-5084}, doi = {10.1029/2020EA001529}, pages = {10}, year = {2021}, abstract = {Both ground- and satellite-based airglow imaging have significantly contributed to understanding the low-latitude ionosphere, especially the morphology and dynamics of the equatorial ionization anomaly (EIA). The NASA Global-scale Observations of the Limb and Disk (GOLD) mission focuses on far-ultraviolet airglow images from a geostationary orbit at 47.5 degrees W. This region is of particular interest at low magnetic latitudes because of the high magnetic declination (i.e., about -20 degrees) and proximity of the South Atlantic magnetic anomaly. In this study, we characterize an exciting feature of the nighttime EIA using GOLD observations from October 5, 2018 to June 30, 2020. It consists of a wavelike structure of a few thousand kilometers seen as poleward and equatorward displacements of the EIA-crests. Initial analyses show that the synoptic-scale structure is symmetric about the dip equator and appears nearly stationary with time over the night. In quasi-dipole coordinates, maxima poleward displacements of the EIA-crests are seen at about +/- 12 degrees latitude and around 20 and 60 degrees longitude (i.e., in geographic longitude at the dip equator, about 53 degrees W and 14 degrees W). The wavelike structure presents typical zonal wavelengths of about 6.7 x 10(3) km and 3.3 x 10(3) km. The structure's occurrence and wavelength are highly variable on a day-to-day basis with no apparent dependence on geomagnetic activity. In addition, a cluster or quasi-periodic wave train of equatorial plasma depletions (EPDs) is often detected within the synoptic-scale structure. We further outline the difference in observing these EPDs from FUV images and in situ measurements during a GOLD and Swarm mission conjunction.}, language = {en} } @article{EshghiMachReichel2021, author = {Eshghi, Nasim and Mach, Thomas and Reichel, Lothar}, title = {New matrix function approximations and quadrature rules based on the Arnoldi process}, series = {Journal of computational and applied mathematics}, volume = {391}, journal = {Journal of computational and applied mathematics}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0377-0427}, doi = {10.1016/j.cam.2021.113442}, pages = {12}, year = {2021}, abstract = {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.}, 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} }