TY  - JOUR
A1  - Dereudre, David
A1  - Houdebert, Pierre
T1  - Sharp phase transition for the continuum Widom-Rowlinson model
JF  - Annales de l'Institut Henri Poincaré. B, Probability and statistics
N2  - The Widom-Rowlinson model (or the Area-interaction model) is a Gibbs point process in R-d with the formal Hamiltonian defined as the volume of Ux epsilon omega B1(x), where. is a locally finite configuration of points and B-1(x) denotes the unit closed ball centred at x. The model is also tuned by two other parameters: the activity z > 0 related to the intensity of the process and the inverse temperature beta >= 0 related to the strength of the interaction. In the present paper we investigate the phase transition of the model in the point of view of percolation theory and the liquid-gas transition. First, considering the graph connecting points with distance smaller than 2r > 0, we show that for any beta >= 0, there exists 0 <(similar to a)(zc) (beta, r) < +infinity such that an exponential decay of connectivity at distance n occurs in the subcritical phase (i.e. z <(similar to a)(zc) (beta, r)) and a linear lower bound of the connection at infinity holds in the supercritical case (i.e. z >(similar to a)(zc) (beta, r)). These results are in the spirit of recent works using the theory of randomised tree algorithms (Probab. Theory Related Fields 173 (2019) 479-490, Ann. of Math. 189 (2019) 75-99, Duminil-Copin, Raoufi and Tassion (2018)). Secondly we study a standard liquid-gas phase transition related to the uniqueness/non-uniqueness of Gibbs states depending on the parameters z, beta. Old results (Phys. Rev. Lett. 27 (1971) 1040-1041, J. Chem. Phys. 52 (1970) 1670-1684) claim that a non-uniqueness regime occurs for z = beta large enough and it is conjectured that the uniqueness should hold outside such an half line ( z = beta >= beta(c) > 0). We solve partially this conjecture in any dimension by showing that for beta large enough the non-uniqueness holds if and only if z = beta. We show also that this critical value z = beta corresponds to the percolation threshold (similar to a)(zc) (beta, r) = beta for beta large enough, providing a straight connection between these two notions of phase transition.
KW  - Gibbs point process
KW  - DLR equations
KW  - Boolean model
KW  - Continuum
KW  - percolation
KW  - Random cluster model
KW  - Fortuin-Kasteleyn representation
KW  - Randomised tree algorithm
KW  - OSSS inequality
Y1  - 2018
U6  - https://doi.org/10.1214/20-AIHP1082
SN  - 0246-0203
SN  - 1778-7017
VL  - 57
IS  - 1
SP  - 387
EP  - 407
PB  - Association des Publications de l'Institut Henri Poincaré
CY  - Bethesda, Md.
ER  - 
TY  - JOUR
A1  - Cozzoni, Barbara
A1  - Maibaum, Michael
A1  - Hamm, Maximilian
T1  - Thermal analysis and constraints for the MASCOT landing site selection on the asteroid Ryugu
JF  - Planetary and space science
N2  - In June 2018, after 4 years of cruise, the Japanese space probe Hayabusa2 [1-Watanabe S. et al.: Hayabusa2 Mission Overview. (2017)] reached the Near-Earth Asteroid (162173) Ryugu. Hayabusa2 carried a small Lander named MASCOT (Mobile Asteroid Surface Scout) [2-Ho T. M. et al.: MASCOT-The Mobile Asteroid Surface Scout onboard the Hayabusa2 mission. (2017)], jointly developed by the German Aerospace Center (DLR) and the French Space Agency (CNES), to investigate Ryugu's surface structure, composition and physical properties including its thermal behaviour and magnetization in-situ. The Microgravity User Support Centre (DLR-MUSC) in Cologne was in charge of providing all thermal conditions and constraints necessary for the selection of the final landing site and for the final operations of the Lander MASCOT on the surface of the asteroid Ryugu. This article provides a comprehensive assessment of these thermal conditions and constraints, based on predictions performed with the Thermal Mathematical Model (TMM) of MASCOT using different asteroid surface thermal models, ephemeris data for approach as well as descent and hopping trajectories, the related operation sequences and scenarios and the possible environmental conditions driven by the Hayabusa2 spacecraft. A comparison with the real telemetry data confirms the analysis and provides further information about the asteroid characteristics.
KW  - MASCOT
KW  - Thermal mathematical model
KW  - Landing site selection
KW  - Small
KW  - spacecraft operations
Y1  - 2021
U6  - https://doi.org/10.1016/j.pss.2021.105286
SN  - 0032-0633
SN  - 1873-5088
VL  - 205
PB  - Elsevier
CY  - Oxford
ER  - 
TY  - JOUR
A1  - Hinz, Michael
A1  - Schwarz, Michael
T1  - A note on Neumann problems on graphs
JF  - Positivity
N2  - We discuss Neumann problems for self-adjoint Laplacians on (possibly infinite) graphs. Under the assumption that the heat semigroup is ultracontractive we discuss the unique solvability for non-empty subgraphs with respect to the vertex boundary and provide analytic and probabilistic representations for Neumann solutions. A second result deals with Neumann problems on canonically compactifiable graphs with respect to the Royden boundary and provides conditions for unique solvability and analytic and probabilistic representations.
KW  - Graphs
KW  - Discrete Dirichlet forms
KW  - Neumann problem
KW  - Royden boundary
Y1  - 2022
U6  - https://doi.org/10.1007/s11117-022-00930-0
SN  - 1385-1292
SN  - 1572-9281
VL  - 26
IS  - 4
PB  - Springer
CY  - Dordrecht
ER  - 
TY  - JOUR
A1  - Mera, Azal Jaafar Musa
A1  - Tarkhanov, Nikolai
T1  - An elliptic equation of finite index in a domain
JF  - Boletin de la Sociedad Matemática Mexicana
N2  - We give an example of first order elliptic equation for a complex-valued function in a plane domain which has a finite number of linearly independent solutions for any right-hand side. No boundary value conditions are thus required.
KW  - elliptic equation
KW  - Fredholm operator
KW  - index
Y1  - 2022
U6  - https://doi.org/10.1007/s40590-022-00442-7
SN  - 1405-213X
SN  - 2296-4495
VL  - 28
IS  - 2
PB  - Springer International
CY  - New York [u.a.]
ER  - 
TY  - JOUR
A1  - Kortenkamp, Ulrich
A1  - Kuzle, Ana
A1  - Reitz-Koncebovski, Karen
T1  - Fachdidaktisches Wissen aus dem Fachwissen generieren
BT  - Design Research zur Verknüpfung von Fachwissenschaft und Fachdidaktik in der Lehrkräftebildung Mathematik
JF  - PSI-Potsdam: Ergebnisbericht zu den Aktivitäten im Rahmen der Qualitätsoffensive Lehrerbildung (2019-2023) (Potsdamer Beiträge zur Lehrerbildung und Bildungsforschung ; 3)
N2  - Das Mathematik-Teilprojekt SPIES-M zielt auf eine stärkere Professionsorientierung und die Verknüpfung von Fachwissenschaft und Fachdidaktik in der universitären Lehrkräftebildung. Zu allen großen Inhaltsgebieten der Mathematik wurden neue Lehrveranstaltungen konzipiert und in den Studienordnungen sämtlicher Lehrämter Mathematik an der Universität Potsdam implementiert. Für die Konzeption wurden theoriebasiert Gestaltungsprinzipien herausgearbeitet, die sowohl für das Design als auch für die Evaluation und Weiterentwicklung der Lehrveranstaltungen nach dem Design-Research-Ansatz genutzt werden können. Die Umsetzung der Gestaltungsprinzipien wird am Beispiel der Fundamentalen Idee der Proportionalität verdeutlicht und dabei aufgezeigt, wie Studierende dazu befähigt werden können, fachdidaktisches Wissen aus fachmathematischen Inhalten zu generieren. Die Entwicklung des Professionswissens der Studierenden wird mithilfe unterschiedlicher Instrumente untersucht, um Rückschlüsse auf die Wirksamkeit der neu konzipierten Lehrveranstaltungen zu ziehen. Für die Untersuchungen im Mixed-Methods-Design werden neben Beobachtungen in Lehrveranstaltungen eigens konzipierte Wissenstests, Gruppeninterviews, Unterrichtsentwürfe aus Praxisphasen und Lerntagebücher genutzt. Die Studierendenperspektive wird durch Befragungen zur wahrgenommenen (Berufs-)Relevanz der Lehrveranstaltungen erhoben. Weiteres wesentliches Element der Begleitforschung ist die kollegiale Supervision durch sogenannte „Spies“ (Spione), die die Veranstaltungen kriteriengeleitet beobachten und anschließend gemeinsam mit den Dozierenden reflektieren. Die bisherigen Ergebnisse werden hier präsentiert und hinsichtlich ihrer Implikationen diskutiert. Die im Projekt entwickelten Gestaltungsprinzipien als Werkzeug für Design und Evaluation sowie das Spies-Konzept der kollegialen Supervision werden für die Qualitätsentwicklung von Lehrveranstaltungen zum Transfer vorgeschlagen.
N2  - The mathematics sub-project SPIES-M aims at a stronger professional orientation and the linking of subject-specific knowledge and subject-specific didactics in university teacher training. New courses were designed for all major mathematical content areas and implemented in the academic regulations of all mathematics teacher training programs at the University of Potsdam. For the course design, theory-based design principles were developed, which can be used both for the design, and for the evaluation and further development of the courses according to the design-research approach. The implementation of the design principles is exemplary illustrated for the fundamental idea of proportionality, by showing how students can be empowered to generate subject didactic knowledge from subject mathematical content. For this study, an explorative mixed-methods design was chosen, in which the development of the students’ professional knowledge was examined with the help of different instruments in order to draw conclusions about the effectiveness of the newly designed courses. In addition to course observations, specially designed knowledge tests, group interviews, lesson plans from practical phases, and learning diaries were used. The students’ perspective was examined through surveys on the perceived (professional) relevance of the courses. Another important element of the accompanying research was the collegial supervision by so-called „spies“, who observed the courses according to criteria and then reflected on them together with the course lecturers. Here, the current results are presented and discussed regarding their diverse implications. Lastly, the developed design principles as a tool for the design and evaluation of the mathematics courses as well as the spies concept of collegial supervision are proposed for transfer for the quality development of courses in general.
KW  - Lehrkräftebildung Mathematik
KW  - Professionswissen
KW  - Verknüpfung Fachwissenschaft und Fachdidaktik
KW  - Design Research
KW  - Gestaltungsprinzipien
KW  - kollegiale Supervision
KW  - teacher training mathematics
KW  - professional knowledge
KW  - linking of subject science and didactic
KW  - design research
KW  - design elements
KW  - collegial supervision
Y1  - 2023
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-617602
SN  - 978-3-86956-568-2
SN  - 2626-3556
SN  - 2626-4722
IS  - 3
SP  - 171
EP  - 191
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Bär, Christian
A1  - Bandara, Lashi
T1  - Boundary value problems for general first-order elliptic differential operators
JF  - Journal of functional analysis
N2  - We study boundary value problems for first-order elliptic differential operators on manifolds with compact boundary. The adapted boundary operator need not be selfadjoint and the boundary condition need not be pseudo-local.We show the equivalence of various characterisations of elliptic boundary conditions and demonstrate how the boundary conditions traditionally considered in the literature fit in our framework. The regularity of the solutions up to the boundary is proven. We show that imposing elliptic boundary conditions yields a Fredholm operator if the manifold is compact. We provide examples which are conveniently treated by our methods.
KW  - elliptic differential operators of firstorder
KW  - elliptic boundary
KW  - conditions
KW  - boundary regularity
KW  - Fredholm property
KW  - H-infinity-functional calculus
KW  - maximal regularity
KW  - Rarita-Schwinger
KW  - operator
Y1  - 2022
U6  - https://doi.org/10.1016/j.jfa.2022.109445
SN  - 0022-1236
SN  - 1096-0783
VL  - 282
IS  - 12
PB  - Elsevier
CY  - Amsterdam [u.a.]
ER  - 
TY  - THES
A1  - Malem-Shinitski, Noa
T1  - Bayesian inference and modeling for point processes with applications from neuronal activity to scene viewing
T1  - Bayessche Inferenz und Modellierung für Punktprozesse mit Anwendungen von neuronaler Aktivität bis Szenenbetrachtung
N2  - Point processes are a common methodology to model sets of events. From earthquakes to social media posts, from the arrival times of neuronal spikes to the timing of crimes, from stock prices to disease spreading -- these phenomena can be reduced to the occurrences of events concentrated in points. Often, these events happen one after the other defining a time--series.

Models of point processes can be used to deepen our understanding of such events and for classification and prediction. Such models include an underlying random process that generates the events. This work uses Bayesian methodology to infer the underlying generative process from observed data. Our contribution is twofold -- we develop new models and new inference methods for these processes.

We propose a model that extends the family of point processes where the occurrence of an event depends on the previous events. This family is known as Hawkes processes. Whereas in most existing models of such processes, past events are assumed to have only an excitatory effect on future events, we focus on the newly developed nonlinear Hawkes process, where past events could have excitatory and inhibitory effects. After defining the model, we present its inference method and apply it to data from different fields, among others, to neuronal activity.

The second model described in the thesis concerns a specific instance of point processes --- the decision process underlying human gaze control. This process results in a series of fixated locations in an image. We developed a new model to describe this process, motivated by the known Exploration--Exploitation dilemma. Alongside the model, we present a Bayesian inference algorithm to infer the model parameters.

Remaining in the realm of human scene viewing, we identify the lack of best practices for Bayesian inference in this field. We survey four popular algorithms and compare their performances for parameter inference in two scan path models.

The novel models and inference algorithms presented in this dissertation enrich the understanding of point process data and allow us to uncover meaningful insights.
N2  - Punktprozesse sind eine gängige Methode zur Modellierung von Ereignismengen. Von Erdbeben bis zu Social-Media-Posts, von den neuronalen Spikes bis zum Zeitpunkt von Verbrechen, von Aktienkursen bis zur Ausbreitung von Krankheiten - diese Phänomene lassen sich auf das Auftreten von Ereignissen reduzieren, die in Punkten konzentriert sind. Häufig treten diese Ereignisse nacheinander auf und bilden eine Zeitreihe.

Modelle von Punktprozessen können verwendet werden, um unser Verständnis solcher Ereignisse für Klassifizierung und Vorhersage zu vertiefen. Solche Modelle umfassen einen zugrunde liegenden Zufallsprozess, der die Ereignisse erzeugt. In dieser Arbeit wird die Bayes'sche Methodik verwendet, um den zugrunde liegenden generativen Prozess aus den beobachteten Daten abzuleiten. Wir leisten einen doppelten Beitrag: Wir entwickeln neue Modelle und neue Inferenzmethoden für diese Prozesse.

Wir schlagen ein Modell vor, das die Familie der Punktprozesse erweitert, bei denen das Auftreten eines Ereignisses von den vorherigen Ereignissen abhängt. Diese Familie ist als Hawkes-Prozesse bekannt. Während in den meisten bestehenden Modellen solcher Prozesse davon ausgegangen wird, dass vergangene Ereignisse nur eine exzitatorische Wirkung auf zukünftige Ereignisse haben, konzentrieren wir uns auf den neu entwickelten nichtlinearen Hawkes-Prozess, bei dem vergangene Ereignisse exzitatorische und hemmende Wirkungen haben können. Nach der Definition des Modells stellen wir seine Inferenzmethode vor und wenden sie auf Daten aus verschiedenen Bereichen an, unter anderem auf die neuronale Aktivität.

Das zweite Modell, das in dieser Arbeit beschrieben wird, betrifft einen speziellen Fall von Punktprozessen - den Entscheidungsprozess, der der menschlichen Blicksteuerung zugrunde liegt. Dieser Prozess führt zu einer Reihe von fixierten Positionen in einem Bild. Wir haben ein neues Modell entwickelt, um diesen Prozess zu beschreiben, motiviert durch das bekannte Exploration-Exploitation-Dilemma. Neben dem Modell stellen wir einen Bayes'schen Inferenzalgorithmus vor, um die Modellparameter abzuleiten.

Wir bleiben auf dem Gebiet der menschlichen Szenenbetrachtung und stellen fest, dass es in diesem Bereich keine bewährten Verfahren für die Bayes'sche Inferenz gibt. Wir geben einen Überblick über vier gängige Algorithmen und vergleichen ihre Leistungen bei der Ableitung von Parametern für zwei Scanpfadmodelle.

Die in dieser Dissertation vorgestellten neuen Modelle und Inferenzalgorithmen bereichern das Verständnis von Punktprozessdaten und ermöglichen es uns, sinnvolle Erkenntnisse zu gewinnen.
KW  - Bayesian inference
KW  - point process
KW  - statistical machine learning
KW  - sampling
KW  - modeling
KW  - Bayessche Inferenz
KW  - Modellierung
KW  - Punktprozess
KW  - Stichprobenentnahme aus einem statistischen Modell
KW  - statistisches maschinelles Lernen
Y1  - 2023
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-614952
ER  - 
TY  - JOUR
A1  - Reich, Sebastian
A1  - Weissmann, Simon
T1  - Fokker-Planck particle systems for Bayesian inference: computational approaches
JF  - SIAM ASA journal on uncertainty quantification
N2  - Bayesian inference can be embedded into an appropriately defined dynamics in the space of probability measures. In this paper, we take Brownian motion and its associated Fokker-Planck equation as a starting point for such embeddings and explore several interacting particle approximations. More specifically, we consider both deterministic and stochastic interacting particle systems and combine them with the idea of preconditioning by the empirical covariance matrix. In addition to leading to affine invariant formulations which asymptotically speed up convergence, preconditioning allows for gradient-free implementations in the spirit of the ensemble Kalman filter. While such gradient-free implementations have been demonstrated to work well for posterior measures that are nearly Gaussian, we extend their scope of applicability to multimodal measures by introducing localized gradient-free approximations. Numerical results demonstrate the effectiveness of the considered methodologies.
KW  - Bayesian inverse problems
KW  - Fokker-Planck equation
KW  - gradient flow
KW  - affine
KW  - invariance
KW  - gradient-free sampling methods
KW  - localization
Y1  - 2021
U6  - https://doi.org/10.1137/19M1303162
SN  - 2166-2525
VL  - 9
IS  - 2
SP  - 446
EP  - 482
PB  - Society for Industrial and Applied Mathematics
CY  - Philadelphia
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  - Shlapunov, Alexander
A1  - Tarchanov, Nikolaj Nikolaevič
T1  - An open mapping theorem for the Navier-Stokes type equations associated with the de Rham complex over R-n
JF  - Siberian electronic mathematical reports = Sibirskie ėlektronnye matematičeskie izvestija
N2  - We consider an initial problem for the Navier-Stokes type equations associated with the de Rham complex over R-n x[0, T], n >= 3, with a positive time T. We prove that the problem induces an open injective mappings on the scales of specially constructed function spaces of Bochner-Sobolev type. In particular, the corresponding statement on the intersection of these classes gives an open mapping theorem for smooth solutions to the Navier-Stokes equations.
KW  - Navier-Stokes equations
KW  - de Rham complex
KW  - open mapping theorem
Y1  - 2021
U6  - https://doi.org/10.33048/semi.2021.18.108
SN  - 1813-3304
VL  - 18
IS  - 2
SP  - 1433
EP  - 1466
PB  - Institut Matematiki Imeni S. L. Soboleva
CY  - Novosibirsk
ER  - 
TY  - JOUR
A1  - Beckus, Siegfried
A1  - Eliaz, Latif
T1  - Eigenfunctions growth of R-limits on graphs
JF  - Journal of spectral theory / European Mathematical Society
N2  - A characterization of the essential spectrum of Schrodinger operators on infinite graphs is derived involving the concept of R-limits. This concept, which was introduced previously for operators on N and Z(d) as "right-limits," captures the behaviour of the operator at infinity. For graphs with sub-exponential growth rate, we show that each point in sigma(ss)(H) corresponds to a bounded generalized eigenfunction of a corresponding R-limit of H. If, additionally, the graph is of uniform sub-exponential growth, also the converse inclusion holds.
KW  - Essential spectrum
KW  - Schrodinger operators
KW  - graphs
KW  - right limits
KW  - generalized eigenfunctions
Y1  - 2021
U6  - https://doi.org/10.4171/JST/389
SN  - 1664-039X
SN  - 1664-0403
VL  - 11
IS  - 4
SP  - 1895
EP  - 1933
PB  - EMS Press, an imprint of the European Mathematical Society - EMS - Publishing House GmbH, Institut für Mathematik, Technische Universität
CY  - Berlin
ER  - 
TY  - JOUR
A1  - Ropp, Guillaume
A1  - Lesur, Vincent
A1  - Bärenzung, Julien
A1  - Holschneider, Matthias
T1  - Sequential modelling of the Earth’s core magnetic field
JF  - Earth, Planets and Space
N2  - We describe a new, original approach to the modelling of the Earth's magnetic field. The overall objective of this study is to reliably render fast variations of the core field and its secular variation. This method combines a sequential modelling approach, a Kalman filter, and a correlation-based modelling step. Sources that most significantly contribute to the field measured at the surface of the Earth are modelled. Their separation is based on strong prior information on their spatial and temporal behaviours. We obtain a time series of model distributions which display behaviours similar to those of recent models based on more classic approaches, particularly at large temporal and spatial scales. Interesting new features and periodicities are visible in our models at smaller time and spatial scales. An important aspect of our method is to yield reliable error bars for all model parameters. These errors, however, are only as reliable as the description of the different sources and the prior information used are realistic. Finally, we used a slightly different version of our method to produce candidate models for the thirteenth edition of the International Geomagnetic Reference Field.
KW  - geomagnetic field
KW  - secular variation
KW  - Kalman filter
KW  - IGRF
Y1  - 2020
U6  - https://doi.org/10.1186/s40623-020-01230-1
SN  - 1880-5981
VL  - 72
IS  - 1
PB  - Springer
CY  - New York
ER  - 
TY  - JOUR
A1  - Matzka, Jürgen
A1  - Stolle, Claudia
A1  - Yamazaki, Yosuke
A1  - Bronkalla, Oliver
A1  - Morschhauser, Achim
T1  - The geomagnetic Kp index and derived indices of geomagnetic activity
JF  - Space weather : the international journal of research and applications
N2  - The geomagnetic Kp index is one of the most extensively used indices of geomagnetic activity, both for scientific and operational purposes. This article reviews the properties of the Kp index and provides a reference for users of the Kp index and associated data products as derived and distributed by the GFZ German Research Centre for Geosciences. The near real-time production of the nowcast Kp index is of particular interest for space weather services and here we describe and evaluate its current setup.
Y1  - 2021
U6  - https://doi.org/10.1029/2020SW002641
SN  - 1542-7390
VL  - 19
IS  - 5
PB  - Wiley
CY  - New York
ER  - 
TY  - JOUR
A1  - Pathiraja, Sahani Darschika
A1  - Reich, Sebastian
A1  - Stannat, Wilhelm
T1  - McKean-Vlasov SDEs in nonlinear filtering
JF  - SIAM journal on control and optimization : a publication of the Society for Industrial and Applied Mathematics
N2  - Various particle filters have been proposed over the last couple of decades with the common feature that the update step is governed by a type of control law. This feature makes them an attractive alternative to traditional sequential Monte Carlo which scales poorly with the state dimension due to weight degeneracy. This article proposes a unifying framework that allows us to systematically derive the McKean-Vlasov representations of these filters for the discrete time and continuous time observation case, taking inspiration from the smooth approximation of the data considered in [D. Crisan and J. Xiong, Stochastics, 82 (2010), pp. 53-68; J. M. Clark and D. Crisan, Probab. Theory Related Fields, 133 (2005), pp. 43-56]. We consider three filters that have been proposed in the literature and use this framework to derive Ito representations of their limiting forms as the approximation parameter delta -> 0. All filters require the solution of a Poisson equation defined on R-d, for which existence and uniqueness of solutions can be a nontrivial issue. We additionally establish conditions on the signal-observation system that ensures well-posedness of the weighted Poisson equation arising in one of the filters.
KW  - data assimilation
KW  - feedback particle filter
KW  - Poincare inequality
KW  - well-posedness
KW  - nonlinear filtering
KW  - McKean-Vlasov
KW  - mean-field equations
Y1  - 2022
U6  - https://doi.org/10.1137/20M1355197
SN  - 0363-0129
SN  - 1095-7138
VL  - 59
IS  - 6
SP  - 4188
EP  - 4215
PB  - Society for Industrial and Applied Mathematics
CY  - Philadelphia
ER  - 
TY  - JOUR
A1  - Garmendia, Alfonso
A1  - Zambon, Marco
T1  - Quotients of singular foliations and Lie 2-group actions
JF  - Journal of noncommutative geometry
N2  - Androulidakis-Skandalis (2009) showed that every singular foliation has an associated topological groupoid, called holonomy groupoid. In this note, we exhibit some functorial properties of this assignment: if a foliated manifold (M, FM ) is the quotient of a foliated manifold (P, FP ) along a surjective submersion with connected fibers, then the same is true for the corresponding holonomy groupoids. For quotients by a Lie group action, an analogue statement holds under suitable assumptions, yielding a Lie 2-group action on the holonomy groupoid.
KW  - Lie groupoid
KW  - singular foliation
KW  - fibration
Y1  - 2021
U6  - https://doi.org/10.4171/JNCG/434
SN  - 1661-6952
SN  - 1661-6960
VL  - 15
IS  - 4
SP  - 1251
EP  - 1283
PB  - EMS Press, an imprint of the European Mathematical Society - EMS - Publishing House GmbH, Institut für Mathematik, Technische Universität Berlin
CY  - Berlin
ER  - 
TY  - JOUR
A1  - Ruchi, Sangeetika
A1  - Dubinkina, Svetlana
A1  - Wiljes, Jana de
T1  - Fast hybrid tempered ensemble transform filter formulation for Bayesian elliptical problems via Sinkhorn approximation
JF  - Nonlinear processes in geophysics / European Geosciences Union ; American Geophysical Union
N2  - Identification of unknown parameters on the basis of partial and noisy data is a challenging task, in particular in high dimensional and non-linear settings. Gaussian approximations to the problem, such as ensemble Kalman inversion, tend to be robust and computationally cheap and often produce astonishingly accurate estimations despite the simplifying underlying assumptions. Yet there is a lot of room for improvement, specifically regarding a correct approximation of a non-Gaussian posterior distribution. The tempered ensemble transform particle filter is an adaptive Sequential Monte Carlo (SMC) method, whereby resampling is based on optimal transport mapping. Unlike ensemble Kalman inversion, it does not require any assumptions regarding the posterior distribution and hence has shown to provide promising results for non-linear non-Gaussian inverse problems. However, the improved accuracy comes with the price of much higher computational complexity, and the method is not as robust as ensemble Kalman inversion in high dimensional problems. In this work, we add an entropy-inspired regularisation factor to the underlying optimal transport problem that allows the high computational cost to be considerably reduced via Sinkhorn iterations. Further, the robustness of the method is increased via an ensemble Kalman inversion proposal step before each update of the samples, which is also referred to as a hybrid approach. The promising performance of the introduced method is numerically verified by testing it on a steady-state single-phase Darcy flow model with two different permeability configurations. The results are compared to the output of ensemble Kalman inversion, and Markov chain Monte Carlo methods results are computed as a benchmark.
Y1  - 2021
U6  - https://doi.org/10.5194/npg-28-23-2021
SN  - 1023-5809
SN  - 1607-7946
VL  - 28
IS  - 1
SP  - 23
EP  - 41
PB  - Copernicus
CY  - Göttingen
ER  - 
TY  - JOUR
A1  - Schanner, Maximilian Arthus
A1  - Mauerberger, Stefan
A1  - Korte, Monika
A1  - Holschneider, Matthias
T1  - Correlation based time evolution of the archeomagnetic field
JF  - Journal of geophysical research : JGR ; an international quarterly. B, Solid earth
N2  - In a previous study, a new snapshot modeling concept for the archeomagnetic field was introduced (Mauerberger et al., 2020, ). By assuming a Gaussian process for the geomagnetic potential, a correlation-based algorithm was presented, which incorporates a closed-form spatial correlation function. This work extends the suggested modeling strategy to the temporal domain. A space-time correlation kernel is constructed from the tensor product of the closed-form spatial correlation kernel with a squared exponential kernel in time. Dating uncertainties are incorporated into the modeling concept using a noisy input Gaussian process. All but one modeling hyperparameters are marginalized, to reduce their influence on the outcome and to translate their variability to the posterior variance. The resulting distribution incorporates uncertainties related to dating, measurement and modeling process. Results from application to archeomagnetic data show less variation in the dipole than comparable models, but are in general agreement with previous findings.
Y1  - 2021
U6  - https://doi.org/10.1029/2020JB021548
SN  - 2169-9313
SN  - 2169-9356
VL  - 126
IS  - 7
PB  - American Geophysical Union
CY  - Washington
ER  - 
TY  - JOUR
A1  - Démaris, Alix
A1  - Widigson, Ella S. K.
A1  - Ilvemark, Johan F. K. F.
A1  - Steenholdt, Casper
A1  - Seidelin, Jakob B.
A1  - Huisinga, Wilhelm
A1  - Michelet, Robin
A1  - Aulin, Linda B. S.
A1  - Kloft, Charlotte
T1  - Ulcerative colitis and acute severe ulcerative colitis patients are overlooked in infliximab population pharmacokinetic models
BT  - results from a comprehensive review
JF  - Pharmaceutics / Molecular Diversity Preservation International
N2  - Ulcerative colitis (UC) is part of the inflammatory bowels diseases, and moderate to severe UC patients can be treated with anti-tumour necrosis alpha monoclonal antibodies, including infliximab (IFX). Even though treatment of UC patients by IFX has been in place for over a decade, many gaps in modelling of IFX PK in this population remain. This is even more true for acute severe UC (ASUC) patients for which early prediction of IFX pharmacokinetic (PK) could highly improve treatment outcome. Thus, this review aims to compile and analyse published population PK models of IFX in UC and ASUC patients, and to assess the current knowledge on disease activity impact on IFX PK. For this, a semi-systematic literature search was conducted, from which 26 publications including a population PK model analysis of UC patients receiving IFX therapy were selected. Amongst those, only four developed a model specifically for UC patients, and only three populations included severe UC patients. Investigations of disease activity impact on PK were reported in only 4 of the 14 models selected. In addition, the lack of reported model codes and assessment of predictive performance make the use of published models in a clinical setting challenging. Thus, more comprehensive investigation of PK in UC and ASUC is needed as well as more adequate reports on developed models and their evaluation in order to apply them in a clinical setting.
KW  - infliximab
KW  - inflammatory bowel disease
KW  - ulcerative colitis
KW  - acute severe
KW  - disease activity
KW  - pharmacokinetic
KW  - pharmacometrics
Y1  - 2022
U6  - https://doi.org/10.3390/pharmaceutics14102095
SN  - 1999-4923
VL  - 14
IS  - 10
PB  - MDPI
CY  - Basel
ER  - 
TY  - JOUR
A1  - Baerenzung, Julien
A1  - Holschneider, Matthias
A1  - Wicht, Johannes
A1  - Lesur, Vincent
A1  - Sanchez, Sabrina
T1  - The Kalmag model as a candidate for IGRF-13
JF  - Earth, planets and space
N2  - We present a new model of the geomagnetic field spanning the last 20 years and called Kalmag. Deriving from the assimilation of CHAMP and Swarm vector field measurements, it separates the different contributions to the observable field through parameterized prior covariance matrices. To make the inverse problem numerically feasible, it has been sequentialized in time through the combination of a Kalman filter and a smoothing algorithm. The model provides reliable estimates of past, present and future mean fields and associated uncertainties. The version presented here is an update of our IGRF candidates; the amount of assimilated data has been doubled and the considered time window has been extended from [2000.5, 2019.74] to [2000.5, 2020.33].
KW  - Geomagnetic field
KW  - Secular variation
KW  - Assimilation
KW  - Kalman filter
KW  - Machine learning
Y1  - 2020
U6  - https://doi.org/10.1186/s40623-020-01295-y
SN  - 1880-5981
VL  - 72
IS  - 1
PB  - Springer
CY  - New York
ER  - 
TY  - JOUR
A1  - Hastermann, Gottfried
A1  - Reinhardt, Maria
A1  - Klein, Rupert
A1  - Reich, Sebastian
T1  - Balanced data assimilation for highly oscillatory mechanical systems
JF  - Communications in applied mathematics and computational science : CAMCoS
N2  - Data assimilation algorithms are used to estimate the states of a dynamical system using partial and noisy observations. The ensemble Kalman filter has become a popular data assimilation scheme due to its simplicity and robustness for a wide range of application areas. Nevertheless, this filter also has limitations due to its inherent assumptions of Gaussianity and linearity, which can manifest themselves in the form of dynamically inconsistent state estimates. This issue is investigated here for balanced, slowly evolving solutions to highly oscillatory Hamiltonian systems which are prototypical for applications in numerical weather prediction. It is demonstrated that the standard ensemble Kalman filter can lead to state estimates that do not satisfy the pertinent balance relations and ultimately lead to filter divergence. Two remedies are proposed, one in terms of blended asymptotically consistent time-stepping schemes, and one in terms of minimization-based postprocessing methods. The effects of these modifications to the standard ensemble Kalman filter are discussed and demonstrated numerically for balanced motions of two prototypical Hamiltonian reference systems.
KW  - data assimilation
KW  - ensemble Kalman filter
KW  - balanced dynamics
KW  - highly
KW  - oscillatory systems
KW  - Hamiltonian dynamics
KW  - geophysics
Y1  - 2021
U6  - https://doi.org/10.2140/camcos.2021.16.119
SN  - 1559-3940
SN  - 2157-5452
VL  - 16
IS  - 1
SP  - 119
EP  - 154
PB  - Mathematical Sciences Publishers
CY  - Berkeley
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  - JOUR
A1  - Clavier, Pierre
A1  - Guo, Li
A1  - Paycha, Sylvie
A1  - Zhang, Bin
T1  - Locality and renormalization: universal properties and integrals on trees
JF  - Journal of mathematical physics
N2  - The purpose of this paper is to build an algebraic framework suited to regularize branched structures emanating from rooted forests and which encodes the locality principle. This is achieved by means of the universal properties in the locality framework of properly decorated rooted forests. These universal properties are then applied to derive the multivariate regularization of integrals indexed by rooted forests. We study their renormalization, along the lines of Kreimer's toy model for Feynman integrals.
Y1  - 2020
U6  - https://doi.org/10.1063/1.5116381
SN  - 0022-2488
SN  - 1089-7658
VL  - 61
IS  - 2
PB  - American Institute of Physics
CY  - College Park, Md.
ER  - 
TY  - GEN
A1  - Ehlen, Tobias
A1  - Flöge, Annie
A1  - Göbel, Franziska
A1  - Keller, Peter
A1  - Rœlly, Sylvie
ED  - Keller, Peter
ED  - Rœlly, Sylvie
T1  - Übungsbuch zur Stochastik
BT  - Aufgaben und Lösungen  ; Grundlegende Konzepte und Anwendungen
N2  - Dieses Buch stellt Übungen zu den Grundbegriffen und Grundsätzen der Stochastik und ihre Lösungen zur Verfügung. So wie man Tonleitern in der Musik trainiert, so berechnet man Übungsaufgaben in der Mathematik. In diesem Sinne soll dieses Übungsbuch vor allem als Vorlage dienen für das eigenständige, eigenverantwortliche Lernen und Üben.
Die Schönheit und Einzigartigkeit der Wahrscheinlichkeitstheorie besteht darin, dass sie eine Vielzahl von realen Phänomenen modellieren kann. Daher findet man hier Aufgaben mit Verbindungen zur Geometrie, zu Glücksspielen, zur Versicherungsmathematik, zur Demographie und vielen anderen Themen.
N2  - This book provides exercises on the basic concepts and principles of stochastics and their solutions. Just as one trains scales in music, one calculates exercises in mathematics. In this sense, this exercise book is primarily intended to serve as a template for independent learning and practice.
The beauty and uniqueness of probability theory is that it can model a variety of real phenomena. Therefore, one can find exercises with connections to geometry, gambling, actuarial mathematics, demography and many other topics.
KW  - Aufgabensammlung
KW  - Wahrscheinlichkeitstheorie
KW  - Stochastik
KW  - Wahrscheinlichkeitsverteilung
KW  - Zufallsvariable
KW  - Grenzwertsatz
KW  - Konfidenzintervall
KW  - exercise collection
KW  - probability theory
KW  - stochastics
KW  - probability distribution
KW  - random variable
KW  - limit theorem
KW  - confidence interval
Y1  - 2023
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-595939
SN  - 978-3-86956-563-7
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Bär, Christian
A1  - Hanke, Bernhard
T1  - Local flexibility for open partial differential relations
JF  - Communications on pure and applied mathematics / issued by the Courant Institute of Mathematical Sciences, New York Univ.
N2  - We show that local deformations, near closed subsets, of solutions to open partial differential relations can be extended to global deformations, provided all but the highest derivatives stay constant along the subset. The applicability of this general result is illustrated by a number of examples, dealing with convex embeddings of hypersurfaces, differential forms, and lapse functions in Lorentzian geometry.
The main application is a general approximation result by sections that have very restrictive local properties on open dense subsets. This shows, for instance, that given any K is an element of Double-struck capital R every manifold of dimension at least 2 carries a complete C-1,C- 1-metric which, on a dense open subset, is smooth with constant sectional curvature K. Of course, this is impossible for C-2-metrics in general.
Y1  - 2021
U6  - https://doi.org/10.1002/cpa.21982
SN  - 0010-3640
SN  - 1097-0312
VL  - 75
IS  - 6
SP  - 1377
EP  - 1415
PB  - Wiley
CY  - Hoboken
ER  - 
TY  - JOUR
A1  - Roos, Saskia
A1  - Otoba, Nobuhiko
T1  - Scalar curvature and the multiconformal class of a direct product Riemannian manifold
JF  - Geometriae dedicata
N2  - For a closed, connected direct product Riemannian manifold (M, g) = (M-1, g(1)) x ... x (M-l, g(l)), we define its multiconformal class [[g]] as the totality {integral(2)(1)g(1) circle plus center dot center dot center dot integral(2)(l)g(l)} of all Riemannian metrics obtained from multiplying the metric gi of each factor Mi by a positive function fi on the total space M. A multiconformal class [[ g]] contains not only all warped product type deformations of g but also the whole conformal class [(g) over tilde] of every (g) over tilde is an element of[[ g]]. In this article, we prove that [[g]] contains a metric of positive scalar curvature if and only if the conformal class of some factor (Mi, gi) does, under the technical assumption dim M-i = 2. We also show that, even in the case where every factor (M-i, g(i)) has positive scalar curvature, [[g]] contains a metric of scalar curvature constantly equal to -1 and with arbitrarily large volume, provided l = 2 and dim M = 3.
KW  - Positive scalar curvature
KW  - Constant scalar curvature
KW  - The Yamabe
KW  - problem
KW  - Warped product
KW  - Umbilic product
KW  - Twisted product
Y1  - 2021
U6  - https://doi.org/10.1007/s10711-021-00636-9
SN  - 0046-5755
SN  - 1572-9168
VL  - 214
IS  - 1
SP  - 801
EP  - 829
PB  - Springer
CY  - Dordrecht
ER  - 
TY  - JOUR
A1  - Mauerberger, Stefan
A1  - Schanner, Maximilian Arthus
A1  - Korte, Monika
A1  - Holschneider, Matthias
T1  - Correlation based snapshot models of the archeomagnetic field
JF  - Geophysical journal international
N2  - For the time stationary global geomagnetic field, a new modelling concept is presented. A Bayesian non-parametric approach provides realistic location dependent uncertainty estimates. Modelling related variabilities are dealt with systematically by making little subjective apriori assumptions. Rather than parametrizing the model by Gauss coefficients, a functional analytic approach is applied. The geomagnetic potential is assumed a Gaussian process to describe a distribution over functions. Apriori correlations are given by an explicit kernel function with non-informative dipole contribution. A refined modelling strategy is proposed that accommodates non-linearities of archeomagnetic observables: First, a rough field estimate is obtained considering only sites that provide full field vector records. Subsequently, this estimate supports the linearization that incorporates the remaining incomplete records. The comparison of results for the archeomagnetic field over the past 1000 yr is in general agreement with previous models while improved model uncertainty estimates are provided.
KW  - geopotential theory
KW  - archaeomagnetism
KW  - magnetic field variations through
KW  - time
KW  - palaeomagnetism
KW  - inverse theory
KW  - statistical methods
Y1  - 2020
U6  - https://doi.org/10.1093/gji/ggaa336
SN  - 0956-540X
SN  - 1365-246X
VL  - 223
IS  - 1
SP  - 648
EP  - 665
PB  - Oxford Univ. Press
CY  - Oxford
ER  - 
TY  - JOUR
A1  - Clavier, Pierre J.
T1  - Borel-Écalle resummation of a two-point function
JF  - Annales Henri Poincaré : a journal of theoretical and mathematical physics / ed. jointly by the Institut Henri Poincaré and by the Swiss Physical Society
N2  - We provide an overview of the tools and techniques of resurgence theory used in the Borel-ecalle resummation method, which we then apply to the massless Wess-Zumino model. Starting from already known results on the anomalous dimension of the Wess-Zumino model, we solve its renormalisation group equation for the two-point function in a space of formal series. We show that this solution is 1-Gevrey and that its Borel transform is resurgent. The Schwinger-Dyson equation of the model is then used to prove an asymptotic exponential bound for the Borel transformed two-point function on a star-shaped domain of a suitable ramified complex plane. This proves that the two-point function of the Wess-Zumino model is Borel-ecalle summable.
Y1  - 2021
U6  - https://doi.org/10.1007/s00023-021-01057-w
SN  - 1424-0637
SN  - 1424-0661
VL  - 22
IS  - 6
SP  - 2103
EP  - 2136
PB  - Springer
CY  - Cham
ER  - 
TY  - THES
A1  - Dahl, Dorothee Sophie
T1  - Zahlen in den Fingern
T1  - Numbers and fingers
BT  - eine Analyse des Lernspiels Fingu in Bezug auf den frühkindlichen Zahlerwerb im Rahmen der Artifact-Centric Activity Theory
BT  - an analysis of the learning game Fingu in relation to early numeracy acquisition within the framework of the artifact-centric activity theory
N2  - Die Debatte über den Einsatz von digitalen Werkzeugen in der mathematischen Frühförderung ist hoch aktuell. Lernspiele werden konstruiert, mit dem Ziel, mathematisches, informelles Wissen aufzubauen und so einen besseren Schulstart zu ermöglichen. Doch allein die digitale und spielerische Aufarbeitung führt nicht zwingend zu einem Lernerfolg. Daher ist es umso wichtiger, die konkrete Implementation der theoretischen Konstrukte und Interaktionsmöglichkeiten mit den Werkzeugen zu analysieren und passend aufzubereiten.

In dieser Masterarbeit wird dazu exemplarisch ein mathematisches Lernspiel namens „Fingu“ für den Einsatz im vorschulischen Bereich theoretisch und empirisch im Rahmen der Artifact-Centric Activity Theory (ACAT) untersucht. Dazu werden zunächst die theoretischen Hintergründe zum Zahlensinn, Zahlbegriffserwerb, Teil-Ganze-Verständnis, der Anzahlwahrnehmung und -bestimmung, den Anzahlvergleichen und der Anzahldarstellung mithilfe von Fingern gemäß der Embodied Cognition sowie der Verwendung von digitalen Werkzeugen und Multi-Touch-Geräten umfassend beschrieben. Anschließend wird die App Fingu erklärt und dann theoretisch entlang des ACAT-Review-Guides analysiert. Zuletzt wird die selbstständig durchgeführte Studie mit zehn Vorschulkindern erläutert und darauf aufbauend Verbesserungs- und Entwicklungsmöglichkeiten der App auf wissenschaftlicher Grundlage beigetragen. Für Fingu lässt sich abschließend festhalten, dass viele Prozesse wie die (Quasi-)Simultanerfassung oder das Zählen gefördert werden können, für andere wie das Teil-Ganze-Verständnis aber noch Anpassungen und/oder die Begleitung durch Erwachsene nötig ist.
N2  - The current debate about the use of digital tools in early mathematical education has a lot of relevance these days. Educational games are designed with the aim of building mathematical informal knowledge and thus enabling a better start to school. But digital and playful implementation alone does not necessarily lead to learning. Therefore, it is important to analyze the media in detail and with regard to the theoretical constructs.

In this master's thesis, a mathematical learning game called “Fingu” for preschool children is analyzed theoretically and empirically within the framework of the Artifact-Centric Activity Theory (ACAT). First, the theoretical background is described, that is the number sense, number concept acquisition, part-whole understanding, number perception and determination, number comparisons and number representation using fingers according to embodied cognition as well as the use of digital tools and multi-touch. The app itself is explained and then analyzed theoretically using the ACAT review guide. Finally, the conducted study with ten preschool children is presented. Based on those results and the scientific basis, possible improvements and development of the app are explained. For Fingu, it can be concluded that many processes such as perceptual or conceptual subitizing or counting can be improved, but for others such as part-whole understanding, adjustments and/or adult support are still necessary.
KW  - Zahlerwerb
KW  - Frühförderung
KW  - Lernspiele
KW  - Videostudie
KW  - ACAT
KW  - number
KW  - part-whole concept
Y1  - 2023
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-607629
ER  - 
TY  - JOUR
A1  - Gottwald, Georg A.
A1  - Reich, Sebastian
T1  - Supervised learning from noisy observations
BT  - Combining machine-learning techniques with data assimilation
JF  - Physica : D, Nonlinear phenomena
N2  - Data-driven prediction and physics-agnostic machine-learning methods have attracted increased interest in recent years achieving forecast horizons going well beyond those to be expected for chaotic dynamical systems. In a separate strand of research data-assimilation has been successfully used to optimally combine forecast models and their inherent uncertainty with incoming noisy observations. The key idea in our work here is to achieve increased forecast capabilities by judiciously combining machine-learning algorithms and data assimilation. We combine the physics-agnostic data -driven approach of random feature maps as a forecast model within an ensemble Kalman filter data assimilation procedure. The machine-learning model is learned sequentially by incorporating incoming noisy observations. We show that the obtained forecast model has remarkably good forecast skill while being computationally cheap once trained. Going beyond the task of forecasting, we show that our method can be used to generate reliable ensembles for probabilistic forecasting as well as to learn effective model closure in multi-scale systems. (C) 2021 Elsevier B.V. All rights reserved.
KW  - Data-driven modelling
KW  - Random feature maps
KW  - Data assimilation
Y1  - 2021
U6  - https://doi.org/10.1016/j.physd.2021.132911
SN  - 0167-2789
SN  - 1872-8022
VL  - 423
PB  - Elsevier
CY  - Amsterdam
ER  - 
TY  - JOUR
A1  - Redmann, Martin
A1  - Freitag, Melina A.
T1  - Optimization based model order reduction for stochastic systems
JF  - Applied mathematics and computation
N2  - In this paper, we bring together the worlds of model order reduction for stochastic linear systems and H-2-optimal model order reduction for deterministic systems. In particular, we supplement and complete the theory of error bounds for model order reduction of stochastic differential equations. With these error bounds, we establish a link between the output error for stochastic systems (with additive and multiplicative noise) and modified versions of the H-2-norm for both linear and bilinear deterministic systems. When deriving the respective optimality conditions for minimizing the error bounds, we see that model order reduction techniques related to iterative rational Krylov algorithms (IRKA) are very natural and effective methods for reducing the dimension of large-scale stochastic systems with additive and/or multiplicative noise. We apply modified versions of (linear and bilinear) IRKA to stochastic linear systems and show their efficiency in numerical experiments.
KW  - Model order reduction
KW  - Stochastic systems
KW  - Optimality conditions
KW  - Sylvester equations
KW  - Levy process
Y1  - 2021
U6  - https://doi.org/10.1016/j.amc.2020.125783
SN  - 0096-3003
SN  - 1873-5649
VL  - 398
PB  - Elsevier
CY  - New York
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  - 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  - 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  - 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  - JOUR
A1  - Leung, Tsz Yan
A1  - Leutbecher, Martin
A1  - Reich, Sebastian
A1  - Shepherd, Theodore G.
T1  - Impact of the mesoscale range on error growth and the limits to atmospheric predictability
JF  - Journal of the atmospheric sciences
N2  - Global numerical weather prediction (NWP) models have begun to resolve the mesoscale k(-5/3) range of the energy spectrum, which is known to impose an inherently finite range of deterministic predictability per se as errors develop more rapidly on these scales than on the larger scales. However, the dynamics of these errors under the influence of the synoptic-scale k(-3) range is little studied. Within a perfect-model context, the present work examines the error growth behavior under such a hybrid spectrum in Lorenz's original model of 1969, and in a series of identical-twin perturbation experiments using an idealized two-dimensional barotropic turbulence model at a range of resolutions. With the typical resolution of today's global NWP ensembles, error growth remains largely uniform across scales. The theoretically expected fast error growth characteristic of a k(-5/3) spectrum is seen to be largely suppressed in the first decade of the mesoscale range by the synoptic-scale k(-3) range. However, it emerges once models become fully able to resolve features on something like a 20-km scale, which corresponds to a grid resolution on the order of a few kilometers.
KW  - mesoscale forecasting
KW  - numerical weather prediction/forecasting
KW  - short-range prediction
KW  - numerical analysis/modeling
Y1  - 2020
U6  - https://doi.org/10.1175/JAS-D-19-0346.1
SN  - 0022-4928
SN  - 1520-0469
VL  - 77
IS  - 11
SP  - 3769
EP  - 3779
PB  - American Meteorological Soc.
CY  - Boston
ER  - 
TY  - JOUR
A1  - Beckus, Siegfried
A1  - Bellissard, Jean
A1  - De Nittis, Giuseppe
T1  - Spectral continuity for aperiodic quantum systems
BT  - applications of a folklore theorem
JF  - Journal of mathematical physics
N2  - This work provides a necessary and sufficient condition for a symbolic dynamical system to admit a sequence of periodic approximations in the Hausdorff topology. The key result proved and applied here uses graphs that are called De Bruijn graphs, Rauzy graphs, or Anderson-Putnam complex, depending on the community. Combining this with a previous result, the present work justifies rigorously the accuracy and reliability of algorithmic methods used to compute numerically the spectra of a large class of self-adjoint operators. The so-called Hamiltonians describe the effective dynamic of a quantum particle in aperiodic media. No restrictions on the structure of these operators other than general regularity assumptions are imposed. In particular, nearest-neighbor correlation is not necessary. Examples for the Fibonacci and the Golay-Rudin-Shapiro sequences are explicitly provided illustrating this discussion. While the first sequence has been thoroughly studied by physicists and mathematicians alike, a shroud of mystery still surrounds the latter when it comes to spectral properties. In light of this, the present paper gives a new result here that might help uncovering a solution.
Y1  - 2020
U6  - https://doi.org/10.1063/5.0011488
SN  - 0022-2488
SN  - 1089-7658
VL  - 61
IS  - 12
PB  - American Institute of Physics
CY  - Melville, NY
ER  - 
TY  - THES
A1  - Lopez Valencia, Diego Andres
T1  - The Milnor-Moore and Poincaré-Birkhoff-Witt theorems in the locality set up and the polar structure of Shintani zeta functions
T1  - Die Milnor-Moore und Poincaré-Birkhoff-Witt Theoreme in der Lokalität und die polare Struktur der Shintani-Zeta-Abbildungen
N2  - This thesis bridges two areas of mathematics, algebra on the one hand with the Milnor-Moore theorem (also called Cartier-Quillen-Milnor-Moore theorem) as well as the Poincaré-Birkhoff-Witt theorem, and analysis on the other hand with Shintani zeta functions which generalise multiple zeta functions.
The first part is devoted to an algebraic formulation of the locality principle in physics and generalisations of classification theorems such as Milnor-Moore and Poincaré-Birkhoff-Witt theorems to the locality framework. The locality principle roughly says that events that take place far apart in spacetime do not infuence each other. The algebraic formulation of this principle discussed here is useful when analysing singularities which arise from events located far apart in space, in order to renormalise them while keeping a memory of the fact that they do not influence each other. We start by endowing a vector space with a symmetric relation, named the locality relation, which keeps track of elements that are "locally independent". The pair of a vector space together with such relation is called a pre-locality vector space. This concept is extended to tensor products allowing only tensors made of locally independent elements. We extend this concept to the locality tensor algebra, and locality symmetric algebra of a pre-locality vector space and prove the universal properties of each of such structures. We also introduce the pre-locality Lie algebras, together with their associated locality universal enveloping algebras and prove their universal property. We later upgrade all such structures and results from the pre-locality to the locality context, requiring the locality relation to be compatible with the linear structure of the vector space. This allows us to define locality coalgebras, locality bialgebras, and locality Hopf algebras. Finally, all the previous results are used to prove the locality version of the Milnor-Moore and the Poincaré-Birkhoff-Witt theorems. It is worth noticing that the proofs presented, not only generalise the results in the usual (non-locality) setup, but also often use less tools than their counterparts in their non-locality counterparts.
The second part is devoted to study the polar structure of the Shintani zeta functions. Such functions, which generalise the Riemman zeta function, multiple zeta functions, Mordell-Tornheim zeta functions, among others, are parametrised by matrices with real non-negative arguments. It is known that Shintani zeta functions extend to meromorphic functions with poles on afine hyperplanes. We refine this result in showing that the poles lie on hyperplanes parallel to the facets of certain convex polyhedra associated to the defining matrix for the Shintani zeta function. Explicitly, the latter are the Newton polytopes of the polynomials induced by the columns of the underlying matrix. We then prove that the coeficients of the equation which describes the hyperplanes in the canonical basis are either zero or one, similar to the poles arising when renormalising generic Feynman amplitudes. For that purpose, we introduce an algorithm to distribute weight over a graph such that the weight at each vertex satisfies a given lower bound.
N2  - Diese Arbeit schlägt eine Brücke zwischen zwei Bereichen der Mathematik, einerseits der Algebra mit dem Milnor-Moore-Theorem (auch Cartier-Quillen-Milnor-Moore-Theorem genannt) sowie dem Poincaré-Birkhoff-Witt-Theorem und andererseits der Analysis mit den Shintani-Zetafunktionen, die eine Verallgemeinerung der Mehrfach-Zetafunktionen darstellen. 
Der erste Teil ist einer algebraischen Formulierung des Lokalitätsprinzips in der Physik und Verallgemeinerungen von Klassifikationstheoremen wie dem Milnor-Moore- und dem Poincaré-Birkhoff-Witt-Theorem auf den Lokalitätsrahmen gewidmet. Das Lokalitätsprinzip besagt grob, dass Ereignisse, die in der Raumzeit weit voneinander entfernt stattfinden, sich nicht gegenseitig beeinflussen. Die hier erörterte algebraische Formulierung dieses Prinzips ist nützlich bei der Analyse von Singularitäten, die aus weit voneinander entfernten Ereignissen im Raum entstehen, um sie zu renormalisieren und dabei die Tatsache im Gedächtnis zu behalten, dass sie sich nicht gegenseitig beeinflussen. Wir beginnen damit, dass wir einen Vektorraum mit einer symmetrischen Relation, der so genannten Lokalitätsrelation, ausstatten, die die "lokal unabhängigen" Elemente festhält. Das Paar aus einem Vektorraum und einer solchen Relation wird als Vorlokalitäts-Vektorraum bezeichnet. Dieses Konzept wird auf Tensorprodukte erweitert, die nur Tensoren aus lokal unabhängigen Elementen zulassen. Wir erweitern dieses Konzept auf die Lokalitäts-Tensor-Algebra und die symmetrische Lokalitäts-Algebra eines Vorlokalitäts-Vektorraums und beweisen die universellen Eigenschaften jeder dieser Strukturen. Wir führen auch die Vorlokalitäts-Lie-Algebren zusammen mit den zugehörigen universellen Hüllalgebren der Lokalität ein und beweisen ihre universelle Eigenschaft. Später übertragen wir alle diese Strukturen und Ergebnisse aus dem Kontext der Vorlokalität in den Kontext der Lokalität, wobei die Lokalitätsbeziehung mit der linearen Struktur des Vektorraums kompatibel sein muss. Auf diese Weise können wir Lokalitäts-Kohlengebren, Lokalitäts-Bialgebren und Lokalitäts-Hopf-Algebren definieren.  Schließlich werden alle vorherigen Ergebnisse verwendet, um die Lokalitätsversionen des Milnor-Moore- und des Poincaré-Birkhoff-Witt-Theorems zu beweisen. Es ist erwähnenswert, dass die vorgestellten Beweise nicht nur die Ergebnisse im üblichen (Nichtlokalitäts-) Aufbau verallgemeinern, sondern auch oft weniger Hilfsmittel verwenden als ihre Gegenstücke in ihren Nichtlokalitäts-Gegenstücken.
Der zweite Teil ist der Untersuchung der polaren Struktur der Shintani-Zeta-Funktionen gewidmet. Diese Funktionen, die u.a. die Riemman-Zetafunktion, die multiplen Zetafunktionen und die Mordell-Tornheim-Zetafunktionen verallgemeinern, werden durch Matrizen mit reellen, nicht-negativen Argumenten parametrisiert. Es ist bekannt, dass Shintani-Zetafunktionen sich zu meromorphen Funktionen mit Polen auf affinen Hyperebenen erweitern. Wir verfeinern dieses Ergebnis, indem wir zeigen, dass die Pole auf Hyperebenen liegen, die parallel zu den Facetten bestimmter konvexer Polyeder verlaufen, die mit der Definitionsmatrix für die Shintani-Zeta-Funktion assoziiert sind. Letztere sind explizit die Newton-Polytope der Polynome, die durch die Spalten der zugrunde liegenden Matrix induziert werden. Wir beweisen dann, dass die Koeffizienten der Gleichung, die die Hyperebenen in der kanonischen Basis beschreibt, entweder Null oder Eins sind, ähnlich wie die Pole, die bei der Renormierung generischer Feynman-Amplituden entstehen. Zu diesem Zweck führen wir einen Algorithmus ein, um die Gewichte über einen Graphen so zu verteilen, dass das Gewicht an jedem Knoten eine gegebene untere Schranke erfüllt.
KW  - locality principle
KW  - multizeta functions
KW  - meromorphic continuation
KW  - Milnor Moore theorem
KW  - Poincaré Birkhoff Witt theorem
KW  - Newton polytopes
KW  - Satz von Milnor Moore
KW  - Newton Polytope
KW  - Satz von Poincaré Birkhoff Witt
KW  - Lokalitätsprinzip
KW  - meromorphe Fortsetzung
KW  - Multizeta-Abbildungen
Y1  - 2023
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-594213
ER  - 
TY  - JOUR
A1  - Schindler, Daniel
A1  - Moldenhawer, Ted
A1  - Stange, Maike
A1  - Lepro, Valentino
A1  - Beta, Carsten
A1  - Holschneider, Matthias
A1  - Huisinga, Wilhelm
T1  - Analysis of protrusion dynamics in amoeboid cell motility by means of regularized contour flows
JF  - PLoS Computational Biology : a new community journal
N2  - Amoeboid cell motility is essential for a wide range of biological processes including wound healing, embryonic morphogenesis, and cancer metastasis. It relies on complex dynamical patterns of cell shape changes that pose long-standing challenges to mathematical modeling and raise a need for automated and reproducible approaches to extract quantitative morphological features from image sequences. Here, we introduce a theoretical framework and a computational method for obtaining smooth representations of the spatiotemporal contour dynamics from stacks of segmented microscopy images. Based on a Gaussian process regression we propose a one-parameter family of regularized contour flows that allows us to continuously track reference points (virtual markers) between successive cell contours. We use this approach to define a coordinate system on the moving cell boundary and to represent different local geometric quantities in this frame of reference. In particular, we introduce the local marker dispersion as a measure to identify localized membrane expansions and provide a fully automated way to extract the properties of such expansions, including their area and growth time. The methods are available as an open-source software package called AmoePy, a Python-based toolbox for analyzing amoeboid cell motility (based on time-lapse microscopy data), including a graphical user interface and detailed documentation. Due to the mathematical rigor of our framework, we envision it to be of use for the development of novel cell motility models. We mainly use experimental data of the social amoeba Dictyostelium discoideum to illustrate and validate our approach. <br /> Author summary Amoeboid motion is a crawling-like cell migration that plays an important key role in multiple biological processes such as wound healing and cancer metastasis. This type of cell motility results from expanding and simultaneously contracting parts of the cell membrane. From fluorescence images, we obtain a sequence of points, representing the cell membrane, for each time step. By using regression analysis on these sequences, we derive smooth representations, so-called contours, of the membrane. Since the number of measurements is discrete and often limited, the question is raised of how to link consecutive contours with each other. In this work, we present a novel mathematical framework in which these links are described by regularized flows allowing a certain degree of concentration or stretching of neighboring reference points on the same contour. This stretching rate, the so-called local dispersion, is used to identify expansions and contractions of the cell membrane providing a fully automated way of extracting properties of these cell shape changes. We applied our methods to time-lapse microscopy data of the social amoeba Dictyostelium discoideum.
Y1  - 2021
U6  - https://doi.org/10.1371/journal.pcbi.1009268
SN  - 1553-734X
SN  - 1553-7358
VL  - 17
IS  - 8
PB  - PLoS
CY  - San Fransisco
ER  - 
TY  - JOUR
A1  - Keller, Matthias
A1  - Pinchover, Yehuda
A1  - Pogorzelski, Felix
T1  - Criticality theory for Schrödinger operators on graphs
JF  - Journal of spectral theory
N2  - We study Schrodinger operators given by positive quadratic forms on infinite graphs. From there, we develop a criticality theory for Schrodinger operators on general weighted graphs.
KW  - green function
KW  - ground state
KW  - positive solutions
KW  - discrete Schrodinger
KW  - operators
KW  - weighted graphs
Y1  - 2019
U6  - https://doi.org/10.4171/JST/286
SN  - 1664-039X
SN  - 1664-0403
VL  - 10
IS  - 1
SP  - 73
EP  - 114
PB  - European Mathematical Society
CY  - Zürich
ER  - 
TY  - JOUR
A1  - Keller, Matthias
A1  - Pinchover, Yehuda
A1  - Pogorzelski, Felix
T1  - From hardy to rellich inequalities on graphs
JF  - Proceedings of the London Mathematical Society
N2  - We show how to deduce Rellich inequalities from Hardy inequalities on infinite graphs. Specifically, the obtained Rellich inequality gives an upper bound on a function by the Laplacian of the function in terms of weighted norms. These weights involve the Hardy weight and a function which satisfies an eikonal inequality. The results are proven first for Laplacians and are extended to Schrodinger operators afterwards.
KW  - 35R02
KW  - 39A12 (primary)
KW  - 26D15
KW  - 31C20
KW  - 35B09
KW  - 58E35 (secondary)
Y1  - 2020
U6  - https://doi.org/10.1112/plms.12376
SN  - 0024-6115
SN  - 1460-244X
VL  - 122
IS  - 3
SP  - 458
EP  - 477
PB  - Wiley
CY  - Hoboken
ER  - 
TY  - JOUR
A1  - Maier, Corinna Sabrina
A1  - Wiljes, Jana de
A1  - Hartung, Niklas
A1  - Kloft, Charlotte
A1  - Huisinga, Wilhelm
T1  - A continued learning approach for model-informed precision dosing
BT  - Updating models in clinical practice
JF  - CPT: pharmacometrics & systems pharmacology
N2  - Model-informed precision dosing (MIPD) is a quantitative dosing framework that combines prior knowledge on the drug-disease-patient system with patient data from therapeutic drug/ biomarker monitoring (TDM) to support individualized dosing in ongoing treatment. Structural models and prior parameter distributions used in MIPD approaches typically build on prior clinical trials that involve only a limited number of patients selected according to some exclusion/inclusion criteria. Compared to the prior clinical trial population, the patient population in clinical practice can be expected to also include altered behavior and/or increased interindividual variability, the extent of which, however, is typically unknown. Here, we address the question of how to adapt and refine models on the level of the model parameters to better reflect this real-world diversity. We propose an approach for continued learning across patients during MIPD using a sequential hierarchical Bayesian framework. The approach builds on two stages to separate the update of the individual patient parameters from updating the population parameters. Consequently, it enables continued learning across hospitals or study centers, because only summary patient data (on the level of model parameters) need to be shared, but no individual TDM data. We illustrate this continued learning approach with neutrophil-guided dosing of paclitaxel. The present study constitutes an important step toward building confidence in MIPD and eventually establishing MIPD increasingly in everyday therapeutic use.
Y1  - 2021
U6  - https://doi.org/10.1002/psp4.12745
SN  - 2163-8306
VL  - 11
IS  - 2
SP  - 185
EP  - 198
PB  - London
CY  - Nature Publ. Group
ER  - 
TY  - JOUR
A1  - Gottwald, Georg A.
A1  - Reich, Sebastian
T1  - Combining machine learning and data assimilation to forecast dynamical systems from noisy partial observations
JF  - Chaos : an interdisciplinary journal of nonlinear science
N2  - We present a supervised learning method to learn the propagator map of a dynamical system from partial and noisy observations. In our computationally cheap and easy-to-implement framework, a neural network consisting of random feature maps is trained sequentially by incoming observations within a data assimilation procedure. By employing Takens's embedding theorem, the network is trained on delay coordinates. We show that the combination of random feature maps and data assimilation, called RAFDA, outperforms standard random feature maps for which the dynamics is learned using batch data.
Y1  - 2021
U6  - https://doi.org/10.1063/5.0066080
SN  - 1054-1500
SN  - 1089-7682
VL  - 31
IS  - 10
PB  - AIP
CY  - Melville
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Hounnon, Hippolyte
T1  - Partial Menger algebras of terms
JF  - Asian-European journal of mathematics
N2  - The superposition operation S-n,S-A, n >= 1, n is an element of N, maps to each (n + 1)-tuple of n-ary operations on a set A an n-ary operation on A and satisfies the so-called superassociative law, a generalization of the associative law. The corresponding algebraic structures are Menger algebras of rank n. A partial algebra of type (n + 1) which satisfies the superassociative law as weak identity is said to be a partial Menger algebra of rank n. As a generalization of linear terms we define r-terms as terms where each variable occurs at most r-times. It will be proved that n-ary r-terms form partial Menger algebras of rank n. In this paper, some algebraic properties of partial Menger algebras such as generating systems, homomorphic images and freeness are investigated. As generalization of hypersubstitutions and linear hypersubstitutions we consider r-hypersubstitutions.U
KW  - n-ary operation
KW  - n-ary term
KW  - superposition of n-ary operations and n-ary
KW  - terms
KW  - linear term
KW  - r-term
KW  - Menger algebra of rank n
KW  - partial Menger
KW  - algebra of rank n
KW  - r-hypersubstitution
Y1  - 2021
U6  - https://doi.org/10.1142/S1793557121500923
SN  - 1793-5571
SN  - 1793-7183
VL  - 14
IS  - 06
PB  - World Scientific
CY  - Singapore
ER  - 
TY  - JOUR
A1  - Gaidzik, Franziska
A1  - Pathiraja, Sahani Darschika
A1  - Saalfeld, Sylvia
A1  - Stucht, Daniel
A1  - Speck, Oliver
A1  - Thevenin, Dominique
A1  - Janiga, Gabor
T1  - Hemodynamic data assimilation in a subject-specific circle of Willis geometry
JF  - Clinical Neuroradiology
N2  - Purpose The anatomy of the circle of Willis (CoW), the brain's main arterial blood supply system, strongly differs between individuals, resulting in highly variable flow fields and intracranial vascularization patterns. To predict subject-specific hemodynamics with high certainty, we propose a data assimilation (DA) approach that merges fully 4D phase-contrast magnetic resonance imaging (PC-MRI) data with a numerical model in the form of computational fluid dynamics (CFD) simulations. Methods To the best of our knowledge, this study is the first to provide a transient state estimate for the three-dimensional velocity field in a subject-specific CoW geometry using DA. High-resolution velocity state estimates are obtained using the local ensemble transform Kalman filter (LETKF). Results Quantitative evaluation shows a considerable reduction (up to 90%) in the uncertainty of the velocity field state estimate after the data assimilation step. Velocity values in vessel areas that are below the resolution of the PC-MRI data (e.g., in posterior communicating arteries) are provided. Furthermore, the uncertainty of the analysis-based wall shear stress distribution is reduced by a factor of 2 for the data assimilation approach when compared to the CFD model alone. Conclusion This study demonstrates the potential of data assimilation to provide detailed information on vascular flow, and to reduce the uncertainty in such estimates by combining various sources of data in a statistically appropriate fashion.
KW  - hemodynamics
KW  - CFD
KW  - uncertainty quantification
KW  - PC-MRI
KW  - LETKF
Y1  - 2020
U6  - https://doi.org/10.1007/s00062-020-00959-2
SN  - 1869-1439
SN  - 1869-1447
VL  - 31
IS  - 3
SP  - 643
EP  - 651
PB  - Springer
CY  - Heidelberg
ER  - 
TY  - JOUR
A1  - Bär, Christian
A1  - Mazzeo, Rafe
T1  - Manifolds with many Rarita-Schwinger fields
JF  - Communications in mathematical physics
N2  - The Rarita-Schwinger operator is the twisted Dirac operator restricted to 3/2-spinors. Rarita-Schwinger fields are solutions of this operator which are in addition divergence-free. This is an overdetermined problem and solutions are rare; it is even more unexpected for there to be large dimensional spaces of solutions. In this paper we prove the existence of a sequence of compact manifolds in any given dimension greater than or equal to 4 for which the dimension of the space of Rarita-Schwinger fields tends to infinity. These manifolds are either simply connected Kahler-Einstein spin with negative Einstein constant, or products of such spaces with flat tori. Moreover, we construct Calabi-Yau manifolds of even complex dimension with more linearly independent Rarita-Schwinger fields than flat tori of the same dimension.
Y1  - 2021
U6  - https://doi.org/10.1007/s00220-021-04030-0
SN  - 0010-3616
SN  - 1432-0916
VL  - 384
IS  - 1
SP  - 533
EP  - 548
PB  - Springer
CY  - Berlin
ER  - 
TY  - JOUR
A1  - Mariucci, Ester
A1  - Ray, Kolyan
A1  - Szabo, Botond
T1  - A Bayesian nonparametric approach to log-concave density estimation
JF  - Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability
N2  - The estimation of a log-concave density on R is a canonical problem in the area of shape-constrained nonparametric inference. We present a Bayesian nonparametric approach to this problem based on an exponentiated Dirichlet process mixture prior and show that the posterior distribution converges to the log-concave truth at the (near-) minimax rate in Hellinger distance. Our proof proceeds by establishing a general contraction result based on the log-concave maximum likelihood estimator that prevents the need for further metric entropy calculations. We further present computationally more feasible approximations and both an empirical and hierarchical Bayes approach. All priors are illustrated numerically via simulations.
KW  - convergence rate
KW  - density estimation
KW  - Dirichlet mixture
KW  - log-concavity
KW  - nonparametric hypothesis testing
KW  - posterior distribution
Y1  - 2020
U6  - https://doi.org/10.3150/19-BEJ1139
SN  - 1350-7265
SN  - 1573-9759
VL  - 26
IS  - 2
SP  - 1070
EP  - 1097
PB  - International Statistical Institute
CY  - The Hague
ER  - 
TY  - JOUR
A1  - Hyde, Stephen T.
A1  - Evans, Myfanwy E.
T1  - Symmetric tangled Platonic polyhedra
JF  - Proceedings of the National Academy of Sciences of the United States of America
N2  - Conventional embeddings of the edge-graphs of Platonic polyhedra, {f,z}, where f,z denote the number of edges in each face and the edge-valence at each vertex, respectively, are untangled in that they can be placed on a sphere (S-2) such that distinct edges do not intersect, analogous to unknotted loops, which allow crossing-free drawings of S-1 on the sphere. The most symmetric (flag-transitive) realizations of those polyhedral graphs are those of the classical Platonic polyhedra, whose symmetries are *2fz, according to Conway's two-dimensional (2D) orbifold notation (equivalent to Schonflies symbols I-h, O-h, and T-d). Tangled Platonic {f,z} polyhedra-which cannot lie on the sphere without edge-crossings-are constructed as windings of helices with three, five, seven,... strands on multigenus surfaces formed by tubifying the edges of conventional Platonic polyhedra, have (chiral) symmetries 2fz (I, O, and T), whose vertices, edges, and faces are symmetrically identical, realized with two flags. The analysis extends to the "theta(z)" polyhedra, {2,z}. The vertices of these symmetric tangled polyhedra overlap with those of the Platonic polyhedra; however, their helicity requires curvilinear (or kinked) edges in all but one case. We show that these 2fz polyhedral tangles are maximally symmetric; more symmetric embeddings are necessarily untangled. On one hand, their topologies are very constrained: They are either self-entangled graphs (analogous to knots) or mutually catenated entangled compound polyhedra (analogous to links). On the other hand, an endless variety of entanglements can be realized for each topology. Simpler examples resemble patterns observed in synthetic organometallic materials and clathrin coats in vivo.
KW  - regular polyhedra
KW  - compound polyhedra
KW  - helicates
KW  - metal-organic
KW  - frameworks
KW  - clathrin
Y1  - 2022
U6  - https://doi.org/10.1073/pnas.2110345118
SN  - 0027-8424
SN  - 1091-6490
VL  - 119
IS  - 1
PB  - National Acad. of Sciences
CY  - Washington
ER  - 
TY  - JOUR
A1  - Hermann, Andreas
A1  - Humbert, Emmanuel
T1  - Mass functions of a compact manifold
JF  - Journal of geometry and physics : JGP
N2  - Let M be a compact manifold of dimension n. In this paper, we introduce the Mass Function a >= 0 bar right arrow X-+(M)(a) (resp. a >= 0 bar right arrow X--(M)(a)) which is defined as the supremum (resp. infimum) of the masses of all metrics on M whose Yamabe constant is larger than a and which are flat on a ball of radius 1 and centered at a point p is an element of M. Here, the mass of a metric flat around p is the constant term in the expansion of the Green function of the conformal Laplacian at p. We show that these functions are well defined and have many properties which allow to obtain applications to the Yamabe invariant (i.e. the supremum of Yamabe constants over the set of all metrics on M).
KW  - Yamabe operator
KW  - Yamabe invariant
KW  - surgery
KW  - positive mass theorem
Y1  - 2020
U6  - https://doi.org/10.1016/j.geomphys.2020.103650
SN  - 0393-0440
SN  - 1879-1662
VL  - 154
PB  - Elsevier
CY  - Amsterdam [u.a.]
ER  - 
TY  - JOUR
A1  - Kolbe, Benedikt Maximilian
A1  - Evans, Myfanwy E.
T1  - Enumerating isotopy classes of tilings guided by the symmetry of triply
JF  - Siam journal on applied algebra and geometry
N2  - We present a technique for the enumeration of all isotopically distinct ways of tiling a hyperbolic surface of finite genus, possibly nonorientable and with punctures and boundary. This generalizes the enumeration using Delaney--Dress combinatorial tiling theory of combinatorial classes of tilings to isotopy classes of tilings. To accomplish this, we derive an action of the mapping class group of the orbifold associated to the symmetry group of a tiling on the set of tilings. We explicitly give descriptions and presentations of semipure mapping class groups and of tilings as decorations on orbifolds. We apply this enumerative result to generate an array of isotopically distinct tilings of the hyperbolic plane with symmetries generated by rotations that are commensurate with the threedimensional symmetries of the primitive, diamond, and gyroid triply periodic minimal surfaces, which have relevance to a variety of physical systems.
KW  - isotopic tiling theory
KW  - mapping class group
KW  - orbifolds
KW  - group
KW  - presentations
KW  - representations of groups as automorphism groups of
KW  - algebraic systems
KW  - triply periodic minimal surface
KW  - Delaney--Dress
KW  - tiling theory
KW  - hyperbolic tilings
KW  - two-dimensional topology
Y1  - 2022
U6  - https://doi.org/10.1137/20M1358943
SN  - 2470-6566
VL  - 6
IS  - 1
SP  - 1
EP  - 40
PB  - Society for Industrial and Applied Mathematics
CY  - Philadelphia
ER  - 
TY  - JOUR
A1  - Güneysu, Batu
A1  - Keller, Matthias
T1  - Feynman path integrals for magnetic Schrödinger operators on infinite weighted graphs
JF  - Journal d'analyse mathématique
N2  - We prove a Feynman path integral formula for the unitary group exp(-itL(nu,theta)), t >= 0, associated with a discrete magnetic Schrodinger operator L-nu,L-theta on a large class of weighted infinite graphs. As a consequence, we get a new Kato-Simon estimate 
 vertical bar exp(- itL(nu,theta))(x,y)vertical bar <= exp( -tL(-deg,0))(x,y), 
 which controls the unitary group uniformly in the potentials in terms of a Schrodinger semigroup, where the potential deg is the weighted degree function of the graph.
Y1  - 2020
U6  - https://doi.org/10.1007/s11854-020-0110-y
SN  - 0021-7670
SN  - 1565-8538
VL  - 141
IS  - 2
SP  - 751
EP  - 770
PB  - The Magnes Press, the Hebrew Univ.
CY  - Jerusalem
ER  - 
TY  - JOUR
A1  - Azzali, Sara
A1  - Paycha, Sylvie
T1  - Spectral zeta-invariants lifted to coverings
JF  - Transactions of the American Mathematical Society
N2  - The canonical trace and the Wodzicki residue on classical pseudo-differential operators on a closed manifold are characterised by their locality and shown to be preserved under lifting to the universal covering as a result of their local feature. As a consequence, we lift a class of spectral zeta-invariants using lifted defect formulae which express discrepancies of zeta-regularised traces in terms of Wodzicki residues. We derive Atiyah's L-2-index theorem as an instance of the Z(2)-graded generalisation of the canonical lift of spectral zeta-invariants and we show that certain lifted spectral zeta-invariants for geometric operators are integrals of Pontryagin and Chern forms.
Y1  - 2020
U6  - https://doi.org/10.1090/tran/8067
SN  - 0002-9947
SN  - 1088-6850
VL  - 373
IS  - 9
SP  - 6185
EP  - 6226
PB  - American Mathematical Society
CY  - Providence, RI
ER  - 
TY  - JOUR
A1  - Houdebert, Pierre
A1  - Zass, Alexander
T1  - An explicit Dobrushin uniqueness region for Gibbs point processes with repulsive interactions
JF  - Journal of applied probability / Applied Probability Trust
N2  - We present a uniqueness result for Gibbs point processes with interactions that come from a non-negative pair potential; in particular, we provide an explicit uniqueness region in terms of activity z and inverse temperature beta. The technique used relies on applying to the continuous setting the classical Dobrushin criterion. We also present a comparison to the two other uniqueness methods of cluster expansion and disagreement percolation, which can also be applied for this type of interaction.
KW  - Gibbs point process
KW  - DLR equations
KW  - uniqueness
KW  - Dobrushin criterion;
KW  - cluster expansion
KW  - disagreement percolation
Y1  - 2022
U6  - https://doi.org/10.1017/jpr.2021.70
SN  - 0021-9002
SN  - 1475-6072
VL  - 59
IS  - 2
SP  - 541
EP  - 555
PB  - Cambridge Univ. Press
CY  - Cambridge
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  - Maoutsa, Dimitra
A1  - Reich, Sebastian
A1  - Opper, Manfred
T1  - Interacting particle solutions of Fokker–Planck equations through gradient–log–density estimation
JF  - Entropy
N2  - Fokker-Planck equations are extensively employed in various scientific fields as they characterise the behaviour of stochastic systems at the level of probability density functions. Although broadly used, they allow for analytical treatment only in limited settings, and often it is inevitable to resort to numerical solutions. Here, we develop a computational approach for simulating the time evolution of Fokker-Planck solutions in terms of a mean field limit of an interacting particle system. The interactions between particles are determined by the gradient of the logarithm of the particle density, approximated here by a novel statistical estimator. The performance of our method shows promising results, with more accurate and less fluctuating statistics compared to direct stochastic simulations of comparable particle number. Taken together, our framework allows for effortless and reliable particle-based simulations of Fokker-Planck equations in low and moderate dimensions. The proposed gradient-log-density estimator is also of independent interest, for example, in the context of optimal control.
KW  - stochastic systems
KW  - Fokker-Planck equation
KW  - interacting particles
KW  - multiplicative noise
KW  - gradient flow
KW  - stochastic differential equations
Y1  - 2020
U6  - https://doi.org/10.3390/e22080802
SN  - 1099-4300
VL  - 22
IS  - 8
PB  - MDPI
CY  - Basel
ER  - 
TY  - JOUR
A1  - Ludewig, Matthias
A1  - Rosenberger, Elke
T1  - Asymptotic eigenfunctions for Schrödinger operators on a vector bundle
JF  - Reviews in mathematical physics
N2  - In the limit (h) over bar -> 0, we analyze a class of Schrödinger operators H-(h) over bar = (h) over bar L-2 + (h) over barW + V .id(epsilon) acting on sections of a vector bundle epsilon over a Riemannian manifold M where L is a Laplace type operator, W is an endomorphism field and the potential energy V has a non-degenerate minimum at some point p is an element of M. We construct quasimodes of WKB-type near p for eigenfunctions associated with the low-lying eigenvalues of H-(h) over bar. These are obtained from eigenfunctions of the associated harmonic oscillator H-p,H-(h) over bar at p, acting on smooth functions on the tangent space.
KW  - Semi-classical analysis
KW  - WKB approximation
KW  - Schrödinger operators
KW  - semi-classical limit
Y1  - 2020
U6  - https://doi.org/10.1142/S0129055X20500208
SN  - 0129-055X
SN  - 1793-6659
VL  - 32
IS  - 7
PB  - World Scientific
CY  - Singapore
ER  - 
TY  - JOUR
A1  - Hartung, Niklas
A1  - Borghardt, Jens Markus
T1  - A mechanistic framework for a priori pharmacokinetic predictions of orally inhaled drugs
JF  - PLoS Computational Biology : a new community journal
N2  - Author summary <br /> The use of orally inhaled drugs for treating lung diseases is appealing since they have the potential for lung selectivity, i.e. high exposure at the site of action -the lung- without excessive side effects. However, the degree of lung selectivity depends on a large number of factors, including physiochemical properties of drug molecules, patient disease state, and inhalation devices. To predict the impact of these factors on drug exposure and thereby to understand the characteristics of an optimal drug for inhalation, we develop a predictive mathematical framework (a "pharmacokinetic model"). In contrast to previous approaches, our model allows combining knowledge from different sources appropriately and its predictions were able to adequately predict different sets of clinical data. Finally, we compare the impact of different factors and find that the most important factors are the size of the inhaled particles, the affinity of the drug to the lung tissue, as well as the rate of drug dissolution in the lung. In contrast to the common belief, the solubility of a drug in the lining fluids is not found to be relevant. These findings are important to understand how inhaled drugs should be designed to achieve best treatment results in patients. <br /> The fate of orally inhaled drugs is determined by pulmonary pharmacokinetic processes such as particle deposition, pulmonary drug dissolution, and mucociliary clearance. Even though each single process has been systematically investigated, a quantitative understanding on the interaction of processes remains limited and therefore identifying optimal drug and formulation characteristics for orally inhaled drugs is still challenging. To investigate this complex interplay, the pulmonary processes can be integrated into mathematical models. However, existing modeling attempts considerably simplify these processes or are not systematically evaluated against (clinical) data. In this work, we developed a mathematical framework based on physiologically-structured population equations to integrate all relevant pulmonary processes mechanistically. A tailored numerical resolution strategy was chosen and the mechanistic model was evaluated systematically against data from different clinical studies. Without adapting the mechanistic model or estimating kinetic parameters based on individual study data, the developed model was able to predict simultaneously (i) lung retention profiles of inhaled insoluble particles, (ii) particle size-dependent pharmacokinetics of inhaled monodisperse particles, (iii) pharmacokinetic differences between inhaled fluticasone propionate and budesonide, as well as (iv) pharmacokinetic differences between healthy volunteers and asthmatic patients. Finally, to identify the most impactful optimization criteria for orally inhaled drugs, the developed mechanistic model was applied to investigate the impact of input parameters on both the pulmonary and systemic exposure. Interestingly, the solubility of the inhaled drug did not have any relevant impact on the local and systemic pharmacokinetics. Instead, the pulmonary dissolution rate, the particle size, the tissue affinity, and the systemic clearance were the most impactful potential optimization parameters. In the future, the developed prediction framework should be considered a powerful tool for identifying optimal drug and formulation characteristics.
Y1  - 2020
U6  - https://doi.org/10.1371/journal.pcbi.1008466
SN  - 1553-734X
SN  - 1553-7358
VL  - 16
IS  - 12
PB  - PLoS
CY  - San Fransisco
ER  - 
TY  - 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  - JOUR
A1  - Ludewig, Matthias
A1  - Roos, Saskia
T1  - The chiral anomaly of the free fermion in functorial field theory
JF  - Annales Henri Poincaré : a journal of theoretical and mathematical physics
N2  - When trying to cast the free fermion in the framework of functorial field theory, its chiral anomaly manifests in the fact that it assigns the determinant of the Dirac operator to a top-dimensional closed spin manifold, which is not a number as expected, but an element of a complex line. In functorial field theory language, this means that the theory is twisted, which gives rise to an anomaly theory. In this paper, we give a detailed construction of this anomaly theory, as a functor that sends manifolds to infinite-dimensional Clifford algebras and bordisms to bimodules.
Y1  - 2020
U6  - https://doi.org/10.1007/s00023-020-00893-6
SN  - 1424-0637
SN  - 1424-0661
VL  - 21
IS  - 4
SP  - 1191
EP  - 1233
PB  - Springer International Publishing AG
CY  - Cham (ZG)
ER  - 
TY  - JOUR
A1  - Bandara, Lashi
A1  - Bryan, Paul
T1  - Heat kernels and regularity for rough metrics on smooth manifolds
JF  - Mathematische Nachrichten
N2  - We consider rough metrics on smooth manifolds and corresponding Laplacians induced by such metrics. We demonstrate that globally continuous heat kernels exist and are Holder continuous locally in space and time. This is done via local parabolic Harnack estimates for weak solutions of operators in divergence form with bounded measurable coefficients in weighted Sobolev spaces.
KW  - heat kernel
KW  - parabolic Harnack estimate
KW  - rough metrics
Y1  - 2020
U6  - https://doi.org/10.1002/mana.201800459
SN  - 0025-584X
SN  - 1522-2616
VL  - 293
IS  - 12
SP  - 2255
EP  - 2270
PB  - Wiley-VCH
CY  - Weinheim
ER  - 
TY  - JOUR
A1  - Kolbe, Benedikt Maximilian
A1  - Evans, Myfanwy E.
T1  - Isotopic tiling theory for hyperbolic surfaces
JF  - Geometriae dedicata
N2  - In this paper, we develop the mathematical tools needed to explore isotopy classes of tilings on hyperbolic surfaces of finite genus, possibly nonorientable, with boundary, and punctured. More specifically, we generalize results on Delaney-Dress combinatorial tiling theory using an extension of mapping class groups to orbifolds, in turn using this to study tilings of covering spaces of orbifolds. Moreover, we study finite subgroups of these mapping class groups. Our results can be used to extend the Delaney-Dress combinatorial encoding of a tiling to yield a finite symbol encoding the complexity of an isotopy class of tilings. The results of this paper provide the basis for a complete and unambiguous enumeration of isotopically distinct tilings of hyperbolic surfaces.
KW  - isotopic tiling theory
KW  - delaney-dress tiling theory
KW  - mapping class
KW  - groups
KW  - orbifolds
KW  - maps on surfaces
KW  - hyperbolic tilings
Y1  - 2020
U6  - https://doi.org/10.1007/s10711-020-00554-2
SN  - 0046-5755
SN  - 1572-9168
VL  - 212
IS  - 1
SP  - 177
EP  - 204
PB  - Springer
CY  - Dordrecht
ER  - 
TY  - JOUR
A1  - Perera, Upeksha
A1  - Böckmann, Christine
T1  - Solutions of Sturm-Liouville problems
JF  - Mathematics
N2  - This paper further improves the Lie group method with Magnus expansion proposed in a previous paper by the authors, to solve some types of direct singular Sturm-Liouville problems. Next, a concrete implementation to the inverse Sturm-Liouville problem algorithm proposed by Barcilon (1974) is provided. Furthermore, computational feasibility and applicability of this algorithm to solve inverse Sturm-Liouville problems of higher order (for n=2,4) are verified successfully. It is observed that the method is successful even in the presence of significant noise, provided that the assumptions of the algorithm are satisfied. In conclusion, this work provides a method that can be adapted successfully for solving a direct (regular/singular) or inverse Sturm-Liouville problem (SLP) of an arbitrary order with arbitrary boundary conditions.
KW  - Sturm-Liouville problems of higher order
KW  - singular Sturm-Liouville
KW  - problems
KW  - inverse Sturm-Liouville problems
Y1  - 2020
U6  - https://doi.org/10.3390/math8112074
SN  - 2227-7390
VL  - 8
IS  - 11
PB  - MDPI
CY  - Basel
ER  - 
TY  - JOUR
A1  - Beckus, Siegfried
A1  - Pinchover, Yehuda
T1  - Shnol-type theorem for the Agmon ground state
JF  - Journal of spectral theory
N2  - LetH be a Schrodinger operator defined on a noncompact Riemannianmanifold Omega, and let W is an element of L-infinity (Omega; R). Suppose that the operator H + W is critical in Omega, and let phi be the corresponding Agmon ground state. We prove that if u is a generalized eigenfunction ofH satisfying vertical bar u vertical bar <= C-phi in Omega for some constant C > 0, then the corresponding eigenvalue is in the spectrum of H. The conclusion also holds true if for some K is an element of Omega the operator H admits a positive solution in (Omega) over bar = Omega \ K, and vertical bar u vertical bar <= C psi in (Omega) over bar for some constant C > 0, where psi is a positive solution of minimal growth in a neighborhood of infinity in Omega. Under natural assumptions, this result holds also in the context of infinite graphs, and Dirichlet forms.
KW  - Shnol theorem
KW  - Caccioppoli inequality
KW  - Schrodinger operators
KW  - generalized eigenfunction
KW  - ground state
KW  - positive solutions
KW  - weighted
KW  - graphs
Y1  - 2020
U6  - https://doi.org/10.4171/JST/296
SN  - 1664-039X
SN  - 1664-0403
VL  - 10
IS  - 2
SP  - 355
EP  - 377
PB  - EMS Publishing House
CY  - Zürich
ER  - 
TY  - JOUR
A1  - Blanchard, Gilles
A1  - Mücke, Nicole
T1  - Kernel regression, minimax rates and effective dimensionality
BT  - beyond the regular case
JF  - Analysis and applications
N2  - We investigate if kernel regularization methods can achieve minimax convergence rates over a source condition regularity assumption for the target function. These questions have been considered in past literature, but only under specific assumptions about the decay, typically polynomial, of the spectrum of the the kernel mapping covariance operator. In the perspective of distribution-free results, we investigate this issue under much weaker assumption on the eigenvalue decay, allowing for more complex behavior that can reflect different structure of the data at different scales.
KW  - Kernel regression
KW  - minimax optimality
KW  - eigenvalue decay
Y1  - 2020
U6  - https://doi.org/10.1142/S0219530519500258
SN  - 0219-5305
SN  - 1793-6861
VL  - 18
IS  - 4
SP  - 683
EP  - 696
PB  - World Scientific
CY  - New Jersey
ER  - 
TY  - JOUR
A1  - Mazzonetto, Sara
A1  - Salimova, Diyora
T1  - Existence, uniqueness, and numerical approximations for stochastic burgers equations
JF  - Stochastic analysis and applications
N2  - In this article, we propose an all-in-one statement which includes existence, uniqueness, regularity, and numerical approximations of mild solutions for a class of stochastic partial differential equations (SPDEs) with non-globally monotone nonlinearities. The proof of this result exploits the properties of an existing fully explicit space-time discrete approximation scheme, in particular the fact that it satisfies suitable a priori estimates. We also obtain almost sure and strong convergence of the approximation scheme to the mild solutions of the considered SPDEs. We conclude by applying the main result of the article to the stochastic Burgers equations with additive space-time white noise.
KW  - Stochastic Burgers equations
KW  - SPDEs
KW  - mild solution
KW  - existence
KW  - numerical
KW  - approximation
Y1  - 2020
U6  - https://doi.org/10.1080/07362994.2019.1709503
SN  - 0736-2994
SN  - 1532-9356
VL  - 38
IS  - 4
SP  - 623
EP  - 646
PB  - Taylor & Francis Group
CY  - Philadelphia
ER  - 
TY  - THES
A1  - Gehring, Penelope
T1  - Non-local boundary conditions for the spin Dirac operator on spacetimes with timelike boundary
T1  - Nicht-lokale Randbedingungen für den spinorialen Dirac-Operator auf Raumzeiten mit zeitartigen Rand
N2  - Non-local boundary conditions – for example the Atiyah–Patodi–Singer (APS) conditions – for Dirac operators on Riemannian manifolds are rather well-understood, while not much is known for such operators on Lorentzian manifolds. Recently, Bär and Strohmaier [15] and Drago, Große, and Murro [27] introduced APS-like conditions for the spin Dirac operator on Lorentzian manifolds with spacelike and timelike boundary, respectively. While Bär and Strohmaier [15] showed the Fredholmness of the Dirac operator with these boundary conditions, Drago, Große, and Murro [27] proved the well-posedness of the corresponding initial boundary value problem under certain geometric assumptions.
In this thesis, we will follow the footsteps of the latter authors and discuss whether the APS-like conditions for Dirac operators on Lorentzian manifolds with timelike boundary can be replaced by more general conditions such that the associated initial boundary value problems are still wellposed.
We consider boundary conditions that are local in time and non-local in the spatial directions. More precisely, we use the spacetime foliation arising from the Cauchy temporal function and split the Dirac operator along this foliation. This gives rise to a family of elliptic operators each acting on spinors of the spin bundle over the corresponding timeslice. The theory of elliptic operators then ensures that we can find families of non-local boundary conditions with respect to this family of operators. Proceeding, we use such a family of boundary conditions to define a Lorentzian boundary condition on the whole timelike boundary. By analyzing the properties of the Lorentzian boundary conditions, we then find sufficient conditions on the family of non-local boundary conditions that lead to the well-posedness of the corresponding Cauchy problems. The well-posedness itself will then be proven by using classical tools including energy estimates and approximation by solutions of the regularized problems.
Moreover, we use this theory to construct explicit boundary conditions for the Lorentzian Dirac operator. More precisely, we will discuss two examples of boundary conditions – the analogue of the Atiyah–Patodi–Singer and the chirality conditions, respectively, in our setting. For doing this, we will have a closer look at the theory of non-local boundary conditions for elliptic operators and analyze the requirements on the family of non-local boundary conditions for these specific examples.
N2  - Über nicht-lokale Randbedingungen – zum Beispiel dieAtiyah–Patodi–Singer (APS)-Bedingungen – für Dirac Operatoren auf Riemannschen Mannigfaltigkeiten ist recht viel bekannt, während für die hyperbolischen Dirac Operatoren auf Lorentz-Mannigfaltigkeiten dies noch nicht der Fall ist. Kürzlich haben Bär und Strohmaier [15] und Drago, Große und Murro [27] APS-ähnliche Bedingungen für den Spin Dirac Operator auf Lorentz-Mannigfaltigkeiten mit raumartigen bzw. zeitartigen Rand eingeführt. Während Bär und Strohmaier [15] zeigten, dass der Dirac Operator mit diesen Randbedingungen Fredholm ist, bewiesen Drago, Große und Murro [27] die Wohlgestelltheit des entsprechenden Anfangsrandwertproblems unter bestimmten geometrischen Annahmen.
In dieser Arbeit werden wir in die Fußstapfen der letztgenannten Autoren treten und diskutieren, ob die APS-ähnlichen Bedingungen für Dirac Operatoren auf Lorentz-Mannigfaltigkeiten mit zeitartigen Rand durch allgemeinere Bedingungen ersetzt werden können, sodass die zugehörigen Anfangsrandwertprobleme immer noch wohlgestellt sind.
Wir betrachten Randbedingungen, die in der Zeit lokal und in den Raumrichtungen nicht-lokal sind. Genauer gesagt verwenden wir die Raumzeitblätterung, die sich aus der Cauchy Zeitfunktion ergibt, und spalten den Dirac Operator entlang dieser Foliation auf. Daraus ergibt sich eine Familie elliptischer Operatoren, die jeweils auf Spinoren des Spinbündels über den entsprechenden Zeitschnitt wirken. Die Theorie der elliptischen Operatoren stellt dann sicher, dass wir Familien von nichtlokalen Randbedingungen bezüglich dieser Familie von Operatoren finden können. Im weiteren Verlauf verwenden wir solche Familien von Randbedingungen, um eine Lorentzsche Randbedingung auf dem gesamten zeitartigen Rand zu definieren. Durch das Analysieren der Lorentzschen Randbedingungen finden wir dann hinreichende Bedingungen für die Familie der nicht-lokalen Randbedingungen, die zur Wohlgestelltheit der entsprechenden Cauchy-Probleme führen. Die Wohlgestelltheit selbst wird dann mit Hilfe klassischer Methoden bewiesen, einschließlich Energieabschätzungen und Annäherung durch Lösungen der regularisierten Probleme.
Außerdem verwenden wir diese Theorie, um explizite Randbedingungen für den Lorentzschen Dirac Operator zu konstruieren. Genauer gesagt werden wir zwei Beispiele für Randbedingungen diskutieren - das Analogon der Atiyah-Patodi-Singer- bzw. Chiralitäts-Bedingungen für unseren Fall. Dazu werden wir uns die Theorie der nicht-lokalen Randbedingungen für elliptische Operatoren genauer ansehen und die Anforderungen an die Familie der nicht-lokalen Randbedingungen für diese Beispiele analysieren.
KW  - Dirac operator
KW  - Diracoperator
KW  - spacetimes with timelike boundary
KW  - Raumzeiten mit zeitartigen Rand
KW  - boundary conditions
KW  - Randbedingungen
KW  - initial boundary value problem
KW  - Anfangsrandwertproblem
Y1  - 2023
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-577755
ER  - 
TY  - JOUR
A1  - de Wiljes, Jana
A1  - Pathiraja, Sahani Darschika
A1  - Reich, Sebastian
T1  - Ensemble transform algorithms for nonlinear smoothing problems
JF  - SIAM journal on scientific computing
N2  - Several numerical tools designed to overcome the challenges of smoothing in a non-linear and non-Gaussian setting are investigated for a class of particle smoothers. The considered family of smoothers is induced by the class of linear ensemble transform filters which contains classical filters such as the stochastic ensemble Kalman filter, the ensemble square root filter, and the recently introduced nonlinear ensemble transform filter. Further the ensemble transform particle smoother is introduced and particularly highlighted as it is consistent in the particle limit and does not require assumptions with respect to the family of the posterior distribution. The linear update pattern of the considered class of linear ensemble transform smoothers allows one to implement important supplementary techniques such as adaptive spread corrections, hybrid formulations, and localization in order to facilitate their application to complex estimation problems. These additional features are derived and numerically investigated for a sequence of increasingly challenging test problems.
KW  - data assimilation
KW  - smoother
KW  - localization
KW  - optimal transport
KW  - adaptive
KW  - spread correction
Y1  - 2019
U6  - https://doi.org/10.1137/19M1239544
SN  - 1064-8275
SN  - 1095-7197
VL  - 42
IS  - 1
SP  - A87
EP  - A114
PB  - Society for Industrial and Applied Mathematics
CY  - Philadelphia
ER  - 
TY  - THES
A1  - Günther, Claudia-Susanne
T1  - Das Eigene und das Fremde
BT  - eine Untersuchung zum Fremdverstehen von Lehrkräften im Mathematikunterricht
N2  - Die vorliegende Arbeit stellt eine Untersuchung des Fremdverstehens von Lehrkräften im Mathematikunterricht dar. Mit ‚Fremdverstehen‘ soll dabei – in Anlehnung an den Soziologen Alfred Schütz – der Prozess bezeichnet werden, in welchem eine Lehrkraft versucht, das Verhalten einer Schülerin oder eines Schülers zu verstehen, indem sie dieses Verhalten auf ein Erleben zurückführt, das ihm zugrunde gelegen haben könnte. Als ein wesentliches Merkmal des Prozesses stellt Schütz in seiner Theorie des Fremdverstehens heraus, dass das Fremdverstehen eines Menschen immer auch auf seinen eigenen Erlebnissen basiert. Aus diesem Grund wird in der Arbeit ein methodischer Zweischritt vorgenommen: Es werden zunächst die mathematikbezogenen Erlebnisse zweier Lehrkräfte nachgezeichnet, bevor dann ihr Fremdverstehen in konkreten Situationen im Mathematikunterricht rekonstruiert wird. In der ersten Teiluntersuchung (= der Rekonstruktion eigener Erlebnisse der untersuchten Lehrkräfte) erfolgt die Datenerhebung mit Hilfe biographisch-narrativer Interviews, in denen die untersuchten Lehrkräfte angeregt werden, ihre mathematikbezogene Lebensgeschichte zu erzählen. Die Analyse dieser Interviews wird im Sinne der rekonstruktiven Fallanalyse vorgenommen. Insgesamt führt die erste Teiluntersuchung zu textlichen Darstellungen der rekonstruierten mathematikbezogenen Lebensgeschichte der untersuchten Mathematiklehrkräfte. In der zweiten Teiluntersuchung (= der Rekonstruktion des Fremdverstehens der untersuchten Lehrkräfte) werden dann narrative Interviews geführt, in denen die untersuchten Lehrkräfte von ihrem Fremdverstehen in konkreten Situationen im Mathematikunterricht erzählen. Die Analyse dieser Interviews erfolgt mit Hilfe eines dreischrittigen Analyseverfahrens, welches die Autorin eigens zum Zweck der Rekonstruktion von Fremdverstehen entwickelte. Am Ende dieser zweiten Teiluntersuchung werden sowohl das rekonstruierte Fremdverstehen der Lehrkräfte in verschiedenen Unterrichtssituationen dargestellt als auch Strukturen, die sich in ihrem Fremdverstehen abzeichnen. Mit Hilfe einer theoretischen Verallgemeinerung werden schließlich – auf Basis der Ergebnisse der zweiten Teiluntersuchung – Aussagen über fünf Merkmale des Fremdverstehens von Lehrkräften im Mathematikunterricht im Allgemeinen gewonnen. Mit diesen Aussagen vermag die Arbeit eine erste Beschreibung davon hervorzubringen, wie sich das Phänomen des Fremdverstehens von Lehrkräften im Mathematikunterricht ausgestalten kann.
KW  - Fremdverstehen
KW  - Alfred Schütz
KW  - Mathematikunterricht
KW  - rekonstruktive Fallanalyse
Y1  - 2023
ER  - 
TY  - JOUR
A1  - Fischer, Florian
A1  - Keller, Matthias
T1  - Riesz decompositions for Schrödinger operators on graphs
JF  - Journal of mathematical analysis and applications
N2  - We study superharmonic functions for Schrodinger operators on general weighted graphs. Specifically, we prove two decompositions which both go under the name Riesz decomposition in the literature. The first one decomposes a superharmonic function into a harmonic and a potential part. The second one decomposes a superharmonic function into a sum of superharmonic functions with certain upper bounds given by prescribed superharmonic functions. As application we show a Brelot type theorem.
KW  - Potential theory
KW  - Green's function
KW  - Schrödinger operator
KW  - Weighted
KW  - graph
KW  - Subcritical
KW  - Greatest harmonic minorant
Y1  - 2021
U6  - https://doi.org/10.1016/j.jmaa.2020.124674
SN  - 0022-247X
SN  - 1096-0813
VL  - 495
IS  - 1
PB  - Elsevier
CY  - Amsterdam
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  - Clavier, Pierre J.
T1  - Double shuffle relations for arborified zeta values
JF  - Journal of algebra
N2  - Arborified zeta values are defined as iterated series and integrals using the universal properties of rooted trees. This approach allows to study their convergence domain and to relate them to multiple zeta values. Generalisations to rooted trees of the stuffle and shuffle products are defined and studied. It is further shown that arborified zeta values are algebra morphisms for these new products on trees.
KW  - Rooted trees
KW  - Multiple zeta values
KW  - Shuffle products
KW  - Rota-Baxter
KW  - algebras
Y1  - 2020
U6  - https://doi.org/10.1016/j.jalgebra.2019.10.015
SN  - 0021-8693
SN  - 1090-266X
VL  - 543
SP  - 111
EP  - 155
PB  - Elsevier
CY  - San Diego
ER  - 
TY  - JOUR
A1  - Kaya, Adem
A1  - Freitag, Melina A.
T1  - Conditioning analysis for discrete Helmholtz problems
JF  - Computers and mathematics with applications : an international journal
N2  - In this paper, we examine conditioning of the discretization of the Helmholtz problem. Although the discrete Helmholtz problem has been studied from different perspectives, to the best of our knowledge, there is no conditioning analysis for it. We aim to fill this gap in the literature. We propose a novel method in 1D to observe the near-zero eigenvalues of a symmetric indefinite matrix. Standard classification of ill-conditioning based on the matrix condition number is not true for the discrete Helmholtz problem. We relate the ill-conditioning of the discretization of the Helmholtz problem with the condition number of the matrix. We carry out analytical conditioning analysis in 1D and extend our observations to 2D with numerical observations. We examine several discretizations. We find different regions in which the condition number of the problem shows different characteristics. We also explain the general behavior of the solutions in these regions.
KW  - Helmholtz problem
KW  - Condition number
KW  - Ill-conditioning
KW  - Indefinite
KW  - matrices
Y1  - 2022
U6  - https://doi.org/10.1016/j.camwa.2022.05.016
SN  - 0898-1221
SN  - 1873-7668
VL  - 118
SP  - 171
EP  - 182
PB  - Elsevier Science
CY  - Amsterdam
ER  - 
TY  - JOUR
A1  - Chelkh, W.
A1  - Ly, Ibrahim
A1  - Tarkhanov, Nikolai
T1  - A remark on the Laplace transform
JF  - Siberian Mathematical Journal
N2  - The study of the Cauchy problem for solutions of the heat equation in a cylindrical domain with data on the lateral surface by the Fourier method raises the problem of calculating the inverse Laplace transform of the entire function cos root z. This problem has no solution in the standard theory of the Laplace transform. We give an explicit formula for the inverse Laplace transform of cos root z using the theory of analytic functionals. This solution suits well to efficiently develop the regularization of solutions to Cauchy problems for parabolic equations with data on noncharacteristic surfaces.
KW  - Fourier-Laplace transform
KW  - distributions with one-sided support
KW  - holomorphic function
KW  - analytic functional
Y1  - 2020
U6  - https://doi.org/10.1134/S0037446620040151
SN  - 0037-4466
SN  - 1573-9260
VL  - 61
IS  - 4
SP  - 755
EP  - 762
PB  - Consultants Bureau, Springer
CY  - New York
ER  - 
TY  - JOUR
A1  - Seelig, Stefan A.
A1  - Rabe, Maximilian Michael
A1  - Malem-Shinitski, Noa
A1  - Risse, Sarah
A1  - Reich, Sebastian
A1  - Engbert, Ralf
T1  - Bayesian parameter estimation for the SWIFT model of eye-movement control during reading
JF  - Journal of mathematical psychology
N2  - Process-oriented theories of cognition must be evaluated against time-ordered observations. Here we present a representative example for data assimilation of the SWIFT model, a dynamical model of the control of fixation positions and fixation durations during natural reading of single sentences. First, we develop and test an approximate likelihood function of the model, which is a combination of a spatial, pseudo-marginal likelihood and a temporal likelihood obtained by probability density approximation Second, we implement a Bayesian approach to parameter inference using an adaptive Markov chain Monte Carlo procedure. Our results indicate that model parameters can be estimated reliably for individual subjects. We conclude that approximative Bayesian inference represents a considerable step forward for computational models of eye-movement control, where modeling of individual data on the basis of process-based dynamic models has not been possible so far.
KW  - dynamical models
KW  - reading
KW  - eye movements
KW  - saccades
KW  - likelihood function
KW  - Bayesian inference
KW  - MCMC
KW  - interindividual differences
Y1  - 2020
U6  - https://doi.org/10.1016/j.jmp.2019.102313
SN  - 0022-2496
SN  - 1096-0880
VL  - 95
PB  - Elsevier
CY  - San Diego
ER  - 
TY  - JOUR
A1  - Al-Saedy, Ammar Jaffar Muhesin
A1  - Tarchanov, Nikolaj Nikolaevič
T1  - A degree theory for Lagrangian boundary value problems
JF  - Žurnal Sibirskogo Federalʹnogo Universiteta = Journal of Siberian Federal University; mathematics & physics
N2  - We study those nonlinear partial differential equations which appear as Euler-Lagrange equations of variational problems. On defining weak boundary values of solutions to such equations we initiate the theory of Lagrangian boundary value problems in spaces of appropriate smoothness. We also analyse if the concept of mapping degree of current importance applies to Lagrangian problems.
N2  - Мы изучаем те нелинейные уравнения с частными производными, которые возникают как уравнения Эйлера-Лагранжа вариационных задач. Определяя слабые граничные значения решений таких уравнений, мы инициируем теорию лагранжевых краевых задач в функциональных пространствах подходящей гладкости. Мы также анализируем, применяется ли современная концепция степени отображения к лагранжевым проблемам.
KW  - nonlinear equations
KW  - Lagrangian system
KW  - weak boundary values
KW  - quasilinear Fredholm operators
KW  - mapping degree
Y1  - 2020
U6  - https://doi.org/10.17516/1997-1397-2020-13-1-5-25
SN  - 1997-1397
SN  - 2313-6022
VL  - 13
IS  - 1
SP  - 5
EP  - 25
PB  - Sibirskij Federalʹnyj Universitet
CY  - Krasnojarsk
ER  - 
TY  - JOUR
A1  - Saggioro, Elena
A1  - de Wiljes, Jana
A1  - Kretschmer, Marlene
A1  - Runge, Jakob
T1  - Reconstructing regime-dependent causal relationships from observational time series
JF  - Chaos : an interdisciplinary journal of nonlinear science
N2  - Inferring causal relations from observational time series data is a key problem across science and engineering whenever experimental interventions are infeasible or unethical. Increasing data availability over the past few decades has spurred the development of a plethora of causal discovery methods, each addressing particular challenges of this difficult task. In this paper, we focus on an important challenge that is at the core of time series causal discovery: regime-dependent causal relations. Often dynamical systems feature transitions depending on some, often persistent, unobserved background regime, and different regimes may exhibit different causal relations. Here, we assume a persistent and discrete regime variable leading to a finite number of regimes within which we may assume stationary causal relations. To detect regime-dependent causal relations, we combine the conditional independence-based PCMCI method [based on a condition-selection step (PC) followed by the momentary conditional independence (MCI) test] with a regime learning optimization approach. PCMCI allows for causal discovery from high-dimensional and highly correlated time series. Our method, Regime-PCMCI, is evaluated on a number of numerical experiments demonstrating that it can distinguish regimes with different causal directions, time lags, and sign of causal links, as well as changes in the variables' autocorrelation. Furthermore, Regime-PCMCI is employed to observations of El Nino Southern Oscillation and Indian rainfall, demonstrating skill also in real-world datasets.
Y1  - 2020
U6  - https://doi.org/10.1063/5.0020538
SN  - 1054-1500
SN  - 1089-7682
SN  - 1527-2443
VL  - 30
IS  - 11
PB  - American Institute of Physics
CY  - Melville
ER  - 
TY  - JOUR
A1  - Lewandowski, Max
T1  - Hadamard states for bosonic quantum field theory on globally hyperbolic spacetimes
JF  - Journal of mathematical physics
N2  - According to Radzikowski’s celebrated results, bisolutions of a wave operator on a globally hyperbolic spacetime are of the Hadamard form iff they are given by a linear combination of distinguished parametrices i2(G˜aF−G˜F+G˜A−G˜R) in the sense of Duistermaat and Hörmander [Acta Math. 128, 183–269 (1972)] and Radzikowski [Commun. Math. Phys. 179, 529 (1996)]. Inspired by the construction of the corresponding advanced and retarded Green operator GA, GR as done by Bär, Ginoux, and Pfäffle {Wave Equations on Lorentzian Manifolds and Quantization [European Mathematical Society (EMS), Zürich, 2007]}, we construct the remaining two Green operators GF, GaF locally in terms of Hadamard series. Afterward, we provide the global construction of i2(G˜aF−G˜F), which relies on new techniques such as a well-posed Cauchy problem for bisolutions and a patching argument using Čech cohomology. This leads to global bisolutions of the Hadamard form, each of which can be chosen to be a Hadamard two-point-function, i.e., the smooth part can be adapted such that, additionally, the symmetry and the positivity condition are exactly satisfied.
Y1  - 2022
U6  - https://doi.org/10.1063/5.0055753
SN  - 0022-2488
SN  - 1089-7658
VL  - 63
IS  - 1
PB  - American Institute of Physics
CY  - Melville
ER  - 
TY  - JOUR
A1  - Bär, Christian
T1  - The Faddeev-LeVerrier algorithm and the Pfaffian
JF  - Linear algebra and its applications
N2  - We adapt the Faddeev-LeVerrier algorithm for the computation of characteristic polynomials to the computation of the Pfaffian of a skew-symmetric matrix. This yields a very simple, easy to implement and parallelize algorithm of computational cost O(n(beta+1)) where nis the size of the matrix and O(n(beta)) is the cost of multiplying n x n-matrices, beta is an element of [2, 2.37286). We compare its performance to that of other algorithms and show how it can be used to compute the Euler form of a Riemannian manifold using computer algebra.
KW  - Characteristic polynomial
KW  - Determinant
KW  - Pfaffian
KW  - Gauss-Bonnet-Chern
KW  - theorem
Y1  - 2021
U6  - https://doi.org/10.1016/j.laa.2021.07.023
SN  - 0024-3795
SN  - 1873-1856
VL  - 630
SP  - 39
EP  - 55
PB  - Elsevier
CY  - New York
ER  - 
TY  - JOUR
A1  - Ly, Ibrahim
A1  - Tarkhanov, Nikolaj Nikolaevič
T1  - Asymptotic expansions at nonsymmetric cuspidal points
JF  - Mathematical notes
N2  - We study the asymptotics of solutions to the Dirichlet problem in a domain X subset of R3 whose boundary contains a singular point O. In a small neighborhood of this point, the domain has the form {z > root x(2) + y(4)}, i.e., the origin is a nonsymmetric conical point at the boundary. So far, the behavior of solutions to elliptic boundary-value problems has not been studied sufficiently in the case of nonsymmetric singular points. This problem was posed by V.A. Kondrat'ev in 2000. We establish a complete asymptotic expansion of solutions near the singular point.
KW  - Dirichlet problem
KW  - singular points
KW  - asymptotic expansions
Y1  - 2020
U6  - https://doi.org/10.1134/S0001434620070238
SN  - 0001-4346
SN  - 1573-8876
VL  - 108
IS  - 1-2
SP  - 219
EP  - 228
PB  - Springer Science
CY  - New York
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
T1  - Partial clones
JF  - Asian-European journal of mathematics : AEJM
N2  - A set C of operations defined on a nonempty set A is said to be a clone if C is closed under composition of operations and contains all projection mappings. The concept of a clone belongs to the algebraic main concepts and has important applications in Computer Science. A clone can also be regarded as a many-sorted algebra where the sorts are the n-ary operations defined on set A for all natural numbers n >= 1 and the operations are the so-called superposition operations S-m(n) for natural numbers m, n >= 1 and the projection operations as nullary operations. Clones generalize monoids of transformations defined on set A and satisfy three clone axioms. The most important axiom is the superassociative law, a generalization of the associative law. If the superposition operations are partial, i.e. not everywhere defined, instead of the many-sorted clone algebra, one obtains partial many-sorted algebras, the partial clones. Linear terms, linear tree languages or linear formulas form partial clones. In this paper, we give a survey on partial clones and their properties.
KW  - Operation
KW  - term
KW  - formula
KW  - superposition of operations
KW  - terms and
KW  - formulas
KW  - linear term
KW  - linear formula
KW  - linear tree language
KW  - clone
KW  - partial clone
KW  - linear hypersubstitution
KW  - dht-symmetric category
KW  - partial
KW  - theory
Y1  - 2020
U6  - https://doi.org/10.1142/S1793557120501612
SN  - 1793-5571
SN  - 1793-7183
VL  - 13
IS  - 8
PB  - World Scientific
CY  - Singapore
ER  - 
TY  - JOUR
A1  - Zöller, Gert
T1  - A note on the estimation of the maximum possible earthquake magnitude based on extreme value theory for the Groningen Gas Field
JF  - The bulletin of the Seismological Society of America : BSSA
N2  - Extreme value statistics is a popular and frequently used tool to model the occurrence of large earthquakes. The problem of poor statistics arising from rare events is addressed by taking advantage of the validity of general statistical properties in asymptotic regimes. In this note, I argue that the use of extreme value statistics for the purpose of practically modeling the tail of the frequency-magnitude distribution of earthquakes can produce biased and thus misleading results because it is unknown to what degree the tail of the true distribution is sampled by data. Using synthetic data allows to quantify this bias in detail. The implicit assumption that the true M-max is close to the maximum observed magnitude M-max,M-observed restricts the class of the potential models a priori to those with M-max = M-max,M-observed + Delta M with an increment Delta M approximate to 0.5... 1.2. This corresponds to the simple heuristic method suggested by Wheeler (2009) and labeled :M-max equals M-obs plus an increment." The incomplete consideration of the entire model family for the frequency-magnitude distribution neglects, however, the scenario of a large so far unobserved earthquake.
Y1  - 2022
U6  - https://doi.org/10.1785/0120210307
SN  - 0037-1106
SN  - 1943-3573
VL  - 112
IS  - 4
SP  - 1825
EP  - 1831
PB  - Seismological Society of America
CY  - El Cerito, Calif.
ER  - 
TY  - JOUR
A1  - Park, Jaeheung
A1  - Lühr, Hermann
A1  - Kervalishvili, Guram
A1  - Rauberg, Jan
A1  - Stolle, Claudia
A1  - Kwak, Young-Sil
A1  - Lee, Woo Kyoung
T1  - Morphology of high-latitude plasma density perturbations as deduced from the total electron content measurements onboard the Swarm constellation
JF  - Journal of geophysical research : A, Space physics
N2  - In this study, we investigate the climatology of high-latitude total electron content (TEC) variations as observed by the dual-frequency Global Navigation Satellite Systems (GNSS) receivers onboard the Swarm satellite constellation. The distribution of TEC perturbations as a function of geographic/magnetic coordinates and seasons reasonably agrees with that of the Challenging Minisatellite Payload observations published earlier. Categorizing the high-latitude TEC perturbations according to line-of-sight directions between Swarm and GNSS satellites, we can deduce their morphology with respect to the geomagnetic field lines. In the Northern Hemisphere, the perturbation shapes are mostly aligned with the L shell surface, and this anisotropy is strongest in the nightside auroral (substorm) and subauroral regions and weakest in the central polar cap. The results are consistent with the well-known two-cell plasma convection pattern of the high-latitude ionosphere, which is approximately aligned with L shells at auroral regions and crossing different L shells for a significant part of the polar cap. In the Southern Hemisphere, the perturbation structures exhibit noticeable misalignment to the local L shells. Here the direction toward the Sun has an additional influence on the plasma structure, which we attribute to photoionization effects. The larger offset between geographic and geomagnetic poles in the south than in the north is responsible for the hemispheric difference.
Y1  - 2017
U6  - https://doi.org/10.1002/2016JA023086
SN  - 2169-9380
SN  - 2169-9402
VL  - 122
IS  - 1
SP  - 1338
EP  - 1359
PB  - American Geophysical Union
CY  - Washington
ER  - 
TY  - JOUR
A1  - Purinton, Benjamin
A1  - Bookhagen, Bodo
T1  - Multiband (X, C, L) radar amplitude analysis for a mixed sand- and gravel-bed river in the eastern Central Andes
JF  - Remote sensing of environment : an interdisciplinary journal
N2  - Synthetic Aperture Radar (SAR) amplitude measurements from spaceborne sensors are sensitive to surface roughness conditions near their radar wavelength. These backscatter signals are often exploited to assess the roughness of plowed agricultural fields and water surfaces, and less so to complex, heterogeneous geological surfaces. The bedload of mixed sand- and gravel-bed rivers can be considered a mixture of smooth (compacted sand) and rough (gravel) surfaces. Here, we assess backscatter gradients over a large high-mountain alluvial river in the eastern Central Andes with aerially exposed sand and gravel bedload using X-band TerraSAR-X/TanDEM-X, C-band Sentinel-1, and L-band ALOS-2 PALSAR-2 radar scenes. In a first step, we present theory and hypotheses regarding radar response to an alluvial channel bed. We test our hypotheses by comparing backscatter responses over vegetation-free endmember surfaces from inside and outside of the active channel-bed area. We then develop methods to extract smoothed backscatter gradients downstream along the channel using kernel density estimates. In a final step, the local variability of sand-dominated patches is analyzed using Fourier frequency analysis, by fitting stretched-exponential and power-law regression models to the 2-D power spectrum of backscatter amplitude. We find a large range in backscatter depending on the heterogeneity of contiguous smooth- and rough-patches of bedload material. The SAR amplitude signal responds primarily to the fraction of smooth-sand bedload, but is further modified by gravel elements. The sensitivity to gravel is more apparent in longer wavelength L-band radar, whereas C- and X-band is sensitive only to sand variability. Because the spatial extent of smooth sand patches in our study area is typically< 50 m, only higher resolution sensors (e.g., TerraSAR-X/TanDEM-X) are useful for power spectrum analysis. Our results show the potential for mapping sand-gravel transitions and local geomorphic complexity in alluvial rivers with aerially exposed bedload using SAR amplitude.
KW  - SAR amplitude
KW  - Radar backscatter
KW  - Surface roughness
KW  - Fluvial
KW  - geomorphology
KW  - TerraSAR-X/TanDEM-X
KW  - Sentinel-1
KW  - ALOS-2 PALSAR-2
Y1  - 2020
U6  - https://doi.org/10.1016/j.rse.2020.111799
SN  - 0034-4257
SN  - 1879-0704
VL  - 246
PB  - Elsevier
CY  - New York
ER  - 
TY  - JOUR
A1  - Keller, Matthias
A1  - Schwarz, Michael
T1  - Courant’s nodal domain theorem for positivity preserving forms
JF  - Journal of spectral theory
N2  - We introduce a notion of nodal domains for positivity preserving forms. This notion generalizes the classical ones for Laplacians on domains and on graphs. We prove the Courant nodal domain theorem in this generalized setting using purely analytical methods.
KW  - Nodal domain
KW  - eigenfunction
KW  - Dirichlet form
KW  - compact resolvent
Y1  - 2020
U6  - https://doi.org/10.4171/JST/292
SN  - 1664-039X
SN  - 1664-0403
VL  - 10
IS  - 1
SP  - 271
EP  - 309
PB  - EMS Publishing House
CY  - Zürich
ER  - 
TY  - JOUR
A1  - Engbert, Ralf
A1  - Rabe, Maximilian Michael
A1  - Kliegl, Reinhold
A1  - Reich, Sebastian
T1  - Sequential data assimilation of the stochastic SEIR epidemic model for regional COVID-19 dynamics
JF  - Bulletin of mathematical biology : official journal of the Society for Mathematical Biology
N2  - Newly emerging pandemics like COVID-19 call for predictive models to implement precisely tuned responses to limit their deep impact on society. Standard epidemic models provide a theoretically well-founded dynamical description of disease incidence. For COVID-19 with infectiousness peaking before and at symptom onset, the SEIR model explains the hidden build-up of exposed individuals which creates challenges for containment strategies. However, spatial heterogeneity raises questions about the adequacy of modeling epidemic outbreaks on the level of a whole country. Here, we show that by applying sequential data assimilation to the stochastic SEIR epidemic model, we can capture the dynamic behavior of outbreaks on a regional level. Regional modeling, with relatively low numbers of infected and demographic noise, accounts for both spatial heterogeneity and stochasticity. Based on adapted models, short-term predictions can be achieved. Thus, with the help of these sequential data assimilation methods, more realistic epidemic models are within reach.
KW  - Stochastic epidemic model
KW  - Sequential data assimilation
KW  - Ensemble Kalman
KW  - filter
KW  - COVID-19
Y1  - 2020
U6  - https://doi.org/10.1007/s11538-020-00834-8
SN  - 0092-8240
SN  - 1522-9602
VL  - 83
IS  - 1
PB  - Springer
CY  - New York
ER  - 
TY  - JOUR
A1  - Engbert, Ralf
A1  - Rabe, Maximilian Michael
A1  - Schwetlick, Lisa
A1  - Seelig, Stefan A.
A1  - Reich, Sebastian
A1  - Vasishth, Shravan
T1  - Data assimilation in dynamical cognitive science
JF  - Trends in cognitive sciences
N2  - Dynamical models make specific assumptions about cognitive processes that generate human behavior. In data assimilation, these models are tested against timeordered data. Recent progress on Bayesian data assimilation demonstrates that this approach combines the strengths of statistical modeling of individual differences with the those of dynamical cognitive models.
Y1  - 2022
U6  - https://doi.org/10.1016/j.tics.2021.11.006
SN  - 1364-6613
SN  - 1879-307X
VL  - 26
IS  - 2
SP  - 99
EP  - 102
PB  - Elsevier
CY  - Amsterdam
ER  - 
TY  - JOUR
A1  - Rastogi, Abhishake
T1  - Tikhonov regularization with oversmoothing penalty for nonlinear statistical inverse problems
JF  - Communications on Pure and Applied Analysis
N2  - In this paper, we consider the nonlinear ill-posed inverse problem with noisy data in the statistical learning setting. The Tikhonov regularization scheme in Hilbert scales is considered to reconstruct the estimator from the random noisy data. In this statistical learning setting, we derive the rates of convergence for the regularized solution under certain assumptions on the nonlinear forward operator and the prior assumptions. We discuss estimates of the reconstruction error using the approach of reproducing kernel Hilbert spaces.
KW  - Statistical inverse problem
KW  - Tikhonov regularization
KW  - Hilbert Scales
KW  - reproducing kernel Hilbert space
KW  - minimax convergence rates
Y1  - 2020
U6  - https://doi.org/10.3934/cpaa.2020183
SN  - 1534-0392
SN  - 1553-5258
VL  - 19
IS  - 8
SP  - 4111
EP  - 4126
PB  - American Institute of Mathematical Sciences
CY  - Springfield
ER  - 
TY  - JOUR
A1  - Gräter, Joachim
T1  - Free division rings of fractions of crossed products of groups with Conradian left-orders
JF  - Forum mathematicum
N2  - Let D be a division ring of fractions of a crossed product F[G, eta, alpha], where F is a skew field and G is a group with Conradian left-order <=. For D we introduce the notion of freeness with respect to <= and show that D is free in this sense if and only if D can canonically be embedded into the endomorphism ring of the right F-vector space F((G)) of all formal power series in G over F with respect to <=. From this we obtain that all division rings of fractions of F[G, eta, alpha] which are free with respect to at least one Conradian left-order of G are isomorphic and that they are free with respect to any Conradian left-order of G. Moreover, F[G, eta, alpha] possesses a division ring of fraction which is free in this sense if and only if the rational closure of F[G, eta, alpha] in the endomorphism ring of the corresponding right F-vector space F((G)) is a skew field.
KW  - crossed product
KW  - group ring
KW  - ordered group
KW  - Conradian left-order
KW  - locally indicable group
KW  - division ring of fractions
KW  - Hughes-free
KW  - formal
KW  - power series
Y1  - 2020
U6  - https://doi.org/10.1515/forum-2019-0264
SN  - 0933-7741
SN  - 1435-5337
VL  - 32
IS  - 3
SP  - 739
EP  - 772
PB  - De Gruyter
CY  - Berlin
ER  - 
TY  - JOUR
A1  - Klein, Markus
A1  - Rosenberger, Elke
T1  - The tunneling effect for Schrödinger operators on a vector bundle
JF  - Analysis and mathematical physics
N2  - In the semiclassical limit (h) over bar -> 0, we analyze a class of self-adjoint Schrodinger operators H-(h) over bar = (h) over bar L-2 + (h) over barW + V center dot id(E) acting on sections of a vector bundle E over an oriented Riemannian manifold M where L is a Laplace type operator, W is an endomorphism field and the potential energy V has non-degenerate minima at a finite number of points m(1),... m(r) is an element of M, called potential wells. Using quasimodes of WKB-type near m(j) for eigenfunctions associated with the low lying eigenvalues of H-(h) over bar, we analyze the tunneling effect, i.e. the splitting between low lying eigenvalues, which e.g. arises in certain symmetric configurations. Technically, we treat the coupling between different potential wells by an interaction matrix and we consider the case of a single minimal geodesic (with respect to the associated Agmon metric) connecting two potential wells and the case of a submanifold of minimal geodesics of dimension l + 1. This dimension l determines the polynomial prefactor for exponentially small eigenvalue splitting.
KW  - Laplace-type operator
KW  - Vector bundle
KW  - WKB-expansion
KW  - Quasimodes
KW  - Tunneling
KW  - Spectral gap
KW  - Complete asymptotics
Y1  - 2021
U6  - https://doi.org/10.1007/s13324-021-00485-5
SN  - 1664-2368
SN  - 1664-235X
VL  - 11
IS  - 2
PB  - Springer International Publishing AG
CY  - Cham (ZG)
ER  - 
TY  - GEN
A1  - Evans, Myfanwy E.
A1  - Hyde, Stephen T.
T1  - Symmetric Tangling of Honeycomb Networks
T2  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - Symmetric, elegantly entangled structures are a curious mathematical construction that has found their way into the heart of the chemistry lab and the toolbox of constructive geometry. Of particular interest are those structures—knots, links and weavings—which are composed locally of simple twisted strands and are globally symmetric. This paper considers the symmetric tangling of multiple 2-periodic honeycomb networks. We do this using a constructive methodology borrowing elements of graph theory, low-dimensional topology and geometry. The result is a wide-ranging enumeration of symmetric tangled honeycomb networks, providing a foundation for their exploration in both the chemistry lab and the geometers toolbox.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1282 
KW  - tangles
KW  - knots
KW  - networks
KW  - periodic entanglement
KW  - molecular weaving
KW  - graphs
Y1  - 2022
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-570842
SN  - 1866-8372
IS  - 1282
ER  - 
TY  - JOUR
A1  - Evans, Myfanwy E.
A1  - Hyde, Stephen T.
T1  - Symmetric Tangling of Honeycomb Networks
JF  - Symmetry
N2  - Symmetric, elegantly entangled structures are a curious mathematical construction that has found their way into the heart of the chemistry lab and the toolbox of constructive geometry. Of particular interest are those structures—knots, links and weavings—which are composed locally of simple twisted strands and are globally symmetric. This paper considers the symmetric tangling of multiple 2-periodic honeycomb networks. We do this using a constructive methodology borrowing elements of graph theory, low-dimensional topology and geometry. The result is a wide-ranging enumeration of symmetric tangled honeycomb networks, providing a foundation for their exploration in both the chemistry lab and the geometers toolbox.
KW  - tangles
KW  - knots
KW  - networks
KW  - periodic entanglement
KW  - molecular weaving
KW  - graphs
Y1  - 2022
U6  - https://doi.org/10.3390/sym14091805
SN  - 2073-8994
VL  - 14
SP  - 1
EP  - 13
PB  - MDPI
CY  - Basel, Schweiz
ET  - 9
ER  - 
TY  - JOUR
A1  - Malass, Ihsane
A1  - Tarkhanov, Nikolaj Nikolaevič
T1  - A perturbation of the de Rham complex
T1  - Возмущение комплекса де Рама
JF  - Journal of Siberian Federal University : Mathematics & Physics
JF  - Žurnal Sibirskogo Federalʹnogo Universiteta : Matematika i fizika
N2  - We consider a perturbation of the de Rham complex on a compact manifold with boundary. This perturbation goes beyond the framework of complexes, and so cohomology does not apply to it. On the other hand, its curvature is "small", hence there is a natural way to introduce an Euler characteristic and develop a Lefschetz theory for the perturbation. This work is intended as an attempt to develop a cohomology theory for arbitrary sequences of linear mappings.
N2  - Рассмотрим возмущение комплекса де Рама на компактном многообразии с краем. Это возмущение выходит за рамки комплексов, и поэтому когомологии к нему не относятся. С другой стороны, его кривизна "мала", поэтому существует естественный способ ввести характеристику Эйлера и разработать теорию Лефшеца для возмущения. Данная работа предназначена для попытки разработать теорию когомологий для произвольных последовательностей линейных отображений.
KW  - de Rham complex
KW  - cohomology
KW  - Hodge theory
KW  - Neumann problem
KW  - комплекс де Рама
KW  - когомологии
KW  - теория Ходжа
KW  - проблема Неймана
Y1  - 2020
U6  - https://doi.org/10.17516/1997-1397-2020-13-5-519-532
SN  - 1997-1397
SN  - 2313-6022
VL  - 13
IS  - 5
SP  - 519
EP  - 532
PB  - Siberian Federal University
CY  - Krasnojarsk
ER  - 
TY  - JOUR
A1  - Ly, Ibrahim
T1  - A Cauchy problem for the Cauchy-Riemann operator
JF  - Afrika Matematika
N2  - We study the Cauchy problem for a nonlinear elliptic equation with data on a piece S of the boundary surface partial derivative X. By the Cauchy problem is meant any boundary value problem for an unknown function u in a domain X with the property that the data on S, if combined with the differential equations in X, allows one to determine all derivatives of u on S by means of functional equations. In the case of real analytic data of the Cauchy problem, the existence of a local solution near S is guaranteed by the Cauchy-Kovalevskaya theorem. We discuss a variational setting of the Cauchy problem which always possesses a generalized solution.
KW  - nonlinear PDI
KW  - Cauchy problem
KW  - Zaremba problem
Y1  - 2020
U6  - https://doi.org/10.1007/s13370-020-00810-4
SN  - 1012-9405
SN  - 2190-7668
VL  - 32
IS  - 1-2
SP  - 69
EP  - 76
PB  - Springer
CY  - Heidelberg
ER  - 
TY  - JOUR
A1  - Bandara, Lashi
T1  - Functional calculus and harmonic analysis in geometry
JF  - São Paulo journal of mathematical sciences / Instituto de Matemática e Estatística da Universidade de São Paulo
N2  - In this short survey article, we showcase a number of non-trivial geometric problems that have recently been resolved by marrying methods from functional calculus and real-variable harmonic analysis. We give a brief description of these methods as well as their interplay. This is a succinct survey that hopes to inspire geometers and analysts alike to study these methods so that they can be further developed to be potentially applied to a broader range of questions.
KW  - Functional calculus
KW  - Real-variable harmonic analysis
KW  - Elliptic boundary
KW  - value problems
KW  - Kato square root problem
KW  - Spectral flow
KW  - Riesz topology
KW  - Gigli-Mantegazza flow
KW  - Bisectorial operator
Y1  - 2021
U6  - https://doi.org/10.1007/s40863-019-00149-0
SN  - 1982-6907
SN  - 2316-9028
VL  - 15
IS  - 1
SP  - 20
EP  - 53
PB  - Springer
CY  - Cham
ER  - 
TY  - JOUR
A1  - Somogyvári, Márk
A1  - Reich, Sebastian
T1  - Convergence tests for transdimensional Markov chains in geoscience imaging
JF  - Mathematical geosciences : the official journal of the International Association for Mathematical Geosciences
N2  - Classic inversion methods adjust a model with a predefined number of parameters to the observed data. With transdimensional inversion algorithms such as the reversible-jump Markov chain Monte Carlo (rjMCMC), it is possible to vary this number during the inversion and to interpret the observations in a more flexible way. Geoscience imaging applications use this behaviour to automatically adjust model resolution to the inhomogeneities of the investigated system, while keeping the model parameters on an optimal level. The rjMCMC algorithm produces an ensemble as result, a set of model realizations, which together represent the posterior probability distribution of the investigated problem. The realizations are evolved via sequential updates from a randomly chosen initial solution and converge toward the target posterior distribution of the inverse problem. Up to a point in the chain, the realizations may be strongly biased by the initial model, and must be discarded from the final ensemble. With convergence assessment techniques, this point in the chain can be identified. Transdimensional MCMC methods produce ensembles that are not suitable for classic convergence assessment techniques because of the changes in parameter numbers. To overcome this hurdle, three solutions are introduced to convert model realizations to a common dimensionality while maintaining the statistical characteristics of the ensemble. A scalar, a vector and a matrix representation for models is presented, inferred from tomographic subsurface investigations, and three classic convergence assessment techniques are applied on them. It is shown that appropriately chosen scalar conversions of the models could retain similar statistical ensemble properties as geologic projections created by rasterization.
KW  - transdimensional inversion
KW  - MCMC modelling
KW  - convergence assessment
Y1  - 2019
U6  - https://doi.org/10.1007/s11004-019-09811-x
SN  - 1874-8961
SN  - 1874-8953
VL  - 52
IS  - 5
SP  - 651
EP  - 668
PB  - Springer
CY  - Heidelberg
ER  - 
TY  - JOUR
A1  - Zöller, Gert
A1  - Ullah, Shahid
A1  - Bindi, Dino
A1  - Parolai, Stefano
A1  - Mikhailova, Natalya
T1  - The largest expected earthquake magnitudes in Central Asia
BT  - statistical inference from an earthquake catalogue with uncertain magnitudes
JF  - Seismicity, fault rupture and earthquake hazards in slowly deforming regions
N2  - The knowledge of the largest expected earthquake magnitude in a region is one of the key issues in probabilistic seismic hazard calculations and the estimation of worst-case scenarios. Earthquake catalogues are the most informative source of information for the inference of earthquake magnitudes. We analysed the earthquake catalogue for Central Asia with respect to the largest expected magnitudes m(T) in a pre-defined time horizon T-f using a recently developed statistical methodology, extended by the explicit probabilistic consideration of magnitude errors. For this aim, we assumed broad error distributions for historical events, whereas the magnitudes of recently recorded instrumental earthquakes had smaller errors. The results indicate high probabilities for the occurrence of large events (M >= 8), even in short time intervals of a few decades. The expected magnitudes relative to the assumed maximum possible magnitude are generally higher for intermediate-depth earthquakes (51-300 km) than for shallow events (0-50 km). For long future time horizons, for example, a few hundred years, earthquakes with M >= 8.5 have to be taken into account, although, apart from the 1889 Chilik earthquake, it is probable that no such event occurred during the observation period of the catalogue.
Y1  - 2017
SN  - 978-1-86239-745-3
SN  - 978-1-86239-964-8
U6  - https://doi.org/10.1144/SP432.3
SN  - 0305-8719
VL  - 432
SP  - 29
EP  - 40
PB  - The Geological Society
CY  - London
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  - Hamm, Maximilian
A1  - Pelivan, Ivanka
A1  - Grott, Matthias
A1  - de Wiljes, Jana
T1  - Thermophysical modelling and parameter estimation of small solar system bodies via data assimilation
JF  - Monthly notices of the Royal Astronomical Society
N2  - Deriving thermophysical properties such as thermal inertia from thermal infrared observations provides useful insights into the structure of the surface material on planetary bodies. The estimation of these properties is usually done by fitting temperature variations calculated by thermophysical models to infrared observations. For multiple free model parameters, traditional methods such as least-squares fitting or Markov chain Monte Carlo methods become computationally too expensive. Consequently, the simultaneous estimation of several thermophysical parameters, together with their corresponding uncertainties and correlations, is often not computationally feasible and the analysis is usually reduced to fitting one or two parameters. Data assimilation (DA) methods have been shown to be robust while sufficiently accurate and computationally affordable even for a large number of parameters. This paper will introduce a standard sequential DA method, the ensemble square root filter, for thermophysical modelling of asteroid surfaces. This method is used to re-analyse infrared observations of the MARA instrument, which measured the diurnal temperature variation of a single boulder on the surface of near-Earth asteroid (162173) Ryugu. The thermal inertia is estimated to be 295 +/- 18 Jm(-2) K-1 s(-1/2), while all five free parameters of the initial analysis are varied and estimated simultaneously. Based on this thermal inertia estimate the thermal conductivity of the boulder is estimated to be between 0.07 and 0.12,Wm(-1) K-1 and the porosity to be between 0.30 and 0.52. For the first time in thermophysical parameter derivation, correlations and uncertainties of all free model parameters are incorporated in the estimation procedure that is more than 5000 times more efficient than a comparable parameter sweep.
KW  - radiation mechanisms: thermal
KW  - methods: data analysis
KW  - methods
KW  - statistical
KW  - minor planets, asteroids: individual: (162173) Ryugu
Y1  - 2020
U6  - https://doi.org/10.1093/mnras/staa1755
SN  - 0035-8711
SN  - 1365-2966
VL  - 496
IS  - 3
SP  - 2776
EP  - 2785
PB  - Oxford Univ. Press
CY  - Oxford
ER  - 
TY  - JOUR
A1  - Dereudre, David
A1  - Mazzonetto, Sara
A1  - Roelly, Sylvie
T1  - Exact simulation of Brownian diffusions with drift admitting jumps
JF  - SIAM journal on scientific computing
N2  - In this paper, using an algorithm based on the retrospective rejection sampling scheme introduced in [A. Beskos, O. Papaspiliopoulos, and G. O. Roberts,Methodol. Comput. Appl. Probab., 10 (2008), pp. 85-104] and [P. Etore and M. Martinez, ESAIM Probab.Stat., 18 (2014), pp. 686-702], we propose an exact simulation of a Brownian di ff usion whose drift admits several jumps. We treat explicitly and extensively the case of two jumps, providing numerical simulations. Our main contribution is to manage the technical di ffi culty due to the presence of t w o jumps thanks to a new explicit expression of the transition density of the skew Brownian motion with two semipermeable barriers and a constant drift.
KW  - exact simulation methods
KW  - skew Brownian motion
KW  - skew diffusions
KW  - Brownian motion with discontinuous drift
Y1  - 2017
U6  - https://doi.org/10.1137/16M107699X
SN  - 1064-8275
SN  - 1095-7197
VL  - 39
IS  - 3
SP  - A711
EP  - A740
PB  - Society for Industrial and Applied Mathematics
CY  - Philadelphia
ER  - 
TY  - THES
A1  - Fabian, Melina
T1  - Grundvorstellungen bei Zahlbereichserweiterungen
T1  - Basic ideas ('Grundvorstellungen') for numerical extensions
BT  - von N nach Q+ oder von N nach Z?
N2  - Die Erweiterung des natürlichen Zahlbereichs um die positiven Bruchzahlen und die negativen ganzen Zahlen geht für Schülerinnen und Schüler mit großen gedanklichen Hürden und einem Umbruch bis dahin aufgebauter Grundvorstellungen einher. Diese Masterarbeit trägt wesentliche Veränderungen auf der Vorstellungs- und Darstellungsebene für beide Zahlbereiche zusammen und setzt sich mit den kognitiven Herausforderungen für Lernende auseinander. Auf der Grundlage einer Diskussion traditioneller sowie alternativer Lehrgänge der Zahlbereichserweiterung wird eine Unterrichtskonzeption für den Mathematikunterricht entwickelt, die eine parallele Einführung der Bruchzahlen und der negativen Zahlen vorschlägt. Die Empfehlungen der Unterrichtkonzeption erstrecken sich über den Zeitraum von der ersten bis zur siebten Klassenstufe, was der behutsamen Weiterentwicklung und Modifikation des Zahlbegriffs viel Zeit einräumt, und enthalten auch didaktische Überlegungen sowie konkrete Hinweise zu möglichen Aufgabenformaten.
N2  - The extension of the natural number range to include the positive fractions and the negative integers is accompanied by great mental hurdles for students and an upheaval of previously established basic concepts. This Master's thesis brings together essential changes at the level of imagination and representation for both number ranges and deals with the cognitive challenges for learners. Based on a discussion of traditional as well as alternative courses of number range extension, a teaching conception for mathematics lessons is developed that proposes a parallel introduction of fractions and negative numbers. The recommendations of the teaching conception cover the period from the first to the seventh grade, which allows a lot of time for the careful further development and modification of the number concept, and also contain didactic considerations as well as concrete hints on possible task formats.
KW  - Mathematikdidaktik
KW  - Zahlbereichserweiterung
KW  - Grundvorstellungen
KW  - negative Zahlen
KW  - Bruchzahlen
KW  - fractions
KW  - basic ideas ('Grundvorstellungen')
KW  - didactics of mathematics
KW  - numerical extension
KW  - negative numbers
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-565930
ER  - 
TY  - 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  -