@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{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{AyanbayevKlebanovLieetal.2021, author = {Ayanbayev, Birzhan and Klebanov, Ilja and Lie, Han Cheng and Sullivan, Tim J.}, title = {Gamma-convergence of Onsager-Machlup functionals}, series = {Inverse problems : an international journal of inverse problems, inverse methods and computerised inversion of data}, volume = {38}, journal = {Inverse problems : an international journal of inverse problems, inverse methods and computerised inversion of data}, number = {2}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {0266-5611}, doi = {10.1088/1361-6420/ac3f82}, pages = {35}, year = {2021}, abstract = {We derive Onsager-Machlup functionals for countable product measures on weighted l(p) subspaces of the sequence space R-N. Each measure in the product is a shifted and scaled copy of a reference probability measure on R that admits a sufficiently regular Lebesgue density. We study the equicoercivity and Gamma-convergence of sequences of Onsager-Machlup functionals associated to convergent sequences of measures within this class. We use these results to establish analogous results for probability measures on separable Banach or Hilbert spaces, including Gaussian, Cauchy, and Besov measures with summability parameter 1 <= p <= 2. Together with part I of this paper, this provides a basis for analysis of the convergence of maximum a posteriori estimators in Bayesian inverse problems and most likely paths in transition path theory.}, language = {en} } @article{LazaridesRubach2017, author = {Lazarides, Rebecca and Rubach, Charlott}, title = {Instructional characteristics in mathematics classrooms}, series = {Mathematics Education Research Journal}, volume = {29}, journal = {Mathematics Education Research Journal}, publisher = {Springer}, address = {Dordrecht}, issn = {1033-2170}, doi = {10.1007/s13394-017-0196-4}, pages = {201 -- 217}, year = {2017}, abstract = {This longitudinal study examined relationships between student-perceived teaching for meaning, support for autonomy, and competence in mathematic classrooms (Time 1), and students' achievement goal orientations and engagement in mathematics 6 months later (Time 2). We tested whether student-perceived instructional characteristics at Time 1 indirectly related to student engagement at Time 2, via their achievement goal orientations (Time 2), and, whether student gender moderated these relationships. Participants were ninth and tenth graders (55.2\% girls) from 46 classrooms in ten secondary schools in Berlin, Germany. Only data from students who participated at both timepoints were included (N = 746 out of total at Time 1 1118; dropout 33.27\%). Longitudinal structural equation modeling showed that student-perceived teaching for meaning and support for competence indirectly predicted intrinsic motivation and effort, via students' mastery goal orientation. These paths were equivalent for girls and boys. The findings are significant for mathematics education, in identifying motivational processes that partly explain the relationships between student-perceived teaching for meaning and competence support and intrinsic motivation and effort in mathematics.}, 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{Omel'chenkoLaing2022, author = {Omel'chenko, Oleh and Laing, Carlo R.}, title = {Collective states in a ring network of theta neurons}, series = {Proceedings of the Royal Society of London. Series A, Mathematical, physical and engineering sciences}, volume = {478}, journal = {Proceedings of the Royal Society of London. Series A, Mathematical, physical and engineering sciences}, number = {2259}, publisher = {Royal Society}, address = {London}, issn = {1364-5021}, doi = {10.1098/rspa.2021.0817}, pages = {23}, year = {2022}, abstract = {We consider a ring network of theta neurons with non-local homogeneous coupling. We analyse the corresponding continuum evolution equation, analytically describing all possible steady states and their stability. By considering a number of different parameter sets, we determine the typical bifurcation scenarios of the network, and put on a rigorous footing some previously observed numerical results.}, 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{PasemannFlemmingAlonsoetal.2021, author = {Pasemann, Gregor and Flemming, Sven and Alonso, Sergio and Beta, Carsten and Stannat, Wilhelm}, title = {Diffusivity estimation for activator-inhibitor models}, series = {Journal of nonlinear science}, volume = {31}, journal = {Journal of nonlinear science}, number = {3}, publisher = {Springer}, address = {New York}, issn = {0938-8974}, doi = {10.1007/s00332-021-09714-4}, pages = {34}, year = {2021}, abstract = {A theory for diffusivity estimation for spatially extended activator-inhibitor dynamics modeling the evolution of intracellular signaling networks is developed in the mathematical framework of stochastic reaction-diffusion systems. In order to account for model uncertainties, we extend the results for parameter estimation for semilinear stochastic partial differential equations, as developed in Pasemann and Stannat (Electron J Stat 14(1):547-579, 2020), to the problem of joint estimation of diffusivity and parametrized reaction terms. Our theoretical findings are applied to the estimation of effective diffusivity of signaling components contributing to intracellular dynamics of the actin cytoskeleton in the model organism Dictyostelium discoideum.}, 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{HehnMendezUebernickeletal.2019, author = {Hehn, Jennifer and Mendez, Daniel and Uebernickel, Falk and Brenner, Walter and Broy, Manfred}, title = {On integrating design thinking for human-centered requirements engineering}, series = {IEEE software}, volume = {37}, journal = {IEEE software}, number = {2}, publisher = {Inst. of Electr. and Electronics Engineers}, address = {Los Alamitos}, issn = {0740-7459}, doi = {10.1109/MS.2019.2957715}, pages = {25 -- 31}, year = {2019}, abstract = {We elaborate on the possibilities and needs to integrate design thinking into requirements engineering, drawing from our research and project experiences. We suggest three approaches for tailoring and integrating design thinking and requirements engineering with complementary synergies and point at open challenges for research and practice.}, language = {en} } @article{RosenauPikovskij2021, author = {Rosenau, Philip and Pikovskij, Arkadij}, title = {Waves in strongly nonlinear Gardner-like equations on a lattice}, series = {Nonlinearity / the Institute of Physics and the London Mathematical Society}, volume = {34}, journal = {Nonlinearity / the Institute of Physics and the London Mathematical Society}, number = {8}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {0951-7715}, doi = {10.1088/1361-6544/ac0f51}, pages = {5872 -- 5896}, year = {2021}, abstract = {We introduce and study a family of lattice equations which may be viewed either as a strongly nonlinear discrete extension of the Gardner equation, or a non-convex variant of the Lotka-Volterra chain. Their deceptively simple form supports a very rich family of complex solitary patterns. Some of these patterns are also found in the quasi-continuum rendition, but the more intriguing ones, like interlaced pairs of solitary waves, or waves which may reverse their direction either spontaneously or due a collision, are an intrinsic feature of the discrete realm.}, language = {en} } @article{CvetkovićConradLie2021, author = {Cvetković, Nada and Conrad, Tim and Lie, Han Cheng}, title = {A convergent discretization method for transition path theory for diffusion processes}, series = {Multiscale modeling \& simulation : a SIAM interdisciplinary journal}, volume = {19}, journal = {Multiscale modeling \& simulation : a SIAM interdisciplinary journal}, number = {1}, publisher = {Society for Industrial and Applied Mathematics}, address = {Philadelphia}, issn = {1540-3459}, doi = {10.1137/20M1329354}, pages = {242 -- 266}, year = {2021}, abstract = {Transition path theory (TPT) for diffusion processes is a framework for analyzing the transitions of multiscale ergodic diffusion processes between disjoint metastable subsets of state space. Most methods for applying TPT involve the construction of a Markov state model on a discretization of state space that approximates the underlying diffusion process. However, the assumption of Markovianity is difficult to verify in practice, and there are to date no known error bounds or convergence results for these methods. We propose a Monte Carlo method for approximating the forward committor, probability current, and streamlines from TPT for diffusion processes. Our method uses only sample trajectory data and partitions of state space based on Voronoi tessellations. It does not require the construction of a Markovian approximating process. We rigorously prove error bounds for the approximate TPT objects and use these bounds to show convergence to their exact counterparts in the limit of arbitrarily fine discretization. We illustrate some features of our method by application to a process that solves the Smoluchowski equation on a triple-well potential.}, language = {en} } @article{PereraBoeckmann2019, author = {Perera, Upeksha and B{\"o}ckmann, Christine}, title = {Solutions of Direct and Inverse Even-Order Sturm-Liouville Problems Using Magnus Expansion}, series = {Mathematics}, volume = {7}, journal = {Mathematics}, number = {6}, publisher = {MDPI}, address = {Basel, Schweiz}, issn = {2227-7390}, doi = {10.3390/math7060544}, pages = {24}, year = {2019}, abstract = {In this paper Lie group method in combination with Magnus expansion is utilized to develop a universal method applicable to solving a Sturm-Liouville problem (SLP) of any order with arbitrary boundary conditions. It is shown that the method has ability to solve direct regular (and some singular) SLPs of even orders (tested for up to eight), with a mix of (including non-separable and finite singular endpoints) boundary conditions, accurately and efficiently. The present technique is successfully applied to overcome the difficulties in finding suitable sets of eigenvalues so that the inverse SLP problem can be effectively solved. The inverse SLP algorithm proposed by Barcilon (1974) is utilized in combination with the Magnus method so that a direct SLP of any (even) order and an inverse SLP of order two can be solved effectively.}, language = {en} } @article{CsehKavitha2021, author = {Cseh, {\´A}gnes and Kavitha, Telikepalli}, title = {Popular matchings in complete graphs}, series = {Algorithmica : an international journal in computer science}, volume = {83}, journal = {Algorithmica : an international journal in computer science}, number = {5}, publisher = {Springer}, address = {New York}, issn = {0178-4617}, doi = {10.1007/s00453-020-00791-7}, pages = {1493 -- 1523}, year = {2021}, abstract = {Our input is a complete graph G on n vertices where each vertex has a strict ranking of all other vertices in G. The goal is to construct a matching in G that is popular. A matching M is popular if M does not lose a head-to-head election against any matching M ': here each vertex casts a vote for the matching in {M,M '} in which it gets a better assignment. Popular matchings need not exist in the given instance G and the popular matching problem is to decide whether one exists or not. The popular matching problem in G is easy to solve for odd n. Surprisingly, the problem becomes NP-complete for even n, as we show here. This is one of the few graph theoretic problems efficiently solvable when n has one parity and NP-complete when n has the other parity.}, language = {en} } @article{ChangMahmoudiSchulze2018, author = {Chang, Der-Chen and Mahmoudi, Mahdi Hedayat and Schulze, Bert-Wolfgang}, title = {Volterra operators in the edge-calculus}, series = {Analysis and Mathematical Physics}, volume = {8}, journal = {Analysis and Mathematical Physics}, number = {4}, publisher = {Springer}, address = {Basel}, issn = {1664-2368}, doi = {10.1007/s13324-018-0238-4}, pages = {551 -- 570}, year = {2018}, abstract = {We study the Volterra property of a class of anisotropic pseudo-differential operators on R x B for a manifold B with edge Y and time-variable t. This exposition belongs to a program for studying parabolicity in such a situation. In the present consideration we establish non-smoothing elements in a subalgebra with anisotropic operator-valued symbols of Mellin type with holomorphic symbols in the complex Mellin covariable from the cone theory, where the covariable t of t extends to symbolswith respect to t to the lower complex v half-plane. The resulting space ofVolterra operators enlarges an approach of Buchholz (Parabolische Pseudodifferentialoperatoren mit operatorwertigen Symbolen. Ph. D. thesis, Universitat Potsdam, 1996) by necessary elements to a new operator algebra containing Volterra parametrices under an appropriate condition of anisotropic ellipticity. Our approach avoids some difficulty in choosing Volterra quantizations in the edge case by generalizing specific achievements from the isotropic edge-calculus, obtained by Seiler (Pseudodifferential calculus on manifolds with non-compact edges, Ph. D. thesis, University of Potsdam, 1997), see also Gil et al. (in: Demuth et al (eds) Mathematical research, vol 100. Akademic Verlag, Berlin, pp 113-137, 1997; Osaka J Math 37: 221-260, 2000).}, 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{RungrottheeraLyuSchulze2018, author = {Rungrottheera, Wannarut and Lyu, Xiaojing and Schulze, Bert-Wolfgang}, title = {Parameter-dependent edge calculus and corner parametrices}, series = {Journal of nonlinear and convex analysis : an international journal}, volume = {19}, journal = {Journal of nonlinear and convex analysis : an international journal}, number = {12}, publisher = {Yokohama Publishers}, address = {Yokohama}, issn = {1345-4773}, pages = {2021 -- 2051}, year = {2018}, abstract = {Let B be a compact manifold with smooth edge of dimension > 0. We study the interplay between parameter-dependent edge algebra algebra on B and operator families belonging to the corner calculus, and we characterize parametrices in the corner case.}, language = {en} } @article{StaufferMengeshaSeifertetal.2022, author = {Stauffer, Maxime and Mengesha, Isaak and Seifert, Konrad and Krawczuk, Igor and Fischer, Jens and Serugendo, Giovanna Di Marzo}, title = {A computational turn in policy process studies}, series = {Complexity}, volume = {2022}, journal = {Complexity}, publisher = {Wiley-Hindawi}, address = {London}, issn = {1076-2787}, doi = {10.1155/2022/8210732}, pages = {17}, year = {2022}, abstract = {The past three decades of policy process studies have seen the emergence of a clear intellectual lineage with regard to complexity. Implicitly or explicitly, scholars have employed complexity theory to examine the intricate dynamics of collective action in political contexts. However, the methodological counterparts to complexity theory, such as computational methods, are rarely used and, even if they are, they are often detached from established policy process theory. Building on a critical review of the application of complexity theory to policy process studies, we present and implement a baseline model of policy processes using the logic of coevolving networks. Our model suggests that an actor's influence depends on their environment and on exogenous events facilitating dialogue and consensus-building. Our results validate previous opinion dynamics models and generate novel patterns. Our discussion provides ground for further research and outlines the path for the field to achieve a computational turn.}, language = {en} } @article{HedayatMahmoudiSchulze2016, author = {Hedayat Mahmoudi, Mahdi and Schulze, Bert-Wolfgang}, title = {Corner boundary value problems}, series = {Asian-European journal of mathematics}, volume = {10}, journal = {Asian-European journal of mathematics}, number = {1}, publisher = {World Scientific}, address = {Singapore}, issn = {1793-5571}, doi = {10.1142/S1793557117500541}, pages = {45}, year = {2016}, abstract = {The paper develops some crucial steps in extending the first-order cone or edge calculus to higher singularity orders. We focus here on order 2, but the ideas are motivated by an iterative approach for higher singularities.}, language = {en} } @article{CsehFaenzaKavithaetal.2022, author = {Cseh, Agnes and Faenza, Yuri and Kavitha, Telikepalli and Powers, Vladlena}, title = {Understanding popular matchings via stable matchings}, series = {SIAM journal on discrete mathematics}, volume = {36}, journal = {SIAM journal on discrete mathematics}, number = {1}, publisher = {Society for Industrial and Applied Mathematics}, address = {Philadelphia}, issn = {0895-4801}, doi = {10.1137/19M124770X}, pages = {188 -- 213}, year = {2022}, abstract = {An instance of the marriage problem is given by a graph G = (A boolean OR B, E), together with, for each vertex of G, a strict preference order over its neighbors. A matching M of G is popular in the marriage instance if M does not lose a head-to-head election against any matching where vertices are voters. Every stable matching is a min-size popular matching; another subclass of popular matchings that always exists and can be easily computed is the set of dominant matchings. A popular matching M is dominant if M wins the head-to-head election against any larger matching. Thus, every dominant matching is a max-size popular matching, and it is known that the set of dominant matchings is the linear image of the set of stable matchings in an auxiliary graph. Results from the literature seem to suggest that stable and dominant matchings behave, from a complexity theory point of view, in a very similar manner within the class of popular matchings. The goal of this paper is to show that there are instead differences in the tractability of stable and dominant matchings and to investigate further their importance for popular matchings. First, we show that it is easy to check if all popular matchings are also stable; however, it is co-NP hard to check if all popular matchings are also dominant. Second, we show how some new and recent hardness results on popular matching problems can be deduced from the NP-hardness of certain problems on stable matchings, also studied in this paper, thus showing that stable matchings can be employed to show not only positive results on popular matchings (as is known) but also most negative ones. Problems for which we show new hardness results include finding a min-size (resp., max-size) popular matching that is not stable (resp., dominant). A known result for which we give a new and simple proof is the NP-hardness of finding a popular matching when G is nonbipartite.}, 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{EckertHerdenStiftetal.2022, author = {Eckert, Silvia and Herden, Jasmin and Stift, Marc and Durka, Walter and Kleunen, Mark van and Joshi, Jasmin Radha}, title = {Traces of genetic but not epigenetic adaptation in the invasive goldenrod Solidago canadensis despite the absence of population structure}, series = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, journal = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {1866-8372}, doi = {10.25932/publishup-56675}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-566758}, pages = {1 -- 17}, year = {2022}, abstract = {Biological invasions may result from multiple introductions, which might compensate for reduced gene pools caused by bottleneck events, but could also dilute adaptive processes. A previous common-garden experiment showed heritable latitudinal clines in fitness-related traits in the invasive goldenrod Solidago canadensis in Central Europe. These latitudinal clines remained stable even in plants chemically treated with zebularine to reduce epigenetic variation. However, despite the heritability of traits investigated, genetic isolation-by-distance was non-significant. Utilizing the same specimens, we applied a molecular analysis of (epi)genetic differentiation with standard and methylation-sensitive (MSAP) AFLPs. We tested whether this variation was spatially structured among populations and whether zebularine had altered epigenetic variation. Additionally, we used genome scans to mine for putative outlier loci susceptible to selection processes in the invaded range. Despite the absence of isolation-by-distance, we found spatial genetic neighborhoods among populations and two AFLP clusters differentiating northern and southern Solidago populations. Genetic and epigenetic diversity were significantly correlated, but not linked to phenotypic variation. Hence, no spatial epigenetic patterns were detected along the latitudinal gradient sampled. Applying genome-scan approaches (BAYESCAN, BAYESCENV, RDA, and LFMM), we found 51 genetic and epigenetic loci putatively responding to selection. One of these genetic loci was significantly more frequent in populations at the northern range. Also, one epigenetic locus was more frequent in populations in the southern range, but this pattern was lost under zebularine treatment. Our results point to some genetic, but not epigenetic adaptation processes along a large-scale latitudinal gradient of S. canadensis in its invasive range.}, 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{PornsawadSapsakulBoeckmann2019, author = {Pornsawad, Pornsarp and Sapsakul, Nantawan and B{\"o}ckmann, Christine}, title = {A modified asymptotical regularization of nonlinear ill-posed problems}, series = {Mathematics}, volume = {7}, journal = {Mathematics}, edition = {5}, publisher = {MDPI}, address = {Basel, Schweiz}, issn = {2227-7390}, doi = {10.3390/math7050419}, pages = {19}, year = {2019}, abstract = {In this paper, we investigate the continuous version of modified iterative Runge-Kutta-type methods for nonlinear inverse ill-posed problems proposed in a previous work. The convergence analysis is proved under the tangential cone condition, a modified discrepancy principle, i.e., the stopping time T is a solution of ∥𝐹(𝑥𝛿(𝑇))-𝑦𝛿∥=𝜏𝛿+ for some 𝛿+>𝛿, and an appropriate source condition. We yield the optimal rate of convergence.}, language = {en} } @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{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{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{PengSandevKocarev2021, author = {Peng, Junhao and Sandev, Trifce and Kocarev, Ljupco}, title = {First encounters on Bethe lattices and Cayley trees}, series = {Communications in nonlinear science \& numerical simulation}, volume = {95}, journal = {Communications in nonlinear science \& numerical simulation}, publisher = {Elsevier}, address = {Amsterdam}, issn = {1007-5704}, doi = {10.1016/j.cnsns.2020.105594}, pages = {15}, year = {2021}, abstract = {In this work we consider the first encounter problems between a fixed and/or mobile target A and a moving trap B on Bethe lattices and Cayley trees. The survival probabilities (SPs) of the target A on the both kinds of structures are considered analytically and compared. On Bethe lattices, the results show that the fixed target will still prolong its survival time, whereas, on Cayley trees, there are some initial positions where the target should move to prolong its survival time. The mean first encounter time (MFET) for mobile target A is evaluated numerically and compared with the mean first passage time (MFPT) for the fixed target A. Different initial settings are addressed and clear boundaries are obtained. These findings are helpful for optimizing the strategy to prolong the survival time of the target or to speed up the search process on Cayley trees, in relation to the target's movement and the initial position configuration of the two walkers. We also present a new method, which uses a small amount of memory, for simulating random walks on Cayley trees. (C) 2020 Elsevier B.V. All rights reserved.}, language = {en} } @article{AndjelkovicSimevskiChenetal.2022, author = {Andjelkovic, Marko and Simevski, Aleksandar and Chen, Junchao and Schrape, Oliver and Stamenkovic, Zoran and Krstić, Miloš and Ilic, Stefan and Ristic, Goran and Jaksic, Aleksandar and Vasovic, Nikola and Duane, Russell and Palma, Alberto J. and Lallena, Antonio M. and Carvajal, Miguel A.}, title = {A design concept for radiation hardened RADFET readout system for space applications}, series = {Microprocessors and microsystems}, volume = {90}, journal = {Microprocessors and microsystems}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0141-9331}, doi = {10.1016/j.micpro.2022.104486}, pages = {18}, year = {2022}, abstract = {Instruments for measuring the absorbed dose and dose rate under radiation exposure, known as radiation dosimeters, are indispensable in space missions. They are composed of radiation sensors that generate current or voltage response when exposed to ionizing radiation, and processing electronics for computing the absorbed dose and dose rate. Among a wide range of existing radiation sensors, the Radiation Sensitive Field Effect Transistors (RADFETs) have unique advantages for absorbed dose measurement, and a proven record of successful exploitation in space missions. It has been shown that the RADFETs may be also used for the dose rate monitoring. In that regard, we propose a unique design concept that supports the simultaneous operation of a single RADFET as absorbed dose and dose rate monitor. This enables to reduce the cost of implementation, since the need for other types of radiation sensors can be minimized or eliminated. For processing the RADFET's response we propose a readout system composed of analog signal conditioner (ASC) and a self-adaptive multiprocessing system-on-chip (MPSoC). The soft error rate of MPSoC is monitored in real time with embedded sensors, allowing the autonomous switching between three operating modes (high-performance, de-stress and fault-tolerant), according to the application requirements and radiation conditions.}, language = {en} } @article{ChangSchulze2018, author = {Chang, Der-Chen and Schulze, Bert-Wolfgang}, title = {Corner spaces and Mellin quantization}, series = {Journal of nonlinear and convex analysis : an international journal}, volume = {19}, journal = {Journal of nonlinear and convex analysis : an international journal}, number = {2}, publisher = {Yokohama Publishers}, address = {Yokohama}, issn = {1345-4773}, pages = {179 -- 195}, year = {2018}, abstract = {Manifolds with corners in the present investigation are non-smooth configurations - specific stratified spaces - with an incomplete metric such as cones, manifolds with edges, or corners of piecewise smooth domains in Euclidean space. We focus here on operators on such "corner manifolds" of singularity order <= 2, acting in weighted corner Sobolev spaces. The corresponding corner degenerate pseudo-differential operators are formulated via Mellin quantizations, and they also make sense on infinite singular cones.}, language = {en} } @article{ChangSchulze2017, author = {Chang, Der-Chen and Schulze, Bert-Wolfgang}, title = {Ellipticity on spaces with higher singularities}, series = {Science China Mathematics}, volume = {60}, journal = {Science China Mathematics}, number = {11}, publisher = {Science China Press}, address = {Beijing}, issn = {1674-7283}, doi = {10.1007/s11425-016-0519-9}, pages = {2053 -- 2076}, year = {2017}, abstract = {We study corner-degenerate pseudo-differential operators of any singularity order and develop ellipticity based on the principal symbolic hierarchy, associated with the stratification of the underlying space. We construct parametrices within the calculus and discuss the aspect of additional trace and potential conditions along lower-dimensional strata.}, language = {en} } @article{KhalilSchulze2017, author = {Khalil, Sara and Schulze, Bert-Wolfgang}, title = {Boundary problems on a manifold with edge}, series = {Asian-European Journal of Mathematics}, volume = {10}, journal = {Asian-European Journal of Mathematics}, number = {2}, publisher = {World Scientific}, address = {Singapore}, issn = {1793-5571}, doi = {10.1142/S1793557117500875}, pages = {43}, year = {2017}, abstract = {We establish a calculus of boundary value problems (BVPs) on a manifold N with boundary and edge, based on Boutet de Monvel's theory of BVPs in the case of a smooth boundary and on the edge calculus, where in the present case the model cone has a base which is a compact manifold with boundary. The corresponding calculus with boundary and edge is a unification of both structures and controls different operator-valued symbolic structures, in order to obtain ellipticity and parametrices.}, language = {en} } @article{ChangHedayatMahmoudiSchulze2017, author = {Chang, Der-Chen and Hedayat Mahmoudi, Mahdi and Schulze, Bert-Wolfgang}, title = {Singular degenerate operators}, series = {Applicable analysis : an international journal}, volume = {96}, journal = {Applicable analysis : an international journal}, number = {14}, publisher = {Routledge, Taylor \& Francis Group}, address = {Abingdon}, issn = {0003-6811}, doi = {10.1080/00036811.2017.1336546}, pages = {2434 -- 2456}, year = {2017}, abstract = {We outline some simplified and more general method for constructing parametrices on higher singular spaces. We also outline basic ideas on operators on manifolds with conical or edge singularities.}, language = {en} } @article{HarutyunyanSchulze2006, author = {Harutyunyan, Gohar and Schulze, Bert-Wolfgang}, title = {The Zaremba problem with singular interfaces as a corner boundary value problem}, series = {Potential analysis : an international journal devoted to the interactions between potential theory, probability theory, geometry and functional analysis}, volume = {25}, journal = {Potential analysis : an international journal devoted to the interactions between potential theory, probability theory, geometry and functional analysis}, publisher = {Springer}, address = {Dordrecht}, issn = {0926-2601}, doi = {10.1007/s11118-006-9020-6}, pages = {327 -- 369}, year = {2006}, abstract = {We study mixed boundary value problems for an elliptic operator A on a manifold X with boundary Y, i.e., Au = f in int X, T (+/-) u = g(+/-) on int Y+/-, where Y is subdivided into subsets Y+/- with an interface Z and boundary conditions T+/- on Y+/- that are Shapiro-Lopatinskij elliptic up to Z from the respective sides. We assume that Z subset of Y is a manifold with conical singularity v. As an example we consider the Zaremba problem, where A is the Laplacian and T- Dirichlet, T+ Neumann conditions. The problem is treated as a corner boundary value problem near v which is the new point and the main difficulty in this paper. Outside v the problem belongs to the edge calculus as is shown in Bull. Sci. Math. ( to appear). With a mixed problem we associate Fredholm operators in weighted corner Sobolev spaces with double weights, under suitable edge conditions along Z {v} of trace and potential type. We construct parametrices within the calculus and establish the regularity of solutions.}, language = {en} } @article{HedayatMahmoudiSchulze2018, author = {Hedayat Mahmoudi, Mahdi and Schulze, Bert-Wolfgang}, title = {A new approach to the second order edge calculus}, series = {Journal of pseudo-differential operators and applications}, volume = {9}, journal = {Journal of pseudo-differential operators and applications}, number = {2}, publisher = {Springer}, address = {Basel}, issn = {1662-9981}, doi = {10.1007/s11868-017-0191-2}, pages = {265 -- 300}, year = {2018}, abstract = {We establish essential steps of an iterative approach to operator algebras, ellipticity and Fredholm property on stratified spaces with singularities of second order. We cover, in particular, corner-degenerate differential operators. Our constructions are focused on the case where no additional conditions of trace and potential type are posed, but this case works well and will be considered in a forthcoming paper as a conclusion of the present calculus.}, language = {en} } @article{KhalilSchulze2019, author = {Khalil, Sara and Schulze, Bert-Wolfgang}, title = {Calculus on a Manifold with Edge and Boundary}, series = {Complex analysis and operator theory}, volume = {13}, journal = {Complex analysis and operator theory}, number = {6}, publisher = {Springer}, address = {Basel}, issn = {1661-8254}, doi = {10.1007/s11785-018-0800-y}, pages = {2627 -- 2670}, year = {2019}, abstract = {We study elements of the calculus of boundary value problems in a variant of Boutet de Monvel's algebra (Acta Math 126:11-51, 1971) on a manifold N with edge and boundary. If the boundary is empty then the approach corresponds to Schulze (Symposium on partial differential equations (Holzhau, 1988), BSB Teubner, Leipzig, 1989) and other papers from the subsequent development. For non-trivial boundary we study Mellin-edge quantizations and compositions within the structure in terms a new Mellin-edge quantization, compared with a more traditional technique. Similar structures in the closed case have been studied in Gil et al.}, language = {en} } @article{SchulzeSeiler2019, author = {Schulze, Bert-Wolfgang and Seiler, J{\"o}rg}, title = {Elliptic complexes on manifolds with boundary}, series = {The journal of geometric analysis}, volume = {29}, journal = {The journal of geometric analysis}, number = {1}, publisher = {Springer}, address = {New York}, issn = {1050-6926}, doi = {10.1007/s12220-018-0014-6}, pages = {656 -- 706}, year = {2019}, abstract = {We show that elliptic complexes of (pseudo) differential operators on smooth compact manifolds with boundary can always be complemented to a Fredholm problem by boundary conditions involving global pseudodifferential projections on the boundary (similarly as the spectral boundary conditions of Atiyah, Patodi, and Singer for a single operator). We prove that boundary conditions without projections can be chosen if, and only if, the topological Atiyah-Bott obstruction vanishes. These results make use of a Fredholm theory for complexes of operators in algebras of generalized pseudodifferential operators of Toeplitz type which we also develop in the present paper.}, 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{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{BiskabornSmithNoetzlietal.2019, author = {Biskaborn, Boris and Smith, Sharon L. and Noetzli, Jeannette and Matthes, Heidrun and Vieira, Goncalo and Streletskiy, Dmitry A. and Schoeneich, Philippe and Romanovsky, Vladimir E. and Lewkowicz, Antoni G. and Abramov, Andrey and Allard, Michel and Boike, Julia and Cable, William L. and Christiansen, Hanne H. and Delaloye, Reynald and Diekmann, Bernhard and Drozdov, Dmitry and Etzelmueller, Bernd and Grosse, Guido and Guglielmin, Mauro and Ingeman-Nielsen, Thomas and Isaksen, Ketil and Ishikawa, Mamoru and Johansson, Margareta and Johannsson, Halldor and Joo, Anseok and Kaverin, Dmitry and Kholodov, Alexander and Konstantinov, Pavel and Kroeger, Tim and Lambiel, Christophe and Lanckman, Jean-Pierre and Luo, Dongliang and Malkova, Galina and Meiklejohn, Ian and Moskalenko, Natalia and Oliva, Marc and Phillips, Marcia and Ramos, Miguel and Sannel, A. Britta K. and Sergeev, Dmitrii and Seybold, Cathy and Skryabin, Pavel and Vasiliev, Alexander and Wu, Qingbai and Yoshikawa, Kenji and Zheleznyak, Mikhail and Lantuit, Hugues}, title = {Permafrost is warming at a global scale}, series = {Nature Communications}, volume = {10}, journal = {Nature Communications}, publisher = {Nature Publ. Group}, address = {London}, issn = {2041-1723}, doi = {10.1038/s41467-018-08240-4}, pages = {11}, year = {2019}, abstract = {Permafrost warming has the potential to amplify global climate change, because when frozen sediments thaw it unlocks soil organic carbon. Yet to date, no globally consistent assessment of permafrost temperature change has been compiled. Here we use a global data set of permafrost temperature time series from the Global Terrestrial Network for Permafrost to evaluate temperature change across permafrost regions for the period since the International Polar Year (2007-2009). During the reference decade between 2007 and 2016, ground temperature near the depth of zero annual amplitude in the continuous permafrost zone increased by 0.39 +/- 0.15 degrees C. Over the same period, discontinuous permafrost warmed by 0.20 +/- 0.10 degrees C. Permafrost in mountains warmed by 0.19 +/- 0.05 degrees C and in Antarctica by 0.37 +/- 0.10 degrees C. Globally, permafrost temperature increased by 0.29 +/- 0.12 degrees C. The observed trend follows the Arctic amplification of air temperature increase in the Northern Hemisphere. In the discontinuous zone, however, ground warming occurred due to increased snow thickness while air temperature remained statistically unchanged.}, language = {en} } @article{MuellerSchoellGroenlandScherfClaveletal.2020, author = {Mueller-Schoell, Anna and Groenland, Stefanie L. and Scherf-Clavel, Oliver and van Dyk, Madele and Huisinga, Wilhelm and Michelet, Robin and Jaehde, Ulrich and Steeghs, Neeltje and Huitema, Alwin D. R. and Kloft, Charlotte}, title = {Therapeutic drug monitoring of oral targeted antineoplastic drugs}, series = {European journal of clinical pharmacology}, volume = {77}, journal = {European journal of clinical pharmacology}, number = {4}, publisher = {Springer}, address = {Heidelberg}, issn = {0031-6970}, doi = {10.1007/s00228-020-03014-8}, pages = {441 -- 464}, year = {2020}, abstract = {Purpose This review provides an overview of the current challenges in oral targeted antineoplastic drug (OAD) dosing and outlines the unexploited value of therapeutic drug monitoring (TDM). Factors influencing the pharmacokinetic exposure in OAD therapy are depicted together with an overview of different TDM approaches. Finally, current evidence for TDM for all approved OADs is reviewed. Methods A comprehensive literature search (covering literature published until April 2020), including primary and secondary scientific literature on pharmacokinetics and dose individualisation strategies for OADs, together with US FDA Clinical Pharmacology and Biopharmaceutics Reviews and the Committee for Medicinal Products for Human Use European Public Assessment Reports was conducted. Results OADs are highly potent drugs, which have substantially changed treatment options for cancer patients. Nevertheless, high pharmacokinetic variability and low treatment adherence are risk factors for treatment failure. TDM is a powerful tool to individualise drug dosing, ensure drug concentrations within the therapeutic window and increase treatment success rates. After reviewing the literature for 71 approved OADs, we show that exposure-response and/or exposure-toxicity relationships have been established for the majority. Moreover, TDM has been proven to be feasible for individualised dosing of abiraterone, everolimus, imatinib, pazopanib, sunitinib and tamoxifen in prospective studies. There is a lack of experience in how to best implement TDM as part of clinical routine in OAD cancer therapy. Conclusion Sub-therapeutic concentrations and severe adverse events are current challenges in OAD treatment, which can both be addressed by the application of TDM-guided dosing, ensuring concentrations within the therapeutic window.}, 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{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{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{WichaHuisingaKloft2017, author = {Wicha, Sebastian G. and Huisinga, Wilhelm and Kloft, Charlotte}, title = {Translational pharmacometric evaluation of typical antibiotic broad-spectrum combination therapies against staphylococcus aureus exploiting in vitro information}, series = {CPT: pharmacometrics \& systems pharmacology}, volume = {6}, journal = {CPT: pharmacometrics \& systems pharmacology}, publisher = {Wiley}, address = {Hoboken}, issn = {2163-8306}, doi = {10.1002/psp4.12197}, pages = {512 -- 522}, year = {2017}, abstract = {Broad-spectrum antibiotic combination therapy is frequently applied due to increasing resistance development of infective pathogens. The objective of the present study was to evaluate two common empiric broad-spectrum combination therapies consisting of either linezolid (LZD) or vancomycin (VAN) combined with meropenem (MER) against Staphylococcus aureus (S. aureus) as the most frequent causative pathogen of severe infections. A semimechanistic pharmacokinetic-pharmacodynamic (PK-PD) model mimicking a simplified bacterial life-cycle of S. aureus was developed upon time-kill curve data to describe the effects of LZD, VAN, and MER alone and in dual combinations. The PK-PD model was successfully (i) evaluated with external data from two clinical S. aureus isolates and further drug combinations and (ii) challenged to predict common clinical PK-PD indices and breakpoints. Finally, clinical trial simulations were performed that revealed that the combination of VAN-MER might be favorable over LZD-MER due to an unfavorable antagonistic interaction between LZD and MER.}, language = {en} } @article{EdlundGrisicSteenholdtetal.2019, author = {Edlund, Helena and Grisic, Ana-Marija and Steenholdt, Casper and Ainsworth, Mark Andrew and Brynskov, Torn and Huisinga, Wilhelm and Kloft, Charlotte}, title = {Absence of Relationship Between Crohn's Disease Activity Index or C-Reactive Protein and Infliximab Exposure Calls for Objective Crohn's Disease Activity Measures for the Evaluation of Treatment Effects at Treatment Failure}, series = {Therapeutic drug monitoring : official journal of the International Association of Therapeutic Drug Monitoring and Clinical Toxicology}, volume = {41}, journal = {Therapeutic drug monitoring : official journal of the International Association of Therapeutic Drug Monitoring and Clinical Toxicology}, number = {2}, publisher = {Lippincott Williams \& Wilkins}, address = {Philadelphia}, issn = {0163-4356}, doi = {10.1097/FTD.0000000000000590}, pages = {235 -- 242}, year = {2019}, abstract = {Background: Circulating infliximab (IFX) concentrations correlate with clinical outcomes, forming the basis of the IFX concentration monitoring in patients with Crohn's disease. This study aims to investigate and refine the exposure-response relationship by linking the disease activity markers "Crohn's disease activity index" (CDAI) and C-reactive protein (CRP) to IFX exposure. In addition, we aim to explore the correlations between different disease markers and exposure metrics. Methods: Data from 47 Crohn's disease patients of a randomized controlled trial were analyzed post hoc. All patients had secondary treatment failure at inclusion and had received intensified IFX of 5 mg/kg every 4 weeks for up to 20 weeks. Graphical analyses were performed to explore exposure-response relationships. Metrics of exposure included area under the concentration-time curve (AUC) and trough concentrations (Cmin). Disease activity was measured by CDAI and CRP values, their change from baseline/last visit, and response/remission outcomes at week 12. Results: Although trends toward lower Cmin and lower AUC in nonresponders were observed, neither CDAI nor CRP showed consistent trends of lower disease activity with higher IFX exposure across the 30 evaluated relationships. As can be expected, Cmin and AUC were strongly correlated with each other. Contrarily, the disease activity markers were only weakly correlated with each other. Conclusions: No significant relationship between disease activity, as evaluated by CDAI or CRP, and IFX exposure was identified. AUC did not add benefit compared with Cmin. These findings support the continued use of Cmin and call for stringent objective disease activity (bio-)markers (eg, endoscopy) to form the basis of personalized IFX therapy for Crohn's disease patients with IFX treatment failure.}, language = {en} } @article{KnoechelKloftHuisinga2018, author = {Kn{\"o}chel, Jane and Kloft, Charlotte and Huisinga, Wilhelm}, title = {Understanding and reducing complex systems pharmacology models based on a novel input-response index}, series = {Journal of pharmacokinetics and pharmacodynamics}, volume = {45}, journal = {Journal of pharmacokinetics and pharmacodynamics}, number = {1}, publisher = {Springer Science + Business Media B.V.}, address = {New York}, issn = {1567-567X}, doi = {10.1007/s10928-017-9561-x}, pages = {139 -- 157}, year = {2018}, abstract = {A growing understanding of complex processes in biology has led to large-scale mechanistic models of pharmacologically relevant processes. These models are increasingly used to study the response of the system to a given input or stimulus, e.g., after drug administration. Understanding the input-response relationship, however, is often a challenging task due to the complexity of the interactions between its constituents as well as the size of the models. An approach that quantifies the importance of the different constituents for a given input-output relationship and allows to reduce the dynamics to its essential features is therefore highly desirable. In this article, we present a novel state- and time-dependent quantity called the input-response index that quantifies the importance of state variables for a given input-response relationship at a particular time. It is based on the concept of time-bounded controllability and observability, and defined with respect to a reference dynamics. In application to the brown snake venom-fibrinogen (Fg) network, the input-response indices give insight into the coordinated action of specific coagulation factors and about those factors that contribute only little to the response. We demonstrate how the indices can be used to reduce large-scale models in a two-step procedure: (i) elimination of states whose dynamics have only minor impact on the input-response relationship, and (ii) proper lumping of the remaining (lower order) model. In application to the brown snake venom-fibrinogen network, this resulted in a reduction from 62 to 8 state variables in the first step, and a further reduction to 5 state variables in the second step. We further illustrate that the sequence, in which a recursive algorithm eliminates and/or lumps state variables, has an impact on the final reduced model. The input-response indices are particularly suited to determine an informed sequence, since they are based on the dynamics of the original system. In summary, the novel measure of importance provides a powerful tool for analysing the complex dynamics of large-scale systems and a means for very efficient model order reduction of nonlinear systems.}, 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{HijaziFreitagLandwehr2023, author = {Hijazi, Saddam and Freitag, Melina A. and Landwehr, Niels}, title = {POD-Galerkin reduced order models and physics-informed neural networks for solving inverse problems for the Navier-Stokes equations}, series = {Advanced modeling and simulation in engineering sciences : AMSES}, volume = {10}, journal = {Advanced modeling and simulation in engineering sciences : AMSES}, number = {1}, publisher = {SpringerOpen}, address = {Berlin}, issn = {2213-7467}, doi = {10.1186/s40323-023-00242-2}, pages = {38}, year = {2023}, abstract = {We present a Reduced Order Model (ROM) which exploits recent developments in Physics Informed Neural Networks (PINNs) for solving inverse problems for the Navier-Stokes equations (NSE). In the proposed approach, the presence of simulated data for the fluid dynamics fields is assumed. A POD-Galerkin ROM is then constructed by applying POD on the snapshots matrices of the fluid fields and performing a Galerkin projection of the NSE (or the modified equations in case of turbulence modeling) onto the POD reduced basis. A POD-Galerkin PINN ROM is then derived by introducing deep neural networks which approximate the reduced outputs with the input being time and/or parameters of the model. The neural networks incorporate the physical equations (the POD-Galerkin reduced equations) into their structure as part of the loss function. Using this approach, the reduced model is able to approximate unknown parameters such as physical constants or the boundary conditions. A demonstration of the applicability of the proposed ROM is illustrated by three cases which are the steady flow around a backward step, the flow around a circular cylinder and the unsteady turbulent flow around a surface mounted cubic obstacle.}, language = {en} } @article{MolkenthinDonnerReichetal.2022, author = {Molkenthin, Christian and Donner, Christian and Reich, Sebastian and Z{\"o}ller, Gert and Hainzl, Sebastian and Holschneider, Matthias and Opper, Manfred}, title = {GP-ETAS: semiparametric Bayesian inference for the spatio-temporal epidemic type aftershock sequence model}, series = {Statistics and Computing}, volume = {32}, journal = {Statistics and Computing}, number = {2}, publisher = {Springer}, address = {Dordrecht}, issn = {0960-3174}, doi = {10.1007/s11222-022-10085-3}, pages = {25}, year = {2022}, abstract = {The spatio-temporal epidemic type aftershock sequence (ETAS) model is widely used to describe the self-exciting nature of earthquake occurrences. While traditional inference methods provide only point estimates of the model parameters, we aim at a fully Bayesian treatment of model inference, allowing naturally to incorporate prior knowledge and uncertainty quantification of the resulting estimates. Therefore, we introduce a highly flexible, non-parametric representation for the spatially varying ETAS background intensity through a Gaussian process (GP) prior. Combined with classical triggering functions this results in a new model formulation, namely the GP-ETAS model. We enable tractable and efficient Gibbs sampling by deriving an augmented form of the GP-ETAS inference problem. This novel sampling approach allows us to assess the posterior model variables conditioned on observed earthquake catalogues, i.e., the spatial background intensity and the parameters of the triggering function. Empirical results on two synthetic data sets indicate that GP-ETAS outperforms standard models and thus demonstrate the predictive power for observed earthquake catalogues including uncertainty quantification for the estimated parameters. Finally, a case study for the l'Aquila region, Italy, with the devastating event on 6 April 2009, is presented.}, language = {en} } @article{KucharskiErgintavAhmadetal.2019, author = {Kucharski, Maciej and Ergintav, Arzu and Ahmad, Wael Abdullah and Krstić, Miloš and Ng, Herman Jalli and Kissinger, Dietmar}, title = {A Scalable 79-GHz Radar Platform Based on Single-Channel Transceivers}, series = {IEEE Transactions on Microwave Theory and Techniques}, volume = {67}, journal = {IEEE Transactions on Microwave Theory and Techniques}, number = {9}, publisher = {Inst. of Electr. and Electronics Engineers}, address = {Piscataway}, issn = {0018-9480}, doi = {10.1109/TMTT.2019.2914104}, pages = {3882 -- 3896}, year = {2019}, abstract = {This paper presents a scalable E-band radar platform based on single-channel fully integrated transceivers (TRX) manufactured using 130-nm silicon-germanium (SiGe) BiCMOS technology. The TRX is suitable for flexible radar systems exploiting massive multiple-input-multipleoutput (MIMO) techniques for multidimensional sensing. A fully integrated fractional-N phase-locked loop (PLL) comprising a 39.5-GHz voltage-controlled oscillator is used to generate wideband frequency-modulated continuous-wave (FMCW) chirp for E-band radar front ends. The TRX is equipped with a vector modulator (VM) for high-speed carrier modulation and beam-forming techniques. A single TRX achieves 19.2-dBm maximum output power and 27.5-dB total conversion gain with input-referred 1-dB compression point of -10 dBm. It consumes 220 mA from 3.3-V supply and occupies 3.96 mm(2) silicon area. A two-channel radar platform based on full-custom TRXs and PLL was fabricated to demonstrate high-precision and high-resolution FMCW sensing. The radar enables up to 10-GHz frequency ramp generation in 74-84-GHz range, which results in 1.5-cm spatial resolution. Due to high output power, thus high signal-to-noise ratio (SNR), a ranging precision of 7.5 mu m for a target at 2 m was achieved. The proposed architecture supports scalable multichannel applications for automotive FMCW using a single local oscillator (LO).}, language = {en} } @article{SharmaHainzlZoelleretal.2020, author = {Sharma, Shubham and Hainzl, Sebastian and Z{\"o}ller, Gert and Holschneider, Matthias}, title = {Is Coulomb stress the best choice for aftershock forecasting?}, series = {Journal of geophysical research : Solid earth}, volume = {125}, journal = {Journal of geophysical research : Solid earth}, number = {9}, publisher = {American Geophysical Union}, address = {Washington}, issn = {2169-9313}, doi = {10.1029/2020JB019553}, pages = {12}, year = {2020}, abstract = {The Coulomb failure stress (CFS) criterion is the most commonly used method for predicting spatial distributions of aftershocks following large earthquakes. However, large uncertainties are always associated with the calculation of Coulomb stress change. The uncertainties mainly arise due to nonunique slip inversions and unknown receiver faults; especially for the latter, results are highly dependent on the choice of the assumed receiver mechanism. Based on binary tests (aftershocks yes/no), recent studies suggest that alternative stress quantities, a distance-slip probabilistic model as well as deep neural network (DNN) approaches, all are superior to CFS with predefined receiver mechanism. To challenge this conclusion, which might have large implications, we use 289 slip inversions from SRCMOD database to calculate more realistic CFS values for a layered half-space and variable receiver mechanisms. We also analyze the effect of the magnitude cutoff, grid size variation, and aftershock duration to verify the use of receiver operating characteristic (ROC) analysis for the ranking of stress metrics. The observations suggest that introducing a layered half-space does not improve the stress maps and ROC curves. However, results significantly improve for larger aftershocks and shorter time periods but without changing the ranking. We also go beyond binary testing and apply alternative statistics to test the ability to estimate aftershock numbers, which confirm that simple stress metrics perform better than the classic Coulomb failure stress calculations and are also better than the distance-slip probabilistic model.}, language = {en} } @article{EngbertRabeKliegletal.2021, author = {Engbert, Ralf and Rabe, Maximilian Michael and Kliegl, Reinhold and Reich, Sebastian}, title = {Sequential data assimilation of the stochastic SEIR epidemic model for regional COVID-19 dynamics}, series = {Bulletin of mathematical biology : official journal of the Society for Mathematical Biology}, volume = {83}, journal = {Bulletin of mathematical biology : official journal of the Society for Mathematical Biology}, number = {1}, publisher = {Springer}, address = {New York}, issn = {0092-8240}, doi = {10.1007/s11538-020-00834-8}, pages = {16}, year = {2021}, abstract = {Newly emerging pandemics like COVID-19 call for predictive models to implement precisely tuned responses to limit their deep impact on society. Standard epidemic models provide a theoretically well-founded dynamical description of disease incidence. For COVID-19 with infectiousness peaking before and at symptom onset, the SEIR model explains the hidden build-up of exposed individuals which creates challenges for containment strategies. However, spatial heterogeneity raises questions about the adequacy of modeling epidemic outbreaks on the level of a whole country. Here, we show that by applying sequential data assimilation to the stochastic SEIR epidemic model, we can capture the dynamic behavior of outbreaks on a regional level. Regional modeling, with relatively low numbers of infected and demographic noise, accounts for both spatial heterogeneity and stochasticity. Based on adapted models, short-term predictions can be achieved. Thus, with the help of these sequential data assimilation methods, more realistic epidemic models are within reach.}, language = {en} } @article{GerlachGlueckKunze2023, author = {Gerlach, Moritz and Gl{\"u}ck, Jochen and Kunze, Markus}, title = {Stability of transition semigroups and applications to parabolic equations}, series = {Transactions of the American Mathematical Society}, volume = {376}, journal = {Transactions of the American Mathematical Society}, number = {1}, publisher = {American Mathematical Soc.}, address = {Providence}, issn = {0002-9947}, doi = {10.1090/tran/8620}, pages = {153 -- 180}, year = {2023}, abstract = {This paper deals with the long-term behavior of positive operator semigroups on spaces of bounded functions and of signed measures, which have applications to parabolic equations with unbounded coefficients and to stochas-tic analysis. The main results are a Tauberian type theorem characterizing the convergence to equilibrium of strongly Feller semigroups and a generalization of a classical convergence theorem of Doob. None of these results requires any kind of time regularity of the semigroup.}, 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{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} } @article{KretzschmarAshbyFearonetal.2022, author = {Kretzschmar, Mirjam E. and Ashby, Ben and Fearon, Elizabeth and Overton, Christopher E. and Panovska-Griffiths, Jasmina and Pellis, Lorenzo and Quaife, Matthew and Rozhnova, Ganna and Scarabel, Francesca and Stage, Helena B. and Swallow, Ben and Thompson, Robin N. and Tildesley, Michael J. and Villela, Daniel Campos}, title = {Challenges for modelling interventions for future pandemics}, series = {Epidemics}, volume = {38}, journal = {Epidemics}, publisher = {Elsevier}, address = {Amsterdam}, issn = {1755-4365}, doi = {10.1016/j.epidem.2022.100546}, pages = {13}, year = {2022}, abstract = {Mathematical modelling and statistical inference provide a framework to evaluate different non-pharmaceutical and pharmaceutical interventions for the control of epidemics that has been widely used during the COVID-19 pandemic. In this paper, lessons learned from this and previous epidemics are used to highlight the challenges for future pandemic control. We consider the availability and use of data, as well as the need for correct parameterisation and calibration for different model frameworks. We discuss challenges that arise in describing and distinguishing between different interventions, within different modelling structures, and allowing both within and between host dynamics. We also highlight challenges in modelling the health economic and political aspects of interventions. Given the diversity of these challenges, a broad variety of interdisciplinary expertise is needed to address them, combining mathematical knowledge with biological and social insights, and including health economics and communication skills. Addressing these challenges for the future requires strong cross disciplinary collaboration together with close communication between scientists and policy makers.}, language = {en} } @article{GerlachGlueck2017, author = {Gerlach, Moritz Reinhardt and Gl{\"u}ck, Jochen}, title = {On a convergence theorem for semigroups of positive integral operators}, series = {Comptes Rendus Mathematique}, volume = {355}, journal = {Comptes Rendus Mathematique}, publisher = {Elsevier}, address = {Paris}, issn = {1631-073X}, doi = {10.1016/j.crma.2017.07.017}, pages = {973 -- 976}, year = {2017}, abstract = {We give a new and very short proof of a theorem of Greiner asserting that a positive and contractive -semigroup on an -space is strongly convergent in case it has a strictly positive fixed point and contains an integral operator. Our proof is a streamlined version of a much more general approach to the asymptotic theory of positive semigroups developed recently by the authors. Under the assumptions of Greiner's theorem, this approach becomes particularly elegant and simple. We also give an outlook on several generalisations of this result.}, language = {en} } @article{Gerlach2018, author = {Gerlach, Moritz Reinhardt}, title = {Convergence of dynamics and the Perron-Frobenius operator}, series = {Israel Journal of Mathematics}, volume = {225}, journal = {Israel Journal of Mathematics}, number = {1}, publisher = {Hebrew univ magnes press}, address = {Jerusalem}, issn = {0021-2172}, doi = {10.1007/s11856-018-1671-7}, pages = {451 -- 463}, year = {2018}, abstract = {We complete the picture how the asymptotic behavior of a dynamical system is reflected by properties of the associated Perron-Frobenius operator. Our main result states that strong convergence of the powers of the Perron-Frobenius operator is equivalent to setwise convergence of the underlying dynamic in the measure algebra. This situation is furthermore characterized by uniform mixing-like properties of the system.}, language = {en} } @article{GerlachGlueck2019, author = {Gerlach, Moritz Reinhardt and Gl{\"u}ck, Jochen}, title = {Convergence of positive operator semigroups}, series = {Transactions of the American Mathematical Society}, volume = {372}, journal = {Transactions of the American Mathematical Society}, number = {9}, publisher = {American Mathematical Soc.}, address = {Providence}, issn = {0002-9947}, doi = {10.1090/tran/7836}, pages = {6603 -- 6627}, year = {2019}, abstract = {We present new conditions for semigroups of positive operators to converge strongly as time tends to infinity. Our proofs are based on a novel approach combining the well-known splitting theorem by Jacobs, de Leeuw, and Glicksberg with a purely algebraic result about positive group representations. Thus, we obtain convergence theorems not only for one-parameter semigroups but also for a much larger class of semigroup representations. Our results allow for a unified treatment of various theorems from the literature that, under technical assumptions, a bounded positive C-0-semigroup containing or dominating a kernel operator converges strongly as t ->infinity. We gain new insights into the structure theoretical background of those theorems and generalize them in several respects; especially we drop any kind of continuity or regularity assumption with respect to the time parameter.}, language = {en} } @article{EdekoGerlachKuehner2019, author = {Edeko, Nikolai and Gerlach, Moritz Reinhardt and K{\"u}hner, Viktoria}, title = {Measure-preserving semiflows and one-parameter Koopman semigroups}, series = {Semigroup forum}, volume = {98}, journal = {Semigroup forum}, number = {1}, publisher = {Springer}, address = {New York}, issn = {0037-1912}, doi = {10.1007/s00233-018-9960-3}, pages = {48 -- 63}, year = {2019}, abstract = {For a finite measure space X, we characterize strongly continuous Markov lattice semigroups on Lp(X) by showing that their generator A acts as a derivation on the dense subspace D(A)L(X). We then use this to characterize Koopman semigroups on Lp(X) if X is a standard probability space. In addition, we show that every measurable and measure-preserving flow on a standard probability space is isomorphic to a continuous flow on a compact Borel probability space.}, language = {en} } @article{GerlachGlueck2018, author = {Gerlach, Moritz Reinhardt and Gl{\"u}ck, Jochen}, title = {Lower bounds and the asymptotic behaviour of positive operator semigroups}, series = {Ergodic theory and dynamical systems}, volume = {38}, journal = {Ergodic theory and dynamical systems}, publisher = {Cambridge Univ. Press}, address = {New York}, issn = {0143-3857}, doi = {10.1017/etds.2017.9}, pages = {3012 -- 3041}, year = {2018}, abstract = {If (T-t) is a semigroup of Markov operators on an L-1-space that admits a nontrivial lower bound, then a well-known theorem of Lasota and Yorke asserts that the semigroup is strongly convergent as t -> infinity. In this article we generalize and improve this result in several respects. First, we give a new and very simple proof for the fact that the same conclusion also holds if the semigroup is merely assumed to be bounded instead of Markov. As a main result, we then prove a version of this theorem for semigroups which only admit certain individual lower bounds. Moreover, we generalize a theorem of Ding on semigroups of Frobenius-Perron operators. We also demonstrate how our results can be adapted to the setting of general Banach lattices and we give some counterexamples to show optimality of our results. Our methods combine some rather concrete estimates and approximation arguments with abstract functional analytical tools. One of these tools is a theorem which relates the convergence of a time-continuous operator semigroup to the convergence of embedded discrete semigroups.}, language = {en} } @article{GerlachGlueck2019, author = {Gerlach, Moritz Reinhardt and Gl{\"u}ck, Jochen}, title = {Mean ergodicity vs weak almost periodicity}, series = {Studia mathematica}, volume = {248}, journal = {Studia mathematica}, number = {1}, publisher = {Polska Akademia Nauk, Instytut Matematyczny}, address = {Warszawa}, issn = {0039-3223}, doi = {10.4064/sm170918-20-3}, pages = {45 -- 56}, year = {2019}, abstract = {We provide explicit examples of positive and power-bounded operators on c(0) and l(infinity) which are mean ergodic but not weakly almost periodic. As a consequence we prove that a countably order complete Banach lattice on which every positive and power-bounded mean ergodic operator is weakly almost periodic is necessarily a KB-space. This answers several open questions from the literature. Finally, we prove that if T is a positive mean ergodic operator with zero fixed space on an arbitrary Banach lattice, then so is every power of T .}, language = {en} } @article{HanischLudewig2022, author = {Hanisch, Florian and Ludewig, Matthias}, title = {The fermionic integral on loop space and the Pfaffian line bundle}, series = {Journal of mathematical physics}, volume = {63}, journal = {Journal of mathematical physics}, number = {12}, publisher = {American Inst. of Physics}, address = {College Park, Md.}, issn = {0022-2488}, doi = {10.1063/5.0060355}, pages = {26}, year = {2022}, abstract = {As the loop space of a Riemannian manifold is infinite-dimensional, it is a non-trivial problem to make sense of the "top degree component " of a differential form on it. In this paper, we show that a formula from finite dimensions generalizes to assign a sensible "top degree component " to certain composite forms, obtained by wedging with the exponential (in the exterior algebra) of the canonical presymplectic 2-form on the loop space. This construction is a crucial ingredient for the definition of the supersymmetric path integral on the loop space.}, language = {en} } @article{Metzger2023, author = {Metzger, Jan}, title = {Refined position estimates for surfaces of Willmore type in Riemannian manifolds}, series = {Communications in analysis and geometry}, volume = {30}, journal = {Communications in analysis and geometry}, number = {10}, publisher = {International Press of Boston}, address = {Somerville, Mass.}, issn = {1019-8385}, doi = {10.4310/CAG.2022.v30.n10.a5}, pages = {2315 -- 2346}, year = {2023}, abstract = {In this paper we consider surfaces which are critical points of the Willmore functional subject to constrained area. In the case of small area we calculate the corrections to the intrinsic geometry induced by the ambient curvature. These estimates together with the choice of an adapted geometric center of mass lead to refined position estimates in relation to the scalar curvature of the ambient manifold.}, language = {en} } @article{RœllyZass2020, author = {Rœlly, Sylvie and Zass, Alexander}, title = {Marked Gibbs point processes with unbounded interaction}, series = {Journal of statistical physics}, volume = {179}, journal = {Journal of statistical physics}, number = {4}, publisher = {Springer}, address = {New York}, issn = {0022-4715}, doi = {10.1007/s10955-020-02559-3}, pages = {972 -- 996}, year = {2020}, abstract = {We construct marked Gibbs point processes in R-d under quite general assumptions. Firstly, we allow for interaction functionals that may be unbounded and whose range is not assumed to be uniformly bounded. Indeed, our typical interaction admits an a.s. finite but random range. Secondly, the random marks-attached to the locations in R-d-belong to a general normed space G. They are not bounded, but their law should admit a super-exponential moment. The approach used here relies on the so-called entropy method and large-deviation tools in order to prove tightness of a family of finite-volume Gibbs point processes. An application to infinite-dimensional interacting diffusions is also presented.}, language = {en} } @article{Seyedhosseini2022, author = {Seyedhosseini, Mehran}, title = {A variant of Roe algebras for spaces with cylindrical ends with applications in relative higher index theory}, series = {Journal of noncommutative geometry}, volume = {16}, journal = {Journal of noncommutative geometry}, number = {2}, publisher = {European Mathematical Society}, address = {Zurich}, issn = {1661-6952}, doi = {10.4171/JNCG/457}, pages = {595 -- 624}, year = {2022}, abstract = {In this paper, we define a variant of Roe algebras for spaces with cylindrical ends and use this to study questions regarding existence and classification of metrics of positive scalar curvature on such manifolds which are collared on the cylindrical end. We discuss how our constructions are related to relative higher index theory as developed by Chang, Weinberger, and Yu and use this relationship to define higher rho-invariants for positive scalar curvature metrics on manifolds with boundary. This paves the way for the classification of these metrics. Finally, we use the machinery developed here to give a concise proof of a result of Schick and the author, which relates the relative higher index with indices defined in the presence of positive scalar curvature on the boundary.}, language = {en} } @article{Zass2021, author = {Zass, Alexander}, title = {Gibbs point processes on path space}, series = {Markov processes and related fields}, volume = {28}, journal = {Markov processes and related fields}, number = {3}, publisher = {Polymat}, address = {Moscow}, issn = {1024-2953}, pages = {329 -- 364}, year = {2021}, abstract = {We present general existence and uniqueness results for marked models with pair interactions, exemplified through Gibbs point processes on path space. More precisely, we study a class of infinite-dimensional diffusions under Gibbsian interactions, in the context of marked point configurations: the starting points belong to R-d, and the marks are the paths of Langevin diffusions. We use the entropy method to prove existence of an infinite-volume Gibbs point process and use cluster expansion tools to provide an explicit activity domain in which uniqueness holds.}, language = {en} } @article{HuangHuangReichetal.2022, author = {Huang, Daniel Zhengyu and Huang, Jiaoyang and Reich, Sebastian and Stuart, Andrew M.}, title = {Efficient derivative-free Bayesian inference for large-scale inverse problems}, series = {Inverse problems : an international journal of inverse problems, inverse methods and computerised inversion of data}, volume = {38}, journal = {Inverse problems : an international journal of inverse problems, inverse methods and computerised inversion of data}, number = {12}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {0266-5611}, doi = {10.1088/1361-6420/ac99fa}, pages = {40}, year = {2022}, abstract = {We consider Bayesian inference for large-scale inverse problems, where computational challenges arise from the need for repeated evaluations of an expensive forward model. This renders most Markov chain Monte Carlo approaches infeasible, since they typically require O(10(4)) model runs, or more. Moreover, the forward model is often given as a black box or is impractical to differentiate. Therefore derivative-free algorithms are highly desirable. We propose a framework, which is built on Kalman methodology, to efficiently perform Bayesian inference in such inverse problems. The basic method is based on an approximation of the filtering distribution of a novel mean-field dynamical system, into which the inverse problem is embedded as an observation operator. Theoretical properties are established for linear inverse problems, demonstrating that the desired Bayesian posterior is given by the steady state of the law of the filtering distribution of the mean-field dynamical system, and proving exponential convergence to it. This suggests that, for nonlinear problems which are close to Gaussian, sequentially computing this law provides the basis for efficient iterative methods to approximate the Bayesian posterior. Ensemble methods are applied to obtain interacting particle system approximations of the filtering distribution of the mean-field model; and practical strategies to further reduce the computational and memory cost of the methodology are presented, including low-rank approximation and a bi-fidelity approach. The effectiveness of the framework is demonstrated in several numerical experiments, including proof-of-concept linear/nonlinear examples and two large-scale applications: learning of permeability parameters in subsurface flow; and learning subgrid-scale parameters in a global climate model. Moreover, the stochastic ensemble Kalman filter and various ensemble square-root Kalman filters are all employed and are compared numerically. The results demonstrate that the proposed method, based on exponential convergence to the filtering distribution of a mean-field dynamical system, is competitive with pre-existing Kalman-based methods for inverse problems.}, language = {en} } @article{ShlapunovTarchanov2022, author = {Shlapunov, Alexander A. and Tarchanov, Nikolaj Nikolaevič}, title = {Inverse image of precompact sets and regular solutions to the Navier-Stokes equations}, series = {Vestnik Udmurtskogo Universiteta. Matematika, mechanika, kompʹjuternye nauki}, volume = {32}, journal = {Vestnik Udmurtskogo Universiteta. Matematika, mechanika, kompʹjuternye nauki}, number = {2}, publisher = {Udmurtskij gosudarstvennyj universitet}, address = {Iževsk}, issn = {1994-9197}, doi = {10.35634/vm220208}, pages = {278 -- 297}, year = {2022}, abstract = {We consider the initial value problem for the Navier-Stokes equations over R-3 x [0, T] with time T > 0 in the spatially periodic setting. We prove that it induces open injective mappings A(s): B-1(s) -> B-2(s-1) where B-1(s), B-2(s-1) are elements from scales of specially constructed function spaces of Bochner-Sobolev typeparametrized with the smoothness index s is an element of N. Finally, we prove that a map Asis surjective if and only if the inverse image A(s)(- 1) (K) of any pre compact set K from the range of the map Asis bounded in the Bochner space L-s([0, T], L-r(T-3))with the Ladyzhenskaya-Prodi-Serrin numbers s, r.}, language = {en} } @article{JulienMatthiasSaynischWagneretal.2022, author = {Julien, B{\"a}renzung and Matthias, Holschneider and Saynisch-Wagner, Jan and Thomas, Maik}, title = {Kalmag: a high spatio-temporal model of the geomagnetic field}, series = {Earth, planets and space}, volume = {74}, journal = {Earth, planets and space}, number = {1}, publisher = {Springer}, address = {New York}, issn = {1880-5981}, doi = {10.1186/s40623-022-01692-5}, pages = {22}, year = {2022}, abstract = {We present the extension of the Kalmag model, proposed as a candidate for IGRF-13, to the twentieth century. The dataset serving its derivation has been complemented by new measurements coming from satellites, ground-based observatories and land, marine and airborne surveys. As its predecessor, this version is derived from a combination of a Kalman filter and a smoothing algorithm, providing mean models and associated uncertainties. These quantities permit a precise estimation of locations where mean solutions can be considered as reliable or not. The temporal resolution of the core field and the secular variation was set to 0.1 year over the 122 years the model is spanning. Nevertheless, it can be shown through ensembles a posteriori sampled, that this resolution can be effectively achieved only by a limited amount of spatial scales and during certain time periods. Unsurprisingly, highest accuracy in both space and time of the core field and the secular variation is achieved during the CHAMP and Swarm era. In this version of Kalmag, a particular effort was made for resolving the small-scale lithospheric field. Under specific statistical assumptions, the latter was modeled up to spherical harmonic degree and order 1000, and signal from both satellite and survey measurements contributed to its development. External and induced fields were jointly estimated with the rest of the model. We show that their large scales could be accurately extracted from direct measurements whenever the latter exhibit a sufficiently high temporal coverage. Temporally resolving these fields down to 3 hours during the CHAMP and Swarm missions, gave us access to the link between induced and magnetospheric fields. In particular, the period dependence of the driving signal on the induced one could be directly observed. The model is available through various physical and statistical quantities on a dedicated website at https://ionocovar.agnld.uni-potsdam.de/Kalmag/.}, language = {en} } @article{TianLiang2022, author = {Tian, Peibo and Liang, Yingjie}, title = {Material coordinate driven variable-order fractal derivative model of water anomalous adsorption in swelling soil}, series = {Chaos, solitons \& fractals}, volume = {164}, journal = {Chaos, solitons \& fractals}, publisher = {Elsevier}, address = {Oxford}, issn = {0960-0779}, doi = {10.1016/j.chaos.2022.112754}, pages = {8}, year = {2022}, abstract = {The diffusion process of water in swelling (expansive) soil often deviates from normal Fick diffusion and belongs to anomalous diffusion. The process of water adsorption by swelling soil often changes with time, in which the microstructure evolves with time and the absorption rate changes along a fractal dimension gradient function. Thus, based on the material coordinate theory, this paper proposes a variable order derivative fractal model to describe the cumulative adsorption of water in the expansive soil, and the variable order is time dependent linearly. The cumulative adsorption is a power law function of the anomalous sorptivity, and patterns of the variable order. The variable-order fractal derivative model is tested to describe the cumulative adsorption in chernozemic surface soil, Wunnamurra clay and sandy loam. The results show that the fractal derivative model with linearly time dependent variable-order has much better accuracy than the fractal derivative model with a constant derivative order and the integer order model in the application cases. The derivative order can be used to distinguish the evolution of the anomalous adsorption process. The variable-order fractal derivative model can serve as an alternative approach to describe water anomalous adsorption in swelling soil.}, language = {en} }