@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{Junek2020,
  author    = {Junek, Heinz},
  title     = {Zyklizit{\"a}t in Raum, zeit und geist : {\"u}ber Pflasterungen, Rollkurven, Dezimalbr{\"u}che, Schwingungen, Wellen, Iteration und Neuronale Netze},
  series = {Zyklizit{\"a}t \& Rhythmik: eine multidisziplin{\"a}re Vorlesungsreihe},
  journal   = {Zyklizit{\"a}t \& Rhythmik: eine multidisziplin{\"a}re Vorlesungsreihe},
  publisher = {trafo},
  address   = {Berlin},
  isbn      = {978-3-86464-169-5},
  pages     = {85 -- 103},
  year      = {2020},
  language  = {de}
}
@article{Denecke2020,
  author    = {Denecke, Klaus-Dieter},
  title     = {Partial clones},
  series = {Asian-European journal of mathematics : AEJM},
  volume    = {13},
  journal   = {Asian-European journal of mathematics : AEJM},
  number    = {8},
  publisher = {World Scientific},
  address   = {Singapore},
  issn      = {1793-5571},
  doi       = {10.1142/S1793557120501612},
  pages     = {19},
  year      = {2020},
  abstract  = {A set C of operations defined on a nonempty set A is said to be a clone if C is closed under composition of operations and contains all projection mappings. The concept of a clone belongs to the algebraic main concepts and has important applications in Computer Science. A clone can also be regarded as a many-sorted algebra where the sorts are the n-ary operations defined on set A for all natural numbers n >= 1 and the operations are the so-called superposition operations S-m(n) for natural numbers m, n >= 1 and the projection operations as nullary operations. Clones generalize monoids of transformations defined on set A and satisfy three clone axioms. The most important axiom is the superassociative law, a generalization of the associative law. If the superposition operations are partial, i.e. not everywhere defined, instead of the many-sorted clone algebra, one obtains partial many-sorted algebras, the partial clones. Linear terms, linear tree languages or linear formulas form partial clones. In this paper, we give a survey on partial clones and their properties.},
  language  = {en}
}
@article{SomogyvariReich2020,
  author    = {Somogyv{\´a}ri, M{\´a}rk and Reich, Sebastian},
  title     = {Convergence tests for transdimensional Markov chains in geoscience imaging},
  series = {Mathematical geosciences : the official journal of the International Association for Mathematical Geosciences},
  volume    = {52},
  journal   = {Mathematical geosciences : the official journal of the International Association for Mathematical Geosciences},
  number    = {5},
  publisher = {Springer},
  address   = {Heidelberg},
  issn      = {1874-8961},
  doi       = {10.1007/s11004-019-09811-x},
  pages     = {651 -- 668},
  year      = {2020},
  abstract  = {Classic inversion methods adjust a model with a predefined number of parameters to the observed data. With transdimensional inversion algorithms such as the reversible-jump Markov chain Monte Carlo (rjMCMC), it is possible to vary this number during the inversion and to interpret the observations in a more flexible way. Geoscience imaging applications use this behaviour to automatically adjust model resolution to the inhomogeneities of the investigated system, while keeping the model parameters on an optimal level. The rjMCMC algorithm produces an ensemble as result, a set of model realizations, which together represent the posterior probability distribution of the investigated problem. The realizations are evolved via sequential updates from a randomly chosen initial solution and converge toward the target posterior distribution of the inverse problem. Up to a point in the chain, the realizations may be strongly biased by the initial model, and must be discarded from the final ensemble. With convergence assessment techniques, this point in the chain can be identified. Transdimensional MCMC methods produce ensembles that are not suitable for classic convergence assessment techniques because of the changes in parameter numbers. To overcome this hurdle, three solutions are introduced to convert model realizations to a common dimensionality while maintaining the statistical characteristics of the ensemble. A scalar, a vector and a matrix representation for models is presented, inferred from tomographic subsurface investigations, and three classic convergence assessment techniques are applied on them. It is shown that appropriately chosen scalar conversions of the models could retain similar statistical ensemble properties as geologic projections created by rasterization.},
  language  = {en}
}
@article{Ly2020,
  author    = {Ly, Ibrahim},
  title     = {A Cauchy problem for the Cauchy-Riemann operator},
  series = {Afrika Matematika},
  volume    = {32},
  journal   = {Afrika Matematika},
  number    = {1-2},
  publisher = {Springer},
  address   = {Heidelberg},
  issn      = {1012-9405},
  doi       = {10.1007/s13370-020-00810-4},
  pages     = {69 -- 76},
  year      = {2020},
  abstract  = {We study the Cauchy problem for a nonlinear elliptic equation with data on a piece S of the boundary surface partial derivative X. By the Cauchy problem is meant any boundary value problem for an unknown function u in a domain X with the property that the data on S, if combined with the differential equations in X, allows one to determine all derivatives of u on S by means of functional equations. In the case of real analytic data of the Cauchy problem, the existence of a local solution near S is guaranteed by the Cauchy-Kovalevskaya theorem. We discuss a variational setting of the Cauchy problem which always possesses a generalized solution.},
  language  = {en}
}
@article{MalassTarkhanov2020,
  author    = {Malass, Ihsane and Tarkhanov, Nikolaj Nikolaevič},
  title     = {A perturbation of the de Rham complex},
  series = {Journal of Siberian Federal University : Mathematics \& Physics},
  volume    = {13},
  journal   = {Journal of Siberian Federal University : Mathematics \& Physics},
  number    = {5},
  publisher = {Siberian Federal University},
  address   = {Krasnojarsk},
  issn      = {1997-1397},
  doi       = {10.17516/1997-1397-2020-13-5-519-532},
  pages     = {519 -- 532},
  year      = {2020},
  abstract  = {We consider a perturbation of the de Rham complex on a compact manifold with boundary. This perturbation goes beyond the framework of complexes, and so cohomology does not apply to it. On the other hand, its curvature is "small", hence there is a natural way to introduce an Euler characteristic and develop a Lefschetz theory for the perturbation. This work is intended as an attempt to develop a cohomology theory for arbitrary sequences of linear mappings.},
  language  = {en}
}
@article{AlSaedyTarchanov2020,
  author    = {Al-Saedy, Ammar Jaffar Muhesin and Tarchanov, Nikolaj Nikolaevič},
  title     = {A degree theory for Lagrangian boundary value problems},
  series = {Žurnal Sibirskogo Federalʹnogo Universiteta = Journal of Siberian Federal University; mathematics \& physics},
  volume    = {13},
  journal   = {Žurnal Sibirskogo Federalʹnogo Universiteta = Journal of Siberian Federal University; mathematics \& physics},
  number    = {1},
  publisher = {Sibirskij Federalʹnyj Universitet},
  address   = {Krasnojarsk},
  issn      = {1997-1397},
  doi       = {10.17516/1997-1397-2020-13-1-5-25},
  pages     = {5 -- 25},
  year      = {2020},
  abstract  = {We study those nonlinear partial differential equations which appear as Euler-Lagrange equations of variational problems. On defining weak boundary values of solutions to such equations we initiate the theory of Lagrangian boundary value problems in spaces of appropriate smoothness. We also analyse if the concept of mapping degree of current importance applies to Lagrangian problems.},
  language  = {en}
}
@incollection{ClavierGuoPaychaetal.2020,
  author    = {Clavier, Pierre J. and Guo, Li and Paycha, Sylvie and Zhang, Bin},
  title     = {Renormalisation and locality},
  series = {Algebraic Combinatorics, Resurgence, Moulds and Applications (CARMA) Volume 2},
  booktitle = {Algebraic Combinatorics, Resurgence, Moulds and Applications (CARMA) Volume 2},
  publisher = {European Mathematical Society Publishing House},
  address   = {Z{\"u}rich},
  isbn      = {978-3-03719-205-4 print},
  doi       = {10.4171/205},
  pages     = {85 -- 132},
  year      = {2020},
  language  = {en}
}
@article{ChelkhLyTarkhanov2020,
  author    = {Chelkh, W. and Ly, Ibrahim and Tarkhanov, Nikolai},
  title     = {A remark on the Laplace transform},
  series = {Siberian Mathematical Journal},
  volume    = {61},
  journal   = {Siberian Mathematical Journal},
  number    = {4},
  publisher = {Consultants Bureau, Springer},
  address   = {New York},
  issn      = {0037-4466},
  doi       = {10.1134/S0037446620040151},
  pages     = {755 -- 762},
  year      = {2020},
  abstract  = {The study of the Cauchy problem for solutions of the heat equation in a cylindrical domain with data on the lateral surface by the Fourier method raises the problem of calculating the inverse Laplace transform of the entire function cos root z. This problem has no solution in the standard theory of the Laplace transform. We give an explicit formula for the inverse Laplace transform of cos root z using the theory of analytic functionals. This solution suits well to efficiently develop the regularization of solutions to Cauchy problems for parabolic equations with data on noncharacteristic surfaces.},
  language  = {en}
}
@article{KellerSchwarz2020,
  author    = {Keller, Matthias and Schwarz, Michael},
  title     = {Courant's nodal domain theorem for positivity preserving forms},
  series = {Journal of spectral theory},
  volume    = {10},
  journal   = {Journal of spectral theory},
  number    = {1},
  publisher = {EMS Publishing House},
  address   = {Z{\"u}rich},
  issn      = {1664-039X},
  doi       = {10.4171/JST/292},
  pages     = {271 -- 309},
  year      = {2020},
  abstract  = {We introduce a notion of nodal domains for positivity preserving forms. This notion generalizes the classical ones for Laplacians on domains and on graphs. We prove the Courant nodal domain theorem in this generalized setting using purely analytical methods.},
  language  = {en}
}
@article{LyTarkhanov2020,
  author    = {Ly, Ibrahim and Tarkhanov, Nikolaj Nikolaevič},
  title     = {Asymptotic expansions at nonsymmetric cuspidal points},
  series = {Mathematical notes},
  volume    = {108},
  journal   = {Mathematical notes},
  number    = {1-2},
  publisher = {Springer Science},
  address   = {New York},
  issn      = {0001-4346},
  doi       = {10.1134/S0001434620070238},
  pages     = {219 -- 228},
  year      = {2020},
  abstract  = {We study the asymptotics of solutions to the Dirichlet problem in a domain X subset of R3 whose boundary contains a singular point O. In a small neighborhood of this point, the domain has the form {z > root x(2) + y(4)}, i.e., the origin is a nonsymmetric conical point at the boundary. So far, the behavior of solutions to elliptic boundary-value problems has not been studied sufficiently in the case of nonsymmetric singular points. This problem was posed by V.A. Kondrat'ev in 2000. We establish a complete asymptotic expansion of solutions near the singular point.},
  language  = {en}
}
@article{Clavier2020,
  author    = {Clavier, Pierre J.},
  title     = {Double shuffle relations for arborified zeta values},
  series = {Journal of algebra},
  volume    = {543},
  journal   = {Journal of algebra},
  publisher = {Elsevier},
  address   = {San Diego},
  issn      = {0021-8693},
  doi       = {10.1016/j.jalgebra.2019.10.015},
  pages     = {111 -- 155},
  year      = {2020},
  abstract  = {Arborified zeta values are defined as iterated series and integrals using the universal properties of rooted trees. This approach allows to study their convergence domain and to relate them to multiple zeta values. Generalisations to rooted trees of the stuffle and shuffle products are defined and studied. It is further shown that arborified zeta values are algebra morphisms for these new products on trees.},
  language  = {en}
}
@article{HammPelivanGrottetal.2020,
  author    = {Hamm, Maximilian and Pelivan, Ivanka and Grott, Matthias and de Wiljes, Jana},
  title     = {Thermophysical modelling and parameter estimation of small solar system bodies via data assimilation},
  series = {Monthly notices of the Royal Astronomical Society},
  volume    = {496},
  journal   = {Monthly notices of the Royal Astronomical Society},
  number    = {3},
  publisher = {Oxford Univ. Press},
  address   = {Oxford},
  issn      = {0035-8711},
  doi       = {10.1093/mnras/staa1755},
  pages     = {2776 -- 2785},
  year      = {2020},
  abstract  = {Deriving thermophysical properties such as thermal inertia from thermal infrared observations provides useful insights into the structure of the surface material on planetary bodies. The estimation of these properties is usually done by fitting temperature variations calculated by thermophysical models to infrared observations. For multiple free model parameters, traditional methods such as least-squares fitting or Markov chain Monte Carlo methods become computationally too expensive. Consequently, the simultaneous estimation of several thermophysical parameters, together with their corresponding uncertainties and correlations, is often not computationally feasible and the analysis is usually reduced to fitting one or two parameters. Data assimilation (DA) methods have been shown to be robust while sufficiently accurate and computationally affordable even for a large number of parameters. This paper will introduce a standard sequential DA method, the ensemble square root filter, for thermophysical modelling of asteroid surfaces. This method is used to re-analyse infrared observations of the MARA instrument, which measured the diurnal temperature variation of a single boulder on the surface of near-Earth asteroid (162173) Ryugu. The thermal inertia is estimated to be 295 +/- 18 Jm(-2) K-1 s(-1/2), while all five free parameters of the initial analysis are varied and estimated simultaneously. Based on this thermal inertia estimate the thermal conductivity of the boulder is estimated to be between 0.07 and 0.12,Wm(-1) K-1 and the porosity to be between 0.30 and 0.52. For the first time in thermophysical parameter derivation, correlations and uncertainties of all free model parameters are incorporated in the estimation procedure that is more than 5000 times more efficient than a comparable parameter sweep.},
  language  = {en}
}
@article{LudewigRoos2020,
  author    = {Ludewig, Matthias and Roos, Saskia},
  title     = {The chiral anomaly of the free fermion in functorial field theory},
  series = {Annales Henri Poincar{\´e} : a journal of theoretical and mathematical physics},
  volume    = {21},
  journal   = {Annales Henri Poincar{\´e} : a journal of theoretical and mathematical physics},
  number    = {4},
  publisher = {Springer International Publishing AG},
  address   = {Cham (ZG)},
  issn      = {1424-0637},
  doi       = {10.1007/s00023-020-00893-6},
  pages     = {1191 -- 1233},
  year      = {2020},
  abstract  = {When trying to cast the free fermion in the framework of functorial field theory, its chiral anomaly manifests in the fact that it assigns the determinant of the Dirac operator to a top-dimensional closed spin manifold, which is not a number as expected, but an element of a complex line. In functorial field theory language, this means that the theory is twisted, which gives rise to an anomaly theory. In this paper, we give a detailed construction of this anomaly theory, as a functor that sends manifolds to infinite-dimensional Clifford algebras and bordisms to bimodules.},
  language  = {en}
}
@article{HartungBorghardt2020,
  author    = {Hartung, Niklas and Borghardt, Jens Markus},
  title     = {A mechanistic framework for a priori pharmacokinetic predictions of orally inhaled drugs},
  series = {PLoS Computational Biology : a new community journal},
  volume    = {16},
  journal   = {PLoS Computational Biology : a new community journal},
  number    = {12},
  publisher = {PLoS},
  address   = {San Fransisco},
  issn      = {1553-734X},
  doi       = {10.1371/journal.pcbi.1008466},
  pages     = {24},
  year      = {2020},
  abstract  = {Author summary <br /> The use of orally inhaled drugs for treating lung diseases is appealing since they have the potential for lung selectivity, i.e. high exposure at the site of action -the lung- without excessive side effects. However, the degree of lung selectivity depends on a large number of factors, including physiochemical properties of drug molecules, patient disease state, and inhalation devices. To predict the impact of these factors on drug exposure and thereby to understand the characteristics of an optimal drug for inhalation, we develop a predictive mathematical framework (a "pharmacokinetic model"). In contrast to previous approaches, our model allows combining knowledge from different sources appropriately and its predictions were able to adequately predict different sets of clinical data. Finally, we compare the impact of different factors and find that the most important factors are the size of the inhaled particles, the affinity of the drug to the lung tissue, as well as the rate of drug dissolution in the lung. In contrast to the common belief, the solubility of a drug in the lining fluids is not found to be relevant. These findings are important to understand how inhaled drugs should be designed to achieve best treatment results in patients. <br /> The fate of orally inhaled drugs is determined by pulmonary pharmacokinetic processes such as particle deposition, pulmonary drug dissolution, and mucociliary clearance. Even though each single process has been systematically investigated, a quantitative understanding on the interaction of processes remains limited and therefore identifying optimal drug and formulation characteristics for orally inhaled drugs is still challenging. To investigate this complex interplay, the pulmonary processes can be integrated into mathematical models. However, existing modeling attempts considerably simplify these processes or are not systematically evaluated against (clinical) data. In this work, we developed a mathematical framework based on physiologically-structured population equations to integrate all relevant pulmonary processes mechanistically. A tailored numerical resolution strategy was chosen and the mechanistic model was evaluated systematically against data from different clinical studies. Without adapting the mechanistic model or estimating kinetic parameters based on individual study data, the developed model was able to predict simultaneously (i) lung retention profiles of inhaled insoluble particles, (ii) particle size-dependent pharmacokinetics of inhaled monodisperse particles, (iii) pharmacokinetic differences between inhaled fluticasone propionate and budesonide, as well as (iv) pharmacokinetic differences between healthy volunteers and asthmatic patients. Finally, to identify the most impactful optimization criteria for orally inhaled drugs, the developed mechanistic model was applied to investigate the impact of input parameters on both the pulmonary and systemic exposure. Interestingly, the solubility of the inhaled drug did not have any relevant impact on the local and systemic pharmacokinetics. Instead, the pulmonary dissolution rate, the particle size, the tissue affinity, and the systemic clearance were the most impactful potential optimization parameters. In the future, the developed prediction framework should be considered a powerful tool for identifying optimal drug and formulation characteristics.},
  language  = {en}
}
@phdthesis{Reinhardt2020,
  author    = {Reinhardt, Maria},
  title     = {Hybrid filters and multi-scale models},
  doi       = {10.25932/publishup-47435},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-474356},
  school      = {Universit{\"a}t Potsdam},
  pages     = {xiii, 102},
  year      = {2020},
  abstract  = {This thesis is concerned with Data Assimilation, the process of combining model predictions with observations. So called filters are of special interest. One is inter- ested in computing the probability distribution of the state of a physical process in the future, given (possibly) imperfect measurements. This is done using Bayes' rule. The first part focuses on hybrid filters, that bridge between the two main groups of filters: ensemble Kalman filters (EnKF) and particle filters. The first are a group of very stable and computationally cheap algorithms, but they request certain strong assumptions. Particle filters on the other hand are more generally applicable, but computationally expensive and as such not always suitable for high dimensional systems. Therefore it exists a need to combine both groups to benefit from the advantages of each. This can be achieved by splitting the likelihood function, when assimilating a new observation and treating one part of it with an EnKF and the other part with a particle filter. The second part of this thesis deals with the application of Data Assimilation to multi-scale models and the problems that arise from that. One of the main areas of application for Data Assimilation techniques is predicting the development of oceans and the atmosphere. These processes involve several scales and often balance rela- tions between the state variables. The use of Data Assimilation procedures most often violates relations of that kind, which leads to unrealistic and non-physical pre- dictions of the future development of the process eventually. This work discusses the inclusion of a post-processing step after each assimilation step, in which a minimi- sation problem is solved, which penalises the imbalance. This method is tested on four different models, two Hamiltonian systems and two spatially extended models, which adds even more difficulties.},
  language  = {en}
}
@misc{PornsawadSungcharoenBoeckmann2020,
  author    = {Pornsawad, Pornsarp and Sungcharoen, Parada and B{\"o}ckmann, Christine},
  title     = {Convergence rate of the modified Landweber method for solving inverse potential problems},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  number    = {1034},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-47194},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-471942},
  pages     = {24},
  year      = {2020},
  abstract  = {In this paper, we present the convergence rate analysis of the modified Landweber method under logarithmic source condition for nonlinear ill-posed problems. The regularization parameter is chosen according to the discrepancy principle. The reconstructions of the shape of an unknown domain for an inverse potential problem by using the modified Landweber method are exhibited.},
  language  = {en}
}
@article{Zagrebnov2020,
  author    = {Zagrebnov, Valentin},
  title     = {Trotter product formula on Hilbert and Banach spaces for operator-norm convergence},
  series = {Lectures in pure and applied mathematics},
  journal   = {Lectures in pure and applied mathematics},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  isbn      = {978-3-86956-485-2},
  issn      = {2199-4951},
  doi       = {10.25932/publishup-47197},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-471971},
  pages     = {23 -- 34},
  year      = {2020},
  language  = {en}
}
@article{Zass2020,
  author    = {Zass, Alexander},
  title     = {A Gibbs point process of diffusions: Existence and uniqueness},
  series = {Lectures in pure and applied mathematics},
  journal   = {Lectures in pure and applied mathematics},
  number    = {6},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  isbn      = {978-3-86956-485-2},
  issn      = {2199-4951},
  doi       = {10.25932/publishup-47195},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-471951},
  pages     = {13 -- 22},
  year      = {2020},
  language  = {en}
}
@article{SukiasyanMelkonyan2020,
  author    = {Sukiasyan, Hayk and Melkonyan, Tatev},
  title     = {Semi-recursive algorithm of piecewise linear approximation of two-dimensional function by the method of worst segment dividing},
  series = {Lectures in pure and applied mathematics},
  journal   = {Lectures in pure and applied mathematics},
  number    = {6},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  isbn      = {978-3-86956-485-2},
  issn      = {2199-4951},
  doi       = {10.25932/publishup-47198},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-471982},
  pages     = {35 -- 44},
  year      = {2020},
  language  = {en}
}