TY - JOUR A1 - Denecke, Klaus-Dieter T1 - Partial clones JF - Asian-European journal of mathematics : AEJM N2 - 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. KW - Operation KW - term KW - formula KW - superposition of operations KW - terms and KW - formulas KW - linear term KW - linear formula KW - linear tree language KW - clone KW - partial clone KW - linear hypersubstitution KW - dht-symmetric category KW - partial KW - theory Y1 - 2020 U6 - https://doi.org/10.1142/S1793557120501612 SN - 1793-5571 SN - 1793-7183 VL - 13 IS - 8 PB - World Scientific CY - Singapore ER - TY - JOUR A1 - Somogyvári, Márk A1 - Reich, Sebastian T1 - Convergence tests for transdimensional Markov chains in geoscience imaging JF - Mathematical geosciences : the official journal of the International Association for Mathematical Geosciences N2 - 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. KW - transdimensional inversion KW - MCMC modelling KW - convergence assessment Y1 - 2019 U6 - https://doi.org/10.1007/s11004-019-09811-x SN - 1874-8961 SN - 1874-8953 VL - 52 IS - 5 SP - 651 EP - 668 PB - Springer CY - Heidelberg ER - TY - JOUR A1 - Ly, Ibrahim T1 - A Cauchy problem for the Cauchy-Riemann operator JF - Afrika Matematika N2 - 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. KW - nonlinear PDI KW - Cauchy problem KW - Zaremba problem Y1 - 2020 U6 - https://doi.org/10.1007/s13370-020-00810-4 SN - 1012-9405 SN - 2190-7668 VL - 32 IS - 1-2 SP - 69 EP - 76 PB - Springer CY - Heidelberg ER - TY - JOUR A1 - Malass, Ihsane A1 - Tarkhanov, Nikolaj Nikolaevič T1 - A perturbation of the de Rham complex T1 - Возмущение комплекса де Рама JF - Journal of Siberian Federal University : Mathematics & Physics JF - Žurnal Sibirskogo Federalʹnogo Universiteta : Matematika i fizika N2 - 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. N2 - Рассмотрим возмущение комплекса де Рама на компактном многообразии с краем. Это возмущение выходит за рамки комплексов, и поэтому когомологии к нему не относятся. С другой стороны, его кривизна "мала", поэтому существует естественный способ ввести характеристику Эйлера и разработать теорию Лефшеца для возмущения. Данная работа предназначена для попытки разработать теорию когомологий для произвольных последовательностей линейных отображений. KW - de Rham complex KW - cohomology KW - Hodge theory KW - Neumann problem KW - комплекс де Рама KW - когомологии KW - теория Ходжа KW - проблема Неймана Y1 - 2020 U6 - https://doi.org/10.17516/1997-1397-2020-13-5-519-532 SN - 1997-1397 SN - 2313-6022 VL - 13 IS - 5 SP - 519 EP - 532 PB - Siberian Federal University CY - Krasnojarsk ER - TY - JOUR A1 - Al-Saedy, Ammar Jaffar Muhesin A1 - Tarchanov, Nikolaj Nikolaevič T1 - A degree theory for Lagrangian boundary value problems JF - Žurnal Sibirskogo Federalʹnogo Universiteta = Journal of Siberian Federal University; mathematics & physics N2 - 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. N2 - Мы изучаем те нелинейные уравнения с частными производными, которые возникают как уравнения Эйлера-Лагранжа вариационных задач. Определяя слабые граничные значения решений таких уравнений, мы инициируем теорию лагранжевых краевых задач в функциональных пространствах подходящей гладкости. Мы также анализируем, применяется ли современная концепция степени отображения к лагранжевым проблемам. KW - nonlinear equations KW - Lagrangian system KW - weak boundary values KW - quasilinear Fredholm operators KW - mapping degree Y1 - 2020 U6 - https://doi.org/10.17516/1997-1397-2020-13-1-5-25 SN - 1997-1397 SN - 2313-6022 VL - 13 IS - 1 SP - 5 EP - 25 PB - Sibirskij Federalʹnyj Universitet CY - Krasnojarsk ER - TY - CHAP A1 - Clavier, Pierre J. A1 - Guo, Li A1 - Paycha, Sylvie A1 - Zhang, Bin T1 - Renormalisation and locality BT - branched zeta values T2 - Algebraic Combinatorics, Resurgence, Moulds and Applications (CARMA) Volume 2 Y1 - 2020 SN - 978-3-03719-205-4 print SN - 978-3-03719-705-9 online U6 - https://doi.org/10.4171/205 SP - 85 EP - 132 PB - European Mathematical Society Publishing House CY - Zürich ER - TY - JOUR A1 - Chelkh, W. A1 - Ly, Ibrahim A1 - Tarkhanov, Nikolai T1 - A remark on the Laplace transform JF - Siberian Mathematical Journal N2 - 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. KW - Fourier-Laplace transform KW - distributions with one-sided support KW - holomorphic function KW - analytic functional Y1 - 2020 U6 - https://doi.org/10.1134/S0037446620040151 SN - 0037-4466 SN - 1573-9260 VL - 61 IS - 4 SP - 755 EP - 762 PB - Consultants Bureau, Springer CY - New York ER - TY - JOUR A1 - Keller, Matthias A1 - Schwarz, Michael T1 - Courant’s nodal domain theorem for positivity preserving forms JF - Journal of spectral theory N2 - 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. KW - Nodal domain KW - eigenfunction KW - Dirichlet form KW - compact resolvent Y1 - 2020 U6 - https://doi.org/10.4171/JST/292 SN - 1664-039X SN - 1664-0403 VL - 10 IS - 1 SP - 271 EP - 309 PB - EMS Publishing House CY - Zürich ER - TY - JOUR A1 - Ly, Ibrahim A1 - Tarkhanov, Nikolaj Nikolaevič T1 - Asymptotic expansions at nonsymmetric cuspidal points JF - Mathematical notes N2 - 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. KW - Dirichlet problem KW - singular points KW - asymptotic expansions Y1 - 2020 U6 - https://doi.org/10.1134/S0001434620070238 SN - 0001-4346 SN - 1573-8876 VL - 108 IS - 1-2 SP - 219 EP - 228 PB - Springer Science CY - New York ER - TY - JOUR A1 - Clavier, Pierre J. T1 - Double shuffle relations for arborified zeta values JF - Journal of algebra N2 - 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. KW - Rooted trees KW - Multiple zeta values KW - Shuffle products KW - Rota-Baxter KW - algebras Y1 - 2020 U6 - https://doi.org/10.1016/j.jalgebra.2019.10.015 SN - 0021-8693 SN - 1090-266X VL - 543 SP - 111 EP - 155 PB - Elsevier CY - San Diego ER - TY - JOUR A1 - Hamm, Maximilian A1 - Pelivan, Ivanka A1 - Grott, Matthias A1 - de Wiljes, Jana T1 - Thermophysical modelling and parameter estimation of small solar system bodies via data assimilation JF - Monthly notices of the Royal Astronomical Society N2 - 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. KW - radiation mechanisms: thermal KW - methods: data analysis KW - methods KW - statistical KW - minor planets, asteroids: individual: (162173) Ryugu Y1 - 2020 U6 - https://doi.org/10.1093/mnras/staa1755 SN - 0035-8711 SN - 1365-2966 VL - 496 IS - 3 SP - 2776 EP - 2785 PB - Oxford Univ. Press CY - Oxford ER - TY - JOUR A1 - Ludewig, Matthias A1 - Roos, Saskia T1 - The chiral anomaly of the free fermion in functorial field theory JF - Annales Henri Poincaré : a journal of theoretical and mathematical physics N2 - 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. Y1 - 2020 U6 - https://doi.org/10.1007/s00023-020-00893-6 SN - 1424-0637 SN - 1424-0661 VL - 21 IS - 4 SP - 1191 EP - 1233 PB - Springer International Publishing AG CY - Cham (ZG) ER - TY - GEN A1 - Pornsawad, Pornsarp A1 - Sungcharoen, Parada A1 - Böckmann, Christine T1 - Convergence rate of the modified Landweber method for solving inverse potential problems T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - 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. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1034 KW - nonlinear operator KW - regularization KW - modified Landweber method KW - discrepancy principle KW - logarithmic source condition Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-471942 SN - 1866-8372 IS - 1034 ER - TY - JOUR A1 - Zagrebnov, Valentin T1 - Trotter product formula on Hilbert and Banach spaces for operator-norm convergence JF - Lectures in pure and applied mathematics KW - random point processes KW - statistical mechanics KW - stochastic analysis Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-471971 SN - 978-3-86956-485-2 SN - 2199-4951 SN - 2199-496X SP - 23 EP - 34 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Sukiasyan, Hayk A1 - Melkonyan, Tatev T1 - Semi-recursive algorithm of piecewise linear approximation of two-dimensional function by the method of worst segment dividing JF - Lectures in pure and applied mathematics KW - random point processes KW - statistical mechanics KW - stochastic analysis Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-471982 SN - 978-3-86956-485-2 SN - 2199-4951 SN - 2199-496X IS - 6 SP - 35 EP - 44 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Boldrighini, Carlo A1 - Frigio, Sandro A1 - Maponi, Pierluigi A1 - Pellegrinotti, Alessandro A1 - Sinai, Yakov G. T1 - 3-D incompressible Navier-Stokes equations: Complex blow-up and related real flows JF - Lectures in pure and applied mathematics KW - random point processes KW - statistical mechanics KW - stochastic analysis Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472201 SN - 978-3-86956-485-2 SN - 2199-4951 SN - 2199-496X IS - 6 SP - 185 EP - 194 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Figari, Rodolfo A1 - Teta, Alessandro T1 - Zero-range hamiltonians for three quantum particles JF - Lectures in pure and applied mathematics KW - random point processes KW - statistical mechanics KW - stochastic analysis Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472189 SN - 978-3-86956-485-2 SN - 2199-4951 SN - 2199-496X IS - 6 SP - 175 EP - 184 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Houdebert, Pierre T1 - Numerical study for the phase transition of the area-interaction model JF - Lectures in pure and applied mathematics KW - random point processes KW - statistical mechanics KW - stochastic analysis Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472177 SN - 978-3-86956-485-2 SN - 2199-4951 SN - 2199-496X IS - 6 SP - 165 EP - 174 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Jansen, Sabine A1 - Kuna, Tobias A1 - Tsagkarogiannis, Dimitrios T1 - Virial inversion for inhomogeneous systems JF - Lectures in pure and applied mathematics KW - random point processes KW - statistical mechanics KW - stochastic analysis Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472111 SN - 978-3-86956-485-2 SN - 2199-4951 SN - 2199-496X IS - 6 SP - 135 EP - 144 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Hryniv, Ostap A1 - Wallace, Clare T1 - Phase separation and sharp large deviations JF - Lectures in pure and applied mathematics KW - random point processes KW - statistical mechanics KW - stochastic analysis Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472168 SN - 978-3-86956-485-2 SN - 2199-4951 SN - 2199-496X IS - 6 SP - 155 EP - 164 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Jansen, Sabine A1 - Kolesnikov, Leonid T1 - Activity expansions for Gibbs correlation functions JF - Lectures in pure and applied mathematics KW - random point processes KW - statistical mechanics KW - stochastic analysis Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472121 SN - 978-3-86956-485-2 SN - 2199-4951 SN - 2199-496X IS - 6 SP - 145 EP - 154 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Jansen, Sabine A1 - Tsagkarogiannis, Dimitrios T1 - Mayer expansion for the Asakura-Oosawa model of colloid theory JF - Lectures in pure and applied mathematics KW - random point processes KW - statistical mechanics KW - stochastic analysis Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472109 SN - 978-3-86956-485-2 SN - 2199-4951 SN - 2199-496X IS - 6 SP - 127 EP - 134 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Piatnitski, Andrey A1 - Zhizhina, Elena T1 - Non-local convolution type parabolic equations with fractional and regular time derivative JF - Lectures in pure and applied mathematics KW - random point processes KW - statistical mechanics KW - stochastic analysis Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472024 SN - 978-3-86956-485-2 SN - 2199-4951 SN - 2199-496X IS - 6 SP - 65 EP - 67 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Jursenas, Rytis T1 - The peak model for finite rank supersingular perturbations JF - Lectures in pure and applied mathematics KW - random point processes KW - statistical mechanics KW - stochastic analysis Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472090 IS - 6 SP - 117 EP - 126 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Mazzonetto, Sara T1 - On an approximation of 2-D stochastic Navier-Stokes equations JF - Lectures in pure and applied mathematics KW - random point processes KW - statistical mechanics KW - stochastic analysis Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472053 SN - 978-3-86956-485-2 SN - 2199-4951 SN - 2199-496X IS - 6 SP - 87 EP - 96 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Pechersky, Eugeny A1 - Pirogov, Sergei A1 - Yambartsev, Anatoly T1 - Large emissions BT - Hawking-Penrose black hole model JF - Lectures in pure and applied mathematics KW - random point processes KW - statistical mechanics KW - stochastic analysis Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472049 SN - 978-3-86956-485-2 SN - 2199-4951 SN - 2199-496X IS - 6 SP - 77 EP - 86 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Poghosyan, Suren A1 - Zessin, Hans T1 - Construction of limiting Gibbs processes and the uniqueness of Gibbs processes JF - Lectures in pure and applied mathematics KW - random point processes KW - statistical mechanics KW - stochastic analysis Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472015 SN - 978-3-86956-485-2 SN - 2199-4951 SN - 2199-496X IS - 6 SP - 55 EP - 64 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Lykov, Alexander A1 - Malyshev, Vadim T1 - When bounded chaos becomes unbounded JF - Lectures in pure and applied mathematics KW - random point processes KW - statistical mechanics KW - stochastic analysis Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472060 SN - 978-3-86956-485-2 SN - 2199-4951 SN - 2199-496X IS - 6 SP - 97 EP - 106 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Khachatryan, Linda A1 - Nahapetian, Boris T1 - On direct and inverse problems in the description of lattice random fields JF - Lectures in pure and applied mathematics KW - random point processes KW - statistical mechanics KW - stochastic analysis Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472083 SN - 978-3-86956-485-2 SN - 2199-4951 SN - 2199-496X IS - 6 SP - 107 EP - 116 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Rafler, Mathias T1 - Pinned Gibbs processes JF - Lectures in pure and applied mathematics KW - random point processes KW - statistical mechanics KW - stochastic analysis Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472007 SN - 978-3-86956-485-2 SN - 2199-4951 SN - 2199-496X IS - 6 SP - 45 EP - 53 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Rœlly, Sylvie A1 - Zass, Alexander T1 - Marked Gibbs point processes with unbounded interaction BT - An existence result JF - Journal of statistical physics N2 - 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. KW - Marked Gibbs process KW - Infinite-dimensional interacting diffusion KW - Specific entropy KW - DLR equation Y1 - 2020 U6 - https://doi.org/10.1007/s10955-020-02559-3 SN - 0022-4715 SN - 1572-9613 VL - 179 IS - 4 SP - 972 EP - 996 PB - Springer CY - New York ER - TY - JOUR A1 - Sanchez, Sabrina A1 - Wicht, Johannes A1 - Bärenzung, Julien T1 - Predictions of the geomagnetic secular variation based on the ensemble sequential assimilation of geomagnetic field models by dynamo simulations JF - Earth, planets and space N2 - The IGRF offers an important incentive for testing algorithms predicting the Earth's magnetic field changes, known as secular variation (SV), in a 5-year range. Here, we present a SV candidate model for the 13th IGRF that stems from a sequential ensemble data assimilation approach (EnKF). The ensemble consists of a number of parallel-running 3D-dynamo simulations. The assimilated data are geomagnetic field snapshots covering the years 1840 to 2000 from the COV-OBS.x1 model and for 2001 to 2020 from the Kalmag model. A spectral covariance localization method, considering the couplings between spherical harmonics of the same equatorial symmetry and same azimuthal wave number, allows decreasing the ensemble size to about a 100 while maintaining the stability of the assimilation. The quality of 5-year predictions is tested for the past two decades. These tests show that the assimilation scheme is able to reconstruct the overall SV evolution. They also suggest that a better 5-year forecast is obtained keeping the SV constant compared to the dynamically evolving SV. However, the quality of the dynamical forecast steadily improves over the full assimilation window (180 years). We therefore propose the instantaneous SV estimate for 2020 from our assimilation as a candidate model for the IGRF-13. The ensemble approach provides uncertainty estimates, which closely match the residual differences with respect to the IGRF-13. Longer term predictions for the evolution of the main magnetic field features over a 50-year range are also presented. We observe the further decrease of the axial dipole at a mean rate of 8 nT/year as well as a deepening and broadening of the South Atlantic Anomaly. The magnetic dip poles are seen to approach an eccentric dipole configuration. KW - Earth's magnetic field KW - Geomagnetic secular variation KW - Dynamo KW - simulations KW - Data assimilation Y1 - 2020 U6 - https://doi.org/10.1186/s40623-020-01279-y SN - 1880-5981 VL - 72 IS - 1 PB - Springer CY - New York ER - TY - JOUR A1 - Garbuno-Inigo, Alfredo A1 - Nüsken, Nikolas A1 - Reich, Sebastian T1 - Affine invariant interacting Langevin dynamics for Bayesian inference JF - SIAM journal on applied dynamical systems N2 - We propose a computational method (with acronym ALDI) for sampling from a given target distribution based on first-order (overdamped) Langevin dynamics which satisfies the property of affine invariance. The central idea of ALDI is to run an ensemble of particles with their empirical covariance serving as a preconditioner for their underlying Langevin dynamics. ALDI does not require taking the inverse or square root of the empirical covariance matrix, which enables application to high-dimensional sampling problems. The theoretical properties of ALDI are studied in terms of nondegeneracy and ergodicity. Furthermore, we study its connections to diffusion on Riemannian manifolds and Wasserstein gradient flows. Bayesian inference serves as a main application area for ALDI. In case of a forward problem with additive Gaussian measurement errors, ALDI allows for a gradient-free approximation in the spirit of the ensemble Kalman filter. A computational comparison between gradient-free and gradient-based ALDI is provided for a PDE constrained Bayesian inverse problem. KW - Langevin dynamics KW - interacting particle systems KW - Bayesian inference KW - gradient flow KW - multiplicative noise KW - affine invariance KW - gradient-free Y1 - 2020 U6 - https://doi.org/10.1137/19M1304891 SN - 1536-0040 VL - 19 IS - 3 SP - 1633 EP - 1658 PB - Society for Industrial and Applied Mathematics CY - Philadelphia ER - TY - JOUR A1 - Froyland, Gary A1 - Koltai, Peter A1 - Stahn, Martin T1 - Computation and optimal perturbation of finite-time coherent sets for aperiodic flows without trajectory integration JF - SIAM journal on applied dynamical systems N2 - Understanding the macroscopic behavior of dynamical systems is an important tool to unravel transport mechanisms in complex flows. A decomposition of the state space into coherent sets is a popular way to reveal this essential macroscopic evolution. To compute coherent sets from an aperiodic time-dependent dynamical system we consider the relevant transfer operators and their infinitesimal generators on an augmented space-time manifold. This space-time generator approach avoids trajectory integration and creates a convenient linearization of the aperiodic evolution. This linearization can be further exploited to create a simple and effective spectral optimization methodology for diminishing or enhancing coherence. We obtain explicit solutions for these optimization problems using Lagrange multipliers and illustrate this technique by increasing and decreasing mixing of spatial regions through small velocity field perturbations. KW - coherent set KW - mixing KW - transfer operator KW - infinitesimal generator KW - unsteady flow KW - mixing optimization Y1 - 2020 U6 - https://doi.org/10.1137/19M1261791 SN - 1536-0040 VL - 19 IS - 3 SP - 1659 EP - 1700 PB - Society for Industrial and Applied Mathematics CY - Philadelphia ER - TY - JOUR A1 - Rastogi, Abhishake T1 - Tikhonov regularization with oversmoothing penalty for nonlinear statistical inverse problems JF - Communications on Pure and Applied Analysis N2 - In this paper, we consider the nonlinear ill-posed inverse problem with noisy data in the statistical learning setting. The Tikhonov regularization scheme in Hilbert scales is considered to reconstruct the estimator from the random noisy data. In this statistical learning setting, we derive the rates of convergence for the regularized solution under certain assumptions on the nonlinear forward operator and the prior assumptions. We discuss estimates of the reconstruction error using the approach of reproducing kernel Hilbert spaces. KW - Statistical inverse problem KW - Tikhonov regularization KW - Hilbert Scales KW - reproducing kernel Hilbert space KW - minimax convergence rates Y1 - 2020 U6 - https://doi.org/10.3934/cpaa.2020183 SN - 1534-0392 SN - 1553-5258 VL - 19 IS - 8 SP - 4111 EP - 4126 PB - American Institute of Mathematical Sciences CY - Springfield ER - TY - JOUR A1 - Chauhan, Ankit A1 - Friedrich, Tobias A1 - Rothenberger, Ralf T1 - Greed is good for deterministic scale-free networks JF - Algorithmica : an international journal in computer science N2 - Large real-world networks typically follow a power-law degree distribution. To study such networks, numerous random graph models have been proposed. However, real-world networks are not drawn at random. Therefore, Brach et al. (27th symposium on discrete algorithms (SODA), pp 1306-1325, 2016) introduced two natural deterministic conditions: (1) a power-law upper bound on the degree distribution (PLB-U) and (2) power-law neighborhoods, that is, the degree distribution of neighbors of each vertex is also upper bounded by a power law (PLB-N). They showed that many real-world networks satisfy both properties and exploit them to design faster algorithms for a number of classical graph problems. We complement their work by showing that some well-studied random graph models exhibit both of the mentioned PLB properties. PLB-U and PLB-N hold with high probability for Chung-Lu Random Graphs and Geometric Inhomogeneous Random Graphs and almost surely for Hyperbolic Random Graphs. As a consequence, all results of Brach et al. also hold with high probability or almost surely for those random graph classes. In the second part we study three classical NP-hard optimization problems on PLB networks. It is known that on general graphs with maximum degree Delta, a greedy algorithm, which chooses nodes in the order of their degree, only achieves a Omega (ln Delta)-approximation forMinimum Vertex Cover and Minimum Dominating Set, and a Omega(Delta)-approximation forMaximum Independent Set. We prove that the PLB-U property with beta>2 suffices for the greedy approach to achieve a constant-factor approximation for all three problems. We also show that these problems are APX-hard even if PLB-U, PLB-N, and an additional power-law lower bound on the degree distribution hold. Hence, a PTAS cannot be expected unless P = NP. Furthermore, we prove that all three problems are in MAX SNP if the PLB-U property holds. KW - random graphs KW - deterministic properties KW - power-law KW - approximation KW - APX-hardness Y1 - 2020 U6 - https://doi.org/10.1007/s00453-020-00729-z SN - 0178-4617 SN - 1432-0541 VL - 82 IS - 11 SP - 3338 EP - 3389 PB - Springer CY - New York ER - TY - JOUR A1 - Gräter, Joachim T1 - Free division rings of fractions of crossed products of groups with Conradian left-orders JF - Forum mathematicum N2 - Let D be a division ring of fractions of a crossed product F[G, eta, alpha], where F is a skew field and G is a group with Conradian left-order <=. For D we introduce the notion of freeness with respect to <= and show that D is free in this sense if and only if D can canonically be embedded into the endomorphism ring of the right F-vector space F((G)) of all formal power series in G over F with respect to <=. From this we obtain that all division rings of fractions of F[G, eta, alpha] which are free with respect to at least one Conradian left-order of G are isomorphic and that they are free with respect to any Conradian left-order of G. Moreover, F[G, eta, alpha] possesses a division ring of fraction which is free in this sense if and only if the rational closure of F[G, eta, alpha] in the endomorphism ring of the corresponding right F-vector space F((G)) is a skew field. KW - crossed product KW - group ring KW - ordered group KW - Conradian left-order KW - locally indicable group KW - division ring of fractions KW - Hughes-free KW - formal KW - power series Y1 - 2020 U6 - https://doi.org/10.1515/forum-2019-0264 SN - 0933-7741 SN - 1435-5337 VL - 32 IS - 3 SP - 739 EP - 772 PB - De Gruyter CY - Berlin ER - TY - JOUR A1 - Schirmer, Philipp A1 - Papenbrock, Thorsten A1 - Koumarelas, Ioannis A1 - Naumann, Felix T1 - Efficient discovery of matching dependencies JF - ACM transactions on database systems : TODS N2 - Matching dependencies (MDs) are data profiling results that are often used for data integration, data cleaning, and entity matching. They are a generalization of functional dependencies (FDs) matching similar rather than same elements. As their discovery is very difficult, existing profiling algorithms find either only small subsets of all MDs or their scope is limited to only small datasets. We focus on the efficient discovery of all interesting MDs in real-world datasets. For this purpose, we propose HyMD, a novel MD discovery algorithm that finds all minimal, non-trivial MDs within given similarity boundaries. The algorithm extracts the exact similarity thresholds for the individual MDs from the data instead of using predefined similarity thresholds. For this reason, it is the first approach to solve the MD discovery problem in an exact and truly complete way. If needed, the algorithm can, however, enforce certain properties on the reported MDs, such as disjointness and minimum support, to focus the discovery on such results that are actually required by downstream use cases. HyMD is technically a hybrid approach that combines the two most popular dependency discovery strategies in related work: lattice traversal and inference from record pairs. Despite the additional effort of finding exact similarity thresholds for all MD candidates, the algorithm is still able to efficiently process large datasets, e.g., datasets larger than 3 GB. KW - matching dependencies KW - functional dependencies KW - dependency discovery KW - data profiling KW - data matching KW - entity resolution KW - similarity measures Y1 - 2020 U6 - https://doi.org/10.1145/3392778 SN - 0362-5915 SN - 1557-4644 VL - 45 IS - 3 PB - Association for Computing Machinery CY - New York ER - TY - JOUR A1 - Maoutsa, Dimitra A1 - Reich, Sebastian A1 - Opper, Manfred T1 - Interacting particle solutions of Fokker–Planck equations through gradient–log–density estimation JF - Entropy N2 - Fokker-Planck equations are extensively employed in various scientific fields as they characterise the behaviour of stochastic systems at the level of probability density functions. Although broadly used, they allow for analytical treatment only in limited settings, and often it is inevitable to resort to numerical solutions. Here, we develop a computational approach for simulating the time evolution of Fokker-Planck solutions in terms of a mean field limit of an interacting particle system. The interactions between particles are determined by the gradient of the logarithm of the particle density, approximated here by a novel statistical estimator. The performance of our method shows promising results, with more accurate and less fluctuating statistics compared to direct stochastic simulations of comparable particle number. Taken together, our framework allows for effortless and reliable particle-based simulations of Fokker-Planck equations in low and moderate dimensions. The proposed gradient-log-density estimator is also of independent interest, for example, in the context of optimal control. KW - stochastic systems KW - Fokker-Planck equation KW - interacting particles KW - multiplicative noise KW - gradient flow KW - stochastic differential equations Y1 - 2020 U6 - https://doi.org/10.3390/e22080802 SN - 1099-4300 VL - 22 IS - 8 PB - MDPI CY - Basel ER - TY - JOUR A1 - Bandara, Lashi A1 - Bryan, Paul T1 - Heat kernels and regularity for rough metrics on smooth manifolds JF - Mathematische Nachrichten N2 - We consider rough metrics on smooth manifolds and corresponding Laplacians induced by such metrics. We demonstrate that globally continuous heat kernels exist and are Holder continuous locally in space and time. This is done via local parabolic Harnack estimates for weak solutions of operators in divergence form with bounded measurable coefficients in weighted Sobolev spaces. KW - heat kernel KW - parabolic Harnack estimate KW - rough metrics Y1 - 2020 U6 - https://doi.org/10.1002/mana.201800459 SN - 0025-584X SN - 1522-2616 VL - 293 IS - 12 SP - 2255 EP - 2270 PB - Wiley-VCH CY - Weinheim ER - TY - JOUR A1 - Azzali, Sara A1 - Paycha, Sylvie T1 - Spectral zeta-invariants lifted to coverings JF - Transactions of the American Mathematical Society N2 - The canonical trace and the Wodzicki residue on classical pseudo-differential operators on a closed manifold are characterised by their locality and shown to be preserved under lifting to the universal covering as a result of their local feature. As a consequence, we lift a class of spectral zeta-invariants using lifted defect formulae which express discrepancies of zeta-regularised traces in terms of Wodzicki residues. We derive Atiyah's L-2-index theorem as an instance of the Z(2)-graded generalisation of the canonical lift of spectral zeta-invariants and we show that certain lifted spectral zeta-invariants for geometric operators are integrals of Pontryagin and Chern forms. Y1 - 2020 U6 - https://doi.org/10.1090/tran/8067 SN - 0002-9947 SN - 1088-6850 VL - 373 IS - 9 SP - 6185 EP - 6226 PB - American Mathematical Society CY - Providence, RI ER - TY - JOUR A1 - Blanchard, Gilles A1 - Mücke, Nicole T1 - Kernel regression, minimax rates and effective dimensionality BT - beyond the regular case JF - Analysis and applications N2 - We investigate if kernel regularization methods can achieve minimax convergence rates over a source condition regularity assumption for the target function. These questions have been considered in past literature, but only under specific assumptions about the decay, typically polynomial, of the spectrum of the the kernel mapping covariance operator. In the perspective of distribution-free results, we investigate this issue under much weaker assumption on the eigenvalue decay, allowing for more complex behavior that can reflect different structure of the data at different scales. KW - Kernel regression KW - minimax optimality KW - eigenvalue decay Y1 - 2020 U6 - https://doi.org/10.1142/S0219530519500258 SN - 0219-5305 SN - 1793-6861 VL - 18 IS - 4 SP - 683 EP - 696 PB - World Scientific CY - New Jersey ER - TY - JOUR A1 - Perera, Upeksha A1 - Böckmann, Christine T1 - Solutions of Sturm-Liouville problems JF - Mathematics N2 - This paper further improves the Lie group method with Magnus expansion proposed in a previous paper by the authors, to solve some types of direct singular Sturm-Liouville problems. Next, a concrete implementation to the inverse Sturm-Liouville problem algorithm proposed by Barcilon (1974) is provided. Furthermore, computational feasibility and applicability of this algorithm to solve inverse Sturm-Liouville problems of higher order (for n=2,4) are verified successfully. It is observed that the method is successful even in the presence of significant noise, provided that the assumptions of the algorithm are satisfied. In conclusion, this work provides a method that can be adapted successfully for solving a direct (regular/singular) or inverse Sturm-Liouville problem (SLP) of an arbitrary order with arbitrary boundary conditions. KW - Sturm-Liouville problems of higher order KW - singular Sturm-Liouville KW - problems KW - inverse Sturm-Liouville problems Y1 - 2020 U6 - https://doi.org/10.3390/math8112074 SN - 2227-7390 VL - 8 IS - 11 PB - MDPI CY - Basel ER - TY - JOUR A1 - Mariucci, Ester A1 - Ray, Kolyan A1 - Szabo, Botond T1 - A Bayesian nonparametric approach to log-concave density estimation JF - Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability N2 - The estimation of a log-concave density on R is a canonical problem in the area of shape-constrained nonparametric inference. We present a Bayesian nonparametric approach to this problem based on an exponentiated Dirichlet process mixture prior and show that the posterior distribution converges to the log-concave truth at the (near-) minimax rate in Hellinger distance. Our proof proceeds by establishing a general contraction result based on the log-concave maximum likelihood estimator that prevents the need for further metric entropy calculations. We further present computationally more feasible approximations and both an empirical and hierarchical Bayes approach. All priors are illustrated numerically via simulations. KW - convergence rate KW - density estimation KW - Dirichlet mixture KW - log-concavity KW - nonparametric hypothesis testing KW - posterior distribution Y1 - 2020 U6 - https://doi.org/10.3150/19-BEJ1139 SN - 1350-7265 SN - 1573-9759 VL - 26 IS - 2 SP - 1070 EP - 1097 PB - International Statistical Institute CY - The Hague ER - TY - JOUR A1 - Schoppa, Lukas A1 - Sieg, Tobias A1 - Vogel, Kristin A1 - Zöller, Gert A1 - Kreibich, Heidi T1 - Probabilistic flood loss models for companies JF - Water resources research N2 - Flood loss modeling is a central component of flood risk analysis. Conventionally, this involves univariable and deterministic stage-damage functions. Recent advancements in the field promote the use of multivariable and probabilistic loss models, which consider variables beyond inundation depth and account for prediction uncertainty. Although companies contribute significantly to total loss figures, novel modeling approaches for companies are lacking. Scarce data and the heterogeneity among companies impede the development of company flood loss models. We present three multivariable flood loss models for companies from the manufacturing, commercial, financial, and service sector that intrinsically quantify prediction uncertainty. Based on object-level loss data (n = 1,306), we comparatively evaluate the predictive capacity of Bayesian networks, Bayesian regression, and random forest in relation to deterministic and probabilistic stage-damage functions, serving as benchmarks. The company loss data stem from four postevent surveys in Germany between 2002 and 2013 and include information on flood intensity, company characteristics, emergency response, private precaution, and resulting loss to building, equipment, and goods and stock. We find that the multivariable probabilistic models successfully identify and reproduce essential relationships of flood damage processes in the data. The assessment of model skill focuses on the precision of the probabilistic predictions and reveals that the candidate models outperform the stage-damage functions, while differences among the proposed models are negligible. Although the combination of multivariable and probabilistic loss estimation improves predictive accuracy over the entire data set, wide predictive distributions stress the necessity for the quantification of uncertainty. KW - flood loss estimation KW - probabilistic modeling KW - companies KW - multivariable KW - models Y1 - 2020 U6 - https://doi.org/10.1029/2020WR027649 SN - 0043-1397 SN - 1944-7973 VL - 56 IS - 9 PB - American Geophysical Union CY - Washington ER - TY - THES A1 - Fabian, Melina T1 - Grundvorstellungen bei Zahlbereichserweiterungen T1 - Basic ideas ('Grundvorstellungen') for numerical extensions BT - von N nach Q+ oder von N nach Z? N2 - Die Erweiterung des natürlichen Zahlbereichs um die positiven Bruchzahlen und die negativen ganzen Zahlen geht für Schülerinnen und Schüler mit großen gedanklichen Hürden und einem Umbruch bis dahin aufgebauter Grundvorstellungen einher. Diese Masterarbeit trägt wesentliche Veränderungen auf der Vorstellungs- und Darstellungsebene für beide Zahlbereiche zusammen und setzt sich mit den kognitiven Herausforderungen für Lernende auseinander. Auf der Grundlage einer Diskussion traditioneller sowie alternativer Lehrgänge der Zahlbereichserweiterung wird eine Unterrichtskonzeption für den Mathematikunterricht entwickelt, die eine parallele Einführung der Bruchzahlen und der negativen Zahlen vorschlägt. Die Empfehlungen der Unterrichtkonzeption erstrecken sich über den Zeitraum von der ersten bis zur siebten Klassenstufe, was der behutsamen Weiterentwicklung und Modifikation des Zahlbegriffs viel Zeit einräumt, und enthalten auch didaktische Überlegungen sowie konkrete Hinweise zu möglichen Aufgabenformaten. N2 - The extension of the natural number range to include the positive fractions and the negative integers is accompanied by great mental hurdles for students and an upheaval of previously established basic concepts. This Master's thesis brings together essential changes at the level of imagination and representation for both number ranges and deals with the cognitive challenges for learners. Based on a discussion of traditional as well as alternative courses of number range extension, a teaching conception for mathematics lessons is developed that proposes a parallel introduction of fractions and negative numbers. The recommendations of the teaching conception cover the period from the first to the seventh grade, which allows a lot of time for the careful further development and modification of the number concept, and also contain didactic considerations as well as concrete hints on possible task formats. KW - Mathematikdidaktik KW - Zahlbereichserweiterung KW - Grundvorstellungen KW - negative Zahlen KW - Bruchzahlen KW - fractions KW - basic ideas ('Grundvorstellungen') KW - didactics of mathematics KW - numerical extension KW - negative numbers Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-565930 ER - TY - JOUR A1 - Güneysu, Batu A1 - Keller, Matthias T1 - Feynman path integrals for magnetic Schrödinger operators on infinite weighted graphs JF - Journal d'analyse mathématique N2 - We prove a Feynman path integral formula for the unitary group exp(-itL(nu,theta)), t >= 0, associated with a discrete magnetic Schrodinger operator L-nu,L-theta on a large class of weighted infinite graphs. As a consequence, we get a new Kato-Simon estimate vertical bar exp(- itL(nu,theta))(x,y)vertical bar <= exp( -tL(-deg,0))(x,y), which controls the unitary group uniformly in the potentials in terms of a Schrodinger semigroup, where the potential deg is the weighted degree function of the graph. Y1 - 2020 U6 - https://doi.org/10.1007/s11854-020-0110-y SN - 0021-7670 SN - 1565-8538 VL - 141 IS - 2 SP - 751 EP - 770 PB - The Magnes Press, the Hebrew Univ. CY - Jerusalem ER - TY - JOUR A1 - Hermann, Andreas A1 - Humbert, Emmanuel T1 - Mass functions of a compact manifold JF - Journal of geometry and physics : JGP N2 - Let M be a compact manifold of dimension n. In this paper, we introduce the Mass Function a >= 0 bar right arrow X-+(M)(a) (resp. a >= 0 bar right arrow X--(M)(a)) which is defined as the supremum (resp. infimum) of the masses of all metrics on M whose Yamabe constant is larger than a and which are flat on a ball of radius 1 and centered at a point p is an element of M. Here, the mass of a metric flat around p is the constant term in the expansion of the Green function of the conformal Laplacian at p. We show that these functions are well defined and have many properties which allow to obtain applications to the Yamabe invariant (i.e. the supremum of Yamabe constants over the set of all metrics on M). KW - Yamabe operator KW - Yamabe invariant KW - surgery KW - positive mass theorem Y1 - 2020 U6 - https://doi.org/10.1016/j.geomphys.2020.103650 SN - 0393-0440 SN - 1879-1662 VL - 154 PB - Elsevier CY - Amsterdam [u.a.] ER - TY - JOUR A1 - Mauerberger, Stefan A1 - Schanner, Maximilian Arthus A1 - Korte, Monika A1 - Holschneider, Matthias T1 - Correlation based snapshot models of the archeomagnetic field JF - Geophysical journal international N2 - For the time stationary global geomagnetic field, a new modelling concept is presented. A Bayesian non-parametric approach provides realistic location dependent uncertainty estimates. Modelling related variabilities are dealt with systematically by making little subjective apriori assumptions. Rather than parametrizing the model by Gauss coefficients, a functional analytic approach is applied. The geomagnetic potential is assumed a Gaussian process to describe a distribution over functions. Apriori correlations are given by an explicit kernel function with non-informative dipole contribution. A refined modelling strategy is proposed that accommodates non-linearities of archeomagnetic observables: First, a rough field estimate is obtained considering only sites that provide full field vector records. Subsequently, this estimate supports the linearization that incorporates the remaining incomplete records. The comparison of results for the archeomagnetic field over the past 1000 yr is in general agreement with previous models while improved model uncertainty estimates are provided. KW - geopotential theory KW - archaeomagnetism KW - magnetic field variations through KW - time KW - palaeomagnetism KW - inverse theory KW - statistical methods Y1 - 2020 U6 - https://doi.org/10.1093/gji/ggaa336 SN - 0956-540X SN - 1365-246X VL - 223 IS - 1 SP - 648 EP - 665 PB - Oxford Univ. Press CY - Oxford ER - TY - JOUR A1 - Beckus, Siegfried A1 - Bellissard, Jean A1 - De Nittis, Giuseppe T1 - Spectral continuity for aperiodic quantum systems BT - applications of a folklore theorem JF - Journal of mathematical physics N2 - This work provides a necessary and sufficient condition for a symbolic dynamical system to admit a sequence of periodic approximations in the Hausdorff topology. The key result proved and applied here uses graphs that are called De Bruijn graphs, Rauzy graphs, or Anderson-Putnam complex, depending on the community. Combining this with a previous result, the present work justifies rigorously the accuracy and reliability of algorithmic methods used to compute numerically the spectra of a large class of self-adjoint operators. The so-called Hamiltonians describe the effective dynamic of a quantum particle in aperiodic media. No restrictions on the structure of these operators other than general regularity assumptions are imposed. In particular, nearest-neighbor correlation is not necessary. Examples for the Fibonacci and the Golay-Rudin-Shapiro sequences are explicitly provided illustrating this discussion. While the first sequence has been thoroughly studied by physicists and mathematicians alike, a shroud of mystery still surrounds the latter when it comes to spectral properties. In light of this, the present paper gives a new result here that might help uncovering a solution. Y1 - 2020 U6 - https://doi.org/10.1063/5.0011488 SN - 0022-2488 SN - 1089-7658 VL - 61 IS - 12 PB - American Institute of Physics CY - Melville, NY ER -