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
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.
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 -