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  - JOUR
A1  - Hartung, Niklas
A1  - Borghardt, Jens Markus
T1  - A mechanistic framework for a priori pharmacokinetic predictions of orally inhaled drugs
JF  - PLoS Computational Biology : a new community journal
N2  - Author summary <br /> The use of orally inhaled drugs for treating lung diseases is appealing since they have the potential for lung selectivity, i.e. high exposure at the site of action -the lung- without excessive side effects. However, the degree of lung selectivity depends on a large number of factors, including physiochemical properties of drug molecules, patient disease state, and inhalation devices. To predict the impact of these factors on drug exposure and thereby to understand the characteristics of an optimal drug for inhalation, we develop a predictive mathematical framework (a "pharmacokinetic model"). In contrast to previous approaches, our model allows combining knowledge from different sources appropriately and its predictions were able to adequately predict different sets of clinical data. Finally, we compare the impact of different factors and find that the most important factors are the size of the inhaled particles, the affinity of the drug to the lung tissue, as well as the rate of drug dissolution in the lung. In contrast to the common belief, the solubility of a drug in the lining fluids is not found to be relevant. These findings are important to understand how inhaled drugs should be designed to achieve best treatment results in patients. <br /> The fate of orally inhaled drugs is determined by pulmonary pharmacokinetic processes such as particle deposition, pulmonary drug dissolution, and mucociliary clearance. Even though each single process has been systematically investigated, a quantitative understanding on the interaction of processes remains limited and therefore identifying optimal drug and formulation characteristics for orally inhaled drugs is still challenging. To investigate this complex interplay, the pulmonary processes can be integrated into mathematical models. However, existing modeling attempts considerably simplify these processes or are not systematically evaluated against (clinical) data. In this work, we developed a mathematical framework based on physiologically-structured population equations to integrate all relevant pulmonary processes mechanistically. A tailored numerical resolution strategy was chosen and the mechanistic model was evaluated systematically against data from different clinical studies. Without adapting the mechanistic model or estimating kinetic parameters based on individual study data, the developed model was able to predict simultaneously (i) lung retention profiles of inhaled insoluble particles, (ii) particle size-dependent pharmacokinetics of inhaled monodisperse particles, (iii) pharmacokinetic differences between inhaled fluticasone propionate and budesonide, as well as (iv) pharmacokinetic differences between healthy volunteers and asthmatic patients. Finally, to identify the most impactful optimization criteria for orally inhaled drugs, the developed mechanistic model was applied to investigate the impact of input parameters on both the pulmonary and systemic exposure. Interestingly, the solubility of the inhaled drug did not have any relevant impact on the local and systemic pharmacokinetics. Instead, the pulmonary dissolution rate, the particle size, the tissue affinity, and the systemic clearance were the most impactful potential optimization parameters. In the future, the developed prediction framework should be considered a powerful tool for identifying optimal drug and formulation characteristics.
Y1  - 2020
U6  - https://doi.org/10.1371/journal.pcbi.1008466
SN  - 1553-734X
SN  - 1553-7358
VL  - 16
IS  - 12
PB  - PLoS
CY  - San Fransisco
ER  - 
TY  - THES
A1  - Reinhardt, Maria
T1  - Hybrid filters and multi-scale models
N2  - This thesis is concerned with Data Assimilation, the process of combining model predictions with observations. So called filters are of special interest. One is inter- ested in computing the probability distribution of the state of a physical process in the future, given (possibly) imperfect measurements. This is done using Bayes’ rule. The first part focuses on hybrid filters, that bridge between the two main groups of filters: ensemble Kalman filters (EnKF) and particle filters. The first are a group of very stable and computationally cheap algorithms, but they request certain strong assumptions. Particle filters on the other hand are more generally applicable, but computationally expensive and as such not always suitable for high dimensional systems. Therefore it exists a need to combine both groups to benefit from the advantages of each. This can be achieved by splitting the likelihood function, when assimilating a new observation and treating one part of it with an EnKF and the other part with a particle filter.
The second part of this thesis deals with the application of Data Assimilation to multi-scale models and the problems that arise from that. One of the main areas of application for Data Assimilation techniques is predicting the development of oceans and the atmosphere. These processes involve several scales and often balance rela- tions between the state variables. The use of Data Assimilation procedures most often violates relations of that kind, which leads to unrealistic and non-physical pre- dictions of the future development of the process eventually. This work discusses the inclusion of a post-processing step after each assimilation step, in which a minimi- sation problem is solved, which penalises the imbalance. This method is tested on four different models, two Hamiltonian systems and two spatially extended models, which adds even more difficulties.
N2  - Diese Dissertation beschäftigt sich mit Daten Assimilation - die Kombination von Modellvorhersagen mit Beobachtungen. Sogenannte Filter sind dabei von beson- derem Interesse. Diese Algorithmen berechnen die Wahrscheinlichkeitsverteilung des Zustandes eines physikalischen Prozesses in der Zukunft unter der Bedingung, dass wir (meist) fehlerbehaftete Messungen vorliegen haben. Der erste Teil bezieht sich auf Hybridfilter, welche eine Brücke zwischen den beiden Hauptgruppen von Filtern schlagen: Ensemble-Kalman-Filter (EnKF) und Teilchenfilter. Die erst- genannten sind sehr stabil und rechnerisch unaufwändig, aber basieren auf recht starken Voraussetzungen. Teilchenfilter hingegen sind allgemeiner aber recheninten- siv und daher nicht immer geeignet für höherdimensionale Systeme. Daher besteht die Notwen-
digkeit beide Gruppen zu kombinieren um von den Vorteilen beider Filter zu prof- itieren. Dies kann erreicht werden, indem man, wenn eine Beobachtung assimiliert werden soll, die Likelihood-Funktion in zwei Teile spaltet und auf den einen Teil einen EnKF und auf den anderen einen Teilchenfilter anwendet.
Der zweite Teil dieser Arbeit befasst sich mit der Anwendung von Daten Assimilation auf mehrskalige Modelle und die Probleme die daraus entstehen. Eines der Haup- tanwendungsgebiete für Daten Assimilation ist die Vorhersage der Entwicklung von Ozeanen und der Atmosphäre. Diese Prozesse finden auf mehreren Skalen statt und häufig bestehen Balancerelationen zwischen den Zustandsvariablen. Die Nutzung von Daten Assimilationstechniken zerstört diese Beziehungen häufig, was schließlich zu unrealistischen und unphysikalischen Vorhersagen führt. In dieser Dissertation wird vorgeschlagen, nach jedem Assimilationsschritt ein Minimierungsproblem zu lösen, welches die Imbalance als Strafterm beinhaltet. Diese Methode wird an vier verschiedenen Modellen getestet, zwei Hamiltonische Systeme und zwei Modelle mit räumlicher Ausdehnung, was zusätzliche Schwierigkeiten schafft.
T2  - Hybridfilter und Multiskalen-Modelle
KW  - Data Assimilation
KW  - Daten Assimilation
KW  - Bayesian Inference
KW  - bayessche Inferenz
KW  - Uncertainty Quantification
KW  - Quantifizierung von Unsicherheit
KW  - Data-Driven Methods
KW  - Datengetriebene Methoden
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-474356
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  - Zass, Alexander
T1  - A Gibbs point process of diffusions: Existence and uniqueness
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-opus4-471951
SN  - 978-3-86956-485-2
SN  - 2199-4951
SN  - 2199-496X
IS  - 6
SP  - 13
EP  - 22
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  - 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  - Ludewig, Matthias
A1  - Rosenberger, Elke
T1  - Asymptotic eigenfunctions for Schrödinger operators on a vector bundle
JF  - Reviews in mathematical physics
N2  - In the limit (h) over bar -> 0, we analyze a class of Schrödinger operators H-(h) over bar = (h) over bar L-2 + (h) over barW + V .id(epsilon) acting on sections of a vector bundle epsilon over a Riemannian manifold M where L is a Laplace type operator, W is an endomorphism field and the potential energy V has a non-degenerate minimum at some point p is an element of M. We construct quasimodes of WKB-type near p for eigenfunctions associated with the low-lying eigenvalues of H-(h) over bar. These are obtained from eigenfunctions of the associated harmonic oscillator H-p,H-(h) over bar at p, acting on smooth functions on the tangent space.
KW  - Semi-classical analysis
KW  - WKB approximation
KW  - Schrödinger operators
KW  - semi-classical limit
Y1  - 2020
U6  - https://doi.org/10.1142/S0129055X20500208
SN  - 0129-055X
SN  - 1793-6659
VL  - 32
IS  - 7
PB  - World Scientific
CY  - Singapore
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  - Beckus, Siegfried
A1  - Pinchover, Yehuda
T1  - Shnol-type theorem for the Agmon ground state
JF  - Journal of spectral theory
N2  - LetH be a Schrodinger operator defined on a noncompact Riemannianmanifold Omega, and let W is an element of L-infinity (Omega; R). Suppose that the operator H + W is critical in Omega, and let phi be the corresponding Agmon ground state. We prove that if u is a generalized eigenfunction ofH satisfying vertical bar u vertical bar <= C-phi in Omega for some constant C > 0, then the corresponding eigenvalue is in the spectrum of H. The conclusion also holds true if for some K is an element of Omega the operator H admits a positive solution in (Omega) over bar = Omega \ K, and vertical bar u vertical bar <= C psi in (Omega) over bar for some constant C > 0, where psi is a positive solution of minimal growth in a neighborhood of infinity in Omega. Under natural assumptions, this result holds also in the context of infinite graphs, and Dirichlet forms.
KW  - Shnol theorem
KW  - Caccioppoli inequality
KW  - Schrodinger operators
KW  - generalized eigenfunction
KW  - ground state
KW  - positive solutions
KW  - weighted
KW  - graphs
Y1  - 2020
U6  - https://doi.org/10.4171/JST/296
SN  - 1664-039X
SN  - 1664-0403
VL  - 10
IS  - 2
SP  - 355
EP  - 377
PB  - EMS Publishing House
CY  - Zürich
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  - THES
A1  - Rothe, Viktoria
T1  - Das Yamabe-Problem auf global-hyperbolischen Lorentz-Mannigfaltigkeiten
N2  - Im Jahre 1960 behauptete Yamabe folgende Aussage bewiesen zu haben: Auf jeder kompakten Riemannschen Mannigfaltigkeit (M,g) der Dimension n ≥ 3 existiert eine zu g konform äquivalente Metrik mit konstanter Skalarkrümmung. Diese Aussage ist äquivalent zur Existenz einer Lösung einer bestimmten semilinearen elliptischen Differentialgleichung, der Yamabe-Gleichung. 1968 fand Trudinger einen Fehler in seinem Beweis und infolgedessen beschäftigten sich viele Mathematiker mit diesem nach Yamabe benannten Yamabe-Problem. In den 80er Jahren konnte durch die Arbeiten von Trudinger, Aubin und Schoen gezeigt werden, dass diese Aussage tatsächlich zutrifft. Dadurch ergeben sich viele Vorteile, z.B. kann beim Analysieren von konform invarianten partiellen Differentialgleichungen auf kompakten Riemannschen Mannigfaltigkeiten die Skalarkrümmung als konstant vorausgesetzt werden.
Es stellt sich nun die Frage, ob die entsprechende Aussage auch auf Lorentz-Mannigfaltigkeiten gilt. Das Lorentz'sche Yamabe Problem lautet somit: Existiert zu einer gegebenen räumlich kompakten global-hyperbolischen Lorentz-Mannigfaltigkeit (M,g) eine zu g konform äquivalente Metrik mit konstanter Skalarkrümmung? Das Ziel dieser Arbeit ist es, dieses Problem zu untersuchen. 
Bei der  sich aus dieser Fragestellung ergebenden Yamabe-Gleichung handelt es sich um eine semilineare Wellengleichung, deren Lösung eine positive glatte Funktion ist und aus der sich der konforme Faktor ergibt. Um die für die Behandlung des Yamabe-Problems benötigten Grundlagen so allgemein wie möglich zu halten, wird im ersten Teil dieser Arbeit die lokale Existenztheorie für beliebige semilineare Wellengleichungen für Schnitte auf Vektorbündeln im Rahmen eines Cauchy-Problems entwickelt. Hierzu wird der Umkehrsatz für Banachräume angewendet, um mithilfe von bereits existierenden Existenzergebnissen zu linearen Wellengleichungen, Existenzaussagen zu semilinearen Wellengleichungen machen zu können. Es wird bewiesen, dass, falls die Nichtlinearität bestimmte Bedingungen erfüllt, eine fast zeitglobale Lösung des Cauchy-Problems für kleine Anfangsdaten sowie eine zeitlokale Lösung für beliebige Anfangsdaten existiert. 
Der zweite Teil der Arbeit befasst sich mit der Yamabe-Gleichung auf global-hyperbolischen Lorentz-Mannigfaltigkeiten. Zuerst wird gezeigt, dass die Nichtlinearität der Yamabe-Gleichung die geforderten Bedingungen aus dem ersten Teil erfüllt, so dass, falls die Skalarkrümmung der gegebenen Metrik nahe an einer Konstanten liegt, kleine Anfangsdaten existieren, so dass die Yamabe-Gleichung eine fast zeitglobale Lösung besitzt. Mithilfe von Energieabschätzungen wird anschließend für 4-dimensionale global-hyperbolische Lorentz-Mannigfaltigkeiten gezeigt, dass unter der Annahme, dass die konstante Skalarkrümmung der konform äquivalenten Metrik nichtpositiv ist, eine zeitglobale Lösung der Yamabe-Gleichung existiert, die allerdings nicht notwendigerweise positiv ist. Außerdem wird gezeigt, dass, falls die H2-Norm der Skalarkrümmung bezüglich der gegebenen Metrik auf einem kompakten Zeitintervall auf eine bestimmte Weise beschränkt ist, die Lösung positiv auf diesem Zeitintervall ist. Hierbei wird ebenfalls angenommen, dass die konstante Skalarkrümmung der konform äquivalenten Metrik nichtpositiv ist. Falls zusätzlich hierzu gilt, dass die Skalarkrümmung bezüglich der gegebenen Metrik negativ ist und die Metrik gewisse Bedingungen erfüllt, dann ist die Lösung für alle Zeiten in einem kompakten Zeitintervall positiv, auf dem der Gradient der Skalarkrümmung auf eine bestimmte Weise beschränkt ist. In beiden Fällen folgt unter den angeführten Bedingungen die Existenz einer zeitglobalen positiven Lösung, falls M = I x Σ für ein beschränktes offenes Intervall I ist. Zum Schluss wird für M = R x Σ ein Beispiel für die Nichtexistenz einer globalen positiven Lösung angeführt.
N2  - Yamabe claimed in 1960 that he had proven the following theorem: Any Riemannian metric g on a compact smooth manifold M of dimension n ≥ 3 is conformal to a metric with constant scalar curvature. An equivalent formulation of this theorem is the existence of a solution to a certain semilinear elliptic differential equation, the so-called Yamabe equation. In 1968 Trudinger found a mistake in Yamabe's paper and consequently many mathematicians dealt with this so-called Yamabe problem. In the 80s Trudinger, Aubin and Shoen were able to fix the mistake and prove that Yamabe's theorem was indeed true. This has many advantages, for example when analyzing a conformally invariant partial differential equation on compact Riemannian manifolds one can assume that the scalar curvature is constant. 
The question now arises whether the analogous statement on Lorentzian manifolds also applies. The Lorentzian Yamabe Problem can be stated as follows: Given a spatially compact globally hyperbolic Lorentzian manifold (M, g), does there exist a metric conformal to g with constant scalar curvature? The goal of this dissertation is to examine this problem. 
The Yamabe equation which arises from this question is a semilinear wave equation which must have a positive smooth solution. In the first part of this dissertation the local theory of existence of general semilinear wave equations for sections on vector bundles was developed. For this the inverse function theorem and already existing statements about the existence of solutions to linear wave equation on Lorentzian manifolds were used. It will be proven that there exists an almost global solution to the corresponding Cauchy problem for small initial data as well as a time local solution for arbitrary initial data if the nonlinearity fulfills certain conditions. 
The second part of the dissertation deals with the Yamabe equation on globally hyperbolic Lorentzian manifolds. First by using the results of the first part it will be proven that there exist initial data such that the Yamabe equation has an almost time global solution if the scalar curvature of the given metric is sufficiently close to a constant. Afterwards by using energy estimates it will be shown in the case of 4-dimensional Lorentzian manifolds that under the assumption that the constant scalar curvature of the conformal metric is non-positive there exists a global smooth solution to the Yamabe equation which is not necessarily positive. But it will be proven that the solution is positive on a compact time interval if the H2-Norm of the scalar curvature of the given metric is bounded on this time interval in a certain way or if the scalar curvature is negative and the gradient of the scalar curvature is bounded in a specific way. In both cases the existence of a global positive smooth solution follows, if the Lorentzian manifold has the form M = I x Σ where I is an open bounded time interval and Σ is a Riemannian manifold. At the end an example for the nonexistence of a global positive solution in the case of M= R x Σ will be presented.
T2  - The Yamabe problem on globally hyperbolic Lorentzian manifolds
KW  - Yamabe-Problem
KW  - Yamabe problem
KW  - wave equation
KW  - globally hyperbolic
KW  - global-hyperbolisch
KW  - Wellengleichung
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-486012
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  - THES
A1  - Tschisgale, Paul
T1  - Introduction to the Glauber dynamics for the Curie-Weiss Potts model
N2  - This thesis aims at presenting in an organized fashion the required basics to understand the Glauber dynamics as a way of simulating configurations according to the Gibbs distribution of the Curie-Weiss Potts model. Therefore, essential aspects of discrete-time Markov chains on a finite state space are examined, especially their convergence behavior and related mixing times. Furthermore, special emphasis is placed on a consistent and comprehensive presentation of the Curie-Weiss Potts model and its analysis. Finally, the Glauber dynamics is studied in general and applied afterwards in an exemplary way to the Curie-Weiss model as well as the Curie-Weiss Potts model. The associated considerations are supplemented with two computer simulations aiming to show the cutoff phenomenon and the temperature dependence of the convergence behavior.
N2  - Die vorliegende Arbeit verfolgt das Ziel, die erforderlichen Grundlagen für das Verständnis der Glauber Dynamik auf organisierte Art und Weise darzustellen. Die Glauber Dynamik stellt eine Möglichkeit der Simulation von Konfigurationen der Gibbs Verteilung des Curie-Weiss Potts Modells dar. Es werden zunächst die zum Verständnis notwendigen Grundlagen von endlichen Markov-Ketten in diskreter Zeit beleuchtet, insbesondere ihr Konvergenzverhalten und die damit verbundene Mischzeit. Darüber hinaus legt diese Arbeit einen Schwerpunkt auf eine konsistente sowie verständliche Darbietung und Analyse des Curie-Weiss Potts Modells. Schließlich wird explizit die Glauber Dynamik betrachtet und anschließend exemplarisch auf das Curie-Weiss Modell und auf das Curie-Weiss Potts Modell angewandt. Die dazugehörigen Betrachtungen werden durch zwei Computersimulationen ergänzt, welche darauf abzielen, das Cutoff-Phänomen sowie die Temperaturabhängigkeit des Konvergenzverhaltens darzustellen bzw. zu verdeutlichen.
T2  - Einführung in die Glauber Dynamik des Curie-Weiss Potts Modells
KW  - Glauber Dynamics
KW  - Curie-Weiss Potts Model
KW  - Mixing Times
KW  - MCMC
KW  - Glauber Dynamik
KW  - Curie-Weiss Potts Modell
KW  - Mischzeiten
KW  - MCMC-Verfahren
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-486769
ER  - 
TY  - THES
A1  - Friedrich, Alexander
T1  - Minimizers of generalized Willmore energies and applications in general relativity
N2  - Das Willmore Funktional ist eine Funktion die jeder Fläche in einer Riemannschen Mannigfaltigkeit, ihre totale mittlere Krümmung zuweist. Ein klassisches Problem der Differentialgeometrie ist es geschlossene (kompakt und ohne Rand) Flächen zu finden die das Willmore funktional minimieren, beziehungsweise die kritische Punkte des Willmore Funktionals sind.

In dieser Doktorarbeit entwickeln wir ein Konzept von verallgemeinerten Willmore Funktionalen für Flächen in Riemannschen Mannigfaltigkeiten, wobei wir uns von physikalischen Modellen leiten lassen. Insbesondere ist hier die Hawking Energie der allgemeinen Relativitätstheorie und die Biegungsenergie von dünnen Membranen zu nennen.

Für dieses verallgemeinerten Willmore Funktionale beweisen wir die Existenz von Minimieren mit vorgeschriebenen Flächeninhalt, in einer geeigneten Klasse von verallgemeinerten Flächen. Insbesondere konstruieren wir Minimierer der oben erwähnten Biegungsenergie mit vorgeschrieben Flächeninhalt und vorgeschriebenen, eingeschlossenem Volumen. Außerdem beweisen wir,  dass kritische Punkte von verallgemeinerten Willmore Funktionalen mit vorgeschriebenen Flächeninhalt abseits endlich vieler Punkte glatt sind. Dabei stützen wir uns, wie auch im folgenden, auf die bestehende Theorie für das Willmore Funktional.

An diese allgemeinen Resultate schließen wir eine detailliertere Analyse der Hawking Energie an. 

Im Kontext der allgemeinen Relativitätstheorie beschreibt die Umgebungsmannigfaltigkeit den Raum zu einem Zeitpunkt. Daher sind wir an dem Wechselspiel zwischen der Hawking Energie und der umgebenden Mannigfaltigkeit interessiert.

Wir charakterisieren Punkte in der umgebenden Mannigfaltigkeit für die es in jeder Umgebung eine kritische Fläche mit vorgeschriebenem, kleinem Flächeninhalt gibt. Diese Punnkte werden als Konzentrationspunkte der Hawking Energie interpretiert. Außerdem berechnen wir eine Entwicklung der Hawking Energie auf kleinen, runden Sphären. Dadurch können wir eine Art Energiedichte der Hawking Energie identifizieren.

Hierbei ist anzumerken, dass unsere Resultate im Kontrast zu Ergebnissen in der Literatur stehen. Dort wurde berechnet, dass die Entwicklung der Hawking Energie auf Sphären im Lichtkegel eines Punktes der umgebenden Mannigfaltigkeit in führender Ordnung proportional zur der klassischen Energiedichte der allgemeinen Relativitätstheorie ist.  Zu diesem Zeitpunkt ist nicht klar wie diese Diskrepanz zu begründen ist.

Ferner betrachten wir asymptotisch Schwarzschild Mannigfaltigkeiten. Sie sind ein Spezialfall von asymptotisch flachen Mannigfaltigkeiten, welche in der allgemeinen Relativitätstheorie als Modelle für isolierte Systeme dienen.    

Die Schwarzschild Raumzeit selbst ist eine rotationssymmetrische Raumzeit die schwarzen Loch beschreibt. In diesen asymptotisch Schwarzschild Mannigfaltigkeiten konstruieren wir eine Blätterung des äußeren Bereiches durch kritische Flächen der Hawking Energie mit vorgeschriebenen Flächeninhalt. Diese Blätterung kann in einem verallgemeinertem Sinne als Schwerpunkt des isolierten Systems betrachtet werden. Außerdem zeigen wir, dass die Hawking Energie entlang der Blätterung wächst je größer die Flächen werden.
N2  - The Willmore functional is a function that maps an immersed Riemannian manifold to its total mean curvature. Finding closed surfaces that minimizes the Willmore energy, or more generally finding critical surfaces, is a classic problem of differential geometry.

In this thesis we will develop the concept of generalized Willmore functionals for surfaces in Riemannian manifolds. We are guided by models in mathematical physics, such as the Hawking energy of general relativity and the bending energies for thin membranes.

We prove the existence of minimizers under area constraint for these generalized Willmore functionals in a  suitable class of generalized surfaces. In particular, we construct minimizers of the bending energy mentioned above for prescribed area and enclosed volume.
 
Furthermore, we prove that critical surfaces of generalized Willmore functionals with prescribed area are smooth, away from finitely many points. These results and the following are based on the existing theory for the Willmore functional.

This  general discussion is succeeded by a detailed analysis of the Hawking energy. In the context of general relativity the surrounding manifold describes the space at a given time, hence we strive  to understand the interplay between the Hawking energy and the ambient space. We characterize points in the surrounding manifold for which there are small critical spheres with prescribed area in any neighborhood. These points are interpreted as concentration points of the Hawking energy.

Additionally, we calculate an expansion of the Hawking energy on small, round spheres. This allows us to identify a kind of energy density of the Hawking energy.

It needs to be mentioned that our results stand in contrast to previous expansions of the Hawking energy. However, these expansions are obtained on spheres along the light cone at a given point. At this point it is not clear how to explain the discrepancy.

Finally, we consider asymptotically Schwarzschild manifolds. They are a special case of asymptotically flat manifolds, which serf as models for isolated systems. The Schwarzschild spacetime itself is a classical solution to the Einstein equations and yields a simple description of a black hole.   

In these asymptotically Schwarzschild manifolds we construct a  foliation of the exterior region by critical spheres of the Hawking energy with prescribed large area. This foliation can be seen as a generalized notion of the center of mass of the isolated system. Additionally, the Hawking energy of grows along the foliation as the area of the surfaces grows.
T2  - Minimierer von Verallgemeinerten Willmore Energien und Anwendungen in der Allgemeinen Relativitätstheorie
KW  - Partial Differential Equations
KW  - Calculus of Variation
KW  - Differential Geometry
KW  - Geometric Analysis
KW  - Mathematical Physics
KW  - Partielle Differential Gleichungen
KW  - Variationsrechung
KW  - Differential Geometrie
KW  - Geometrische Analysis
KW  - Mathematische Physik
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-481423
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  - 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  - JOUR
A1  - Gaidzik, Franziska
A1  - Pathiraja, Sahani Darschika
A1  - Saalfeld, Sylvia
A1  - Stucht, Daniel
A1  - Speck, Oliver
A1  - Thevenin, Dominique
A1  - Janiga, Gabor
T1  - Hemodynamic data assimilation in a subject-specific circle of Willis geometry
JF  - Clinical Neuroradiology
N2  - Purpose The anatomy of the circle of Willis (CoW), the brain's main arterial blood supply system, strongly differs between individuals, resulting in highly variable flow fields and intracranial vascularization patterns. To predict subject-specific hemodynamics with high certainty, we propose a data assimilation (DA) approach that merges fully 4D phase-contrast magnetic resonance imaging (PC-MRI) data with a numerical model in the form of computational fluid dynamics (CFD) simulations. Methods To the best of our knowledge, this study is the first to provide a transient state estimate for the three-dimensional velocity field in a subject-specific CoW geometry using DA. High-resolution velocity state estimates are obtained using the local ensemble transform Kalman filter (LETKF). Results Quantitative evaluation shows a considerable reduction (up to 90%) in the uncertainty of the velocity field state estimate after the data assimilation step. Velocity values in vessel areas that are below the resolution of the PC-MRI data (e.g., in posterior communicating arteries) are provided. Furthermore, the uncertainty of the analysis-based wall shear stress distribution is reduced by a factor of 2 for the data assimilation approach when compared to the CFD model alone. Conclusion This study demonstrates the potential of data assimilation to provide detailed information on vascular flow, and to reduce the uncertainty in such estimates by combining various sources of data in a statistically appropriate fashion.
KW  - hemodynamics
KW  - CFD
KW  - uncertainty quantification
KW  - PC-MRI
KW  - LETKF
Y1  - 2020
U6  - https://doi.org/10.1007/s00062-020-00959-2
SN  - 1869-1439
SN  - 1869-1447
VL  - 31
IS  - 3
SP  - 643
EP  - 651
PB  - Springer
CY  - Heidelberg
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  - JOUR
A1  - Xiong, Chao
A1  - Stolle, Claudia
A1  - Alken, Patrick
A1  - Rauberg, Jan
T1  - Relationship between large-scale ionospheric field-aligned currents and electron/ion precipitations
BT  - DMSP observations
JF  - Earth, planets and space
N2  - In this study, we have derived field-aligned currents (FACs) from magnetometers onboard the Defense Meteorological Satellite Project (DMSP) satellites. The magnetic latitude versus local time distribution of FACs from DMSP shows comparable dependences with previous findings on the intensity and orientation of interplanetary magnetic field (IMF)B(y)andB(z)components, which confirms the reliability of DMSP FAC data set. With simultaneous measurements of precipitating particles from DMSP, we further investigate the relation between large-scale FACs and precipitating particles. Our result shows that precipitation electron and ion fluxes both increase in magnitude and extend to lower latitude for enhanced southward IMFBz, which is similar to the behavior of FACs. Under weak northward and southwardB(z)conditions, the locations of the R2 current maxima, at both dusk and dawn sides and in both hemispheres, are found to be close to the maxima of the particle energy fluxes; while for the same IMF conditions, R1 currents are displaced further to the respective particle flux peaks. Largest displacement (about 3.5 degrees) is found between the downward R1 current and ion flux peak at the dawn side. Our results suggest that there exists systematic differences in locations of electron/ion precipitation and large-scale upward/downward FACs. As outlined by the statistical mean of these two parameters, the FAC peaks enclose the particle energy flux peaks in an auroral band at both dusk and dawn sides. Our comparisons also found that particle precipitation at dawn and dusk and in both hemispheres maximizes near the mean R2 current peaks. The particle precipitation flux maxima closer to the R1 current peaks are lower in magnitude. This is opposite to the known feature that R1 currents are on average stronger than R2 currents.
KW  - field-aligned currents
KW  - aurora
KW  - particle precipitation
KW  - DMSP
Y1  - 2020
U6  - https://doi.org/10.1186/s40623-020-01286-z
SN  - 1880-5981
VL  - 72
IS  - 1
PB  - Springer
CY  - New York
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  - Buttig, Steve
T1  - Europa Universalis IV
BT  - „Wir alle treffen Entscheidungen im Leben, aber letztendlich treffen unsere Entscheidungen uns.“ : didaktische Potenziale digitaler Spielwelten
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-485695
SN  - 978-3-86956-489-0
SP  - 159
EP  - 174
PB  - Universitätsverlag Potsdam
CY  - Potsdam
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  - CHAP
A1  - Démaris, Alise
A1  - Grišić, Ana-Marija
A1  - Huisinga, Wilhelm
A1  - Walter, Reinisch
A1  - Kloft, Charlotte
T1  - Evaluation of dosing strategies of anti-TNF alpha monoclonal antibodies using pharmacokinetic modelling and simulation
T2  - Journal of Crohn's and Colitis
N2  - Background:
Anti-TNFα monoclonal antibodies (mAbs) are a well-established treatment for patients with Crohn’s disease (CD). However, subtherapeutic concentrations of mAbs have been related to a loss of response during the first year of therapy1. Therefore, an appropriate dosing strategy is crucial to prevent the underexposure of mAbs for those patients. The aim of our study was to assess the impact of different dosing strategies (fixed dose or body size descriptor adapted) on drug exposure and the target concentration attainment for two different anti-TNFα mAbs: infliximab (IFX, body weight (BW)-based dosing) and certolizumab pegol (CZP, fixed dosing). For this purpose, a comprehensive pharmacokinetic (PK) simulation study was performed.

Methods:
A virtual population of 1000 clinically representative CD patients was generated based on the distribution of CD patient characteristics from an in-house clinical database (n = 116). Seven dosing regimens were investigated: fixed dose and per BW, lean BW (LBW), body surface area, height, body mass index and fat-free mass. The individual body size-adjusted doses were calculated from patient generated body size descriptor values. Then, using published PK models for IFX and CZP in CD patients2,3, for each patient, 1000 concentration–time profiles were simulated to consider the typical profile of a specific patient as well as the range of possible individual profiles due to unexplained PK variability across patients. For each dosing strategy, the variability in maximum and minimum mAb concentrations (Cmax and Cmin, respectively), area under the concentration-time curve (AUC) and the per cent of patients reaching target concentration were assessed during maintenance therapy.

Results:
For IFX and CZP, Cmin showed the highest variability between patients (CV ≈110% and CV ≈80%, respectively) with a similar extent across all dosing strategies. For IFX, the per cent of patients reaching the target (Cmin = 5 µg/ml) was similar across all dosing strategies (~15%). For CZP, the per cent of patients reaching the target average concentration of 17 µg/ml ranged substantially (52–71%), being the highest for LBW-adjusted dosing.

Conclusion:
By using a PK simulation approach, different dosing regimen of IFX and CZP revealed the highest variability for Cmin, the most commonly used PK parameter guiding treatment decisions, independent upon dosing regimen. Our results demonstrate similar target attainment with fixed dosing of IFX compared with currently recommended BW-based dosing. For CZP, the current fixed dosing strategy leads to comparable percentage of patients reaching target as the best performing body size-adjusted dosing (66% vs. 71%, respectively).
KW  - linical databases
KW  - crohn's disease
KW  - regimen
KW  - monoclonal antibodies
KW  - body surface area
KW  - infliximab
KW  - fat-free mass
KW  - certolizumab pegol
KW  - body mass index procedure
Y1  - 2020
U6  - https://doi.org/10.1093/ecco-jcc/jjz203.201
SN  - 1873-9946
SN  - 1876-4479
VL  - 14
IS  - Supp. 1
SP  - S171
EP  - S172
PB  - Oxford Univ. Press
CY  - Oxford
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  - 
TY  - JOUR
A1  - Roos, Saskia
T1  - The Dirac operator under collapse to a smooth limit space
JF  - Annals of global analysis and geometry
N2  - Let (M-i, g(i))(i is an element of N) be a sequence of spin manifolds with uniform bounded curvature and diameter that converges to a lower-dimensional Riemannian manifold (B, h) in the Gromov-Hausdorff topology. Then, it happens that the spectrum of the Dirac operator converges to the spectrum of a certain first-order elliptic differential operator D-B on B. We give an explicit description of D-B and characterize the special case where D-B equals the Dirac operator on B.
KW  - Collapse
KW  - Dirac operator
KW  - Spin geometry
Y1  - 2019
U6  - https://doi.org/10.1007/s10455-019-09691-8
SN  - 0232-704X
SN  - 1572-9060
VL  - 57
IS  - 1
SP  - 121
EP  - 151
PB  - Springer
CY  - Dordrecht
ER  - 
TY  - JOUR
A1  - Leung, Tsz Yan
A1  - Leutbecher, Martin
A1  - Reich, Sebastian
A1  - Shepherd, Theodore G.
T1  - Atmospheric Predictability: Revisiting the Inherent Finite-Time Barrier
JF  - Journal of the atmospheric sciences
N2  - The accepted idea that there exists an inherent finite-time barrier in deterministically predicting atmospheric flows originates from Edward N. Lorenz’s 1969 work based on two-dimensional (2D) turbulence. Yet, known analytic results on the 2D Navier–Stokes (N-S) equations suggest that one can skillfully predict the 2D N-S system indefinitely far ahead should the initial-condition error become sufficiently small, thereby presenting a potential conflict with Lorenz’s theory. Aided by numerical simulations, the present work reexamines Lorenz’s model and reviews both sides of the argument, paying particular attention to the roles played by the slope of the kinetic energy spectrum. It is found that when this slope is shallower than −3, the Lipschitz continuity of analytic solutions (with respect to initial conditions) breaks down as the model resolution increases, unless the viscous range of the real system is resolved—which remains practically impossible. This breakdown leads to the inherent finite-time limit. If, on the other hand, the spectral slope is steeper than −3, then the breakdown does not occur. In this way, the apparent contradiction between the analytic results and Lorenz’s theory is reconciled.
KW  - Atmosphere
KW  - Turbulence
KW  - Error analysis
KW  - Spectral analysis
KW  - models
KW  - distribution
KW  - Numerical weather prediction
KW  - forecasting
Y1  - 2019
U6  - https://doi.org/10.1175/JAS-D-19-0057.1
SN  - 0022-4928
SN  - 1520-0469
VL  - 76
IS  - 12
SP  - 3883
EP  - 3892
PB  - American Meteorological Soc.
CY  - Boston
ER  - 
TY  - GEN
A1  - Beckus, Siegfried
A1  - Bellissard, Jean
A1  - De Nittis, Giuseppe
T1  - Corrigendum to:  Spectral continuity for aperiodic quantum systems I. General theory. - [Journal of functional analysis. - 275 (2018), 11, S. 2917 – 2977]
T2  - Journal of functional analysis
N2  - A correct statement of Theorem 4 in [1] is provided. The change does not affect the main results.
KW  - Haar system
Y1  - 2019
U6  - https://doi.org/10.1016/j.jfa.2019.06.001
SN  - 0022-1236
SN  - 1096-0783
VL  - 277
IS  - 9
SP  - 3351
EP  - 3353
PB  - Elsevier
CY  - San Diego
ER  - 
TY  - JOUR
A1  - Fernandes, Vitor H.
A1  - Koppitz, Jörg
A1  - Musunthia, Tiwadee
T1  - The Rank of the Semigroup of All Order-Preserving Transformations on a Finite Fence
JF  - Bulletin of the Malaysian Mathematical Sciences Society volume
N2  - A zig-zag (or fence) order is a special partial order on a (finite) set. In this paper, we consider the semigroup TFn of all order-preserving transformations on an n-element zig-zag-ordered set. We determine the rank of TFn and provide a minimal generating set for TFn. Moreover, a formula for the number of idempotents in TFn is given.
KW  - Transformation semigroups
KW  - Rank of semigroup
KW  - Idempotents
KW  - Order-preserving
KW  - Fence
KW  - Zig-zag order
Y1  - 2019
U6  - https://doi.org/10.1007/s40840-017-0598-1
SN  - 0126-6705
SN  - 2180-4206
VL  - 42
IS  - 5
SP  - 2191
EP  - 2211
PB  - Malaysian mathematical sciences sciences soc
CY  - Pulau Punang
ER  - 
TY  - JOUR
A1  - Shcherbakov, Robert
A1  - Zhuang, Jiancang
A1  - Zöller, Gert
A1  - Ogata, Yosihiko
T1  - Forecasting the magnitude of the largest expected earthquake
JF  - Nature Communications
N2  - The majority of earthquakes occur unexpectedly and can trigger subsequent sequences of events that can culminate in more powerful earthquakes. This self-exciting nature of seismicity generates complex clustering of earthquakes in space and time. Therefore, the problem of constraining the magnitude of the largest expected earthquake during a future time interval is of critical importance in mitigating earthquake hazard. We address this problem by developing a methodology to compute the probabilities for such extreme earthquakes to be above certain magnitudes. We combine the Bayesian methods with the extreme value theory and assume that the occurrence of earthquakes can be described by the Epidemic Type Aftershock Sequence process. We analyze in detail the application of this methodology to the 2016 Kumamoto, Japan, earthquake sequence. We are able to estimate retrospectively the probabilities of having large subsequent earthquakes during several stages of the evolution of this sequence.
Y1  - 2019
U6  - https://doi.org/10.1038/s41467-019-11958-4
SN  - 2041-1723
VL  - 10
PB  - Nature Publishing Group
CY  - London
ER  - 
TY  - JOUR
A1  - Conforti, Giovanni
A1  - Kosenkova, Tetiana
A1  - Roelly, Sylvie
T1  - Conditioned Point Processes with Application to Levy Bridges
JF  - Journal of theoretical probability
N2  - Our first result concerns a characterization by means of a functional equation of Poisson point processes conditioned by the value of their first moment. It leads to a generalized version of Mecke’s formula. En passant, it also allows us to gain quantitative results about stochastic domination for Poisson point processes under linear constraints. Since bridges of a pure jump Lévy process in Rd with a height a can be interpreted as a Poisson point process on space–time conditioned by pinning its first moment to a, our approach allows us to characterize bridges of Lévy processes by means of a functional equation. The latter result has two direct applications: First, we obtain a constructive and simple way to sample Lévy bridge dynamics; second, it allows us to estimate the number of jumps for such bridges. We finally show that our method remains valid for linearly perturbed Lévy processes like periodic Ornstein–Uhlenbeck processes driven by Lévy noise.
KW  - Ornstein-Uhlenbeck
Y1  - 2019
U6  - https://doi.org/10.1007/s10959-018-0863-8
SN  - 0894-9840
SN  - 1572-9230
VL  - 32
IS  - 4
SP  - 2111
EP  - 2134
PB  - Springer
CY  - New York
ER  - 
TY  - JOUR
A1  - Salamat, Mona
A1  - Zöller, Gert
A1  - Amini, Morteza
T1  - Prediction of the Maximum Expected Earthquake Magnitude in Iran:
BT  - from a Catalog with Varying Magnitude of Completeness and Uncertain Magnitudes
JF  - Pure and applied geophysics
N2  - This paper concerns the problem of predicting the maximum expected earthquake magnitude μ in a future time interval Tf given a catalog covering a time period T in the past. Different studies show the divergence of the confidence interval of the maximum possible earthquake magnitude m_{ max } for high levels of confidence (Salamat et al. 2017). Therefore, m_{ max } should be better replaced by μ (Holschneider et al. 2011). In a previous study (Salamat et al. 2018), μ is estimated for an instrumental earthquake catalog of Iran from 1900 onwards with a constant level of completeness ( {m0 = 5.5} ). In the current study, the Bayesian methodology developed by Zöller et al. (2014, 2015) is applied for the purpose of predicting μ based on the catalog consisting of both historical and instrumental parts. The catalog is first subdivided into six subcatalogs corresponding to six seismotectonic zones, and each of those zone catalogs is subsequently subdivided according to changes in completeness level and magnitude uncertainty. For this, broad and small error distributions are considered for historical and instrumental earthquakes, respectively. We assume that earthquakes follow a Poisson process in time and Gutenberg-Richter law in the magnitude domain with a priori unknown a and b values which are first estimated by Bayes' theorem and subsequently used to estimate μ. Imposing different values of m_{ max } for different seismotectonic zones namely Alborz, Azerbaijan, Central Iran, Zagros, Kopet Dagh and Makran, the results show considerable probabilities for the occurrence of earthquakes with Mw ≥ 7.5 in short Tf , whereas for long Tf, μ is almost equal to m_{ max }
KW  - Maximum expected earthquake magnitude
KW  - completeness levels
KW  - magnitude errors
KW  - Bayesian method
KW  - Iran
Y1  - 2019
U6  - https://doi.org/10.1007/s00024-019-02141-3
SN  - 0033-4553
SN  - 1420-9136
VL  - 176
IS  - 8
SP  - 3425
EP  - 3438
PB  - Springer
CY  - Basel
ER  - 
TY  - JOUR
A1  - Bär, Christian
A1  - Strohmaier, Alexander
T1  - An index theorem for Lorentzian manifolds with compact
spacelike Cauchy boundary
JF  - American Journal of Mathematics
N2  - We show that the Dirac operator on a compact globally hyperbolic Lorentzian spacetime with spacelike Cauchy boundary is a Fredholm operator if appropriate boundary conditions are imposed. We prove that the index of this operator is given by the same expression as in the index formula of Atiyah-Patodi-Singer for Riemannian manifolds with boundary. The index is also shown to equal that of a certain operator constructed from the evolution operator and a spectral projection on the boundary. In case the metric is of product type near the boundary a Feynman parametrix is constructed.
Y1  - 2019
U6  - https://doi.org/10.1353/ajm.2019.0037
SN  - 0002-9327
SN  - 1080-6377
VL  - 141
IS  - 5
SP  - 1421
EP  - 1455
PB  - Johns Hopkins Univ. Press
CY  - Baltimore
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
T1  - The partial clone of linear formulas
JF  - Siberian mathematical journal
N2  - A term t is linear if no variable occurs more than once in t. An identity s ≈ t is said to be linear if s and t are linear terms. Identities are particular formulas. As for terms superposition operations can be defined for formulas too. We define the arbitrary linear formulas and seek for a condition for the set of all linear formulas to be closed under superposition. This will be used to define the partial superposition operations on the set of linear formulas and a partial many-sorted algebra Formclonelin(τ, τ′). This algebra has similar properties with the partial many-sorted clone of all linear terms. We extend the concept of a hypersubstitution of type τ to the linear hypersubstitutions of type (τ, τ′) for algebraic systems. The extensions of linear hypersubstitutions of type (τ, τ′) send linear formulas to linear formulas, presenting weak endomorphisms of Formclonelin(τ, τ′).
KW  - term
KW  - formula
KW  - superposition
KW  - linear term
KW  - linear formula
KW  - clone
KW  - partial clone
KW  - linear hypersubstitution
Y1  - 2019
U6  - https://doi.org/10.1134/S0037446619040037
SN  - 0037-4466
SN  - 1573-9260
VL  - 60
IS  - 4
SP  - 572
EP  - 584
PB  - Pleiades Publ.
CY  - New York
ER  - 
TY  - JOUR
A1  - Lekkoksung, Nareupanat
A1  - Denecke, Klaus-Dieter
T1  - The partial clone of linear tree languages
JF  - Siberian mathematical journal
N2  - A term, also called a tree, is said to be linear, if each variable occurs in the term only once. The linear terms and sets of linear terms, the so-called linear tree languages, play some role in automata theory and in the theory of formal languages in connection with recognizability. We define a partial superposition operation on sets of linear trees of a given type and study the properties of some many-sorted partial clones that have sets of linear trees as elements and partial superposition operations as fundamental operations. The endomorphisms of those algebras correspond to nondeterministic linear hypersubstitutions.
KW  - linear term
KW  - linear tree language
KW  - clone
KW  - partial clone
KW  - linear hypersubstitution
KW  - nondeterministic linear hypersubstitution
Y1  - 2019
U6  - https://doi.org/10.1134/S0037446619030121
SN  - 0037-4466
SN  - 1573-9260
VL  - 60
IS  - 3
SP  - 497
EP  - 507
PB  - Pleiades Publ.
CY  - New York
ER  - 
TY  - THES
A1  - Jakobs, Friedrich
T1  - Dubrovin–rings and their connection to Hughes–free skew fields of fractions
T1  - Dubrovinringe und ihre Verbindung zu Hughes-freien Quotientenschiefkörpern
N2  - One method of embedding groups into skew fields was introduced by A. I. Mal'tsev and B. H. Neumann (cf. [18, 19]). If G is an ordered group and F is a skew field, the set F((G)) of formal power series over F in G with well-ordered support forms a skew field into which the group ring F[G] can be embedded. Unfortunately it is not suficient that G is left-ordered since F((G)) is only an F-vector space in this case as there is no natural way to define a multiplication on F((G)). One way to extend the original idea onto left-ordered groups is to examine the endomorphism ring of F((G)) as explored by N. I. Dubrovin (cf. [5, 6]). It is possible to embed any crossed product ring F[G; η, σ] into the endomorphism ring of F((G)) such that each non-zero element of F[G; η, σ] defines an automorphism of F((G)) (cf. [5, 10]). Thus, the rational closure of F[G; η, σ] in the endomorphism ring of F((G)), which we will call the Dubrovin-ring of F[G; η, σ], is a potential candidate for a skew field of fractions of F[G; η, σ]. The methods of N. I. Dubrovin allowed to show that specific classes of groups can be embedded into a skew field. For example, N. I. Dubrovin contrived some special criteria, which are applicable on the universal covering group of SL(2, R). These methods have also been explored by J. Gräter and R. P. Sperner (cf. [10]) as well as N.H. Halimi and T. Ito (cf. [11]). Furthermore, it is of interest to know if skew fields of fractions are unique. For example, left and right Ore domains have unique skew fields of fractions (cf. [2]). This is not the general case as for example the free group with 2 generators can be embedded into non-isomorphic skew fields of fractions (cf. [12]). It seems likely that Ore domains are the most general case for which unique skew fields of fractions exist. One approach to gain uniqueness is to restrict the search to skew fields of fractions with additional properties. I. Hughes has defined skew fields of fractions of crossed product rings F[G; η, σ] with locally indicable G which fulfill a special condition. These are called Hughes-free skew fields of fractions and I. Hughes has proven that they are unique if they exist [13, 14]. This thesis will connect the ideas of N. I. Dubrovin and I. Hughes. The first chapter contains the basic terminology and concepts used in this thesis. We present methods provided by N. I. Dubrovin such as the complexity of elements in rational closures and special properties of endomorphisms of the vector space of formal power series F((G)). To combine the ideas of N.I. Dubrovin and I. Hughes we introduce Conradian left-ordered groups of maximal rank and examine their connection to locally indicable groups. Furthermore we provide notations for crossed product rings, skew fields of fractions as well as Dubrovin-rings and prove some technical statements which are used in later parts. The second chapter focuses on Hughes-free skew fields of fractions and their connection to Dubrovin-rings. For that purpose we introduce series representations to interpret elements of Hughes-free skew fields of fractions as skew formal Laurent series. This 1 Introduction allows us to prove that for Conradian left-ordered groups G of maximal rank the statement "F[G; η, σ] has a Hughes-free skew field of fractions" implies "The Dubrovin ring of F [G; η, σ] is a skew field". We will also prove the reverse and apply the results to give a new prove of Theorem 1 in [13]. Furthermore we will show how to extend injective ring homomorphisms of some crossed product rings onto their Hughes-free skew fields of fractions. At last we will be able to answer the open question whether Hughes--free skew fields are strongly Hughes-free (cf. [17, page 53]).
N2  - In dieser Arbeit beschäftigen wir uns mit Quotientenschiefkörpern von verschränkten Produkten F [G; η, σ], wobei G eine Gruppe und F ein Schiefkörper ist. Eine Methode Gruppen in Schiefkörper einzubetten stammt von A. I. Mal’tsev und B. H. Neumann. Ist G eine beidseitig geordnete Gruppe, so lässt sich die Menge der formalen Potenzreihen F ((G)) über F in G mit wohlgeordnetem Träger als Schiefkörper interpretieren. In diesen lässt sich jedes verschränkte Produkt F [G; η, σ] einbetten. Möchte man die Klasse der einzubettenden Gruppen erweitern, so bieten sich links–geordnete Gruppen an. In diesem Fall hat F ((G)) keine natürliche Ringstruktur, aber man kann nutzen, dass F ((G)) ein rechter F–Vektorraum ist und seinen Endomorphismenring untersuchen. Jedes Verschränkte Produkt F [G; η, σ] lässt sich derart in den Endomorphismenring einbetten, dass die zugehörigen von Null verschiedenen Endomorphismen Automorphismen sind. Der rationale Abschluss von F [G; η, σ] in End(F ((G))), den wir Dubrovinring von F [G; η, σ] nennen, ist somit ein potentieller Quotientenschiefkörper von F [G; η, σ]. Neben der Existenz von Quotientenschiefkörpern ist deren Eindeutigkeit (bis auf Isomorphie) von Interesse. Im Gegensatz zum kommutativen Fall sind Quotientenschiefkörper im Allgemeinen nicht eindeutig. So lässt sich beispielsweise die freie Gruppe mit zwei Erzeugenden in nicht–isomorphe Quotientenschiefkörper einbetten. Eine große Klasse an Ringen, die eindeutige Quotientenschiefkörper besitzen, sind Ore–Bereiche. Vermutlich lässt sich diese Klasse nicht erweitern, ohne zusätzliche Eigenschaften der Quotientenschiefkörper zu verlangen. Eine solche Eigenschaft, im Folgenden Hughes–frei genannt, wurde von I. Hughes vorgeschlagen. Er konnte beweisen, dass Hughes–freie Quotientenschiefkörper eindeutig sind, wenn sie existieren. In dieser Arbeit verbinden wir die Ideen von I. Hughes und N. I. Dubrovin. Wir zeigen, dass die Elemente von Hughes–freien Quotientenschiefkörpern als formale schiefe Laurent–Reihen dargestellt werden können und dass diese Darstellungen in gewisser Weise eindeutig sind. Dieses Ergebnis nutzen wir um zu beweisen, dass die Aussagen “F [G; η, σ] besitzt einen Hughes–freien Quotientenschiefkörper” und “Der Dubrovinring von F [G; η, σ] ist ein Schiefkörper” äquivalent sind, wenn G eine links–geordnete Gruppe von Conrad–Typ mit maximalem Rang ist. Wir stellen den nötigen Begriffsapparat zur Verfügung. Dieser basiert vorwiegend auf den Arbeiten von N. I. Dubrovin und umfasst spezielle Eigenschaften der Endomorphismen von F ((G)) sowie die Komplexität von Elementen in rationalen Abschlüssen. Des Weiteren gehen wir auf links–geordnete Gruppen von Conrad–Typ ein und untersuchen ihren Zusammenhang mit lokal indizierbaren Gruppen, die eine grundlegende Rolle für Hughes–freie Quotientenschiefkörper spielen. Wir werden zeigen können, dass Dubrovinringe, die Schiefkörper sind, stark Hughes–freie Quotientenschiefkörper sind, was die offene Frage beantwortet, ob Hughes–freie Quotientenschiefkörper stark Hughes–frei sind. Außerdem werden wir einen alternativen Beweis der Eindeutigkeit von Hughes–freien Quotientenschiefkörpern präsentieren und die Fortsetzbarkeit von Automorphismen eines verschränkten Produkts auf Hughes–freie Quotientenschiefkörper untersuchen.
KW  - Hughes-free
KW  - Dubrovinring
KW  - left ordered groups
KW  - Conradian ordered groups
KW  - skew field of fraction
KW  - locally indicable
KW  - series representation
KW  - strongly Hughes-free
KW  - Hughes-frei
KW  - Dubrovinring
KW  - linksgeordnete Gruppen
KW  - geordnete Gruppen von Conrad-Typ
KW  - Quotientenschiefkörper
KW  - lokal indizierbar
KW  - Reihendarstellungen
KW  - stark Hughes-frei
Y1  - 2019
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-435561
ER  - 
TY  - JOUR
A1  - Clavier, Pierre J.
A1  - Guo, Li
A1  - Paycha, Sylvie
A1  - Zhang, Bin
T1  - An algebraic formulation of the locality principle in renormalisation
JF  - European Journal of Mathematics
N2  - We study the mathematical structure underlying the concept of locality which lies at the heart of classical and quantum field theory, and develop a machinery used to preserve locality during the renormalisation procedure. Viewing renormalisation in the framework of Connes and Kreimer as the algebraic Birkhoff factorisation of characters on a Hopf algebra with values in a Rota-Baxter algebra, we build locality variants of these algebraic structures, leading to a locality variant of the algebraic Birkhoff factorisation. This provides an algebraic formulation of the conservation of locality while renormalising. As an application in the context of the Euler-Maclaurin formula on lattice cones, we renormalise the exponential generating function which sums over the lattice points in a lattice cone. As a consequence, for a suitable multivariate regularisation, renormalisation from the algebraic Birkhoff factorisation amounts to composition by a projection onto holomorphic multivariate germs.
KW  - Locality
KW  - Renormalisation
KW  - Algebraic Birkhoff factorisation
KW  - Partial algebra
KW  - Hopf algebra
KW  - Rota-Baxter algebra
KW  - Multivariate meromorphic functions
KW  - Lattice cones
Y1  - 2019
U6  - https://doi.org/10.1007/s40879-018-0255-8
SN  - 2199-675X
SN  - 2199-6768
VL  - 5
IS  - 2
SP  - 356
EP  - 394
PB  - Springer
CY  - Cham
ER  - 
TY  - JOUR
A1  - Koltai, Peter
A1  - Lie, Han Cheng
A1  - Plonka, Martin
T1  - Frechet differentiable drift dependence of Perron-Frobenius and Koopman operators for non-deterministic dynamics
JF  - Nonlinearity
N2  - We prove the Fréchet differentiability with respect to the drift of Perron–Frobenius and Koopman operators associated to time-inhomogeneous ordinary stochastic differential equations. This result relies on a similar differentiability result for pathwise expectations of path functionals of the solution of the stochastic differential equation, which we establish using Girsanov's formula. We demonstrate the significance of our result in the context of dynamical systems and operator theory, by proving continuously differentiable drift dependence of the simple eigen- and singular values and the corresponding eigen- and singular functions of the stochastic Perron–Frobenius and Koopman operators.
KW  - stochastic differential equations
KW  - transfer operator
KW  - Koopman operator
KW  - Perron-Frobenius operator
KW  - smooth drift dependence
KW  - linear response
KW  - pathwise expectations
Y1  - 2019
U6  - https://doi.org/10.1088/1361-6544/ab1f2a
SN  - 0951-7715
SN  - 1361-6544
VL  - 32
IS  - 11
SP  - 4232
EP  - 4257
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  - 
TY  - JOUR
A1  - Sanchez, S.
A1  - Wicht, J.
A1  - Baerenzung, Julien
A1  - Holschneider, Matthias
T1  - Sequential assimilation of geomagnetic observations
BT  - perspectives for the reconstruction and prediction of core dynamics
JF  - Geophysical journal international
N2  - High-precision observations of the present-day geomagnetic field by ground-based observatories and satellites provide unprecedented conditions for unveiling the dynamics of the Earth’s core. Combining geomagnetic observations with dynamo simulations in a data assimilation (DA) framework allows the reconstruction of past and present states of the internal core dynamics. The essential information that couples the internal state to the observations is provided by the statistical correlations from a numerical dynamo model in the form of a model covariance matrix. Here we test a sequential DA framework, working through a succession of forecast and analysis steps, that extracts the correlations from an ensemble of dynamo models. The primary correlations couple variables of the same azimuthal wave number, reflecting the predominant axial symmetry of the magnetic field. Synthetic tests show that the scheme becomes unstable when confronted with high-precision geomagnetic observations. Our study has identified spurious secondary correlations as the origin of the problem. Keeping only the primary correlations by localizing the covariance matrix with respect to the azimuthal wave number suffices to stabilize the assimilation. While the first analysis step is fundamental in constraining the large-scale interior state, further assimilation steps refine the smaller and more dynamical scales. This refinement turns out to be critical for long-term geomagnetic predictions. Increasing the assimilation steps from one to 18 roughly doubles the prediction horizon for the dipole from about  tree to six centuries, and from 30 to about  60 yr for smaller observable scales. This improvement is also reflected on the predictability of surface intensity features such as the South Atlantic Anomaly. Intensity prediction errors are decreased roughly by a half when assimilating long observation sequences.
KW  - Magnetic field variations through time
KW  - Core dynamics
KW  - Dynamo: theories and simulations
KW  - Inverse theory
KW  - Probabilistic forecasting
Y1  - 2019
U6  - https://doi.org/10.1093/gji/ggz090
SN  - 0956-540X
SN  - 1365-246X
VL  - 217
IS  - 2
SP  - 1434
EP  - 1450
PB  - Oxford Univ. Press
CY  - Oxford
ER  - 
TY  - JOUR
A1  - van Leeuwen, Peter Jan
A1  - Kunsch, Hans R.
A1  - Nerger, Lars
A1  - Potthast, Roland
A1  - Reich, Sebastian
T1  - Particle filters for high-dimensional geoscience applications: A review
JF  - Quarterly journal of the Royal Meteorological Society
N2  - Particle filters contain the promise of fully nonlinear data assimilation. They have been applied in numerous science areas, including the geosciences, but their application to high-dimensional geoscience systems has been limited due to their inefficiency in high-dimensional systems in standard settings. However, huge progress has been made, and this limitation is disappearing fast due to recent developments in proposal densities, the use of ideas from (optimal) transportation, the use of localization and intelligent adaptive resampling strategies. Furthermore, powerful hybrids between particle filters and ensemble Kalman filters and variational methods have been developed. We present a state-of-the-art discussion of present efforts of developing particle filters for high-dimensional nonlinear geoscience state-estimation problems, with an emphasis on atmospheric and oceanic applications, including many new ideas, derivations and unifications, highlighting hidden connections, including pseudo-code, and generating a valuable tool and guide for the community. Initial experiments show that particle filters can be competitive with present-day methods for numerical weather prediction, suggesting that they will become mainstream soon.
KW  - hybrids
KW  - localization
KW  - nonlinear data assimilation
KW  - particle filters
KW  - proposal densities
Y1  - 2019
U6  - https://doi.org/10.1002/qj.3551
SN  - 0035-9009
SN  - 1477-870X
VL  - 145
IS  - 723
SP  - 2335
EP  - 2365
PB  - Wiley
CY  - Hoboken
ER  - 
TY  - JOUR
A1  - Bandara, Menaka Lashitha
A1  - Rosen, Andreas
T1  - Riesz continuity of the Atiyah-Singer Dirac operator under perturbations of local boundary conditions
JF  - Communications in partial differential equations
N2  - On a smooth complete Riemannian spin manifold with smooth compact boundary, we demonstrate that Atiyah-Singer Dirac operator in depends Riesz continuously on perturbations of local boundary conditions The Lipschitz bound for the map depends on Lipschitz smoothness and ellipticity of and bounds on Ricci curvature and its first derivatives as well as a lower bound on injectivity radius away from a compact neighbourhood of the boundary. More generally, we prove perturbation estimates for functional calculi of elliptic operators on manifolds with local boundary conditions.
KW  - Boundary value problems
KW  - Dirac operator
KW  - functional calculus
KW  - real-variable harmonic analysis
KW  - Riesz continuity
KW  - spectral flow
Y1  - 2019
U6  - https://doi.org/10.1080/03605302.2019.1611847
SN  - 0360-5302
SN  - 1532-4133
VL  - 44
IS  - 12
SP  - 1253
EP  - 1284
PB  - Taylor & Francis Group
CY  - Philadelphia
ER  - 
TY  - JOUR
A1  - Ringel, Lisa Maria
A1  - Somogyvári, Márk
A1  - Jalali, Mohammadreza
A1  - Bayer, Peter
T1  - Comparison of hydraulic and tracer tomography for discrete fracture network inversion
JF  - Geosciences
N2  - Fractures serve as highly conductive preferential flow paths for fluids in rocks, which are difficult to exactly reconstruct in numerical models. Especially, in low-conductive rocks, fractures are often the only pathways for advection of solutes and heat. The presented study compares the results from hydraulic and tracer tomography applied to invert a theoretical discrete fracture network (DFN) that is based on data from synthetic cross-well testing. For hydraulic tomography, pressure pulses in various injection intervals are induced and the pressure responses in the monitoring intervals of a nearby observation well are recorded. For tracer tomography, a conservative tracer is injected in different well levels and the depth-dependent breakthrough of the tracer is monitored. A recently introduced transdimensional Bayesian inversion procedure is applied for both tomographical methods, which adjusts the fracture positions, orientations, and numbers based on given geometrical fracture statistics. The used Metropolis-Hastings-Green algorithm is refined by the simultaneous estimation of the measurement error’s variance, that is, the measurement noise. Based on the presented application to invert the two-dimensional cross-section between source and the receiver well, the hydraulic tomography reveals itself to be more suitable for reconstructing the original DFN. This is based on a probabilistic representation of the inverted results by means of fracture probabilities.
KW  - hydraulic tomography
KW  - tracer tomography
KW  - DFN
KW  - Bayesian inversion
KW  - heterogeneity
KW  - fracture
KW  - hydrogeophysics
Y1  - 2019
U6  - https://doi.org/10.3390/geosciences9060274
SN  - 2076-3263
VL  - 9
IS  - 6
PB  - MDPI
CY  - Basel
ER  - 
TY  - JOUR
A1  - Beckus, Siegfried
A1  - Bellissard, Jean
A1  - Cornean, Horia
T1  - Holder Continuity of the Spectra for Aperiodic Hamiltonians
JF  - Annales de l'Institut Henri Poincaré
N2  - We study the spectral location of a strongly pattern equivariant Hamiltonians arising through configurations on a colored lattice. Roughly speaking, two configurations are "close to each other" if, up to a translation, they "almost coincide" on a large fixed ball. The larger this ball, the more similar they are, and this induces a metric on the space of the corresponding dynamical systems. Our main result states that the map which sends a given configuration into the spectrum of its associated Hamiltonian, is Holder (even Lipschitz) continuous in the usual Hausdorff metric. Specifically, the spectral distance of two Hamiltonians is estimated by the distance of the corresponding dynamical systems.
Y1  - 2019
U6  - https://doi.org/10.1007/s00023-019-00848-6
SN  - 1424-0637
SN  - 1424-0661
VL  - 20
IS  - 11
SP  - 3603
EP  - 3631
PB  - Springer
CY  - Cham
ER  - 
TY  - JOUR
A1  - Blanchard, Gilles
A1  - Zadorozhnyi, Oleksandr
T1  - Concentration of weakly dependent Banach-valued sums and applications to statistical learning methods
JF  - Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability
N2  - We obtain a Bernstein-type inequality for sums of Banach-valued random variables satisfying a weak dependence assumption of general type and under certain smoothness assumptions of the underlying Banach norm. We use this inequality in order to investigate in the asymptotical regime the error upper bounds for the broad family of spectral regularization methods for reproducing kernel decision rules, when trained on a sample coming from a tau-mixing process.
KW  - Banach-valued process
KW  - Bernstein inequality
KW  - concentration
KW  - spectral regularization
KW  - weak dependence
Y1  - 2019
U6  - https://doi.org/10.3150/18-BEJ1095
SN  - 1350-7265
SN  - 1573-9759
VL  - 25
IS  - 4B
SP  - 3421
EP  - 3458
PB  - International Statistical Institute
CY  - Voorburg
ER  -