@article{SilveriiMaccaferriRichteretal.2021, author = {Silverii, Francesca and Maccaferri, Francesco and Richter, Gudrun and Gonzalez Cansado, Borja and Wang, Rongjiang and Hainzl, Sebastian and Dahm, Torsten}, title = {Poroelastic model in a vertically sealed gas storage}, series = {Geophysical journal international / the Royal Astronomical Society, the Deutsche Geophysikalische Gesellschaft and the European Geophysical Society}, volume = {227}, journal = {Geophysical journal international / the Royal Astronomical Society, the Deutsche Geophysikalische Gesellschaft and the European Geophysical Society}, number = {2}, publisher = {Oxford Univ. Press}, address = {Oxford}, issn = {0956-540X}, doi = {10.1093/gji/ggab268}, pages = {1322 -- 1338}, year = {2021}, abstract = {Natural gas can be temporarily stored in a variety of underground facilities, such as depleted gas and oil fields, natural aquifers and caverns in salt rocks. Being extensively monitored during operations, these systems provide a favourable opportunity to investigate how pressure varies in time and space and possibly induces/triggers earthquakes on nearby faults. Elaborate and detailed numerical modelling techniques are often applied to study gas reservoirs. Here we show the possibilities and discuss the limitations of a flexible and easily formulated tool that can be straightforwardly applied to simulate temporal pore-pressure variations and study the relation with recorded microseismic events. We use the software POEL (POroELastic diffusion and deformation) which computes the poroelastic response to fluid injection/extraction in a horizontally layered poroelastic structure. We further develop its application to address the presence of vertical impermeable faults bounding the reservoir and of multiple injection/extraction sources. Exploiting available information on the reservoir geometry and physical parameters, and records of injection/extraction rates for a gas reservoir in southern Europe, we perform an extensive parametric study considering different model configurations. Comparing modelled spatiotemporal pore-pressure variations with in situ measurements, we show that the inclusion of vertical impermeable faults provides an improvement in reproducing the observations and results in pore-pressure accumulation near the faults and in a variation of the temporal pore-pressure diffusion pattern. To study the relation between gas storage activity and recorded local microseismicity, we applied different seismicity models based on the estimated porepressure distribution. This analysis helps to understand the spatial distribution of seismicity and its temporal modulation. The results show that the observed microseismicity could be partly linked to the storage activity, but the contribution of tectonic background seismicity cannot be excluded.}, language = {en} } @article{ClavierFoissyPaycha2022, author = {Clavier, Pierre J. and Foissy, Loic and Paycha, Sylvie}, title = {From non-unitary wheeled PROPs to smooth amplitudes and generalised convolutions}, series = {European journal of mathematics}, volume = {8}, journal = {European journal of mathematics}, number = {Supplement 2}, publisher = {Springer}, address = {Berlin}, issn = {2199-675X}, doi = {10.1007/s40879-022-00557-1}, pages = {411 -- 480}, year = {2022}, abstract = {We introduce the concept of TRAP (Traces and Permutations), which can roughly be viewed as a wheeled PROP (Products and Permutations) without unit. TRAPs are equipped with a horizontal concatenation and partial trace maps. Continuous morphisms on an infinite-dimensional topological space and smooth kernels (respectively, smoothing operators) on a closed manifold form a TRAP but not a wheeled PROP. We build the free objects in the category of TRAPs as TRAPs of graphs and show that a TRAP can be completed to a unitary TRAP (or wheeled PROP). We further show that it can be equipped with a vertical concatenation, which on the TRAP of linear homomorphisms of a vector space, amounts to the usual composition. The vertical concatenation in the TRAP of smooth kernels gives rise to generalised convolutions. Graphs whose vertices are decorated by smooth kernels (respectively, smoothing operators) on a closed manifold form a TRAP. From their universal properties we build smooth amplitudes associated with the graph.}, language = {en} } @article{RoseWei2022, author = {Rose, Christian and Wei, Guofang}, title = {Eigenvalue estimates for Kato-type Ricci curvature conditions}, series = {Analysis \& PDE}, volume = {15}, journal = {Analysis \& PDE}, number = {7}, publisher = {Mathematical Sciences Publishers}, address = {Berkeley}, issn = {1948-206X}, doi = {10.2140/apde.2022.15.1703}, pages = {1703 -- 1724}, year = {2022}, abstract = {We prove that optimal lower eigenvalue estimates of Zhong-Yang type as well as a Cheng-type upper bound for the first eigenvalue hold on closed manifolds assuming only a Kato condition on the negative part of the Ricci curvature. This generalizes all earlier results on Lp-curvature assumptions. Moreover, we introduce the Kato condition on compact manifolds with boundary with respect to the Neumann Laplacian, leading to Harnack estimates for the Neumann heat kernel and lower bounds for all Neumann eigenvalues, which provides a first insight in handling variable Ricci curvature assumptions in this case.}, language = {en} } @article{JendeKoppitz2022, author = {Jende, Alexander and Koppitz, J{\"o}rg}, title = {A characterization of strong semilattices of periodic groups and rectangular bands by disjunction of identities}, series = {Asian-European Journal of Mathematics (AEJM)}, volume = {15}, journal = {Asian-European Journal of Mathematics (AEJM)}, number = {11}, publisher = {World Scientific}, address = {Singapore}, issn = {1793-5571}, doi = {10.1142/S1793557122501960}, pages = {10}, year = {2022}, abstract = {Each completely regular semigroup is a semilattice of completely simple semigroups. The more specific concept of a strong semilattice provides the concrete product between two arbitrary elements. We characterize strong semilattices of rectangular groups by so-called disjunctions of identities. Disjunctions of identities generalize the classical concept of an identity and of a variety, respectively. The rectangular groups will be on the one hand left zero semigroups and right zero semigroups and on the other hand groups of exponent p is an element of P, where P is any set of pairwise coprime natural numbers.}, language = {en} } @article{OsterDiasWolffetal.2021, author = {Oster, Mathias and Dias, Marcelo A. and Wolff, Timo de and Evans, Myfanwy}, title = {Reentrant tensegrity}, series = {Science advances / American Association for the Advancement of Science}, volume = {7}, journal = {Science advances / American Association for the Advancement of Science}, number = {50}, publisher = {American Association for the Advancement of Science}, address = {Washington}, issn = {2375-2548}, doi = {10.1126/sciadv.abj6737}, pages = {6}, year = {2021}, abstract = {We present a three-periodic, chiral, tensegrity structure and demonstrate that it is auxetic. Our tensegrity structure is constructed using the chiral symmetry Pi(+) cylinder packing, transforming cylinders to elastic elements and cylinder contacts to incompressible rods. The resulting structure displays local reentrant geometry at its vertices and is shown to be auxetic when modeled as an equilibrium configuration of spatial constraints subject to a quasi-static deformation. When the structure is subsequently modeled as a lattice material with elastic elements, the auxetic behavior is again confirmed through finite element modeling. The cubic symmetry of the original structure means that the auxetic behavior is observed in both perpendicular directions and is close to isotropic in magnitude. This structure could be the simplest three-dimensional analog to the two-dimensional reentrant honeycomb. This, alongside the chirality of the structure, makes it an interesting design target for multifunctional materials.}, language = {en} } @article{MaoutsaOpper2022, author = {Maoutsa, Dimitra Despoina and Opper, Manfred}, title = {Deterministic particle flows for constraining stochastic nonlinear systems}, series = {Physical Review Research / American Physical Society}, volume = {4}, journal = {Physical Review Research / American Physical Society}, number = {4}, publisher = {American Physical Society}, address = {College Park}, issn = {2643-1564}, doi = {10.1103/PhysRevResearch.4.043035}, pages = {17}, year = {2022}, abstract = {Devising optimal interventions for constraining stochastic systems is a challenging endeavor that has to confront the interplay between randomness and dynamical nonlinearity. Existing intervention methods that employ stochastic path sampling scale poorly with increasing system dimension and are slow to converge. Here we propose a generally applicable and practically feasible methodology that computes the optimal interventions in a noniterative scheme. We formulate the optimal dynamical adjustments in terms of deterministically sampled probability flows approximated by an interacting particle system. Applied to several biologically inspired models, we demonstrate that our method provides the necessary optimal controls in settings with terminal, transient, or generalized collective state constraints and arbitrary system dynamics.}, language = {en} } @article{HanischStrohmaierWaters2022, author = {Hanisch, Florian and Strohmaier, Alexander and Waters, Alden}, title = {A relative trace formula for obstacle scattering}, series = {Duke mathematical journal}, volume = {171}, journal = {Duke mathematical journal}, number = {11}, publisher = {Duke Univ. Press}, address = {Durham, NC}, issn = {0012-7094}, doi = {10.1215/00127094-2022-0053}, pages = {2233 -- 2274}, year = {2022}, abstract = {We consider the case of scattering by several obstacles in Rd for d ≥ 2. In this setting, the absolutely continuous part of the Laplace operator Δ with Dirichlet boundary conditions and the free Laplace operator Δ0 are unitarily equivalent. For suitable functions that decay sufficiently fast, we have that the difference g(Δ) - g(Δ0) is a trace-class operator and its trace is described by the Krein spectral shift function. In this article, we study the contribution to the trace (and hence the Krein spectral shift function) that arises from assembling several obstacles relative to a setting where the obstacles are completely separated. In the case of two obstacles, we consider the Laplace operators Δ1 and Δ2 obtained by imposing Dirichlet boundary conditions only on one of the objects. Our main result in this case states that then g(Δ) - g(Δ1) - g(Δ2) C g(Δ0) is a trace-class operator for a much larger class of functions (including functions of polynomial growth) and that this trace may still be computed by a modification of the Birman-Krein formula. In case g(x) D x 2 , 1 the relative trace has a physical meaning as the vacuum energy of the massless scalar field and is expressible as an integral involving boundary layer operators. Such integrals have been derived in the physics literature using nonrigorous path integral derivations and our formula provides both a rigorous justification as well as a generalization.}, 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{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{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{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{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{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} } @misc{Reimann2024, type = {Master Thesis}, author = {Reimann, Hans}, title = {Towards robust inference for Bayesian filtering of linear Gaussian dynamical systems subject to additive change}, doi = {10.25932/publishup-64946}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-649469}, school = {Universit{\"a}t Potsdam}, pages = {ix, 156}, year = {2024}, abstract = {State space models enjoy wide popularity in mathematical and statistical modelling across disciplines and research fields. Frequent solutions to problems of estimation and forecasting of a latent signal such as the celebrated Kalman filter hereby rely on a set of strong assumptions such as linearity of system dynamics and Gaussianity of noise terms. We investigate fallacy in mis-specification of the noise terms, that is signal noise and observation noise, regarding heavy tailedness in that the true dynamic frequently produces observation outliers or abrupt jumps of the signal state due to realizations of these heavy tails not considered by the model. We propose a formalisation of observation noise mis-specification in terms of Huber's ε-contamination as well as a computationally cheap solution via generalised Bayesian posteriors with a diffusion Stein divergence loss resulting in the diffusion score matching Kalman filter - a modified algorithm akin in complexity to the regular Kalman filter. For this new filter interpretations of novel terms, stability and an ensemble variant are discussed. Regarding signal noise mis-specification, we propose a formalisation in the frame work of change point detection and join ideas from the popular CUSUM algo- rithm with ideas from Bayesian online change point detection to combine frequent reliability constraints and online inference resulting in a Gaussian mixture model variant of multiple Kalman filters. We hereby exploit open-end sequential probability ratio tests on the evidence of Kalman filters on observation sub-sequences for aggregated inference under notions of plausibility. Both proposed methods are combined to investigate the double mis-specification problem and discussed regarding their capabilities in reliable and well-tuned uncertainty quantification. Each section provides an introduction to required terminology and tools as well as simulation experiments on the popular target tracking task and the non-linear, chaotic Lorenz-63 system to showcase practical performance of theoretical considerations.}, language = {en} } @phdthesis{Fischer2024, author = {Fischer, Florian}, title = {Hardy inequalities on graphs}, doi = {10.25932/publishup-64773}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-647730}, school = {Universit{\"a}t Potsdam}, pages = {vi, 160}, year = {2024}, abstract = {Die Dissertation befasst sich mit einer zentralen Ungleichung der nicht-linearen Potentialtheorie, der Hardy-Ungleichung. Sie besagt, dass das nicht-lineare Energiefunktional von unten durch eine p-te Potenz einer gewichteten p-Norm abgesch{\"a}tzt werden kann, p>1. Das Energiefunktional besteht dabei aus einem Divergenz- und einem beliebigen Potentialteil. Als zugrundeliegender Raum wurden hier lokal summierbare unendliche Graphen gew{\"a}hlt. Bisherige Ver{\"o}ffentlichungen zu Hardy-Ungleichungen auf Graphen haben vor allem den Spezialfall p=2 betrachtet, oder lokal endliche Graphen ohne Potentialteil. Zwei grundlegende Fragestellungen ergeben sich nun ganz nat{\"u}rlich: F{\"u}r welche Graphen gibt {\"u}berhaupt es eine Hardy-Ungleichung? Und, wenn es sie gibt, gibt es einen Weg um ein optimales Gewicht zu erhalten? Antworten auf diese Fragen werden in Theorem 10.1 und Theorem 12.1 gegeben. Theorem 10.1 gibt eine Reihe an Charakterisierungen an; unter anderem gibt es eine Hardy-Ungleichung auf einem Graphen genau dann, wenn es eine Greensche Funktion gibt. Theorem 12.1 gibt eine explizite Formel an, um optimale Hardy-Gewichte f{\"u}r lokal endliche Graphen unter einigen technischen Zusatzannahmen zu berechnen. In Beispielen wird gezeigt, dass Greensche Funktionen gute Kandidaten sind um in die Formel eingesetzt zu werden. Um diese beiden Theoreme beweisen zu k{\"o}nnen, m{\"u}ssen eine Vielzahl an Techniken erarbeitet werden, welche in den ersten Kapiteln behandelt werden. Dabei sind eine Verallgemeinerung der Grundzustandstransformation (Theorem 4.1), ein Agmon-Allegretto-Piepenbrink-artiges Resultat (Theorem 6.1) und das Vergleichsprinzip (Proposition 7.3) besonders hervorzuheben, da diese Resultate sehr h{\"a}ufig angewendet werden und somit das Fundament der Dissertation bilden. Es wird zudem darauf Wert gelegt die Theorie durch Beispiele zu veranschaulichen. Hierbei wird der Fokus auf die nat{\"u}rlichen Zahlen, Euklidische Gitter, B{\"a}ume und Sterne gelegt. Als Abschluss werden noch eine nicht-lineare Version der Heisenbergschen Unsch{\"a}rferelation und eine Rellich-Ungleichung aus der Hardy-Ungleichung geschlussfolgert.}, 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{SharmaHainzlZoeller2023, author = {Sharma, Shubham and Hainzl, Sebastian and Z{\"o}ller, Gert}, title = {Seismicity parameters dependence on main shock-induced co-seismic stress}, series = {Geophysical journal international}, volume = {235}, journal = {Geophysical journal international}, number = {1}, publisher = {Oxford Univ. Press}, address = {Oxford}, issn = {0956-540X}, doi = {10.1093/gji/ggad201}, pages = {509 -- 517}, year = {2023}, abstract = {The Gutenberg-Richter (GR) and the Omori-Utsu (OU) law describe the earthquakes' energy release and temporal clustering and are thus of great importance for seismic hazard assessment. Motivated by experimental results, which indicate stress-dependent parameters, we consider a combined global data set of 127 main shock-aftershock sequences and perform a systematic study of the relationship between main shock-induced stress changes and associated seismicity patterns. For this purpose, we calculate space-dependent Coulomb Stress (\& UDelta;CFS) and alternative receiver-independent stress metrics in the surrounding of the main shocks. Our results indicate a clear positive correlation between the GR b-value and the induced stress, contrasting expectations from laboratory experiments and suggesting a crucial role of structural heterogeneity and strength variations. Furthermore, we demonstrate that the aftershock productivity increases nonlinearly with stress, while the OU parameters c and p systematically decrease for increasing stress changes. Our partly unexpected findings can have an important impact on future estimations of the aftershock hazard.}, language = {en} } @phdthesis{Sareeto2024, author = {Sareeto, Apatsara}, title = {Algebraic properties of a subsemigroup of the symmetric inverse semigroup}, school = {Universit{\"a}t Potsdam}, pages = {92}, year = {2024}, 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{FalkenhagenKnoechelKloftetal.2023, author = {Falkenhagen, Undine and Kn{\"o}chel, Jane and Kloft, Charlotte and Huisinga, Wilhelm}, title = {Deriving mechanism-based pharmacodynamic models by reducing quantitative systems pharmacology models}, series = {CPT: Pharmacometrics \& Systems Pharmacology}, volume = {12}, journal = {CPT: Pharmacometrics \& Systems Pharmacology}, number = {4}, publisher = {Wiley}, address = {Hoboken}, issn = {2163-8306}, doi = {10.1002/psp4.12903}, pages = {432 -- 443}, year = {2023}, abstract = {Quantitative systems pharmacology (QSP) models integrate comprehensive qualitative and quantitative knowledge about pharmacologically relevant processes. We previously proposed a first approach to leverage the knowledge in QSP models to derive simpler, mechanism-based pharmacodynamic (PD) models. Their complexity, however, is typically still too large to be used in the population analysis of clinical data. Here, we extend the approach beyond state reduction to also include the simplification of reaction rates, elimination of reactions, and analytic solutions. We additionally ensure that the reduced model maintains a prespecified approximation quality not only for a reference individual but also for a diverse virtual population. We illustrate the extended approach for the warfarin effect on blood coagulation. Using the model-reduction approach, we derive a novel small-scale warfarin/international normalized ratio model and demonstrate its suitability for biomarker identification. Due to the systematic nature of the approach in comparison with empirical model building, the proposed model-reduction algorithm provides an improved rationale to build PD models also from QSP models in other applications.}, language = {en} }