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Die Dissertation beschäftigt sich mit einer neuartigen Art von Branch-and-Bound Algorithmen, deren Unterschied zu klassischen Branch-and-Bound Algorithmen darin besteht, dass
das Branching durch die Addition von nicht-negativen Straftermen zur Zielfunktion erfolgt
anstatt durch das Hinzufügen weiterer Nebenbedingungen. Die Arbeit zeigt die theoretische Korrektheit des Algorithmusprinzips für verschiedene allgemeine Klassen von Problemen und evaluiert die Methode für verschiedene konkrete Problemklassen. Für diese Problemklassen, genauer Monotone und Nicht-Monotone Gemischtganzzahlige Lineare Komplementaritätsprobleme und Gemischtganzzahlige Lineare Probleme, präsentiert die Arbeit
verschiedene problemspezifische Verbesserungsmöglichkeiten und evaluiert diese numerisch.
Weiterhin vergleicht die Arbeit die neue Methode mit verschiedenen Benchmark-Methoden
mit größtenteils guten Ergebnissen und gibt einen Ausblick auf weitere Anwendungsgebiete
und zu beantwortende Forschungsfragen.

Allocating scarce resources efficiently is a major task in mechanism design. One of the most fundamental problems in mechanism design theory is the problem of selling a single indivisible item to bidders with private valuations for the item. In this setting, the classic Vickrey auction of~\citet{vickrey1961} describes a simple mechanism to implement a social welfare maximizing allocation.
The Vickrey auction for a single item asks every buyer to report its valuation and allocates the item to the highest bidder for a price of the second highest bid. This auction features some desirable properties, e.g., buyers cannot benefit from misreporting their true value for the item (incentive compatibility) and the auction can be executed in polynomial time.
However, when there is more than one item for sale and buyers' valuations for sets of items are not additive or the set of feasible allocations is constrained, then constructing mechanisms that implement efficient allocations and have polynomial runtime might be very challenging. Consider a single seller selling $n\in \N$ heterogeneous indivisible items to several bidders. The Vickrey-Clarke-Groves auction generalizes the idea of the Vickrey auction to this multi-item setting. Naturally, every bidder has an intrinsic value for every subset of items. As in in the Vickrey auction, bidders report their valuations (Now, for every subset of items!). Then, the auctioneer computes a social welfare maximizing allocation according to the submitted bids and charges buyers the social cost of their winning that is incurred by the rest of the buyers. (This is the analogue to charging the second highest bid to the winning bidder in the single item Vickrey auction.) It turns out that the Vickrey-Clarke-Groves auction is also incentive compatible but it poses some problems: In fact, say for $n=40$, bidders would have to submit $2^{40}-1$ values (one value for each nonempty subset of the ground set) in total. Thus, asking every bidder for its valuation might be impossible due to time complexity issues. Therefore, even though the Vickrey-Clarke-Groves auction implements a social welfare maximizing allocation in this multi-item setting it might be impractical and there is need for alternative approaches to implement social welfare maximizing allocations.
This dissertation represents the results of three independent research papers all of them tackling the problem of implementing efficient allocations in different combinatorial settings.

Energy transport networks are one of the most important infrastructures for the planned energy transition. They form the interface between energy producers and consumers and their features make them good candidates for the tools that mathematical optimization can offer. Nevertheless, the operation of energy networks comes with two major challenges. First, the nonconvexity of the equations that model the physics in the network render the resulting problems extremely hard to solve for large-scale networks. Second, the uncertainty associated to the behavior of the different agents involved, the production of energy, and the consumption of energy make the resulting problems hard to solve if a representative description of uncertainty is to be considered.
In this cumulative dissertation we study adaptive refinement algorithms designed to cope with the nonconvexity and stochasticity of equations arising in energy networks. Adaptive refinement algorithms approximate the original problem by sequentially refining the model of a simpler optimization problem. More specifically, in this thesis, the focus of the adaptive algorithm is on adapting the discretization and description of a set of constraints.
In the first part of this thesis, we propose a generalization of the different adaptive refinement ideas that we study. We sequentially describe model catalogs, error measures, marking strategies, and switching strategies that are used to set up the adaptive refinement algorithm. Afterward, the effect of the adaptive refinement algorithm on two energy network applications is studied. The first application treats the stationary operation of district heating networks. Here, the strength of adaptive refinement algorithms for approximating the ordinary differential equation that describes the transport of energy is highlighted. We introduce the resulting nonlinear problem, consider network expansion, and obtain realistic controls by applying the adaptive refinement algorithm. The second application concerns quantile-constrained optimization problems and highlights the ability of the adaptive refinement algorithm to cope with large scenario sets via clustering. We introduce the resulting mixed-integer linear problem, discuss generic solution techniques, make the link with the generalized framework, and measure the impact of the proposed solution techniques.
The second part of this thesis assembles the papers that inspired the contents of the first part of this thesis. Hence, they describe in detail the topics that are covered and will be referenced throughout the first part.

THE NONLOCAL NEUMANN PROBLEM
(2023)

Instead of presuming only local interaction, we assume nonlocal interactions. By doing so, mass
at a point in space does not only interact with an arbitrarily small neighborhood surrounding it,
but it can also interact with mass somewhere far, far away. Thus, mass jumping from one point to
another is also a possibility we can consider in our models. So, if we consider a region in space, this
region interacts in a local model at most with its closure. While in a nonlocal model this region may
interact with the whole space. Therefore, in the formulation of nonlocal boundary value problems
the enforcement of boundary conditions on the topological boundary may not suffice. Furthermore,
choosing the complement as nonlocal boundary may work for Dirichlet boundary conditions, but
in the case of Neumann boundary conditions this may lead to an overfitted model.
In this thesis, we introduce a nonlocal boundary and study the well-posedness of a nonlocal Neu-
mann problem. We present sufficient assumptions which guarantee the existence of a weak solution.
As in a local model our weak formulation is derived from an integration by parts formula. However,
we also study a different weak formulation where the nonlocal boundary conditions are incorporated
into the nonlocal diffusion-convection operator.
After studying the well-posedness of our nonlocal Neumann problem, we consider some applications
of this problem. For example, we take a look at a system of coupled Neumann problems and analyze
the difference between a local coupled Neumann problems and a nonlocal one. Furthermore, we let
our Neumann problem be the state equation of an optimal control problem which we then study. We
also add a time component to our Neumann problem and analyze this nonlocal parabolic evolution
equation.
As mentioned before, in a local model mass at a point in space only interacts with an arbitrarily
small neighborhood surrounding it. We analyze what happens if we consider a family of nonlocal
models where the interaction shrinks so that, in limit, mass at a point in space only interacts with
an arbitrarily small neighborhood surrounding it.

Traditional workflow management systems support process participants in fulfilling business tasks through guidance along a predefined workflow model.
Flexibility has gained a lot of attention in recent decades through a shift from mass production to customization. Various approaches to workflow flexibility exist that either require extensive knowledge acquisition and modelling effort or an active intervention during execution and re-modelling of deviating behaviour. The pursuit of flexibility by deviation is to compensate both of these disadvantages through allowing alternative unforeseen execution paths at run time without demanding the process participant to adapt the workflow model. However, the implementation of this approach has been little researched so far.
This work proposes a novel approach to flexibility by deviation. The approach aims at supporting process participants during the execution of a workflow through suggesting work items based on predefined strategies or experiential knowledge even in case of deviations. The developed concepts combine two renowned methods from the field of artificial intelligence - constraint satisfaction problem solving with process-oriented case-based reasoning. This mainly consists of a constraint-based workflow engine in combination with a case-based deviation management. The declarative representation of workflows through constraints allows for implicit flexibility and a simple possibility to restore consistency in case of deviations. Furthermore, the combined model, integrating procedural with declarative structures through a transformation function, increases the capabilities for flexibility. For an adequate handling of deviations the methodology of case-based reasoning fits perfectly, through its approach that similar problems have similar solutions. Thus, previous made experiences are transferred to currently regarded problems, under the assumption that a similar deviation has been handled successfully in the past.
Necessary foundations from the field of workflow management with a focus on flexibility are presented first.
As formal foundation, a constraint-based workflow model was developed that allows for a declarative specification of foremost sequential dependencies of tasks. Procedural and declarative models can be combined in the approach, as a transformation function was specified that converts procedural workflow models to declarative constraints.
One main component of the approach is the constraint-based workflow engine that utilizes this declarative model as input for a constraint solving algorithm. This algorithm computes the worklist, which is proposed to the process participant during workflow execution. With predefined deviation handling strategies that determine how the constraint model is modified in order to restore consistency, the support is continuous even in case of deviations.
The second major component of the proposed approach constitutes the case-based deviation management, which aims at improving the support of process participants on the basis of experiential knowledge. For the retrieve phase, a sophisticated similarity measure was developed that integrates specific characteristics of deviating workflows and combines several sequence similarity measures. Two alternative methods for the reuse phase were developed, a null adaptation and a generative adaptation. The null adaptation simply proposes tasks from the most similar workflow as work items, whereas the generative adaptation modifies the constraint-based workflow model based on the most similar workflow in order to re-enable the constraint-based workflow engine to suggest work items.
The experimental evaluation of the approach consisted of a simulation of several types of process participants in the exemplary domain of deficiency management in construction. The results showed high utility values and a promising potential for an investigation of the transfer on other domains and the applicability in practice, which is part of future work.
Concluding, the contributions are summarized and research perspectives are pointed out.

Official business surveys form the basis for national and regional business statistics and are thus of great importance for analysing the state and performance of the economy. However, both the heterogeneity of business data and their high dynamics pose a particular challenge to the feasibility of sampling and the quality of the resulting estimates. A widely used sampling frame for creating the design of an official business survey is an extract from an official business register. However, if this frame does not accurately represent the target population, frame errors arise. Amplified by the heterogeneity and dynamics of business populations, these errors can significantly affect the estimation quality and lead to inefficiencies and biases. This dissertation therefore deals with design-based methods for optimising business surveys with respect to different types of frame errors.
First, methods for adjusting the sampling design of business surveys are addressed. These approaches integrate auxiliary information about the expected structures of frame errors into the sampling design. The aim is to increase the number of sampled businesses that are subject to frame errors. The element-specific frame error probability is estimated based on auxiliary information about frame errors observed in previous samples. The approaches discussed consider different types of frame errors and can be incorporated into predefined designs with fixed strata.
As the second main pillar of this work, methods for adjusting weights to correct for frame errors during estimation are developed and investigated. As a result of frame errors, the assumptions under which the original design weights were determined based on the sampling design no longer hold. The developed methods correct the design weights taking into account the errors identified for sampled elements. Case-number-based reweighting approaches, on the one hand, attempt to reconstruct the unknown size of the individual strata in the target population. In the context of weight smoothing methods, on the other hand, design weights are modelled and smoothed as a function of target or auxiliary variables. This serves to avoid inefficiencies in the estimation due to highly scattering weights or weak correlations between weights and target variables. In addition, possibilities of correcting frame errors by calibration weighting are elaborated. Especially when the sampling frame shows over- and/or undercoverage, the inclusion of external auxiliary information can provide a significant improvement of the estimation quality. For those methods whose quality cannot be measured using standard procedures, a procedure for estimating the variance based on a rescaling bootstrap is proposed. This enables an assessment of the estimation quality when using the methods in practice.
In the context of two extensive simulation studies, the methods presented in this dissertation are evaluated and compared with each other. First, in the environment of an experimental simulation, it is assessed which approaches are particularly suitable with regard to different data situations. In a second simulation study, which is based on the structural survey in the services sector, the applicability of the methods in practice is evaluated under realistic conditions.

Wasserbezogene regulierende und versorgende Ökosystemdienstleistungen (ÖSDL) wurden im Hinblick auf das Abflussregime und die Grundwasserneubildung im Biosphärenreservat Pfälzerwald im Südwesten Deutschlands anhand hydrologischer Modellierung unter Verwendung des Soil and Water Assessment Tool (SWAT+) untersucht. Dabei wurde ein holistischer Ansatz verfolgt, wonach den ÖSDL Indikatoren für funktionale und strukturelle ökologische Prozesse zugeordnet werden. Potenzielle Risikofaktoren für die Verschlechterung von wasserbedingten ÖSDL des Waldes, wie Bodenverdichtung durch Befahren mit schweren Maschinen im Zuge von Holzerntearbeiten, Schadflächen mit Verjüngung, entweder durch waldbauliche Bewirtschaftungspraktiken oder durch Windwurf, Schädlinge und Kalamitäten im Zuge des Klimawandels, sowie der Kli-mawandel selbst als wesentlicher Stressor für Waldökosysteme wurden hinsichtlich ihrer Auswirkungen auf hydrologische Prozesse analysiert. Für jeden dieser Einflussfaktoren wurden separate SWAT+-Modellszenarien erstellt und mit dem kalibrierten Basismodell verglichen, das die aktuellen Wassereinzugsgebietsbedingungen basierend auf Felddaten repräsentierte. Die Simulationen bestätigten günstige Bedingungen für die Grundwasserneubildung im Pfälzerwald. Im Zusammenhang mit der hohen Versickerungskapazität der Bodensubstrate der Buntsandsteinverwitterung, sowie dem verzögernden und puffernden Einfluss der Baumkronen auf das Niederschlagswasser, wurde eine signifikante Minderungswirkung auf die Oberflächenabflussbildung und ein ausgeprägtes räumliches und zeitliches Rückhaltepotential im Einzugsgebiet simuliert. Dabei wurde festgestellt, dass erhöhte Niederschlagsmengen, die die Versickerungskapazität der sandigen Böden übersteigen, zu einer kurz geschlossenen Abflussreaktion mit ausgeprägten Oberflächenabflussspitzen führen. Die Simulationen zeigten Wechselwirkungen zwischen Wald und Wasserkreislauf sowie die hydrologische Wirksamkeit des Klimawandels, verschlechterter Bodenfunktionen und altersbezogener Bestandesstrukturen im Zusammenhang mit Unterschieden in der Baumkronenausprägung. Zukunfts-Klimaprojektionen, die mit BIAS-bereinigten REKLIES- und EURO-CORDEX-Regionalklimamodellen (RCM) simuliert wurden, prognostizierten einen höheren Verdunstungsbedarf und eine Verlängerung der Vegetationsperiode bei gleichzeitig häufiger auftretenden Dürreperioden innerhalb der Vegetationszeit, was eine Verkürzung der Periode für die Grundwasserneubildung induzierte, und folglich zu einem prognostizierten Rückgang der Grundwasserneubildungsrate bis zur Mitte des Jahrhunderts führte. Aufgrund der starken Korrelation mit Niederschlagsintensitäten und der Dauer von Niederschlagsereignissen, bei allen Unsicherheiten in ihrer Vorhersage, wurde für die Oberflächenabflussgenese eine Steigerung bis zum Ende des Jahrhunderts prognostiziert.
Für die Simulation der Bodenverdichtung wurden die Trockenrohdichte des Bodens und die SCS Curve Number in SWAT+ gemäß Daten aus Befahrungsversuchen im Gebiet angepasst. Die günstigen Infiltrationsbedingungen und die relativ geringe Anfälligkeit für Bodenverdichtung der grobkörnigen Buntsandsteinverwitterung dominierten die hydrologischen Auswirkungen auf Wassereinzugsgebietsebene, sodass lediglich moderate Verschlechterungen wasserbezogener ÖSDL angezeigt wurden. Die Simulationen zeigten weiterhin einen deutlichen Einfluss der Bodenart auf die hydrologische Reaktion nach Bodenverdichtung auf Rückegassen und stützen damit die Annahme, dass die Anfälligkeit von Böden gegenüber Verdichtung mit dem Anteil an Schluff- und Tonbodenpartikeln zunimmt. Eine erhöhte Oberflächenabflussgenese ergab sich durch das Wegenetz im Gesamtgebiet.
Schadflächen mit Bestandesverjüngung wurden anhand eines artifiziellen Modells innerhalb eines Teileinzugsgebiets unter der Annahme von 3-jährigen Baumsetzlingen in einem Entwicklungszeitraum von 10 Jahren simuliert und hinsichtlich spezifischer Was-serhaushaltskomponenten mit Altbeständen (30 bis 80 Jahre) verglichen. Die Simulation ließ darauf schließen, dass bei fehlender Kronenüberschirmung die hydrologisch verzögernde Wirkung der Bestände beeinträchtigt wird, was die Entstehung von Oberflächenabfluss begünstigt und eine quantitativ geringfügig höhere Tiefensickerung fördert. Hydrologische Unterschiede zwischen dem geschlossenem Kronendach der Altbestände und Jungbeständen mit annähernden Freilandniederschlagsbedingungen wurden durch die dominierenden Faktoren atmosphärischer Verdunstungsanstoß, Niederschlagsmengen und Kronenüberschirmungsgrad bestimmt. Je weniger entwickelt das Kronendach von verjüngten Waldbeständen im Vergleich zu Altbeständen, je höher der atmosphärische Verdunstungsanstoß und je geringer die eingetragenen Niederschlagsmengen, desto größer war der hydrologische Unterschied zwischen den Bestandestypen.
Verbesserungsmaßnahmen für den dezentralen Hochwasserschutz sollten folglich kritische Bereiche für die Abflussbildung im Wald (CSA) berücksichtigen. Die hohe Sensibilität und Anfälligkeit der Wälder gegenüber Verschlechterungen der Ökosystembedingungen legen nahe, dass die Erhaltung des komplexen Gefüges und von intakten Wechselbeziehungen, insbesondere unter der gegebenen Herausforderung des Klimawandels, sorgfältig angepasste Schutzmaßnahmen, Anstrengungen bei der Identifizierung von CSA sowie die Erhaltung und Wiederherstellung der hydrologischen Kontinuität in Waldbeständen erfordern.

No Longer Printing the Legend: The Aporia of Heteronormativity in the American Western (1903-1969)
(2023)

This study critically investigates the U.S.-American Western and its construction of sexuality and gender, revealing that the heteronormative matrix that is upheld and defended in the genre is consistently preceded by the exploration of alternative sexualities and ways to think gender beyond the binary. The endeavor to naturalize heterosexuality seems to be baked in the formula of the U.S.-Western. However, as I show in this study, this endeavor relies on an aporia, because the U.S.-Western can only ever attempt to naturalize gender by constructing it first, hence inevitably and simultaneously construct evidence that supports the opposite: the unnaturalness and contingency of gender and sexuality.
My study relies on the works of Raewyn Connell, Pierre Bourdieu, and Judith Butler, and amalgamates in its methodology established approaches from film and literary studies (i.e., close readings) with a Foucaultian understanding of discourse and discourse analysis, which allows me to relate individual texts to cultural, socio-political and economical contexts that invariably informed the production and reception of any filmic text. In an analysis of 14 U.S.-Westerns (excluding three excursions) that appeared between 1903 and 1969 I give ample and minute narrative and film-aesthetical evidence to reveal the complex and contradictory construction of gender and sexuality in the U.S.-Western, aiming to reveal both the normative power of those categories and its structural instability and inconsistency.
This study proofs that the Western up until 1969 did not find a stable pattern to represent the gender binary. The U.S.-Western is not necessarily always looking to confirm or stabilize governing constructs of (gendered) power. However, it without fail explores and negotiates its legitimacy. Heterosexuality and male hegemony are never natural, self-evident, incontestable, or preordained. Quite conversely: the U.S.-Western repeatedly – and in a surprisingly diverse and versatile way – reveals the illogical constructedness of the heteronormative matrix.
My study therefore offers a fresh perspective on the genre and shows that the critical exploration and negotiation of the legitimacy of heteronormativity as a way to organize society is constitutive for the U.S.-Western. It is the inquiry – not necessarily the affirmation – of the legitimacy of this model that gives the U.S.-Western its ideological currency and significance as an artifact of U.S.-American popular culture.

Non-probability sampling is a topic of growing relevance, especially due to its occurrence in the context of new emerging data sources like web surveys and Big Data.
This thesis addresses statistical challenges arising from non-probability samples, where unknown or uncontrolled sampling mechanisms raise concerns in terms of data quality and representativity.
Various methods to quantify and reduce the potential selectivity and biases of non-probability samples in estimation and inference are discussed. The thesis introduces new forms of prediction and weighting methods, namely
a) semi-parametric artificial neural networks (ANNs) that integrate B-spline layers with optimal knot positioning in the general structure and fitting procedure of artificial neural networks, and
b) calibrated semi-parametric ANNs that determine weights for non-probability samples by integrating an ANN as response model with calibration constraints for totals, covariances and correlations.
Custom-made computational implementations are developed for fitting (calibrated) semi-parametric ANNs by means of stochastic gradient descent, BFGS and sequential quadratic programming algorithms.
The performance of all the discussed methods is evaluated and compared for a bandwidth of non-probability sampling scenarios in a Monte Carlo simulation study as well as an application to a real non-probability sample, the WageIndicator web survey.
Potentials and limitations of the different methods for dealing with the challenges of non-probability sampling under various circumstances are highlighted. It is shown that the best strategy for using non-probability samples heavily depends on the particular selection mechanism, research interest and available auxiliary information.
Nevertheless, the findings show that existing as well as newly proposed methods can be used to ease or even fully counterbalance the issues of non-probability samples and highlight the conditions under which this is possible.

Modern decision making in the digital age is highly driven by the massive amount of
data collected from different technologies and thus affects both individuals as well as
economic businesses. The benefit of using these data and turning them into knowledge
requires appropriate statistical models that describe the underlying observations well.
Imposing a certain parametric statistical model goes along with the need of finding
optimal parameters such that the model describes the data best. This often results in
challenging mathematical optimization problems with respect to the model’s parameters
which potentially involve covariance matrices. Positive definiteness of covariance matrices
is required for many advanced statistical models and these constraints must be imposed
for standard Euclidean nonlinear optimization methods which often results in a high
computational effort. As Riemannian optimization techniques proved efficient to handle
difficult matrix-valued geometric constraints, we consider optimization over the manifold
of positive definite matrices to estimate parameters of statistical models. The statistical
models treated in this thesis assume that the underlying data sets used for parameter
fitting have a clustering structure which results in complex optimization problems. This
motivates to use the intrinsic geometric structure of the parameter space. In this thesis,
we analyze the appropriateness of Riemannian optimization over the manifold of positive
definite matrices on two advanced statistical models. We establish important problem-
specific Riemannian characteristics of the two problems and demonstrate the importance
of exploiting the Riemannian geometry of covariance matrices based on numerical studies.

Survey data can be viewed as incomplete or partially missing from a variety of perspectives and there are different ways of dealing with this kind of data in the prediction and the estimation of economic quantities. In this thesis, we present two selected research contexts in which the prediction or estimation of economic quantities is examined under incomplete survey data.
These contexts are first the investigation of composite estimators in the German Microcensus (Chapters 3 and 4) and second extensions of multivariate Fay-Herriot (MFH) models (Chapters 5 and 6), which are applied to small area problems.
Composite estimators are estimation methods that take into account the sample overlap in rotating panel surveys such as the German Microcensus in order to stabilise the estimation of the statistics of interest (e.g. employment statistics). Due to the partial sample overlaps, information from previous samples is only available for some of the respondents, so the data are partially missing.
MFH models are model-based estimation methods that work with aggregated survey data in order to obtain more precise estimation results for small area problems compared to classical estimation methods. In these models, several variables of interest are modelled simultaneously. The survey estimates of these variables, which are used as input in the MFH models, are often partially missing. If the domains of interest are not explicitly accounted for in a sampling design, the sizes of the samples allocated to them can, by chance, be small. As a result, it can happen that either no estimates can be calculated at all or that the estimated values are not published by statistical offices because their variances are too large.

Coastal erosion describes the displacement of land caused by destructive sea waves,
currents or tides. Due to the global climate change and associated phenomena such as
melting polar ice caps and changing current patterns of the oceans, which result in rising
sea levels or increased current velocities, the need for countermeasures is continuously
increasing. Today, major efforts have been made to mitigate these effects using groins,
breakwaters and various other structures.
This thesis will find a novel approach to address this problem by applying shape optimization
on the obstacles. Due to this reason, results of this thesis always contain the
following three distinct aspects:
The selected wave propagation model, i.e. the modeling of wave propagation towards
the coastline, using various wave formulations, ranging from steady to unsteady descriptions,
described from the Lagrangian or Eulerian viewpoint with all its specialties. More
precisely, in the Eulerian setting is first a steady Helmholtz equation in the form of a
scattering problem investigated and followed subsequently by shallow water equations,
in classical form, equipped with porosity, sediment portability and further subtleties.
Secondly, in a Lagrangian framework the Lagrangian shallow water equations form the
center of interest.
The chosen discretization, i.e. dependent on the nature and peculiarity of the constraining
partial differential equation, we choose between finite elements in conjunction
with a continuous Galerkin and discontinuous Galerkin method for investigations in the
Eulerian description. In addition, the Lagrangian viewpoint offers itself for mesh-free,
particle-based discretizations, where smoothed particle hydrodynamics are used.
The method for shape optimization w.r.t. the obstacle’s shape over an appropriate
cost function, constrained by the solution of the selected wave-propagation model. In
this sense, we rely on a differentiate-then-discretize approach for free-form shape optimization
in the Eulerian set-up, and reverse the order in Lagrangian computations.

Behavioural traces from interactions with digital technologies are diverse and abundant. Yet, their capacity for theory-driven research is still to be constituted. In the present cumulative dissertation project, I deliberate the caveats and potentials of digital behavioural trace data in behavioural and social science research. One use case is online radicalisation research. The three studies included, set out to discern the state-of-the-art of methods and constructs employed in radicalization research, at the intersection of traditional methods and digital behavioural trace data. Firstly, I display, based on a systematic literature review of empirical work, the prevalence of digital behavioural trace data across different research strands and discern determinants and outcomes of radicalisation constructs. Secondly, I extract, based on this literature review, hypotheses and constructs and integrate them to a framework from network theory. This graph of hypotheses, in turn, makes the relative importance of theoretical considerations explicit. One implication of visualising the assumptions in the field is to systematise bottlenecks for the analysis of digital behavioural trace data and to provide the grounds for the genesis of new hypotheses. Thirdly, I provide a proof-of-concept for incorporating a theoretical framework from conspiracy theory research (as a specific form of radicalisation) and digital behavioural traces. I argue for marrying theoretical assumptions derived from temporal signals of posting behaviour and semantic meaning from textual content that rests on a framework from evolutionary psychology. In the light of these findings, I conclude by discussing important potential biases at different stages in the research cycle and practical implications.

Issues in Price Measurement
(2022)

This thesis focuses on the issues in price measurement and consists of three chapters. Due to outdated weighting information, a Laspeyres-based consumer price index (CPI) is prone to accumulating upward bias. Therefore, chapter 1 introduces and examines simple and transparent revision approaches that retrospectively address the source of the bias. They provide a consistent long-run time series of the CPI and require no additional information. Furthermore, a coherent decomposition of the bias into the contributions of individual product groups is developed. In a case study, the approaches are applied to a Laspeyres-based CPI. The empirical results confirm the theoretical predictions. The proposed revision approaches are adoptable not only to most national CPIs but also to other price-level measures such as the producer price index or the import and export price indices.
Chapter 2 is dedicated to the measurement of import and export price indices. Such indices are complicated by the impact of exchange rates. These indices are usually also compiled by some Laspeyres type index. Therefore, substitution bias is an issue. The terms of trade (ratio of export and import price index) are therefore also likely to be distorted. The underlying substitution bias accumulates over time. The present article applies a simple and transparent retroactive correction approach that addresses the source of the substitution bias and produces meaningful long-run time series of import and export price levels and, therefore, of the terms of trade. Furthermore, an empirical case study is conducted that demonstrates the efficacy and versatility of the correction approach.
Chapter 3 leaves the field of index revision and studies another issue in price measurement, namely, the economic evaluation of digital products in monetary terms that have zero market prices. This chapter explores different methods of economic valuation and pricing of free digital products and proposes an alternative way to calculate the economic value and a shadow price of free digital products: the Usage Cost Model (UCM). The goal of the chapter is, first of all, to formulate a theoretical framework and incorporate an alternative measure of the value of free digital products. However, an empirical application is also made to show the work of the theoretical model. Some conclusions on applicability are drawn at the end of the chapter.

Broadcast media such as television have spread rapidly worldwide in the last century. They provide viewers with access to new information and also represent a source of entertainment that unconsciously exposes them to different social norms and moral values. Although the potential impact of exposure to television content have been studied intensively in economic research in recent years, studies examining the long-term causal effects of media exposure are still rare. Therefore, Chapters 2 to 4 of this thesis contribute to the better understanding of long-term effects of television exposure.
Chapter 2 empirically investigates whether access to reliable environmental information through television can influence individuals' environmental awareness and pro-environmental behavior. Analyzing exogenous variation in Western television reception in the German Democratic Republic shows that access to objective reporting on environmental pollution can enhance concerns regarding pollution and affect the likelihood of being active in environmental interest groups.
Chapter 3 utilizes the same natural experiment and explores the relationship between exposure to foreign mass media content and xenophobia. In contrast to the state television broadcaster in the German Democratic Republic, West German television regularly confronted its viewers with foreign (non-German) broadcasts. By applying multiple measures for xenophobic attitudes, our findings indicate a persistent mitigating impact of foreign media content on xenophobia.
Chapter 4 deals with another unique feature of West German television. In contrast to East German media, Western television programs regularly exposed their audience to unmarried and childless characters. The results suggest that exposure to different gender stereotypes contained in television programs can affect marriage, divorce, and birth rates. However, our findings indicate that mainly women were affected by the exposure to unmarried and childless characters.
Chapter 5 examines the influence of social media marketing on crowd participation in equity crowdfunding. By analyzing 26,883 investment decisions on three German equity crowdfunding platforms, our results show that startups can influence the success of their equity crowdfunding campaign through social media posts on Facebook and Twitter.
In Chapter 6, we incorporate the concept of habit formation into the theoretical literature on trade unions and contribute to a better understanding of how internal habit preferences influence trade union behavior. The results reveal that such internal reference points lead trade unions to raise wages over time, which in turn reduces employment. Conducting a numerical example illustrates that the wage effects and the decline in employment can be substantial.

Stress gilt als zentrales Gesundheitsrisiko des 21. Jahrhunderts und wird in der Forschung als multidimensionales Konstrukt auf psychologischer und biologischer Ebene untersucht. Wäh-rend die subjektive Wahrnehmung von Stress nicht mit der biologischen Stressreaktivität zu-sammenhängen muss, ist der negative Einfluss stressassoziierter biologischer Prozesse auf Wohlbefinden und Gesundheit gut belegt. Bereits im Grundschulalter zeigen Kinder eine mit Erwachsenen vergleichbare Stressbelastung und gesundheitliche Folgen, Bewältigungsstrategien sind in diesem Alter allerdings noch nicht vollständig entwickelt. Präventionsprogramme im Grundschulalter sollen Kinder in ihren sich entwickelnden Stressbewältigungsfähigkeiten fördern, wobei sowohl emotionsfokussierte und problemorientierte Ansätze als auch soziale Unterstützung wichtige Faktoren darstellen könnten.
Das einleitende Literatur-Review evaluiert bisherige Stresspräventionsstudien und verdeutlicht, dass zwar die Wirksamkeit und Anwendbarkeit von mehrfaktoriellen Stresspräventionsprogrammen im Rahmen psychometrischer Erhebungen gezeigt werden konnten, biologische Prozesse in der Forschung bisher allerdings nicht erhoben und außer Acht gelassen wurden.
Die empirische Untersuchung in Studie 1 zeigt, dass eine multidimensionale psychobiologische Betrachtungsweise sinnvoll ist, indem sowohl die Psychometrie, als auch psychobiologische Prozesse der Stressreaktion miteinbezogen und die Auswirkungen von Stressprävention auf den verschiedenen Ebenen untersucht wurden. Zwei Kurzinterventionen wurden dazu miteinander verglichen und ihre Wirkung auf psychophysiologischen Ebenen (z.B. Kortisol, α-Amylase und Herzrate) in einem Prä-Post Design geprüft. Eine statistisch signifikante Abnahme psychophysiologischer Stressreaktivität, sowie stressassoziierter psychologischer Symptome verdeutlichte die multidimensionale Wirksamkeit von Stressmanagementtrainings.
Studie 2 wurde im Rahmen der Covid-19-Pandemie entworfen. Die in Studie 1 trainierten Kinder wurden mittels Online-Fragebogenerhebung mit einer Kontrollgruppe hinsichtlich ihrer Stressbelastung verglichen. Die Ergebnisse zeigten eine geringere Belastung und vermehrte günstige Bewältigungsstrategien trainierter Kinder im Vergleich zur Kontrollgruppe.
Diese Ergebnisse heben die Relevanz einer multidimensionalen Betrachtung kindlichen Stresses hervor. Es wurde gezeigt, dass Stresspräventionsprogramme auf den unterschiedlichen Ebenen der Stressreaktion wirken und sogar in gesamtgesellschaftlichen Krisensituationen stresspro-tektiv wirken können. Zukünftige Studien sollten Stresspräventionen im Grundschulalter psychophysiologisch evaluieren und deren Wirkung in Längsschnittstudien beurteilen, um das Verständnis der zugrundeliegenden Mechanismen zu verbessern.

Die endemischen Arganbestände in Südmarokko sind die Quelle des wertvollen Arganöls, sind aber durch bspw. Überweidung oder illegale Feuerholzgewinnung stark übernutzt. Aufforstungsmaßnahmen sind vorhanden, sind aber aufgrund von zu kurz angelegten Bewässerungs- und Schutzverträgen häufig nicht erfolgreich. Das Aufkommen von Neuwuchs ist durch das beinahe restlose Sammeln von Kernen kaum möglich, durch Fällen oder Absterben von Bäumen verringert sich die kronenüberdeckte Fläche und unbedeckte Flächen zwischen den Bäumen nehmen zu.
Die Entwicklung der Arganbestände wurde über den Zeitraum von 1972 und 2018 mit historischen und aktuellen Satellitenbildern untersucht, ein Großteil der Bäume hat sich in dieser Zeit kaum verändert. Zustandsaufnahmen von 2018 zeigten, dass viele dieser Bäume durch Überweidung und Abholzung nur als Sträucher wachsen und so in degradiertem Zustand stabil sind.
Trotz der Degradierung einiger Bäume zeigt sich, dass der Boden unter den Bäumen die höchsten Gehalte an organischer Bodensubstanz und Nährstoffen auf den Flächen aufweist, zwischen zwei Bäumen sind die Gehalte am niedrigsten. Der Einfluss des Baumes auf den Boden geht über die Krone hinaus in Richtung Norden durch Beschattung in der Mittagssonne, Osten durch Windverwehung von Streu und Bodenpartikeln und hangabwärts durch Verspülung von Material.
Über experimentelle Methoden unter und zwischen den Arganbäumen wurden Erkenntnisse zur Bodenerosion gewonnen. Die hydraulische Leitfähigkeit unter Bäumen ist um den Faktor 1,2-1,5 höher als zwischen den Bäumen, Oberflächenabflüsse und Bodenabträge sind unter den Bäumen etwas niedriger, bei degradierten Bäumen ähnlich den Bereichen zwischen den Bäumen. Die unterschiedlichen Flächenbeschaffenheiten wurden mit einem Windkanal untersucht und zeigten, dass gerade frisch gepflügte Flächen hohe Windemissionen verursachen, während Flächen mit hoher Steinbedeckung kaum von Winderosion betroffen sind.
Die Oberflächenabflüsse von den unterschiedlichen Flächentypen werden in die Vorfluter abgeleitet. Die Sedimentdynamik in diesen Wadis wird hauptsächlich von Niederschlag zwischen den Messungen, Einzugsgebiet und Wadilänge und kaum von den verschiedenen Landnutzungen beeinflusst.
Das Landschaftssystem Argan konnte über diesen Multi-Methodenansatz auf verschiedenen Ebenen analysiert werden.

Climate fluctuations and the pyroclastic depositions from volcanic activity both influence ecosystem functioning and biogeochemical cycling in terrestrial and marine environments globally. These controlling factors are crucial for the evolution and fate of the pristine but fragile fjord ecosystem in the Magellanic moorlands (~53°S) of southernmost Patagonia, which is considered a critical hotspot for organic carbon burial and marine bioproductivity. At this active continental margin in the core zone of the southern westerly wind belt (SWW), frequent Plinian eruptions and the extremely variable, hyper-humid climate should have efficiently shaped ecosystem functioning and land-to-fjord mass transfer throughout the Late Holocene. However, a better understanding of the complex process network defining the biogeochemical cycling at this land-to-fjord continuum principally requires a detailed knowledge of substrate weathering and pedogenesis in the context of the extreme climate. Yet, research on soils, the ubiquitous presence of tephra and the associated chemical weathering, secondary mineral (trans)formation and organic matter (OM) turnover processes is rare in this remote region. This complicates an accurate reconstruction of the ecosystem´s potentially sensitive response to past environmental impacts, including the dynamics of Late Holocene land-to-fjord fluxes as a function of volcanic activity and strong hydroclimate variability.
Against this background, this PhD thesis aims to disentangle the controlling factors that modulate the terrigenous element mobilization and export mechanisms in the hyper-humid Patagonian Andes and assesses their significance for fjord primary productivity over the past 4.5 kyrs BP. For the first time, distinct biogeochemical characteristics of the regional weathering system serve as major criterion in paleoenvironmental reconstruction in the area. This approach includes broad-scale mineralogical and geochemical analyses of basement lithologies, four soil profiles, volcanic ash deposits, the non-karst stalagmite MA1 and two lacustrine sediment cores. In order to pay special attention to the possibly important temporal variations of pedosphere-atmosphere interaction and ecological consequences initiated by volcanic eruptions, the novel data were evaluated together with previously published reconstructions of paleoclimate and paleoenvironmental conditions.
The devastative high-tephra loading of a single eruption from Mt. Burney volcano (MB2 at 4.216 kyrs BP) sustainably transformed this vulnerable fjord ecosystem, while acidic peaty Andosols developed from ~2.5 kyrs BP onwards after the recovery from millennium-scale acidification. The special setting is dominated by most variable redox-pH conditions, profound volcanic ash weathering and intense OM turnover processes, which are closely linked and ultimately regulated by SWW-induced water-level fluctuations. Constant nutrient supply though sea spray deposition represents a further important control on peat accumulation and OM turnover dynamics. These extreme environmental conditions constrain the biogeochemical framework for an extended land-to-fjord export of leachates comprising various organic and inorganic colloids (i.e., Al-humus complexes and Fe-(hydr)oxides). Such tephra- and/or Andosol-sourced flux contains high proportions of terrigenous organic carbon (OCterr) and mobilized essential (micro)nutrients, e.g., bio-available Fe, that are beneficial for fjord bioproductivity. It can be assumed that this supply of bio-available Fe produced by specific Fe-(hydr)oxide (trans)formation processes from tephra components may outlast more than 6 kyrs and surpasses the contribution from basement rock weathering and glacial meltwaters. However, the land-to-fjord exports of OCterr and bio-available Fe occur mostly asynchronous and are determined by the frequency and duration of redox cycles in soils or are initiated by SWW-induced extreme weather events.
The verification of (crypto)tephra layers embedded stalagmite MA1 enabled the accurate dating of three smaller Late Holocene eruptions from Mt. Burney (MB3 at 2.291 kyrs BP and MB4 at 0.853 kyrs BP) and Aguilera (A1 at 2.978 kyrs BP) volcanoes. Irrespective of the improvement of the regional tephrochronology, the obtained precise 230Th/U-ages allowed constraints on the ecological consequences caused by these Plinian eruptions. The deposition of these thin tephra layers should have entailed a very beneficial short-term stimulation of fjord bioproductivity with bio-available Fe and other (micro)nutrients, which affected the entire area between 52°S and 53°S 30´, respectively. For such beneficial effects, the thickness of tephra deposited to this highly vulnerable peatland ecosystem should be below a threshold of 1 cm.
The Late Holocene element mobilization and land-to-fjord transport was mainly controlled by (i) volcanic activity and tephra thickness, (ii) SWW-induced and southern hemispheric climate variability and (iii) the current state of the ecosystem. The influence of cascading climate and environmental impacts on OCterr and Fe-(hydr)oxide fluxes to can be categorized by four individual, in part overlapping scenarios. These different scenarios take into account the previously specified fundamental biogeochemical mechanisms and define frequently recurring patterns of ecosystem feedbacks governing the land-to-fjord mass transfer in the hyper-humid Patagonian Andes on the centennial-scale. This PhD thesis provides first evidence for a primarily tephra-sourced, continuous and long-lasting (micro)nutrient fertilization for phytoplankton growth in South Patagonian fjords, which is ultimately modulated by variations in SWW-intensity. It highlights the climate sensitivity of such critical land-to-fjord element transport and particularly emphasizes the important but so far underappreciated significance of volcanic ash inputs for biogeochemical cycles at active continental margins.

Let K be a compact subset of the complex plane. Then the family of polynomials P is dense in A(K), the space of all continuous functions on K that are holomorphic on the interior of K, endowed with the uniform norm, if and only if the complement of K is connected. This is the statement of Mergelyan's celebrated theorem.
There are, however, situations where not all polynomials are required to approximate every f ϵ A(K) but where there are strict subspaces of P that are still dense in A(K). If, for example, K is a singleton, then the subspace of all constant polynomials is dense in A(K). On the other hand, if 0 is an interior point of K, then no strict subspace of P can be dense in A(K).
In between these extreme cases, the situation is much more complicated. It turns out that it is mostly determined by the geometry of K and its location in the complex plane which subspaces of P are dense in A(K). In Chapter 1, we give an overview of the known results.
Our first main theorem, which we will give in Chapter 3, deals with the case where the origin is not an interior point of K. We will show that if K is a compact set with connected complement and if 0 is not an interior point of K, then any subspace Q ⊂ P which contains the constant functions and all but finitely many monomials is dense in A(K).
There is a close connection between lacunary approximation and the theory of universality. At the end of Chapter 3, we will illustrate this connection by applying the above result to prove the existence of certain universal power series. To be specific, if K is a compact set with connected complement, if 0 is a boundary point of K and if A_0(K) denotes the subspace of A(K) of those functions that satisfy f(0) = 0, then there exists an A_0(K)-universal formal power series s, where A_0(K)-universal means that the family of partial sums of s forms a dense subset of A_0(K).
In addition, we will show that no formal power series is simultaneously universal for all such K.
The condition on the subspace Q in the main result of Chapter 3 is quite restrictive, but this should not be too surprising: The result applies to the largest possible class of compact sets.
In Chapter 4, we impose a further restriction on the compact sets under consideration, and this will allow us to weaken the condition on the subspace Q. The result that we are going to give is similar to one of those presented in the first chapter, namely the one due to Anderson. In his article “Müntz-Szasz type approximation and the angular growth of lacunary integral functions”, he gives a criterion for a subspace Q of P to be dense in A(K) where K is entirely contained in some closed sector with vertex at the origin.
We will consider compact sets with connected complement that are -- with the possible exception of the origin -- entirely contained in some open sector with vertex at the origin. What we are going to show is that if K\{0} is contained in an open sector of opening angle 2α and if Λ is some subset of the nonnegative integers, then the span of {z → z^λ : λ ϵ Λ} is dense in A(K) whenever 0 ϵ Λ and some Müntz-type condition is satisfied.
Conversely, we will show that if a similar condition is not satisfied, then we can always find a compact set K with connected complement such that K\{0} is contained in some open sector of opening angle 2α and such that the span of {z → z^λ : λ ϵ Λ} fails to be dense in A(K).

The present dissertation was developed to emphasize the importance of self-regulatory abilities and to derive novel opportunities to empower self-regulation. From the perspective of PSI (Personality Systems Interactions) theory (Kuhl, 2001), interindividual differences in self-regulation (action vs. state orientation) and their underlying mechanisms are examined in detail. Based on these insights, target-oriented interventions are derived, developed, and scientifically evaluated. The present work comprises a total of four studies which, on the one hand, highlight the advantages of a good self-regulation (e.g., enacting difficult intentions under demands; relation with prosocial power motive enactment and well-being). On the other hand, mental contrasting (Oettingen et al., 2001), an established self-regulation method, is examined from a PSI perspective and evaluated as a method to support individuals that struggle with self-regulatory deficits. Further, derived from PSI theory`s assumptions, I developed and evaluated a novel method (affective shifting) that aims to support individuals in overcoming self-regulatory deficits. Thereby affective shifting supports the decisive changes in positive affect for successful intention enactment (Baumann & Scheffer, 2010). The results of the present dissertation show that self-regulated changes between high and low positive affect are crucial for efficient intention enactment and that methods such as mental contrasting and affective shifting can empower self-regulation to support individuals to successfully close the gap between intention and action.