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  - Hanisch, Florian
A1  - Ludewig, Matthias
T1  - The fermionic integral on loop space and the Pfaffian line bundle
JF  - Journal of mathematical physics
N2  - As the loop space of a Riemannian manifold is infinite-dimensional, it is a non-trivial problem to make sense of the "top degree component " of a differential form on it. 
In this paper, we show that a formula from finite dimensions generalizes to assign a sensible "top degree component " to certain composite forms, obtained by wedging with the exponential (in the exterior algebra) of the canonical presymplectic 2-form on the loop space. 
This construction is a crucial ingredient for the definition of the supersymmetric path integral on the loop space.
Y1  - 2022
U6  - https://doi.org/10.1063/5.0060355
SN  - 0022-2488
SN  - 1089-7658
SN  - 1527-2427
VL  - 63
IS  - 12
PB  - American Inst. of Physics
CY  - College Park, Md.
ER  - 
TY  - JOUR
A1  - Metzger, Jan
T1  - Refined position estimates for surfaces of Willmore type in Riemannian manifolds
JF  - Communications in analysis and geometry
N2  - In this paper we consider surfaces which are critical points of the Willmore functional subject to constrained area. 
In the case of small area we calculate the corrections to the intrinsic geometry induced by the ambient curvature. 
These estimates together with the choice of an adapted geometric center of mass lead to refined position estimates in relation to the scalar curvature of the ambient manifold.
Y1  - 2023
U6  - https://doi.org/10.4310/CAG.2022.v30.n10.a5
SN  - 1019-8385
SN  - 1944-9992
VL  - 30
IS  - 10
SP  - 2315
EP  - 2346
PB  - International Press of Boston
CY  - Somerville, Mass.
ER  - 
TY  - JOUR
A1  - Rœlly, Sylvie
A1  - Zass, Alexander
T1  - Marked Gibbs point processes with unbounded interaction
BT  - An existence result
JF  - Journal of statistical physics
N2  - We construct marked Gibbs point processes in R-d under quite general assumptions. Firstly, we allow for interaction functionals that may be unbounded and whose range is not assumed to be uniformly bounded. Indeed, our typical interaction admits an a.s. finite but random range. Secondly, the random marks-attached to the locations in R-d-belong to a general normed space G. They are not bounded, but their law should admit a super-exponential moment. The approach used here relies on the so-called entropy method and large-deviation tools in order to prove tightness of a family of finite-volume Gibbs point processes. An application to infinite-dimensional interacting diffusions is also presented.
KW  - Marked Gibbs process
KW  - Infinite-dimensional interacting diffusion
KW  - Specific entropy
KW  - DLR equation
Y1  - 2020
U6  - https://doi.org/10.1007/s10955-020-02559-3
SN  - 0022-4715
SN  - 1572-9613
VL  - 179
IS  - 4
SP  - 972
EP  - 996
PB  - Springer
CY  - New York
ER  - 
TY  - JOUR
A1  - Seyedhosseini, Mehran
T1  - A variant of Roe algebras for spaces with cylindrical ends with applications in relative higher index theory
JF  - Journal of noncommutative geometry
N2  - In this paper, we define a variant of Roe algebras for spaces with cylindrical ends and use this to study questions regarding existence and classification of metrics of positive scalar curvature on such manifolds which are collared on the cylindrical end. 
We discuss how our constructions are related to relative higher index theory as developed by Chang, Weinberger, and Yu and use this relationship to define higher rho-invariants for positive scalar curvature metrics on manifolds with boundary. 
This paves the way for the classification of these metrics. 
Finally, we use the machinery developed here to give a concise proof of a result of Schick and the author, which relates the relative higher index with indices defined in the presence of positive scalar curvature on the boundary.
KW  - positive scalar curvature
KW  - higher index theory
KW  - rho-invariants
KW  - Roe algebras
KW  - manifolds with cylindrical ends
KW  - manifolds with boundary
Y1  - 2022
U6  - https://doi.org/10.4171/JNCG/457
SN  - 1661-6952
SN  - 1661-6960
VL  - 16
IS  - 2
SP  - 595
EP  - 624
PB  - European Mathematical Society
CY  - Zurich
ER  - 
TY  - THES
A1  - Hecher, Markus
T1  - Advanced tools and methods for treewidth-based problem solving
N2  - In the last decades, there was a notable progress in solving the well-known Boolean satisfiability (Sat) problem, which can be witnessed by powerful Sat solvers. One of the reasons why these solvers are so fast are structural properties of instances that are utilized by the solver’s interna. This thesis deals with the well-studied structural property treewidth, which measures the closeness of an instance to being a tree. In fact, there are many problems parameterized by treewidth that are solvable in polynomial time in the instance size when parameterized by treewidth.
In this work, we study advanced treewidth-based methods and tools for problems in knowledge representation and reasoning (KR). Thereby, we provide means to establish precise runtime results (upper bounds) for canonical problems relevant to KR. Then, we present a new type of problem reduction, which we call decomposition-guided (DG) that
allows us to precisely monitor the treewidth when reducing from one problem to another problem. This new reduction type will be the basis for a long-open lower bound result for quantified Boolean formulas and allows us to design a new methodology for establishing runtime lower bounds for problems parameterized by treewidth.
Finally, despite these lower bounds, we provide an efficient implementation of algorithms that adhere to treewidth. Our approach finds suitable abstractions of instances, which are subsequently refined in a recursive fashion, and it uses Sat solvers for solving subproblems. It turns out that our resulting solver is quite competitive for two canonical counting problems related to Sat.
N2  - In den letzten Jahrzehnten konnte ein beachtlicher Fortschritt im Bereich der Aussagenlogik verzeichnet werden. Dieser äußerte sich dadurch, dass für das wichtigste Problem in diesem Bereich, genannt „Sat“, welches sich mit der Fragestellung befasst, ob eine gegebene aussagenlogische Formel erfüllbar ist oder nicht, überwältigend schnelle Computerprogramme („Solver“) entwickelt werden konnten. Interessanterweise liefern diese Solver eine beeindruckende Leistung, weil sie oft selbst Probleminstanzen mit mehreren Millionen von Variablen spielend leicht lösen können. Auf der anderen Seite jedoch glaubt man in der Wissenschaft weitgehend an die Exponentialzeithypothese (ETH), welche besagt, dass man im schlimmsten Fall für das Lösen einer Instanz in diesem Bereich exponentielle Laufzeit in der Anzahl der Variablen benötigt. Dieser vermeintliche Widerspruch ist noch immer nicht vollständig geklärt, denn wahrscheinlich gibt es viele ineinandergreifende Gründe für die Schnelligkeit aktueller Sat Solver. Einer dieser Gründe befasst sich weitgehend mit strukturellen Eigenschaften von Probleminstanzen, die wohl indirekt und intern von diesen Solvern ausgenützt werden.

Diese Dissertation beschäftigt sich mit solchen strukturellen Eigenschaften, nämlich mit der sogenannten Baumweite. Die Baumweite ist sehr gut erforscht und versucht zu messen, wie groß der Abstand von Probleminstanzen zu Bäumen ist (Baumnähe). Allerdings ist dieser Parameter sehr generisch und bei Weitem nicht auf Problemstellungen der Aussagenlogik beschränkt. Tatsächlich gibt es viele weitere Probleme, die parametrisiert mit Baumweite in polynomieller Zeit gelöst werden können. Interessanterweise gibt es auch viele Probleme in der Wissensrepräsentation (KR), von denen man davon ausgeht, dass sie härter sind als das Problem Sat, die bei beschränkter Baumweite in polynomieller Zeit gelöst werden können. Ein prominentes Beispiel solcher Probleme ist das Problem QSat, welches sich für die Gültigkeit einer gegebenen quantifizierten, aussagenlogischen Formel (QBF), das sind aussagenlogische Formeln, wo gewisse Variablen existenziell bzw. universell quantifiziert werden können, befasst. Bemerkenswerterweise wird allerdings auch im Zusammenhang mit Baumweite, ähnlich zu Methoden der klassischen Komplexitätstheorie, die tatsächliche Komplexität (Härte) solcher Problemen quantifiziert, wo man die exakte Laufzeitabhängigkeit beim Problemlösen in der Baumweite (Stufe der Exponentialität) beschreibt.

Diese Arbeit befasst sich mit fortgeschrittenen, Baumweite-basierenden Methoden und Werkzeugen für Probleme der Wissensrepräsentation und künstlichen Intelligenz (AI). Dabei präsentieren wir Methoden, um präzise Laufzeitresultate (obere Schranken) für prominente Fragmente der Antwortmengenprogrammierung (ASP), welche ein kanonisches Paradigma zum Lösen von Problemen der Wissensrepräsentation darstellt, zu erhalten. Unsere Resultate basieren auf dem Konzept der dynamischen Programmierung, die angeleitet durch eine sogenannte Baumzerlegung und ähnlich dem Prinzip „Teile-und-herrsche“ funktioniert. Solch eine Baumzerlegung ist eine konkrete, strukturelle Zerlegung einer Probleminstanz, die sich stark an der Baumweite orientiert.

Des Weiteren präsentieren wir einen neuen Typ von Problemreduktion, den wir als „decomposition-guided (DG)“, also „zerlegungsangeleitet“, bezeichnen. Dieser Reduktionstyp erlaubt es, Baumweiteerhöhungen und -verringerungen während einer Problemreduktion von einem bestimmten Problem zu einem anderen Problem präzise zu untersuchen und zu kontrollieren. Zusätzlich ist dieser neue Reduktionstyp die Basis, um ein lange offen gebliebenes Resultat betreffend quantifizierter, aussagenlogischer Formeln zu zeigen. Tatsächlich sind wir damit in der Lage, präzise untere Schranken, unter der Annahme der Exponentialzeithypothese, für das Problem QSat bei beschränkter Baumweite zu zeigen. Genauer gesagt können wir mit diesem Konzept der DG Reduktionen zeigen, dass das Problem QSat, beschränkt auf Quantifizierungsrang ` und parametrisiert mit Baumweite k, im Allgemeinen nicht besser als in einer Laufzeit, die `-fach exponentiell in der Baumweite und polynomiell in der Instanzgröße ist1, lösen. Dieses Resultat hebt auf nicht-inkrementelle Weise ein bekanntes Ergebnis für Quantifizierungsrang 2 auf beliebige Quantifizierungsränge, allerdings impliziert es auch sehr viele weitere Konsequenzen.

Das Resultat über die untere Schranke des Problems QSat erlaubt es, eine neue Methodologie zum Zeigen unterer Schranken einer Vielzahl von Problemen der Wissensrepräsentation und künstlichen Intelligenz, zu etablieren. In weiterer Konsequenz können wir damit auch zeigen, dass die oberen Schranken sowie die DG Reduktionen dieser Arbeit unter der Hypothese ETH „eng“ sind, d.h., sie können wahrscheinlich nicht mehr signifikant verbessert werden. Die Ergebnisse betreffend der unteren Schranken für QSat und die dazugehörige Methodologie konstituieren in gewisser Weise eine Hierarchie von über Baumweite parametrisierte Laufzeitklassen. Diese Laufzeitklassen können verwendet werden, um die Härte von Problemen für das Ausnützen von Baumweite zu quantifizieren und diese entsprechend ihrer Laufzeitabhängigkeit bezüglich Baumweite zu kategorisieren.

Schlussendlich und trotz der genannten Resultate betreffend unterer Schranken sind wir im Stande, eine effiziente Implementierung von Algorithmen basierend auf dynamischer Programmierung, die entlang einer Baumzerlegung angeleitet wird, zur Verfügung zu stellen. Dabei funktioniert unser Ansatz dahingehend, indem er probiert, passende Abstraktionen von Instanzen zu finden, die dann im Endeffekt sukzessive und auf rekursive Art und Weise verfeinert und verbessert werden. Inspiriert durch die enorme Effizienz und Effektivität der Sat Solver, ist unsere Implementierung ein hybrider Ansatz, weil sie den starken Gebrauch von Sat Solvern zum Lösen diverser Subprobleme, die während der dynamischen Programmierung auftreten, pflegt. Dabei stellt sich heraus, dass der resultierende Solver unserer Implementierung im Bezug auf Effizienz beim Lösen von zwei kanonischen, Sat-verwandten Zählproblemen mit bestehenden Solvern locker mithalten kann. Tatsächlich sind wir im Stande, Instanzen, wo die oberen Schranken von Baumweite 260 übersteigen, zu lösen. Diese überraschende Beobachtung zeigt daher, dass Baumweite ein wichtiger Parameter sein könnte, der wohl in modernen Designs von Solvern berücksichtigt werden sollte.
KW  - Treewidth
KW  - Dynamic Programming
KW  - Knowledge Representation and Reasoning
KW  - Artificial Intelligence
KW  - Computational Complexity
KW  - Parameterized Complexity
KW  - Answer Set Programming
KW  - Exponential Time Hypothesis
KW  - Lower Bounds
KW  - Algorithms
KW  - Algorithmen
KW  - Antwortmengenprogrammierung
KW  - Künstliche Intelligenz
KW  - Komplexitätstheorie
KW  - Dynamische Programmierung
KW  - Exponentialzeit Hypothese
KW  - Wissensrepräsentation und Schlussfolgerung
KW  - Untere Schranken
KW  - Parametrisierte Komplexität
KW  - Baumweite
Y1  - 2021
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-512519
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  - 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  - THES
A1  - Fischer, Florian
T1  - Hardy inequalities on graphs
T1  - Hardy-Ungleichungen auf Graphen
N2  - Die Dissertation befasst sich mit einer zentralen Ungleichung der nicht-linearen Potentialtheorie, der Hardy-Ungleichung. Sie besagt, dass das nicht-lineare Energiefunktional von unten durch eine p-te Potenz einer gewichteten p-Norm abgeschätzt werden kann, p>1. Das Energiefunktional besteht dabei aus einem  Divergenz- und einem beliebigen Potentialteil. Als zugrundeliegender Raum wurden hier lokal summierbare unendliche Graphen gewählt. Bisherige Veröffentlichungen zu Hardy-Ungleichungen auf Graphen haben vor allem den Spezialfall p=2 betrachtet, oder lokal endliche Graphen ohne Potentialteil.
	
Zwei grundlegende Fragestellungen ergeben sich nun ganz natürlich: Für welche Graphen gibt überhaupt es eine Hardy-Ungleichung? Und, wenn es sie gibt, gibt es einen Weg um ein optimales Gewicht zu erhalten? Antworten auf diese Fragen werden in Theorem 10.1 und Theorem 12.1 gegeben. Theorem 10.1 gibt eine Reihe an Charakterisierungen an; unter anderem gibt es eine Hardy-Ungleichung auf einem Graphen genau dann, wenn es eine Greensche Funktion gibt. Theorem 12.1 gibt eine explizite Formel an, um optimale Hardy-Gewichte für lokal endliche Graphen unter einigen technischen Zusatzannahmen zu berechnen. In Beispielen wird gezeigt, dass Greensche Funktionen gute Kandidaten sind um in die Formel eingesetzt zu werden.
	
Um diese beiden Theoreme beweisen zu können, müssen eine Vielzahl an Techniken erarbeitet werden, welche in den ersten Kapiteln behandelt werden. Dabei sind eine Verallgemeinerung der Grundzustandstransformation (Theorem 4.1), ein Agmon-Allegretto-Piepenbrink-artiges Resultat (Theorem 6.1) und das Vergleichsprinzip (Proposition 7.3) besonders hervorzuheben, da diese Resultate sehr häufig angewendet werden und somit das Fundament der Dissertation bilden.

Es wird zudem darauf Wert gelegt die Theorie durch Beispiele zu veranschaulichen. Hierbei wird der Fokus auf die natürlichen Zahlen, Euklidische Gitter, Bäume und Sterne gelegt. Als Abschluss werden noch eine nicht-lineare Version der Heisenbergschen Unschärferelation und eine Rellich-Ungleichung aus der Hardy-Ungleichung geschlussfolgert.
N2  - The dissertation deals with a central inequality of non-linear potential theory, the Hardy inequality. It states that the non-linear energy functional can be estimated from below by a pth power of a weighted p-norm, p>1. The energy functional consists of a divergence part and an arbitrary potential part. Locally summable infinite graphs were chosen as the underlying space. Previous publications on Hardy inequalities on graphs have mainly considered the special case p=2, or locally finite graphs without a potential part.
	
Two fundamental questions now arise quite naturally: For which graphs is there a Hardy inequality at all? And, if it exists, is there a way to obtain an optimal weight? Answers to these questions are given in Theorem 10.1 and Theorem 12.1. Theorem 10.1 gives a number of characterizations; among others, there is a Hardy inequality on a graph if and only if there is a Green's function. Theorem 12.1 gives an explicit formula to compute optimal Hardy weights for locally finite graphs under some additional technical assumptions. Examples show that Green's functions are good candidates to be used in the formula.

Emphasis is also placed on illustrating the theory with examples. The focus is on natural numbers, Euclidean lattices, trees and star graphs. Finally, a non-linear version of the Heisenberg uncertainty principle and a Rellich inequality are derived from the Hardy inequality.
KW  - graph theory
KW  - Hardy inequality
KW  - quasi-linear potential theory
KW  - p-Laplacian
KW  - criticality theory
KW  - Graphentheorie
KW  - Hardy-Ungleichung
KW  - quasilineare Potentialtheorie
KW  - p-Laplace-Operator
KW  - Kritikalitätstheorie
Y1  - 2024
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-647730
ER  - 
TY  - JOUR
A1  - Zass, Alexander
T1  - Gibbs point processes on path space
BT  - existence, cluster expansion and uniqueness
JF  - Markov processes and related fields
N2  - We present general existence and uniqueness results for marked models with pair interactions, exemplified through Gibbs point processes on path space. 
More precisely, we study a class of infinite-dimensional diffusions under Gibbsian interactions, in the context of marked point configurations: the starting points belong to R-d, and the marks are the paths of Langevin diffusions. 

We use the entropy method to prove existence of an infinite-volume Gibbs point process and use cluster expansion tools to provide an explicit activity domain in which uniqueness holds.
KW  - marked Gibbs point processes
KW  - DLR equations
KW  - uniqueness
KW  - cluster
KW  - expansion
KW  - infinite-dimensional diffusions
Y1  - 2021
UR  - https://math-mprf.org/journal/articles/id1643/
SN  - 1024-2953
VL  - 28
IS  - 3
SP  - 329
EP  - 364
PB  - Polymat
CY  - Moscow
ER  - 
TY  - JOUR
A1  - Huang, Daniel Zhengyu
A1  - Huang, Jiaoyang
A1  - Reich, Sebastian
A1  - Stuart, Andrew M.
T1  - Efficient derivative-free Bayesian inference for large-scale inverse problems
JF  - Inverse problems : an international journal of inverse problems, inverse methods and computerised inversion of data
N2  - We consider Bayesian inference for large-scale inverse problems, where computational challenges arise from the need for repeated evaluations of an expensive forward model. 
This renders most Markov chain Monte Carlo approaches infeasible, since they typically require O(10(4)) model runs, or more. 
Moreover, the forward model is often given as a black box or is impractical to differentiate. 
Therefore derivative-free algorithms are highly desirable. We propose a framework, which is built on Kalman methodology, to efficiently perform Bayesian inference in such inverse problems. 
The basic method is based on an approximation of the filtering distribution of a novel mean-field dynamical system, into which the inverse problem is embedded as an observation operator. 
Theoretical properties are established for linear inverse problems, demonstrating that the desired Bayesian posterior is given by the steady state of the law of the filtering distribution of the mean-field dynamical system, and proving exponential convergence to it. 
This suggests that, for nonlinear problems which are close to Gaussian, sequentially computing this law provides the basis for efficient iterative methods to approximate the Bayesian posterior. 
Ensemble methods are applied to obtain interacting particle system approximations of the filtering distribution of the mean-field model; and practical strategies to further reduce the computational and memory cost of the methodology are presented, including low-rank approximation and a bi-fidelity approach. 
The effectiveness of the framework is demonstrated in several numerical experiments, including proof-of-concept linear/nonlinear examples and two large-scale applications: learning of permeability parameters in subsurface flow; and learning subgrid-scale parameters in a global climate model. 

Moreover, the stochastic ensemble Kalman filter and various ensemble square-root Kalman filters are all employed and are compared numerically. 
The results demonstrate that the proposed method, based on exponential convergence to the filtering distribution of a mean-field dynamical system, is competitive with pre-existing Kalman-based methods for inverse problems.
KW  - inverse problem
KW  - uncertainty quantification
KW  - Bayesian inference
KW  - derivative-free optimization
KW  - mean-field dynamical system
KW  - interacting particle system
KW  - ensemble Kalman filter
Y1  - 2022
U6  - https://doi.org/10.1088/1361-6420/ac99fa
SN  - 0266-5611
SN  - 1361-6420
VL  - 38
IS  - 12
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  - 
TY  - JOUR
A1  - Shlapunov, Alexander  A.
A1  - Tarchanov, Nikolaj Nikolaevič
T1  - Inverse image of precompact sets and regular solutions to the Navier-Stokes equations
JF  - Vestnik Udmurtskogo Universiteta. Matematika, mechanika, kompʹjuternye nauki
N2  - We consider the initial value problem for the Navier-Stokes equations over R-3 x [0, T] with time T > 0 in the spatially periodic setting. 
We prove that it induces open injective mappings A(s): B-1(s) -> B-2(s-1) where B-1(s), B-2(s-1) are elements from scales of specially constructed function spaces of Bochner-Sobolev typeparametrized with the smoothness index s is an element of N. 
Finally, we prove that a map Asis surjective if and only if the inverse image A(s)(- 1) (K) of any pre compact set K from the range of the map Asis bounded in the Bochner space L-s([0, T], L-r(T-3))with the Ladyzhenskaya-Prodi-Serrin numbers s, r.
KW  - Navier-Stokes equations
KW  - regular solutions
Y1  - 2022
U6  - https://doi.org/10.35634/vm220208
SN  - 1994-9197
SN  - 2076-5959
VL  - 32
IS  - 2
SP  - 278
EP  - 297
PB  - Udmurtskij gosudarstvennyj universitet
CY  - Iževsk
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  -