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This thesis is concerned with two classes of optimization problems which stem
mainly from statistics: clustering problems and cardinality-constrained optimization problems. We are particularly interested in the development of computational techniques to exactly or heuristically solve instances of these two classes
of optimization problems.
The minimum sum-of-squares clustering (MSSC) problem is widely used
to find clusters within a set of data points. The problem is also known as
the $k$-means problem, since the most prominent heuristic to compute a feasible
point of this optimization problem is the $k$-means method. In many modern
applications, however, the clustering suffers from uncertain input data due to,
e.g., unstructured measurement errors. The reason for this is that the clustering
result then represents a clustering of the erroneous measurements instead of
retrieving the true underlying clustering structure. We address this issue by
applying robust optimization techniques: we derive the strictly and $\Gamma$-robust
counterparts of the MSSC problem, which are as challenging to solve as the
original model. Moreover, we develop alternating direction methods to quickly
compute feasible points of good quality. Our experiments reveal that the more
conservative strictly robust model consistently provides better clustering solutions
than the nominal and the less conservative $\Gamma$-robust models.
In the context of clustering problems, however, using only a heuristic solution
comes with severe disadvantages regarding the interpretation of the clustering.
This motivates us to study globally optimal algorithms for the MSSC problem.
We note that although some algorithms have already been proposed for this
problem, it is still far from being “practically solved”. Therefore, we propose
mixed-integer programming techniques, which are mainly based on geometric
ideas and which can be incorporated in a
branch-and-cut based algorithm tailored
to the MSSC problem. Our numerical experiments show that these techniques
significantly improve the solution process of a
state-of-the-art MINLP solver
when applied to the problem.
We then turn to the study of cardinality-constrained optimization problems.
We consider two famous problem instances of this class: sparse portfolio optimization and sparse regression problems. In many modern applications, it is common
to consider problems with thousands of variables. Therefore, globally optimal
algorithms are not always computationally viable and the study of sophisticated
heuristics is very desirable. Since these problems have a discrete-continuous
structure, decomposition methods are particularly well suited. We then apply a
penalty alternating direction method that explores this structure and provides
very good feasible points in a reasonable amount of time. Our computational
study shows that our methods are competitive to
state-of-the-art solvers and heuristics.
Soil organic matter (SOM) is an indispensable component of terrestrial ecosystems. Soil organic carbon (SOC) dynamics are influenced by a number of well-known abiotic factors such as clay content, soil pH, or pedogenic oxides. These parameters interact with each other and vary in their influence on SOC depending on local conditions. To investigate the latter, the dependence of SOC accumulation on parameters and parameter combinations was statistically assessed that vary on a local scale depending on parent material, soil texture class, and land use. To this end, topsoils were sampled from arable and grassland sites in south-western Germany in four regions with different soil parent material. Principal component analysis (PCA) revealed a distinct clustering of data according to parent material and soil texture that varied largely between the local sampling regions, while land use explained PCA results only to a small extent. The PCA clusters were differentiated into total clusters that contain the entire dataset or major proportions of it and local clusters representing only a smaller part of the dataset. All clusters were analysed for the relationships between SOC concentrations (SOC %) and mineral-phase parameters in order to assess specific parameter combinations explaining SOC and its labile fractions hot water-extractable C (HWEC) and microbial biomass C (MBC). Analyses were focused on soil parameters that are known as possible predictors for the occurrence and stabilization of SOC (e.g. fine silt plus clay and pedogenic oxides). Regarding the total clusters, we found significant relationships, by bivariate models, between SOC, its labile fractions HWEC and MBC, and the applied predictors. However, partly low explained variances indicated the limited suitability of bivariate models. Hence, mixed-effect models were used to identify specific parameter combinations that significantly explain SOC and its labile fractions of the different clusters. Comparing measured and mixed-effect-model-predicted SOC values revealed acceptable to very good regression coefficients (R2=0.41–0.91) and low to acceptable root mean square error (RMSE = 0.20 %–0.42 %). Thereby, the predictors and predictor combinations clearly differed between models obtained for the whole dataset and the different cluster groups. At a local scale, site-specific combinations of parameters explained the variability of organic carbon notably better, while the application of total models to local clusters resulted in less explained variance and a higher RMSE. Independently of that, the explained variance by marginal fixed effects decreased in the order SOC > HWEC > MBC, showing that labile fractions depend less on soil properties but presumably more on processes such as organic carbon input and turnover in soil.
Surveys play a major role in studying social and behavioral phenomena that are difficult to
observe. Survey data provide insights into the determinants and consequences of human
behavior and social interactions. Many domains rely on high quality survey data for decision
making and policy implementation including politics, health, business, and the social
sciences. Given a certain research question in a specific context, finding the most appropriate
survey design to ensure data quality and keep fieldwork costs low at the same time is a
difficult task. The aim of examining survey research methodology is to provide the best
evidence to estimate the costs and errors of different survey design options. The goal of this
thesis is to support and optimize the accumulation and sustainable use of evidence in survey
methodology in four steps:
(1) Identifying the gaps in meta-analytic evidence in survey methodology by a systematic
review of the existing evidence along the dimensions of a central framework in the
field
(2) Filling in these gaps with two meta-analyses in the field of survey methodology, one
on response rates in psychological online surveys, the other on panel conditioning
effects for sensitive items
(3) Assessing the robustness and sufficiency of the results of the two meta-analyses
(4) Proposing a publication format for the accumulation and dissemination of metaanalytic
evidence
Im August und September 2019 wurde unter allen Lehrenden im Fach Gesellschaftslehre (GL) an rheinland-pfälzischen Integrierten Gesamtschulen (IGS) eine Fragebogenstudie durchgeführt. Sie ermöglicht differenzierte Einblicke in die Selbstwahrnehmung der Lehrenden und in ihre Betrachtung der Schul- und Unterrichtspraxis. Die Ergebnisse zeigen Stärken und Schwächen des Integrationsfachs auf und eröffnen didaktische wie bildungspolitische Entwicklungsperspektiven. Die Erhebung erfolgte im Rahmen des von der Nikolaus Koch Stiftung und dem Ministerium für Bildung des Landes Rheinland-Pfalz geförderten Projekts „pe:GL – Praxis- und Entwicklungsforschung: Gesellschaftslehre“ an der Universität Trier.
Forest inventories provide significant monitoring information on forest health, biodiversity,
resilience against disturbance, as well as its biomass and timber harvesting potential. For this
purpose, modern inventories increasingly exploit the advantages of airborne laser scanning (ALS)
and terrestrial laser scanning (TLS).
Although tree crown detection and delineation using ALS can be seen as a mature discipline, the
identification of individual stems is a rarely addressed task. In particular, the informative value of
the stem attributes—especially the inclination characteristics—is hardly known. In addition, a lack
of tools for the processing and fusion of forest-related data sources can be identified. The given
thesis addresses these research gaps in four peer-reviewed papers, while a focus is set on the
suitability of ALS data for the detection and analysis of tree stems.
In addition to providing a novel post-processing strategy for geo-referencing forest inventory plots,
the thesis could show that ALS-based stem detections are very reliable and their positions are
accurate. In particular, the stems have shown to be suited to study prevailing trunk inclination
angles and orientations, while a species-specific down-slope inclination of the tree stems and a
leeward orientation of conifers could be observed.
Die Effekte diverser Hormone auf das Sozialverhalten von Männern und Frauen sind nicht vollständig geklärt, da eine genaue Messung dieser, sowie eine Ableitung kausaler Zusammenhänge, die Forschung seither vor Herausforderungen stellt. Umso wichtiger sind Studien, welche versuchen für konfundierende Aspekte zu kontrollieren und die hormonellen oder endokrinen Effekte auf das Sozialverhalten und die soziale Kognition zu untersuchen. Während Studien bereits Effekte von akutem Stress auf Sozialverhalten zeigten, sind die zugrundeliegenden neurobiologischen Mechanismen nicht vollständig bekannt, da hierfür ein rein pharmakologischer Ansatz von Nöten wäre. Die wenigen Studien, die einen solchen wählten, zeigen konträre Befunde. Bisherige Untersuchungen mit psychosozialen Stressoren lassen jedoch prosoziale Tendenzen nach Stress sowohl für Männer als auch für Frauen vermuten. Darüber hinaus sind auch Untersuchungen zu weiblichen Geschlechtshormonen und ihrem Einfluss auf Sozialverhalten sowie die soziale Kognition bei Frauen besonders herausfordernd durch die hormonellen Schwankungen während des Menstruationszyklus oder auch Veränderungen durch die Einnahme oraler Kontrazeptiva. Studien die sowohl Zyklusphasen als auch die Effekte von oralen Kontrazeptiva untersuchten, deuten aber bereits auf Unterschiede zwischen den verschiedenen Phasen, sowie Frauen mit natürlichem Zyklus und Einnahme oraler Kontrazeptiva hin.
Der theoretische Teil beschreibt die Grundlagen zur Stressreaktion des Menschen und die hormonellen Veränderungen weiblicher Geschlechtshormone. Folgend, soll ein Kapitel zur aktuellen Forschungslage zu Effekten von akutem Stress auf Sozialverhalten und die soziale Kognition einen Überblick über die bisherige Befundlage schaffen. Die erste empirische Studie, welche die Effekte von Hydrocortison auf das Sozialverhalten und die Emotionserkennung untersucht, soll anschließend in diese aktuelle Befundlage eingeordnet werden und zu der weniger erforschten Sparte der pharmakologischen Studien beitragen. Die zweite empirische Studie befasst sich folgend mit den Effekten weiblicher Geschlechtshormone auf Sozialverhalten und Empathie, genauer wie auch Zyklusphasen und orale Kontrazeptiva (über Hormone vermittelt) einen Einfluss bei Frauen nehmen. Abschließend sollen die Effekte von Stresshormonen bei Männern, und modulierende Eigenschaften weiblicher Geschlechtshormone, Zyklusphasen und oraler Kontrazeptiva bei Frauen, jeweils in Hinblick auf Sozialverhalten und die soziale Kognition diskutiert werden.
Wenn es darum geht, Menschen aus Politik und Gesellschaft in die Schule einzuladen, stellen sich Lehrpersonen meist zahlreiche Fragen. Vor allem, wenn es sich um Politiker*innen handelt, wird manchen gern bang ums Herz. Wie kann man sicherstellen, dass der Austausch gewinnbringend für alle Seiten ist?
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.
Due to the transition towards climate neutrality, energy markets are rapidly evolving. New technologies are developed that allow electricity from renewable energy sources to be stored or to be converted into other energy commodities. As a consequence, new players enter the markets and existing players gain more importance. Market equilibrium problems are capable of capturing these changes and therefore enable us to answer contemporary research questions with regard to energy market design and climate policy.
This cumulative dissertation is devoted to the study of different market equilibrium problems that address such emerging aspects in liberalized energy markets. In the first part, we review a well-studied competitive equilibrium model for energy commodity markets and extend this model by sector coupling, by temporal coupling, and by a more detailed representation of physical laws and technical requirements. Moreover, we summarize our main contributions of the last years with respect to analyzing the market equilibria of the resulting equilibrium problems.
For the extension regarding sector coupling, we derive sufficient conditions for ensuring uniqueness of the short-run equilibrium a priori and for verifying uniqueness of the long-run equilibrium a posteriori. Furthermore, we present illustrative examples that each of the derived conditions is indeed necessary to guarantee uniqueness in general.
For the extension regarding temporal coupling, we provide sufficient conditions for ensuring uniqueness of demand and production a priori. These conditions also imply uniqueness of the short-run equilibrium in case of a single storage operator. However, in case of multiple storage operators, examples illustrate that charging and discharging decisions are not unique in general. We conclude the equilibrium analysis with an a posteriori criterion for verifying uniqueness of a given short-run equilibrium. Since the computation of equilibria is much more challenging due to the temporal coupling, we shortly review why a tailored parallel and distributed alternating direction method of multipliers enables to efficiently compute market equilibria.
For the extension regarding physical laws and technical requirements, we show that, in nonconvex settings, existence of an equilibrium is not guaranteed and that the fundamental welfare theorems therefore fail to hold. In addition, we argue that the welfare theorems can be re-established in a market design in which the system operator is committed to a welfare objective. For the case of a profit-maximizing system operator, we propose an algorithm that indicates existence of an equilibrium and that computes an equilibrium in the case of existence. Based on well-known instances from the literature on the gas and electricity sector, we demonstrate the broad applicability of our algorithm. Our computational results suggest that an equilibrium often exists for an application involving nonconvex but continuous stationary gas physics. In turn, integralities introduced due to the switchability of DC lines in DC electricity networks lead to many instances without an equilibrium. Finally, we state sufficient conditions under which the gas application has a unique equilibrium and the line switching application has finitely many.
In the second part, all preprints belonging to this cumulative dissertation are provided. These preprints, as well as two journal articles to which the author of this thesis contributed, are referenced within the extended summary in the first part and contain more details.