TY - JOUR A1 - Jende, Alexander A1 - Koppitz, Jörg T1 - A characterization of strong semilattices of periodic groups and rectangular bands by disjunction of identities JF - Asian-European Journal of Mathematics (AEJM) N2 - 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. KW - orthogroup KW - strong semilattice of semigroups KW - clifford semigroup KW - normal band KW - alternative variety Y1 - 2022 U6 - https://doi.org/10.1142/S1793557122501960 SN - 1793-5571 SN - 1793-7183 VL - 15 IS - 11 PB - World Scientific CY - Singapore ER - TY - JOUR A1 - Oster, Mathias A1 - Dias, Marcelo A. A1 - Wolff, Timo de A1 - Evans, Myfanwy T1 - Reentrant tensegrity BT - a three-periodic, chiral, tensegrity structure that is auxetic JF - Science advances / American Association for the Advancement of Science N2 - 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. Y1 - 2021 U6 - https://doi.org/10.1126/sciadv.abj6737 SN - 2375-2548 VL - 7 IS - 50 PB - American Association for the Advancement of Science CY - Washington ER - TY - JOUR A1 - Maoutsa, Dimitra Despoina A1 - Opper, Manfred T1 - Deterministic particle flows for constraining stochastic nonlinear systems JF - Physical Review Research / American Physical Society N2 - 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. Y1 - 2022 U6 - https://doi.org/10.1103/PhysRevResearch.4.043035 SN - 2643-1564 VL - 4 IS - 4 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Hanisch, Florian A1 - Strohmaier, Alexander A1 - Waters, Alden T1 - A relative trace formula for obstacle scattering JF - Duke mathematical journal N2 - 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. KW - Birman–Krein formula KW - Casimir energy KW - obstacle scattering KW - trace formula Y1 - 2022 U6 - https://doi.org/10.1215/00127094-2022-0053 SN - 0012-7094 SN - 1547-7398 VL - 171 IS - 11 SP - 2233 EP - 2274 PB - Duke Univ. Press CY - Durham, NC ER - TY - JOUR A1 - Julien, Bärenzung A1 - Matthias, Holschneider A1 - Saynisch-Wagner, Jan A1 - Thomas, Maik T1 - Kalmag: a high spatio-temporal model of the geomagnetic field JF - Earth, planets and space N2 - 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/. KW - geomagnetic field KW - lithospheric field KW - secular variation KW - magnetospheric field KW - induced field KW - assimilation KW - Kalman filter KW - machine learning Y1 - 2022 U6 - https://doi.org/10.1186/s40623-022-01692-5 SN - 1880-5981 VL - 74 IS - 1 PB - Springer CY - New York ER - TY - JOUR A1 - Shlapunov, Alexander A. A1 - Tarchanov, Nikolaj Nikolaevič T1 - Inverse image of precompact sets and regular solutions to the Navier-Stokes equations JF - Vestnik Udmurtskogo Universiteta. Matematika, mechanika, kompʹjuternye nauki N2 - 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. KW - Navier-Stokes equations KW - regular solutions Y1 - 2022 U6 - https://doi.org/10.35634/vm220208 SN - 1994-9197 SN - 2076-5959 VL - 32 IS - 2 SP - 278 EP - 297 PB - Udmurtskij gosudarstvennyj universitet CY - Iževsk ER - TY - JOUR A1 - Huang, Daniel Zhengyu A1 - Huang, Jiaoyang A1 - Reich, Sebastian A1 - Stuart, Andrew M. T1 - Efficient derivative-free Bayesian inference for large-scale inverse problems JF - Inverse problems : an international journal of inverse problems, inverse methods and computerised inversion of data N2 - 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. KW - inverse problem KW - uncertainty quantification KW - Bayesian inference KW - derivative-free optimization KW - mean-field dynamical system KW - interacting particle system KW - ensemble Kalman filter Y1 - 2022 U6 - https://doi.org/10.1088/1361-6420/ac99fa SN - 0266-5611 SN - 1361-6420 VL - 38 IS - 12 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Seyedhosseini, Mehran T1 - A variant of Roe algebras for spaces with cylindrical ends with applications in relative higher index theory JF - Journal of noncommutative geometry N2 - 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. KW - positive scalar curvature KW - higher index theory KW - rho-invariants KW - Roe algebras KW - manifolds with cylindrical ends KW - manifolds with boundary Y1 - 2022 U6 - https://doi.org/10.4171/JNCG/457 SN - 1661-6952 SN - 1661-6960 VL - 16 IS - 2 SP - 595 EP - 624 PB - European Mathematical Society CY - Zurich ER - TY - JOUR A1 - Metzger, Jan T1 - Refined position estimates for surfaces of Willmore type in Riemannian manifolds JF - Communications in analysis and geometry N2 - 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. Y1 - 2023 U6 - https://doi.org/10.4310/CAG.2022.v30.n10.a5 SN - 1019-8385 SN - 1944-9992 VL - 30 IS - 10 SP - 2315 EP - 2346 PB - International Press of Boston CY - Somerville, Mass. ER - TY - JOUR A1 - Hanisch, Florian A1 - Ludewig, Matthias T1 - The fermionic integral on loop space and the Pfaffian line bundle JF - Journal of mathematical physics N2 - 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. Y1 - 2022 U6 - https://doi.org/10.1063/5.0060355 SN - 0022-2488 SN - 1089-7658 SN - 1527-2427 VL - 63 IS - 12 PB - American Inst. of Physics CY - College Park, Md. ER -