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.

Advances in eye tracking technology have enabled the development of interactive experimental setups to study social attention. Since these setups differ substantially from the eye tracker manufacturer’s test conditions, validation is essential with regard to the quality of gaze data and other factors potentially threatening the validity of this signal. In this study, we evaluated the impact of accuracy and areas of interest (AOIs) size on the classification of simulated gaze (fixation) data. We defined AOIs of different sizes using the Limited-Radius Voronoi-Tessellation (LRVT) method, and simulated gaze data for facial target points with varying accuracy. As hypothesized, we found that accuracy and AOI size had strong effects on gaze classification. In addition, these effects were not independent and differed in falsely classified gaze inside AOIs (Type I errors; false alarms) and falsely classified gaze outside the predefined AOIs (Type II errors; misses). Our results indicate that smaller AOIs generally minimize false classifications as long as accuracy is good enough. For studies with lower accuracy, Type II errors can still be compensated to some extent by using larger AOIs, but at the cost of more probable Type I errors. Proper estimation of accuracy is therefore essential for making informed decisions regarding the size of AOIs in eye tracking research.

We examined the long-term relationship of psychosocial risk and health behaviors on clinical events in patients awaiting heart transplantation (HTx). Psychosocial characteristics (e.g., depression), health behaviors (e.g., dietary habits, smoking), medical factors (e.g., creatinine), and demographics (e.g., age, sex) were collected at the time of listing in 318 patients (82% male, mean age = 53 years) enrolled in the Waiting for a New Heart Study. Clinical events were death/delisting due to deterioration, high-urgency status transplantation (HU-HTx), elective transplantation, and delisting due to clinical improvement. Within 7 years of follow-up, 92 patients died or were delisted due to deterioration, 121 received HU-HTx, 43 received elective transplantation, and 39 were delisted due to improvement. Adjusting for demographic and medical characteristics, the results indicated that frequent consumption of healthy foods (i.e., foods high in unsaturated fats) and being physically active increased the likelihood of delisting due improvement, while smoking and depressive symptoms were related to death/delisting due to clinical deterioration while awaiting HTx. In conclusion, psychosocial and behavioral characteristics are clearly associated with clinical outcomes in this population. Interventions that target psychosocial risk, smoking, dietary habits, and physical activity may be beneficial for patients with advanced heart failure waiting for a cardiac transplant.

The Belt and Road Initiative (BRI) has had a significant impact on China in political, economic, and cultural terms. This study focuses on the cultural domain, especially on scholarship students from the countries that signed bilateral cooperation agreements with China under the BRI. Using an integrated approach combining the difference-in-differences method and the gravity model, we explore the correlation between the BRI and the increasing number of international scholarship students funded by the Chinese government, as well as the determinants of students' decision to study in China. The panel data from 2010 to 2018 show that the launch of BRI has had a positive impact on the number of scholarship students from BRI countries. The number of scholarship recipients from non-BRI countries also increased, but at a much slower rate than those from BRI countries. The sole exception is the United States, which has trended downward for both state-funded and self-funded students.

Despite significant advances in terms of the adoption of formal Intellectual Property Rights (IPR) protection, enforcement of and compliance with IPR regulations remains a contested issue in one of the world's major contemporary economies—China. The present review seeks to offer insights into possible reasons for this discrepancy as well as possible paths of future development by reviewing prior literature on IPR in China. Specifically, it focuses on the public's perspective, which is a crucial determinant of the effectiveness of any IPR regime. It uncovers possible differences with public perspectives in other countries and points to mechanisms (e.g., political, economic, cultural, and institutional) that may foster transitions over time in both formal IPR regulation and in the public perception of and compliance with IPR in China. On this basis, the review advances suggestions for future research in order to improve scholars' understanding of the public's perspective of IPR in China, its antecedents and implications.