Differential equations yield solutions that necessarily contain a certain amount of regularity and are based on local interactions. There are various natural phenomena that are not well described by local models. An important class of models that describe long-range interactions are the so-called nonlocal models, which are the subject of this work. The nonlocal operators considered here are integral operators with a finite range of interaction and the resulting models can be applied to anomalous diffusion, mechanics and multiscale problems. While the range of applications is vast, the applicability of nonlocal models can face problems such as the high computational and algorithmic complexity of fundamental tasks. One of them is the assembly of finite element discretizations of truncated, nonlocal operators. The first contribution of this thesis is therefore an openly accessible, documented Python code which allows to compute finite element approximations for nonlocal convection-diffusion problems with truncated interaction horizon. Another difficulty in the solution of nonlocal problems is that the discrete systems may be ill-conditioned which complicates the application of iterative solvers. Thus, the second contribution of this work is the construction and study of a domain decomposition type solver that is inspired by substructuring methods for differential equations. The numerical results are based on the abstract framework of nonlocal subdivisions which is introduced here and which can serve as a guideline for general nonlocal domain decomposition methods.

Left ventricular assist devices (LVADs) have become a valuable treatment for patients with advanced heart failure. Women appear to be disadvantaged in the usage of LVADs and concerning clinical outcomes such as death and adverse events after LVAD implant. Contrary to typical clinical characteristics (e.g., disease severity), device-related factors such as the intended device strategy, bridge to a heart transplantation or destination therapy, are often not considered in research on gender differences. In addition, the relevance of pre-implant psychosocial risk factors, such as substance abuse and limited social support, for LVAD outcomes is currently unclear. Thus, the aim of this dissertation is to explore the role of pre-implant psychosocial risk factors for gender differences in clinical outcomes, accounting for clinical and device-related risk factors. In the first article, gender differences in pre-implant characteristics of patients registered in The European Registry for Patients with Mechanical Circulatory Support (EUROMACS) were investigated. It was found that women and men differed in multiple pre-implant characteristics depending on device strategy. In the second article, gender differences in major clinical outcomes (i.e., death, heart transplant, device explant due to cardiac recovery, device replacement due to complications) were evaluated for patients in the device strategy destination therapy in the Interagency Registry for Mechanically Assisted Circulation (INTERMACS). Additionally, the association of gender and psychosocial risk factors with the major outcomes were analyzed. Women had similar probabilities to die on LVAD support, and even higher probabilities to experience explant of the device due to cardiac recovery compared with men in the destination therapy subgroup. Pre-implant psychosocial risk factors were not associated with major outcomes. The third article focused on gender differences in 10 adverse events (e.g., device malfunction, bleeding) after LVAD implant in INTERMACS. The association of a psychosocial risk indicator with gender and adverse events after LVAD implantation was evaluated. Women were less likely to have psychosocial risk pre-implant but more likely to experience seven out of 10 adverse events compared with men. Pre-implant psychosocial risk was associated with adverse events, even suggesting a dose response-relationship. These associations appeared to be more pronounced in women. In conclusion, women appear to have similar survival to men when accounting for device strategy. They have higher probabilities of recovery, but higher probabilities of device replacement and adverse events compared with men. Regarding these adverse events, women may be more susceptible to psychosocial risk factors than men. The results of this dissertation illustrate the importance of gender-sensitive research and suggest considering device strategy when studying gender differences in LVAD recipients. Further research is warranted to elucidate the role of specific psychosocial risk factors that lead to higher probabilities of adverse events, to intervene early and improve patient care in both, women and men

Sozialunternehmen haben mindestens zwei Ziele: die Erfüllung ihrer sozialen bzw. ökologischen Mission und finanzielle Ziele. Zwischen diesen Zielen können Spannungen entstehen. Wenn sie sich in diesem Spannungsfeld wiederholt zugunsten der finanziellen Ziele entscheiden, kommt es zum Mission Drift. Die Priorisierung der finanziellen Ziele überlagert dabei die soziale Mission. Auch wenn das Phänomen in der Praxis mehrfach beobachtet und in Einzelfallanalysen beschrieben wurde, gibt es bislang wenig Forschung zu Mission Drift. Der Fokus der vorliegenden Arbeit liegt darauf, diese Forschungslücke zu schließen und eigene Erkenntnisse für die Auslöser und Treiber des Mission Drifts von Sozialunternehmen zu ermitteln. Ein Augenmerk liegt auf den verhaltensökonomischen Theorien und der Mixed-Gamble-Logik. Dieser Logik zufolge liegt bei Entscheidungen immer eine Gleichzeitigkeit von Gewinnen und Verlusten vor, sodass Entscheidungsträger die Furcht vor Verlusten gegenüber der Aussicht auf Gewinne abwägen müssen. Das Modell wird genutzt, um eine neue theoretische Betrachtungsweise auf die Abwägung zwischen sozialen und finanziellen Zielen bzw. Mission Drift zu erhalten. Mit einem Conjoint Experiment werden Daten über das Entscheidungsverhalten von Sozialunternehmern generiert. Im Zentrum steht die Abwägung zwischen sozialen und finanziellen Zielen in verschiedenen Szenarien (Krisen- und Wachstumssituationen). Mithilfe einer eigens erstellten Stichprobe von 1.222 Sozialunternehmen aus Deutschland, Österreich und der Schweiz wurden 187 Teilnehmende für die Studie gewonnen. Die Ergebnisse dieser Arbeit zeigen, dass eine Krisensituation Auslöser für Mission Drift von Sozialunternehmen sein kann, weil in diesem Szenario den finanziellen Zielen die größte Bedeutung zugemessen wird. Für eine Wachstumssituation konnten hingegen keine solche Belege gefunden werden. Hinzu kommen weitere Einflussfaktoren, welche die finanzielle Orientierung verstärken können, nämlich die Gründeridentitäten der Sozialunternehmer, eine hohe Innovativität der Unternehmen und bestimmte Stakeholder. Die Arbeit schließt mit einer ausführlichen Diskussion der Ergebnisse. Es werden Empfehlungen gegeben, wie Sozialunternehmen ihren Zielen bestmöglich treu bleiben können. Außerdem werden die Limitationen der Studie und Wege für zukünftige Forschung im Bereich Mission Drift aufgezeigt.

Data fusions are becoming increasingly relevant in official statistics. The aim of a data fusion is to combine two or more data sources using statistical methods in order to be able to analyse different characteristics that were not jointly observed in one data source. Record linkage of official data sources using unique identifiers is often not possible due to methodological and legal restrictions. Appropriate data fusion methods are therefore of central importance in order to use the diverse data sources of official statistics more effectively and to be able to jointly analyse different characteristics. However, the literature lacks comprehensive evaluations of which fusion approaches provide promising results for which data constellations. Therefore, the central aim of this thesis is to evaluate a concrete plethora of possible fusion algorithms, which includes classical imputation approaches as well as statistical and machine learning methods, in selected data constellations. To specify and identify these data contexts, data and imputation-related scenario types of a data fusion are introduced: Explicit scenarios, implicit scenarios and imputation scenarios. From these three scenario types, fusion scenarios that are particularly relevant for official statistics are selected as the basis for the simulations and evaluations. The explicit scenarios are the fulfilment or violation of the Conditional Independence Assumption (CIA) and varying sample sizes of the data to be matched. Both aspects are likely to have a direct, that is, explicit, effect on the performance of different fusion methods. The summed sample size of the data sources to be fused and the scale level of the variable to be imputed are considered as implicit scenarios. Both aspects suggest or exclude the applicability of certain fusion methods due to the nature of the data. The univariate or simultaneous, multivariate imputation solution and the imputation of artificially generated or previously observed values in the case of metric characteristics serve as imputation scenarios. With regard to the concrete plethora of possible fusion algorithms, three classical imputation approaches are considered: Distance Hot Deck (DHD), the Regression Model (RM) and Predictive Mean Matching (PMM). With Decision Trees (DT) and Random Forest (RF), two prominent tree-based methods from the field of statistical learning are discussed in the context of data fusion. However, such prediction methods aim to predict individual values as accurately as possible, which can clash with the primary objective of data fusion, namely the reproduction of joint distributions. In addition, DT and RF only comprise univariate imputation solutions and, in the case of metric variables, artificially generated values are imputed instead of real observed values. Therefore, Predictive Value Matching (PVM) is introduced as a new, statistical learning-based nearest neighbour method, which could overcome the distributional disadvantages of DT and RF, offers a univariate and multivariate imputation solution and, in addition, imputes real and previously observed values for metric characteristics. All prediction methods can form the basis of the new PVM approach. In this thesis, PVM based on Decision Trees (PVM-DT) and Random Forest (PVM-RF) is considered. The underlying fusion methods are investigated in comprehensive simulations and evaluations. The evaluation of the various data fusion techniques focusses on the selected fusion scenarios. The basis for this is formed by two concrete and current use cases of data fusion in official statistics, the fusion of EU-SILC and the Household Budget Survey on the one hand and of the Tax Statistics and the Microcensus on the other. Both use cases show significant differences with regard to different fusion scenarios and thus serve the purpose of covering a variety of data constellations. Simulation designs are developed from both use cases, whereby the explicit scenarios in particular are incorporated into the simulations. The results show that PVM-RF in particular is a promising and universal fusion approach under compliance with the CIA. This is because PVM-RF provides satisfactory results for both categorical and metric variables to be imputed and also offers a univariate and multivariate imputation solution, regardless of the scale level. PMM also represents an adequate fusion method, but only in relation to metric characteristics. The results also imply that the application of statistical learning methods is both an opportunity and a risk. In the case of CIA violation, potential correlation-related exaggeration effects of DT and RF, and in some cases also of RM, can be useful. In contrast, the other methods induce poor results if the CIA is violated. However, if the CIA is fulfilled, there is a risk that the prediction methods RM, DT and RF will overestimate correlations. The size ratios of the studies to be fused in turn have a rather minor influence on the performance of fusion methods. This is an important indication that the larger dataset does not necessarily have to serve as a donor study, as was previously the case. The results of the simulations and evaluations provide concrete implications as to which data fusion methods should be used and considered under the selected data and imputation constellations. Science in general and official statistics in particular benefit from these implications. This is because they provide important indications for future data fusion projects in order to assess which specific data fusion method could provide adequate results along the data constellations analysed in this thesis. Furthermore, with PVM this thesis offers a promising methodological innovation for future data fusions and for imputation problems in general.

Visualizing brain simulation data is in many aspects a challenging task. For one, data used in brain simulations and the resulting datasets is heterogeneous and insight is derived by relating all different kinds of it. Second, the analysis process is rapidly changing while creating hypotheses about the results. Third, the scale of data entities in these heterogeneous datasets is manifold, reaching from single neurons to brain areas interconnecting millions. Fourth, the heterogeneous data consists of a variety of modalities, e.g.: from time series data to connectivity data, from single parameters to a set of parameters spanning parameter spaces with multiple possible and biological meaningful solutions; from geometrical data to hierarchies and textual descriptions, all on mostly different scales. Fifth, visualizing includes finding suitable representations and providing real-time interaction while supporting varying analysis workflows. To this end, this thesis presents a scalable and flexible software architecture for visualizing, integrating and interacting with brain simulations data. The scalability and flexibility is achieved by interconnected services forming in a series of Coordinated Multiple View (CMV) systems. Multiple use cases are presented, introducing views leveraging this architecture, extending its ecosystem and resulting in a Problem Solving Environment (PSE) from which custom-tailored CMV systems can be build. The construction of such CMV system is assisted by semantic reasoning hence the term semantic-aware CMVs.

In machine learning, classification is the task of predicting a label for each point within a data set. When the class of each point in the labeled subset is already known, this information is used to recognize patterns and make predictions about the points in the remainder of the set, referred to as the unlabeled set. This scenario falls in the field of supervised learning. However, the number of labeled points can be restricted, because, e.g., it is expensive to obtain this information. Besides, this subset may be biased, such as in the case of self-selection in a survey. Consequently, the classification performance for unlabeled points may be limited. To improve the reliability of the results, semi-supervised learning tackles the setting of labeled and unlabeled data. Moreover, in many cases, additional information about the size of each class can be available from undisclosed sources. This cumulative thesis presents different studies to combine this external cardinality constraint information within three important algorithms for binary classification in the supervised context: support vector machines (SVM), classification trees, and random forests. From a mathematical point of view, we focus on mixed-integer programming (MIP) models for semi-supervised approaches that consider a cardinality constraint for each class for each algorithm. Furthermore, since the proposed MIP models are computationally challenging, we also present techniques that simplify the process of solving these problems. In the SVM setting, we introduce a re-clustering method and further computational techniques to reduce the computational cost. In the context of classification trees, we provide correct values for certain bounds that play a crucial role for the solver performance. For the random forest model, we develop preprocessing techniques and an intuitive branching rule to reduce the solution time. For all three methods, our numerical results show that our approaches have better statistical performances for biased samples than the standard approach.

In bilevel optimization, some of the variables of an optimization problem have to be an optimal solution to another nested optimization problem. This specific structure renders bilevel optimization a powerful tool for modeling hierarchical decision-making processes, which arise in various real-world applications such as in critical infrastructure defense, transportation, or energy. Due to their nested structure, however, bilevel problems are also inherently hard to solve—both in theory and in practice. Further challenges arise if, e.g., bilevel problems under uncertainty are considered. In this dissertation, we address different types of uncertainties in bilevel optimization using techniques from robust optimization. We study mixed-integer linear bilevel problems with lower-level objective uncertainty, which we tackle using the notion of Gamma-robustness. We present two exact branch-and-cut approaches to solve these Gamma-robust bilevel problems, along with cuts tailored to the important class of monotone interdiction problems. Given the overall hardness of the considered problems, we additionally propose heuristic approaches for mixed-integer, linear, and Gamma-robust bilevel problems. The latter rely on solving a linear number of deterministic bilevel problems so that no problem-specific tailoring is required. We assess the performance of both the exact and the heuristic approaches through extensive computational studies. In addition, we study the problem of determining optimal tolls in a traffic network in which the network users hedge against uncertain travel costs in a robust way. The overall toll-setting problem can be seen as a single-leader multi-follower problem with multiple robustified followers. We model this setting as a mathematical problem with equilibrium constraints, for which we present a mixed-integer, nonlinear, and nonconvex reformulation that can be tackled using state-of-the-art general-purpose solvers. We further illustrate the impact of considering robustified followers on the toll-setting policies through a case study. Finally, we highlight that the sources of uncertainty in bilevel optimization are much richer compared to single-level optimization. To this end, we study two aspects related to so-called decision uncertainty. First, we propose a strictly robust approach in which the follower hedges against erroneous observations of the leader's decision. Second, we consider an exemplary bilevel problem with a continuous but nonconvex lower level in which algorithmic necessities prevent the follower from making a globally optimal decision in an exact sense. The example illustrates that even very small deviations in the follower's decision may lead to arbitrarily large discrepancies between exact and computationally obtained bilevel solutions.

Veterinärantibiotika werden weltweit in großem Umfang zur Behandlung von Tierkrankheiten eingesetzt. Aufgrund der schlechten Resorption der Mittel im Darm der Tiere gelangen sie zum Großteil unverändert über Ausscheidungen auf landwirtschaftliche Nutzflächen. Dort können sie von Nichtzielorganismen, wie Gefäßpflanzen, aufgenommen werden und deren frühe Entwicklung bedrohen. In diesem Kontext wurde bisher vor allem der Einfluss auf Kulturpflanzen untersucht, während Wildpflanzenarten des ökologisch bedeutsamen Kulturgraslandes, die vor allem durch Gülleausbringung in Kontakt mit Antibiotikastoffen kommen, deutlich weniger fokussiert wurden. Deshalb wurde in dieser Arbeit der Einfluss realistischer Konzentrationen (0,1 - 20 mg/L) zweier häufig verwendeter Veterinärantibiotika, Tetracyclin und Sulfamethazin, auf die Keimung und das frühe Wachstum von typischen Arten des temperaten Kulturgraslandes untersucht. Da in der Natur oft mehrere Stressoren gleichzeitig auf einen Organismus einwirken, wurden auch zwei Multistressszenarien, nämlich Pharmazeutikamischungen und das Zusammenspiel von pharmazeutischem Wirkstoff mit abiotischen Bedingungen (Trockenstress) untersucht. In vier Themenblöcken wurden sowohl standardisierte Laborversuche als auch naturnähere Topf- und Feldversuche durchgeführt. Die Ergebnisse zeigten, dass sowohl die Keimung als auch das frühe Wachstum durch beide Wirkstoffe, jedoch häufiger durch Tetracyclin, beeinträchtigt wurden. Während die Keimung uneinheitlich in Bezug auf die Effektrichtung beeinflusst wurde, zeigte sich eine starke, antibiotika- und konzentrationsabhängige Reduktion der Wurzellänge vor allem durch Tetracyclin, in den Petrischalenversuchen (20 mg/L bis 96 %, bei Dactylis glomerata). Das oberirdische Wachstum (Blattlänge, Wuchshöhe, Biomasse) wurde geringer beinflusst, und dabei oft wachstumsfördernd. In der gesamten Arbeit zeigten sich immer wieder Hormesis- Effekte, d.h. geringe Konzentrationen, die stimulierend wirkten, während höhere Konzentrationen toxisch wirkten. Die betrachteten Kombinationen verschiedener Faktoren führten entgegen der Erwartung nicht eindeutig zu stärkeren oder alleinigen Einflüssen. In einzelnen Fällen zeigten sich solche Muster, jedoch wurden auch Verluste von Einzeleffekten bei den Kombinationen beobachtet oder Einzeleffekte, die sich dort erneut abbildeten. Es zeigten sich, wenn auch uneinheitlich, signifikante Einflüsse auf die frühen Entwicklungsstadien von typischen Wildpflanzenarten, die bereits durch andere Faktoren einen Rückgang erfahren. Gerade im Hinblick auf die wiederholte Ausbringung von Gülle und die potenzielle Akkumulation dieser hoch persistenten Stoffe stellen Veterinärantibiotika einen weiteren wichtigen Einflussfaktor dar, der die Biodiversität und Artzusammensetzung gefährdet, weshalb zu einem umweltbewussten Umgang mit ihnen geraten wird.

Based on data collected from two surveys conducted in Germany and Taiwan, my first paper (Chapter 2) examines the impact of culture through language priming (Chinese vs. German or English) on individuals’ price fairness perception and attitudes towards government intervention and economic policy involving inequality. We document large cross-language differences: in both surveys, subjects who were asked and answered in Chinese demonstrated significantly higher perceived price fairness in a free market mechanism than their counterparts who completed the survey in German or English language. They were also more inclined to accept a Pareto improvement policy which increases social and economic inequality. In the second survey, Chinese language induced also a lower readiness to accept government intervention in markets with price limits compared to English language. Since language functions as a cultural mindset prime, our findings imply that culture plays an important role in fairness perception and preferences regarding social and economic inequality. Chapter 3 of this work deals with patriotism priming. By conducting two online experimental studies conducted in Germany and China, we tested three different kinds of priming methods for constructive and blind patriotism respectively. Subjects were randomly distributed to one of three treatments motivated by previous studies in different countries: a constructive patriotism priming treatment, a blind patriotism priming treatment and a non-priming baseline. While the first experiment had a between-subject design, the second one enabled both a between-subject and within-subject comparison, since the level of patriotism of individuals was measured before and after priming respectively. The design of the second survey also enabled a comparison among the three priming methods for constructive and blind patriotism. The results showed that the tested methods, especially the national achievements as a priming mechanism, functioned well overall for constructive patriotism. Surprisingly, the priming for blind patriotism did not work in either Germany or China and the opposite results were observed. Discussion and implications for future studies are provided at the end of the chapter. Using data from the same studies as in Chapter 3, Chapter 4 examines the impact of patriotism on individuals’ fairness perception and preferences regarding inequality and on their attitudes toward economic policy involving inequality. Across surveys and countries, a positive and significant effect of blind patriotism on economic individualism was found. For China, we also found a significant relationship between blind patriotism and the agreement to unequal economic policy. In contrast to blind patriotism, we did not find an association of constructive patriotism to economic individualism and to attitudes toward economic policy involving inequality. Political and economic implications based on the results are discussed. The last chapter (Chapter 5) studies the self-serving bias (when an individual’s perception about fairness is biased by self-interest) in the context of price setting and profit distribution. By analyzing data from four surveys conducted in six countries, we found that the stated appropriate product price and the fair allocation of profit was significantly higher, when the outcome was favorable to oneself. This self-serving bias in price fairness perception, however, differed across countries significantly and was significantly higher in Germany, Taiwan and China than in Vietnam, Estonia and Japan. Although economic individualism and masculinity were found to have a significant negative effect on self-interest bias in price fairness judgment, they did not sufficiently explain the differences in self-interest bias between countries. Furthermore, we also observed an increase of self-interest bias in profit allocation over time in time-series data for one country (Germany) with data from 2011 to 2023. The four papers are all co-authored with Prof. Marc Oliver Rieger, and the first paper has been accepted for publications in Review of Behavioral Economics.

In dieser Dissertation wird der Workflow der Erstellung einer Augmented Reality App für das Projekt „ARmob” auf Androidgeräten beschrieben. Diese App positioniert durch SfM-Technik erstellte, nach dem neuesten Stand der Forschung rekonstruierte 3D-Objekte an ihren ursprünglichen Standort in der Realität. Die virtuellen Objekte werden jeweils vom Standpunkt und Blickwinkel des Betrachters passend in die reale Welt eingeblendet, so dass der Eindruck entsteht, die Objekte seien Teil der Realität. Die lagegenaue Darstellung ist abhängig von der Satellitenerreichbarkeit der GNSS und der Genauigkeit der weiteren Sensoren. Die App soll als Grundlage und Framework für weitere Apps zur Erforschung der Raumwahrnehmung im Bereich der Kartographie dienen.