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  - 
TY  - JOUR
A1  - Kolbe, Benedikt Maximilian
A1  - Evans, Myfanwy E.
T1  - Isotopic tiling theory for hyperbolic surfaces
JF  - Geometriae dedicata
N2  - In this paper, we develop the mathematical tools needed to explore isotopy classes of tilings on hyperbolic surfaces of finite genus, possibly nonorientable, with boundary, and punctured. More specifically, we generalize results on Delaney-Dress combinatorial tiling theory using an extension of mapping class groups to orbifolds, in turn using this to study tilings of covering spaces of orbifolds. Moreover, we study finite subgroups of these mapping class groups. Our results can be used to extend the Delaney-Dress combinatorial encoding of a tiling to yield a finite symbol encoding the complexity of an isotopy class of tilings. The results of this paper provide the basis for a complete and unambiguous enumeration of isotopically distinct tilings of hyperbolic surfaces.
KW  - isotopic tiling theory
KW  - delaney-dress tiling theory
KW  - mapping class
KW  - groups
KW  - orbifolds
KW  - maps on surfaces
KW  - hyperbolic tilings
Y1  - 2020
U6  - https://doi.org/10.1007/s10711-020-00554-2
SN  - 0046-5755
SN  - 1572-9168
VL  - 212
IS  - 1
SP  - 177
EP  - 204
PB  - Springer
CY  - Dordrecht
ER  - 
TY  - JOUR
A1  - Ropp, Guillaume
A1  - Lesur, Vincent
A1  - Bärenzung, Julien
A1  - Holschneider, Matthias
T1  - Sequential modelling of the Earth’s core magnetic field
JF  - Earth, Planets and Space
N2  - We describe a new, original approach to the modelling of the Earth's magnetic field. The overall objective of this study is to reliably render fast variations of the core field and its secular variation. This method combines a sequential modelling approach, a Kalman filter, and a correlation-based modelling step. Sources that most significantly contribute to the field measured at the surface of the Earth are modelled. Their separation is based on strong prior information on their spatial and temporal behaviours. We obtain a time series of model distributions which display behaviours similar to those of recent models based on more classic approaches, particularly at large temporal and spatial scales. Interesting new features and periodicities are visible in our models at smaller time and spatial scales. An important aspect of our method is to yield reliable error bars for all model parameters. These errors, however, are only as reliable as the description of the different sources and the prior information used are realistic. Finally, we used a slightly different version of our method to produce candidate models for the thirteenth edition of the International Geomagnetic Reference Field.
KW  - geomagnetic field
KW  - secular variation
KW  - Kalman filter
KW  - IGRF
Y1  - 2020
U6  - https://doi.org/10.1186/s40623-020-01230-1
SN  - 1880-5981
VL  - 72
IS  - 1
PB  - Springer
CY  - New York
ER  - 
TY  - JOUR
A1  - Mazzonetto, Sara
A1  - Salimova, Diyora
T1  - Existence, uniqueness, and numerical approximations for stochastic burgers equations
JF  - Stochastic analysis and applications
N2  - In this article, we propose an all-in-one statement which includes existence, uniqueness, regularity, and numerical approximations of mild solutions for a class of stochastic partial differential equations (SPDEs) with non-globally monotone nonlinearities. The proof of this result exploits the properties of an existing fully explicit space-time discrete approximation scheme, in particular the fact that it satisfies suitable a priori estimates. We also obtain almost sure and strong convergence of the approximation scheme to the mild solutions of the considered SPDEs. We conclude by applying the main result of the article to the stochastic Burgers equations with additive space-time white noise.
KW  - Stochastic Burgers equations
KW  - SPDEs
KW  - mild solution
KW  - existence
KW  - numerical
KW  - approximation
Y1  - 2020
U6  - https://doi.org/10.1080/07362994.2019.1709503
SN  - 0736-2994
SN  - 1532-9356
VL  - 38
IS  - 4
SP  - 623
EP  - 646
PB  - Taylor & Francis Group
CY  - Philadelphia
ER  - 
TY  - JOUR
A1  - Keller, Matthias
A1  - Pinchover, Yehuda
A1  - Pogorzelski, Felix
T1  - From hardy to rellich inequalities on graphs
JF  - Proceedings of the London Mathematical Society
N2  - We show how to deduce Rellich inequalities from Hardy inequalities on infinite graphs. Specifically, the obtained Rellich inequality gives an upper bound on a function by the Laplacian of the function in terms of weighted norms. These weights involve the Hardy weight and a function which satisfies an eikonal inequality. The results are proven first for Laplacians and are extended to Schrodinger operators afterwards.
KW  - 35R02
KW  - 39A12 (primary)
KW  - 26D15
KW  - 31C20
KW  - 35B09
KW  - 58E35 (secondary)
Y1  - 2020
U6  - https://doi.org/10.1112/plms.12376
SN  - 0024-6115
SN  - 1460-244X
VL  - 122
IS  - 3
SP  - 458
EP  - 477
PB  - Wiley
CY  - Hoboken
ER  - 
TY  - JOUR
A1  - Capała, Karol
A1  - Padash, Amin
A1  - Chechkin, Aleksei V.
A1  - Shokri, Babak
A1  - Metzler, Ralf
A1  - Dybiec, Bartłomiej
T1  - Levy noise-driven escape from arctangent potential wells
JF  - Chaos : an interdisciplinary journal of nonlinear science
N2  - The escape from a potential well is an archetypal problem in the study of stochastic dynamical systems, representing real-world situations from chemical reactions to leaving an established home range in movement ecology. Concurrently, Levy noise is a well-established approach to model systems characterized by statistical outliers and diverging higher order moments, ranging from gene expression control to the movement patterns of animals and humans. Here, we study the problem of Levy noise-driven escape from an almost rectangular, arctangent potential well restricted by two absorbing boundaries, mostly under the action of the Cauchy noise. We unveil analogies of the observed transient dynamics to the general properties of stationary states of Levy processes in single-well potentials. The first-escape dynamics is shown to exhibit exponential tails. We examine the dependence of the escape on the shape parameters, steepness, and height of the arctangent potential. Finally, we explore in detail the behavior of the probability densities of the first-escape time and the last-hitting point.
Y1  - 2020
U6  - https://doi.org/10.1063/5.0021795
SN  - 1054-1500
SN  - 1089-7682
VL  - 30
IS  - 12
PB  - American Institute of Physics
CY  - Woodbury, NY
ER  - 
TY  - JOUR
A1  - Clavier, Pierre
A1  - Guo, Li
A1  - Paycha, Sylvie
A1  - Zhang, Bin
T1  - Locality and renormalization: universal properties and integrals on trees
JF  - Journal of mathematical physics
N2  - The purpose of this paper is to build an algebraic framework suited to regularize branched structures emanating from rooted forests and which encodes the locality principle. This is achieved by means of the universal properties in the locality framework of properly decorated rooted forests. These universal properties are then applied to derive the multivariate regularization of integrals indexed by rooted forests. We study their renormalization, along the lines of Kreimer's toy model for Feynman integrals.
Y1  - 2020
U6  - https://doi.org/10.1063/1.5116381
SN  - 0022-2488
SN  - 1089-7658
VL  - 61
IS  - 2
PB  - American Institute of Physics
CY  - College Park, Md.
ER  - 
TY  - JOUR
A1  - Baerenzung, Julien
A1  - Holschneider, Matthias
A1  - Wicht, Johannes
A1  - Lesur, Vincent
A1  - Sanchez, Sabrina
T1  - The Kalmag model as a candidate for IGRF-13
JF  - Earth, planets and space
N2  - We present a new model of the geomagnetic field spanning the last 20 years and called Kalmag. Deriving from the assimilation of CHAMP and Swarm vector field measurements, it separates the different contributions to the observable field through parameterized prior covariance matrices. To make the inverse problem numerically feasible, it has been sequentialized in time through the combination of a Kalman filter and a smoothing algorithm. The model provides reliable estimates of past, present and future mean fields and associated uncertainties. The version presented here is an update of our IGRF candidates; the amount of assimilated data has been doubled and the considered time window has been extended from [2000.5, 2019.74] to [2000.5, 2020.33].
KW  - Geomagnetic field
KW  - Secular variation
KW  - Assimilation
KW  - Kalman filter
KW  - Machine learning
Y1  - 2020
U6  - https://doi.org/10.1186/s40623-020-01295-y
SN  - 1880-5981
VL  - 72
IS  - 1
PB  - Springer
CY  - New York
ER  - 
TY  - JOUR
A1  - Leung, Tsz Yan
A1  - Leutbecher, Martin
A1  - Reich, Sebastian
A1  - Shepherd, Theodore G.
T1  - Impact of the mesoscale range on error growth and the limits to atmospheric predictability
JF  - Journal of the atmospheric sciences
N2  - Global numerical weather prediction (NWP) models have begun to resolve the mesoscale k(-5/3) range of the energy spectrum, which is known to impose an inherently finite range of deterministic predictability per se as errors develop more rapidly on these scales than on the larger scales. However, the dynamics of these errors under the influence of the synoptic-scale k(-3) range is little studied. Within a perfect-model context, the present work examines the error growth behavior under such a hybrid spectrum in Lorenz's original model of 1969, and in a series of identical-twin perturbation experiments using an idealized two-dimensional barotropic turbulence model at a range of resolutions. With the typical resolution of today's global NWP ensembles, error growth remains largely uniform across scales. The theoretically expected fast error growth characteristic of a k(-5/3) spectrum is seen to be largely suppressed in the first decade of the mesoscale range by the synoptic-scale k(-3) range. However, it emerges once models become fully able to resolve features on something like a 20-km scale, which corresponds to a grid resolution on the order of a few kilometers.
KW  - mesoscale forecasting
KW  - numerical weather prediction/forecasting
KW  - short-range prediction
KW  - numerical analysis/modeling
Y1  - 2020
U6  - https://doi.org/10.1175/JAS-D-19-0346.1
SN  - 0022-4928
SN  - 1520-0469
VL  - 77
IS  - 11
SP  - 3769
EP  - 3779
PB  - American Meteorological Soc.
CY  - Boston
ER  - 
TY  - JOUR
A1  - Saggioro, Elena
A1  - de Wiljes, Jana
A1  - Kretschmer, Marlene
A1  - Runge, Jakob
T1  - Reconstructing regime-dependent causal relationships from observational time series
JF  - Chaos : an interdisciplinary journal of nonlinear science
N2  - Inferring causal relations from observational time series data is a key problem across science and engineering whenever experimental interventions are infeasible or unethical. Increasing data availability over the past few decades has spurred the development of a plethora of causal discovery methods, each addressing particular challenges of this difficult task. In this paper, we focus on an important challenge that is at the core of time series causal discovery: regime-dependent causal relations. Often dynamical systems feature transitions depending on some, often persistent, unobserved background regime, and different regimes may exhibit different causal relations. Here, we assume a persistent and discrete regime variable leading to a finite number of regimes within which we may assume stationary causal relations. To detect regime-dependent causal relations, we combine the conditional independence-based PCMCI method [based on a condition-selection step (PC) followed by the momentary conditional independence (MCI) test] with a regime learning optimization approach. PCMCI allows for causal discovery from high-dimensional and highly correlated time series. Our method, Regime-PCMCI, is evaluated on a number of numerical experiments demonstrating that it can distinguish regimes with different causal directions, time lags, and sign of causal links, as well as changes in the variables' autocorrelation. Furthermore, Regime-PCMCI is employed to observations of El Nino Southern Oscillation and Indian rainfall, demonstrating skill also in real-world datasets.
Y1  - 2020
U6  - https://doi.org/10.1063/5.0020538
SN  - 1054-1500
SN  - 1089-7682
SN  - 1527-2443
VL  - 30
IS  - 11
PB  - American Institute of Physics
CY  - Melville
ER  - 
TY  - GEN
A1  - Wiljes, Jana de
A1  - Tong, Xin T.
T1  - Analysis of a localised nonlinear ensemble Kalman Bucy filter with complete and accurate observations
T2  - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - Concurrent observation technologies have made high-precision real-time data available in large quantities. Data assimilation (DA) is concerned with how to combine this data with physical models to produce accurate predictions. For spatial-temporal models, the ensemble Kalman filter with proper localisation techniques is considered to be a state-of-the-art DA methodology. This article proposes and investigates a localised ensemble Kalman Bucy filter for nonlinear models with short-range interactions. We derive dimension-independent and component-wise error bounds and show the long time path-wise error only has logarithmic dependence on the time range. The theoretical results are verified through some simple numerical tests.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1221 
KW  - data assimilation
KW  - stability and accuracy
KW  - dimension independent bound
KW  - localisation
KW  - high dimensional
KW  - filter
KW  - nonlinear
Y1  - 2022
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-540417
SN  - 1866-8372
VL  - 33
IS  - 9
SP  - 4752
EP  - 4782
PB  - IOP Publ.
CY  - Bristol
ER  - 
TY  - THES
A1  - Schwarz, Michael
T1  - Nodal domains and boundary representation for Dirichlet forms
Y1  - 2020
ER  - 
TY  - JOUR
A1  - Seelig, Stefan A.
A1  - Rabe, Maximilian Michael
A1  - Malem-Shinitski, Noa
A1  - Risse, Sarah
A1  - Reich, Sebastian
A1  - Engbert, Ralf
T1  - Bayesian parameter estimation for the SWIFT model of eye-movement control during reading
JF  - Journal of mathematical psychology
N2  - Process-oriented theories of cognition must be evaluated against time-ordered observations. Here we present a representative example for data assimilation of the SWIFT model, a dynamical model of the control of fixation positions and fixation durations during natural reading of single sentences. First, we develop and test an approximate likelihood function of the model, which is a combination of a spatial, pseudo-marginal likelihood and a temporal likelihood obtained by probability density approximation Second, we implement a Bayesian approach to parameter inference using an adaptive Markov chain Monte Carlo procedure. Our results indicate that model parameters can be estimated reliably for individual subjects. We conclude that approximative Bayesian inference represents a considerable step forward for computational models of eye-movement control, where modeling of individual data on the basis of process-based dynamic models has not been possible so far.
KW  - dynamical models
KW  - reading
KW  - eye movements
KW  - saccades
KW  - likelihood function
KW  - Bayesian inference
KW  - MCMC
KW  - interindividual differences
Y1  - 2020
U6  - https://doi.org/10.1016/j.jmp.2019.102313
SN  - 0022-2496
SN  - 1096-0880
VL  - 95
PB  - Elsevier
CY  - San Diego
ER  - 
TY  - JOUR
A1  - Wiljes, Jana de
A1  - Tong, Xin T.
T1  - Analysis of a localised nonlinear ensemble Kalman Bucy filter with complete and accurate observations
JF  - Nonlinearity
N2  - Concurrent observation technologies have made high-precision real-time data available in large quantities. Data assimilation (DA) is concerned with how to combine this data with physical models to produce accurate predictions. For spatial-temporal models, the ensemble Kalman filter with proper localisation techniques is considered to be a state-of-the-art DA methodology. This article proposes and investigates a localised ensemble Kalman Bucy filter for nonlinear models with short-range interactions. We derive dimension-independent and component-wise error bounds and show the long time path-wise error only has logarithmic dependence on the time range. The theoretical results are verified through some simple numerical tests.
KW  - data assimilation
KW  - stability and accuracy
KW  - dimension independent bound
KW  - localisation
KW  - high dimensional
KW  - filter
KW  - nonlinear
Y1  - 2020
U6  - https://doi.org/10.1088/1361-6544/ab8d14
SN  - 0951-7715
SN  - 1361-6544
VL  - 33
IS  - 9
SP  - 4752
EP  - 4782
PB  - IOP Publ.
CY  - Bristol
ER  - 
TY  - JOUR
A1  - Purinton, Benjamin
A1  - Bookhagen, Bodo
T1  - Multiband (X, C, L) radar amplitude analysis for a mixed sand- and gravel-bed river in the eastern Central Andes
JF  - Remote sensing of environment : an interdisciplinary journal
N2  - Synthetic Aperture Radar (SAR) amplitude measurements from spaceborne sensors are sensitive to surface roughness conditions near their radar wavelength. These backscatter signals are often exploited to assess the roughness of plowed agricultural fields and water surfaces, and less so to complex, heterogeneous geological surfaces. The bedload of mixed sand- and gravel-bed rivers can be considered a mixture of smooth (compacted sand) and rough (gravel) surfaces. Here, we assess backscatter gradients over a large high-mountain alluvial river in the eastern Central Andes with aerially exposed sand and gravel bedload using X-band TerraSAR-X/TanDEM-X, C-band Sentinel-1, and L-band ALOS-2 PALSAR-2 radar scenes. In a first step, we present theory and hypotheses regarding radar response to an alluvial channel bed. We test our hypotheses by comparing backscatter responses over vegetation-free endmember surfaces from inside and outside of the active channel-bed area. We then develop methods to extract smoothed backscatter gradients downstream along the channel using kernel density estimates. In a final step, the local variability of sand-dominated patches is analyzed using Fourier frequency analysis, by fitting stretched-exponential and power-law regression models to the 2-D power spectrum of backscatter amplitude. We find a large range in backscatter depending on the heterogeneity of contiguous smooth- and rough-patches of bedload material. The SAR amplitude signal responds primarily to the fraction of smooth-sand bedload, but is further modified by gravel elements. The sensitivity to gravel is more apparent in longer wavelength L-band radar, whereas C- and X-band is sensitive only to sand variability. Because the spatial extent of smooth sand patches in our study area is typically< 50 m, only higher resolution sensors (e.g., TerraSAR-X/TanDEM-X) are useful for power spectrum analysis. Our results show the potential for mapping sand-gravel transitions and local geomorphic complexity in alluvial rivers with aerially exposed bedload using SAR amplitude.
KW  - SAR amplitude
KW  - Radar backscatter
KW  - Surface roughness
KW  - Fluvial
KW  - geomorphology
KW  - TerraSAR-X/TanDEM-X
KW  - Sentinel-1
KW  - ALOS-2 PALSAR-2
Y1  - 2020
U6  - https://doi.org/10.1016/j.rse.2020.111799
SN  - 0034-4257
SN  - 1879-0704
VL  - 246
PB  - Elsevier
CY  - New York
ER  - 
TY  - JOUR
A1  - Malem-Shinitski, Noa
A1  - Opper, Manfred
A1  - Reich, Sebastian
A1  - Schwetlick, Lisa
A1  - Seelig, Stefan A.
A1  - Engbert, Ralf
T1  - A mathematical model of local and global attention in natural scene viewing
JF  - PLoS Computational Biology : a new community journal
N2  - Author summary <br /> Switching between local and global attention is a general strategy in human information processing. We investigate whether this strategy is a viable approach to model sequences of fixations generated by a human observer in a free viewing task with natural scenes. Variants of the basic model are used to predict the experimental data based on Bayesian inference. Results indicate a high predictive power for both aggregated data and individual differences across observers. The combination of a novel model with state-of-the-art Bayesian methods lends support to our two-state model using local and global internal attention states for controlling eye movements. <br /> Understanding the decision process underlying gaze control is an important question in cognitive neuroscience with applications in diverse fields ranging from psychology to computer vision. The decision for choosing an upcoming saccade target can be framed as a selection process between two states: Should the observer further inspect the information near the current gaze position (local attention) or continue with exploration of other patches of the given scene (global attention)? Here we propose and investigate a mathematical model motivated by switching between these two attentional states during scene viewing. The model is derived from a minimal set of assumptions that generates realistic eye movement behavior. We implemented a Bayesian approach for model parameter inference based on the model's likelihood function. In order to simplify the inference, we applied data augmentation methods that allowed the use of conjugate priors and the construction of an efficient Gibbs sampler. This approach turned out to be numerically efficient and permitted fitting interindividual differences in saccade statistics. Thus, the main contribution of our modeling approach is two-fold; first, we propose a new model for saccade generation in scene viewing. Second, we demonstrate the use of novel methods from Bayesian inference in the field of scan path modeling.
Y1  - 2020
U6  - https://doi.org/10.1371/journal.pcbi.1007880
SN  - 1553-734X
SN  - 1553-7358
VL  - 16
IS  - 12
PB  - PLoS
CY  - San Fransisco
ER  - 
TY  - JOUR
A1  - Pornsawad, Pornsarp
A1  - Sungcharoen, Parada
A1  - Böckmann, Christine
T1  - Convergence rate of the modified Landweber method for solving inverse potential problems
JF  - Mathematics : open access journal
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.
KW  - nonlinear operator
KW  - regularization
KW  - modified Landweber method
KW  - discrepancy principle
KW  - logarithmic source condition
Y1  - 2020
U6  - https://doi.org/10.3390/math8040608
SN  - 2227-7390
VL  - 8
IS  - 4
PB  - MDPI
CY  - Basel
ER  - 
TY  - JOUR
A1  - de Wiljes, Jana
A1  - Pathiraja, Sahani Darschika
A1  - Reich, Sebastian
T1  - Ensemble transform algorithms for nonlinear smoothing problems
JF  - SIAM journal on scientific computing
N2  - Several numerical tools designed to overcome the challenges of smoothing in a non-linear and non-Gaussian setting are investigated for a class of particle smoothers. The considered family of smoothers is induced by the class of linear ensemble transform filters which contains classical filters such as the stochastic ensemble Kalman filter, the ensemble square root filter, and the recently introduced nonlinear ensemble transform filter. Further the ensemble transform particle smoother is introduced and particularly highlighted as it is consistent in the particle limit and does not require assumptions with respect to the family of the posterior distribution. The linear update pattern of the considered class of linear ensemble transform smoothers allows one to implement important supplementary techniques such as adaptive spread corrections, hybrid formulations, and localization in order to facilitate their application to complex estimation problems. These additional features are derived and numerically investigated for a sequence of increasingly challenging test problems.
KW  - data assimilation
KW  - smoother
KW  - localization
KW  - optimal transport
KW  - adaptive
KW  - spread correction
Y1  - 2019
U6  - https://doi.org/10.1137/19M1239544
SN  - 1064-8275
SN  - 1095-7197
VL  - 42
IS  - 1
SP  - A87
EP  - A114
PB  - Society for Industrial and Applied Mathematics
CY  - Philadelphia
ER  - 
TY  - GEN
A1  - Kolbe, Benedikt Maximilian
A1  - Evans, Myfanwy E.
T1  - Isotopic tiling theory for hyperbolic surfaces
T2  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - In this paper, we develop the mathematical tools needed to explore isotopy classes of tilings on hyperbolic surfaces of finite genus, possibly nonorientable, with boundary, and punctured. More specifically, we generalize results on Delaney-Dress combinatorial tiling theory using an extension of mapping class groups to orbifolds, in turn using this to study tilings of covering spaces of orbifolds. Moreover, we study finite subgroups of these mapping class groups. Our results can be used to extend the Delaney-Dress combinatorial encoding of a tiling to yield a finite symbol encoding the complexity of an isotopy class of tilings. The results of this paper provide the basis for a complete and unambiguous enumeration of isotopically distinct tilings of hyperbolic surfaces.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1347 
KW  - isotopic tiling theory
KW  - Delaney–Dress tiling theory
KW  - mapping class groups
KW  - Orbifolds
KW  - maps on surfaces
KW  - hyperbolic tilings
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-544285
SN  - 1866-8372
IS  - 1
ER  - 
TY  - BOOK
A1  - Zass, Alexander
A1  - Zagrebnov, Valentin
A1  - Sukiasyan, Hayk
A1  - Melkonyan, Tatev
A1  - Rafler, Mathias
A1  - Poghosyan, Suren
A1  - Zessin, Hans
A1  - Piatnitski, Andrey
A1  - Zhizhina, Elena
A1  - Pechersky, Eugeny
A1  - Pirogov, Sergei
A1  - Yambartsev, Anatoly
A1  - Mazzonetto, Sara
A1  - Lykov, Alexander
A1  - Malyshev, Vadim
A1  - Khachatryan, Linda
A1  - Nahapetian, Boris
A1  - Jursenas, Rytis
A1  - Jansen, Sabine
A1  - Tsagkarogiannis, Dimitrios
A1  - Kuna, Tobias
A1  - Kolesnikov, Leonid
A1  - Hryniv, Ostap
A1  - Wallace, Clare
A1  - Houdebert, Pierre
A1  - Figari, Rodolfo
A1  - Teta, Alessandro
A1  - Boldrighini, Carlo
A1  - Frigio, Sandro
A1  - Maponi, Pierluigi
A1  - Pellegrinotti, Alessandro
A1  - Sinai, Yakov G.
ED  - Roelly, Sylvie
ED  - Rafler, Mathias
ED  - Poghosyan, Suren
T1  - Proceedings of the XI international conference stochastic and analytic methods in mathematical physics
N2  - The XI international conference Stochastic and Analytic Methods in Mathematical Physics was held in Yerevan 2 – 7 September 2019 and was dedicated to the memory of the great mathematician Robert Adol’fovich Minlos, who passed away in January 2018.
The present volume collects a large majority of the contributions presented at the conference on the following domains of contemporary interest: classical and quantum statistical physics, mathematical methods in quantum mechanics, stochastic analysis, applications of point processes in statistical mechanics. The authors are specialists from Armenia, Czech Republic, Denmark, France, Germany, Italy, Japan, Lithuania, Russia, UK and Uzbekistan.
A particular aim of this volume is to offer young scientists basic material in order to inspire their future research in the wide fields presented here.
T3  - Lectures in pure and applied mathematics - 6 
KW  - statistical mechanics
KW  - random point processes
KW  - stochastic analysis
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-459192
SN  - 978-3-86956-485-2
SN  - 2199-4951
SN  - 2199-496X
IS  - 6
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - GEN
A1  - Mazzonetto, Sara
A1  - Salimova, Diyora
T1  - Existence, uniqueness, and numerical approximations for stochastic burgers equations
T2  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - In this article, we propose an all-in-one statement which includes existence, uniqueness, regularity, and numerical approximations of mild solutions for a class of stochastic partial differential equations (SPDEs) with non-globally monotone nonlinearities. The proof of this result exploits the properties of an existing fully explicit space-time discrete approximation scheme, in particular the fact that it satisfies suitable a priori estimates. We also obtain almost sure and strong convergence of the approximation scheme to the mild solutions of the considered SPDEs. We conclude by applying the main result of the article to the stochastic Burgers equations with additive space-time white noise.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1393 
KW  - stochastic Burgers equations
KW  - SPDEs
KW  - mild solution
KW  - existence
KW  - numerical approximation
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-515796
SN  - 1866-8372
IS  - 4
ER  - 
TY  - GEN
A1  - Keller, Matthias
A1  - Pinchover, Yehuda
A1  - Pogorzelski, Felix
T1  - From hardy to rellich inequalities on graphs
T2  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - We show how to deduce Rellich inequalities from Hardy inequalities on infinite graphs. Specifically, the obtained Rellich inequality gives an upper bound on a function by the Laplacian of the function in terms of weighted norms. These weights involve the Hardy weight and a function which satisfies an eikonal inequality. The results are proven first for Laplacians and are extended to Schrodinger operators afterwards.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1379 
KW  - 35R02
KW  - 39A12 (primary)
KW  - 26D15
KW  - 31C20
KW  - 35B09
KW  - 58E35 (secondary)
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-542140
SN  - 1866-8372
IS  - 3
ER  - 
TY  - JOUR
A1  - Kürschner, Patrick
A1  - Freitag, Melina A.
T1  - Inexact methods for the low rank solution to large scale Lyapunov equations
JF  - BIT : numerical mathematics ; the leading applied mathematics journal for all computational mathematicians
N2  - The rational Krylov subspace method (RKSM) and the low-rank alternating directions implicit (LR-ADI) iteration are established numerical tools for computing low-rank solution factors of large-scale Lyapunov equations. In order to generate the basis vectors for the RKSM, or extend the low-rank factors within the LR-ADI method, the repeated solution to a shifted linear system of equations is necessary. For very large systems this solve is usually implemented using iterative methods, leading to inexact solves within this inner iteration (and therefore to "inexact methods"). We will show that one can terminate this inner iteration before full precision has been reached and still obtain very good accuracy in the final solution to the Lyapunov equation. In particular, for both the RKSM and the LR-ADI method we derive theory for a relaxation strategy (e.g. increasing the solve tolerance of the inner iteration, as the outer iteration proceeds) within the iterative methods for solving the large linear systems. These theoretical choices involve unknown quantities, therefore practical criteria for relaxing the solution tolerance within the inner linear system are then provided. The theory is supported by several numerical examples, which show that the total amount of work for solving Lyapunov equations can be reduced significantly.
KW  - Lyapunov equation
KW  - alternating direction implicit
KW  - rational Krylov
KW  - subspaces
KW  - low-rank approximations
Y1  - 2019
U6  - https://doi.org/10.1007/s10543-020-00813-4
SN  - 0006-3835
SN  - 1572-9125
VL  - 60
IS  - 4
SP  - 1221
EP  - 1259
PB  - Springer
CY  - Dordrecht
ER  - 
TY  - JOUR
A1  - Flad, Heinz-Jürgen
A1  - Flad-Harutyunyan, Gohar
A1  - Schulze, Bert-Wolfgang
T1  - Explicit Green operators for quantum mechanical Hamiltonians
BT  - II. edge-type singularities of the helium atom
JF  - Asian-European journal of mathematics : AEJM
N2  - We extend our approach of asymptotic parametrix construction for Hamiltonian operators from conical to edge-type singularities which is applicable to coalescence points of two particles of the helium atom and related two electron systems including the hydrogen molecule. Up to second-order, we have calculated the symbols of an asymptotic parametrix of the nonrelativistic Hamiltonian of the helium atom within the Born-Oppenheimer approximation and provide explicit formulas for the corresponding Green operators which encode the asymptotic behavior of the eigenfunctions near an edge.
KW  - Singular analysis
KW  - Schrodinger equation
KW  - many-electron systems
KW  - asymptotic properties of eigenfunctions
Y1  - 2020
U6  - https://doi.org/10.1142/S1793557120501223
SN  - 1793-5571
SN  - 1793-7183
VL  - 13
IS  - 7
PB  - World Scientific
CY  - Singapore
ER  - 
TY  - CHAP
A1  - Rungrottheera, Wannarut
A1  - Chang, Der-Chen
A1  - Schulze, Bert-Wolfgang
T1  - The edge calculus of singularity order >3
T2  - Journal of nonlinear and convex analysis : an international journal
N2  - We study Mellin pseudo-differential algebras on singular straight cones and manifolds with singularity of order >= 3. Those are necessary to express parametrices of elliptic differential operators with a corresponding cornerdegenerate behavior, and we obtain regularity in weighted spaces.
KW  - Pseudo-differential algebras
KW  - symbols
KW  - singular manifolds
KW  - Mellin
KW  - operator calculus
Y1  - 2020
SN  - 1345-4773
SN  - 1880-5221
VL  - 21
IS  - 2
SP  - 387
EP  - 401
PB  - Yokohama Publishers
CY  - Yokohama
ER  - 
TY  - JOUR
A1  - Zöller, Gert
A1  - Hainzl, Sebastian
A1  - Tilmann, Frederik
A1  - Woith, Heiko
A1  - Dahm, Torsten
T1  - Comment on: Wikelski, Martin; Müller, Uschi; Scocco, Paola; Catorci, Andrea; Desinov, Lev V.; Belyaev, Mikhail Y.; Keim, Daniel A.; Pohlmeier, Winfried; Fechteler, Gerhard; Mai, Martin P. : Potential short-term earthquake forecasting by farm animal monitoring. - Ethology. - 126 (2020), 9. - S. 931 - 941. -ISSN 0179-1613. - eISSN 1439-0310. - doi 10.1111/eth.13078
JF  - Ethology
N2  - Based on an analysis of continuous monitoring of farm animal behavior in the region of the 2016 M6.6 Norcia earthquake in Italy, Wikelski et al., 2020; (Seismol Res Lett, 89, 2020, 1238) conclude that animal activity can be anticipated with subsequent seismic activity and that this finding might help to design a "short-term earthquake forecasting method." We show that this result is based on an incomplete analysis and misleading interpretations. Applying state-of-the-art methods of statistics, we demonstrate that the proposed anticipatory patterns cannot be distinguished from random patterns, and consequently, the observed anomalies in animal activity do not have any forecasting power.
KW  - animal behavior
KW  - earthquake precursor
KW  - error diagram
KW  - prediction
KW  - randomness
KW  - statistics
Y1  - 2020
U6  - https://doi.org/10.1111/eth.13105
SN  - 0179-1613
SN  - 1439-0310
VL  - 127
IS  - 3
SP  - 302
EP  - 306
PB  - Wiley
CY  - Hoboken
ER  - 
TY  - JOUR
A1  - Mueller-Schoell, Anna
A1  - Groenland, Stefanie L.
A1  - Scherf-Clavel, Oliver
A1  - van Dyk, Madele
A1  - Huisinga, Wilhelm
A1  - Michelet, Robin
A1  - Jaehde, Ulrich
A1  - Steeghs, Neeltje
A1  - Huitema, Alwin D. R.
A1  - Kloft, Charlotte
T1  - Therapeutic drug monitoring of oral targeted antineoplastic drugs
JF  - European journal of clinical pharmacology
N2  - Purpose This review provides an overview of the current challenges in oral targeted antineoplastic drug (OAD) dosing and outlines the unexploited value of therapeutic drug monitoring (TDM). Factors influencing the pharmacokinetic exposure in OAD therapy are depicted together with an overview of different TDM approaches. Finally, current evidence for TDM for all approved OADs is reviewed. Methods A comprehensive literature search (covering literature published until April 2020), including primary and secondary scientific literature on pharmacokinetics and dose individualisation strategies for OADs, together with US FDA Clinical Pharmacology and Biopharmaceutics Reviews and the Committee for Medicinal Products for Human Use European Public Assessment Reports was conducted. Results OADs are highly potent drugs, which have substantially changed treatment options for cancer patients. Nevertheless, high pharmacokinetic variability and low treatment adherence are risk factors for treatment failure. TDM is a powerful tool to individualise drug dosing, ensure drug concentrations within the therapeutic window and increase treatment success rates. After reviewing the literature for 71 approved OADs, we show that exposure-response and/or exposure-toxicity relationships have been established for the majority. Moreover, TDM has been proven to be feasible for individualised dosing of abiraterone, everolimus, imatinib, pazopanib, sunitinib and tamoxifen in prospective studies. There is a lack of experience in how to best implement TDM as part of clinical routine in OAD cancer therapy. Conclusion Sub-therapeutic concentrations and severe adverse events are current challenges in OAD treatment, which can both be addressed by the application of TDM-guided dosing, ensuring concentrations within the therapeutic window.
KW  - targeted antineoplastic drugs
KW  - tyrosine kinase inhibitors
KW  - therapeutic
KW  - drug monitoring
KW  - oral anticancer drugs
KW  - personalised medicine
Y1  - 2020
U6  - https://doi.org/10.1007/s00228-020-03014-8
SN  - 0031-6970
SN  - 1432-1041
VL  - 77
IS  - 4
SP  - 441
EP  - 464
PB  - Springer
CY  - Heidelberg
ER  - 
TY  - JOUR
A1  - Grisic, Ana-Marija
A1  - Eser, Alexander
A1  - Huisinga, Wilhelm
A1  - Reinisch, Walter
A1  - Kloft, Charlotte
T1  - Quantitative relationship between infliximab exposure and inhibition of C-reactive protein synthesis to support inflammatory bowel disease management
JF  - British journal of clinical pharmacology
N2  - Aim Quantitative and kinetic insights into the drug exposure-disease response relationship might enhance our knowledge on loss of response and support more effective monitoring of inflammatory activity by biomarkers in patients with inflammatory bowel disease (IBD) treated with infliximab (IFX). This study aimed to derive recommendations for dose adjustment and treatment optimisation based on mechanistic characterisation of the relationship between IFX serum concentration and C-reactive protein (CRP) concentration. <br /> Methods Data from an investigator-initiated trial included 121 patients with IBD during IFX maintenance treatment. Serum concentrations of IFX, antidrug antibodies (ADA), CRP, and disease-related covariates were determined at the mid-term and end of a dosing interval. Data were analysed using a pharmacometric nonlinear mixed-effects modelling approach. An IFX exposure-CRP model was generated and applied to evaluate dosing regimens to achieve CRP remission. <br /> Results The generated quantitative model showed that IFX has the potential to inhibit up to 72% (9% relative standard error [RSE]) of CRP synthesis in a patient. IFX concentration leading to 90% of the maximum CRP synthesis inhibition was 18.4 mu g/mL (43% RSE). Presence of ADA was the most influential factor on IFX exposure. With standard dosing strategy, >= 55% of ADA+ patients experienced CRP nonremission. Shortening the dosing interval and co-therapy with immunomodulators were found to be the most beneficial strategies to maintain CRP remission. <br /> Conclusions With the generated model we could for the first time establish a robust relationship between IFX exposure and CRP synthesis inhibition, which could be utilised for treatment optimisation in IBD patients.
KW  - C‐ reactive protein remission
KW  - inflammatory bowel disease
KW  - infliximab dosing
Y1  - 2020
U6  - https://doi.org/10.1111/bcp.14648
SN  - 0306-5251
SN  - 1365-2125
VL  - 87
IS  - 5
SP  - 2374
EP  - 2384
PB  - Wiley
CY  - Hoboken
ER  - 
TY  - JOUR
A1  - Kluwe, Franziska
A1  - Michelet, Robin
A1  - Müller-Schöll, Anna
A1  - Maier, Corinna
A1  - Klopp-Schulze, Lena
A1  - van Dyk, Madele
A1  - Mikus, Gerd
A1  - Huisinga, Wilhelm
A1  - Kloft, Charlotte
T1  - Perspectives on model-informed precision dosing in the digital health era
BT  - challenges, opportunities, and recommendations
JF  - Clinical pharmacology & therapeutics
Y1  - 2020
U6  - https://doi.org/10.1002/cpt.2049
SN  - 0009-9236
SN  - 1532-6535
VL  - 109
IS  - 1
SP  - 29
EP  - 36
PB  - Wiley
CY  - Hoboken
ER  - 
TY  - JOUR
A1  - Sharma, Shubham
A1  - Hainzl, Sebastian
A1  - Zöller, Gert
A1  - Holschneider, Matthias
T1  - Is Coulomb stress the best choice for aftershock forecasting?
JF  - Journal of geophysical research : Solid earth
N2  - The Coulomb failure stress (CFS) criterion is the most commonly used method for predicting spatial distributions of aftershocks following large earthquakes. However, large uncertainties are always associated with the calculation of Coulomb stress change. The uncertainties mainly arise due to nonunique slip inversions and unknown receiver faults; especially for the latter, results are highly dependent on the choice of the assumed receiver mechanism. Based on binary tests (aftershocks yes/no), recent studies suggest that alternative stress quantities, a distance-slip probabilistic model as well as deep neural network (DNN) approaches, all are superior to CFS with predefined receiver mechanism. To challenge this conclusion, which might have large implications, we use 289 slip inversions from SRCMOD database to calculate more realistic CFS values for a layered half-space and variable receiver mechanisms. We also analyze the effect of the magnitude cutoff, grid size variation, and aftershock duration to verify the use of receiver operating characteristic (ROC) analysis for the ranking of stress metrics. The observations suggest that introducing a layered half-space does not improve the stress maps and ROC curves. However, results significantly improve for larger aftershocks and shorter time periods but without changing the ranking. We also go beyond binary testing and apply alternative statistics to test the ability to estimate aftershock numbers, which confirm that simple stress metrics perform better than the classic Coulomb failure stress calculations and are also better than the distance-slip probabilistic model.
Y1  - 2020
U6  - https://doi.org/10.1029/2020JB019553
SN  - 2169-9313
SN  - 2169-9356
VL  - 125
IS  - 9
PB  - American Geophysical Union
CY  - Washington
ER  - 
TY  - JOUR
A1  - Dimitrova, Ilinka
A1  - Koppitz, Jörg
T1  - On relative ranks of the semigroup of orientation-preserving transformations on infinite chains
JF  - Asian-European journal of mathematics
N2  - In this paper, we determine the relative rank of the semigroup OP(X) of all orientation-preserving transformations on infinite chains modulo the semigroup O(X) of all order-preserving transformations.
KW  - Transformation semigroups on infinite chains
KW  - order-preserving
KW  - transformations
KW  - orientation-preserving transformations
KW  - relative rank
Y1  - 2020
U6  - https://doi.org/10.1142/S1793557121501461
SN  - 1793-5571
SN  - 1793-7183
VL  - 14
IS  - 08
PB  - World Scientific
CY  - Singapore
ER  -