The Billiard Configuration Space was first introduced by Farber and Tabachnikov to explore the number of periodic billiard trajectories within a smooth, strictly convex domain in Euclidean space. Estimating the Lusternik–Schnirelmann category of the Billiard Configuration Space for a sphere is crucial for establishing bounds on the number of such periodic trajectories. A related concept—topological complexity—was introduced by Farber to address problems in motion planning. Farber, in collaboration with Yuzvinsky and later with Grant, computed the topological complexity of the (standard) Configuration Space in a series of papers. This thesis aims to extend these ideas by providing bounds on the topological complexity and calculating the Lusternik–Schnirelmann category of the Billiard Configuration Space using obstruction theory. Furthermore, we present two Salvetti-type cellular models: the first is applied to compute the fundamental group of the Billiard Configuration Space, while the second allows for the application of obstruction theory.

The first long-distance observations made by Perseverance from the Kodiak butte con- firmed Gilbert-type delta deposition within a closed-lake system in Jezero crater, Mars. Several outcrops at the delta proper were also imaged later during science campaign but their geology and potential relationship to Kodiak needed to be explored. In this thesis, Perseverance image data with a focus on Mastcam-Z and Supercam was used in digital outcrop modeling, applying the Structure-From-motion (SFM) photogram- metry software Agisoft Metashape and georeferenced with SPICE-derived position and orientation. The digital outcrop models (DOMs) were analyzed in the Pro3D software, extracting dip and strike measurements as well as scale bars for determining 2D-clast size-frequency distributions with the ImageJ software. Seven high-resolution, textured and accurate digital outcrop models were created. Evidence gathered from the DOMs shows sedimentary facies associated with Gilbert-type delta stratal architectures. Fore- set and lower foreset facies were identified at the outcrops Franklin Cliff, Whale Moun- tain, Kodiak and Scarp A. Topset facies were found at every outcrop, except Scarp D. “Whale Mountain“ also displays a prominent mouth bar deposit. Six clast samples were collected, all associated with a fluvial origin. Three samples were identified as channel base deposits in a topset environment, one interpreted as a foreset debrite, one debris flow, and one high-energy flood conglomerate. Topset-foreset boundaries differ in alti- tude between outcrops, suggesting different phases of delta progradation. Inferred paleo flows from Whale Mountain and Franklin Cliff link those to the delta strata found at Kodiak, further indicating that the butte was once part of the delta. This thesis demon- strates how digital outcrop models can be used to conduct virtual fieldwork also in the remote environment of Mars.

Increasing urbanization (UN DESA 2019) in combination with the impacts of global climate change (IPCC 2023) require effective climate adaptation strategies, especially in urban regions. Remote sensing analysis methods can supplement or replace classic in-situ surveys (Gray et al. 2021; Ho et al. 2022). A central challenge of the increasingly used deep learning algorithms is the increased demand for high-quality training data (Hoeser et al. 2020). One approach is the use of synthetic data (Tremblay et al. 2018; Hoeser et al. 2022). In most cases, however, only real training data or a combination of real and synthetic data is utilized. The main focus of this work is to investigate the question of whether the exclusive use of synthetic training data together with already trained models does not also achieve good results and thus enable further time and cost reductions. For this purpose, a workflow for tree crown segmentation in high-resolution RGB aerial images is developed, different network architectures are compared with regard to the accuracies they can achieve and the influence of the level of detail of synthetic training data is considered. For this purpose, five data sets with increasing visual complexity are created using the ArcGIS CityEngine (ESRI 2022) and used for the adaptation of ten neural networks. The specific scripts and the workflow as a Python library syntreesizer are published on GitHub. Generating the training datasets took several days to approximately two weeks. Good results were achieved on the validation datasets with a Dice index of at least 85 %. More detailed datasets even allowed accuracies of 97,4 % and 97,9 % for the model with ResNet-34 and ResNet-50 backbone respectively. Acceptable results were achieved on aerial photographs of Berlin: On the complete test data set, a model with ResNet-34 backbone achieved the highest accuracy of 59,29 %. When aligning the test data with the training data, the accuracies increase — a model with ResNet-50 backbone could achieve a final Dice accuracy of 66,65 %. The differences in accuraccies between the experiments were reduced. Synthetic training data allows the models to generalize what they have learned to previously unseen data. At the same time, it was found that an increased level of detail in the training data did not consistently lead to better performing models. Furthermore, the deeper neural networks did not achieve a convincing improvement of the binary tree crown masks. An in-depth examination of the algorithms used is one of the most important tasks for future work.

The relation between Charles Mills and the Enlightenment has often been overlooked or seen as antithetical. Yet Mills considered his philosophy a part of the (black) radical Enlightenment. The latter, he claimed, is true to the core principles of Enlightenment philosophy – objectivism, universalism, and rationalism – but radicalizes them with a focus on actual (racial) socio-political domination. In this paper, I argue that the principles of Enlightenment philosophy play a fundamental role in Mills’s project of locating real-world racial domination and the struggle against it at the center of philosophical reflection. I also show that, according to Mills, only the radical Enlightenment is able to substantively realize these principles. More generally, my discussion sheds light on Mills’s understanding of Enlightenment philosophy and the radical Enlightenment in particular.

A Chinese food network specializing in vegetable crops has existed since the onset of labor migration from southeast China to British Columbia in the 19th century. By 1940, the network achieved market prominence in the local production and distribution of vegetables. This thesis examines the socio-economic history of the network’s emergence and development during the historical period between 1880 and 1940 – the height of white supremacy and discriminatory policies. It seeks to explain how the economic success came about under structural disadvantages. Two theoretical concerns guide the methodologies and historical analysis: How do social relations bear on economic actions? How do migrants interact with the environment in which they find themselves? To deconstruct the narrative that Chinese market gardeners, peddlers, and greengrocers were victims simply pushed into the agri-food sector, this thesis reads for economic difference from data scattered across secondary literature, archival materials, and oral histories. Economic subjectivities and actions are re-aligned to present an alternative picture: small-business entrepreneurship in agriculture as a vehicle to a good life. Adopting mixed embeddedness approach, it traces the interplay between the actors within the network and the structural context of colonialism and capitalism. It identifies the ways in which they utilized resources and devised strategies to adapt to and transform societies. Furthermore, the multifaceted ways in which social relations, especially migrant networks, influenced the emergence and development of the Chinese food network are elaborated.

Political trust as a conditional relationship between citizens and institutions is essential for the stability of political systems. Although the EU-Institutions are extending increasingly their competences (Tallberg, 2002), trust in them is mostly determined by national trust (Harteveld et al., 2013). Two theories, how national trust spills over to the EU-Level, are introduced: The congruence theory (Anderson, 1998) assumes a positive relation on the individual level based on proxy-theory and the compensation theory (Sánchez-Cuenca, 2000) postulates a negative one, applying a cost-benefit approach. To combine both theories, the latter was shifted to the aggregated level of EU-member-states (Muñoz et al., 2011). With the help of the ESS Round 9 (2018), both theories are analyzed comprehensively. The findings clearly confirm the existence of a congruence effect to explain variation inside a country. Between EU-member-states differences can be partly explained by the compensation theory, but the results are less robust.

The biodiversity crisis of rapid species extinction is met with conservation measures on a global scale. The current thesis examines the case of German development cooperation as the biggest financier of biodiversity conservation in the Global South, focusing on the in-volvement of Indigenous Peoples and local communities (IP&LC) in the planning and imple-mentation of biodiversity projects in Bolivia, Colombia, Ecuador, and Peru. Based on inter-views with practitioners in German development cooperation and the protocol of a Bundes-tag hearing it is worked out how German conservation approaches often (still) follow a logic of ecological modernisation. On the other hand, the involvement of IP&LC is gaining sali-ence. By applying a post-colonial political ecology perspective, it is shown that on the imple-mentation level German development actors are aware of the importance of integrating the rights, worldviews and contributions of IP&LC into conservation. However, when it comes to policymaking, IP&LC are often still excluded due to structural obstacles. This bears the risk that IP&LC are merely included for the implementation of Western-designed conservation projects. Conversely, there is a chance that the growing awareness for IP&LC will translate into more participatory conservation that places human well-being at the centre.

Kurt Gödels ontologischer Gottesbeweis, in dem er die notwendige Existenz Gottes über die maximale Menge der positiven Eigenschaften beweist, wurde 1970 veröffentlicht. In den Jahrzehnten zuvor wurden seine Unvollständigkeitssätze (1931), seine Beweisskizze über die Vereinbarkeit der ZF-Mengenlehre mit dem Auswahlaxiom und der allgemeinen Kontinuumshypothese (1939), Arbeiten zur Erweiterung der Mengenlehre, sowie metamathematische Texte und Vorträge zur Grundlegung der Mathematik veröffentlicht. In der vorliegenden Arbeit wird der Zusammenhang dieser unterschiedlichen Arbeiten Gödels beschrieben und seine Auswirkungen auf die Grundlegung der Mathematik diskutiert. Dabei wird insbesondere Gödels Forderung nach neuen Begriffen, seine philosophische Anschauung zur mathematischen Intuition und Konzeptbildung und der Aufbau seines philosophischen, metamathematischen Programms auf der absoluten Unendlichkeit (in Anlehnung an Leibniz’ Monadologie und seine Urmonade), herausgestellt. In diesem Zusammenhang wird ein neuer Mengenbegriff etabliert, der als Analogie zur Allklasse und zum Prinzip der Unerreichbarkeit von V als Grund-Axiom die Verbindung zwischen den hier diskutierten verschieden Gebieten und Gödels ontologischem Gottesbeweis darstellt, in dem das Maximum der positiven Eigenschaften über einen offenen, homogenen Mengenbegriff erreicht und so die notwendige Existenz Gottes bewiesen wird.

Higher-order logic (HOL) offers a simple syntax and semantics for representing and reasoning about typed mathematical concepts. There are many state-of-the-art automated theorem provers for HOL. But the type system of HOL lacks advanced features where types may depend on terms. This is useful as many mathematical notions are inherently dependent typed. Dependent type theory offers such a rich type system but has rather substantial conceptual differences to HOL and isn’t supported as well by automated theorem provers. We introduce a dependently typed extension DHOLP of HOL that supports dependent types while retaining the style and conceptual framework of HOL. Moreover, we describe one translation from DHOLP and a second one from one of its fragments to HOL and prove the soundness and completeness of the translations. We implement both translations within the MMT system—a system for formalizing mathematics—where they are combined with a HOL prover into an automated theorem prover for DHOLP. Finally, we formalize basic set theory notions in DHOLP and outline how such a formalization can be combined with a recent translation of the language of the Mizar proof assistant to MMT to obtain an automated theorem prover for problems in the language of the Mizar proof assistant.

Planning and mental imagery interventions are two inexpensive evidence-based strategies that hold promise in facilitating changes in health behavior. This systematic review explores whether incorporating mental imagery techniques alongside planning enhances the effectiveness of planning interventions aimed at promoting health-related behaviors. Specifically, the main hypothesis examined whether combining planning with either process simulation or outcome simulation would be more effective in changing behavior than planning alone. It was further hypothesized that each individual intervention component would effectively change behavioral outcomes compared to a control condition. The review yielded 7 original studies analyzing data from a total of 1646 participants. Preliminary evidence was found that multicomponent interventions might be ineffective in changing health behavior relative to each of the components alone. The review also found preliminary evidence suggesting that planning and mental imagery may individually have limited effectiveness in promoting health behavior change. The results are discussed considering the limitations of the included trials and review methods, while also exploring practical implications and directions for future research.

To ensure lecturers can improve their teaching quality, the Faculty of Mathematics and Computer Science employs an evaluation process every semester, during which students can evaluate their lecturers anonymous and directly. In addition to individual results, the faculty also manually creates an evaluation report for all institutes belonging to it. To support the evaluation committee in generating the report, a reproducible pipeline will be created to automate this task as much as possible. Special focus will be applied to the concepts of code understandability and (computa- tional) reproducibility, while following modern design, documentation, coding guidelines and specifications. This ensures the pipeline is usable by anyone and continues to stay so in the future. Along with the pipeline, a prototype for a dashboard will be developed with minimal functionality to demonstrate how the processed data can be used to convey results in a way that extends the current evaluation report.

Diese Untersuchung beleuchtet aus demokratietheoretischer Perspektive die Spielräume und Grenzen demokratischer Entscheidungsfreiheit in der Migrationspolitik. Ausgangspunkt ist die These, dass Migration ein besonderes Politikfeld darstellt, dessen Besonderheiten die Legitimität demokratischer Entscheidungen beeinflussen. Ziel ist es, die Gründe für diese demokratische Sonderstellung der Migrationspolitik zu erörtern und die daraus resultierenden Konsequenzen zu analysieren. Es wird argumentiert, dass politische Gemeinschaften zwar über Spielräume bei migrationspolitischen Regelungen verfügen, diese aber mehrfach begrenzt sind.