TY  - INPR
A1  - Krainer, Thomas
A1  - Schulze, Bert-Wolfgang
T1  - On the inverse of parabolic systems of partial differential equations of general form in an infinite space-time cylinder [Part 2: Chapter 3-5]
N2  - We consider general parabolic systems of equations on the infinite time interval in case of the underlying spatial configuration is a closed manifold. The solvability of equations is studied both with respect to time and spatial variables in exponentially weighted anisotropic Sobolev spaces, and existence and maximal regularity statements for parabolic equations are proved. Moreover, we analyze the long-time behaiour of solutions in terms of complete asymptotic expansions. These results are deduced from a pseudodifferential calculus that we construct explicitly. This algebra of operators is specifically designed to contain both the classical systems of parabolic equations of general form and their inverses, parabolicity being reflected purely on symbolic level. To this end, we assign t = ∞ the meaning of an anisotropic conical point, and prove that this interprtation is consistent with the natural setting in the analysis of parabolic PDE. Hence, major parts of this work consist of the construction of an appropriate anisotropiccone calculus of so-called Volterra operators. In particular, which is the most important aspect, we obtain the complete characterization of the microlocal and the global kernel structure of the inverse of parabolicsystems in an infinite space-time cylinder. Moreover, we obtain perturbation results for parabolic equations from the investigation of the ideal structure of the calculus.
T3  - Preprint - (2001) 15 
Y1  - 2001
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25992
ER  - 
TY  - INPR
A1  - Krainer, Thomas
A1  - Schulze, Bert-Wolfgang
T1  - On the inverse of parabolic systems of partial differential equations of general form in an infinite space-time cylinder [Part 3: Chapter 6+7]
N2  - We consider general parabolic systems of equations on the infinite time interval in case of the underlying spatial configuration is a closed manifold. The solvability of equations is studied both with respect to time and spatial variables in exponentially weighted anisotropic Sobolev spaces, and existence and maximal regularity statements for parabolic equations are proved. Moreover, we analyze the long-time behaiour of solutions in terms of complete asymptotic expansions. These results are deduced from a pseudodifferential calculus that we construct explicitly. This algebra of operators is specifically designed to contain both the classical systems of parabolic equations of general form and their inverses, parabolicity being reflected purely on symbolic level. To this end, we assign t = ∞ the meaning of an anisotropic conical point, and prove that this interprtation is consistent with the natural setting in the analysis of parabolic PDE. Hence, major parts of this work consist of the construction of an appropriate anisotropiccone calculus of so-called Volterra operators. In particular, which is the most important aspect, we obtain the complete characterization of the microlocal and the global kernel structure of the inverse of parabolicsystems in an infinite space-time cylinder. Moreover, we obtain perturbation results for parabolic equations from the investigation of the ideal structure of the calculus.
T3  - Preprint - (2001) 16 
Y1  - 2001
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26000
ER  - 
TY  - INPR
A1  - Schulze, Bert-Wolfgang
T1  - Operators with symbol hierarchies and iterated asymptotics
N2  - Contents: Introduction 1 Edge calculus with parameters 1.1 Cone asymptotics and Green symbols 1.2 Mellin edge symbols 1.3 The edge symbol algebra 1.4 Operators on a manifold with edges 2 Corner symbols and iterated asymptotics 2.1 Holomorphic corner symbols 2.2 Meromorphic corner symbols and ellipicity 2.3 Weighted corner Sobolev spaces 2.4 Iterated asymptotics 3 The edge corner algebra with trace and potential conditions 3.1 Green corner operators 3.2 Smoothing Mellin corner operators 3.3 The edge corner algebra 3.4 Ellipicity and regularity with asymptotics 3.5 Examples and remarks
T3  - Preprint - (2001) 10 
Y1  - 2001
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25948
ER  - 
TY  - INPR
A1  - Kapanadze, David
A1  - Schulze, Bert-Wolfgang
T1  - Symbolic calculus for boundary value problems on manifolds with edges
N2  - Boundary value problems for (pseudo-) differential operators on a manifold with edges can be characterised by a hierarchy of symbols. The symbol structure is responsible or ellipicity and for the nature of parametrices within an algebra of "edge-degenerate" pseudo-differential operators. The edge symbol component of that hierarchy takes values in boundary value problems on an infinite model cone, with edge variables and covariables as parameters. Edge symbols play a crucial role in this theory, in particular, the contribution with holomorphic operatot-valued Mellin symbols. We establish a calculus in s framework of "twisted homogenity" that refers to strongly continuous groups of isomorphisms on weighted cone Sobolev spaces. We then derive an equivalent representation with a particularly transparent composition behaviour.
T3  - Preprint - (2001) 21 
KW  - pseudo-differential boundary value problems
KW  - operators on manifolds with singularities
Y1  - 2001
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26046
ER  - 
TY  - INPR
A1  - Nazaikinskii, Vladimir
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
T1  - Quantization methods in differential equations : Chapter 11: Noncommutative analysis and high-frequency asymptotics
N2  - Content: Chapter 11: Noncommutative Analysis and High-Frequency Asymptotics 11.1 Statement of the Problem 11.2 Mixed Asymptotics: the General Scheme 11.3 The Asymptotic Solution of Main Problem 11.4 Analysis of the Asymptotic Solution
T3  - Preprint - (2000) 20 
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25857
ER  - 
TY  - INPR
A1  - Kytmanov, Aleksandr
A1  - Myslivets, Simona
A1  - Schulze, Bert-Wolfgang
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Elliptic problems for the Dolbeault complex
N2  - The inhomogeneous ∂-equations is an inexhaustible source of locally unsolvable equations, subelliptic estimates and other phenomena in partial differential equations. Loosely speaking, for the anaysis on complex manifolds with boundary nonelliptic problems are typical rather than elliptic ones. Using explicit integral representations we assign a Fredholm complex to the Dolbeault complex over an arbitrary bounded domain in C up(n).
T3  - Preprint - (2001) 13 
Y1  - 2001
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25979
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  - Rungrottheera, Wannarut
A1  - Lyu, Xiaojing
A1  - Schulze, Bert-Wolfgang
T1  - Parameter-dependent edge calculus and corner parametrices
JF  - Journal of nonlinear and convex analysis : an international journal
N2  - Let B be a compact manifold with smooth edge of dimension > 0. We study the interplay between parameter-dependent edge algebra algebra on B and operator families belonging to the corner calculus, and we characterize parametrices in the corner case.
KW  - Edge calculus
KW  - corner parametrices
Y1  - 2018
SN  - 1345-4773
SN  - 1880-5221
VL  - 19
IS  - 12
SP  - 2021
EP  - 2051
PB  - Yokohama Publishers
CY  - Yokohama
ER  - 
TY  - JOUR
A1  - Stauffer, Maxime
A1  - Mengesha, Isaak
A1  - Seifert, Konrad
A1  - Krawczuk, Igor
A1  - Fischer, Jens
A1  - Serugendo, Giovanna Di Marzo
T1  - A computational turn in policy process studies
BT  - coevolving network dynamics of policy change
JF  - Complexity
N2  - The past three decades of policy process studies have seen the emergence of a clear intellectual lineage with regard to complexity. Implicitly or explicitly, scholars have employed complexity theory to examine the intricate dynamics of collective action in political contexts. However, the methodological counterparts to complexity theory, such as computational methods, are rarely used and, even if they are, they are often detached from established policy process theory. Building on a critical review of the application of complexity theory to policy process studies, we present and implement a baseline model of policy processes using the logic of coevolving networks. Our model suggests that an actor's influence depends on their environment and on exogenous events facilitating dialogue and consensus-building. Our results validate previous opinion dynamics models and generate novel patterns. Our discussion provides ground for further research and outlines the path for the field to achieve a computational turn.
Y1  - 2022
U6  - https://doi.org/10.1155/2022/8210732
SN  - 1076-2787
SN  - 1099-0526
VL  - 2022
PB  - Wiley-Hindawi
CY  - London
ER  - 
TY  - JOUR
A1  - Hedayat Mahmoudi, Mahdi
A1  - Schulze, Bert-Wolfgang
T1  - Corner boundary value problems
JF  - Asian-European journal of mathematics
N2  - The paper develops some crucial steps in extending the first-order cone or edge calculus to higher singularity orders. We focus here on order 2, but the ideas are motivated by an iterative approach for higher singularities.
KW  - Mellin operators
KW  - Mellin oscillatory integrals
KW  - exit calculus
KW  - weighted Sobolev spaces
Y1  - 2016
U6  - https://doi.org/10.1142/S1793557117500541
SN  - 1793-5571
SN  - 1793-7183
VL  - 10
IS  - 1
PB  - World Scientific
CY  - Singapore
ER  - 
TY  - JOUR
A1  - Cseh, Agnes
A1  - Faenza, Yuri
A1  - Kavitha, Telikepalli
A1  - Powers, Vladlena
T1  - Understanding popular matchings via stable matchings
JF  - SIAM journal on discrete mathematics
N2  - An instance of the marriage problem is given by a graph G = (A boolean OR B, E), together with, for each vertex of G, a strict preference order over its neighbors. A matching M of G is popular in the marriage instance if M does not lose a head-to-head election against any matching where vertices are voters. Every stable matching is a min-size popular matching; another subclass of popular matchings that always exists and can be easily computed is the set of dominant matchings. A popular matching M is dominant if M wins the head-to-head election against any larger matching. Thus, every dominant matching is a max-size popular matching, and it is known that the set of dominant matchings is the linear image of the set of stable matchings in an auxiliary graph. Results from the literature seem to suggest that stable and dominant matchings behave, from a complexity theory point of view, in a very similar manner within the class of popular matchings. The goal of this paper is to show that there are instead differences in the tractability of stable and dominant matchings and to investigate further their importance for popular matchings. First, we show that it is easy to check if all popular matchings are also stable; however, it is co-NP hard to check if all popular matchings are also dominant. Second, we show how some new and recent hardness results on popular matching problems can be deduced from the NP-hardness of certain problems on stable matchings, also studied in this paper, thus showing that stable matchings can be employed to show not only positive results on popular matchings (as is known) but also most negative ones. Problems for which we show new hardness results include finding a min-size (resp., max-size) popular matching that is not stable (resp., dominant). A known result for which we give a new and simple proof is the NP-hardness of finding a popular matching when G is nonbipartite.
KW  - popular matching
KW  - stable matching
KW  - complexity
KW  - dominant matching
Y1  - 2022
U6  - https://doi.org/10.1137/19M124770X
SN  - 0895-4801
SN  - 1095-7146
VL  - 36
IS  - 1
SP  - 188
EP  - 213
PB  - Society for Industrial and Applied Mathematics
CY  - Philadelphia
ER  - 
TY  - THES
A1  - Khalil, Sara
T1  - Boundary Value Problems on Manifolds with Singularities
T1  - Randwertprobleme auf Mannigfaltigkeiten mit Singularitäten
N2  - In the thesis there are constructed new quantizations for pseudo-differential boundary value problems (BVPs) on manifolds with edge. The shape of operators comes from Boutet de Monvel’s calculus which exists on smooth manifolds with boundary. The singular case, here with edge and boundary, is much more complicated. The present approach simplifies the operator-valued symbolic structures by using suitable Mellin quantizations on infinite stretched model cones of wedges with boundary. The Mellin symbols themselves are, modulo smoothing ones, with asymptotics, holomorphic in the complex Mellin covariable. One of the main results is the construction of parametrices of elliptic elements in the corresponding operator algebra, including elliptic edge conditions.
N2  - In der Dissertation wurden neue Quantisierungen konstruiert für
pseudo-differentielle Randwertprobleme auf Mannigfaltigkeiten mit
Kanten-Singularitäten. Die Gestalt der hier behandelten Operatoren
ist motiviert durch Boutet de Monvels Kalkül, der auf glatten
Mannigfaltigkeiten mit Rand bekannt ist. Der singuläre Fall, hier mit
Kanten und Rand, ist weitaus komplizierter. Der gegenwärtige Zugang
vereinfacht die operatarwertigen Symbolstrukturen unter Verwendung
geeigneter Mellin-Quantisierungen auf unendlichen gestreckten Modell-
Kegeln, die entsprechenden Keilen mit Rand zugeordnet sind. Die
Mellin-Symbole selbst sind holomorph in der komplexen Mellin
Kovariablen bis auf glättende Restglieder mit Asymptotiken. Zu den
Hauptresultaten gehört die Konstruktion von Parametrices elliptischer
Elemente in der erzeugten Operator-Algebra, einschließlich
elliptischer Kanten-Bedingungen.
KW  - manifolds with singularities
KW  - boundary value problems
KW  - pseudo-differential equation
KW  - manifolds with edge
KW  - Boutet de Monvel's calculus
KW  - edge boundary value problems
KW  - Mannigfaltigkeiten mit Singularitäten
KW  - Randwertprobleme
KW  - pseudo-differentielle Gleichungen
KW  - Mannigfaltigkeiten mit Kante
KW  - Boutet de Monvels Kalkül
KW  - Kanten-Randwertprobleme
Y1  - 2018
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-419018
ER  - 
TY  - JOUR
A1  - Chang, Der-Chen
A1  - Khalil, Sara
A1  - Schulze, Bert-Wolfgang
T1  - Analysis on regular corner spaces
JF  - The journal of geometric analysis
N2  - We establish a new approach of treating elliptic boundary value problems (BVPs) on manifolds with boundary and regular corners, up to singularity order 2. Ellipticity and parametrices are obtained in terms of symbols taking values in algebras of BVPs on manifolds of corresponding lower singularity orders. Those refer to Boutet de Monvel's calculus of operators with the transmission property, see Boutet de Monvel (Acta Math 126:11-51, 1971) for the case of smooth boundary. On corner configuration operators act in spaces with multiple weights. We mainly study the case of upper left entries in the respective 2 x 2 operator block-matrices of such a calculus. Green operators in the sense of Boutet de Monvel (Acta Math 126:11-51, 1971) analogously appear in singular cases, and they are complemented by contributions of Mellin type. We formulate a result on ellipticity and the Fredholm property in weighted corner spaces, with parametrices of analogous kind.
KW  - Boutet de Monvel's calculus
KW  - Pseudo-differential operators
KW  - Singular cones
KW  - Mellin symbols with values in the edge calculus
KW  - Parametrices of elliptic operators
KW  - Kegel space
Y1  - 2021
U6  - https://doi.org/10.1007/s12220-021-00614-3
SN  - 1050-6926
SN  - 1559-002X
VL  - 31
IS  - 9
SP  - 9199
EP  - 9240
PB  - Springer
CY  - New York
ER  - 
TY  - THES
A1  - Mauerberger, Stefan
T1  - Correlation based Bayesian modeling
T1  - Korrelationsbasierte Bayesianische Modellierung
BT  - with applications in travel time tomography, seismic source inversion and magnetic field modeling
BT  - mit Anwendungen in der Laufzeittomographie, Seismischer Quellinversion und Magnetfeldmodellierung
N2  - The motivation for this work was the question of reliability and robustness of seismic tomography. The problem is that many earth models exist which can describe the underlying ground motion records equally well. Most algorithms for reconstructing earth models provide a solution, but rarely quantify their variability. If there is no way to verify the imaged structures, an interpretation is hardly reliable. The initial idea was to explore the space of equivalent earth models using Bayesian inference. However, it quickly became apparent that the rigorous quantification of tomographic uncertainties could not be accomplished within the scope of a dissertation.

In order to maintain the fundamental concept of statistical inference, less complex problems from the geosciences are treated instead. This dissertation aims to anchor Bayesian inference more deeply in the geosciences and to transfer knowledge from applied mathematics. The underlying idea is to use well-known methods and techniques from statistics to quantify the uncertainties of inverse problems in the geosciences. This work is divided into three parts:

Part I introduces the necessary mathematics and should be understood as a kind of toolbox. With a physical application in mind, this section provides a compact summary of all methods and techniques used. The introduction of Bayesian inference makes the beginning. Then, as a special case, the focus is on regression with Gaussian processes under linear transformations. The chapters on the derivation of covariance functions and the approximation of non-linearities are discussed in more detail.

Part II presents two proof of concept studies in the field of seismology. The aim is to present the conceptual application of the introduced methods and techniques with moderate complexity. The example about traveltime tomography applies the approximation of non-linear relationships. The derivation of a covariance function using the wave equation is shown in the example of a damped vibrating string. With these two synthetic applications, a consistent concept for the quantification of modeling uncertainties has been developed.

Part III presents the reconstruction of the Earth's archeomagnetic field. This application uses the whole toolbox presented in Part I and is correspondingly complex. The modeling of the past 1000 years is based on real data and reliably quantifies the spatial modeling uncertainties. The statistical model presented is widely used and is under active development.

The three applications mentioned are intentionally kept flexible to allow transferability to similar problems. The entire work focuses on the non-uniqueness of inverse problems in the geosciences. It is intended to be of relevance to those interested in the concepts of Bayesian inference.
N2  - Die Motivation für diese Arbeit war die Frage nach Verlässlichkeit und Belastbarkeit der seismischen Tomographie. Das Problem besteht darin, dass sehr viele Erdmodelle existieren welche die zugrundeliegenden seismischen Aufzeichnungen gleich gut beschreiben können. Die meisten Algorithmen zur Rekonstruktion von Erdmodellen liefern zwar eine Lösung, quantifizierten jedoch kaum deren Variabilität. Wenn es keine Möglichkeit gibt die abgebildeten Strukturen zu verifizieren, so ist eine Interpretation kaum verlässlich. Der ursprüngliche Gedanke war den Raum äquivalenter Erdmodelle mithilfe Bayesianische Inferenz zu erkunden. Es stellte sich jedoch schnell heraus, dass die vollständige Quantifizierung tomographischer Unsicherheiten im Rahmen einer Promotion nicht zu bewältigen ist.

Um das wesentliche Konzept der statistischen Inferenz beizubehalten werden stattdessen weniger komplexe Problemstellungen aus den Geowissenschaften behandelt. Diese Dissertation hat das Ziel die Bayesianische Inferenz tiefer in den Geowissenschaften zu verankern und Wissen aus der angewandten Mathematik zu transferieren. Die zugrundeliegende Idee besteht darin auf bekannte Methoden und Techniken der Statistik zurückzugreifen um die Unsicherheiten inverser Probleme in den Geowissenschaften zu quantifizieren. Diese Arbeit gliedert sich in drei Teile:

Teil I führt die notwendige Mathematik ein und soll als eine Art Werkzeugkasten verstanden werden. In Hinblick auf eine physikalische Anwendung bietet dieser Abschnitt eine kompakte Zusammenfassung aller eingesetzter Methoden und Techniken. Den Anfang macht die Einführung der Bayesianische Inferenz. Danach steht als Spezialfall die Regression mit Gauß-Prozessen unter linearen Transformationen im Vordergrund. Die Kapitel zur Herleitung von Kovarianzfunktionen und die Approximation von Nichtlinearitäten gehen etwas weiter in die Tiefe.

Teil II präsentiert zwei Konzeptstudien aus dem Bereich der Seismologie. Ziel ist es bei moderater Komplexität die prinzipielle Anwendung der eingeführten Methoden und Techniken zu präsentieren. Das Beispiel zur Laufzeittomographie wendet die Näherungs\-methoden für nichtlineare Zusammenhänge an. Die Herleitung einer Kovarianzfunktion mithilfe der Wellengleichung ist am Beispiel der gedämpften Saitenschwingung gezeigt. Mit diesen beiden synthetischen Anwendungen wurde ein konsistentes Konzept zur Quantifizierung von Modellierungsunsicherheiten erarbeitet.

Teil III präsentiert die Rekonstruktion des archeomagnetischen Feldes unserer Erde. Diese Anwendung nutzt den gesamten Werkzeugkasten aus Teil I und ist entsprechend umfangreich. Die Modellierung der vergangenen 1000 Jahre basiert auf echten Daten und quantifiziert zuverlässig die räumlichen Modellierungsunsicherheiten. Das präsentierte statistische Modell findet breite Anwendung und wird aktiv weiter entwickelt.

Die drei genannten Anwendungen sind bewusst flexibel gehalten um die Übertragbarkeit auf ähnliche Problemstellungen zu ermöglichen. Die gesamte Arbeit legt den Fokus auf die nicht-Eindeutigkeit inverser Probleme in den Geowissenschaften. Sie will für all Jene von Relevanz sein, die sich für die Konzepte der Bayesianischen Inferenz interessieren.
KW  - statistical inference
KW  - Bayesian inversion
KW  - travel time tomography
KW  - seismic source inversion
KW  - magnetic field modeling
KW  - mit Anwendungen in der Laufzeittomographie, Seismischer Quellinversion und Magnetfeldmodellierung
KW  - Magnetfeldmodellierung
KW  - seismische Quellinversion
KW  - statistische Inferenz
KW  - Laufzeittomographie
Y1  - 2022
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-537827
ER  - 
TY  - JOUR
A1  - Eckert, Silvia
A1  - Herden, Jasmin
A1  - Stift, Marc
A1  - Durka, Walter
A1  - Kleunen, Mark van
A1  - Joshi, Jasmin Radha
T1  - Traces of genetic but not epigenetic adaptation in the invasive goldenrod Solidago canadensis despite the absence of population structure
JF  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - Biological invasions may result from multiple introductions, which might compensate for reduced gene pools caused by bottleneck events, but could also dilute adaptive processes. A previous common-garden experiment showed heritable latitudinal clines in fitness-related traits in the invasive goldenrod Solidago canadensis in Central Europe. These latitudinal clines remained stable even in plants chemically treated with zebularine to reduce epigenetic variation. However, despite the heritability of traits investigated, genetic isolation-by-distance was non-significant. Utilizing the same specimens, we applied a molecular analysis of (epi)genetic differentiation with standard and methylation-sensitive (MSAP) AFLPs. We tested whether this variation was spatially structured among populations and whether zebularine had altered epigenetic variation. Additionally, we used genome scans to mine for putative outlier loci susceptible to selection processes in the invaded range. Despite the absence of isolation-by-distance, we found spatial genetic neighborhoods among populations and two AFLP clusters differentiating northern and southern Solidago populations. Genetic and epigenetic diversity were significantly correlated, but not linked to phenotypic variation. Hence, no spatial epigenetic patterns were detected along the latitudinal gradient sampled. Applying genome-scan approaches (BAYESCAN, BAYESCENV, RDA, and LFMM), we found 51 genetic and epigenetic loci putatively responding to selection. One of these genetic loci was significantly more frequent in populations at the northern range. Also, one epigenetic locus was more frequent in populations in the southern range, but this pattern was lost under zebularine treatment. Our results point to some genetic, but not epigenetic adaptation processes along a large-scale latitudinal gradient of S. canadensis in its invasive range.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1271 
KW  - AFLP
KW  - MSAP
KW  - cytosine methylation
KW  - spatial autocorrelation
KW  - genome scan
Y1  - 2022
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-566758
SN  - 1866-8372
SP  - 1
EP  - 17
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - GEN
A1  - Böckmann, Christine
A1  - Ritter, Christoph
A1  - Cappelletti, David
T1  - Mathematical tool for a closure study of aerosol microphysical property retrieval using lidar and photometer data
T2  - IGARSS 2018 - 2018 IEEE International Geoscience and Remote Sensing Symposium
N2  - We present a project combining lidar, photometer and particle counter data with a regularization software tool for a closure study of aerosol microphysical property retrieval. In a first step only lidar data are used to retrieve the particle size distribution (PSD). Secondly, photometer data are added, which results in a good consistency of the retrieved PSDs. Finally, those retrieved PSDs may be compared with the measured PSD from a particle counter. The data here were taken in Ny Alesund, Svalbard, as an example.
KW  - Aerosol
KW  - Raman lidar
KW  - photometer
KW  - inversion
KW  - regularization
KW  - particle microphysics
Y1  - 2018
SN  - 978-1-5386-7150-4
U6  - https://doi.org/10.1109/IGARSS.2018.8518674
SN  - 2153-6996
SP  - 5575
EP  - 5578
PB  - IEEE
CY  - New York
ER  - 
TY  - JOUR
A1  - Dube, Jonas
A1  - Böckmann, Christine
A1  - Ritter, Christoph
T1  - Lidar-Derived Aerosol Properties from Ny-Ålesund, Svalbard during the MOSAiC Spring 2020
JF  - Remote sensing / Molecular Diversity Preservation International (MDPI)
N2  - In this work, we present Raman lidar data (from a Nd:YAG operating at 355 nm, 532 nm and 1064 nm) from the international research village Ny-Alesund for the time period of January to April 2020 during the Arctic haze season of the MOSAiC winter. We present values of the aerosol backscatter, the lidar ratio and the backscatter Angstrom exponent, though the latter depends on wavelength. The aerosol polarization was generally below 2%, indicating mostly spherical particles. We observed that events with high backscatter and high lidar ratio did not coincide. In fact, the highest lidar ratios (LR > 75 sr at 532 nm) were already found by January and may have been caused by hygroscopic growth, rather than by advection of more continental aerosol. Further, we performed an inversion of the lidar data to retrieve a refractive index and a size distribution of the aerosol. Our results suggest that in the free troposphere (above approximate to 2500 m) the aerosol size distribution is quite constant in time, with dominance of small particles with a modal radius well below 100 nm. On the contrary, below approximate to 2000 m in altitude, we frequently found gradients in aerosol backscatter and even size distribution, sometimes in accordance with gradients of wind speed, humidity or elevated temperature inversions, as if the aerosol was strongly modified by vertical displacement in what we call the "mechanical boundary layer". Finally, we present an indication that additional meteorological soundings during MOSAiC campaign did not necessarily improve the fidelity of air backtrajectories.
KW  - aerosol
KW  - Arctic haze
KW  - lidar
KW  - microphysical properties
KW  - backtrajectories;
KW  - Ny-Alesund
KW  - Svalbard
KW  - MOSAiC
KW  - aerosol-boundary layer interactions
Y1  - 2022
U6  - https://doi.org/10.3390/rs14112578
SN  - 2072-4292
VL  - 14
IS  - 11
PB  - MDPI
CY  - Basel
ER  - 
TY  - JOUR
A1  - Pornsawad, Pornsarp
A1  - Sapsakul, Nantawan
A1  - Böckmann, Christine
T1  - A modified asymptotical regularization of nonlinear ill-posed problems
JF  - Mathematics
N2  - In this paper, we investigate the continuous version of modified iterative Runge–Kutta-type methods for nonlinear inverse ill-posed problems proposed in a previous work. The convergence analysis is proved under the tangential cone condition, a modified discrepancy principle, i.e., the stopping time T is a solution of ∥𝐹(𝑥𝛿(𝑇))−𝑦𝛿∥=𝜏𝛿+ for some 𝛿+>𝛿, and an appropriate source condition. We yield the optimal rate of convergence.
KW  - nonlinear operator
KW  - regularization
KW  - discrepancy principle
KW  - asymptotic method
KW  - optimal rate
Y1  - 2019
U6  - https://doi.org/10.3390/math7050419
SN  - 2227-7390
VL  - 7
PB  - MDPI
CY  - Basel, Schweiz
ET  - 5
ER  - 
TY  - INPR
A1  - Pornsawad, Pornsarp
A1  - Böckmann, Christine
T1  - Modified iterative Runge-Kutta-type methods for nonlinear ill-posed problems
N2  - This work is devoted to the convergence analysis of a modified Runge-Kutta-type iterative regularization method for solving nonlinear ill-posed problems under a priori and a posteriori stopping rules. The convergence rate results of the proposed method can be obtained under Hölder-type source-wise condition if the Fréchet derivative is properly scaled and locally Lipschitz continuous. Numerical results are achieved by using the Levenberg-Marquardt and Radau methods.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 3 (2014) 7 
KW  - ill-posed problems
KW  - Runge-Kutta methods
KW  - regularization methods
KW  - Hölder-type source condition
KW  - stopping rules
Y1  - 2014
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-70834
SN  - 2193-6943
VL  - 3
IS  - 7
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Pornsawad, Pornsarp
A1  - Böckmann, Christine
A1  - Panitsupakamon, Wannapa
T1  - The Levenberg–Marquardt regularization for the backward heat equation with fractional derivative
JF  - Electronic transactions on numerical analysis - ETNA
N2  - The backward heat problem with time-fractional derivative in Caputo's sense is studied. The inverse problem is severely ill-posed in the case when the fractional order is close to unity. A Levenberg-Marquardt method with a new a posteriori stopping rule is investigated. We show that optimal order can be obtained for the proposed method under a Hölder-type source condition. Numerical examples for one and two dimensions are provided.
KW  - ill-posed problems
KW  - time-fractional derivative
KW  - backward heat problem
KW  - Levenberg-Marquardt method
KW  - a posteriori stopping rule
KW  - optimal order
Y1  - 2022
SN  - 978-3-7001-8258-0
U6  - https://doi.org/10.1553/etna_vol57s67
SN  - 1068-9613
VL  - 57
SP  - 67
EP  - 79
PB  - Kent State University
CY  - Kent
ER  - 
TY  - GEN
A1  - Perera, Upeksha
A1  - Böckmann, Christine
T1  - Solutions of direct and inverse even-order Sturm-Liouville problems using Magnus expansion
T2  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - In this paper Lie group method in combination with Magnus expansion is utilized to develop a universal method applicable to solving a Sturm–Liouville problem (SLP) of any order with arbitrary boundary conditions. It is shown that the method has ability to solve direct regular (and some singular) SLPs of even orders (tested for up to eight), with a mix of (including non-separable and finite singular endpoints) boundary conditions, accurately and efficiently. The present technique is successfully applied to overcome the difficulties in finding suitable sets of eigenvalues so that the inverse SLP problem can be effectively solved. The inverse SLP algorithm proposed by Barcilon (1974) is utilized in combination with the Magnus method so that a direct SLP of any (even) order and an inverse SLP of order two can be solved effectively.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1336 
KW  - higher-order Sturm–Liouville problems
KW  - inverse Sturm–Liouville problems
KW  - Magnus expansion
Y1  - 2019
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-473414
SN  - 1866-8372
IS  - 1336
ER  - 
TY  - GEN
A1  - Pornsawad, Pornsarp
A1  - Sapsakul, Nantawan
A1  - Böckmann, Christine
T1  - A modified asymptotical regularization of nonlinear ill-posed problems
T2  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - In this paper, we investigate the continuous version of modified iterative Runge–Kutta-type methods for nonlinear inverse ill-posed problems proposed in a previous work. The convergence analysis is proved under the tangential cone condition, a modified discrepancy principle, i.e., the stopping time T is a solution of ∥𝐹(𝑥𝛿(𝑇))−𝑦𝛿∥=𝜏𝛿+ for some 𝛿+>𝛿, and an appropriate source condition. We yield the optimal rate of convergence.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1335 
KW  - nonlinear operator
KW  - regularization
KW  - discrepancy principle
KW  - asymptotic method
KW  - optimal rate
Y1  - 2019
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-473433
SN  - 1866-8372
IS  - 1335
ER  - 
TY  - JOUR
A1  - Wormell, Caroline L.
A1  - Reich, Sebastian
T1  - Spectral convergence of diffusion maps
BT  - Improved error bounds and an alternative normalization
JF  - SIAM journal on numerical analysis / Society for Industrial and Applied Mathematics
N2  - Diffusion maps is a manifold learning algorithm widely used for dimensionality reduction. Using a sample from a distribution, it approximates the eigenvalues and eigenfunctions of associated Laplace-Beltrami operators. Theoretical bounds on the approximation error are, however, generally much weaker than the rates that are seen in practice. This paper uses new approaches to improve the error bounds in the model case where the distribution is supported on a hypertorus. For the data sampling (variance) component of the error we make spatially localized compact embedding estimates on certain Hardy spaces; we study the deterministic (bias) component as a perturbation of the Laplace-Beltrami operator's associated PDE and apply relevant spectral stability results. Using these approaches, we match long-standing pointwise error bounds for both the spectral data and the norm convergence of the operator discretization. We also introduce an alternative normalization for diffusion maps based on Sinkhorn weights. This normalization approximates a Langevin diffusion on the sample and yields a symmetric operator approximation. We prove that it has better convergence compared with the standard normalization on flat domains, and we present a highly efficient rigorous algorithm to compute the Sinkhorn weights.
KW  - diffusion maps
KW  - graph Laplacian
KW  - Sinkhorn problem
KW  - kernel methods
Y1  - 2021
U6  - https://doi.org/10.1137/20M1344093
SN  - 0036-1429
SN  - 1095-7170
VL  - 59
IS  - 3
SP  - 1687
EP  - 1734
PB  - Society for Industrial and Applied Mathematics
CY  - Philadelphia
ER  - 
TY  - JOUR
A1  - Keller, Matthias
A1  - Liu, Shiping
A1  - Peyerimhoff, Norbert
T1  - A note on eigenvalue bounds for non-compact manifolds
JF  - Mathematische Nachrichten
N2  - In this article we prove upper bounds for the Laplace eigenvalues lambda(k) below the essential spectrum for strictly negatively curved Cartan-Hadamard manifolds. Our bound is given in terms of k(2) and specific geometric data of the manifold. This applies also to the particular case of non-compact manifolds whose sectional curvature tends to -infinity, where no essential spectrum is present due to a theorem of Donnelly/Li. The result stands in clear contrast to Laplacians on graphs where such a bound fails to be true in general.
KW  - Cheeger inequality
KW  - eigenvalues
KW  - Laplacian
KW  - negative curvature
KW  - Riemannian manifold
Y1  - 2021
U6  - https://doi.org/10.1002/mana.201900209
SN  - 0025-584X
SN  - 1522-2616
VL  - 294
IS  - 6
SP  - 1134
EP  - 1139
PB  - Wiley-VCH
CY  - Weinheim
ER  - 
TY  - JOUR
A1  - Peng, Junhao
A1  - Sandev, Trifce
A1  - Kocarev, Ljupco
T1  - First encounters on Bethe lattices and Cayley trees
JF  - Communications in nonlinear science & numerical simulation
N2  - In this work we consider the first encounter problems between a fixed and/or mobile target A and a moving trap B on Bethe lattices and Cayley trees. The survival probabilities (SPs) of the target A on the both kinds of structures are considered analytically and compared. On Bethe lattices, the results show that the fixed target will still prolong its survival time, whereas, on Cayley trees, there are some initial positions where the target should move to prolong its survival time. The mean first encounter time (MFET) for mobile target A is evaluated numerically and compared with the mean first passage time (MFPT) for the fixed target A. Different initial settings are addressed and clear boundaries are obtained. These findings are helpful for optimizing the strategy to prolong the survival time of the target or to speed up the search process on Cayley trees, in relation to the target's movement and the initial position configuration of the two walkers. We also present a new method, which uses a small amount of memory, for simulating random walks on Cayley trees. (C) 2020 Elsevier B.V. All rights reserved.
KW  - Random walks
KW  - Survival probability
KW  - Mean first encounter time
KW  - Bethe
KW  - lattices
KW  - Cayley trees
Y1  - 2021
U6  - https://doi.org/10.1016/j.cnsns.2020.105594
SN  - 1007-5704
SN  - 1878-7274
VL  - 95
PB  - Elsevier
CY  - Amsterdam
ER  - 
TY  - JOUR
A1  - Andjelkovic, Marko
A1  - Simevski, Aleksandar
A1  - Chen, Junchao
A1  - Schrape, Oliver
A1  - Stamenkovic, Zoran
A1  - Krstić, Miloš
A1  - Ilic, Stefan
A1  - Ristic, Goran
A1  - Jaksic, Aleksandar
A1  - Vasovic, Nikola
A1  - Duane, Russell
A1  - Palma, Alberto J.
A1  - Lallena, Antonio M.
A1  - Carvajal, Miguel A.
T1  - A design concept for radiation hardened RADFET readout system for space applications
JF  - Microprocessors and microsystems
N2  - Instruments for measuring the absorbed dose and dose rate under radiation exposure, known as radiation dosimeters, are indispensable in space missions. They are composed of radiation sensors that generate current or voltage response when exposed to ionizing radiation, and processing electronics for computing the absorbed dose and dose rate. Among a wide range of existing radiation sensors, the Radiation Sensitive Field Effect Transistors (RADFETs) have unique advantages for absorbed dose measurement, and a proven record of successful exploitation in space missions. It has been shown that the RADFETs may be also used for the dose rate monitoring. In that regard, we propose a unique design concept that supports the simultaneous operation of a single RADFET as absorbed dose and dose rate monitor. This enables to reduce the cost of implementation, since the need for other types of radiation sensors can be minimized or eliminated. For processing the RADFET's response we propose a readout system composed of analog signal conditioner (ASC) and a self-adaptive multiprocessing system-on-chip (MPSoC). The soft error rate of MPSoC is monitored in real time with embedded sensors, allowing the autonomous switching between three operating modes (high-performance, de-stress and fault-tolerant), according to the application requirements and radiation conditions.
KW  - RADFET
KW  - Radiation hardness
KW  - Absorbed dose
KW  - Dose rate
KW  - Self-adaptive MPSoC
Y1  - 2022
U6  - https://doi.org/10.1016/j.micpro.2022.104486
SN  - 0141-9331
SN  - 1872-9436
VL  - 90
PB  - Elsevier
CY  - Amsterdam
ER  - 
TY  - JOUR
A1  - Chang, Der-Chen
A1  - Schulze, Bert-Wolfgang
T1  - Corner spaces and Mellin quantization
JF  - Journal of nonlinear and convex analysis : an international journal
N2  - Manifolds with corners in the present investigation are non-smooth configurations - specific stratified spaces - with an incomplete metric such as cones, manifolds with edges, or corners of piecewise smooth domains in Euclidean space. We focus here on operators on such "corner manifolds" of singularity order <= 2, acting in weighted corner Sobolev spaces. The corresponding corner degenerate pseudo-differential operators are formulated via Mellin quantizations, and they also make sense on infinite singular cones.
KW  - Mellin quantizations
KW  - operator-valued symbols
KW  - weighted edge and corner spaces
Y1  - 2018
SN  - 1345-4773
SN  - 1880-5221
VL  - 19
IS  - 2
SP  - 179
EP  - 195
PB  - Yokohama Publishers
CY  - Yokohama
ER  - 
TY  - JOUR
A1  - Chang, Der-Chen
A1  - Schulze, Bert-Wolfgang
T1  - Ellipticity on spaces with higher singularities
JF  - Science China Mathematics
N2  - We study corner-degenerate pseudo-differential operators of any singularity order and develop ellipticity based on the principal symbolic hierarchy, associated with the stratification of the underlying space. We construct parametrices within the calculus and discuss the aspect of additional trace and potential conditions along lower-dimensional strata.
KW  - pseudo-differential operators
KW  - operator-valued symbols
KW  - Fourier and Mellin transforms
Y1  - 2017
U6  - https://doi.org/10.1007/s11425-016-0519-9
SN  - 1674-7283
SN  - 1869-1862
VL  - 60
IS  - 11
SP  - 2053
EP  - 2076
PB  - Science China Press
CY  - Beijing
ER  - 
TY  - JOUR
A1  - Khalil, Sara
A1  - Schulze, Bert-Wolfgang
T1  - Boundary problems on a manifold with edge
JF  - Asian-European Journal of Mathematics
N2  - We establish a calculus of boundary value problems (BVPs) on a manifold N with boundary and edge, based on Boutet de Monvel’s theory of BVPs in the case of a smooth boundary and on the edge calculus, where in the present case the model cone has a base which is a compact manifold with boundary. The corresponding calculus with boundary and edge is a unification of both structures and controls different operator-valued symbolic structures, in order to obtain ellipticity and parametrices.
KW  - manifolds with edge and boundary
KW  - distribution with asymptotics
KW  - ellipticity
KW  - Fredholm property
Y1  - 2017
U6  - https://doi.org/10.1142/S1793557117500875
SN  - 1793-5571
SN  - 1793-7183
VL  - 10
IS  - 2
PB  - World Scientific
CY  - Singapore
ER  - 
TY  - JOUR
A1  - Chang, Der-Chen
A1  - Hedayat Mahmoudi, Mahdi
A1  - Schulze, Bert-Wolfgang
T1  - Singular degenerate operators
JF  - Applicable analysis : an international journal
N2  - We outline some simplified and more general method for constructing parametrices on higher singular spaces. We also outline basic ideas on operators on manifolds with conical or edge singularities.
KW  - Operators on singular cones
KW  - Mellin symbols with values in the edge calculus
KW  - parametrices of elliptic operators
Y1  - 2017
U6  - https://doi.org/10.1080/00036811.2017.1336546
SN  - 0003-6811
SN  - 1563-504X
VL  - 96
IS  - 14
SP  - 2434
EP  - 2456
PB  - Routledge, Taylor & Francis Group
CY  - Abingdon
ER  - 
TY  - JOUR
A1  - Harutyunyan, Gohar
A1  - Schulze, Bert-Wolfgang
T1  - The Zaremba problem with singular interfaces as a corner boundary value problem
JF  - Potential analysis : an international journal devoted to the interactions between potential theory, probability theory, geometry and functional analysis
N2  - We study mixed boundary value problems for an elliptic operator A on a manifold X with boundary Y, i.e., Au = f in int X, T (+/-) u = g(+/-) on int Y+/-, where Y is subdivided into subsets Y+/- with an interface Z and boundary conditions T+/- on Y+/- that are Shapiro-Lopatinskij elliptic up to Z from the respective sides. We assume that Z subset of Y is a manifold with conical singularity v. As an example we consider the Zaremba problem, where A is the Laplacian and T- Dirichlet, T+ Neumann conditions. The problem is treated as a corner boundary value problem near v which is the new point and the main difficulty in this paper. Outside v the problem belongs to the edge calculus as is shown in Bull. Sci. Math. ( to appear). With a mixed problem we associate Fredholm operators in weighted corner Sobolev spaces with double weights, under suitable edge conditions along Z {v} of trace and potential type. We construct parametrices within the calculus and establish the regularity of solutions.
KW  - Zaremba problem
KW  - corner Sobolev spaces with double weights
KW  - pseudo-differential boundary value problems
Y1  - 2006
U6  - https://doi.org/10.1007/s11118-006-9020-6
SN  - 0926-2601
VL  - 25
SP  - 327
EP  - 369
PB  - Springer
CY  - Dordrecht
ER  - 
TY  - JOUR
A1  - Hedayat Mahmoudi, Mahdi
A1  - Schulze, Bert-Wolfgang
T1  - A new approach to the second order edge calculus
JF  - Journal of pseudo-differential operators and applications
N2  - We establish essential steps of an iterative approach to operator algebras, ellipticity and Fredholm property on stratified spaces with singularities of second order. We cover, in particular, corner-degenerate differential operators. Our constructions are focused on the case where no additional conditions of trace and potential type are posed, but this case works well and will be considered in a forthcoming paper as a conclusion of the present calculus.
KW  - Operators on singular manifolds
KW  - Mellin transform
KW  - Stratified spaces
KW  - Ellipticity and parametrices
Y1  - 2018
U6  - https://doi.org/10.1007/s11868-017-0191-2
SN  - 1662-9981
SN  - 1662-999X
VL  - 9
IS  - 2
SP  - 265
EP  - 300
PB  - Springer
CY  - Basel
ER  - 
TY  - JOUR
A1  - Khalil, Sara
A1  - Schulze, Bert-Wolfgang
T1  - Calculus on a Manifold with Edge and Boundary
JF  - Complex analysis and operator theory
N2  - We study elements of the calculus of boundary value problems in a variant of Boutet de Monvel’s algebra (Acta Math 126:11–51, 1971) on a manifold N with edge and boundary. If the boundary is empty then the approach corresponds to Schulze (Symposium on partial differential equations (Holzhau, 1988), BSB Teubner, Leipzig, 1989) and other papers from the subsequent development. For non-trivial boundary we study Mellin-edge quantizations and compositions within the structure in terms a new Mellin-edge quantization, compared with a more traditional technique. Similar structures in the closed case have been studied in Gil et al.
KW  - algebra
KW  - Mellin quantization
Y1  - 2019
U6  - https://doi.org/10.1007/s11785-018-0800-y
SN  - 1661-8254
SN  - 1661-8262
VL  - 13
IS  - 6
SP  - 2627
EP  - 2670
PB  - Springer
CY  - Basel
ER  - 
TY  - JOUR
A1  - Schulze, Bert-Wolfgang
A1  - Seiler, Jörg
T1  - Elliptic complexes on manifolds with boundary
JF  - The journal of geometric analysis
N2  - We show that elliptic complexes of (pseudo) differential operators on smooth compact manifolds with boundary can always be complemented to a Fredholm problem by boundary conditions involving global pseudodifferential projections on the boundary (similarly as the spectral boundary conditions of Atiyah, Patodi, and Singer for a single operator). We prove that boundary conditions without projections can be chosen if, and only if, the topological Atiyah-Bott obstruction vanishes. These results make use of a Fredholm theory for complexes of operators in algebras of generalized pseudodifferential operators of Toeplitz type which we also develop in the present paper.
KW  - Elliptic complexes
KW  - Manifolds with boundary
KW  - Atiyah-Bott obstruction
KW  - Toeplitz-type pseudodifferential operators
Y1  - 2018
U6  - https://doi.org/10.1007/s12220-018-0014-6
SN  - 1050-6926
SN  - 1559-002X
VL  - 29
IS  - 1
SP  - 656
EP  - 706
PB  - Springer
CY  - New York
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  - INPR
A1  - Schulze, Bert-Wolfgang
T1  - Toeplitz operators, and ellipticity of boundary value problems with global projection conditions
N2  - Ellipticity of (pseudo-) differential operators A on a compact manifold X with boundary (or with edges) Y is connected with boundary (or edge) conditions of trace and potential type, formulated in terms of global projections on Y together with an additional symbolic structure. This gives rise to operator block matrices A with A in the upper left corner. We study an algebra of such operators, where ellipticity is equivalent to the Fredhom property in suitable scales of spaces: Sobolev spaces on X plus closed subspaces of Sobolev spaces on Y which are the range of corresponding pseudo-differential projections. Moreover, we express parametrices of elliptic elements within our algebra and discuss spectral boundary value problems for differential operators.
T3  - Preprint - (2003) 03 
Y1  - 2003
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26510
ER  - 
TY  - INPR
A1  - Nazaikinskii, Vladimir
A1  - Savin, Anton
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
T1  - Elliptic theory on manifolds with nonisolated singularities : V. Index formulas for elliptic problems on manifolds with edges
N2  - For elliptic problems on manifolds with edges, we construct index formulas in form of a sum of homotopy invariant contributions of the strata (the interior of the manifold and the edge). Both terms are the indices of elliptic operators, one of which acts in spaces of sections of finite-dimensional vector bundles on a compact closed manifold and the other in spaces of sections of infinite-dimensional vector bundles over the edge.
T3  - Preprint - (2003) 02 
KW  - manifold with edge
KW  - elliptic problem
KW  - index formula
KW  - symmetry conditions
Y1  - 2003
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26500
ER  - 
TY  - INPR
A1  - Fedosov, Boris
A1  - Schulze, Bert-Wolfgang
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - On index theorem for symplectic orbifolds
N2  - We give an explicit construction of the trace on the algebra of quantum observables on a symplectic orbifold and propose an index formula.
T3  - Preprint - (2003) 07 
KW  - star product
KW  - symmetry group
KW  - G-trace
KW  - G-index
Y1  - 2003
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26550
ER  - 
TY  - INPR
A1  - Harutjunjan, Gohar
A1  - Schulze, Bert-Wolfgang
T1  - Asymptotics and relative index on a cylinder with conical cross section
N2  - We study pseudodifferential operators on a cylinder IR x B with cross section B that conical singularities. Configurations of that kind are the local model of cornere singularities with base spaces B. Operators A in our calculus are assumed to have symbols α which are meromorphic in the complex covariable with values in the space of all cone operators on B. In case α is dependent of the axial variable t ∈ IR, we show an explicit formula for solutions of the homogeneous equation. Each non-bjectivity point of the symbol in the complex plane corresponds to a finite-dimensional space of solutions. Moreover, we give a relative index formula.
T3  - Preprint - (2002) 27 
KW  - Meromorphic operator functions
KW  - relative index formulas
KW  - parameter-dependent cone operators
Y1  - 2002
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26446
ER  - 
TY  - INPR
A1  - Nazaikinskii, Vladimir
A1  - Savin, Anton
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
T1  - Differential operators on manifolds with singularities : analysis and topology : Chapter 1: Localization (surgery) in elliptic theory
N2  - Contents: Chapter 1: Localization (Surgery) in Elliptic Theory 1.1. The Index Locality Principle 1.1.1. What is locality? 1.1.2. A pilot example 1.1.3. Collar spaces 1.1.4. Elliptic operators 1.1.5. Surgery and the relative index theorem 1.2. Surgery in Index Theory on Smooth Manifolds 1.2.1. The Booß–Wojciechowski theorem 1.2.2. The Gromov–Lawson theorem 1.3. Surgery for Boundary Value Problems 1.3.1. Notation 1.3.2. General boundary value problems 1.3.3. A model boundary value problem on a cylinder 1.3.4. The Agranovich–Dynin theorem 1.3.5. The Agranovich theorem 1.3.6. Bojarski’s theorem and its generalizations 1.4. (Micro)localization in Lefschetz theory 1.4.1. The Lefschetz number 1.4.2. Localization and the contributions of singular points 1.4.3. The semiclassical method and microlocalization 1.4.4. The classical Atiyah–Bott–Lefschetz theorem
T3  - Preprint - (2003) 06 
Y1  - 2003
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26546
ER  - 
TY  - INPR
A1  - Kapanadze, David
A1  - Schulze, Bert-Wolfgang
T1  - Asymptotics of potentials in the edge calculus
N2  - Boundary value problems on manifolds with conical singularities or edges contain potential operators as well as trace and Green operators which play a similar role as the corresponding operators in (pseudo-differential) boundary value problems on a smooth manifold. There is then a specific asymptotic behaviour of these operators close to the singularities. We characterise potential operators in terms of actions of cone or edge pseudo-differential operators (in the neighbouring space) on densities supported by sbmanifolds which also have conical or edge singularities. As a byproduct we show the continuity of such potentials as continuous perators between cone or edge Sobolev spaces and subspaces with asymptotics.
T3  - Preprint - (2003) 05 
KW  - Surface potentials with asymptotics
KW  - edge Sobolev spaces
KW  - operators on manifolds with conical and edge singularities
Y1  - 2003
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26530
ER  - 
TY  - INPR
A1  - De Donno, G.
A1  - Schulze, Bert-Wolfgang
T1  - Meromorphic symbolic structures for boundary value problems on manifolds with edges
N2  - We investigate the ideal of Green and Mellin operators with asymtotics for a manifold with edge-corner singularities and boundary which belongs to the structure of parametrices of elliptic boundary value problems on a configuration with corners whose base manifolds have edges.
T3  - Preprint - (2003) 10 
Y1  - 2003
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26570
ER  - 
TY  - INPR
A1  - Nazaikinskii, Vladimir
A1  - Savin, Anton
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
T1  - Elliptic theory on manifolds with nonisolated singularities : I. The index of families of cone-degenerate operators
N2  - We study the index problem for families of elliptic operators on manifolds with conical singularities. The relative index theorem concerning changes of the weight line is obtained. AN index theorem for families whose conormal symbols satisfy some symmetry conditions is derived.
T3  - Preprint - (2002) 14 
KW  - elliptic family
KW  - conormal symbol
KW  - relative index
KW  - index formulas
KW  - symmetry conditions
Y1  - 2002
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26327
ER  - 
TY  - INPR
A1  - Egorov, Yu.
A1  - Kondratiev, V.
A1  - Schulze, Bert-Wolfgang
T1  - On completeness of eigenfunctions of an elliptic operator on a manifold with conical points
N2  - Contents: 1 Introduction 2 Definitions 3 Rays of minimal growth 4 Completeness of root functions
T3  - Preprint - (2001) 04 
Y1  - 2001
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25937
ER  - 
TY  - INPR
A1  - Flad, Heinz-Jürgen
A1  - Schneider, Reinhold
A1  - Schulze, Bert-Wolfgang
T1  - Asymptotic regularity of solutions of Hartree-Fock equations with coulomb potential
N2  - We study the asymptotic regularity of solutions of Hartree-Fock equations for Coulomb systems. In order to deal with singular Coulomb potentials, Fock operators are discussed within the calculus of pseudo-differential operators on conical manifolds. First, the non-self-consistent-field case is considered which means that the functions that enter into the nonlinear terms are not the eigenfunctions of the Fock operator itself. We introduce asymptotic regularity conditions on the functions that build up the Fock operator which guarantee ellipticity for the local part of the Fock operator on the open stretched cone R+ × S². This proves existence of a parametrix with a corresponding smoothing remainder from which it follows, via a bootstrap argument, that the eigenfunctions of the Fock operator again satisfy asymptotic regularity conditions. Using a fixed-point approach based on Cances and Le Bris analysis of the level-shifting algorithm, we show via another bootstrap argument, that the corresponding self-consistent-field solutions of the Hartree-Fock equation have the same type of asymptotic regularity.
T3  - Preprint - (2007) 05 
Y1  - 2007
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30268
ER  - 
TY  - INPR
A1  - Schulze, Bert-Wolfgang
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Asymptotics of solutions to elliptic equatons on manifolds with corners
N2  - We show an explicit link between the nature of a singular point and behaviour of the coefficients of the equation, under which formal asymptotic expansions are still available.
T3  - Preprint - (2000) 05 
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25716
ER  - 
TY  - INPR
A1  - Schulze, Bert-Wolfgang
T1  - Operator algebras with symbol hierarchies on manifolds with singularities
N2  - Problems for elliptic partial differential equations on manifolds M with singularities M' (here with piece-wise smooth geometry)are studied in terms of pseudo-differential algebras with hierarchies of symbols that consist of scalar and operator-valued components. Classical boundary value problems (with or without the transmission property) belong to the examples. They are a model for operator algebras on manifolds M with higher "polyhedral" singularities. The operators are block matrices that have upper left corners containing the pseudo-differential operators on the regular M\M' (plus certain Mellin and Green summands) and are degenerate (in streched coordinates) in a typical way near M'. By definition M' is again a manifold with singularities. The same is true of M'', and so on. The block matrices consist of trace, potential and Mellin and Green operators, acting between weighted Sobolev spaces on M(j) and M(k), with 0 ≤ j, k ≤ ord M; here M(0) denotes M, M(1) denotes M', etc. We generate these algebras, including their symbol hierarchies, by iterating so-called "edgifications" and "conifications" os algebras that have already been constructed, and we study ellipicity, parametrics and Fredholm property within these algebras.
T3  - Preprint - (1999) 30 
Y1  - 1999
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25647
ER  - 
TY  - INPR
A1  - Schulze, Bert-Wolfgang
T1  - An algebra of boundary value problems not requiring Shapiro-Lopatinskil conditions
N2  - We construct an algebra of pseudo-differential boundary value problems that contains the classical Shapiro-Lopatinskij elliptic problems as well as all differential elliptic problems of Dirac type with APS boundary conditions, together with their parametrices. Global pseudo-differential projections on the boundary are used to define ellipticity and to show the Fredholm property in suitable scales of spaces.
T3  - Preprint - (1999) 24 
Y1  - 1999
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25596
ER  - 
TY  - INPR
A1  - Kapanadze, David
A1  - Schulze, Bert-Wolfgang
A1  - Witt, Ingo
T1  - Coordinate invariance of the cone algebra with asymptotics
N2  - The cone algebra with discrete asymptotics on a manifold with conical singularities is shown to be invariant under natural coordinate changes, where the symbol structure (i.e., the Fuchsian interior symbol, conormal symbols of all orders) follows a corresponding transformation rule.
T3  - Preprint - (2000) 01 
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25671
ER  - 
TY  - INPR
A1  - Nazaikinskii, Vladimir
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
T1  - Quantization methods in differential equations : Part II: Quantization by the method of ordered operators (Noncommutative Analysis) : Chapter 1: Noncommutative Analysis: Main Ideas, Definitions, and Theorems
N2  - Content: 0.1 Preliminary Remarks Chapter 1: Noncommutative Analysis: Main Ideas, Definitions, and Theorems 1.1 Functions of One Operator (Functional Calculi) 1.2 Functions of Several Operators 1.3 Main Formulas of Operator Calculus 1.4 Main Tools of Noncommutative Analysis 1.5 Composition Laws and Ordered Representations
T3  - Preprint - (2000) 11 
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25762
ER  - 
TY  - INPR
A1  - Rabinovich, Vladimir
A1  - Schulze, Bert-Wolfgang
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Boundary value problems in domains with corners
N2  - We describe Fredholm boundary value problems for differential equations in domains with intersecting cuspidal edges on the boundary.
T3  - Preprint - (1999) 19 
Y1  - 1999
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25552
ER  - 
TY  - INPR
A1  - Nazaikinskii, Vladimir E.
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
T1  - Quantization methods in differential equations : Chapter 2: Quantization of Lagrangian modules
N2  - In this chapter we use the wave packet transform described in Chapter 1 to quantize extended classical states represented by so-called Lagrangian sumbanifolds of the phase space. Functions on a Lagrangian manifold form a module over the ring of classical Hamiltonian functions on the phase space (with respect to pointwise multiplication). The quantization procedure intertwines this multiplication with the action of the corresponding quantum Hamiltonians; hence we speak of quantization of Lagrangian modules. The semiclassical states obtained by this quantization procedure provide asymptotic solutions to differential equations with a small parameter. Locally, such solutions can be represented by WKB elements. Global solutions are given by Maslov's canonical operator [2]; also see, e.g., [3] and the references therein. Here the canonical operator is obtained in the framework of the universal quantization procedure provided by the wave packet transform. This procedure was suggested in [4] (see also the references there) and further developed in [5]; our exposition is in the spirit of these papers. Some further bibliographical remarks can be found in the beginning of Chapter 1.
T3  - Preprint - (1999) 22 
Y1  - 1999
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25582
ER  - 
TY  - INPR
A1  - Savin, Anton
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
T1  - Elliptic operators in subspaces
N2  - We construct elliptic theory in the subspaces, determined by pseudodifferential projections. The finiteness theorem as well as index formula are obtained for elliptic operators acting in the subspaces. Topological (K-theoretic) aspects of the theory are studied in detail.
T3  - Preprint - (2000) 04 
KW  - pseudodifferential subspaces
KW  - elliptic operators in subspaces
KW  - Fredholm property
KW  - index
KW  - K-theory
KW  - problem of classification
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25701
ER  - 
TY  - INPR
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
A1  - Savin, Anton
T1  - The homotopy classification and the index of boundary value problems for general elliptic operators
N2  - We give the homotopy classification and compute the index of boundary value problems for elliptic equations. The classical case of operators that satisfy the Atiyah-Bott condition is studied first. We also consider the general case of boundary value problems for operators that do not necessarily satisfy the Atiyah-Bott condition.
T3  - Preprint - (1999) 20 
KW  - elliptic boundary value problems
KW  - Atiyah-Bott condition
KW  - index theory
KW  - K-theory
KW  - homotopy classification
Y1  - 1999
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25568
ER  - 
TY  - INPR
A1  - Maniccia, L.
A1  - Schulze, Bert-Wolfgang
T1  - An algebra of meromorphic corner symbols
N2  - Operators on manifolds with corners that have base configurations with geometric singularities can be analysed in the frame of a conormal symbolic structure which is in spirit similar to the one for conical singularities of Kondrat'ev's work. Solvability of elliptic equations and asymptotics of solutions are determined by meromorphic conormal symbols. We study the case when the base has edge singularities which is a natural assumption in a number of applications. There are new phenomena, caused by a specific kind of higher degeneracy of the underlying symbols. We introduce an algebra of meromorphic edge operators that depend on complex parameters and investigate meromorphic inverses in the parameter-dependent elliptic case. Among the examples are resolvents of elliptic differential operators on manifolds with edges.
T3  - Preprint - (2002) 18 
Y1  - 2002
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26360
ER  - 
TY  - INPR
A1  - Oliaro, Alessandro
A1  - Schulze, Bert-Wolfgang
T1  - Parameter-dependent boundary value problems on manifolds with edges
N2  - As is known from Kondratyev's work, boundary value problems for elliptic operators on a manifold with conical singularities and boundary are controlled by a principal symbolic hierarchy, where the conormal symbols belong to the typical new components, compared with the smooth case, with interior and boundary symbols. A similar picture may be expected on manifolds with corners when the base of the cone itself is a manifold with conical or edge singularities. This is a natural situation in a number of applications, though with essential new difficulties. We investigate here corresponding conormal symbols in terms of a calculus of holomorphic parameter-dependent edge boundary value problems on the base. We show that a certain kernel cut-off procedure generates all such holomorphic families, modulo smoothing elements, and we establish conormal symbols as an algebra as is necessary for a parametrix constructions in the elliptic case.
T3  - Preprint - (2002) 25 
Y1  - 2002
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26424
ER  - 
TY  - INPR
A1  - Coriasco, Sandro
A1  - Schulze, Bert-Wolfgang
T1  - Edge problems on configurations with model cones of different dimensions
N2  - Elliptic equations on configurations W = W1 ∪ ... ∪ Wn with edge Y and components Wj of different dimension can be treated in the frame of pseudo-differential analysis on manifolds with geometric singularities, here, edges. Starting from edge-degenerate operators on Wj, j = 1, ..., N, we construct an algebra with extra "transmission" conditions on Y that satisfy an analogue of the Shapiro-Lopatinskij condition. Ellipticity refers to a two-component symbolic hierarchy with an interior and an edge part; the latter one is operator-valued, operating on the union of different dimensional model cones. We construct parametrices within our calculus, where exchange of information between the various components is encoded in Green and Mellin operators that are smoothing on W\Y. Moreover, we obtain regularity of solutions in weighted edge spaces with asymptotics.
T3  - Preprint - (2002) 26 
Y1  - 2002
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26438
ER  - 
TY  - INPR
A1  - Schulze, Bert-Wolfgang
A1  - Seiler, Jörg
T1  - Pseudodifferential boundary value problems with global projection conditions
N2  - Contents: Introduction 1 Operators with the transmission property 1.1 Operators on a manifold with boundary 1.2 Conditions with pseudodifferential projections 1.3 Projections and Fredholm families 2 Boundary value problems not requiring the transmission property 2.1 Interior operators 2.2 Edge amplitude functions 2.3 Boundary value problems 3 Operators with global projection conditions 3.1 Construction for boundary symbols 3.2 Ellipticity of boundary value problems with projection data 3.3 Operators of order zero
T3  - Preprint - (2002) 04 
Y1  - 2002
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26233
ER  - 
TY  - INPR
A1  - Nazaikinskii, Vladimir
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
T1  - Localization problem in index theory of elliptic operators
N2  - This is a survey of recent results concerning the general index locality principle, associated surgery, and their applications to elliptic operators on smooth manifolds and manifolds with singularities as well as boundary value problems. The full version of the paper is submitted for publication in Russian Mathematical Surveys.
T3  - Preprint - (2001) 34 
KW  - elliptic operators
KW  - index theory
KW  - surgery
KW  - relative index
KW  - manifold with singularities
Y1  - 2001
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26175
ER  - 
TY  - INPR
A1  - Nazaikinskii, Vladimir
A1  - Savin, Anton
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
T1  - Elliptic theory on manifolds with nonisolated singularities : III. The spectral flow of families of conormal symbols
N2  - When studyind elliptic operators on manifolds with nonisolated singularities one naturally encounters families of conormal symbols (i.e. operators elliptic with parameter p ∈ IR in the sense of Agranovich-Vishik) parametrized by the set of singular points. For homotopies of such families we define the notion of spectral flow, which in this case is an element of the K-group of the parameter space. We prove that the spectral flow is equal to the index of some family of operators on the infinite cone.
T3  - Preprint - (2002) 20 
KW  - elliptic family
KW  - conormal symbol
KW  - spectral flow
KW  - relative index
Y1  - 2002
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26386
ER  - 
TY  - INPR
A1  - Harutjunjan, G.
A1  - Schulze, Bert-Wolfgang
T1  - Reduction of orders in boundary value problems without the transmission property
N2  - Given an algebra of pseudo-differential operators on a manifold, an elliptic element is said to be a reduction of orders, if it induces isomorphisms of Sobolev spaces with a corresponding shift of smoothness. Reductions of orders on a manifold with boundary refer to boundary value problems. We consider smooth symbols and ellipticity without additional boundary conditions which is the relevant case on a manifold with boundary. Starting from a class of symbols that has been investigated before for integer orders in boundary value problems with the transmission property we study operators of arbitrary real orders that play a similar role for operators without the transmission property. Moreover, we show that order reducing symbols have the Volterra property and are parabolic of anisotropy 1; analogous relations are formulated for arbitrary anisotropies. We finally investigate parameter-dependent operators, apply a kernel cut-off construction with respect to the parameter and show that corresponding holomorphic operator-valued Mellin symbols reduce orders in weighted Sobolev spaces on a cone with boundary.
T3  - Preprint - (2002) 03 
KW  - Boundary value problems
KW  - elliptic operators
KW  - order reduction
KW  - Volterra symbols
Y1  - 2002
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26220
ER  - 
TY  - INPR
A1  - Nazaikinskii, Vladimir
A1  - Savin, Anton
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
T1  - Elliptic theory on manifolds with nonisolated singularities : IV. Obstructions to elliptic problems on manifolds with edges
N2  - The obstruction to the existence of Fredholm problems for elliptic differentail operators on manifolds with edges is a topological invariant of the operator. We give an explicit general formula for this invariant. As an application we compute this obstruction for geometric operators.
T3  - Preprint - (2002) 24 
KW  - manifolds with edges
KW  - edge-degenerate operators
KW  - elliptic families
KW  - edge symbol
KW  - Atiyah-Bott obstruction
KW  - parameter-dependent ellipticity
Y1  - 2002
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26415
ER  - 
TY  - INPR
A1  - Nazaikinskii, Vladimir
A1  - Savin, Anton
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
T1  - Elliptic theory on manifolds with nonisolated singularities : II. Products in elliptic theory on manifolds with edges
N2  - Exterior tensor products of elliptic operators on smooth manifolds and manifolds with conical singularities are used to obtain examples of elliptic operators on manifolds with edges that do not admit well-posed edge boundary and coboundary conditions.
T3  - Preprint - (2002) 15 
KW  - exterior tensor product
KW  - edge-degenerate operators
KW  - elliptic families
KW  - conormal symbol
KW  - Atiyah-Bott obstruction
Y1  - 2002
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26335
ER  - 
TY  - INPR
A1  - Nazaikinskii, Vladimir
A1  - Savin, Anton
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
T1  - Differential operators on manifolds with singularities : analysis and topology : Chapter 5: Manifolds with isolated singularities
N2  - Contents: Chapter 5: Manifolds with Isolated Singularities 5.1. Differential Operators and the Geometry of Singularities 5.1.1. How do isolated singularities arise? Examples 5.1.2. Definition and methods for the description of manifolds with isolated singularities 5.1.3. Bundles. The cotangent bundle 5.2. Asymptotics of Solutions, Function Spaces,Conormal Symbols 5.2.1. Conical singularities 5.2.2. Cuspidal singularities 5.3. A Universal Representation of Degenerate Operators and the Finiteness Theorem 5.3.1. The cylindrical representation 5.3.2. Continuity and compactness 5.3.3. Ellipticity and the finiteness theorem 5.4. Calculus of ΨDO 5.4.1. General ΨDO 5.4.2. The subalgebra of stabilizing ΨDO 5.4.3. Ellipticity and the finiteness theorem
T3  - Preprint - (2003) 23 
Y1  - 2003
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26659
ER  - 
TY  - INPR
A1  - Dines, Nicoleta
A1  - Schulze, Bert-Wolfgang
T1  - Mellin-edge representations of elliptic operators
N2  - We construct a class of elliptic operators in the edge algebra on a manifold M with an embedded submanifold Y interpreted as an edge. The ellipticity refers to a principal symbolic structure consisting of the standard interior symbol and an operator-valued edge symbol. Given a differential operator A on M for every (sufficiently large) s we construct an associated operator As in the edge calculus. We show that ellipticity of A in the usual sense entails ellipticity of As as an edge operator (up to a discrete set of reals s). Parametrices P of A then correspond to parametrices Ps of As, interpreted as Mellin-edge representations of P.
T3  - Preprint - (2003) 18 
KW  - Pseudo-differential operators
KW  - edge algebra
KW  - ellipticity with interface conditions
Y1  - 2003
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26627
ER  - 
TY  - INPR
A1  - Krainer, Thomas
A1  - Schulze, Bert-Wolfgang
T1  - The conormal symbolic structure of corner boundary value problems
N2  - Ellipticity of operators on manifolds with conical singularities or parabolicity on space-time cylinders are known to be linked to parameter-dependent operators (conormal symbols) on a corresponding base manifold. We introduce the conormal symbolic structure for the case of corner manifolds, where the base itself is a manifold with edges and boundary. The specific nature of parameter-dependence requires a systematic approach in terms of meromorphic functions with values in edge-boundary value problems. We develop here a corresponding calculus, and we construct inverses of elliptic elements.
T3  - Preprint - (2004) 01 
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26662
ER  - 
TY  - INPR
A1  - Nazaikinskii, Vladimir
A1  - Savin, Anton
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
T1  - Differential operators on manifolds with singularities : analysis and topology : Chapter 7: The index problem on manifolds with singularities
N2  - Contents: Chapter 7: The Index Problemon Manifolds with Singularities Preface 7.1. The Simplest Index Formulas 7.1.1. General properties of the index 7.1.2. The index of invariant operators on the cylinder 7.1.3. Relative index formulas 7.1.4. The index of general operators on the cylinder 7.1.5. The index of operators of the form 1 + G with a Green operator G 7.1.6. The index of operators of the form 1 + G on manifolds with edges 7.1.7. The index on bundles with smooth base and fiber having conical points 7.2. The Index Problem for Manifolds with Isolated Singularities 7.2.1. Statement of the index splitting problem 7.2.2. The obstruction to the index splitting 7.2.3. Computation of the obstruction in topological terms 7.2.4. Examples. Operators with symmetries 7.3. The Index Problem for Manifolds with Edges 7.3.1. The index excision property 7.3.2. The obstruction to the index splitting 7.4. Bibliographical Remarks
T3  - Preprint - (2004) 06 
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26700
ER  - 
TY  - INPR
A1  - Harutjunjan, Gohar
A1  - Schulze, Bert-Wolfgang
T1  - Boundary problems with meromorphic symbols in cylindrical domains
N2  - We show relative index formulas for boundary value problems in cylindrical domains and Sobolev spaces with different weigths at ±∞. The amplitude functions are meromorphic in the axial covariable and take values in the space of boundary value problems on the cross section of the cylinder.
T3  - Preprint - (2004) 12 
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26735
ER  - 
TY  - JOUR
A1  - Pohle, Jennifer
A1  - Adam, Timo
A1  - Beumer, Larissa
T1  - Flexible estimation of the state dwell-time distribution in hidden semi-Markov models
JF  - Computational statistics & data analysis
N2  - Hidden semi-Markov models generalise hidden Markov models by explicitly modelling the time spent in a given state, the so-called dwell time, using some distribution defined on the natural numbers. While the (shifted) Poisson and negative binomial distribution provide natural choices for such distributions, in practice, parametric distributions can lack the flexibility to adequately model the dwell times. To overcome this problem, a penalised maximum likelihood approach is proposed that allows for a flexible and data-driven estimation of the dwell-time distributions without the need to make any distributional assumption. This approach is suitable for direct modelling purposes or as an exploratory tool to investigate the latent state dynamics. The feasibility and potential of the suggested approach is illustrated in a simulation study and by modelling muskox movements in northeast Greenland using GPS tracking data. The proposed method is implemented in the R-package PHSMM which is available on CRAN.
KW  - Penalized likelihood
KW  - Smoothing
KW  - Time series
KW  - Animal movement modeling
Y1  - 2022
U6  - https://doi.org/10.1016/j.csda.2022.107479
SN  - 0167-9473
SN  - 1872-7352
VL  - 172
PB  - Elsevier
CY  - Amsterdam
ER  - 
TY  - JOUR
A1  - Biskaborn, Boris
A1  - Smith, Sharon L.
A1  - Noetzli, Jeannette
A1  - Matthes, Heidrun
A1  - Vieira, Goncalo
A1  - Streletskiy, Dmitry A.
A1  - Schoeneich, Philippe
A1  - Romanovsky, Vladimir E.
A1  - Lewkowicz, Antoni G.
A1  - Abramov, Andrey
A1  - Allard, Michel
A1  - Boike, Julia
A1  - Cable, William L.
A1  - Christiansen, Hanne H.
A1  - Delaloye, Reynald
A1  - Diekmann, Bernhard
A1  - Drozdov, Dmitry
A1  - Etzelmueller, Bernd
A1  - Grosse, Guido
A1  - Guglielmin, Mauro
A1  - Ingeman-Nielsen, Thomas
A1  - Isaksen, Ketil
A1  - Ishikawa, Mamoru
A1  - Johansson, Margareta
A1  - Johannsson, Halldor
A1  - Joo, Anseok
A1  - Kaverin, Dmitry
A1  - Kholodov, Alexander
A1  - Konstantinov, Pavel
A1  - Kroeger, Tim
A1  - Lambiel, Christophe
A1  - Lanckman, Jean-Pierre
A1  - Luo, Dongliang
A1  - Malkova, Galina
A1  - Meiklejohn, Ian
A1  - Moskalenko, Natalia
A1  - Oliva, Marc
A1  - Phillips, Marcia
A1  - Ramos, Miguel
A1  - Sannel, A. Britta K.
A1  - Sergeev, Dmitrii
A1  - Seybold, Cathy
A1  - Skryabin, Pavel
A1  - Vasiliev, Alexander
A1  - Wu, Qingbai
A1  - Yoshikawa, Kenji
A1  - Zheleznyak, Mikhail
A1  - Lantuit, Hugues
T1  - Permafrost is warming at a global scale
JF  - Nature Communications
N2  - Permafrost warming has the potential to amplify global climate change, because when frozen sediments thaw it unlocks soil organic carbon. Yet to date, no globally consistent assessment of permafrost temperature change has been compiled. Here we use a global data set of permafrost temperature time series from the Global Terrestrial Network for Permafrost to evaluate temperature change across permafrost regions for the period since the International Polar Year (2007-2009). During the reference decade between 2007 and 2016, ground temperature near the depth of zero annual amplitude in the continuous permafrost zone increased by 0.39 +/- 0.15 degrees C. Over the same period, discontinuous permafrost warmed by 0.20 +/- 0.10 degrees C. Permafrost in mountains warmed by 0.19 +/- 0.05 degrees C and in Antarctica by 0.37 +/- 0.10 degrees C. Globally, permafrost temperature increased by 0.29 +/- 0.12 degrees C. The observed trend follows the Arctic amplification of air temperature increase in the Northern Hemisphere. In the discontinuous zone, however, ground warming occurred due to increased snow thickness while air temperature remained statistically unchanged.
Y1  - 2019
U6  - https://doi.org/10.1038/s41467-018-08240-4
SN  - 2041-1723
VL  - 10
PB  - Nature Publ. Group
CY  - London
ER  - 
TY  - BOOK
ED  - Kuzle, Ana
ED  - Rott, Benjamin
ED  - Gebel, Inga
T1  - Implementation research on problem solving in school settings
BT  - Proceedings of the 2018 Joint Conference of ProMath and the GDM Working Group on Problem Solving
T3  - Ars inveniendi et dejudicandi ; 13
Y1  - 2019
SN  - 978-3-95987-116-7
SN  - 978-3-95987-115-0
PB  - WTM-Verlag
CY  - Münster
ER  - 
TY  - GEN
A1  - Krause, Andreas
A1  - Kloft, Charlotte
A1  - Huisinga, Wilhelm
A1  - Karlsson, Mats
A1  - Pinheiro, José
A1  - Bies, Robert
A1  - Rogers, James
A1  - Mentré, France
A1  - Musser, Bret J.
T1  - Comment on Jaki et al., A proposal for a new PhD level curriculum on quantitative methods for drug development
T2  - Pharmaceutical statistics : the journal of applied statistics in the pharmaceutical industry
Y1  - 2019
SN  - 1539-1604
SN  - 1539-1612
VL  - 18
IS  - 3
SP  - 278
EP  - 281
PB  - Wiley
CY  - Hoboken
ER  - 
TY  - THES
A1  - Seuring, Markus
T1  - Output space compaction for testing and concurrent checking
N2  - In der Dissertation werden neue Entwurfsmethoden für Kompaktoren für die Ausgänge von digitalen Schaltungen beschrieben, die die Anzahl der zu testenden Ausgänge drastisch verkleinern und dabei die Testbarkeit der Schaltungen nur wenig oder gar nicht verschlechtern. Der erste Teil der Arbeit behandelt für kombinatorische Schaltungen Methoden, die die Struktur der Schaltungen beim Entwurf der Kompaktoren berücksichtigen. Verschiedene Algorithmen zur Analyse von Schaltungsstrukturen werden zum ersten Mal vorgestellt und untersucht. Die Komplexität der vorgestellten Verfahren zur Erzeugung von Kompaktoren ist linear bezüglich der Anzahl der Gatter in der Schaltung und ist damit auf sehr große Schaltungen anwendbar. Im zweiten Teil wird erstmals ein solches Verfahren für sequentielle Schaltkreise beschrieben. Dieses Verfahren baut im wesentlichen auf das erste auf. Der dritte Teil beschreibt eine Entwurfsmethode, die keine Informationen über die interne Struktur der Schaltung oder über das zugrundeliegende Fehlermodell benötigt. Der Entwurf basiert alleine auf einem vorgegebenen Satz von Testvektoren und die dazugehörenden Testantworten der fehlerfreien Schaltung. Ein nach diesem Verfahren erzeugter Kompaktor maskiert keinen der Fehler, die durch das Testen mit den vorgegebenen Vektoren an den Ausgängen der Schaltung beobachtbar sind.
N2  - The objective of this thesis is to provide new space compaction techniques for testing or concurrent checking of digital circuits. In particular, the work focuses on the design of space compactors that achieve high compaction ratio and minimal loss of testability of the circuits. In the first part, the compactors are designed for combinational circuits based on the knowledge of the circuit structure. Several algorithms for analyzing circuit structures are introduced and discussed for the first time. The complexity of each design procedure is linear with respect to the number of gates of the circuit. Thus, the procedures are applicable to large circuits. In the second part, the first structural approach for output compaction for sequential circuits is introduced. Essentially, it enhances the first part. For the approach introduced in the third part it is assumed that the structure of the circuit and the underlying fault model are unknown. The space compaction approach requires only the knowledge of the fault-free test responses for a precomputed test set. The proposed compactor design guarantees zero-aliasing with respect to the precomputed test set.
KW  - digital circuit
KW  - output space compaction
KW  - zero-aliasing
KW  - test
KW  - concurrent checking
KW  - propagation probability
KW  - IP core
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-0000165
ER  - 
TY  - JOUR
A1  - Mueller-Schoell, Anna
A1  - Groenland, Stefanie L.
A1  - Scherf-Clavel, Oliver
A1  - van Dyk, Madele
A1  - Huisinga, Wilhelm
A1  - Michelet, Robin
A1  - Jaehde, Ulrich
A1  - Steeghs, Neeltje
A1  - Huitema, Alwin D. R.
A1  - Kloft, Charlotte
T1  - Therapeutic drug monitoring of oral targeted antineoplastic drugs
JF  - European journal of clinical pharmacology
N2  - Purpose This review provides an overview of the current challenges in oral targeted antineoplastic drug (OAD) dosing and outlines the unexploited value of therapeutic drug monitoring (TDM). Factors influencing the pharmacokinetic exposure in OAD therapy are depicted together with an overview of different TDM approaches. Finally, current evidence for TDM for all approved OADs is reviewed. Methods A comprehensive literature search (covering literature published until April 2020), including primary and secondary scientific literature on pharmacokinetics and dose individualisation strategies for OADs, together with US FDA Clinical Pharmacology and Biopharmaceutics Reviews and the Committee for Medicinal Products for Human Use European Public Assessment Reports was conducted. Results OADs are highly potent drugs, which have substantially changed treatment options for cancer patients. Nevertheless, high pharmacokinetic variability and low treatment adherence are risk factors for treatment failure. TDM is a powerful tool to individualise drug dosing, ensure drug concentrations within the therapeutic window and increase treatment success rates. After reviewing the literature for 71 approved OADs, we show that exposure-response and/or exposure-toxicity relationships have been established for the majority. Moreover, TDM has been proven to be feasible for individualised dosing of abiraterone, everolimus, imatinib, pazopanib, sunitinib and tamoxifen in prospective studies. There is a lack of experience in how to best implement TDM as part of clinical routine in OAD cancer therapy. Conclusion Sub-therapeutic concentrations and severe adverse events are current challenges in OAD treatment, which can both be addressed by the application of TDM-guided dosing, ensuring concentrations within the therapeutic window.
KW  - targeted antineoplastic drugs
KW  - tyrosine kinase inhibitors
KW  - therapeutic
KW  - drug monitoring
KW  - oral anticancer drugs
KW  - personalised medicine
Y1  - 2020
U6  - https://doi.org/10.1007/s00228-020-03014-8
SN  - 0031-6970
SN  - 1432-1041
VL  - 77
IS  - 4
SP  - 441
EP  - 464
PB  - Springer
CY  - Heidelberg
ER  - 
TY  - JOUR
A1  - Grisic, Ana-Marija
A1  - Eser, Alexander
A1  - Huisinga, Wilhelm
A1  - Reinisch, Walter
A1  - Kloft, Charlotte
T1  - Quantitative relationship between infliximab exposure and inhibition of C-reactive protein synthesis to support inflammatory bowel disease management
JF  - British journal of clinical pharmacology
N2  - Aim Quantitative and kinetic insights into the drug exposure-disease response relationship might enhance our knowledge on loss of response and support more effective monitoring of inflammatory activity by biomarkers in patients with inflammatory bowel disease (IBD) treated with infliximab (IFX). This study aimed to derive recommendations for dose adjustment and treatment optimisation based on mechanistic characterisation of the relationship between IFX serum concentration and C-reactive protein (CRP) concentration. <br /> Methods Data from an investigator-initiated trial included 121 patients with IBD during IFX maintenance treatment. Serum concentrations of IFX, antidrug antibodies (ADA), CRP, and disease-related covariates were determined at the mid-term and end of a dosing interval. Data were analysed using a pharmacometric nonlinear mixed-effects modelling approach. An IFX exposure-CRP model was generated and applied to evaluate dosing regimens to achieve CRP remission. <br /> Results The generated quantitative model showed that IFX has the potential to inhibit up to 72% (9% relative standard error [RSE]) of CRP synthesis in a patient. IFX concentration leading to 90% of the maximum CRP synthesis inhibition was 18.4 mu g/mL (43% RSE). Presence of ADA was the most influential factor on IFX exposure. With standard dosing strategy, >= 55% of ADA+ patients experienced CRP nonremission. Shortening the dosing interval and co-therapy with immunomodulators were found to be the most beneficial strategies to maintain CRP remission. <br /> Conclusions With the generated model we could for the first time establish a robust relationship between IFX exposure and CRP synthesis inhibition, which could be utilised for treatment optimisation in IBD patients.
KW  - C‐ reactive protein remission
KW  - inflammatory bowel disease
KW  - infliximab dosing
Y1  - 2020
U6  - https://doi.org/10.1111/bcp.14648
SN  - 0306-5251
SN  - 1365-2125
VL  - 87
IS  - 5
SP  - 2374
EP  - 2384
PB  - Wiley
CY  - Hoboken
ER  - 
TY  - JOUR
A1  - Kluwe, Franziska
A1  - Michelet, Robin
A1  - Müller-Schöll, Anna
A1  - Maier, Corinna
A1  - Klopp-Schulze, Lena
A1  - van Dyk, Madele
A1  - Mikus, Gerd
A1  - Huisinga, Wilhelm
A1  - Kloft, Charlotte
T1  - Perspectives on model-informed precision dosing in the digital health era
BT  - challenges, opportunities, and recommendations
JF  - Clinical pharmacology & therapeutics
Y1  - 2020
U6  - https://doi.org/10.1002/cpt.2049
SN  - 0009-9236
SN  - 1532-6535
VL  - 109
IS  - 1
SP  - 29
EP  - 36
PB  - Wiley
CY  - Hoboken
ER  - 
TY  - JOUR
A1  - Nassar, Yomna M.
A1  - Hohmann, Nicolas
A1  - Michelet, Robin
A1  - Gottwalt, Katharina
A1  - Meid, Andreas D.
A1  - Burhenne, Jürgen
A1  - Huisinga, Wilhelm
A1  - Haefeli, Walter E.
A1  - Mikus, Gerd
A1  - Kloft, Charlotte
T1  - Quantification of the Time Course of CYP3A Inhibition, Activation, and Induction Using a Population Pharmacokinetic Model of Microdosed Midazolam Continuous Infusion
JF  - Clinical Pharmacokinetics
N2  - Background
Cytochrome P450 (CYP) 3A contributes to the metabolism of many approved drugs. CYP3A perpetrator drugs can profoundly alter the exposure of CYP3A substrates. However, effects of such drug-drug interactions are usually reported as maximum effects rather than studied as time-dependent processes. Identification of the time course of CYP3A modulation can provide insight into when significant changes to CYP3A activity occurs, help better design drug-drug interaction studies, and manage drug-drug interactions in clinical practice. 

Objective
We aimed to quantify the time course and extent of the in vivo modulation of different CYP3A perpetrator drugs on hepatic CYP3A activity and distinguish different modulatory mechanisms by their time of onset, using pharmacologically inactive intravenous microgram doses of the CYP3A-specific substrate midazolam, as a marker of CYP3A activity.

Methods
Twenty-four healthy individuals received an intravenous midazolam bolus followed by a continuous infusion for 10 or 36 h. Individuals were randomized into four arms: within each arm, two individuals served as a placebo control and, 2 h after start of the midazolam infusion, four individuals received the CYP3A perpetrator drug: voriconazole (inhibitor, orally or intravenously), rifampicin (inducer, orally), or efavirenz (activator, orally). After midazolam bolus administration, blood samples were taken every hour (rifampicin arm) or every 15 min (remaining study arms) until the end of midazolam infusion. A total of 1858 concentrations were equally divided between midazolam and its metabolite, 1'-hydroxymidazolam. A nonlinear mixed-effects population pharmacokinetic model of both compounds was developed using NONMEM (R). CYP3A activity modulation was quantified over time, as the relative change of midazolam clearance encountered by the perpetrator drug, compared to the corresponding clearance value in the placebo arm. 

Results
Time course of CYP3A modulation and magnitude of maximum effect were identified for each perpetrator drug. While efavirenz CYP3A activation was relatively fast and short, reaching a maximum after approximately 2-3 h, the induction effect of rifampicin could only be observed after 22 h, with a maximum after approximately 28-30 h followed by a steep drop to almost baseline within 1-2 h. In contrast, the inhibitory impact of both oral and intravenous voriconazole was prolonged with a steady inhibition of CYP3A activity followed by a gradual increase in the inhibitory effect until the end of sampling at 8 h. Relative maximum clearance changes were +59.1%, +46.7%, -70.6%, and -61.1% for efavirenz, rifampicin, oral voriconazole, and intravenous voriconazole, respectively.

Conclusions
We could distinguish between different mechanisms of CYP3A modulation by the time of onset. Identification of the time at which clearance significantly changes, per perpetrator drug, can guide the design of an optimal sampling schedule for future drug-drug interaction studies. The impact of a short-term combination of different perpetrator drugs on the paradigm CYP3A substrate midazolam was characterized and can define combination intervals in which no relevant interaction is to be expected.
Y1  - 2022
U6  - https://doi.org/10.1007/s40262-022-01175-6
SN  - 0312-5963
SN  - 1179-1926
VL  - 61
IS  - 11
SP  - 1595
EP  - 1607
PB  - Springer
CY  - Northcote
ER  - 
TY  - GEN
A1  - Weisser, Karin
A1  - Stübler, Sabine
A1  - Matheis, Walter
A1  - Huisinga, Wilhelm
T1  - Towards toxicokinetic modelling of aluminium exposure from adjuvants in medicinal products
T2  - Regulatory toxicology and pharmacology : official journal of the International Society for Regulatory Toxicology and Pharmacology
N2  - As a potentially toxic agent on nervous system and bone, the safety of aluminium exposure from adjuvants in vaccines and subcutaneous immune therapy (SCIT) products has to be continuously reevaluated, especially regarding concomitant administrations. For this purpose, knowledge on absorption and disposition of aluminium in plasma and tissues is essential. Pharmacokinetic data after vaccination in humans, however, are not available, and for methodological and ethical reasons difficult to obtain. To overcome these limitations, we discuss the possibility of an in vitro-in silico approach combining a toxicokinetic model for aluminium disposition with biorelevant kinetic absorption parameters from adjuvants. We critically review available kinetic aluminium-26 data for model building and, on the basis of a reparameterized toxicokinetic model (Nolte et al., 2001), we identify main modelling gaps. The potential of in vitro dissolution experiments for the prediction of intramuscular absorption kinetics of aluminium after vaccination is explored. It becomes apparent that there is need for detailed in vitro dissolution and in vivo absorption data to establish an in vitro-in vivo correlation (IVIVC) for aluminium adjuvants. We conclude that a combination of new experimental data and further refinement of the Nolte model has the potential to fill a gap in aluminium risk assessment. (C) 2017 Elsevier Inc. All rights reserved.
KW  - Aluminium
KW  - Aluminium adjuvants
KW  - Absorption kinetics
KW  - Toxicokinetic modelling
KW  - In vitro dissolution
Y1  - 2017
U6  - https://doi.org/10.1016/j.yrtph.2017.02.018
SN  - 0273-2300
SN  - 1096-0295
VL  - 88
SP  - 310
EP  - 321
PB  - Elsevier
CY  - San Diego
ER  - 
TY  - JOUR
A1  - Wicha, Sebastian G.
A1  - Huisinga, Wilhelm
A1  - Kloft, Charlotte
T1  - Translational pharmacometric evaluation of typical antibiotic broad-spectrum combination therapies against staphylococcus aureus exploiting in vitro information
JF  - CPT: pharmacometrics & systems pharmacology
N2  - Broad-spectrum antibiotic combination therapy is frequently applied due to increasing resistance development of infective pathogens. The objective of the present study was to evaluate two common empiric broad-spectrum combination therapies consisting of either linezolid (LZD) or vancomycin (VAN) combined with meropenem (MER) against Staphylococcus aureus (S. aureus) as the most frequent causative pathogen of severe infections. A semimechanistic pharmacokinetic-pharmacodynamic (PK-PD) model mimicking a simplified bacterial life-cycle of S. aureus was developed upon time-kill curve data to describe the effects of LZD, VAN, and MER alone and in dual combinations. The PK-PD model was successfully (i) evaluated with external data from two clinical S. aureus isolates and further drug combinations and (ii) challenged to predict common clinical PK-PD indices and breakpoints. Finally, clinical trial simulations were performed that revealed that the combination of VAN-MER might be favorable over LZD-MER due to an unfavorable antagonistic interaction between LZD and MER.
Y1  - 2017
U6  - https://doi.org/10.1002/psp4.12197
SN  - 2163-8306
VL  - 6
SP  - 512
EP  - 522
PB  - Wiley
CY  - Hoboken
ER  - 
TY  - JOUR
A1  - Edlund, Helena
A1  - Grisic, Ana-Marija
A1  - Steenholdt, Casper
A1  - Ainsworth, Mark Andrew
A1  - Brynskov, Torn
A1  - Huisinga, Wilhelm
A1  - Kloft, Charlotte
T1  - Absence of Relationship Between Crohn's Disease Activity Index or C-Reactive Protein and Infliximab Exposure Calls for Objective Crohn's Disease Activity Measures for the Evaluation of Treatment Effects at Treatment Failure
JF  - Therapeutic drug monitoring : official journal of the International Association of Therapeutic Drug Monitoring and Clinical Toxicology
N2  - Background: Circulating infliximab (IFX) concentrations correlate with clinical outcomes, forming the basis of the IFX concentration monitoring in patients with Crohn's disease. This study aims to investigate and refine the exposure-response relationship by linking the disease activity markers "Crohn's disease activity index" (CDAI) and C-reactive protein (CRP) to IFX exposure. In addition, we aim to explore the correlations between different disease markers and exposure metrics.

Methods: Data from 47 Crohn's disease patients of a randomized controlled trial were analyzed post hoc. All patients had secondary treatment failure at inclusion and had received intensified IFX of 5 mg/kg every 4 weeks for up to 20 weeks. Graphical analyses were performed to explore exposure-response relationships. Metrics of exposure included area under the concentration-time curve (AUC) and trough concentrations (Cmin). Disease activity was measured by CDAI and CRP values, their change from baseline/last visit, and response/remission outcomes at week 12.

Results: Although trends toward lower Cmin and lower AUC in nonresponders were observed, neither CDAI nor CRP showed consistent trends of lower disease activity with higher IFX exposure across the 30 evaluated relationships. As can be expected, Cmin and AUC were strongly correlated with each other. Contrarily, the disease activity markers were only weakly correlated with each other.

Conclusions: No significant relationship between disease activity, as evaluated by CDAI or CRP, and IFX exposure was identified. AUC did not add benefit compared with Cmin. These findings support the continued use of Cmin and call for stringent objective disease activity (bio-)markers (eg, endoscopy) to form the basis of personalized IFX therapy for Crohn's disease patients with IFX treatment failure.
Y1  - 2019
U6  - https://doi.org/10.1097/FTD.0000000000000590
SN  - 0163-4356
SN  - 1536-3694
VL  - 41
IS  - 2
SP  - 235
EP  - 242
PB  - Lippincott Williams & Wilkins
CY  - Philadelphia
ER  - 
TY  - JOUR
A1  - Knöchel, Jane
A1  - Kloft, Charlotte
A1  - Huisinga, Wilhelm
T1  - Understanding and reducing complex systems pharmacology models based on a novel input-response index
JF  - Journal of pharmacokinetics and pharmacodynamics
N2  - A growing understanding of complex processes in biology has led to large-scale mechanistic models of pharmacologically relevant processes. These models are increasingly used to study the response of the system to a given input or stimulus, e.g., after drug administration. Understanding the input–response relationship, however, is often a challenging task due to the complexity of the interactions between its constituents as well as the size of the models. An approach that quantifies the importance of the different constituents for a given input–output relationship and allows to reduce the dynamics to its essential features is therefore highly desirable. In this article, we present a novel state- and time-dependent quantity called the input–response index that quantifies the importance of state variables for a given input–response relationship at a particular time. It is based on the concept of time-bounded controllability and observability, and defined with respect to a reference dynamics. In application to the brown snake venom–fibrinogen (Fg) network, the input–response indices give insight into the coordinated action of specific coagulation factors and about those factors that contribute only little to the response. We demonstrate how the indices can be used to reduce large-scale models in a two-step procedure: (i) elimination of states whose dynamics have only minor impact on the input–response relationship, and (ii) proper lumping of the remaining (lower order) model. In application to the brown snake venom–fibrinogen network, this resulted in a reduction from 62 to 8 state variables in the first step, and a further reduction to 5 state variables in the second step. We further illustrate that the sequence, in which a recursive algorithm eliminates and/or lumps state variables, has an impact on the final reduced model. The input–response indices are particularly suited to determine an informed sequence, since they are based on the dynamics of the original system. In summary, the novel measure of importance provides a powerful tool for analysing the complex dynamics of large-scale systems and a means for very efficient model order reduction of nonlinear systems.
KW  - Control theory
KW  - Model order reduction
KW  - Blood coagulation network
KW  - Nonlinear systems
Y1  - 2017
U6  - https://doi.org/10.1007/s10928-017-9561-x
SN  - 1567-567X
SN  - 1573-8744
VL  - 45
IS  - 1
SP  - 139
EP  - 157
PB  - Springer Science + Business Media B.V.
CY  - New York
ER  - 
TY  - THES
A1  - Knöchel, Jane
T1  - Model reduction of mechanism-based pharmacodynamic models and its link to classical drug effect models
T1  - Modellreduktion von mechanistischen pharmacodynamischen Modellen und deren Verbindung zu klassischen Wirkstoff-Effekt-Modellen
N2  - Continuous insight into biological processes has led to the development of large-scale, mechanistic systems biology models of pharmacologically relevant networks. While these models are typically designed to study the impact of diverse stimuli or perturbations on multiple system variables, the focus in pharmacological research is often on a specific input, e.g., the dose of a drug, and a specific output related to the drug effect or response in terms of some surrogate marker. 
To study a chosen input-output pair, the complexity of the interactions as well as the size of the models hinders easy access and understanding of the details of the input-output relationship. 
The objective of this thesis is the development of a mathematical approach, in specific a model reduction technique, that allows (i) to quantify the importance of the different state variables for a given input-output relationship, and (ii) to reduce the dynamics to its essential features -- allowing for a physiological interpretation of state variables as well as parameter estimation in the statistical analysis of clinical data. We develop a model reduction technique using a control theoretic setting by first defining a novel type of time-limited controllability and observability gramians for nonlinear systems. We then show the superiority of the time-limited generalised gramians for nonlinear systems in the context of balanced truncation for a benchmark system from control theory.
The concept of time-limited controllability and observability gramians is subsequently used to introduce a state and time-dependent quantity called the input-response (ir) index that quantifies the importance of state variables for a given input-response relationship at a particular time.
We subsequently link our approach to sensitivity analysis, thus, enabling for the first time the use of sensitivity coefficients for state space reduction. The sensitivity based ir-indices are given as a product of two sensitivity coefficients. This allows not only for a computational more efficient calculation but also for a clear distinction of the extent to which the input impacts a state variable and the extent to which a state variable impacts the output. 
The ir-indices give insight into the coordinated action of specific state variables for a chosen input-response relationship. 
Our developed model reduction technique results in reduced models that still allow for a mechanistic interpretation in terms of the quantities/state variables of the original system, which is a key requirement in the field of systems pharmacology and systems biology and distinguished the reduced models from so-called empirical drug effect models. The ir-indices are explicitly defined with respect to a reference trajectory and thereby dependent on the initial state (this is an important feature of the measure). This is demonstrated for an example from the field of systems pharmacology, showing that the reduced models are very informative in their ability to detect (genetic) deficiencies in certain physiological entities. Comparing our novel model reduction technique to the already existing techniques shows its superiority.
The novel input-response index as a measure of the importance of state variables provides a powerful tool for understanding the complex dynamics of large-scale systems in the context of a specific drug-response relationship. Furthermore, the indices provide a means for a very efficient model order reduction and, thus, an important step towards translating insight from biological processes incorporated in detailed systems pharmacology models into the population analysis of clinical data.
N2  - Die kontinuierliche Erforschung von biologischen Prozessen hat zur Entwicklung umfangreicher, mechanistischer systembiologischer Modelle von pharmakologisch relevanten Netzwerken beigetragen. Während diese Modelle in der Regel darauf ausgelegt sind, die Auswirkung von Stimuli oder Störungen auf die Systemdynamik zu untersuchen, liegt der Fokus in der pharmakologis- chen Forschung häufig auf einer bestimmten Kontrolle, z.B. der Dosis eines Wirkstoffes, und einer bestimmten Ausgangsgröße, welche in Bezug steht zu dem Wirkstoff-Effekt oder das Ansprechen auf einen Wirkstoff über einen Surrogatmarker. Die Untersuchung und ein einfaches Verständnis einer spezifischen Eingabe-Ausgabe-Beziehung wird durch die Komplexität der Interaktionen sowie der Größe des Modells erschwert.

Das Ziel dieser vorliegenden Arbeit ist die Entwicklung eines mathematischen Ansatzes, insbesondere eines Modellreduktionsverfahrens, der es ermöglicht, (i) die Bedeutung der verschiedenen Zustandsvariablen für eine gegebene Eingabe-Ausgabe-Beziehung zu quantifizieren, und (ii) die Dynamik des Systems auf seine wesentlichen Merkmale zu reduzieren, während gleichzeitig die physiologische Interpretierbarkeit von Zustandsvariablen sowie eine Parameterschätzung im Rahmen von einer statistischen Analyse klinischer Daten ermöglicht wird. Unter Verwendung eines kontrolltheoretischen Settings entwickeln wir eine Modellreduktionstechnik, indem wir vorerst einen neuartigen Typ von zeitlich begrenzten Kontrolllierbarkeits- und Beobachtbarkeitsgramian für nichtlineare Systeme definieren. Anschließend zeigen wir die Überlegenkeit der zeitlich begrenzten verallgemeinerten Gramian für nichtlineare Systeme im Kontext von Balanced Truncation am Beispiel eines Benchmark-Systems aus der Kontrolltheorie. Wir nutzten das Konzept der zeitlich begrenzten Kontrolllierbarkeits- und Beobachtbarkeitsgramian, um eine neue Zustands- und zeitabhängige Größe, die als Input-Response (IR-) Index bezeichnet wird, einzuführen. Dieser Index quantifiziert die Bedeutung von Zustandsvariablen zu einem bestimmten Zeitpunkt für eine bestimmte Eingabe-Ausgabe-Beziehung. Schließlich verknüpfen wir unseren Ansatz mit der Sensitivitätsanalyse und ermöglichen so erstmals die Verwendung von Sensitivitätskoeffizienten im Rahmen der Reduktion des Zustandsraumes. Wir erhalten die sensitivitätsbasierten IR-Indizes als Produkt zweier Sensitivitätskoeffizienten. Dies ermöglicht nicht nur eine effizientere Berechnung, sondern auch eine klare Unterscheidung, inwieweit die Eingabe eine Zustandsvariable beeinflusst und inwieweit eine Zustandsvariable die Ausgabe beeinflusst. Mit Hilfe der IR-Indizes erhalten wir einen Einblick in den koordinierten Ablauf der Aktivierung von spezifischen Zustandsvariablen für eine ausgewählte Eingabe-Ausgabe-Beziehung. Unser entwickeltes Modellreduktionsverfahren resultiert in reduzierten Modelle, welche eine mechanistische Interpretation hinsichtlich der Originalgrößen und Zustandsvariablen des Ursprungssystems zulassen. Dies war eine wichtige Anforderung an das Verfahren von Seiten der Systempharmakologie und -biologie. Die reduzierten Modelle unterscheiden sich damit wesentlich von den so genannten empirischen Wirkstoff-Effekt-Modellen. Die IR-Indizes sind explizit in Bezug auf eine Referenzlösung definiert und damit vom Anfangszustand abhängig (dies ist ein wichtiges Merkmal der Indizes). Wir zeigen anhand eines Beispiels aus dem Bereich der Systempharmakologie, dass die reduzierten Modelle sehr aussagekräftig sind, um (genetische) Mängel in bestimmten physiologischen Einheiten festzustellen. Der Vergleich unseres neuartigen Modellreduktionsverfahrens mit den bereits vorhandenen Verfahren zeigt dessen Überlegenheit.

Der neuartige IR-Index als Maß für die Wichtigkeit von Zustandsvariablen bietet ein leistungsfähiges mathematisches Werkzeug zum Verständnis und der Analyse der komplexen Dynamik von großen Systemen im Kontext einer bestimmten Wirkstoff-Effekt-Beziehung. Darüber hinaus sind die Indizes eine wichtige Grundlage für das eingeführte und sehr effiziente Modellreduktionsverfahren. Insgesamt stellt dies einen wichtigen Schritt zur Nutzung von Erkenntnissen über biologische Prozesse in Form von detaillierten systempharmakologischen Modellen in der Populationsanalyse klinischer Daten dar.
KW  - model order reduction
KW  - control theory
KW  - large-scale mechanistic systems
KW  - systems pharmacology
KW  - Modellreduktion
KW  - Kontrolltheorie
KW  - komplexe mechanistische Systeme
KW  - Systempharmakologie
Y1  - 2019
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-440598
ER  - 
TY  - THES
A1  - Solms, Alexander Maximilian
T1  - Integrating nonlinear mixed effects and physiologically–based modeling approaches for the analysis of repeated measurement studies
T1  - Integration nicht-linearer gemischter Modelle und physiologie-basierte Modellierung Ansätze in die Auswertung longitudinaler Studien
BT  - with applications in quantitative pharmacology and quantitative 
psycholinguistics
N2  - During the drug discovery & development process, several phases encompassing a number of preclinical and clinical studies have to be successfully passed to demonstrate safety and efficacy of a new drug candidate. As part of these studies, the characterization of the drug's pharmacokinetics (PK) is an important aspect, since the PK is assumed to strongly impact safety and efficacy. To this end, drug concentrations are measured repeatedly over time in a study population. The objectives of such studies are to describe the typical PK time-course and the associated variability between subjects. Furthermore, underlying sources significantly contributing to this variability, e.g. the use of comedication, should be identified. The most commonly used statistical framework to analyse repeated measurement data is the nonlinear mixed effect (NLME) approach. At the same time, ample knowledge about the drug's properties already exists and has been accumulating during the discovery & development process: Before any drug is tested in humans, detailed knowledge about the PK in different animal species has to be collected. This drug-specific knowledge and general knowledge about the species' physiology is exploited in mechanistic physiological based PK (PBPK) modeling approaches -it is, however, ignored in the classical NLME modeling approach.

Mechanistic physiological based models aim to incorporate relevant and known physiological processes which contribute to the overlying process of interest. In comparison to data--driven models they are usually more complex from a mathematical perspective. For example, in many situations, the number of model parameters outrange the number of measurements and thus reliable parameter estimation becomes more complex and partly impossible. As a consequence, the integration of powerful mathematical estimation approaches like the NLME modeling approach -which is widely used in data-driven modeling -and the mechanistic modeling approach is not well established; the observed data is rather used as a confirming instead of a model informing and building input.

Another aggravating circumstance of an integrated approach is the inaccessibility to the details of the NLME methodology so that these approaches can be adapted to the specifics and needs of mechanistic modeling. Despite the fact that the NLME modeling approach exists for several decades, details of the mathematical methodology is scattered around a wide range of literature and a comprehensive, rigorous derivation is lacking. Available literature usually only covers selected parts of the mathematical methodology. Sometimes, important steps are not described or are only heuristically motivated, e.g. the iterative algorithm to finally determine the parameter estimates.

Thus, in the present thesis the mathematical methodology of NLME modeling is systemically described and complemented to a comprehensive description,
comprising the common theme from ideas and motivation to the final parameter estimation. Therein, new insights for the interpretation of different approximation methods used in the context of the NLME modeling approach are given and illustrated; furthermore, similarities and differences between them are outlined. Based on these findings, an expectation-maximization (EM) algorithm to determine estimates of a NLME model is described. 

Using the EM algorithm and the lumping methodology by Pilari2010, a new approach on how PBPK and NLME modeling can be combined is presented and exemplified for the antibiotic levofloxacin. Therein, the lumping identifies which processes are informed by the available data and the respective model reduction improves the robustness in parameter estimation. Furthermore, it is shown how apriori known factors influencing the variability and apriori known unexplained variability is incorporated to further mechanistically drive the model development. Concludingly, correlation between parameters and between covariates is automatically accounted for due to the mechanistic derivation of the lumping and the covariate relationships.

A useful feature of PBPK models compared to classical data-driven PK models is in the possibility to predict drug concentration within all organs and tissue in the body. Thus, the resulting PBPK model for levofloxacin is used to predict drug concentrations and their variability within soft tissues which are the site of action for levofloxacin. These predictions are compared with data of muscle and adipose tissue obtained by microdialysis, which is an invasive technique to measure a proportion of drug in the tissue, allowing to approximate the concentrations in the interstitial fluid of tissues. Because, so far, comparing human in vivo tissue PK and PBPK predictions are not established, a new conceptual framework is derived. The comparison of PBPK model predictions and microdialysis measurements shows an adequate agreement and reveals further strengths of the presented new approach. 

We demonstrated how mechanistic PBPK models, which are usually developed in the early stage of drug development, can be used as basis for model building in the analysis of later stages, i.e. in clinical studies. As a consequence, the extensively collected and accumulated knowledge about species and drug are utilized and updated with specific volunteer or patient data. The NLME approach combined with mechanistic modeling reveals new insights for the mechanistic model, for example identification and quantification of variability in mechanistic processes. This represents a further contribution to the learn & confirm paradigm across different stages of drug development.

Finally, the applicability of mechanism--driven model development is demonstrated on an example from the field of Quantitative Psycholinguistics to analyse repeated eye movement data. Our approach gives new insight into the interpretation of these experiments and the processes behind.
N2  - Für die Erforschung und Entwicklung eines neuen Arzneistoffes wird die sichere und wirksame Anwendung in präklinischen und klinischen Studien systematisch untersucht. Ein wichtiger Bestandteil dieser Studien ist die Bestimmung der Pharmakokinetik (PK), da über diese das Wirkungs- und Nebenwirkungsprofil maßgeblich mitbestimmt wird. Um die PK zu bestimmen wird in der Studienpopulation die Wirkstoffkonzentration im Blut wiederholt über die Zeit gemessen. Damit kann sowohl der Konzentrations-Zeit-Verlauf als auch die dazugehörige Variabilität in der Studienpopulation bestimmt werden. Darüber hinaus ist ein weiteres Ziel, die Ursachen dieser Variabilität zu  identifizieren. Fär die Auswertung der Daten werden nichtlineare, gemischte Effektmodelle (NLME) eingesetzt.

Im Vorfeld der klinischen Studien sind bereits viele Eigenschaften des Wirkstoffes bekannt, da der Wirkstoff-Testung am Menschen die Bestimmung der PK an verschiedenen Tierspezies voraus geht. Auf Basis dieser wirkstoffspezifischen Daten und des Wissens um die spezifische humane Physiologie können mittels mechanistisch physiologiebasierter Modelle Vorhersagen für die humane PK getroffen werden. Bei der Analyse von PK Daten mittels NLME Modellen wird dieses vorhandene Wissen jedoch nicht verwertet.

In physiologiebasierten Modellen werden physiologische Prozesse, die die PK bestimmen und beeinflussen können,  ber+cksichtigt. Aus mathematischer Sicht sind solche mechanistischen Modelle im Allgemeinen deutlich komplexer als empirisch motivierte Modelle. In der Anwendung kommt es deswegen häufig zu Situationen, in denen die Anzahl der Modellparameter die Anzahl der zugrunde liegenden Beobachtungen übertrifft. Daraus folgt unter anderem, dass die Parameterschätzung, wie sie in empirisch motivierten Modellen genutzt wird, in der Regel unzuverlässig bzw. nicht möglich ist. In Folge dessen werden klinische Daten in der mechanistischen Modellierung meist nur zur Modellqualifizierung genutzt und nicht in die Modell(weiter)entwicklung integriert.

Ein weiterer erschwerender Umstand, NLME und PBPK Modelle in der Anwendung zu kombinieren, beruht auch auf der Komplexität des NLME Ansatzes. Obwohl diese Methode seit Jahrzehnten existiert, sind in der Literatur nur ausgewählte Teilstücke der zugrunde liegenden Mathematik beschrieben und hergeleitet; eine lückenlose Beschreibung fehlt. Aus diesem Grund werden in der vorliegenden Arbeit systematisch die Methodik und mathematischen Zusammenhänge des NLME Ansatzes, von der ursprüngliche Idee und Motivation bis zur Parameterschätzung beschrieben. In diesem Kontext werden neue Interpretationen der unterschiedlichen Methoden, die im Rahmen der NLME Modellierung verwendet werden, vorgestellt; zudem werden Gemeinsamkeiten und Unterschiede zwischen diesen herausgearbeitet. Mittels dieser Erkenntnisse wird ein Expectation-Maximization (EM) Algorithmus zur Parameterschätzung in einer NLME Analyse beschrieben.

Mittels des neuen EM Algorithmus, kombiniert mit dem Lumping-Ansatz von Pilari und Huisinga (S. Pilari, W. Huisinga, JPKPD Vol. 37(4), 2010.) wird anhand des Antibiotikums Levofloxacin ein neuer konzeptioneller Ansatz entwickelt, der PBPK- und NLME-Modellierung zur Datenanalyse integriert. Die Lumping-Methode definiert hierbei, welche Prozesse von den verfügbaren Daten informiert werden, sie verbessert somit die Robustheit der Parameterschätzung. Weiterhin wird gezeigt, wie a-priori Wissen über Variabilität und Faktoren, die diese beeinflussen, sowie unerklärte Variabilität in das Modell integriert werden können.

Ein elementarer Vorteil von PBPK Modellen gegenüber empirisch motivieren PK Modellen besteht in der Möglichkeit, Wirkstoffkonzentrationen innerhalb von Organen und Gewebe im Körper vorherzusagen. So kann das PBPK-Modell für Levofloxacin genutzt werden, um Wirkstoffkonzentrationen innerhalb der Gewebe vorherzusagen, in denen typischerweise Infektionen auftreten. Für Muskel- und Fettgewebe werden die PBPK-Vorhersagen mit Mikrodialyse Gewebemessungen verglichen. Die gute übereinstimmung von PBPK-Modell und Mikrodialyse stellt eine noch nicht vorhanden Validierung des PBPK-Gewebemodells im Menschen dar.

In dieser Dissertation wird gezeigt, wie mechanistische PBPK Modelle, die in der Regel in der frühen Phase der Arzneimittelentwicklung entwickelt werden, erfolgreich zur Analyse von klinischen Studien eingesetzt werden können. Das bestehende Wissen über den neuen Wirkstoff wird somit gezielt genutzt und mit klinischen Daten von Probanden oder Patienten aktualisiert. Im Fall von Levofloxacin konnte Variabilität in mechanistischen Prozessen identifiziert und quantifiziert werden. Dieses Vorgehen liefert einen weiteren Beitrag zum learn & confirm Paradigma im Forschungs- und Entwicklungsprozess eines neuen Wirkstoffes.

Abschließend wird anhand eines weiteren real world-Beispieles aus dem Bereich der quantitativen Psycholinguistik die Anwendbarkeit und der Nutzen des vorgestellten integrierten Ansatz aus mechanistischer und NLME Modellierung in der Analyse von Blickbewegungsdaten gezeigt. Mittels eines mechanistisch motivierten Modells wird die Komplexität des Experimentes und der Daten abgebildet, wodurch sich neue Interpretationsmöglichkeiten ergeben.
KW  - NLME
KW  - PBPK
KW  - EM
KW  - lumping
KW  - popPBPK
KW  - mechanistic modeling
KW  - population analysis
KW  - popPK
KW  - microdialysis
KW  - nicht-lineare gemischte Modelle (NLME)
KW  - physiologie-basierte Pharmacokinetic (PBPK)
KW  - EM
KW  - Lumping
KW  - popPBPK
KW  - popPK
KW  - mechanistische Modellierung
KW  - Populations Analyse
KW  - Microdialyse
Y1  - 2017
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-397070
ER  - 
TY  - THES
A1  - Gopalakrishnan, Sathej
T1  - Mathematical modelling of host-disease-drug interactions in HIV disease
T1  - Mathematische Modellierung von Pathogen-Wirkstoff-Wirt-Interaktionen im Kontext der HIV Erkrankung
N2  - The human immunodeficiency virus (HIV) has resisted nearly three decades of efforts targeting a cure. Sustained suppression of the virus has remained a challenge, mainly due
to the remarkable evolutionary adaptation that the virus exhibits by the accumulation of drug-resistant mutations in its genome. Current therapeutic strategies aim at achieving and maintaining a low viral burden and typically involve multiple drugs. The choice of optimal combinations of these drugs is crucial, particularly in the background of treatment failure having occurred previously with certain other drugs. An understanding of the dynamics of viral mutant genotypes aids in the assessment of treatment failure with a certain drug
combination, and exploring potential salvage treatment regimens.

Mathematical models of viral dynamics have proved invaluable in understanding the viral life cycle and the impact of antiretroviral drugs. However, such models typically use simplified and coarse-grained mutation schemes, that curbs the extent of their application to drug-specific clinical mutation data, in order to assess potential next-line therapies. Statistical
models of mutation accumulation have served well in dissecting mechanisms of resistance evolution by reconstructing mutation pathways under different drug-environments. While these models perform well in predicting treatment outcomes by statistical learning, they do not incorporate drug effect mechanistically. Additionally, due to an inherent lack of
temporal features in such models, they are less informative on aspects such as predicting mutational abundance at treatment failure. This limits their application in analyzing the
pharmacology of antiretroviral drugs, in particular, time-dependent characteristics of HIV therapy such as pharmacokinetics and pharmacodynamics, and also in understanding the impact of drug efficacy on mutation dynamics.

In this thesis, we develop an integrated model of in vivo viral dynamics incorporating drug-specific mutation schemes learned from clinical data. Our combined modelling
approach enables us to study the dynamics of different mutant genotypes and assess mutational abundance at virological failure. As an application of our model, we estimate in vivo
fitness characteristics of viral mutants under different drug environments. Our approach also extends naturally to multiple-drug therapies. Further, we demonstrate the versatility of our model by showing how it can be modified to incorporate recently elucidated mechanisms of drug action including molecules that target host factors.

Additionally, we address another important aspect in the clinical management of HIV disease, namely drug pharmacokinetics. It is clear that time-dependent changes in in vivo
drug concentration could have an impact on the antiviral effect, and also influence decisions on dosing intervals. We present a framework that provides an integrated understanding
of key characteristics of multiple-dosing regimens including drug accumulation ratios and half-lifes, and then explore the impact of drug pharmacokinetics on viral suppression.

Finally, parameter identifiability in such nonlinear models of viral dynamics is always a concern, and we investigate techniques that alleviate this issue in our setting.
N2  - Das Humane Immundefiecienz-Virus (HIV) widerstanden hat fast drei Jahrzehnten eff Orts targeting eine Heilung. Eine anhaltende Unterdrückung des Virus hat noch eine Herausforderung, vor allem aufgrund der bemerkenswerten evolutionären Anpassung, dass das Virus Exponate durch die Ansammlung von Medikamenten-resistenten Mutationen in seinem Genom. Aktuelle therapeutische Strategien zielen auf das Erreichen und die Erhaltung einer niedrigen virale Belastung und umfassen in der Regel mehrere Medikamente. Die Wahl der optimalen Kombinationen dieser Medikamente ist von entscheidender Bedeutung, besonders im Hintergrund der Behandlung Fehler eingetreten, die zuvor mit bestimmten anderen Medikamenten. Ein Verständnis für die Dynamik der viralen mutierten Genotypen Aids in die Bewertung der Behandlung Fehler mit einer bestimmten Kombination und der Erkundung potenzieller Bergung Behandlungsschemata.
Mathematische Modelle für virale Dynamik haben sich als unschätzbar erwiesen hat im Verständnis der viralen Lebenszyklus und die Auswirkungen von antiretroviralen Medikamenten. Allerdings sind solche Modelle verwenden in der Regel simplified und grobkörnigen Mutation Regelungen, dass Aufkantungen den Umfang ihrer Anwendung auf Arzneimittel-ganz speziellec Mutation klinische Daten, um zu beurteilen, mögliche nächste-line Therapien. Statistische Modelle der Mutation Anhäufung gedient haben gut in präparieren Mechanismen der Resistenz Evolution durch Mutation Rekonstruktion Pathways unter verschiedenen Medikamenten-Umgebungen. Während diese Modelle führen gut in der Vorhersage der Ergebnisse der Behandlung durch statistische lernen, sie enthalten keine Droge E ffect mechanistisch. Darüber hinaus aufgrund einer innewohnenden Mangel an zeitlichen Funktionen in solchen Modellen, sie sind weniger informativ auf Aspekte wie die Vorhersage mutational Fülle an Versagen der Behandlung. Dies schränkt die Anwendung in der Analyse der Pharmakologie von antiretroviralen Medikamenten, insbesondere, Zeit-abhängige Merkmale der HIV-Therapie wie Pharmakokinetik und Pharmakodynamik, und auch in dem Verständnis der Auswirkungen von Drogen e fficacy auf Mutation Dynamik.
In dieser Arbeit, die wir bei der Entwicklung eines integrierten Modells von In-vivo-virale Dynamik Einbeziehung drug-ganz speziellec Mutation Systeme gelernt aus den klinischen Daten. Unsere kombinierten Modellansatz ermöglicht uns die Untersuchung der Dynamik von diff schiedene mutierten Genotypen und bewerten mutational Fülle an virologischem Versagen. Als Anwendung unseres Modells schätzen wir In-vivo-fitness Merkmale der viralen Mutanten unter di fferent drug Umgebungen. Unser Ansatz erstreckt sich auch natürlich auf mehrere-Therapien. Weitere zeigen wir die Vielseitigkeit unseres Modells zeigen, wie es können Modified zu integrieren kürzlich aufgeklärt Mechanismen der Drug Action einschließlich Molekülen, dass target host Faktoren.
Zusätzlich haben wir Adresse ein weiterer wichtiger Aspekt in der klinischen Management der HIV-Erkrankung, das heißt Drogen Pharmakokinetik. Es ist klar, dass die Zeit-abhängige Änderungen in In-vivo-Wirkstoffkonzentration könnten die Auswirkungen auf die antivirale E ffect und haben auch Einfluss auf die Entscheidungen über Dosierungsintervalle. Wir präsentieren ein Framework, bietet ein integriertes Verständnis der wichtigsten Merkmale von mehreren Dosierungsschemata einschließlich Kumulation Übersetzungen und Halbwertszeiten, und untersuchen Sie die Auswirkungen von Drogen auf die Pharmakokinetik Virussuppression.
Schließlich, Parameter identifiFähigkeit in solchen nichtlineare Modelle der virale Dynamik ist immer ein Anliegen, und wir untersuchen Methoden, um dieses Problem in unserer Einstellung.
KW  - HIV
KW  - mathematical modelling
KW  - viral fitness
KW  - pharmacokinetics
KW  - parameter estimation
KW  - HIV Erkrankung
KW  - Pharmakokinetik
KW  - Fitness
KW  - mathematische Modellierung
KW  - Kombinationstherapie
Y1  - 2016
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-100100
ER  - 
TY  - JOUR
A1  - Stachanow, Viktoria
A1  - Neumann, Uta
A1  - Blankenstein, Oliver
A1  - Bindellini, Davide
A1  - Melin, Johanna
A1  - Ross, Richard
A1  - Whitaker, Martin J. J.
A1  - Huisinga, Wilhelm
A1  - Michelet, Robin
A1  - Kloft, Charlotte
T1  - Exploring dried blood spot cortisol concentrations as an alternative for monitoring pediatric adrenal insufficiency patients
BT  - a model-based analysis
JF  - Frontiers in pharmacology
N2  - Congenital adrenal hyperplasia (CAH) is the most common form of adrenal insufficiency in childhood; it requires cortisol replacement therapy with hydrocortisone (HC, synthetic cortisol) from birth and therapy monitoring for successful treatment. In children, the less invasive dried blood spot (DBS) sampling with whole blood including red blood cells (RBCs) provides an advantageous alternative to plasma sampling. 

Potential differences in binding/association processes between plasma and DBS however need to be considered to correctly interpret DBS measurements for therapy monitoring. While capillary DBS samples would be used in clinical practice, venous cortisol DBS samples from children with adrenal insufficiency were analyzed due to data availability and to directly compare and thus understand potential differences between venous DBS and plasma. A previously published HC plasma pharmacokinetic (PK) model was extended by leveraging these DBS concentrations. 

In addition to previously characterized binding of cortisol to albumin (linear process) and corticosteroid-binding globulin (CBG; saturable process), DBS data enabled the characterization of a linear cortisol association with RBCs, and thereby providing a quantitative link between DBS and plasma cortisol concentrations. The ratio between the observed cortisol plasma and DBS concentrations varies highly from 2 to 8. Deterministic simulations of the different cortisol binding/association fractions demonstrated that with higher blood cortisol concentrations, saturation of cortisol binding to CBG was observed, leading to an increase in all other cortisol binding fractions. 

In conclusion, a mathematical PK model was developed which links DBS measurements to plasma exposure and thus allows for quantitative interpretation of measurements of DBS samples.
KW  - adrenal insufficiency
KW  - cortisol
KW  - dried blood spots
KW  - pediatrics
KW  - pharmacokinetics
KW  - binding
KW  - association
KW  - red blood cells
Y1  - 2022
U6  - https://doi.org/10.3389/fphar.2022.819590
SN  - 1663-9812
VL  - 13
PB  - Frontiers Media
CY  - Lausanne
ER  - 
TY  - THES
A1  - Schindler, Daniel
T1  - Mathematical modeling and simulation of protrusion-driven cell dynamics
T1  - Mathematische Modellierung und Simulation von amöboiden Zelldynamiken
N2  - Amoeboid cell motility takes place in a variety of biomedical processes such as cancer metastasis, embryonic morphogenesis, and wound healing. In contrast to other forms of cell motility, it is mainly driven by substantial cell shape changes. Based on the interplay of explorative membrane protrusions at the front and a slower-acting membrane retraction at the rear, the cell moves in a crawling kind of way. Underlying these protrusions and retractions are multiple physiological processes resulting in changes of the cytoskeleton, a meshwork of different multi-functional proteins. The complexity and versatility of amoeboid cell motility raise the need for novel computational models based on a profound theoretical framework to analyze and simulate the dynamics of the cell shape.

The objective of this thesis is the development of (i) a mathematical framework to describe contour dynamics in time and space, (ii) a computational model to infer expansion and retraction characteristics of individual cell tracks and to produce realistic contour dynamics, (iii) and a complementing Open Science approach to make the above methods fully accessible and easy to use.

In this work, we mainly used single-cell recordings of the model organism Dictyostelium discoideum. Based on stacks of segmented microscopy images, we apply a Bayesian approach to obtain smooth representations of the cell membrane, so-called cell contours. We introduce a one-parameter family of regularized contour flows to track reference points on the contour (virtual markers) in time and space. This way, we define a coordinate system to visualize local geometric and dynamic quantities of individual contour dynamics in so-called kymograph plots. In particular, we introduce the local marker dispersion as a measure to identify membrane protrusions and retractions in a fully automated way.

This mathematical framework is the basis of a novel contour dynamics model, which consists of three biophysiologically motivated components: one stochastic term, accounting for membrane protrusions, and two deterministic terms to control the shape and area of the contour, which account for membrane retractions. Our model provides a fully automated approach to infer protrusion and retraction characteristics from experimental cell tracks while being also capable of simulating realistic and qualitatively different contour dynamics. Furthermore, the model is used to classify two different locomotion types: the amoeboid and a so-called fan-shaped type.

With the complementing Open Science approach, we ensure a high standard regarding the usability of our methods and the reproducibility of our research. In this context, we introduce our software publication named AmoePy, an open-source Python package to segment, analyze, and simulate amoeboid cell motility. Furthermore, we describe measures to improve its usability and extensibility, e.g., by detailed run instructions and an automatically generated source code documentation, and to ensure its functionality and stability, e.g., by automatic software tests, data validation, and a hierarchical package structure.

The mathematical approaches of this work provide substantial improvements regarding the modeling and analysis of amoeboid cell motility. We deem the above methods, due to their generalized nature, to be of greater value for other scientific applications, e.g., varying organisms and experimental setups or the transition from unicellular to multicellular movement. Furthermore, we enable other researchers from different fields, i.e., mathematics, biophysics, and medicine, to apply our mathematical methods. By following Open Science standards, this work is of greater value for the cell migration community and a potential role model for other Open Science contributions.
N2  - Amöboide Zellmotilität findet bei einer Vielzahl biomedizinischer Prozesse wie Krebsmetastasierung, embryonaler Morphogenese und Wundheilung statt. Im Gegensatz zu anderen Formen der Zellmotilität wird sie hauptsächlich durch erhebliche Formveränderungen der Zelle angetrieben. Sie beruht auf dem Zusammenspiel von explorativen Membranausstülpungen an der Vorderseite und einem langsamer wirkenden Membraneinzug an der Rückseite. Die Komplexität amöboider Zellmotilität machen neue Berechnungsmodelle erforderlich, um die Dynamik der Zellform mathematisch fundiert zu analysieren und zu simulieren.

Ziel dieser Arbeit ist die Entwicklung (i) eines mathematischen Frameworks zur Beschreibung der Konturendynamik in Zeit und Raum, (ii) eines Computermodells, um Eigenschaften der Membranveränderungen von einzelnen Zellen zu inferieren und gleichzeitig realistische Konturdynamiken zu simulieren, (iii) und eines ergänzenden Open-Science-Ansatzes, um die oben genannten Methoden vollständig zugänglich und leicht anwendbar zu machen.

Auf der Grundlage von aufeinander folgenden Mikroskopiebildern vom Modellorganismus Dictyostelium discoideum, wenden wir einen Bayesschen Ansatz an, um glatte Darstellungen der Zellmembran, sogenannte Zellkonturen, zu erhalten. Wir führen eine einparametrige Familie von regularisierten Konturflüssen ein, um Referenzpunkte auf der Kontur (virtuelle Marker) in Zeit und Raum zu verfolgen. Auf diese Weise definieren wir ein Koordinatensystem zur Visualisierung lokaler geometrischer und dynamischer Größen der individuellen Konturdynamiken in sogenannten Kymographen-Plots. Insbesondere führen wir die lokale Marker-Dispersion ein, mit der signifikante Membranveränderungen identifiziert werden können.

Dieses mathematische Framework bildet die Grundlage für unser neues Modell zur Beschreibung von Konturendynamiken. Es besteht aus drei biophysiologisch motivierten Komponenten: einem stochastischen Term, der die Membranausstülpungen steuert, und zwei deterministischen Termen, die das Membraneinziehen, unter Berücksichtigung der Konturform und -fläche, steuern. Unser Modell bietet einen vollautomatisierten Ansatz zur Inferrenz der Charakteristiken von Membranveränderungen für experimentelle Zelldaten. Außerdem ermöglicht es die Simulation von realistischen und qualitativ unterschiedlichen Konturendynamiken.

Mit dem ergänzenden Open-Science-Ansatz setzen wir einen hohen Standard hinsichtlich der Nutzbarkeit unserer Methoden und der Reproduzierbarkeit unserer Forschung. In diesem Kontext stellen wir die Softwarepublikation AmoePy vor, ein Open-Source-Pythonpaket zur Segmentierung, Analyse und Simulation von amöboider Zellmotilität. Darüber hinaus beschreiben wir Maßnahmen zur Verbesserung der Benutzerfreundlichkeit und Erweiterbarkeit, z. B. durch detaillierte Ausführanweisungen und eine automatisch generierte Quellcodedokumentation, und zur Gewährleistung der Funktionalität und Stabilität, z. B. durch automatische Softwaretests, Datenvalidierung und eine hierarchische Paketstruktur.

Die mathematischen Methoden dieser Arbeit stellen wesentliche Verbesserungen in der Modellierung und Analyse der amöboiden Zellmotilität dar. Wir sind der Ansicht, dass die oben genannten Methoden aufgrund ihrer Verallgemeinerbarkeit von größerem Wert für andere wissenschaftliche Anwendungen sind und potentiell einsetzbar in verschiedenen Wissenschaftsfeldern sind, u. a. Mathematik, Biophysik und Medizin. Durch die Einhaltung von Open-Science-Standards ist diese Arbeit von größerem Wert und ein potenzielles Vorbild für andere Open-Science-Beiträge.
KW  - amöboide Bewegung
KW  - Zellmotilität
KW  - mathematische Modellierung
KW  - offene Wissenschaft
KW  - amoeboid motion
KW  - cell motility
KW  - mathematical modeling
KW  - open science
Y1  - 2023
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-613275
ER  - 
TY  - JOUR
A1  - Hijazi, Saddam
A1  - Freitag, Melina A.
A1  - Landwehr, Niels
T1  - POD-Galerkin reduced order models and physics-informed neural networks for solving inverse problems for the Navier-Stokes equations
JF  - Advanced modeling and simulation in engineering sciences : AMSES
N2  - We present a Reduced Order Model (ROM) which exploits recent developments in Physics Informed Neural Networks (PINNs) for solving inverse problems for the Navier-Stokes equations (NSE). In the proposed approach, the presence of simulated data for the fluid dynamics fields is assumed. A POD-Galerkin ROM is then constructed by applying POD on the snapshots matrices of the fluid fields and performing a Galerkin projection of the NSE (or the modified equations in case of turbulence modeling) onto the POD reduced basis. A POD-Galerkin PINN ROM is then derived by introducing deep neural networks which approximate the reduced outputs with the input being time and/or parameters of the model. The neural networks incorporate the physical equations (the POD-Galerkin reduced equations) into their structure as part of the loss function. Using this approach, the reduced model is able to approximate unknown parameters such as physical constants or the boundary conditions. A demonstration of the applicability of the proposed ROM is illustrated by three cases which are the steady flow around a backward step, the flow around a circular cylinder and the unsteady turbulent flow around a surface mounted cubic obstacle.
KW  - Proper orthogonal decomposition
KW  - Inverse problems
KW  - Physics-based machine learning
KW  - Navier-Stokes equations
Y1  - 2023
U6  - https://doi.org/10.1186/s40323-023-00242-2
SN  - 2213-7467
VL  - 10
IS  - 1
PB  - SpringerOpen
CY  - Berlin
ER  - 
TY  - JOUR
A1  - Molkenthin, Christian
A1  - Donner, Christian
A1  - Reich, Sebastian
A1  - Zöller, Gert
A1  - Hainzl, Sebastian
A1  - Holschneider, Matthias
A1  - Opper, Manfred
T1  - GP-ETAS: semiparametric Bayesian inference for the spatio-temporal epidemic type aftershock sequence model
JF  - Statistics and Computing
N2  - The spatio-temporal epidemic type aftershock sequence (ETAS) model is widely used to describe the self-exciting nature of earthquake occurrences. While traditional inference methods provide only point estimates of the model parameters, we aim at a fully Bayesian treatment of model inference, allowing naturally to incorporate prior knowledge and uncertainty quantification of the resulting estimates. Therefore, we introduce a highly flexible, non-parametric representation for the spatially varying ETAS background intensity through a Gaussian process (GP) prior. Combined with classical triggering functions this results in a new model formulation, namely the GP-ETAS model. We enable tractable and efficient Gibbs sampling by deriving an augmented form of the GP-ETAS inference problem. This novel sampling approach allows us to assess the posterior model variables conditioned on observed earthquake catalogues, i.e., the spatial background intensity and the parameters of the triggering function. Empirical results on two synthetic data sets indicate that GP-ETAS outperforms standard models and thus demonstrate the predictive power for observed earthquake catalogues including uncertainty quantification for the estimated parameters. Finally, a case study for the l'Aquila region, Italy, with the devastating event on 6 April 2009, is presented.
KW  - Self-exciting point process
KW  - Hawkes process
KW  - Spatio-temporal ETAS model
KW  - Bayesian inference
KW  - Sampling
KW  - Earthquake modeling
KW  - Gaussian process
KW  - Data augmentation
Y1  - 2022
U6  - https://doi.org/10.1007/s11222-022-10085-3
SN  - 0960-3174
SN  - 1573-1375
VL  - 32
IS  - 2
PB  - Springer
CY  - Dordrecht
ER  - 
TY  - JOUR
A1  - Kucharski, Maciej
A1  - Ergintav, Arzu
A1  - Ahmad, Wael Abdullah
A1  - Krstić, Miloš
A1  - Ng, Herman Jalli
A1  - Kissinger, Dietmar
T1  - A Scalable 79-GHz Radar Platform Based on Single-Channel Transceivers
JF  - IEEE Transactions on Microwave Theory and Techniques
N2  - This paper presents a scalable E-band radar platform based on single-channel fully integrated transceivers (TRX) manufactured using 130-nm silicon-germanium (SiGe) BiCMOS technology. The TRX is suitable for flexible radar systems exploiting massive multiple-input-multipleoutput (MIMO) techniques for multidimensional sensing. A fully integrated fractional-N phase-locked loop (PLL) comprising a 39.5-GHz voltage-controlled oscillator is used to generate wideband frequency-modulated continuous-wave (FMCW) chirp for E-band radar front ends. The TRX is equipped with a vector modulator (VM) for high-speed carrier modulation and beam-forming techniques. A single TRX achieves 19.2-dBm maximum output power and 27.5-dB total conversion gain with input-referred 1-dB compression point of -10 dBm. It consumes 220 mA from 3.3-V supply and occupies 3.96 mm(2) silicon area. A two-channel radar platform based on full-custom TRXs and PLL was fabricated to demonstrate high-precision and high-resolution FMCW sensing. The radar enables up to 10-GHz frequency ramp generation in 74-84-GHz range, which results in 1.5-cm spatial resolution. Due to high output power, thus high signal-to-noise ratio (SNR), a ranging precision of 7.5 mu m for a target at 2 m was achieved. The proposed architecture supports scalable multichannel applications for automotive FMCW using a single local oscillator (LO).
KW  - Automotive
KW  - E-band
KW  - frequency-modulated continuous-wave (FMCW)
KW  - patch antenna
KW  - phase-locked loop (PLL)
KW  - power amplifier (PA)
KW  - radar
KW  - scalable
KW  - transceiver (TRX)
Y1  - 2019
U6  - https://doi.org/10.1109/TMTT.2019.2914104
SN  - 0018-9480
SN  - 1557-9670
VL  - 67
IS  - 9
SP  - 3882
EP  - 3896
PB  - Inst. of Electr. and Electronics Engineers
CY  - Piscataway
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  - Engbert, Ralf
A1  - Rabe, Maximilian Michael
A1  - Kliegl, Reinhold
A1  - Reich, Sebastian
T1  - Sequential data assimilation of the stochastic SEIR epidemic model for regional COVID-19 dynamics
JF  - Bulletin of mathematical biology : official journal of the Society for Mathematical Biology
N2  - Newly emerging pandemics like COVID-19 call for predictive models to implement precisely tuned responses to limit their deep impact on society. Standard epidemic models provide a theoretically well-founded dynamical description of disease incidence. For COVID-19 with infectiousness peaking before and at symptom onset, the SEIR model explains the hidden build-up of exposed individuals which creates challenges for containment strategies. However, spatial heterogeneity raises questions about the adequacy of modeling epidemic outbreaks on the level of a whole country. Here, we show that by applying sequential data assimilation to the stochastic SEIR epidemic model, we can capture the dynamic behavior of outbreaks on a regional level. Regional modeling, with relatively low numbers of infected and demographic noise, accounts for both spatial heterogeneity and stochasticity. Based on adapted models, short-term predictions can be achieved. Thus, with the help of these sequential data assimilation methods, more realistic epidemic models are within reach.
KW  - Stochastic epidemic model
KW  - Sequential data assimilation
KW  - Ensemble Kalman
KW  - filter
KW  - COVID-19
Y1  - 2020
U6  - https://doi.org/10.1007/s11538-020-00834-8
SN  - 0092-8240
SN  - 1522-9602
VL  - 83
IS  - 1
PB  - Springer
CY  - New York
ER  - 
TY  - JOUR
A1  - Gerlach, Moritz
A1  - Glück, Jochen
A1  - Kunze, Markus
T1  - Stability of transition semigroups and applications to parabolic equations
JF  - Transactions of the American Mathematical Society
N2  - This paper deals with the long-term behavior of positive operator semigroups on spaces of bounded functions and of signed measures, which have applications to parabolic equations with unbounded coefficients and to stochas-tic analysis. The main results are a Tauberian type theorem characterizing the convergence to equilibrium of strongly Feller semigroups and a generalization of a classical convergence theorem of Doob. None of these results requires any kind of time regularity of the semigroup.
KW  - Transition probabilities
KW  - strong Feller property
KW  - asymptotic
KW  - behavior
KW  - invariant measure
KW  - parabolic equations
Y1  - 2023
U6  - https://doi.org/10.1090/tran/8620
SN  - 0002-9947
SN  - 1088-6850
VL  - 376
IS  - 1
SP  - 153
EP  - 180
PB  - American Mathematical Soc.
CY  - Providence
ER  - 
TY  - JOUR
A1  - Dimitrova, Ilinka
A1  - Koppitz, Jörg
T1  - On relative ranks of the semigroup of orientation-preserving transformations on infinite chain with restricted range
JF  - Communications in algebra
N2  - Let X be an infinite linearly ordered set and let Y be a nonempty subset of X. We calculate the relative rank of the semigroup OP(X,Y) of all orientation-preserving transformations on X with restricted range Y modulo the semigroup O(X,Y) of all order-preserving transformations on X with restricted range Y. For Y = X, we characterize the relative generating sets of minimal size.
KW  - Order-preserving transformations
KW  - orientation-preserving
KW  - transformations
KW  - relative rank
KW  - restricted range
KW  - transformation
KW  - semigroups on infinite chain
Y1  - 2022
U6  - https://doi.org/10.1080/00927872.2021.2000998
SN  - 0092-7872
SN  - 1532-4125
VL  - 50
IS  - 5
SP  - 2157
EP  - 2168
PB  - Taylor & Francis Group
CY  - Philadelphia
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  - Kretzschmar, Mirjam E.
A1  - Ashby, Ben
A1  - Fearon, Elizabeth
A1  - Overton, Christopher E.
A1  - Panovska-Griffiths, Jasmina
A1  - Pellis, Lorenzo
A1  - Quaife, Matthew
A1  - Rozhnova, Ganna
A1  - Scarabel, Francesca
A1  - Stage, Helena B.
A1  - Swallow, Ben
A1  - Thompson, Robin N.
A1  - Tildesley, Michael J.
A1  - Villela, Daniel Campos
T1  - Challenges for modelling interventions for future pandemics
JF  - Epidemics
N2  - Mathematical modelling and statistical inference provide a framework to evaluate different non-pharmaceutical and pharmaceutical interventions for the control of epidemics that has been widely used during the COVID-19 pandemic. In this paper, lessons learned from this and previous epidemics are used to highlight the challenges for future pandemic control. We consider the availability and use of data, as well as the need for correct parameterisation and calibration for different model frameworks. We discuss challenges that arise in describing and distinguishing between different interventions, within different modelling structures, and allowing both within and between host dynamics. We also highlight challenges in modelling the health economic and political aspects of interventions. Given the diversity of these challenges, a broad variety of interdisciplinary expertise is needed to address them, combining mathematical knowledge with biological and social insights, and including health economics and communication skills. Addressing these challenges for the future requires strong cross disciplinary collaboration together with close communication between scientists and policy makers.
KW  - Mathematical models
KW  - Pandemics
KW  - Pharmaceutical interventions
KW  - Non-pharmaceutical interventions
KW  - Policy support
Y1  - 2022
U6  - https://doi.org/10.1016/j.epidem.2022.100546
SN  - 1755-4365
SN  - 1878-0067
VL  - 38
PB  - Elsevier
CY  - Amsterdam
ER  - 
TY  - THES
A1  - Sareeto, Apatsara
T1  - Algebraic properties of a subsemigroup of the symmetric inverse semigroup
Y1  - 2024
ER  - 
TY  - JOUR
A1  - Gerlach, Moritz Reinhardt
A1  - Glück, Jochen
T1  - On a convergence theorem for semigroups of positive integral operators
JF  - Comptes Rendus Mathematique
N2  - We give a new and very short proof of a theorem of Greiner asserting that a positive and contractive -semigroup on an -space is strongly convergent in case it has a strictly positive fixed point and contains an integral operator. Our proof is a streamlined version of a much more general approach to the asymptotic theory of positive semigroups developed recently by the authors. Under the assumptions of Greiner's theorem, this approach becomes particularly elegant and simple. We also give an outlook on several generalisations of this result.
Y1  - 2017
U6  - https://doi.org/10.1016/j.crma.2017.07.017
SN  - 1631-073X
SN  - 1778-3569
VL  - 355
SP  - 973
EP  - 976
PB  - Elsevier
CY  - Paris
ER  - 
TY  - JOUR
A1  - Gerlach, Moritz Reinhardt
T1  - Convergence of dynamics and the Perron-Frobenius operator
JF  - Israel Journal of Mathematics
N2  - We complete the picture how the asymptotic behavior of a dynamical system is reflected by properties of the associated Perron-Frobenius operator. Our main result states that strong convergence of the powers of the Perron-Frobenius operator is equivalent to setwise convergence of the underlying dynamic in the measure algebra. This situation is furthermore characterized by uniform mixing-like properties of the system.
Y1  - 2018
U6  - https://doi.org/10.1007/s11856-018-1671-7
SN  - 0021-2172
SN  - 1565-8511
VL  - 225
IS  - 1
SP  - 451
EP  - 463
PB  - Hebrew univ magnes press
CY  - Jerusalem
ER  - 
TY  - JOUR
A1  - Gerlach, Moritz Reinhardt
A1  - Glück, Jochen
T1  - Convergence of positive operator semigroups
JF  - Transactions of the American Mathematical Society
N2  - We present new conditions for semigroups of positive operators to converge strongly as time tends to infinity. Our proofs are based on a novel approach combining the well-known splitting theorem by Jacobs, de Leeuw, and Glicksberg with a purely algebraic result about positive group representations. Thus, we obtain convergence theorems not only for one-parameter semigroups but also for a much larger class of semigroup representations. Our results allow for a unified treatment of various theorems from the literature that, under technical assumptions, a bounded positive C-0-semigroup containing or dominating a kernel operator converges strongly as t ->infinity. We gain new insights into the structure theoretical background of those theorems and generalize them in several respects; especially we drop any kind of continuity or regularity assumption with respect to the time parameter.
KW  - Positive semigroups
KW  - semigroup representations
KW  - asymptotic behavior
KW  - kernel operator
Y1  - 2019
U6  - https://doi.org/10.1090/tran/7836
SN  - 0002-9947
SN  - 1088-6850
VL  - 372
IS  - 9
SP  - 6603
EP  - 6627
PB  - American Mathematical Soc.
CY  - Providence
ER  -