@misc{KolbeEvans2020,
author = {Kolbe, Benedikt Maximilian and Evans, Myfanwy E.},
title = {Isotopic tiling theory for hyperbolic surfaces},
series = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
journal = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
number = {1},
issn = {1866-8372},
doi = {10.25932/publishup-54428},
url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-544285},
pages = {30},
year = {2020},
abstract = {In this paper, we develop the mathematical tools needed to explore isotopy classes of tilings on hyperbolic surfaces of finite genus, possibly nonorientable, with boundary, and punctured. More specifically, we generalize results on Delaney-Dress combinatorial tiling theory using an extension of mapping class groups to orbifolds, in turn using this to study tilings of covering spaces of orbifolds. Moreover, we study finite subgroups of these mapping class groups. Our results can be used to extend the Delaney-Dress combinatorial encoding of a tiling to yield a finite symbol encoding the complexity of an isotopy class of tilings. The results of this paper provide the basis for a complete and unambiguous enumeration of isotopically distinct tilings of hyperbolic surfaces.},
language = {en}
}
@misc{KellerPinchoverPogorzelski2020,
author = {Keller, Matthias and Pinchover, Yehuda and Pogorzelski, Felix},
title = {From hardy to rellich inequalities on graphs},
series = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
journal = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
number = {3},
issn = {1866-8372},
doi = {10.25932/publishup-54214},
url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-542140},
pages = {22},
year = {2020},
abstract = {We show how to deduce Rellich inequalities from Hardy inequalities on infinite graphs. Specifically, the obtained Rellich inequality gives an upper bound on a function by the Laplacian of the function in terms of weighted norms. These weights involve the Hardy weight and a function which satisfies an eikonal inequality. The results are proven first for Laplacians and are extended to Schrodinger operators afterwards.},
language = {en}
}
@misc{MazzonettoSalimova2020,
author = {Mazzonetto, Sara and Salimova, Diyora},
title = {Existence, uniqueness, and numerical approximations for stochastic burgers equations},
series = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
journal = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
number = {4},
issn = {1866-8372},
doi = {10.25932/publishup-51579},
url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-515796},
pages = {26},
year = {2020},
abstract = {In this article, we propose an all-in-one statement which includes existence, uniqueness, regularity, and numerical approximations of mild solutions for a class of stochastic partial differential equations (SPDEs) with non-globally monotone nonlinearities. The proof of this result exploits the properties of an existing fully explicit space-time discrete approximation scheme, in particular the fact that it satisfies suitable a priori estimates. We also obtain almost sure and strong convergence of the approximation scheme to the mild solutions of the considered SPDEs. We conclude by applying the main result of the article to the stochastic Burgers equations with additive space-time white noise.},
language = {en}
}
@article{DimitrovaKoppitz2020,
author = {Dimitrova, Ilinka and Koppitz, J{\"o}rg},
title = {On relative ranks of the semigroup of orientation-preserving transformations on infinite chains},
series = {Asian-European journal of mathematics},
volume = {14},
journal = {Asian-European journal of mathematics},
number = {08},
publisher = {World Scientific},
address = {Singapore},
issn = {1793-5571},
doi = {10.1142/S1793557121501461},
pages = {15},
year = {2020},
abstract = {In this paper, we determine the relative rank of the semigroup OP(X) of all orientation-preserving transformations on infinite chains modulo the semigroup O(X) of all order-preserving transformations.},
language = {en}
}
@inproceedings{RungrottheeraChangSchulze2020,
author = {Rungrottheera, Wannarut and Chang, Der-Chen and Schulze, Bert-Wolfgang},
title = {The edge calculus of singularity order >3},
series = {Journal of nonlinear and convex analysis : an international journal},
volume = {21},
booktitle = {Journal of nonlinear and convex analysis : an international journal},
number = {2},
publisher = {Yokohama Publishers},
address = {Yokohama},
issn = {1345-4773},
pages = {387 -- 401},
year = {2020},
abstract = {We study Mellin pseudo-differential algebras on singular straight cones and manifolds with singularity of order >= 3. Those are necessary to express parametrices of elliptic differential operators with a corresponding cornerdegenerate behavior, and we obtain regularity in weighted spaces.},
language = {en}
}
@article{PornsawadSungcharoenBoeckmann2020,
author = {Pornsawad, Pornsarp and Sungcharoen, Parada and B{\"o}ckmann, Christine},
title = {Convergence rate of the modified Landweber method for solving inverse potential problems},
series = {Mathematics : open access journal},
volume = {8},
journal = {Mathematics : open access journal},
number = {4},
publisher = {MDPI},
address = {Basel},
issn = {2227-7390},
doi = {10.3390/math8040608},
pages = {22},
year = {2020},
abstract = {In this paper, we present the convergence rate analysis of the modified Landweber method under logarithmic source condition for nonlinear ill-posed problems. The regularization parameter is chosen according to the discrepancy principle. The reconstructions of the shape of an unknown domain for an inverse potential problem by using the modified Landweber method are exhibited.},
language = {en}
}
@article{KuerschnerFreitag2020,
author = {K{\"u}rschner, Patrick and Freitag, Melina A.},
title = {Inexact methods for the low rank solution to large scale Lyapunov equations},
series = {BIT : numerical mathematics ; the leading applied mathematics journal for all computational mathematicians},
volume = {60},
journal = {BIT : numerical mathematics ; the leading applied mathematics journal for all computational mathematicians},
number = {4},
publisher = {Springer},
address = {Dordrecht},
issn = {0006-3835},
doi = {10.1007/s10543-020-00813-4},
pages = {1221 -- 1259},
year = {2020},
abstract = {The rational Krylov subspace method (RKSM) and the low-rank alternating directions implicit (LR-ADI) iteration are established numerical tools for computing low-rank solution factors of large-scale Lyapunov equations. In order to generate the basis vectors for the RKSM, or extend the low-rank factors within the LR-ADI method, the repeated solution to a shifted linear system of equations is necessary. For very large systems this solve is usually implemented using iterative methods, leading to inexact solves within this inner iteration (and therefore to "inexact methods"). We will show that one can terminate this inner iteration before full precision has been reached and still obtain very good accuracy in the final solution to the Lyapunov equation. In particular, for both the RKSM and the LR-ADI method we derive theory for a relaxation strategy (e.g. increasing the solve tolerance of the inner iteration, as the outer iteration proceeds) within the iterative methods for solving the large linear systems. These theoretical choices involve unknown quantities, therefore practical criteria for relaxing the solution tolerance within the inner linear system are then provided. The theory is supported by several numerical examples, which show that the total amount of work for solving Lyapunov equations can be reduced significantly.},
language = {en}
}
@article{WiljesTong2020,
author = {Wiljes, Jana de and Tong, Xin T.},
title = {Analysis of a localised nonlinear ensemble Kalman Bucy filter with complete and accurate observations},
series = {Nonlinearity},
volume = {33},
journal = {Nonlinearity},
number = {9},
publisher = {IOP Publ.},
address = {Bristol},
issn = {0951-7715},
doi = {10.1088/1361-6544/ab8d14},
pages = {4752 -- 4782},
year = {2020},
abstract = {Concurrent observation technologies have made high-precision real-time data available in large quantities. Data assimilation (DA) is concerned with how to combine this data with physical models to produce accurate predictions. For spatial-temporal models, the ensemble Kalman filter with proper localisation techniques is considered to be a state-of-the-art DA methodology. This article proposes and investigates a localised ensemble Kalman Bucy filter for nonlinear models with short-range interactions. We derive dimension-independent and component-wise error bounds and show the long time path-wise error only has logarithmic dependence on the time range. The theoretical results are verified through some simple numerical tests.},
language = {en}
}
@article{RoppLesurBaerenzungetal.2020,
author = {Ropp, Guillaume and Lesur, Vincent and B{\"a}renzung, Julien and Holschneider, Matthias},
title = {Sequential modelling of the Earth's core magnetic field},
series = {Earth, Planets and Space},
volume = {72},
journal = {Earth, Planets and Space},
number = {1},
publisher = {Springer},
address = {New York},
issn = {1880-5981},
doi = {10.1186/s40623-020-01230-1},
pages = {15},
year = {2020},
abstract = {We describe a new, original approach to the modelling of the Earth's magnetic field. The overall objective of this study is to reliably render fast variations of the core field and its secular variation. This method combines a sequential modelling approach, a Kalman filter, and a correlation-based modelling step. Sources that most significantly contribute to the field measured at the surface of the Earth are modelled. Their separation is based on strong prior information on their spatial and temporal behaviours. We obtain a time series of model distributions which display behaviours similar to those of recent models based on more classic approaches, particularly at large temporal and spatial scales. Interesting new features and periodicities are visible in our models at smaller time and spatial scales. An important aspect of our method is to yield reliable error bars for all model parameters. These errors, however, are only as reliable as the description of the different sources and the prior information used are realistic. Finally, we used a slightly different version of our method to produce candidate models for the thirteenth edition of the International Geomagnetic Reference Field.},
language = {en}
}
@article{BaerenzungHolschneiderWichtetal.2020,
author = {Baerenzung, Julien and Holschneider, Matthias and Wicht, Johannes and Lesur, Vincent and Sanchez, Sabrina},
title = {The Kalmag model as a candidate for IGRF-13},
series = {Earth, planets and space},
volume = {72},
journal = {Earth, planets and space},
number = {1},
publisher = {Springer},
address = {New York},
issn = {1880-5981},
doi = {10.1186/s40623-020-01295-y},
pages = {13},
year = {2020},
abstract = {We present a new model of the geomagnetic field spanning the last 20 years and called Kalmag. Deriving from the assimilation of CHAMP and Swarm vector field measurements, it separates the different contributions to the observable field through parameterized prior covariance matrices. To make the inverse problem numerically feasible, it has been sequentialized in time through the combination of a Kalman filter and a smoothing algorithm. The model provides reliable estimates of past, present and future mean fields and associated uncertainties. The version presented here is an update of our IGRF candidates; the amount of assimilated data has been doubled and the considered time window has been extended from [2000.5, 2019.74] to [2000.5, 2020.33].},
language = {en}
}
@article{ClavierGuoPaychaetal.2020,
author = {Clavier, Pierre and Guo, Li and Paycha, Sylvie and Zhang, Bin},
title = {Locality and renormalization: universal properties and integrals on trees},
series = {Journal of mathematical physics},
volume = {61},
journal = {Journal of mathematical physics},
number = {2},
publisher = {American Institute of Physics},
address = {College Park, Md.},
issn = {0022-2488},
doi = {10.1063/1.5116381},
pages = {19},
year = {2020},
abstract = {The purpose of this paper is to build an algebraic framework suited to regularize branched structures emanating from rooted forests and which encodes the locality principle. This is achieved by means of the universal properties in the locality framework of properly decorated rooted forests. These universal properties are then applied to derive the multivariate regularization of integrals indexed by rooted forests. We study their renormalization, along the lines of Kreimer's toy model for Feynman integrals.},
language = {en}
}
@article{MauerbergerSchannerKorteetal.2020,
author = {Mauerberger, Stefan and Schanner, Maximilian Arthus and Korte, Monika and Holschneider, Matthias},
title = {Correlation based snapshot models of the archeomagnetic field},
series = {Geophysical journal international},
volume = {223},
journal = {Geophysical journal international},
number = {1},
publisher = {Oxford Univ. Press},
address = {Oxford},
issn = {0956-540X},
doi = {10.1093/gji/ggaa336},
pages = {648 -- 665},
year = {2020},
abstract = {For the time stationary global geomagnetic field, a new modelling concept is presented. A Bayesian non-parametric approach provides realistic location dependent uncertainty estimates. Modelling related variabilities are dealt with systematically by making little subjective apriori assumptions. Rather than parametrizing the model by Gauss coefficients, a functional analytic approach is applied. The geomagnetic potential is assumed a Gaussian process to describe a distribution over functions. Apriori correlations are given by an explicit kernel function with non-informative dipole contribution. A refined modelling strategy is proposed that accommodates non-linearities of archeomagnetic observables: First, a rough field estimate is obtained considering only sites that provide full field vector records. Subsequently, this estimate supports the linearization that incorporates the remaining incomplete records. The comparison of results for the archeomagnetic field over the past 1000 yr is in general agreement with previous models while improved model uncertainty estimates are provided.},
language = {en}
}
@article{LeungLeutbecherReichetal.2020,
author = {Leung, Tsz Yan and Leutbecher, Martin and Reich, Sebastian and Shepherd, Theodore G.},
title = {Impact of the mesoscale range on error growth and the limits to atmospheric predictability},
series = {Journal of the atmospheric sciences},
volume = {77},
journal = {Journal of the atmospheric sciences},
number = {11},
publisher = {American Meteorological Soc.},
address = {Boston},
issn = {0022-4928},
doi = {10.1175/JAS-D-19-0346.1},
pages = {3769 -- 3779},
year = {2020},
abstract = {Global numerical weather prediction (NWP) models have begun to resolve the mesoscale k(-5/3) range of the energy spectrum, which is known to impose an inherently finite range of deterministic predictability per se as errors develop more rapidly on these scales than on the larger scales. However, the dynamics of these errors under the influence of the synoptic-scale k(-3) range is little studied. Within a perfect-model context, the present work examines the error growth behavior under such a hybrid spectrum in Lorenz's original model of 1969, and in a series of identical-twin perturbation experiments using an idealized two-dimensional barotropic turbulence model at a range of resolutions. With the typical resolution of today's global NWP ensembles, error growth remains largely uniform across scales. The theoretically expected fast error growth characteristic of a k(-5/3) spectrum is seen to be largely suppressed in the first decade of the mesoscale range by the synoptic-scale k(-3) range. However, it emerges once models become fully able to resolve features on something like a 20-km scale, which corresponds to a grid resolution on the order of a few kilometers.},
language = {en}
}
@article{BeckusBellissardDeNittis2020,
author = {Beckus, Siegfried and Bellissard, Jean and De Nittis, Giuseppe},
title = {Spectral continuity for aperiodic quantum systems},
series = {Journal of mathematical physics},
volume = {61},
journal = {Journal of mathematical physics},
number = {12},
publisher = {American Institute of Physics},
address = {Melville, NY},
issn = {0022-2488},
doi = {10.1063/5.0011488},
pages = {19},
year = {2020},
abstract = {This work provides a necessary and sufficient condition for a symbolic dynamical system to admit a sequence of periodic approximations in the Hausdorff topology. The key result proved and applied here uses graphs that are called De Bruijn graphs, Rauzy graphs, or Anderson-Putnam complex, depending on the community. Combining this with a previous result, the present work justifies rigorously the accuracy and reliability of algorithmic methods used to compute numerically the spectra of a large class of self-adjoint operators. The so-called Hamiltonians describe the effective dynamic of a quantum particle in aperiodic media. No restrictions on the structure of these operators other than general regularity assumptions are imposed. In particular, nearest-neighbor correlation is not necessary. Examples for the Fibonacci and the Golay-Rudin-Shapiro sequences are explicitly provided illustrating this discussion. While the first sequence has been thoroughly studied by physicists and mathematicians alike, a shroud of mystery still surrounds the latter when it comes to spectral properties. In light of this, the present paper gives a new result here that might help uncovering a solution.},
language = {en}
}
@article{KellerPinchoverPogorzelski2020,
author = {Keller, Matthias and Pinchover, Yehuda and Pogorzelski, Felix},
title = {From hardy to rellich inequalities on graphs},
series = {Proceedings of the London Mathematical Society},
volume = {122},
journal = {Proceedings of the London Mathematical Society},
number = {3},
publisher = {Wiley},
address = {Hoboken},
issn = {0024-6115},
doi = {10.1112/plms.12376},
pages = {458 -- 477},
year = {2020},
abstract = {We show how to deduce Rellich inequalities from Hardy inequalities on infinite graphs. Specifically, the obtained Rellich inequality gives an upper bound on a function by the Laplacian of the function in terms of weighted norms. These weights involve the Hardy weight and a function which satisfies an eikonal inequality. The results are proven first for Laplacians and are extended to Schrodinger operators afterwards.},
language = {en}
}
@article{GaidzikPathirajaSaalfeldetal.2020,
author = {Gaidzik, Franziska and Pathiraja, Sahani Darschika and Saalfeld, Sylvia and Stucht, Daniel and Speck, Oliver and Thevenin, Dominique and Janiga, Gabor},
title = {Hemodynamic data assimilation in a subject-specific circle of Willis geometry},
series = {Clinical Neuroradiology},
volume = {31},
journal = {Clinical Neuroradiology},
number = {3},
publisher = {Springer},
address = {Heidelberg},
issn = {1869-1439},
doi = {10.1007/s00062-020-00959-2},
pages = {643 -- 651},
year = {2020},
abstract = {Purpose The anatomy of the circle of Willis (CoW), the brain's main arterial blood supply system, strongly differs between individuals, resulting in highly variable flow fields and intracranial vascularization patterns. To predict subject-specific hemodynamics with high certainty, we propose a data assimilation (DA) approach that merges fully 4D phase-contrast magnetic resonance imaging (PC-MRI) data with a numerical model in the form of computational fluid dynamics (CFD) simulations. Methods To the best of our knowledge, this study is the first to provide a transient state estimate for the three-dimensional velocity field in a subject-specific CoW geometry using DA. High-resolution velocity state estimates are obtained using the local ensemble transform Kalman filter (LETKF). Results Quantitative evaluation shows a considerable reduction (up to 90\%) in the uncertainty of the velocity field state estimate after the data assimilation step. Velocity values in vessel areas that are below the resolution of the PC-MRI data (e.g., in posterior communicating arteries) are provided. Furthermore, the uncertainty of the analysis-based wall shear stress distribution is reduced by a factor of 2 for the data assimilation approach when compared to the CFD model alone. Conclusion This study demonstrates the potential of data assimilation to provide detailed information on vascular flow, and to reduce the uncertainty in such estimates by combining various sources of data in a statistically appropriate fashion.},
language = {en}
}
@article{MariucciRaySzabo2020,
author = {Mariucci, Ester and Ray, Kolyan and Szabo, Botond},
title = {A Bayesian nonparametric approach to log-concave density estimation},
series = {Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability},
volume = {26},
journal = {Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability},
number = {2},
publisher = {International Statistical Institute},
address = {The Hague},
issn = {1350-7265},
doi = {10.3150/19-BEJ1139},
pages = {1070 -- 1097},
year = {2020},
abstract = {The estimation of a log-concave density on R is a canonical problem in the area of shape-constrained nonparametric inference. We present a Bayesian nonparametric approach to this problem based on an exponentiated Dirichlet process mixture prior and show that the posterior distribution converges to the log-concave truth at the (near-) minimax rate in Hellinger distance. Our proof proceeds by establishing a general contraction result based on the log-concave maximum likelihood estimator that prevents the need for further metric entropy calculations. We further present computationally more feasible approximations and both an empirical and hierarchical Bayes approach. All priors are illustrated numerically via simulations.},
language = {en}
}
@article{HermannHumbert2020,
author = {Hermann, Andreas and Humbert, Emmanuel},
title = {Mass functions of a compact manifold},
series = {Journal of geometry and physics : JGP},
volume = {154},
journal = {Journal of geometry and physics : JGP},
publisher = {Elsevier},
address = {Amsterdam [u.a.]},
issn = {0393-0440},
doi = {10.1016/j.geomphys.2020.103650},
pages = {14},
year = {2020},
abstract = {Let M be a compact manifold of dimension n. In this paper, we introduce the Mass Function a >= 0 bar right arrow X-+(M)(a) (resp. a >= 0 bar right arrow X--(M)(a)) which is defined as the supremum (resp. infimum) of the masses of all metrics on M whose Yamabe constant is larger than a and which are flat on a ball of radius 1 and centered at a point p is an element of M. Here, the mass of a metric flat around p is the constant term in the expansion of the Green function of the conformal Laplacian at p. We show that these functions are well defined and have many properties which allow to obtain applications to the Yamabe invariant (i.e. the supremum of Yamabe constants over the set of all metrics on M).},
language = {en}
}
@article{GueneysuKeller2020,
author = {G{\"u}neysu, Batu and Keller, Matthias},
title = {Feynman path integrals for magnetic Schr{\"o}dinger operators on infinite weighted graphs},
series = {Journal d'analyse math{\´e}matique},
volume = {141},
journal = {Journal d'analyse math{\´e}matique},
number = {2},
publisher = {The Magnes Press, the Hebrew Univ.},
address = {Jerusalem},
issn = {0021-7670},
doi = {10.1007/s11854-020-0110-y},
pages = {751 -- 770},
year = {2020},
abstract = {We prove a Feynman path integral formula for the unitary group exp(-itL(nu,theta)), t >= 0, associated with a discrete magnetic Schrodinger operator L-nu,L-theta on a large class of weighted infinite graphs. As a consequence, we get a new Kato-Simon estimate vertical bar exp(- itL(nu,theta))(x,y)vertical bar <= exp( -tL(-deg,0))(x,y), which controls the unitary group uniformly in the potentials in terms of a Schrodinger semigroup, where the potential deg is the weighted degree function of the graph.},
language = {en}
}
@article{AzzaliPaycha2020,
author = {Azzali, Sara and Paycha, Sylvie},
title = {Spectral zeta-invariants lifted to coverings},
series = {Transactions of the American Mathematical Society},
volume = {373},
journal = {Transactions of the American Mathematical Society},
number = {9},
publisher = {American Mathematical Society},
address = {Providence, RI},
issn = {0002-9947},
doi = {10.1090/tran/8067},
pages = {6185 -- 6226},
year = {2020},
abstract = {The canonical trace and the Wodzicki residue on classical pseudo-differential operators on a closed manifold are characterised by their locality and shown to be preserved under lifting to the universal covering as a result of their local feature. As a consequence, we lift a class of spectral zeta-invariants using lifted defect formulae which express discrepancies of zeta-regularised traces in terms of Wodzicki residues. We derive Atiyah's L-2-index theorem as an instance of the Z(2)-graded generalisation of the canonical lift of spectral zeta-invariants and we show that certain lifted spectral zeta-invariants for geometric operators are integrals of Pontryagin and Chern forms.},
language = {en}
}
@article{KluweMicheletMuellerSchoelletal.2020,
author = {Kluwe, Franziska and Michelet, Robin and M{\"u}ller-Sch{\"o}ll, Anna and Maier, Corinna and Klopp-Schulze, Lena and van Dyk, Madele and Mikus, Gerd and Huisinga, Wilhelm and Kloft, Charlotte},
title = {Perspectives on model-informed precision dosing in the digital health era},
series = {Clinical pharmacology \& therapeutics},
volume = {109},
journal = {Clinical pharmacology \& therapeutics},
number = {1},
publisher = {Wiley},
address = {Hoboken},
issn = {0009-9236},
doi = {10.1002/cpt.2049},
pages = {29 -- 36},
year = {2020},
language = {en}
}
@article{MaoutsaReichOpper2020,
author = {Maoutsa, Dimitra and Reich, Sebastian and Opper, Manfred},
title = {Interacting particle solutions of Fokker-Planck equations through gradient-log-density estimation},
series = {Entropy},
volume = {22},
journal = {Entropy},
number = {8},
publisher = {MDPI},
address = {Basel},
issn = {1099-4300},
doi = {10.3390/e22080802},
pages = {35},
year = {2020},
abstract = {Fokker-Planck equations are extensively employed in various scientific fields as they characterise the behaviour of stochastic systems at the level of probability density functions. Although broadly used, they allow for analytical treatment only in limited settings, and often it is inevitable to resort to numerical solutions. Here, we develop a computational approach for simulating the time evolution of Fokker-Planck solutions in terms of a mean field limit of an interacting particle system. The interactions between particles are determined by the gradient of the logarithm of the particle density, approximated here by a novel statistical estimator. The performance of our method shows promising results, with more accurate and less fluctuating statistics compared to direct stochastic simulations of comparable particle number. Taken together, our framework allows for effortless and reliable particle-based simulations of Fokker-Planck equations in low and moderate dimensions. The proposed gradient-log-density estimator is also of independent interest, for example, in the context of optimal control.},
language = {en}
}
@article{LudewigRosenberger2020,
author = {Ludewig, Matthias and Rosenberger, Elke},
title = {Asymptotic eigenfunctions for Schr{\"o}dinger operators on a vector bundle},
series = {Reviews in mathematical physics},
volume = {32},
journal = {Reviews in mathematical physics},
number = {7},
publisher = {World Scientific},
address = {Singapore},
issn = {0129-055X},
doi = {10.1142/S0129055X20500208},
pages = {28},
year = {2020},
abstract = {In the limit (h) over bar -> 0, we analyze a class of Schr{\"o}dinger operators H-(h) over bar = (h) over bar L-2 + (h) over barW + V .id(epsilon) acting on sections of a vector bundle epsilon over a Riemannian manifold M where L is a Laplace type operator, W is an endomorphism field and the potential energy V has a non-degenerate minimum at some point p is an element of M. We construct quasimodes of WKB-type near p for eigenfunctions associated with the low-lying eigenvalues of H-(h) over bar. These are obtained from eigenfunctions of the associated harmonic oscillator H-p,H-(h) over bar at p, acting on smooth functions on the tangent space.},
language = {en}
}
@article{HartungBorghardt2020,
author = {Hartung, Niklas and Borghardt, Jens Markus},
title = {A mechanistic framework for a priori pharmacokinetic predictions of orally inhaled drugs},
series = {PLoS Computational Biology : a new community journal},
volume = {16},
journal = {PLoS Computational Biology : a new community journal},
number = {12},
publisher = {PLoS},
address = {San Fransisco},
issn = {1553-734X},
doi = {10.1371/journal.pcbi.1008466},
pages = {24},
year = {2020},
abstract = {Author summary
The use of orally inhaled drugs for treating lung diseases is appealing since they have the potential for lung selectivity, i.e. high exposure at the site of action -the lung- without excessive side effects. However, the degree of lung selectivity depends on a large number of factors, including physiochemical properties of drug molecules, patient disease state, and inhalation devices. To predict the impact of these factors on drug exposure and thereby to understand the characteristics of an optimal drug for inhalation, we develop a predictive mathematical framework (a "pharmacokinetic model"). In contrast to previous approaches, our model allows combining knowledge from different sources appropriately and its predictions were able to adequately predict different sets of clinical data. Finally, we compare the impact of different factors and find that the most important factors are the size of the inhaled particles, the affinity of the drug to the lung tissue, as well as the rate of drug dissolution in the lung. In contrast to the common belief, the solubility of a drug in the lining fluids is not found to be relevant. These findings are important to understand how inhaled drugs should be designed to achieve best treatment results in patients.
The fate of orally inhaled drugs is determined by pulmonary pharmacokinetic processes such as particle deposition, pulmonary drug dissolution, and mucociliary clearance. Even though each single process has been systematically investigated, a quantitative understanding on the interaction of processes remains limited and therefore identifying optimal drug and formulation characteristics for orally inhaled drugs is still challenging. To investigate this complex interplay, the pulmonary processes can be integrated into mathematical models. However, existing modeling attempts considerably simplify these processes or are not systematically evaluated against (clinical) data. In this work, we developed a mathematical framework based on physiologically-structured population equations to integrate all relevant pulmonary processes mechanistically. A tailored numerical resolution strategy was chosen and the mechanistic model was evaluated systematically against data from different clinical studies. Without adapting the mechanistic model or estimating kinetic parameters based on individual study data, the developed model was able to predict simultaneously (i) lung retention profiles of inhaled insoluble particles, (ii) particle size-dependent pharmacokinetics of inhaled monodisperse particles, (iii) pharmacokinetic differences between inhaled fluticasone propionate and budesonide, as well as (iv) pharmacokinetic differences between healthy volunteers and asthmatic patients. Finally, to identify the most impactful optimization criteria for orally inhaled drugs, the developed mechanistic model was applied to investigate the impact of input parameters on both the pulmonary and systemic exposure. Interestingly, the solubility of the inhaled drug did not have any relevant impact on the local and systemic pharmacokinetics. Instead, the pulmonary dissolution rate, the particle size, the tissue affinity, and the systemic clearance were the most impactful potential optimization parameters. In the future, the developed prediction framework should be considered a powerful tool for identifying optimal drug and formulation characteristics.},
language = {en}
}
@article{FladFladHarutyunyanSchulze2020,
author = {Flad, Heinz-J{\"u}rgen and Flad-Harutyunyan, Gohar and Schulze, Bert-Wolfgang},
title = {Explicit Green operators for quantum mechanical Hamiltonians},
series = {Asian-European journal of mathematics : AEJM},
volume = {13},
journal = {Asian-European journal of mathematics : AEJM},
number = {7},
publisher = {World Scientific},
address = {Singapore},
issn = {1793-5571},
doi = {10.1142/S1793557120501223},
pages = {64},
year = {2020},
abstract = {We extend our approach of asymptotic parametrix construction for Hamiltonian operators from conical to edge-type singularities which is applicable to coalescence points of two particles of the helium atom and related two electron systems including the hydrogen molecule. Up to second-order, we have calculated the symbols of an asymptotic parametrix of the nonrelativistic Hamiltonian of the helium atom within the Born-Oppenheimer approximation and provide explicit formulas for the corresponding Green operators which encode the asymptotic behavior of the eigenfunctions near an edge.},
language = {en}
}
@article{LudewigRoos2020,
author = {Ludewig, Matthias and Roos, Saskia},
title = {The chiral anomaly of the free fermion in functorial field theory},
series = {Annales Henri Poincar{\´e} : a journal of theoretical and mathematical physics},
volume = {21},
journal = {Annales Henri Poincar{\´e} : a journal of theoretical and mathematical physics},
number = {4},
publisher = {Springer International Publishing AG},
address = {Cham (ZG)},
issn = {1424-0637},
doi = {10.1007/s00023-020-00893-6},
pages = {1191 -- 1233},
year = {2020},
abstract = {When trying to cast the free fermion in the framework of functorial field theory, its chiral anomaly manifests in the fact that it assigns the determinant of the Dirac operator to a top-dimensional closed spin manifold, which is not a number as expected, but an element of a complex line. In functorial field theory language, this means that the theory is twisted, which gives rise to an anomaly theory. In this paper, we give a detailed construction of this anomaly theory, as a functor that sends manifolds to infinite-dimensional Clifford algebras and bordisms to bimodules.},
language = {en}
}
@article{BandaraBryan2020,
author = {Bandara, Lashi and Bryan, Paul},
title = {Heat kernels and regularity for rough metrics on smooth manifolds},
series = {Mathematische Nachrichten},
volume = {293},
journal = {Mathematische Nachrichten},
number = {12},
publisher = {Wiley-VCH},
address = {Weinheim},
issn = {0025-584X},
doi = {10.1002/mana.201800459},
pages = {2255 -- 2270},
year = {2020},
abstract = {We consider rough metrics on smooth manifolds and corresponding Laplacians induced by such metrics. We demonstrate that globally continuous heat kernels exist and are Holder continuous locally in space and time. This is done via local parabolic Harnack estimates for weak solutions of operators in divergence form with bounded measurable coefficients in weighted Sobolev spaces.},
language = {en}
}
@article{KolbeEvans2020,
author = {Kolbe, Benedikt Maximilian and Evans, Myfanwy E.},
title = {Isotopic tiling theory for hyperbolic surfaces},
series = {Geometriae dedicata},
volume = {212},
journal = {Geometriae dedicata},
number = {1},
publisher = {Springer},
address = {Dordrecht},
issn = {0046-5755},
doi = {10.1007/s10711-020-00554-2},
pages = {177 -- 204},
year = {2020},
abstract = {In this paper, we develop the mathematical tools needed to explore isotopy classes of tilings on hyperbolic surfaces of finite genus, possibly nonorientable, with boundary, and punctured. More specifically, we generalize results on Delaney-Dress combinatorial tiling theory using an extension of mapping class groups to orbifolds, in turn using this to study tilings of covering spaces of orbifolds. Moreover, we study finite subgroups of these mapping class groups. Our results can be used to extend the Delaney-Dress combinatorial encoding of a tiling to yield a finite symbol encoding the complexity of an isotopy class of tilings. The results of this paper provide the basis for a complete and unambiguous enumeration of isotopically distinct tilings of hyperbolic surfaces.},
language = {en}
}
@article{PereraBoeckmann2020,
author = {Perera, Upeksha and B{\"o}ckmann, Christine},
title = {Solutions of Sturm-Liouville problems},
series = {Mathematics},
volume = {8},
journal = {Mathematics},
number = {11},
publisher = {MDPI},
address = {Basel},
issn = {2227-7390},
doi = {10.3390/math8112074},
pages = {14},
year = {2020},
abstract = {This paper further improves the Lie group method with Magnus expansion proposed in a previous paper by the authors, to solve some types of direct singular Sturm-Liouville problems. Next, a concrete implementation to the inverse Sturm-Liouville problem algorithm proposed by Barcilon (1974) is provided. Furthermore, computational feasibility and applicability of this algorithm to solve inverse Sturm-Liouville problems of higher order (for n=2,4) are verified successfully. It is observed that the method is successful even in the presence of significant noise, provided that the assumptions of the algorithm are satisfied. In conclusion, this work provides a method that can be adapted successfully for solving a direct (regular/singular) or inverse Sturm-Liouville problem (SLP) of an arbitrary order with arbitrary boundary conditions.},
language = {en}
}
@article{BeckusPinchover2020,
author = {Beckus, Siegfried and Pinchover, Yehuda},
title = {Shnol-type theorem for the Agmon ground state},
series = {Journal of spectral theory},
volume = {10},
journal = {Journal of spectral theory},
number = {2},
publisher = {EMS Publishing House},
address = {Z{\"u}rich},
issn = {1664-039X},
doi = {10.4171/JST/296},
pages = {355 -- 377},
year = {2020},
abstract = {LetH be a Schrodinger operator defined on a noncompact Riemannianmanifold Omega, and let W is an element of L-infinity (Omega; R). Suppose that the operator H + W is critical in Omega, and let phi be the corresponding Agmon ground state. We prove that if u is a generalized eigenfunction ofH satisfying vertical bar u vertical bar <= C-phi in Omega for some constant C > 0, then the corresponding eigenvalue is in the spectrum of H. The conclusion also holds true if for some K is an element of Omega the operator H admits a positive solution in (Omega) over bar = Omega \ K, and vertical bar u vertical bar <= C psi in (Omega) over bar for some constant C > 0, where psi is a positive solution of minimal growth in a neighborhood of infinity in Omega. Under natural assumptions, this result holds also in the context of infinite graphs, and Dirichlet forms.},
language = {en}
}
@article{BlanchardMuecke2020,
author = {Blanchard, Gilles and M{\"u}cke, Nicole},
title = {Kernel regression, minimax rates and effective dimensionality},
series = {Analysis and applications},
volume = {18},
journal = {Analysis and applications},
number = {4},
publisher = {World Scientific},
address = {New Jersey},
issn = {0219-5305},
doi = {10.1142/S0219530519500258},
pages = {683 -- 696},
year = {2020},
abstract = {We investigate if kernel regularization methods can achieve minimax convergence rates over a source condition regularity assumption for the target function. These questions have been considered in past literature, but only under specific assumptions about the decay, typically polynomial, of the spectrum of the the kernel mapping covariance operator. In the perspective of distribution-free results, we investigate this issue under much weaker assumption on the eigenvalue decay, allowing for more complex behavior that can reflect different structure of the data at different scales.},
language = {en}
}
@article{MazzonettoSalimova2020,
author = {Mazzonetto, Sara and Salimova, Diyora},
title = {Existence, uniqueness, and numerical approximations for stochastic burgers equations},
series = {Stochastic analysis and applications},
volume = {38},
journal = {Stochastic analysis and applications},
number = {4},
publisher = {Taylor \& Francis Group},
address = {Philadelphia},
issn = {0736-2994},
doi = {10.1080/07362994.2019.1709503},
pages = {623 -- 646},
year = {2020},
abstract = {In this article, we propose an all-in-one statement which includes existence, uniqueness, regularity, and numerical approximations of mild solutions for a class of stochastic partial differential equations (SPDEs) with non-globally monotone nonlinearities. The proof of this result exploits the properties of an existing fully explicit space-time discrete approximation scheme, in particular the fact that it satisfies suitable a priori estimates. We also obtain almost sure and strong convergence of the approximation scheme to the mild solutions of the considered SPDEs. We conclude by applying the main result of the article to the stochastic Burgers equations with additive space-time white noise.},
language = {en}
}
@article{deWiljesPathirajaReich2020,
author = {de Wiljes, Jana and Pathiraja, Sahani Darschika and Reich, Sebastian},
title = {Ensemble transform algorithms for nonlinear smoothing problems},
series = {SIAM journal on scientific computing},
volume = {42},
journal = {SIAM journal on scientific computing},
number = {1},
publisher = {Society for Industrial and Applied Mathematics},
address = {Philadelphia},
issn = {1064-8275},
doi = {10.1137/19M1239544},
pages = {A87 -- A114},
year = {2020},
abstract = {Several numerical tools designed to overcome the challenges of smoothing in a non-linear and non-Gaussian setting are investigated for a class of particle smoothers. The considered family of smoothers is induced by the class of linear ensemble transform filters which contains classical filters such as the stochastic ensemble Kalman filter, the ensemble square root filter, and the recently introduced nonlinear ensemble transform filter. Further the ensemble transform particle smoother is introduced and particularly highlighted as it is consistent in the particle limit and does not require assumptions with respect to the family of the posterior distribution. The linear update pattern of the considered class of linear ensemble transform smoothers allows one to implement important supplementary techniques such as adaptive spread corrections, hybrid formulations, and localization in order to facilitate their application to complex estimation problems. These additional features are derived and numerically investigated for a sequence of increasingly challenging test problems.},
language = {en}
}
@article{ZoellerHainzlTilmannetal.2020,
author = {Z{\"o}ller, Gert and Hainzl, Sebastian and Tilmann, Frederik and Woith, Heiko and Dahm, Torsten},
title = {Comment on: Wikelski, Martin; M{\"u}ller, Uschi; Scocco, Paola; Catorci, Andrea; Desinov, Lev V.; Belyaev, Mikhail Y.; Keim, Daniel A.; Pohlmeier, Winfried; Fechteler, Gerhard; Mai, Martin P. : Potential short-term earthquake forecasting by farm animal monitoring. - Ethology. - 126 (2020), 9. - S. 931 - 941. -ISSN 0179-1613. - eISSN 1439-0310. - doi 10.1111/eth.13078},
series = {Ethology},
volume = {127},
journal = {Ethology},
number = {3},
publisher = {Wiley},
address = {Hoboken},
issn = {0179-1613},
doi = {10.1111/eth.13105},
pages = {302 -- 306},
year = {2020},
abstract = {Based on an analysis of continuous monitoring of farm animal behavior in the region of the 2016 M6.6 Norcia earthquake in Italy, Wikelski et al., 2020; (Seismol Res Lett, 89, 2020, 1238) conclude that animal activity can be anticipated with subsequent seismic activity and that this finding might help to design a "short-term earthquake forecasting method." We show that this result is based on an incomplete analysis and misleading interpretations. Applying state-of-the-art methods of statistics, we demonstrate that the proposed anticipatory patterns cannot be distinguished from random patterns, and consequently, the observed anomalies in animal activity do not have any forecasting power.},
language = {en}
}
@article{Clavier2020,
author = {Clavier, Pierre J.},
title = {Double shuffle relations for arborified zeta values},
series = {Journal of algebra},
volume = {543},
journal = {Journal of algebra},
publisher = {Elsevier},
address = {San Diego},
issn = {0021-8693},
doi = {10.1016/j.jalgebra.2019.10.015},
pages = {111 -- 155},
year = {2020},
abstract = {Arborified zeta values are defined as iterated series and integrals using the universal properties of rooted trees. This approach allows to study their convergence domain and to relate them to multiple zeta values. Generalisations to rooted trees of the stuffle and shuffle products are defined and studied. It is further shown that arborified zeta values are algebra morphisms for these new products on trees.},
language = {en}
}
@article{ChelkhLyTarkhanov2020,
author = {Chelkh, W. and Ly, Ibrahim and Tarkhanov, Nikolai},
title = {A remark on the Laplace transform},
series = {Siberian Mathematical Journal},
volume = {61},
journal = {Siberian Mathematical Journal},
number = {4},
publisher = {Consultants Bureau, Springer},
address = {New York},
issn = {0037-4466},
doi = {10.1134/S0037446620040151},
pages = {755 -- 762},
year = {2020},
abstract = {The study of the Cauchy problem for solutions of the heat equation in a cylindrical domain with data on the lateral surface by the Fourier method raises the problem of calculating the inverse Laplace transform of the entire function cos root z. This problem has no solution in the standard theory of the Laplace transform. We give an explicit formula for the inverse Laplace transform of cos root z using the theory of analytic functionals. This solution suits well to efficiently develop the regularization of solutions to Cauchy problems for parabolic equations with data on noncharacteristic surfaces.},
language = {en}
}
@article{SeeligRabeMalemShinitskietal.2020,
author = {Seelig, Stefan A. and Rabe, Maximilian Michael and Malem-Shinitski, Noa and Risse, Sarah and Reich, Sebastian and Engbert, Ralf},
title = {Bayesian parameter estimation for the SWIFT model of eye-movement control during reading},
series = {Journal of mathematical psychology},
volume = {95},
journal = {Journal of mathematical psychology},
publisher = {Elsevier},
address = {San Diego},
issn = {0022-2496},
doi = {10.1016/j.jmp.2019.102313},
pages = {32},
year = {2020},
abstract = {Process-oriented theories of cognition must be evaluated against time-ordered observations. Here we present a representative example for data assimilation of the SWIFT model, a dynamical model of the control of fixation positions and fixation durations during natural reading of single sentences. First, we develop and test an approximate likelihood function of the model, which is a combination of a spatial, pseudo-marginal likelihood and a temporal likelihood obtained by probability density approximation Second, we implement a Bayesian approach to parameter inference using an adaptive Markov chain Monte Carlo procedure. Our results indicate that model parameters can be estimated reliably for individual subjects. We conclude that approximative Bayesian inference represents a considerable step forward for computational models of eye-movement control, where modeling of individual data on the basis of process-based dynamic models has not been possible so far.},
language = {en}
}
@article{AlSaedyTarchanov2020,
author = {Al-Saedy, Ammar Jaffar Muhesin and Tarchanov, Nikolaj Nikolaevič},
title = {A degree theory for Lagrangian boundary value problems},
series = {Žurnal Sibirskogo Federalʹnogo Universiteta = Journal of Siberian Federal University; mathematics \& physics},
volume = {13},
journal = {Žurnal Sibirskogo Federalʹnogo Universiteta = Journal of Siberian Federal University; mathematics \& physics},
number = {1},
publisher = {Sibirskij Federalʹnyj Universitet},
address = {Krasnojarsk},
issn = {1997-1397},
doi = {10.17516/1997-1397-2020-13-1-5-25},
pages = {5 -- 25},
year = {2020},
abstract = {We study those nonlinear partial differential equations which appear as Euler-Lagrange equations of variational problems. On defining weak boundary values of solutions to such equations we initiate the theory of Lagrangian boundary value problems in spaces of appropriate smoothness. We also analyse if the concept of mapping degree of current importance applies to Lagrangian problems.},
language = {en}
}
@article{SaggiorodeWiljesKretschmeretal.2020,
author = {Saggioro, Elena and de Wiljes, Jana and Kretschmer, Marlene and Runge, Jakob},
title = {Reconstructing regime-dependent causal relationships from observational time series},
series = {Chaos : an interdisciplinary journal of nonlinear science},
volume = {30},
journal = {Chaos : an interdisciplinary journal of nonlinear science},
number = {11},
publisher = {American Institute of Physics},
address = {Melville},
issn = {1054-1500},
doi = {10.1063/5.0020538},
pages = {22},
year = {2020},
abstract = {Inferring causal relations from observational time series data is a key problem across science and engineering whenever experimental interventions are infeasible or unethical. Increasing data availability over the past few decades has spurred the development of a plethora of causal discovery methods, each addressing particular challenges of this difficult task. In this paper, we focus on an important challenge that is at the core of time series causal discovery: regime-dependent causal relations. Often dynamical systems feature transitions depending on some, often persistent, unobserved background regime, and different regimes may exhibit different causal relations. Here, we assume a persistent and discrete regime variable leading to a finite number of regimes within which we may assume stationary causal relations. To detect regime-dependent causal relations, we combine the conditional independence-based PCMCI method [based on a condition-selection step (PC) followed by the momentary conditional independence (MCI) test] with a regime learning optimization approach. PCMCI allows for causal discovery from high-dimensional and highly correlated time series. Our method, Regime-PCMCI, is evaluated on a number of numerical experiments demonstrating that it can distinguish regimes with different causal directions, time lags, and sign of causal links, as well as changes in the variables' autocorrelation. Furthermore, Regime-PCMCI is employed to observations of El Nino Southern Oscillation and Indian rainfall, demonstrating skill also in real-world datasets.},
language = {en}
}
@article{LyTarkhanov2020,
author = {Ly, Ibrahim and Tarkhanov, Nikolaj Nikolaevič},
title = {Asymptotic expansions at nonsymmetric cuspidal points},
series = {Mathematical notes},
volume = {108},
journal = {Mathematical notes},
number = {1-2},
publisher = {Springer Science},
address = {New York},
issn = {0001-4346},
doi = {10.1134/S0001434620070238},
pages = {219 -- 228},
year = {2020},
abstract = {We study the asymptotics of solutions to the Dirichlet problem in a domain X subset of R3 whose boundary contains a singular point O. In a small neighborhood of this point, the domain has the form {z > root x(2) + y(4)}, i.e., the origin is a nonsymmetric conical point at the boundary. So far, the behavior of solutions to elliptic boundary-value problems has not been studied sufficiently in the case of nonsymmetric singular points. This problem was posed by V.A. Kondrat'ev in 2000. We establish a complete asymptotic expansion of solutions near the singular point.},
language = {en}
}
@article{Denecke2020,
author = {Denecke, Klaus-Dieter},
title = {Partial clones},
series = {Asian-European journal of mathematics : AEJM},
volume = {13},
journal = {Asian-European journal of mathematics : AEJM},
number = {8},
publisher = {World Scientific},
address = {Singapore},
issn = {1793-5571},
doi = {10.1142/S1793557120501612},
pages = {19},
year = {2020},
abstract = {A set C of operations defined on a nonempty set A is said to be a clone if C is closed under composition of operations and contains all projection mappings. The concept of a clone belongs to the algebraic main concepts and has important applications in Computer Science. A clone can also be regarded as a many-sorted algebra where the sorts are the n-ary operations defined on set A for all natural numbers n >= 1 and the operations are the so-called superposition operations S-m(n) for natural numbers m, n >= 1 and the projection operations as nullary operations. Clones generalize monoids of transformations defined on set A and satisfy three clone axioms. The most important axiom is the superassociative law, a generalization of the associative law. If the superposition operations are partial, i.e. not everywhere defined, instead of the many-sorted clone algebra, one obtains partial many-sorted algebras, the partial clones. Linear terms, linear tree languages or linear formulas form partial clones. In this paper, we give a survey on partial clones and their properties.},
language = {en}
}
@article{PurintonBookhagen2020,
author = {Purinton, Benjamin and Bookhagen, Bodo},
title = {Multiband (X, C, L) radar amplitude analysis for a mixed sand- and gravel-bed river in the eastern Central Andes},
series = {Remote sensing of environment : an interdisciplinary journal},
volume = {246},
journal = {Remote sensing of environment : an interdisciplinary journal},
publisher = {Elsevier},
address = {New York},
issn = {0034-4257},
doi = {10.1016/j.rse.2020.111799},
pages = {16},
year = {2020},
abstract = {Synthetic Aperture Radar (SAR) amplitude measurements from spaceborne sensors are sensitive to surface roughness conditions near their radar wavelength. These backscatter signals are often exploited to assess the roughness of plowed agricultural fields and water surfaces, and less so to complex, heterogeneous geological surfaces. The bedload of mixed sand- and gravel-bed rivers can be considered a mixture of smooth (compacted sand) and rough (gravel) surfaces. Here, we assess backscatter gradients over a large high-mountain alluvial river in the eastern Central Andes with aerially exposed sand and gravel bedload using X-band TerraSAR-X/TanDEM-X, C-band Sentinel-1, and L-band ALOS-2 PALSAR-2 radar scenes. In a first step, we present theory and hypotheses regarding radar response to an alluvial channel bed. We test our hypotheses by comparing backscatter responses over vegetation-free endmember surfaces from inside and outside of the active channel-bed area. We then develop methods to extract smoothed backscatter gradients downstream along the channel using kernel density estimates. In a final step, the local variability of sand-dominated patches is analyzed using Fourier frequency analysis, by fitting stretched-exponential and power-law regression models to the 2-D power spectrum of backscatter amplitude. We find a large range in backscatter depending on the heterogeneity of contiguous smooth- and rough-patches of bedload material. The SAR amplitude signal responds primarily to the fraction of smooth-sand bedload, but is further modified by gravel elements. The sensitivity to gravel is more apparent in longer wavelength L-band radar, whereas C- and X-band is sensitive only to sand variability. Because the spatial extent of smooth sand patches in our study area is typically< 50 m, only higher resolution sensors (e.g., TerraSAR-X/TanDEM-X) are useful for power spectrum analysis. Our results show the potential for mapping sand-gravel transitions and local geomorphic complexity in alluvial rivers with aerially exposed bedload using SAR amplitude.},
language = {en}
}
@article{KellerSchwarz2020,
author = {Keller, Matthias and Schwarz, Michael},
title = {Courant's nodal domain theorem for positivity preserving forms},
series = {Journal of spectral theory},
volume = {10},
journal = {Journal of spectral theory},
number = {1},
publisher = {EMS Publishing House},
address = {Z{\"u}rich},
issn = {1664-039X},
doi = {10.4171/JST/292},
pages = {271 -- 309},
year = {2020},
abstract = {We introduce a notion of nodal domains for positivity preserving forms. This notion generalizes the classical ones for Laplacians on domains and on graphs. We prove the Courant nodal domain theorem in this generalized setting using purely analytical methods.},
language = {en}
}
@article{Rastogi2020,
author = {Rastogi, Abhishake},
title = {Tikhonov regularization with oversmoothing penalty for nonlinear statistical inverse problems},
series = {Communications on Pure and Applied Analysis},
volume = {19},
journal = {Communications on Pure and Applied Analysis},
number = {8},
publisher = {American Institute of Mathematical Sciences},
address = {Springfield},
issn = {1534-0392},
doi = {10.3934/cpaa.2020183},
pages = {4111 -- 4126},
year = {2020},
abstract = {In this paper, we consider the nonlinear ill-posed inverse problem with noisy data in the statistical learning setting. The Tikhonov regularization scheme in Hilbert scales is considered to reconstruct the estimator from the random noisy data. In this statistical learning setting, we derive the rates of convergence for the regularized solution under certain assumptions on the nonlinear forward operator and the prior assumptions. We discuss estimates of the reconstruction error using the approach of reproducing kernel Hilbert spaces.},
language = {en}
}
@article{Graeter2020,
author = {Gr{\"a}ter, Joachim},
title = {Free division rings of fractions of crossed products of groups with Conradian left-orders},
series = {Forum mathematicum},
volume = {32},
journal = {Forum mathematicum},
number = {3},
publisher = {De Gruyter},
address = {Berlin},
issn = {0933-7741},
doi = {10.1515/forum-2019-0264},
pages = {739 -- 772},
year = {2020},
abstract = {Let D be a division ring of fractions of a crossed product F[G, eta, alpha], where F is a skew field and G is a group with Conradian left-order <=. For D we introduce the notion of freeness with respect to <= and show that D is free in this sense if and only if D can canonically be embedded into the endomorphism ring of the right F-vector space F((G)) of all formal power series in G over F with respect to <=. From this we obtain that all division rings of fractions of F[G, eta, alpha] which are free with respect to at least one Conradian left-order of G are isomorphic and that they are free with respect to any Conradian left-order of G. Moreover, F[G, eta, alpha] possesses a division ring of fraction which is free in this sense if and only if the rational closure of F[G, eta, alpha] in the endomorphism ring of the corresponding right F-vector space F((G)) is a skew field.},
language = {en}
}
@article{MalassTarkhanov2020,
author = {Malass, Ihsane and Tarkhanov, Nikolaj Nikolaevič},
title = {A perturbation of the de Rham complex},
series = {Journal of Siberian Federal University : Mathematics \& Physics},
volume = {13},
journal = {Journal of Siberian Federal University : Mathematics \& Physics},
number = {5},
publisher = {Siberian Federal University},
address = {Krasnojarsk},
issn = {1997-1397},
doi = {10.17516/1997-1397-2020-13-5-519-532},
pages = {519 -- 532},
year = {2020},
abstract = {We consider a perturbation of the de Rham complex on a compact manifold with boundary. This perturbation goes beyond the framework of complexes, and so cohomology does not apply to it. On the other hand, its curvature is "small", hence there is a natural way to introduce an Euler characteristic and develop a Lefschetz theory for the perturbation. This work is intended as an attempt to develop a cohomology theory for arbitrary sequences of linear mappings.},
language = {en}
}
@article{Ly2020,
author = {Ly, Ibrahim},
title = {A Cauchy problem for the Cauchy-Riemann operator},
series = {Afrika Matematika},
volume = {32},
journal = {Afrika Matematika},
number = {1-2},
publisher = {Springer},
address = {Heidelberg},
issn = {1012-9405},
doi = {10.1007/s13370-020-00810-4},
pages = {69 -- 76},
year = {2020},
abstract = {We study the Cauchy problem for a nonlinear elliptic equation with data on a piece S of the boundary surface partial derivative X. By the Cauchy problem is meant any boundary value problem for an unknown function u in a domain X with the property that the data on S, if combined with the differential equations in X, allows one to determine all derivatives of u on S by means of functional equations. In the case of real analytic data of the Cauchy problem, the existence of a local solution near S is guaranteed by the Cauchy-Kovalevskaya theorem. We discuss a variational setting of the Cauchy problem which always possesses a generalized solution.},
language = {en}
}
@article{SomogyvariReich2020,
author = {Somogyv{\´a}ri, M{\´a}rk and Reich, Sebastian},
title = {Convergence tests for transdimensional Markov chains in geoscience imaging},
series = {Mathematical geosciences : the official journal of the International Association for Mathematical Geosciences},
volume = {52},
journal = {Mathematical geosciences : the official journal of the International Association for Mathematical Geosciences},
number = {5},
publisher = {Springer},
address = {Heidelberg},
issn = {1874-8961},
doi = {10.1007/s11004-019-09811-x},
pages = {651 -- 668},
year = {2020},
abstract = {Classic inversion methods adjust a model with a predefined number of parameters to the observed data. With transdimensional inversion algorithms such as the reversible-jump Markov chain Monte Carlo (rjMCMC), it is possible to vary this number during the inversion and to interpret the observations in a more flexible way. Geoscience imaging applications use this behaviour to automatically adjust model resolution to the inhomogeneities of the investigated system, while keeping the model parameters on an optimal level. The rjMCMC algorithm produces an ensemble as result, a set of model realizations, which together represent the posterior probability distribution of the investigated problem. The realizations are evolved via sequential updates from a randomly chosen initial solution and converge toward the target posterior distribution of the inverse problem. Up to a point in the chain, the realizations may be strongly biased by the initial model, and must be discarded from the final ensemble. With convergence assessment techniques, this point in the chain can be identified. Transdimensional MCMC methods produce ensembles that are not suitable for classic convergence assessment techniques because of the changes in parameter numbers. To overcome this hurdle, three solutions are introduced to convert model realizations to a common dimensionality while maintaining the statistical characteristics of the ensemble. A scalar, a vector and a matrix representation for models is presented, inferred from tomographic subsurface investigations, and three classic convergence assessment techniques are applied on them. It is shown that appropriately chosen scalar conversions of the models could retain similar statistical ensemble properties as geologic projections created by rasterization.},
language = {en}
}
@article{GrisicEserHuisingaetal.2020,
author = {Grisic, Ana-Marija and Eser, Alexander and Huisinga, Wilhelm and Reinisch, Walter and Kloft, Charlotte},
title = {Quantitative relationship between infliximab exposure and inhibition of C-reactive protein synthesis to support inflammatory bowel disease management},
series = {British journal of clinical pharmacology},
volume = {87},
journal = {British journal of clinical pharmacology},
number = {5},
publisher = {Wiley},
address = {Hoboken},
issn = {0306-5251},
doi = {10.1111/bcp.14648},
pages = {2374 -- 2384},
year = {2020},
abstract = {Aim Quantitative and kinetic insights into the drug exposure-disease response relationship might enhance our knowledge on loss of response and support more effective monitoring of inflammatory activity by biomarkers in patients with inflammatory bowel disease (IBD) treated with infliximab (IFX). This study aimed to derive recommendations for dose adjustment and treatment optimisation based on mechanistic characterisation of the relationship between IFX serum concentration and C-reactive protein (CRP) concentration.
Methods Data from an investigator-initiated trial included 121 patients with IBD during IFX maintenance treatment. Serum concentrations of IFX, antidrug antibodies (ADA), CRP, and disease-related covariates were determined at the mid-term and end of a dosing interval. Data were analysed using a pharmacometric nonlinear mixed-effects modelling approach. An IFX exposure-CRP model was generated and applied to evaluate dosing regimens to achieve CRP remission.
Results The generated quantitative model showed that IFX has the potential to inhibit up to 72\% (9\% relative standard error [RSE]) of CRP synthesis in a patient. IFX concentration leading to 90\% of the maximum CRP synthesis inhibition was 18.4 mu g/mL (43\% RSE). Presence of ADA was the most influential factor on IFX exposure. With standard dosing strategy, >= 55\% of ADA+ patients experienced CRP nonremission. Shortening the dosing interval and co-therapy with immunomodulators were found to be the most beneficial strategies to maintain CRP remission.
Conclusions With the generated model we could for the first time establish a robust relationship between IFX exposure and CRP synthesis inhibition, which could be utilised for treatment optimisation in IBD patients.},
language = {en}
}
@article{HammPelivanGrottetal.2020,
author = {Hamm, Maximilian and Pelivan, Ivanka and Grott, Matthias and de Wiljes, Jana},
title = {Thermophysical modelling and parameter estimation of small solar system bodies via data assimilation},
series = {Monthly notices of the Royal Astronomical Society},
volume = {496},
journal = {Monthly notices of the Royal Astronomical Society},
number = {3},
publisher = {Oxford Univ. Press},
address = {Oxford},
issn = {0035-8711},
doi = {10.1093/mnras/staa1755},
pages = {2776 -- 2785},
year = {2020},
abstract = {Deriving thermophysical properties such as thermal inertia from thermal infrared observations provides useful insights into the structure of the surface material on planetary bodies. The estimation of these properties is usually done by fitting temperature variations calculated by thermophysical models to infrared observations. For multiple free model parameters, traditional methods such as least-squares fitting or Markov chain Monte Carlo methods become computationally too expensive. Consequently, the simultaneous estimation of several thermophysical parameters, together with their corresponding uncertainties and correlations, is often not computationally feasible and the analysis is usually reduced to fitting one or two parameters. Data assimilation (DA) methods have been shown to be robust while sufficiently accurate and computationally affordable even for a large number of parameters. This paper will introduce a standard sequential DA method, the ensemble square root filter, for thermophysical modelling of asteroid surfaces. This method is used to re-analyse infrared observations of the MARA instrument, which measured the diurnal temperature variation of a single boulder on the surface of near-Earth asteroid (162173) Ryugu. The thermal inertia is estimated to be 295 +/- 18 Jm(-2) K-1 s(-1/2), while all five free parameters of the initial analysis are varied and estimated simultaneously. Based on this thermal inertia estimate the thermal conductivity of the boulder is estimated to be between 0.07 and 0.12,Wm(-1) K-1 and the porosity to be between 0.30 and 0.52. For the first time in thermophysical parameter derivation, correlations and uncertainties of all free model parameters are incorporated in the estimation procedure that is more than 5000 times more efficient than a comparable parameter sweep.},
language = {en}
}