TY  - INPR
A1  - Pfäffle, Frank
A1  - Stephan, Christoph A.
T1  - Chiral asymmetry and the spectral action
N2  - We consider orthogonal connections with arbitrary torsion on compact Riemannian manifolds. For the induced Dirac operators, twisted Dirac operators and Dirac operators of Chamseddine-Connes type we compute the spectral action. In addition to the Einstein-Hilbert action and the bosonic part of the Standard Model Lagrangian we find the Holst term from Loop Quantum Gravity, a coupling of the Holst term to the scalar curvature and a prediction for the value of the Barbero-Immirzi parameter.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)20 
Y1  - 2012
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-60046
ER  - 
TY  - INPR
A1  - Bär, Christian
T1  - Renormalized integrals and a path integral formula for the heat kernel on a manifold
N2  - We introduce renormalized integrals which generalize conventional measure theoretic integrals. One approximates the integration domain by measure spaces and defines the integral as the limit of integrals over the approximating spaces. This concept is implicitly present in many mathematical contexts such as Cauchy's principal value, the determinant of operators on a Hilbert space and the Fourier transform of an L^p function. We use renormalized integrals to define a path integral on manifolds by approximation via geodesic polygons. The main part of the paper is dedicated to the proof of a path integral formula for the heat kernel of any self-adjoint generalized Laplace operator acting on sections of a vector bundle over a compact Riemannian manifold.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)21 
KW  - Renormalized integral
KW  - path integral
KW  - Feynman-Kac formula
KW  - generalized Laplace operator
KW  - Riemannian manifold
Y1  - 2012
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-60052
ER  - 
TY  - INPR
A1  - Bär, Christian
T1  - Some properties of solutions to weakly hypoelliptic equations
N2  - A linear differential operator L is called weakly hypoelliptic if any local solution u of Lu = 0 is smooth. We allow for systems, i.e. the coefficients may be matrices, not necessarily of square size. This is a huge class of important operators which covers all elliptic, overdetermined elliptic, subelliptic and parabolic equations. We extend several classical theorems from complex analysis to solutions of any weakly hypoelliptic equation: the Montel theorem providing convergent subsequences, the Vitali theorem ensuring convergence of a given sequence, and Riemann's first removable singularity theorem. In the case of constant coefficients we show that Liouville's theorem holds, any bounded solution must be constant and any L^p solution must vanish.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)22 
KW  - Hypoelliptic operators
KW  - hypoelliptic estimate
KW  - Montel theorem
KW  - Vitali theorem
KW  - Liouville theorem
Y1  - 2012
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-60064
ER  - 
TY  - GEN
A1  - Seiß, Martin
A1  - Spahn, Frank
T1  - Hydrodynamics of Saturn’s dense rings
T2  - Postprints der Universität Potsdam : Postprint Mathematisch Naturwissenschaftliche Reihe
N2  - The space missions Voyager and Cassini together with earthbound observations re-vealed a wealth of structures in Saturn’s rings. There are, for example, waves being excited at ring positions which are in orbital resonance with Saturn’s moons. Other structures can be assigned to embedded moons like empty gaps, moon induced wakes or S-shaped propeller features. Further-more, irregular radial structures are observed in the range from 10 meters until kilometers. Here some of these structures will be discussed in the frame of hydrodynamical modeling of Saturn’s dense rings. For this purpose we will characterize the physical properties of the ring particle ensemble by mean field quantities and point to the special behavior of the transport coefficients. We show that unperturbed rings can become unstable and how diffusion acts in the rings. Additionally, the alternative streamline formalism is introduced to describe perturbed regions of dense rings with applications to the wake damping and the dispersion relation of the density waves.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 574 
KW  - granular gas
KW  - instabilities
KW  - hydrodynamics
KW  - planetary rings
Y1  - 2019
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-413139
SP  - 191
EP  - 218
ER  - 
TY  - GEN
A1  - Mickelsson, Jouko
A1  - Paycha, Sylvie
T1  - The logarithmic residue density of a generalized Laplacian
T2  - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - We show that the residue density of the logarithm of a generalized Laplacian on a closed manifold defines an invariant polynomial-valued differential form. We express it in terms of a finite sum of residues of
classical pseudodifferential symbols. In the case of the square of a Dirac operator, these formulas provide a pedestrian proof of the Atiyah–Singer formula for a pure Dirac operator in four dimensions and for a
twisted Dirac operator on a flat space of any dimension. These correspond to special cases of a more general formula by Scott and Zagier. In our approach, which is of perturbative nature, we use either a Campbell–Hausdorff formula derived by Okikiolu or a noncommutative Taylor-type formula.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 649 
KW  - residue
KW  - index
KW  - Dirac operators
Y1  - 2019
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-413680
SN  - 1866-8372
IS  - 649
ER  - 
TY  - INPR
A1  - Keller, Peter
T1  - Erzeugung gleichverteilter Stichproben von Lozenge-Teilungen mittels Kopplung von Markovketten
N2  - Aus dem Inhalt: 1 Einleitung 2 Eigenschaften der Lozengeteilungen 3 Coupling From The Past (CFTP) 4 Simulation von uniform verteilten Lozengeteilungen 5 Programmlisting und Diskussion der Implementierung 6 Ausblick A Anhang
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2009, 02 
Y1  - 2009
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49506
ER  - 
TY  - INPR
A1  - Zehmisch, René
T1  - Über Waldidentitäten der Brownschen Bewegung
N2  - Aus dem Inhalt: 1 Abraham Wald (1902-1950) 2 Einführung der Grundbegriffe. Einige technische bekannte Ergebnisse 2.1 Martingal und Doob-Ungleichung 2.2 Brownsche Bewegung und spezielle Martingale 2.3 Gleichgradige Integrierbarkeit von Prozessen 2.4 Gestopptes Martingal 2.5 Optionaler Stoppsatz von Doob 2.6 Lokales Martingal 2.7 Quadratische Variation 2.8 Die Dichte der ersten einseitigen Überschreitungszeit der Brown- schen Bewegung 2.9 Waldidentitäten für die Überschreitungszeiten der Brownschen Bewegung 3 Erste Waldidentität 3.1 Burkholder, Gundy und Davis Ungleichungen der gestoppten Brown- schen Bewegung 3.2 Erste Waldidentität für die Brownsche Bewegung 3.3 Verfeinerungen der ersten Waldidentität 3.4 Stärkere Verfeinerung der ersten Waldidentität für die Brown- schen Bewegung 3.5 Verfeinerung der ersten Waldidentität für spezielle Stoppzeiten der Brownschen Bewegung 3.6 Beispiele für lokale Martingale für die Verfeinerung der ersten Waldidentität 3.7 Überschreitungszeiten der Brownschen Bewegung für nichtlineare Schranken 4 Zweite Waldidentität 4.1 Zweite Waldidentität für die Brownsche Bewegung 4.2 Anwendungen der ersten und zweitenWaldidentität für die Brown- schen Bewegung 5 Dritte Waldidentität 5.1 Dritte Waldidentität für die Brownsche Bewegung 5.2 Verfeinerung der dritten Waldidentität 5.3 Eine wichtige Voraussetzung für die Verfeinerung der drittenWal- didentität 5.4 Verfeinerung der dritten Waldidentität für spezielle Stoppzeiten der Brownschen Bewegung 6 Waldidentitäten im Mehrdimensionalen 6.1 Erste Waldidentität im Mehrdimensionalen 6.2 Zweite Waldidentität im Mehrdimensionalen 6.3 Dritte Waldidentität im Mehrdimensionalen 7 Appendix
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2008, 04 
Y1  - 2008
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49469
ER  - 
TY  - INPR
A1  - Klein, Markus
A1  - Zitt, Pierre-André
T1  - Resonances for a diffusion with small noise
N2  - We study resonances for the generator of a diffusion with small noise in R(d) : L = -∈∆ + ∇F * ∇, when the potential F grows slowly at infinity (typically as a square root of the norm). The case when F grows fast is well known, and under suitable conditions one can show that there exists a family of exponentially small eigenvalues, related to the wells of F. We show that, for an F with a slow growth, the spectrum is R+, but we can find a family of resonances whose real parts behave as the eigenvalues of the "quick growth" case, and whose imaginary parts are small.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2008, 02 
Y1  - 2008
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49448
ER  - 
TY  - INPR
A1  - Läuter, Henning
T1  - Empirical Minimax Linear Estimates
N2  - We give the explicit solution for the minimax linear estimate. For scale dependent models an empirical minimax linear estimates is de¯ned and we prove that these estimates are Stein's estimates.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2008, 06 
Y1  - 2008
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49483
ER  - 
TY  - GEN
A1  - Mazzonetto, Sara
A1  - Salimova, Diyora
T1  - Existence, uniqueness, and numerical approximations for stochastic burgers equations
T2  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - In this article, we propose an all-in-one statement which includes existence, uniqueness, regularity, and numerical approximations of mild solutions for a class of stochastic partial differential equations (SPDEs) with non-globally monotone nonlinearities. The proof of this result exploits the properties of an existing fully explicit space-time discrete approximation scheme, in particular the fact that it satisfies suitable a priori estimates. We also obtain almost sure and strong convergence of the approximation scheme to the mild solutions of the considered SPDEs. We conclude by applying the main result of the article to the stochastic Burgers equations with additive space-time white noise.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1393 
KW  - stochastic Burgers equations
KW  - SPDEs
KW  - mild solution
KW  - existence
KW  - numerical approximation
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-515796
SN  - 1866-8372
IS  - 4
ER  - 
TY  - GEN
A1  - Keller, Matthias
A1  - Pinchover, Yehuda
A1  - Pogorzelski, Felix
T1  - From hardy to rellich inequalities on graphs
T2  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - We show how to deduce Rellich inequalities from Hardy inequalities on infinite graphs. Specifically, the obtained Rellich inequality gives an upper bound on a function by the Laplacian of the function in terms of weighted norms. These weights involve the Hardy weight and a function which satisfies an eikonal inequality. The results are proven first for Laplacians and are extended to Schrodinger operators afterwards.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1379 
KW  - 35R02
KW  - 39A12 (primary)
KW  - 26D15
KW  - 31C20
KW  - 35B09
KW  - 58E35 (secondary)
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-542140
SN  - 1866-8372
IS  - 3
ER  - 
TY  - JOUR
A1  - Pasemann, Gregor
A1  - Flemming, Sven
A1  - Alonso, Sergio
A1  - Beta, Carsten
A1  - Stannat, Wilhelm
T1  - Diffusivity estimation for activator-inhibitor models
BT  - theory and application to intracellular dynamics of the actin cytoskeleton
JF  - Journal of nonlinear science
N2  - A theory for diffusivity estimation for spatially extended activator-inhibitor dynamics modeling the evolution of intracellular signaling networks is developed in the mathematical framework of stochastic reaction-diffusion systems. In order to account for model uncertainties, we extend the results for parameter estimation for semilinear stochastic partial differential equations, as developed in Pasemann and Stannat (Electron J Stat 14(1):547-579, 2020), to the problem of joint estimation of diffusivity and parametrized reaction terms. Our theoretical findings are applied to the estimation of effective diffusivity of signaling components contributing to intracellular dynamics of the actin cytoskeleton in the model organism Dictyostelium discoideum.
KW  - Parametric drift estimation
KW  - Stochastic reaction– diffusion
KW  - systems
KW  - Maximum likelihood estimation
KW  - Actin cytoskeleton dynamics
Y1  - 2021
U6  - https://doi.org/10.1007/s00332-021-09714-4
SN  - 0938-8974
SN  - 1432-1467
VL  - 31
IS  - 3
PB  - Springer
CY  - New York
ER  - 
TY  - CHAP
ED  - Kortenkamp, Ulrich
ED  - Kuzle, Ana
T1  - Beiträge zum Mathematikunterricht 2017
BT  - Vorträge auf der 51. Tagung für Didaktik der Mathematik vom 27.02.2017 bis 02.03.2017 in Potsdam
Y1  - 2018
UR  - http://www.wtm-verlag.de/beitraege-zum-mathematikunterricht/
SN  - 978-3-95987-072-6
SN  - 978-3-95987-089-4
PB  - WTM-Verlag
CY  - Münster
ER  - 
TY  - JOUR
A1  - Kürschner, Patrick
A1  - Freitag, Melina A.
T1  - Inexact methods for the low rank solution to large scale Lyapunov equations
JF  - BIT : numerical mathematics ; the leading applied mathematics journal for all computational mathematicians
N2  - The rational Krylov subspace method (RKSM) and the low-rank alternating directions implicit (LR-ADI) iteration are established numerical tools for computing low-rank solution factors of large-scale Lyapunov equations. In order to generate the basis vectors for the RKSM, or extend the low-rank factors within the LR-ADI method, the repeated solution to a shifted linear system of equations is necessary. For very large systems this solve is usually implemented using iterative methods, leading to inexact solves within this inner iteration (and therefore to "inexact methods"). We will show that one can terminate this inner iteration before full precision has been reached and still obtain very good accuracy in the final solution to the Lyapunov equation. In particular, for both the RKSM and the LR-ADI method we derive theory for a relaxation strategy (e.g. increasing the solve tolerance of the inner iteration, as the outer iteration proceeds) within the iterative methods for solving the large linear systems. These theoretical choices involve unknown quantities, therefore practical criteria for relaxing the solution tolerance within the inner linear system are then provided. The theory is supported by several numerical examples, which show that the total amount of work for solving Lyapunov equations can be reduced significantly.
KW  - Lyapunov equation
KW  - alternating direction implicit
KW  - rational Krylov
KW  - subspaces
KW  - low-rank approximations
Y1  - 2019
U6  - https://doi.org/10.1007/s10543-020-00813-4
SN  - 0006-3835
SN  - 1572-9125
VL  - 60
IS  - 4
SP  - 1221
EP  - 1259
PB  - Springer
CY  - Dordrecht
ER  - 
TY  - JOUR
A1  - Hehn, Jennifer
A1  - Mendez, Daniel
A1  - Uebernickel, Falk
A1  - Brenner, Walter
A1  - Broy, Manfred
T1  - On integrating design thinking for human-centered requirements engineering
JF  - IEEE software
N2  - We elaborate on the possibilities and needs to integrate design thinking into requirements engineering, drawing from our research and project experiences. We suggest three approaches for tailoring and integrating design thinking and requirements engineering with complementary synergies and point at open challenges for research and practice.
KW  - requirements engineering
KW  - prototypes
KW  - software
KW  - electronic mail
KW  - tools
KW  - organizations
KW  - design thinking
Y1  - 2019
U6  - https://doi.org/10.1109/MS.2019.2957715
SN  - 0740-7459
SN  - 1937-4194
VL  - 37
IS  - 2
SP  - 25
EP  - 31
PB  - Inst. of Electr. and Electronics Engineers
CY  - Los Alamitos
ER  - 
TY  - JOUR
A1  - Rosenau, Philip
A1  - Pikovskij, Arkadij
T1  - Waves in strongly nonlinear Gardner-like equations on a lattice
JF  - Nonlinearity / the Institute of Physics and the London Mathematical Society
N2  - We introduce and study a family of lattice equations which may be viewed either as a strongly nonlinear discrete extension of the Gardner equation, or a non-convex variant of the Lotka-Volterra chain. Their deceptively simple form supports a very rich family of complex solitary patterns. Some of these patterns are also found in the quasi-continuum rendition, but the more intriguing ones, like interlaced pairs of solitary waves, or waves which may reverse their direction either spontaneously or due a collision, are an intrinsic feature of the discrete realm.
KW  - nonlinear lattice
KW  - solitary wave
KW  - Gardner equation
KW  - compacton
Y1  - 2021
U6  - https://doi.org/10.1088/1361-6544/ac0f51
SN  - 0951-7715
SN  - 1361-6544
VL  - 34
IS  - 8
SP  - 5872
EP  - 5896
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  - 
TY  - BOOK
A1  - Kulik, Alexei Michajlovič
ED  - Roelly, Sylvie
T1  - Introduction to Ergodic rates for Markov chains and processes
BT  - with applications to limit theorems
N2  - The present lecture notes aim for an introduction to the ergodic behaviour of Markov Processes and addresses graduate students, post-graduate students and interested readers.
Different tools and methods for the study of upper bounds on uniform and weak ergodic rates of Markov Processes are introduced. These techniques are then applied to study limit theorems for functionals of Markov processes.
This lecture course originates in two mini courses held at University of Potsdam, Technical University of Berlin and Humboldt University in spring 2013 and Ritsumameikan University in summer 2013. 

Alexei Kulik, Doctor of Sciences, is a Leading researcher at the Institute of Mathematics of Ukrainian National Academy of Sciences.
T3  - Lectures in pure and applied mathematics - 2 
KW  - Markov processes
KW  - Markovprozesse
KW  - long-time behaviour
KW  - Langzeitverhalten
KW  - ergodic rates
KW  - Konvergenzrate
Y1  - 2015
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-79360
SN  - 978-3-86956-338-1
SN  - 2199-4951
SN  - 2199-496X
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Cvetković, Nada
A1  - Conrad, Tim
A1  - Lie, Han Cheng
T1  - A convergent discretization method for transition path theory for diffusion processes
JF  - Multiscale modeling & simulation : a SIAM interdisciplinary journal
N2  - Transition path theory (TPT) for diffusion processes is a framework for analyzing the transitions of multiscale ergodic diffusion processes between disjoint metastable subsets of state space. Most methods for applying TPT involve the construction of a Markov state model on a discretization of state space that approximates the underlying diffusion process. However, the assumption of Markovianity is difficult to verify in practice, and there are to date no known error bounds or convergence results for these methods. We propose a Monte Carlo method for approximating the forward committor, probability current, and streamlines from TPT for diffusion processes. Our method uses only sample trajectory data and partitions of state space based on Voronoi tessellations. It does not require the construction of a Markovian approximating process. We rigorously prove error bounds for the approximate TPT objects and use these bounds to show convergence to their exact counterparts in the limit of arbitrarily fine discretization. We illustrate some features of our method by application to a process that solves the Smoluchowski equation on a triple-well potential.
KW  - ergodic diffusion processes
KW  - transition paths
KW  - rare events
KW  - Monte Carlo
KW  - methods
Y1  - 2021
U6  - https://doi.org/10.1137/20M1329354
SN  - 1540-3459
SN  - 1540-3467
VL  - 19
IS  - 1
SP  - 242
EP  - 266
PB  - Society for Industrial and Applied Mathematics
CY  - Philadelphia
ER  - 
TY  - JOUR
A1  - Perera, Upeksha
A1  - Böckmann, Christine
T1  - Solutions of Direct and Inverse Even-Order Sturm-Liouville Problems Using Magnus Expansion
JF  - Mathematics
N2  - In this paper Lie group method in combination with Magnus expansion is utilized to develop a universal method applicable to solving a Sturm–Liouville problem (SLP) of any order with arbitrary boundary conditions. It is shown that the method has ability to solve direct regular (and some singular) SLPs of even orders (tested for up to eight), with a mix of (including non-separable and finite singular endpoints) boundary conditions, accurately and efficiently. The present technique is successfully applied to overcome the difficulties in finding suitable sets of eigenvalues so that the inverse SLP problem can be effectively solved. The inverse SLP algorithm proposed by Barcilon (1974) is utilized in combination with the Magnus method so that a direct SLP of any (even) order and an inverse SLP of order two can be solved effectively.
KW  - higher-order Sturm–Liouville problems
KW  - inverse Sturm–Liouville problems
KW  - Magnus expansion
Y1  - 2019
U6  - https://doi.org/10.3390/math7060544
SN  - 2227-7390
VL  - 7
IS  - 6
PB  - MDPI
CY  - Basel, Schweiz
ER  - 
TY  - JOUR
A1  - Cseh, Ágnes
A1  - Kavitha, Telikepalli
T1  - Popular matchings in complete graphs
JF  - Algorithmica : an international journal in computer science
N2  - Our input is a complete graph G on n vertices where each vertex has a strict ranking of all other vertices in G. The goal is to construct a matching in G that is popular. A matching M is popular if M does not lose a head-to-head election against any matching M ': here each vertex casts a vote for the matching in {M,M '} in which it gets a better assignment. Popular matchings need not exist in the given instance G and the popular matching problem is to decide whether one exists or not. The popular matching problem in G is easy to solve for odd n. Surprisingly, the problem becomes NP-complete for even n, as we show here. This is one of the few graph theoretic problems efficiently solvable when n has one parity and NP-complete when n has the other parity.
KW  - Popular matching
KW  - Complexity
KW  - Stable matching
Y1  - 2021
U6  - https://doi.org/10.1007/s00453-020-00791-7
SN  - 0178-4617
SN  - 1432-0541
VL  - 83
IS  - 5
SP  - 1493
EP  - 1523
PB  - Springer
CY  - New York
ER  - 
TY  - THES
A1  - Abed, Jamil
T1  - An iterative approach to operators on manifolds with singularities
T1  - Ein iterativer Zugang zu Operatoren auf Mannigfaltigkeiten mit Singularitäten
N2  - We establish elements of a new approach to ellipticity and parametrices within operator algebras on manifolds with higher singularities, only based on some general axiomatic requirements on parameter-dependent operators in suitable scales of spaes. The idea is to model an iterative process with new generations of parameter-dependent operator theories, together with new scales of spaces that satisfy analogous requirements as the original ones, now on a corresponding higher level. The "full" calculus involves two separate theories, one near the tip of the corner and another one at the conical exit to infinity. However, concerning the conical exit to infinity, we establish here a new concrete calculus of edge-degenerate operators which can be iterated to higher singularities.
N2  - Wir führen einen neuen Zugang ein zu Elliptizität und Parametrices in Operatorenalgebren auf Mannigfaltigkeiten mit höheren Singularitäten, nur basierend auf allgemeinen axiomatischen Voraussetzungen über parameter-abhängige Operatoren in geeigneten Skalen von Räumen. Die Idee besteht darin, ein iteratives Verfahren zu modellieren mit neuen Generationen von parameter-abhängigen Operatortheorien, zusammen mit neuen Skalen von Räumen, die analoge Voraussetzungen erfüllen wie die ursprünglichen Objekte, jetzt auf dem entsprechenden höheren Niveau. Der „volle“ Kalkül besteht aus zwei separaten Theorien, eine nahe der Spitze der Ecke und eine andere am konischen Ausgang nach Unendlich. Allerdings, bezüglich des konischen Ausgangs nach Unendlich, bauen wir hier einen neuen konkreten Kalkül von kanten-entarteten Operatoren auf, der für höhere Singularitäten iteriert werden kann.
KW  - Pseudo-Differentialoperatoren
KW  - kanten- und ecken-entartete Symbole
KW  - Elliptizität
KW  - Parametrices
KW  - höhere Singularitäten
KW  - Pseudo-differential operators
KW  - edge- and corner-degenerate symbols
KW  - ellipticity
KW  - parametrices
KW  - higher singularities
Y1  - 2010
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-44757
ER  - 
TY  - THES
A1  - Pirhayati, Mohammad
T1  - Edge operators and boundary value problems
Y1  - 2016
ER  - 
TY  - JOUR
A1  - Chang, Der-Chen
A1  - Mahmoudi, Mahdi Hedayat
A1  - Schulze, Bert-Wolfgang
T1  - Volterra operators in the edge-calculus
JF  - Analysis and Mathematical Physics
N2  - We study the Volterra property of a class of anisotropic pseudo-differential operators on R x B for a manifold B with edge Y and time-variable t. This exposition belongs to a program for studying parabolicity in such a situation. In the present consideration we establish non-smoothing elements in a subalgebra with anisotropic operator-valued symbols of Mellin type with holomorphic symbols in the complex Mellin covariable from the cone theory, where the covariable t of t extends to symbolswith respect to t to the lower complex v half-plane. The resulting space ofVolterra operators enlarges an approach of Buchholz (Parabolische Pseudodifferentialoperatoren mit operatorwertigen Symbolen. Ph. D. thesis, Universitat Potsdam, 1996) by necessary elements to a new operator algebra containing Volterra parametrices under an appropriate condition of anisotropic ellipticity. Our approach avoids some difficulty in choosing Volterra quantizations in the edge case by generalizing specific achievements from the isotropic edge-calculus, obtained by Seiler (Pseudodifferential calculus on manifolds with non-compact edges, Ph. D. thesis, University of Potsdam, 1997), see also Gil et al. (in: Demuth et al (eds) Mathematical research, vol 100. Akademic Verlag, Berlin, pp 113-137, 1997; Osaka J Math 37: 221-260, 2000).
KW  - Volterra operator
KW  - Anisotropic pseudo-differential operators
KW  - Edge calculus
KW  - Operator-valued symbols of Mellin type
Y1  - 2018
U6  - https://doi.org/10.1007/s13324-018-0238-4
SN  - 1664-2368
SN  - 1664-235X
VL  - 8
IS  - 4
SP  - 551
EP  - 570
PB  - Springer
CY  - Basel
ER  - 
TY  - THES
A1  - Lyu, Xiaojing
T1  - Operators on singular manifolds
T1  - Operatoren auf singuläre Mannigfaltigkeiten
N2  - We study the interplay between analysis on manifolds with singularities and complex analysis and develop new structures of operators based on the Mellin transform and tools for iterating the calculus for higher singularities. We refer to the idea of interpreting boundary value problems (BVPs) in terms of pseudo-differential operators with a principal symbolic hierarchy, taking into account that BVPs are a source of cone and edge operator algebras. The respective cone and edge pseudo-differential algebras in turn are the starting point of higher corner theories. In addition there are deep relationships between corner operators and complex analysis. This will be illustrated by the Mellin symbolic calculus.
N2  - Wir studieren den Zusammenhang zwischen Analysis auf Mannigfaltigkeiten mit Singularitäten und komplexer Analysis und entwickeln neue Strukturen von Operatoren basierend auf der Mellin-Transformation und Hilfsmitteln für die Iteration des Kalküls für höhere Singularitäten. Wir beziehen uns auf die Idee von der Interpretation von Randwert-Problemen (BVPs) durch Pseudo-Differential-operatoren und Hauptsymbol-Hierarchien, unter Berüksichtigung der Tatsache, dass BVPs eine Quelle von Konus- und Kanten-Operator- algebren sind. Die betreffenden Konus- und Kanten-Pseudo-differentiellen Algebren sind wiederum der Startpunkt von höheren Eckentheorien. Zusätzlich bestehen tiefe Beziehungen zwischen Ecken-Operatoren und komplexer Analysis. Dies wird illustiert durch den Mellin-Symbol Kalkül.
KW  - order filtration
KW  - Mellin-Symbols
KW  - singular manifolds
KW  - Ordnungs-Filtrierung
KW  - Mellin-Symbole
KW  - singuläre Mannigfaltigkeiten
Y1  - 2016
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-103643
ER  - 
TY  - INPR
A1  - Calvo, D.
A1  - Schulze, Bert-Wolfgang
T1  - Edge symbolic structures of second generation
N2  - Operators on a manifold with (geometric) singularities are degenerate in a natural way. They have a principal symbolic structure with contributions from the different strata of the configuration. We study the calculus of such operators on the level of edge symbols of second generation, based on specific quantizations of the corner-degenerate interior symbols, and show that this structure is preserved under compositions.
T3  - Preprint - (2005) 18 
KW  - Operators on manifolds with second order singularities
KW  - edge quantizations
KW  - continuity in Sobolev spaces with double weights
Y1  - 2005
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-29940
ER  - 
TY  - JOUR
A1  - Flad, Heinz-Jürgen
A1  - Flad-Harutyunyan, Gohar
A1  - Schulze, Bert-Wolfgang
T1  - Explicit Green operators for quantum mechanical Hamiltonians
BT  - II. edge-type singularities of the helium atom
JF  - Asian-European journal of mathematics : AEJM
N2  - We extend our approach of asymptotic parametrix construction for Hamiltonian operators from conical to edge-type singularities which is applicable to coalescence points of two particles of the helium atom and related two electron systems including the hydrogen molecule. Up to second-order, we have calculated the symbols of an asymptotic parametrix of the nonrelativistic Hamiltonian of the helium atom within the Born-Oppenheimer approximation and provide explicit formulas for the corresponding Green operators which encode the asymptotic behavior of the eigenfunctions near an edge.
KW  - Singular analysis
KW  - Schrodinger equation
KW  - many-electron systems
KW  - asymptotic properties of eigenfunctions
Y1  - 2020
U6  - https://doi.org/10.1142/S1793557120501223
SN  - 1793-5571
SN  - 1793-7183
VL  - 13
IS  - 7
PB  - World Scientific
CY  - Singapore
ER  - 
TY  - CHAP
A1  - Rungrottheera, Wannarut
A1  - Chang, Der-Chen
A1  - Schulze, Bert-Wolfgang
T1  - The edge calculus of singularity order >3
T2  - Journal of nonlinear and convex analysis : an international journal
N2  - We study Mellin pseudo-differential algebras on singular straight cones and manifolds with singularity of order >= 3. Those are necessary to express parametrices of elliptic differential operators with a corresponding cornerdegenerate behavior, and we obtain regularity in weighted spaces.
KW  - Pseudo-differential algebras
KW  - symbols
KW  - singular manifolds
KW  - Mellin
KW  - operator calculus
Y1  - 2020
SN  - 1345-4773
SN  - 1880-5221
VL  - 21
IS  - 2
SP  - 387
EP  - 401
PB  - Yokohama Publishers
CY  - Yokohama
ER  - 
TY  - JOUR
A1  - Rungrottheera, Wannarut
A1  - Lyu, Xiaojing
A1  - Schulze, Bert-Wolfgang
T1  - Parameter-dependent edge calculus and corner parametrices
JF  - Journal of nonlinear and convex analysis : an international journal
N2  - Let B be a compact manifold with smooth edge of dimension > 0. We study the interplay between parameter-dependent edge algebra algebra on B and operator families belonging to the corner calculus, and we characterize parametrices in the corner case.
KW  - Edge calculus
KW  - corner parametrices
Y1  - 2018
SN  - 1345-4773
SN  - 1880-5221
VL  - 19
IS  - 12
SP  - 2021
EP  - 2051
PB  - Yokohama Publishers
CY  - Yokohama
ER  - 
TY  - JOUR
A1  - Stauffer, Maxime
A1  - Mengesha, Isaak
A1  - Seifert, Konrad
A1  - Krawczuk, Igor
A1  - Fischer, Jens
A1  - Serugendo, Giovanna Di Marzo
T1  - A computational turn in policy process studies
BT  - coevolving network dynamics of policy change
JF  - Complexity
N2  - The past three decades of policy process studies have seen the emergence of a clear intellectual lineage with regard to complexity. Implicitly or explicitly, scholars have employed complexity theory to examine the intricate dynamics of collective action in political contexts. However, the methodological counterparts to complexity theory, such as computational methods, are rarely used and, even if they are, they are often detached from established policy process theory. Building on a critical review of the application of complexity theory to policy process studies, we present and implement a baseline model of policy processes using the logic of coevolving networks. Our model suggests that an actor's influence depends on their environment and on exogenous events facilitating dialogue and consensus-building. Our results validate previous opinion dynamics models and generate novel patterns. Our discussion provides ground for further research and outlines the path for the field to achieve a computational turn.
Y1  - 2022
U6  - https://doi.org/10.1155/2022/8210732
SN  - 1076-2787
SN  - 1099-0526
VL  - 2022
PB  - Wiley-Hindawi
CY  - London
ER  - 
TY  - JOUR
A1  - Hedayat Mahmoudi, Mahdi
A1  - Schulze, Bert-Wolfgang
T1  - Corner boundary value problems
JF  - Asian-European journal of mathematics
N2  - The paper develops some crucial steps in extending the first-order cone or edge calculus to higher singularity orders. We focus here on order 2, but the ideas are motivated by an iterative approach for higher singularities.
KW  - Mellin operators
KW  - Mellin oscillatory integrals
KW  - exit calculus
KW  - weighted Sobolev spaces
Y1  - 2016
U6  - https://doi.org/10.1142/S1793557117500541
SN  - 1793-5571
SN  - 1793-7183
VL  - 10
IS  - 1
PB  - World Scientific
CY  - Singapore
ER  - 
TY  - JOUR
A1  - Cseh, Agnes
A1  - Faenza, Yuri
A1  - Kavitha, Telikepalli
A1  - Powers, Vladlena
T1  - Understanding popular matchings via stable matchings
JF  - SIAM journal on discrete mathematics
N2  - An instance of the marriage problem is given by a graph G = (A boolean OR B, E), together with, for each vertex of G, a strict preference order over its neighbors. A matching M of G is popular in the marriage instance if M does not lose a head-to-head election against any matching where vertices are voters. Every stable matching is a min-size popular matching; another subclass of popular matchings that always exists and can be easily computed is the set of dominant matchings. A popular matching M is dominant if M wins the head-to-head election against any larger matching. Thus, every dominant matching is a max-size popular matching, and it is known that the set of dominant matchings is the linear image of the set of stable matchings in an auxiliary graph. Results from the literature seem to suggest that stable and dominant matchings behave, from a complexity theory point of view, in a very similar manner within the class of popular matchings. The goal of this paper is to show that there are instead differences in the tractability of stable and dominant matchings and to investigate further their importance for popular matchings. First, we show that it is easy to check if all popular matchings are also stable; however, it is co-NP hard to check if all popular matchings are also dominant. Second, we show how some new and recent hardness results on popular matching problems can be deduced from the NP-hardness of certain problems on stable matchings, also studied in this paper, thus showing that stable matchings can be employed to show not only positive results on popular matchings (as is known) but also most negative ones. Problems for which we show new hardness results include finding a min-size (resp., max-size) popular matching that is not stable (resp., dominant). A known result for which we give a new and simple proof is the NP-hardness of finding a popular matching when G is nonbipartite.
KW  - popular matching
KW  - stable matching
KW  - complexity
KW  - dominant matching
Y1  - 2022
U6  - https://doi.org/10.1137/19M124770X
SN  - 0895-4801
SN  - 1095-7146
VL  - 36
IS  - 1
SP  - 188
EP  - 213
PB  - Society for Industrial and Applied Mathematics
CY  - Philadelphia
ER  - 
TY  - THES
A1  - Khalil, Sara
T1  - Boundary Value Problems on Manifolds with Singularities
T1  - Randwertprobleme auf Mannigfaltigkeiten mit Singularitäten
N2  - In the thesis there are constructed new quantizations for pseudo-differential boundary value problems (BVPs) on manifolds with edge. The shape of operators comes from Boutet de Monvel’s calculus which exists on smooth manifolds with boundary. The singular case, here with edge and boundary, is much more complicated. The present approach simplifies the operator-valued symbolic structures by using suitable Mellin quantizations on infinite stretched model cones of wedges with boundary. The Mellin symbols themselves are, modulo smoothing ones, with asymptotics, holomorphic in the complex Mellin covariable. One of the main results is the construction of parametrices of elliptic elements in the corresponding operator algebra, including elliptic edge conditions.
N2  - In der Dissertation wurden neue Quantisierungen konstruiert für
pseudo-differentielle Randwertprobleme auf Mannigfaltigkeiten mit
Kanten-Singularitäten. Die Gestalt der hier behandelten Operatoren
ist motiviert durch Boutet de Monvels Kalkül, der auf glatten
Mannigfaltigkeiten mit Rand bekannt ist. Der singuläre Fall, hier mit
Kanten und Rand, ist weitaus komplizierter. Der gegenwärtige Zugang
vereinfacht die operatarwertigen Symbolstrukturen unter Verwendung
geeigneter Mellin-Quantisierungen auf unendlichen gestreckten Modell-
Kegeln, die entsprechenden Keilen mit Rand zugeordnet sind. Die
Mellin-Symbole selbst sind holomorph in der komplexen Mellin
Kovariablen bis auf glättende Restglieder mit Asymptotiken. Zu den
Hauptresultaten gehört die Konstruktion von Parametrices elliptischer
Elemente in der erzeugten Operator-Algebra, einschließlich
elliptischer Kanten-Bedingungen.
KW  - manifolds with singularities
KW  - boundary value problems
KW  - pseudo-differential equation
KW  - manifolds with edge
KW  - Boutet de Monvel's calculus
KW  - edge boundary value problems
KW  - Mannigfaltigkeiten mit Singularitäten
KW  - Randwertprobleme
KW  - pseudo-differentielle Gleichungen
KW  - Mannigfaltigkeiten mit Kante
KW  - Boutet de Monvels Kalkül
KW  - Kanten-Randwertprobleme
Y1  - 2018
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-419018
ER  - 
TY  - JOUR
A1  - Chang, Der-Chen
A1  - Khalil, Sara
A1  - Schulze, Bert-Wolfgang
T1  - Analysis on regular corner spaces
JF  - The journal of geometric analysis
N2  - We establish a new approach of treating elliptic boundary value problems (BVPs) on manifolds with boundary and regular corners, up to singularity order 2. Ellipticity and parametrices are obtained in terms of symbols taking values in algebras of BVPs on manifolds of corresponding lower singularity orders. Those refer to Boutet de Monvel's calculus of operators with the transmission property, see Boutet de Monvel (Acta Math 126:11-51, 1971) for the case of smooth boundary. On corner configuration operators act in spaces with multiple weights. We mainly study the case of upper left entries in the respective 2 x 2 operator block-matrices of such a calculus. Green operators in the sense of Boutet de Monvel (Acta Math 126:11-51, 1971) analogously appear in singular cases, and they are complemented by contributions of Mellin type. We formulate a result on ellipticity and the Fredholm property in weighted corner spaces, with parametrices of analogous kind.
KW  - Boutet de Monvel's calculus
KW  - Pseudo-differential operators
KW  - Singular cones
KW  - Mellin symbols with values in the edge calculus
KW  - Parametrices of elliptic operators
KW  - Kegel space
Y1  - 2021
U6  - https://doi.org/10.1007/s12220-021-00614-3
SN  - 1050-6926
SN  - 1559-002X
VL  - 31
IS  - 9
SP  - 9199
EP  - 9240
PB  - Springer
CY  - New York
ER  - 
TY  - THES
A1  - Mauerberger, Stefan
T1  - Correlation based Bayesian modeling
T1  - Korrelationsbasierte Bayesianische Modellierung
BT  - with applications in travel time tomography, seismic source inversion and magnetic field modeling
BT  - mit Anwendungen in der Laufzeittomographie, Seismischer Quellinversion und Magnetfeldmodellierung
N2  - The motivation for this work was the question of reliability and robustness of seismic tomography. The problem is that many earth models exist which can describe the underlying ground motion records equally well. Most algorithms for reconstructing earth models provide a solution, but rarely quantify their variability. If there is no way to verify the imaged structures, an interpretation is hardly reliable. The initial idea was to explore the space of equivalent earth models using Bayesian inference. However, it quickly became apparent that the rigorous quantification of tomographic uncertainties could not be accomplished within the scope of a dissertation.

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

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

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

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

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

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

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

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

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

Die drei genannten Anwendungen sind bewusst flexibel gehalten um die Übertragbarkeit auf ähnliche Problemstellungen zu ermöglichen. Die gesamte Arbeit legt den Fokus auf die nicht-Eindeutigkeit inverser Probleme in den Geowissenschaften. Sie will für all Jene von Relevanz sein, die sich für die Konzepte der Bayesianischen Inferenz interessieren.
KW  - statistical inference
KW  - Bayesian inversion
KW  - travel time tomography
KW  - seismic source inversion
KW  - magnetic field modeling
KW  - mit Anwendungen in der Laufzeittomographie, Seismischer Quellinversion und Magnetfeldmodellierung
KW  - Magnetfeldmodellierung
KW  - seismische Quellinversion
KW  - statistische Inferenz
KW  - Laufzeittomographie
Y1  - 2022
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-537827
ER  - 
TY  - JOUR
A1  - Eckert, Silvia
A1  - Herden, Jasmin
A1  - Stift, Marc
A1  - Durka, Walter
A1  - Kleunen, Mark van
A1  - Joshi, Jasmin Radha
T1  - Traces of genetic but not epigenetic adaptation in the invasive goldenrod Solidago canadensis despite the absence of population structure
JF  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - Biological invasions may result from multiple introductions, which might compensate for reduced gene pools caused by bottleneck events, but could also dilute adaptive processes. A previous common-garden experiment showed heritable latitudinal clines in fitness-related traits in the invasive goldenrod Solidago canadensis in Central Europe. These latitudinal clines remained stable even in plants chemically treated with zebularine to reduce epigenetic variation. However, despite the heritability of traits investigated, genetic isolation-by-distance was non-significant. Utilizing the same specimens, we applied a molecular analysis of (epi)genetic differentiation with standard and methylation-sensitive (MSAP) AFLPs. We tested whether this variation was spatially structured among populations and whether zebularine had altered epigenetic variation. Additionally, we used genome scans to mine for putative outlier loci susceptible to selection processes in the invaded range. Despite the absence of isolation-by-distance, we found spatial genetic neighborhoods among populations and two AFLP clusters differentiating northern and southern Solidago populations. Genetic and epigenetic diversity were significantly correlated, but not linked to phenotypic variation. Hence, no spatial epigenetic patterns were detected along the latitudinal gradient sampled. Applying genome-scan approaches (BAYESCAN, BAYESCENV, RDA, and LFMM), we found 51 genetic and epigenetic loci putatively responding to selection. One of these genetic loci was significantly more frequent in populations at the northern range. Also, one epigenetic locus was more frequent in populations in the southern range, but this pattern was lost under zebularine treatment. Our results point to some genetic, but not epigenetic adaptation processes along a large-scale latitudinal gradient of S. canadensis in its invasive range.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1271 
KW  - AFLP
KW  - MSAP
KW  - cytosine methylation
KW  - spatial autocorrelation
KW  - genome scan
Y1  - 2022
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-566758
SN  - 1866-8372
SP  - 1
EP  - 17
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - GEN
A1  - Böckmann, Christine
A1  - Ritter, Christoph
A1  - Cappelletti, David
T1  - Mathematical tool for a closure study of aerosol microphysical property retrieval using lidar and photometer data
T2  - IGARSS 2018 - 2018 IEEE International Geoscience and Remote Sensing Symposium
N2  - We present a project combining lidar, photometer and particle counter data with a regularization software tool for a closure study of aerosol microphysical property retrieval. In a first step only lidar data are used to retrieve the particle size distribution (PSD). Secondly, photometer data are added, which results in a good consistency of the retrieved PSDs. Finally, those retrieved PSDs may be compared with the measured PSD from a particle counter. The data here were taken in Ny Alesund, Svalbard, as an example.
KW  - Aerosol
KW  - Raman lidar
KW  - photometer
KW  - inversion
KW  - regularization
KW  - particle microphysics
Y1  - 2018
SN  - 978-1-5386-7150-4
U6  - https://doi.org/10.1109/IGARSS.2018.8518674
SN  - 2153-6996
SP  - 5575
EP  - 5578
PB  - IEEE
CY  - New York
ER  - 
TY  - JOUR
A1  - Dube, Jonas
A1  - Böckmann, Christine
A1  - Ritter, Christoph
T1  - Lidar-Derived Aerosol Properties from Ny-Ålesund, Svalbard during the MOSAiC Spring 2020
JF  - Remote sensing / Molecular Diversity Preservation International (MDPI)
N2  - In this work, we present Raman lidar data (from a Nd:YAG operating at 355 nm, 532 nm and 1064 nm) from the international research village Ny-Alesund for the time period of January to April 2020 during the Arctic haze season of the MOSAiC winter. We present values of the aerosol backscatter, the lidar ratio and the backscatter Angstrom exponent, though the latter depends on wavelength. The aerosol polarization was generally below 2%, indicating mostly spherical particles. We observed that events with high backscatter and high lidar ratio did not coincide. In fact, the highest lidar ratios (LR > 75 sr at 532 nm) were already found by January and may have been caused by hygroscopic growth, rather than by advection of more continental aerosol. Further, we performed an inversion of the lidar data to retrieve a refractive index and a size distribution of the aerosol. Our results suggest that in the free troposphere (above approximate to 2500 m) the aerosol size distribution is quite constant in time, with dominance of small particles with a modal radius well below 100 nm. On the contrary, below approximate to 2000 m in altitude, we frequently found gradients in aerosol backscatter and even size distribution, sometimes in accordance with gradients of wind speed, humidity or elevated temperature inversions, as if the aerosol was strongly modified by vertical displacement in what we call the "mechanical boundary layer". Finally, we present an indication that additional meteorological soundings during MOSAiC campaign did not necessarily improve the fidelity of air backtrajectories.
KW  - aerosol
KW  - Arctic haze
KW  - lidar
KW  - microphysical properties
KW  - backtrajectories;
KW  - Ny-Alesund
KW  - Svalbard
KW  - MOSAiC
KW  - aerosol-boundary layer interactions
Y1  - 2022
U6  - https://doi.org/10.3390/rs14112578
SN  - 2072-4292
VL  - 14
IS  - 11
PB  - MDPI
CY  - Basel
ER  - 
TY  - JOUR
A1  - Pornsawad, Pornsarp
A1  - Sapsakul, Nantawan
A1  - Böckmann, Christine
T1  - A modified asymptotical regularization of nonlinear ill-posed problems
JF  - Mathematics
N2  - In this paper, we investigate the continuous version of modified iterative Runge–Kutta-type methods for nonlinear inverse ill-posed problems proposed in a previous work. The convergence analysis is proved under the tangential cone condition, a modified discrepancy principle, i.e., the stopping time T is a solution of ∥𝐹(𝑥𝛿(𝑇))−𝑦𝛿∥=𝜏𝛿+ for some 𝛿+>𝛿, and an appropriate source condition. We yield the optimal rate of convergence.
KW  - nonlinear operator
KW  - regularization
KW  - discrepancy principle
KW  - asymptotic method
KW  - optimal rate
Y1  - 2019
U6  - https://doi.org/10.3390/math7050419
SN  - 2227-7390
VL  - 7
PB  - MDPI
CY  - Basel, Schweiz
ET  - 5
ER  - 
TY  - INPR
A1  - Pornsawad, Pornsarp
A1  - Böckmann, Christine
T1  - Modified iterative Runge-Kutta-type methods for nonlinear ill-posed problems
N2  - This work is devoted to the convergence analysis of a modified Runge-Kutta-type iterative regularization method for solving nonlinear ill-posed problems under a priori and a posteriori stopping rules. The convergence rate results of the proposed method can be obtained under Hölder-type source-wise condition if the Fréchet derivative is properly scaled and locally Lipschitz continuous. Numerical results are achieved by using the Levenberg-Marquardt and Radau methods.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 3 (2014) 7 
KW  - ill-posed problems
KW  - Runge-Kutta methods
KW  - regularization methods
KW  - Hölder-type source condition
KW  - stopping rules
Y1  - 2014
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-70834
SN  - 2193-6943
VL  - 3
IS  - 7
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Pornsawad, Pornsarp
A1  - Böckmann, Christine
A1  - Panitsupakamon, Wannapa
T1  - The Levenberg–Marquardt regularization for the backward heat equation with fractional derivative
JF  - Electronic transactions on numerical analysis - ETNA
N2  - The backward heat problem with time-fractional derivative in Caputo's sense is studied. The inverse problem is severely ill-posed in the case when the fractional order is close to unity. A Levenberg-Marquardt method with a new a posteriori stopping rule is investigated. We show that optimal order can be obtained for the proposed method under a Hölder-type source condition. Numerical examples for one and two dimensions are provided.
KW  - ill-posed problems
KW  - time-fractional derivative
KW  - backward heat problem
KW  - Levenberg-Marquardt method
KW  - a posteriori stopping rule
KW  - optimal order
Y1  - 2022
SN  - 978-3-7001-8258-0
U6  - https://doi.org/10.1553/etna_vol57s67
SN  - 1068-9613
VL  - 57
SP  - 67
EP  - 79
PB  - Kent State University
CY  - Kent
ER  - 
TY  - GEN
A1  - Perera, Upeksha
A1  - Böckmann, Christine
T1  - Solutions of direct and inverse even-order Sturm-Liouville problems using Magnus expansion
T2  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - In this paper Lie group method in combination with Magnus expansion is utilized to develop a universal method applicable to solving a Sturm–Liouville problem (SLP) of any order with arbitrary boundary conditions. It is shown that the method has ability to solve direct regular (and some singular) SLPs of even orders (tested for up to eight), with a mix of (including non-separable and finite singular endpoints) boundary conditions, accurately and efficiently. The present technique is successfully applied to overcome the difficulties in finding suitable sets of eigenvalues so that the inverse SLP problem can be effectively solved. The inverse SLP algorithm proposed by Barcilon (1974) is utilized in combination with the Magnus method so that a direct SLP of any (even) order and an inverse SLP of order two can be solved effectively.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1336 
KW  - higher-order Sturm–Liouville problems
KW  - inverse Sturm–Liouville problems
KW  - Magnus expansion
Y1  - 2019
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-473414
SN  - 1866-8372
IS  - 1336
ER  - 
TY  - GEN
A1  - Pornsawad, Pornsarp
A1  - Sapsakul, Nantawan
A1  - Böckmann, Christine
T1  - A modified asymptotical regularization of nonlinear ill-posed problems
T2  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - In this paper, we investigate the continuous version of modified iterative Runge–Kutta-type methods for nonlinear inverse ill-posed problems proposed in a previous work. The convergence analysis is proved under the tangential cone condition, a modified discrepancy principle, i.e., the stopping time T is a solution of ∥𝐹(𝑥𝛿(𝑇))−𝑦𝛿∥=𝜏𝛿+ for some 𝛿+>𝛿, and an appropriate source condition. We yield the optimal rate of convergence.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1335 
KW  - nonlinear operator
KW  - regularization
KW  - discrepancy principle
KW  - asymptotic method
KW  - optimal rate
Y1  - 2019
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-473433
SN  - 1866-8372
IS  - 1335
ER  - 
TY  - JOUR
A1  - Wormell, Caroline L.
A1  - Reich, Sebastian
T1  - Spectral convergence of diffusion maps
BT  - Improved error bounds and an alternative normalization
JF  - SIAM journal on numerical analysis / Society for Industrial and Applied Mathematics
N2  - Diffusion maps is a manifold learning algorithm widely used for dimensionality reduction. Using a sample from a distribution, it approximates the eigenvalues and eigenfunctions of associated Laplace-Beltrami operators. Theoretical bounds on the approximation error are, however, generally much weaker than the rates that are seen in practice. This paper uses new approaches to improve the error bounds in the model case where the distribution is supported on a hypertorus. For the data sampling (variance) component of the error we make spatially localized compact embedding estimates on certain Hardy spaces; we study the deterministic (bias) component as a perturbation of the Laplace-Beltrami operator's associated PDE and apply relevant spectral stability results. Using these approaches, we match long-standing pointwise error bounds for both the spectral data and the norm convergence of the operator discretization. We also introduce an alternative normalization for diffusion maps based on Sinkhorn weights. This normalization approximates a Langevin diffusion on the sample and yields a symmetric operator approximation. We prove that it has better convergence compared with the standard normalization on flat domains, and we present a highly efficient rigorous algorithm to compute the Sinkhorn weights.
KW  - diffusion maps
KW  - graph Laplacian
KW  - Sinkhorn problem
KW  - kernel methods
Y1  - 2021
U6  - https://doi.org/10.1137/20M1344093
SN  - 0036-1429
SN  - 1095-7170
VL  - 59
IS  - 3
SP  - 1687
EP  - 1734
PB  - Society for Industrial and Applied Mathematics
CY  - Philadelphia
ER  - 
TY  - JOUR
A1  - Keller, Matthias
A1  - Liu, Shiping
A1  - Peyerimhoff, Norbert
T1  - A note on eigenvalue bounds for non-compact manifolds
JF  - Mathematische Nachrichten
N2  - In this article we prove upper bounds for the Laplace eigenvalues lambda(k) below the essential spectrum for strictly negatively curved Cartan-Hadamard manifolds. Our bound is given in terms of k(2) and specific geometric data of the manifold. This applies also to the particular case of non-compact manifolds whose sectional curvature tends to -infinity, where no essential spectrum is present due to a theorem of Donnelly/Li. The result stands in clear contrast to Laplacians on graphs where such a bound fails to be true in general.
KW  - Cheeger inequality
KW  - eigenvalues
KW  - Laplacian
KW  - negative curvature
KW  - Riemannian manifold
Y1  - 2021
U6  - https://doi.org/10.1002/mana.201900209
SN  - 0025-584X
SN  - 1522-2616
VL  - 294
IS  - 6
SP  - 1134
EP  - 1139
PB  - Wiley-VCH
CY  - Weinheim
ER  - 
TY  - JOUR
A1  - Peng, Junhao
A1  - Sandev, Trifce
A1  - Kocarev, Ljupco
T1  - First encounters on Bethe lattices and Cayley trees
JF  - Communications in nonlinear science & numerical simulation
N2  - In this work we consider the first encounter problems between a fixed and/or mobile target A and a moving trap B on Bethe lattices and Cayley trees. The survival probabilities (SPs) of the target A on the both kinds of structures are considered analytically and compared. On Bethe lattices, the results show that the fixed target will still prolong its survival time, whereas, on Cayley trees, there are some initial positions where the target should move to prolong its survival time. The mean first encounter time (MFET) for mobile target A is evaluated numerically and compared with the mean first passage time (MFPT) for the fixed target A. Different initial settings are addressed and clear boundaries are obtained. These findings are helpful for optimizing the strategy to prolong the survival time of the target or to speed up the search process on Cayley trees, in relation to the target's movement and the initial position configuration of the two walkers. We also present a new method, which uses a small amount of memory, for simulating random walks on Cayley trees. (C) 2020 Elsevier B.V. All rights reserved.
KW  - Random walks
KW  - Survival probability
KW  - Mean first encounter time
KW  - Bethe
KW  - lattices
KW  - Cayley trees
Y1  - 2021
U6  - https://doi.org/10.1016/j.cnsns.2020.105594
SN  - 1007-5704
SN  - 1878-7274
VL  - 95
PB  - Elsevier
CY  - Amsterdam
ER  - 
TY  - JOUR
A1  - Andjelkovic, Marko
A1  - Simevski, Aleksandar
A1  - Chen, Junchao
A1  - Schrape, Oliver
A1  - Stamenkovic, Zoran
A1  - Krstić, Miloš
A1  - Ilic, Stefan
A1  - Ristic, Goran
A1  - Jaksic, Aleksandar
A1  - Vasovic, Nikola
A1  - Duane, Russell
A1  - Palma, Alberto J.
A1  - Lallena, Antonio M.
A1  - Carvajal, Miguel A.
T1  - A design concept for radiation hardened RADFET readout system for space applications
JF  - Microprocessors and microsystems
N2  - Instruments for measuring the absorbed dose and dose rate under radiation exposure, known as radiation dosimeters, are indispensable in space missions. They are composed of radiation sensors that generate current or voltage response when exposed to ionizing radiation, and processing electronics for computing the absorbed dose and dose rate. Among a wide range of existing radiation sensors, the Radiation Sensitive Field Effect Transistors (RADFETs) have unique advantages for absorbed dose measurement, and a proven record of successful exploitation in space missions. It has been shown that the RADFETs may be also used for the dose rate monitoring. In that regard, we propose a unique design concept that supports the simultaneous operation of a single RADFET as absorbed dose and dose rate monitor. This enables to reduce the cost of implementation, since the need for other types of radiation sensors can be minimized or eliminated. For processing the RADFET's response we propose a readout system composed of analog signal conditioner (ASC) and a self-adaptive multiprocessing system-on-chip (MPSoC). The soft error rate of MPSoC is monitored in real time with embedded sensors, allowing the autonomous switching between three operating modes (high-performance, de-stress and fault-tolerant), according to the application requirements and radiation conditions.
KW  - RADFET
KW  - Radiation hardness
KW  - Absorbed dose
KW  - Dose rate
KW  - Self-adaptive MPSoC
Y1  - 2022
U6  - https://doi.org/10.1016/j.micpro.2022.104486
SN  - 0141-9331
SN  - 1872-9436
VL  - 90
PB  - Elsevier
CY  - Amsterdam
ER  - 
TY  - JOUR
A1  - Chang, Der-Chen
A1  - Schulze, Bert-Wolfgang
T1  - Corner spaces and Mellin quantization
JF  - Journal of nonlinear and convex analysis : an international journal
N2  - Manifolds with corners in the present investigation are non-smooth configurations - specific stratified spaces - with an incomplete metric such as cones, manifolds with edges, or corners of piecewise smooth domains in Euclidean space. We focus here on operators on such "corner manifolds" of singularity order <= 2, acting in weighted corner Sobolev spaces. The corresponding corner degenerate pseudo-differential operators are formulated via Mellin quantizations, and they also make sense on infinite singular cones.
KW  - Mellin quantizations
KW  - operator-valued symbols
KW  - weighted edge and corner spaces
Y1  - 2018
SN  - 1345-4773
SN  - 1880-5221
VL  - 19
IS  - 2
SP  - 179
EP  - 195
PB  - Yokohama Publishers
CY  - Yokohama
ER  - 
TY  - JOUR
A1  - Chang, Der-Chen
A1  - Schulze, Bert-Wolfgang
T1  - Ellipticity on spaces with higher singularities
JF  - Science China Mathematics
N2  - We study corner-degenerate pseudo-differential operators of any singularity order and develop ellipticity based on the principal symbolic hierarchy, associated with the stratification of the underlying space. We construct parametrices within the calculus and discuss the aspect of additional trace and potential conditions along lower-dimensional strata.
KW  - pseudo-differential operators
KW  - operator-valued symbols
KW  - Fourier and Mellin transforms
Y1  - 2017
U6  - https://doi.org/10.1007/s11425-016-0519-9
SN  - 1674-7283
SN  - 1869-1862
VL  - 60
IS  - 11
SP  - 2053
EP  - 2076
PB  - Science China Press
CY  - Beijing
ER  - 
TY  - JOUR
A1  - Khalil, Sara
A1  - Schulze, Bert-Wolfgang
T1  - Boundary problems on a manifold with edge
JF  - Asian-European Journal of Mathematics
N2  - We establish a calculus of boundary value problems (BVPs) on a manifold N with boundary and edge, based on Boutet de Monvel’s theory of BVPs in the case of a smooth boundary and on the edge calculus, where in the present case the model cone has a base which is a compact manifold with boundary. The corresponding calculus with boundary and edge is a unification of both structures and controls different operator-valued symbolic structures, in order to obtain ellipticity and parametrices.
KW  - manifolds with edge and boundary
KW  - distribution with asymptotics
KW  - ellipticity
KW  - Fredholm property
Y1  - 2017
U6  - https://doi.org/10.1142/S1793557117500875
SN  - 1793-5571
SN  - 1793-7183
VL  - 10
IS  - 2
PB  - World Scientific
CY  - Singapore
ER  - 
TY  - JOUR
A1  - Chang, Der-Chen
A1  - Hedayat Mahmoudi, Mahdi
A1  - Schulze, Bert-Wolfgang
T1  - Singular degenerate operators
JF  - Applicable analysis : an international journal
N2  - We outline some simplified and more general method for constructing parametrices on higher singular spaces. We also outline basic ideas on operators on manifolds with conical or edge singularities.
KW  - Operators on singular cones
KW  - Mellin symbols with values in the edge calculus
KW  - parametrices of elliptic operators
Y1  - 2017
U6  - https://doi.org/10.1080/00036811.2017.1336546
SN  - 0003-6811
SN  - 1563-504X
VL  - 96
IS  - 14
SP  - 2434
EP  - 2456
PB  - Routledge, Taylor & Francis Group
CY  - Abingdon
ER  - 
TY  - JOUR
A1  - Harutyunyan, Gohar
A1  - Schulze, Bert-Wolfgang
T1  - The Zaremba problem with singular interfaces as a corner boundary value problem
JF  - Potential analysis : an international journal devoted to the interactions between potential theory, probability theory, geometry and functional analysis
N2  - We study mixed boundary value problems for an elliptic operator A on a manifold X with boundary Y, i.e., Au = f in int X, T (+/-) u = g(+/-) on int Y+/-, where Y is subdivided into subsets Y+/- with an interface Z and boundary conditions T+/- on Y+/- that are Shapiro-Lopatinskij elliptic up to Z from the respective sides. We assume that Z subset of Y is a manifold with conical singularity v. As an example we consider the Zaremba problem, where A is the Laplacian and T- Dirichlet, T+ Neumann conditions. The problem is treated as a corner boundary value problem near v which is the new point and the main difficulty in this paper. Outside v the problem belongs to the edge calculus as is shown in Bull. Sci. Math. ( to appear). With a mixed problem we associate Fredholm operators in weighted corner Sobolev spaces with double weights, under suitable edge conditions along Z {v} of trace and potential type. We construct parametrices within the calculus and establish the regularity of solutions.
KW  - Zaremba problem
KW  - corner Sobolev spaces with double weights
KW  - pseudo-differential boundary value problems
Y1  - 2006
U6  - https://doi.org/10.1007/s11118-006-9020-6
SN  - 0926-2601
VL  - 25
SP  - 327
EP  - 369
PB  - Springer
CY  - Dordrecht
ER  - 
TY  - JOUR
A1  - Hedayat Mahmoudi, Mahdi
A1  - Schulze, Bert-Wolfgang
T1  - A new approach to the second order edge calculus
JF  - Journal of pseudo-differential operators and applications
N2  - We establish essential steps of an iterative approach to operator algebras, ellipticity and Fredholm property on stratified spaces with singularities of second order. We cover, in particular, corner-degenerate differential operators. Our constructions are focused on the case where no additional conditions of trace and potential type are posed, but this case works well and will be considered in a forthcoming paper as a conclusion of the present calculus.
KW  - Operators on singular manifolds
KW  - Mellin transform
KW  - Stratified spaces
KW  - Ellipticity and parametrices
Y1  - 2018
U6  - https://doi.org/10.1007/s11868-017-0191-2
SN  - 1662-9981
SN  - 1662-999X
VL  - 9
IS  - 2
SP  - 265
EP  - 300
PB  - Springer
CY  - Basel
ER  - 
TY  - JOUR
A1  - Khalil, Sara
A1  - Schulze, Bert-Wolfgang
T1  - Calculus on a Manifold with Edge and Boundary
JF  - Complex analysis and operator theory
N2  - We study elements of the calculus of boundary value problems in a variant of Boutet de Monvel’s algebra (Acta Math 126:11–51, 1971) on a manifold N with edge and boundary. If the boundary is empty then the approach corresponds to Schulze (Symposium on partial differential equations (Holzhau, 1988), BSB Teubner, Leipzig, 1989) and other papers from the subsequent development. For non-trivial boundary we study Mellin-edge quantizations and compositions within the structure in terms a new Mellin-edge quantization, compared with a more traditional technique. Similar structures in the closed case have been studied in Gil et al.
KW  - algebra
KW  - Mellin quantization
Y1  - 2019
U6  - https://doi.org/10.1007/s11785-018-0800-y
SN  - 1661-8254
SN  - 1661-8262
VL  - 13
IS  - 6
SP  - 2627
EP  - 2670
PB  - Springer
CY  - Basel
ER  - 
TY  - JOUR
A1  - Schulze, Bert-Wolfgang
A1  - Seiler, Jörg
T1  - Elliptic complexes on manifolds with boundary
JF  - The journal of geometric analysis
N2  - We show that elliptic complexes of (pseudo) differential operators on smooth compact manifolds with boundary can always be complemented to a Fredholm problem by boundary conditions involving global pseudodifferential projections on the boundary (similarly as the spectral boundary conditions of Atiyah, Patodi, and Singer for a single operator). We prove that boundary conditions without projections can be chosen if, and only if, the topological Atiyah-Bott obstruction vanishes. These results make use of a Fredholm theory for complexes of operators in algebras of generalized pseudodifferential operators of Toeplitz type which we also develop in the present paper.
KW  - Elliptic complexes
KW  - Manifolds with boundary
KW  - Atiyah-Bott obstruction
KW  - Toeplitz-type pseudodifferential operators
Y1  - 2018
U6  - https://doi.org/10.1007/s12220-018-0014-6
SN  - 1050-6926
SN  - 1559-002X
VL  - 29
IS  - 1
SP  - 656
EP  - 706
PB  - Springer
CY  - New York
ER  - 
TY  - JOUR
A1  - Zöller, Gert
A1  - Hainzl, Sebastian
A1  - Tilmann, Frederik
A1  - Woith, Heiko
A1  - Dahm, Torsten
T1  - Comment on: Wikelski, Martin; Müller, Uschi; Scocco, Paola; Catorci, Andrea; Desinov, Lev V.; Belyaev, Mikhail Y.; Keim, Daniel A.; Pohlmeier, Winfried; Fechteler, Gerhard; Mai, Martin P. : Potential short-term earthquake forecasting by farm animal monitoring. - Ethology. - 126 (2020), 9. - S. 931 - 941. -ISSN 0179-1613. - eISSN 1439-0310. - doi 10.1111/eth.13078
JF  - Ethology
N2  - Based on an analysis of continuous monitoring of farm animal behavior in the region of the 2016 M6.6 Norcia earthquake in Italy, Wikelski et al., 2020; (Seismol Res Lett, 89, 2020, 1238) conclude that animal activity can be anticipated with subsequent seismic activity and that this finding might help to design a "short-term earthquake forecasting method." We show that this result is based on an incomplete analysis and misleading interpretations. Applying state-of-the-art methods of statistics, we demonstrate that the proposed anticipatory patterns cannot be distinguished from random patterns, and consequently, the observed anomalies in animal activity do not have any forecasting power.
KW  - animal behavior
KW  - earthquake precursor
KW  - error diagram
KW  - prediction
KW  - randomness
KW  - statistics
Y1  - 2020
U6  - https://doi.org/10.1111/eth.13105
SN  - 0179-1613
SN  - 1439-0310
VL  - 127
IS  - 3
SP  - 302
EP  - 306
PB  - Wiley
CY  - Hoboken
ER  - 
TY  - JOUR
A1  - Pohle, Jennifer
A1  - Adam, Timo
A1  - Beumer, Larissa
T1  - Flexible estimation of the state dwell-time distribution in hidden semi-Markov models
JF  - Computational statistics & data analysis
N2  - Hidden semi-Markov models generalise hidden Markov models by explicitly modelling the time spent in a given state, the so-called dwell time, using some distribution defined on the natural numbers. While the (shifted) Poisson and negative binomial distribution provide natural choices for such distributions, in practice, parametric distributions can lack the flexibility to adequately model the dwell times. To overcome this problem, a penalised maximum likelihood approach is proposed that allows for a flexible and data-driven estimation of the dwell-time distributions without the need to make any distributional assumption. This approach is suitable for direct modelling purposes or as an exploratory tool to investigate the latent state dynamics. The feasibility and potential of the suggested approach is illustrated in a simulation study and by modelling muskox movements in northeast Greenland using GPS tracking data. The proposed method is implemented in the R-package PHSMM which is available on CRAN.
KW  - Penalized likelihood
KW  - Smoothing
KW  - Time series
KW  - Animal movement modeling
Y1  - 2022
U6  - https://doi.org/10.1016/j.csda.2022.107479
SN  - 0167-9473
SN  - 1872-7352
VL  - 172
PB  - Elsevier
CY  - Amsterdam
ER  - 
TY  - JOUR
A1  - Biskaborn, Boris
A1  - Smith, Sharon L.
A1  - Noetzli, Jeannette
A1  - Matthes, Heidrun
A1  - Vieira, Goncalo
A1  - Streletskiy, Dmitry A.
A1  - Schoeneich, Philippe
A1  - Romanovsky, Vladimir E.
A1  - Lewkowicz, Antoni G.
A1  - Abramov, Andrey
A1  - Allard, Michel
A1  - Boike, Julia
A1  - Cable, William L.
A1  - Christiansen, Hanne H.
A1  - Delaloye, Reynald
A1  - Diekmann, Bernhard
A1  - Drozdov, Dmitry
A1  - Etzelmueller, Bernd
A1  - Grosse, Guido
A1  - Guglielmin, Mauro
A1  - Ingeman-Nielsen, Thomas
A1  - Isaksen, Ketil
A1  - Ishikawa, Mamoru
A1  - Johansson, Margareta
A1  - Johannsson, Halldor
A1  - Joo, Anseok
A1  - Kaverin, Dmitry
A1  - Kholodov, Alexander
A1  - Konstantinov, Pavel
A1  - Kroeger, Tim
A1  - Lambiel, Christophe
A1  - Lanckman, Jean-Pierre
A1  - Luo, Dongliang
A1  - Malkova, Galina
A1  - Meiklejohn, Ian
A1  - Moskalenko, Natalia
A1  - Oliva, Marc
A1  - Phillips, Marcia
A1  - Ramos, Miguel
A1  - Sannel, A. Britta K.
A1  - Sergeev, Dmitrii
A1  - Seybold, Cathy
A1  - Skryabin, Pavel
A1  - Vasiliev, Alexander
A1  - Wu, Qingbai
A1  - Yoshikawa, Kenji
A1  - Zheleznyak, Mikhail
A1  - Lantuit, Hugues
T1  - Permafrost is warming at a global scale
JF  - Nature Communications
N2  - Permafrost warming has the potential to amplify global climate change, because when frozen sediments thaw it unlocks soil organic carbon. Yet to date, no globally consistent assessment of permafrost temperature change has been compiled. Here we use a global data set of permafrost temperature time series from the Global Terrestrial Network for Permafrost to evaluate temperature change across permafrost regions for the period since the International Polar Year (2007-2009). During the reference decade between 2007 and 2016, ground temperature near the depth of zero annual amplitude in the continuous permafrost zone increased by 0.39 +/- 0.15 degrees C. Over the same period, discontinuous permafrost warmed by 0.20 +/- 0.10 degrees C. Permafrost in mountains warmed by 0.19 +/- 0.05 degrees C and in Antarctica by 0.37 +/- 0.10 degrees C. Globally, permafrost temperature increased by 0.29 +/- 0.12 degrees C. The observed trend follows the Arctic amplification of air temperature increase in the Northern Hemisphere. In the discontinuous zone, however, ground warming occurred due to increased snow thickness while air temperature remained statistically unchanged.
Y1  - 2019
U6  - https://doi.org/10.1038/s41467-018-08240-4
SN  - 2041-1723
VL  - 10
PB  - Nature Publ. Group
CY  - London
ER  - 
TY  - BOOK
ED  - Kuzle, Ana
ED  - Rott, Benjamin
ED  - Gebel, Inga
T1  - Implementation research on problem solving in school settings
BT  - Proceedings of the 2018 Joint Conference of ProMath and the GDM Working Group on Problem Solving
T3  - Ars inveniendi et dejudicandi ; 13
Y1  - 2019
SN  - 978-3-95987-116-7
SN  - 978-3-95987-115-0
PB  - WTM-Verlag
CY  - Münster
ER  - 
TY  - GEN
A1  - Krause, Andreas
A1  - Kloft, Charlotte
A1  - Huisinga, Wilhelm
A1  - Karlsson, Mats
A1  - Pinheiro, José
A1  - Bies, Robert
A1  - Rogers, James
A1  - Mentré, France
A1  - Musser, Bret J.
T1  - Comment on Jaki et al., A proposal for a new PhD level curriculum on quantitative methods for drug development
T2  - Pharmaceutical statistics : the journal of applied statistics in the pharmaceutical industry
Y1  - 2019
SN  - 1539-1604
SN  - 1539-1612
VL  - 18
IS  - 3
SP  - 278
EP  - 281
PB  - Wiley
CY  - Hoboken
ER  - 
TY  - THES
A1  - Seuring, Markus
T1  - Output space compaction for testing and concurrent checking
N2  - In der Dissertation werden neue Entwurfsmethoden für Kompaktoren für die Ausgänge von digitalen Schaltungen beschrieben, die die Anzahl der zu testenden Ausgänge drastisch verkleinern und dabei die Testbarkeit der Schaltungen nur wenig oder gar nicht verschlechtern. Der erste Teil der Arbeit behandelt für kombinatorische Schaltungen Methoden, die die Struktur der Schaltungen beim Entwurf der Kompaktoren berücksichtigen. Verschiedene Algorithmen zur Analyse von Schaltungsstrukturen werden zum ersten Mal vorgestellt und untersucht. Die Komplexität der vorgestellten Verfahren zur Erzeugung von Kompaktoren ist linear bezüglich der Anzahl der Gatter in der Schaltung und ist damit auf sehr große Schaltungen anwendbar. Im zweiten Teil wird erstmals ein solches Verfahren für sequentielle Schaltkreise beschrieben. Dieses Verfahren baut im wesentlichen auf das erste auf. Der dritte Teil beschreibt eine Entwurfsmethode, die keine Informationen über die interne Struktur der Schaltung oder über das zugrundeliegende Fehlermodell benötigt. Der Entwurf basiert alleine auf einem vorgegebenen Satz von Testvektoren und die dazugehörenden Testantworten der fehlerfreien Schaltung. Ein nach diesem Verfahren erzeugter Kompaktor maskiert keinen der Fehler, die durch das Testen mit den vorgegebenen Vektoren an den Ausgängen der Schaltung beobachtbar sind.
N2  - The objective of this thesis is to provide new space compaction techniques for testing or concurrent checking of digital circuits. In particular, the work focuses on the design of space compactors that achieve high compaction ratio and minimal loss of testability of the circuits. In the first part, the compactors are designed for combinational circuits based on the knowledge of the circuit structure. Several algorithms for analyzing circuit structures are introduced and discussed for the first time. The complexity of each design procedure is linear with respect to the number of gates of the circuit. Thus, the procedures are applicable to large circuits. In the second part, the first structural approach for output compaction for sequential circuits is introduced. Essentially, it enhances the first part. For the approach introduced in the third part it is assumed that the structure of the circuit and the underlying fault model are unknown. The space compaction approach requires only the knowledge of the fault-free test responses for a precomputed test set. The proposed compactor design guarantees zero-aliasing with respect to the precomputed test set.
KW  - digital circuit
KW  - output space compaction
KW  - zero-aliasing
KW  - test
KW  - concurrent checking
KW  - propagation probability
KW  - IP core
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-0000165
ER  - 
TY  - JOUR
A1  - Mueller-Schoell, Anna
A1  - Groenland, Stefanie L.
A1  - Scherf-Clavel, Oliver
A1  - van Dyk, Madele
A1  - Huisinga, Wilhelm
A1  - Michelet, Robin
A1  - Jaehde, Ulrich
A1  - Steeghs, Neeltje
A1  - Huitema, Alwin D. R.
A1  - Kloft, Charlotte
T1  - Therapeutic drug monitoring of oral targeted antineoplastic drugs
JF  - European journal of clinical pharmacology
N2  - Purpose This review provides an overview of the current challenges in oral targeted antineoplastic drug (OAD) dosing and outlines the unexploited value of therapeutic drug monitoring (TDM). Factors influencing the pharmacokinetic exposure in OAD therapy are depicted together with an overview of different TDM approaches. Finally, current evidence for TDM for all approved OADs is reviewed. Methods A comprehensive literature search (covering literature published until April 2020), including primary and secondary scientific literature on pharmacokinetics and dose individualisation strategies for OADs, together with US FDA Clinical Pharmacology and Biopharmaceutics Reviews and the Committee for Medicinal Products for Human Use European Public Assessment Reports was conducted. Results OADs are highly potent drugs, which have substantially changed treatment options for cancer patients. Nevertheless, high pharmacokinetic variability and low treatment adherence are risk factors for treatment failure. TDM is a powerful tool to individualise drug dosing, ensure drug concentrations within the therapeutic window and increase treatment success rates. After reviewing the literature for 71 approved OADs, we show that exposure-response and/or exposure-toxicity relationships have been established for the majority. Moreover, TDM has been proven to be feasible for individualised dosing of abiraterone, everolimus, imatinib, pazopanib, sunitinib and tamoxifen in prospective studies. There is a lack of experience in how to best implement TDM as part of clinical routine in OAD cancer therapy. Conclusion Sub-therapeutic concentrations and severe adverse events are current challenges in OAD treatment, which can both be addressed by the application of TDM-guided dosing, ensuring concentrations within the therapeutic window.
KW  - targeted antineoplastic drugs
KW  - tyrosine kinase inhibitors
KW  - therapeutic
KW  - drug monitoring
KW  - oral anticancer drugs
KW  - personalised medicine
Y1  - 2020
U6  - https://doi.org/10.1007/s00228-020-03014-8
SN  - 0031-6970
SN  - 1432-1041
VL  - 77
IS  - 4
SP  - 441
EP  - 464
PB  - Springer
CY  - Heidelberg
ER  - 
TY  - JOUR
A1  - Grisic, Ana-Marija
A1  - Eser, Alexander
A1  - Huisinga, Wilhelm
A1  - Reinisch, Walter
A1  - Kloft, Charlotte
T1  - Quantitative relationship between infliximab exposure and inhibition of C-reactive protein synthesis to support inflammatory bowel disease management
JF  - British journal of clinical pharmacology
N2  - Aim Quantitative and kinetic insights into the drug exposure-disease response relationship might enhance our knowledge on loss of response and support more effective monitoring of inflammatory activity by biomarkers in patients with inflammatory bowel disease (IBD) treated with infliximab (IFX). This study aimed to derive recommendations for dose adjustment and treatment optimisation based on mechanistic characterisation of the relationship between IFX serum concentration and C-reactive protein (CRP) concentration. <br /> Methods Data from an investigator-initiated trial included 121 patients with IBD during IFX maintenance treatment. Serum concentrations of IFX, antidrug antibodies (ADA), CRP, and disease-related covariates were determined at the mid-term and end of a dosing interval. Data were analysed using a pharmacometric nonlinear mixed-effects modelling approach. An IFX exposure-CRP model was generated and applied to evaluate dosing regimens to achieve CRP remission. <br /> Results The generated quantitative model showed that IFX has the potential to inhibit up to 72% (9% relative standard error [RSE]) of CRP synthesis in a patient. IFX concentration leading to 90% of the maximum CRP synthesis inhibition was 18.4 mu g/mL (43% RSE). Presence of ADA was the most influential factor on IFX exposure. With standard dosing strategy, >= 55% of ADA+ patients experienced CRP nonremission. Shortening the dosing interval and co-therapy with immunomodulators were found to be the most beneficial strategies to maintain CRP remission. <br /> Conclusions With the generated model we could for the first time establish a robust relationship between IFX exposure and CRP synthesis inhibition, which could be utilised for treatment optimisation in IBD patients.
KW  - C‐ reactive protein remission
KW  - inflammatory bowel disease
KW  - infliximab dosing
Y1  - 2020
U6  - https://doi.org/10.1111/bcp.14648
SN  - 0306-5251
SN  - 1365-2125
VL  - 87
IS  - 5
SP  - 2374
EP  - 2384
PB  - Wiley
CY  - Hoboken
ER  - 
TY  - JOUR
A1  - Kluwe, Franziska
A1  - Michelet, Robin
A1  - Müller-Schöll, Anna
A1  - Maier, Corinna
A1  - Klopp-Schulze, Lena
A1  - van Dyk, Madele
A1  - Mikus, Gerd
A1  - Huisinga, Wilhelm
A1  - Kloft, Charlotte
T1  - Perspectives on model-informed precision dosing in the digital health era
BT  - challenges, opportunities, and recommendations
JF  - Clinical pharmacology & therapeutics
Y1  - 2020
U6  - https://doi.org/10.1002/cpt.2049
SN  - 0009-9236
SN  - 1532-6535
VL  - 109
IS  - 1
SP  - 29
EP  - 36
PB  - Wiley
CY  - Hoboken
ER  - 
TY  - JOUR
A1  - Nassar, Yomna M.
A1  - Hohmann, Nicolas
A1  - Michelet, Robin
A1  - Gottwalt, Katharina
A1  - Meid, Andreas D.
A1  - Burhenne, Jürgen
A1  - Huisinga, Wilhelm
A1  - Haefeli, Walter E.
A1  - Mikus, Gerd
A1  - Kloft, Charlotte
T1  - Quantification of the Time Course of CYP3A Inhibition, Activation, and Induction Using a Population Pharmacokinetic Model of Microdosed Midazolam Continuous Infusion
JF  - Clinical Pharmacokinetics
N2  - Background
Cytochrome P450 (CYP) 3A contributes to the metabolism of many approved drugs. CYP3A perpetrator drugs can profoundly alter the exposure of CYP3A substrates. However, effects of such drug-drug interactions are usually reported as maximum effects rather than studied as time-dependent processes. Identification of the time course of CYP3A modulation can provide insight into when significant changes to CYP3A activity occurs, help better design drug-drug interaction studies, and manage drug-drug interactions in clinical practice. 

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Die mathematischen Methoden dieser Arbeit stellen wesentliche Verbesserungen in der Modellierung und Analyse der amöboiden Zellmotilität dar. Wir sind der Ansicht, dass die oben genannten Methoden aufgrund ihrer Verallgemeinerbarkeit von größerem Wert für andere wissenschaftliche Anwendungen sind und potentiell einsetzbar in verschiedenen Wissenschaftsfeldern sind, u. a. Mathematik, Biophysik und Medizin. Durch die Einhaltung von Open-Science-Standards ist diese Arbeit von größerem Wert und ein potenzielles Vorbild für andere Open-Science-Beiträge.
KW  - amöboide Bewegung
KW  - Zellmotilität
KW  - mathematische Modellierung
KW  - offene Wissenschaft
KW  - amoeboid motion
KW  - cell motility
KW  - mathematical modeling
KW  - open science
Y1  - 2023
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-613275
ER  - 
TY  - JOUR
A1  - Hijazi, Saddam
A1  - Freitag, Melina A.
A1  - Landwehr, Niels
T1  - POD-Galerkin reduced order models and physics-informed neural networks for solving inverse problems for the Navier-Stokes equations
JF  - Advanced modeling and simulation in engineering sciences : AMSES
N2  - We present a Reduced Order Model (ROM) which exploits recent developments in Physics Informed Neural Networks (PINNs) for solving inverse problems for the Navier-Stokes equations (NSE). In the proposed approach, the presence of simulated data for the fluid dynamics fields is assumed. A POD-Galerkin ROM is then constructed by applying POD on the snapshots matrices of the fluid fields and performing a Galerkin projection of the NSE (or the modified equations in case of turbulence modeling) onto the POD reduced basis. A POD-Galerkin PINN ROM is then derived by introducing deep neural networks which approximate the reduced outputs with the input being time and/or parameters of the model. The neural networks incorporate the physical equations (the POD-Galerkin reduced equations) into their structure as part of the loss function. Using this approach, the reduced model is able to approximate unknown parameters such as physical constants or the boundary conditions. A demonstration of the applicability of the proposed ROM is illustrated by three cases which are the steady flow around a backward step, the flow around a circular cylinder and the unsteady turbulent flow around a surface mounted cubic obstacle.
KW  - Proper orthogonal decomposition
KW  - Inverse problems
KW  - Physics-based machine learning
KW  - Navier-Stokes equations
Y1  - 2023
U6  - https://doi.org/10.1186/s40323-023-00242-2
SN  - 2213-7467
VL  - 10
IS  - 1
PB  - SpringerOpen
CY  - Berlin
ER  - 
TY  - JOUR
A1  - Molkenthin, Christian
A1  - Donner, Christian
A1  - Reich, Sebastian
A1  - Zöller, Gert
A1  - Hainzl, Sebastian
A1  - Holschneider, Matthias
A1  - Opper, Manfred
T1  - GP-ETAS: semiparametric Bayesian inference for the spatio-temporal epidemic type aftershock sequence model
JF  - Statistics and Computing
N2  - The spatio-temporal epidemic type aftershock sequence (ETAS) model is widely used to describe the self-exciting nature of earthquake occurrences. While traditional inference methods provide only point estimates of the model parameters, we aim at a fully Bayesian treatment of model inference, allowing naturally to incorporate prior knowledge and uncertainty quantification of the resulting estimates. Therefore, we introduce a highly flexible, non-parametric representation for the spatially varying ETAS background intensity through a Gaussian process (GP) prior. Combined with classical triggering functions this results in a new model formulation, namely the GP-ETAS model. We enable tractable and efficient Gibbs sampling by deriving an augmented form of the GP-ETAS inference problem. This novel sampling approach allows us to assess the posterior model variables conditioned on observed earthquake catalogues, i.e., the spatial background intensity and the parameters of the triggering function. Empirical results on two synthetic data sets indicate that GP-ETAS outperforms standard models and thus demonstrate the predictive power for observed earthquake catalogues including uncertainty quantification for the estimated parameters. Finally, a case study for the l'Aquila region, Italy, with the devastating event on 6 April 2009, is presented.
KW  - Self-exciting point process
KW  - Hawkes process
KW  - Spatio-temporal ETAS model
KW  - Bayesian inference
KW  - Sampling
KW  - Earthquake modeling
KW  - Gaussian process
KW  - Data augmentation
Y1  - 2022
U6  - https://doi.org/10.1007/s11222-022-10085-3
SN  - 0960-3174
SN  - 1573-1375
VL  - 32
IS  - 2
PB  - Springer
CY  - Dordrecht
ER  - 
TY  - JOUR
A1  - Kucharski, Maciej
A1  - Ergintav, Arzu
A1  - Ahmad, Wael Abdullah
A1  - Krstić, Miloš
A1  - Ng, Herman Jalli
A1  - Kissinger, Dietmar
T1  - A Scalable 79-GHz Radar Platform Based on Single-Channel Transceivers
JF  - IEEE Transactions on Microwave Theory and Techniques
N2  - This paper presents a scalable E-band radar platform based on single-channel fully integrated transceivers (TRX) manufactured using 130-nm silicon-germanium (SiGe) BiCMOS technology. The TRX is suitable for flexible radar systems exploiting massive multiple-input-multipleoutput (MIMO) techniques for multidimensional sensing. A fully integrated fractional-N phase-locked loop (PLL) comprising a 39.5-GHz voltage-controlled oscillator is used to generate wideband frequency-modulated continuous-wave (FMCW) chirp for E-band radar front ends. The TRX is equipped with a vector modulator (VM) for high-speed carrier modulation and beam-forming techniques. A single TRX achieves 19.2-dBm maximum output power and 27.5-dB total conversion gain with input-referred 1-dB compression point of -10 dBm. It consumes 220 mA from 3.3-V supply and occupies 3.96 mm(2) silicon area. A two-channel radar platform based on full-custom TRXs and PLL was fabricated to demonstrate high-precision and high-resolution FMCW sensing. The radar enables up to 10-GHz frequency ramp generation in 74-84-GHz range, which results in 1.5-cm spatial resolution. Due to high output power, thus high signal-to-noise ratio (SNR), a ranging precision of 7.5 mu m for a target at 2 m was achieved. The proposed architecture supports scalable multichannel applications for automotive FMCW using a single local oscillator (LO).
KW  - Automotive
KW  - E-band
KW  - frequency-modulated continuous-wave (FMCW)
KW  - patch antenna
KW  - phase-locked loop (PLL)
KW  - power amplifier (PA)
KW  - radar
KW  - scalable
KW  - transceiver (TRX)
Y1  - 2019
U6  - https://doi.org/10.1109/TMTT.2019.2914104
SN  - 0018-9480
SN  - 1557-9670
VL  - 67
IS  - 9
SP  - 3882
EP  - 3896
PB  - Inst. of Electr. and Electronics Engineers
CY  - Piscataway
ER  - 
TY  - JOUR
A1  - Sharma, Shubham
A1  - Hainzl, Sebastian
A1  - Zöller, Gert
A1  - Holschneider, Matthias
T1  - Is Coulomb stress the best choice for aftershock forecasting?
JF  - Journal of geophysical research : Solid earth
N2  - The Coulomb failure stress (CFS) criterion is the most commonly used method for predicting spatial distributions of aftershocks following large earthquakes. However, large uncertainties are always associated with the calculation of Coulomb stress change. The uncertainties mainly arise due to nonunique slip inversions and unknown receiver faults; especially for the latter, results are highly dependent on the choice of the assumed receiver mechanism. Based on binary tests (aftershocks yes/no), recent studies suggest that alternative stress quantities, a distance-slip probabilistic model as well as deep neural network (DNN) approaches, all are superior to CFS with predefined receiver mechanism. To challenge this conclusion, which might have large implications, we use 289 slip inversions from SRCMOD database to calculate more realistic CFS values for a layered half-space and variable receiver mechanisms. We also analyze the effect of the magnitude cutoff, grid size variation, and aftershock duration to verify the use of receiver operating characteristic (ROC) analysis for the ranking of stress metrics. The observations suggest that introducing a layered half-space does not improve the stress maps and ROC curves. However, results significantly improve for larger aftershocks and shorter time periods but without changing the ranking. We also go beyond binary testing and apply alternative statistics to test the ability to estimate aftershock numbers, which confirm that simple stress metrics perform better than the classic Coulomb failure stress calculations and are also better than the distance-slip probabilistic model.
Y1  - 2020
U6  - https://doi.org/10.1029/2020JB019553
SN  - 2169-9313
SN  - 2169-9356
VL  - 125
IS  - 9
PB  - American Geophysical Union
CY  - Washington
ER  - 
TY  - JOUR
A1  - Engbert, Ralf
A1  - Rabe, Maximilian Michael
A1  - Kliegl, Reinhold
A1  - Reich, Sebastian
T1  - Sequential data assimilation of the stochastic SEIR epidemic model for regional COVID-19 dynamics
JF  - Bulletin of mathematical biology : official journal of the Society for Mathematical Biology
N2  - Newly emerging pandemics like COVID-19 call for predictive models to implement precisely tuned responses to limit their deep impact on society. Standard epidemic models provide a theoretically well-founded dynamical description of disease incidence. For COVID-19 with infectiousness peaking before and at symptom onset, the SEIR model explains the hidden build-up of exposed individuals which creates challenges for containment strategies. However, spatial heterogeneity raises questions about the adequacy of modeling epidemic outbreaks on the level of a whole country. Here, we show that by applying sequential data assimilation to the stochastic SEIR epidemic model, we can capture the dynamic behavior of outbreaks on a regional level. Regional modeling, with relatively low numbers of infected and demographic noise, accounts for both spatial heterogeneity and stochasticity. Based on adapted models, short-term predictions can be achieved. Thus, with the help of these sequential data assimilation methods, more realistic epidemic models are within reach.
KW  - Stochastic epidemic model
KW  - Sequential data assimilation
KW  - Ensemble Kalman
KW  - filter
KW  - COVID-19
Y1  - 2020
U6  - https://doi.org/10.1007/s11538-020-00834-8
SN  - 0092-8240
SN  - 1522-9602
VL  - 83
IS  - 1
PB  - Springer
CY  - New York
ER  - 
TY  - THES
A1  - Sareeto, Apatsara
T1  - Algebraic properties of a subsemigroup of the symmetric inverse semigroup
Y1  - 2024
ER  - 
TY  - JOUR
A1  - Gerlach, Moritz Reinhardt
A1  - Glück, Jochen
T1  - On a convergence theorem for semigroups of positive integral operators
JF  - Comptes Rendus Mathematique
N2  - We give a new and very short proof of a theorem of Greiner asserting that a positive and contractive -semigroup on an -space is strongly convergent in case it has a strictly positive fixed point and contains an integral operator. Our proof is a streamlined version of a much more general approach to the asymptotic theory of positive semigroups developed recently by the authors. Under the assumptions of Greiner's theorem, this approach becomes particularly elegant and simple. We also give an outlook on several generalisations of this result.
Y1  - 2017
U6  - https://doi.org/10.1016/j.crma.2017.07.017
SN  - 1631-073X
SN  - 1778-3569
VL  - 355
SP  - 973
EP  - 976
PB  - Elsevier
CY  - Paris
ER  - 
TY  - JOUR
A1  - Gerlach, Moritz Reinhardt
T1  - Convergence of dynamics and the Perron-Frobenius operator
JF  - Israel Journal of Mathematics
N2  - We complete the picture how the asymptotic behavior of a dynamical system is reflected by properties of the associated Perron-Frobenius operator. Our main result states that strong convergence of the powers of the Perron-Frobenius operator is equivalent to setwise convergence of the underlying dynamic in the measure algebra. This situation is furthermore characterized by uniform mixing-like properties of the system.
Y1  - 2018
U6  - https://doi.org/10.1007/s11856-018-1671-7
SN  - 0021-2172
SN  - 1565-8511
VL  - 225
IS  - 1
SP  - 451
EP  - 463
PB  - Hebrew univ magnes press
CY  - Jerusalem
ER  - 
TY  - JOUR
A1  - Gerlach, Moritz Reinhardt
A1  - Glück, Jochen
T1  - Convergence of positive operator semigroups
JF  - Transactions of the American Mathematical Society
N2  - We present new conditions for semigroups of positive operators to converge strongly as time tends to infinity. Our proofs are based on a novel approach combining the well-known splitting theorem by Jacobs, de Leeuw, and Glicksberg with a purely algebraic result about positive group representations. Thus, we obtain convergence theorems not only for one-parameter semigroups but also for a much larger class of semigroup representations. Our results allow for a unified treatment of various theorems from the literature that, under technical assumptions, a bounded positive C-0-semigroup containing or dominating a kernel operator converges strongly as t ->infinity. We gain new insights into the structure theoretical background of those theorems and generalize them in several respects; especially we drop any kind of continuity or regularity assumption with respect to the time parameter.
KW  - Positive semigroups
KW  - semigroup representations
KW  - asymptotic behavior
KW  - kernel operator
Y1  - 2019
U6  - https://doi.org/10.1090/tran/7836
SN  - 0002-9947
SN  - 1088-6850
VL  - 372
IS  - 9
SP  - 6603
EP  - 6627
PB  - American Mathematical Soc.
CY  - Providence
ER  - 
TY  - JOUR
A1  - Edeko, Nikolai
A1  - Gerlach, Moritz Reinhardt
A1  - Kühner, Viktoria
T1  - Measure-preserving semiflows and one-parameter Koopman semigroups
JF  - Semigroup forum
N2  - For a finite measure space X, we characterize strongly continuous Markov lattice semigroups on Lp(X) by showing that their generator A acts as a derivation on the dense subspace D(A)L(X). We then use this to characterize Koopman semigroups on Lp(X) if X is a standard probability space. In addition, we show that every measurable and measure-preserving flow on a standard probability space is isomorphic to a continuous flow on a compact Borel probability space.
KW  - Measure-preserving semiflow
KW  - Koopman semigroup
KW  - Derivation
KW  - Topological model
Y1  - 2019
U6  - https://doi.org/10.1007/s00233-018-9960-3
SN  - 0037-1912
SN  - 1432-2137
VL  - 98
IS  - 1
SP  - 48
EP  - 63
PB  - Springer
CY  - New York
ER  - 
TY  - JOUR
A1  - Gerlach, Moritz Reinhardt
A1  - Glück, Jochen
T1  - Lower bounds and the asymptotic behaviour of positive operator semigroups
JF  - Ergodic theory and dynamical systems
N2  - If (T-t) is a semigroup of Markov operators on an L-1-space that admits a nontrivial lower bound, then a well-known theorem of Lasota and Yorke asserts that the semigroup is strongly convergent as t -> infinity. In this article we generalize and improve this result in several respects. First, we give a new and very simple proof for the fact that the same conclusion also holds if the semigroup is merely assumed to be bounded instead of Markov. As a main result, we then prove a version of this theorem for semigroups which only admit certain individual lower bounds. Moreover, we generalize a theorem of Ding on semigroups of Frobenius-Perron operators. We also demonstrate how our results can be adapted to the setting of general Banach lattices and we give some counterexamples to show optimality of our results. Our methods combine some rather concrete estimates and approximation arguments with abstract functional analytical tools. One of these tools is a theorem which relates the convergence of a time-continuous operator semigroup to the convergence of embedded discrete semigroups.
Y1  - 2017
U6  - https://doi.org/10.1017/etds.2017.9
SN  - 0143-3857
SN  - 1469-4417
VL  - 38
SP  - 3012
EP  - 3041
PB  - Cambridge Univ. Press
CY  - New York
ER  - 
TY  - JOUR
A1  - Gerlach, Moritz Reinhardt
A1  - Glück, Jochen
T1  - Mean ergodicity vs weak almost periodicity
JF  - Studia mathematica
N2  - We provide explicit examples of positive and power-bounded operators on c(0) and l(infinity) which are mean ergodic but not weakly almost periodic. As a consequence we prove that a countably order complete Banach lattice on which every positive and power-bounded mean ergodic operator is weakly almost periodic is necessarily a KB-space. This answers several open questions from the literature. Finally, we prove that if T is a positive mean ergodic operator with zero fixed space on an arbitrary Banach lattice, then so is every power of T .
KW  - positive operators
KW  - weakly almost periodic
KW  - order continuous norm
KW  - KB-space
KW  - mean ergodic
Y1  - 2019
U6  - https://doi.org/10.4064/sm170918-20-3
SN  - 0039-3223
SN  - 1730-6337
VL  - 248
IS  - 1
SP  - 45
EP  - 56
PB  - Polska Akademia Nauk, Instytut Matematyczny
CY  - Warszawa
ER  - 
TY  - JOUR
A1  - Gerlach, Moritz
A1  - Glück, Jochen
A1  - Kunze, Markus
T1  - Stability of transition semigroups and applications to parabolic equations
JF  - Transactions of the American Mathematical Society
N2  - This paper deals with the long-term behavior of positive operator semigroups on spaces of bounded functions and of signed measures, which have applications to parabolic equations with unbounded coefficients and to stochas-tic analysis. The main results are a Tauberian type theorem characterizing the convergence to equilibrium of strongly Feller semigroups and a generalization of a classical convergence theorem of Doob. None of these results requires any kind of time regularity of the semigroup.
KW  - Transition probabilities
KW  - strong Feller property
KW  - asymptotic
KW  - behavior
KW  - invariant measure
KW  - parabolic equations
Y1  - 2023
U6  - https://doi.org/10.1090/tran/8620
SN  - 0002-9947
SN  - 1088-6850
VL  - 376
IS  - 1
SP  - 153
EP  - 180
PB  - American Mathematical Soc.
CY  - Providence
ER  - 
TY  - JOUR
A1  - Dimitrova, Ilinka
A1  - Koppitz, Jörg
T1  - On relative ranks of the semigroup of orientation-preserving transformations on infinite chain with restricted range
JF  - Communications in algebra
N2  - Let X be an infinite linearly ordered set and let Y be a nonempty subset of X. We calculate the relative rank of the semigroup OP(X,Y) of all orientation-preserving transformations on X with restricted range Y modulo the semigroup O(X,Y) of all order-preserving transformations on X with restricted range Y. For Y = X, we characterize the relative generating sets of minimal size.
KW  - Order-preserving transformations
KW  - orientation-preserving
KW  - transformations
KW  - relative rank
KW  - restricted range
KW  - transformation
KW  - semigroups on infinite chain
Y1  - 2022
U6  - https://doi.org/10.1080/00927872.2021.2000998
SN  - 0092-7872
SN  - 1532-4125
VL  - 50
IS  - 5
SP  - 2157
EP  - 2168
PB  - Taylor & Francis Group
CY  - Philadelphia
ER  - 
TY  - JOUR
A1  - Dimitrova, Ilinka
A1  - Koppitz, Jörg
T1  - On relative ranks of the semigroup of orientation-preserving transformations on infinite chains
JF  - Asian-European journal of mathematics
N2  - In this paper, we determine the relative rank of the semigroup OP(X) of all orientation-preserving transformations on infinite chains modulo the semigroup O(X) of all order-preserving transformations.
KW  - Transformation semigroups on infinite chains
KW  - order-preserving
KW  - transformations
KW  - orientation-preserving transformations
KW  - relative rank
Y1  - 2020
U6  - https://doi.org/10.1142/S1793557121501461
SN  - 1793-5571
SN  - 1793-7183
VL  - 14
IS  - 08
PB  - World Scientific
CY  - Singapore
ER  - 
TY  - JOUR
A1  - Kretzschmar, Mirjam E.
A1  - Ashby, Ben
A1  - Fearon, Elizabeth
A1  - Overton, Christopher E.
A1  - Panovska-Griffiths, Jasmina
A1  - Pellis, Lorenzo
A1  - Quaife, Matthew
A1  - Rozhnova, Ganna
A1  - Scarabel, Francesca
A1  - Stage, Helena B.
A1  - Swallow, Ben
A1  - Thompson, Robin N.
A1  - Tildesley, Michael J.
A1  - Villela, Daniel Campos
T1  - Challenges for modelling interventions for future pandemics
JF  - Epidemics
N2  - Mathematical modelling and statistical inference provide a framework to evaluate different non-pharmaceutical and pharmaceutical interventions for the control of epidemics that has been widely used during the COVID-19 pandemic. In this paper, lessons learned from this and previous epidemics are used to highlight the challenges for future pandemic control. We consider the availability and use of data, as well as the need for correct parameterisation and calibration for different model frameworks. We discuss challenges that arise in describing and distinguishing between different interventions, within different modelling structures, and allowing both within and between host dynamics. We also highlight challenges in modelling the health economic and political aspects of interventions. Given the diversity of these challenges, a broad variety of interdisciplinary expertise is needed to address them, combining mathematical knowledge with biological and social insights, and including health economics and communication skills. Addressing these challenges for the future requires strong cross disciplinary collaboration together with close communication between scientists and policy makers.
KW  - Mathematical models
KW  - Pandemics
KW  - Pharmaceutical interventions
KW  - Non-pharmaceutical interventions
KW  - Policy support
Y1  - 2022
U6  - https://doi.org/10.1016/j.epidem.2022.100546
SN  - 1755-4365
SN  - 1878-0067
VL  - 38
PB  - Elsevier
CY  - Amsterdam
ER  -