http://hdl.handle.net/10900/42133 2026-06-12T11:32:11Z http://hdl.handle.net/10900/180749 Structural and Enumerative Studies of Tropical Curves and Covers Cobigo-Bihavan, Lou-Jean Leila Die vorliegende Dissertation ist dem strukturellen und enumerativen Studium tropischer Kurven und Überlagerungen gewidmet. Die Analyse erfolgt anhand zweier spezifischer Forschungsfragen: Tropische spaltende Jacobische und tropische spin Hurwitzzahlen mit abgeschlossenen Zykeln. In Teil 1 geht es umdasZusammenspielvontropischenKurvenundtropischen abelschen Varietäten. Wir untersuchen strukturelle Aspekte tropischer spaltender Jacobischer von Kur ven vom Geschlecht 2, und zwar sowohl auf globaler wie auch auf atomarer Ebene. Global erreichen wir ihre Charakterisierung in der Kategorie tropischer Kurven TC (durch Über lagerungen) und in der Kategorie tropischer abelscher Varietäten TA (als Quotient eines direktes Produkt von zwei elliptischen Kurven). Atomar identifizieren wir ihre Bausteine, ein Paar von Geschlecht 1 Kurven zusammen mit einer gewissen Untergruppe ihres direkten Produkts, und rekonstruieren daraus die Charakterisierungen in TA und TC. Wir nutzen die atomare Perspektive, um unser Verständnis von spaltenden Jacobischen weiter zu kon densieren und gehen zu ihrer Betrachtung im Modulraum tropischer Kurven bzw. prinzipiell polarisierter tropischer abelscher Varietäten über. Hier untersuchen wir eine Variante des tropischen Schottky Problems für spaltende Jacobische bzw. dessen Umkehrung. Wann immer möglich, nutzen wir tropische Geometrie, um abstrakte Charakterisierungen durch konkrete Algorithmen zu untermauern. In Teil 2 geht es um das Zusammenspiel von tropischer Geometrie mit anderen Diszi plinen. Wir nutzen diese Interaktion (im Rahmen der enumerativen Geometrie) zur Unter suchung einer geometrisch motivierten Zahl aus, der Spin Hurwitzzahlmit abgeschlossenen Zykeln. Dazu führen wir eine tropische Zählung von verzweigten Überlagerungen ein, welche mit der ursprünglichen Zahl übereinstimmt, und verwenden schließlich Methoden der tropischen Geometrie, um strukturelle Eigenschaften dieser Zahl (Polynomialität und Wanddurchquerungsformeln) zu untersuchen. 2026-06-12T00:00:00Z http://hdl.handle.net/10900/180747 Epifadin – A New Antimicrobial Peptide Polyene from the Human Microbiome and Chemical Total Syntheses to Study Lugdunin and Epifadin Motifs Dema, Taulant The alarming rise of antimicrobial resistance demands the discovery of novel compounds and mechanisms to combat multidrug-resistant pathogens. In this thesis, three natural products, namely epifadin, cystargolide, and lugdunin, were investigated through chemical synthesis, analytical methods, biological assays, and mechanistic studies. Epifadin, a highly unstable NRPS-PKS-NRPS hybrid isolated from Staphylococcus epidermidis, was structurally elucidated and shown to have a wide antimicrobial target spectrum while not exhibiting cytotoxicity. Due to its instability under physiological conditions, synthetic efforts focused on developing stable building blocks and epifadin-like derivatives to enable further structure-activity relationship studies. In addition, N-ethylcystargolides were obtained via semisynthetic modification of natural cystargolides and exhibited enhanced bioactivity compared to their parent compounds. Hemolysis and growth inhibition assays suggested that the improvement results from better cell penetration and ClpP protease inhibition. Finally, the mode of action of lugdunin was investigated using derivatives synthesized through solid-phase peptide synthesis and a combination of biological, spectroscopic, and computational methods. It was demonstrated that hydrogen bonding is essential for activity and that lugdunin forms peptide nanotubes that translocate protons and ions across bacterial membranes. Moreover, targeted structural modifications enabled lugdunin to penetrate the outer membrane of Gram-negative bacteria, leading to an extended antimicrobial spectrum. Overall, this thesis provides new insights into three antimicrobial scaffolds and contributes to the development of promising antibiotic candidates. 2026-06-12T00:00:00Z http://hdl.handle.net/10900/180746 Improved Exploration through Transfer Learning in Multi-Armed Bandits Bilaj, Steven Reinforcement learning is a branch of machine learning that focuses on training an agent to interact with a dynamic environment to maximize its expected cumulative reward. In contrast to offline learning problems, where the training data is immediately available, the agent typically assembles its own data set by interacting with the environment. Since model performances heavily depend on the gathered training data, a key challenge is determining an exploration strategy at the potential cost of low immediate rewards to find a policy. This is known as the exploration-exploitation trade-off. This dissertation examines how to effectively re-balance the exploration-exploitation trade-off by transferring knowledge between tasks with a shared structure to enhance the agent's overall performance. The primary focus is on developing algorithms that reduce uncertainties in the model estimations by transferring information given various assumptions while providing theoretical bounds on the regret. The contributions span single-task transfer, meta-learning, multi-task learning and non-stationary environments in the multi-armed bandit setting. In a straightforward task-to-task transfer approach, where an expert is assumed to be available to the learner, we propose a dynamic convex combination of the expert and target model. We prove that when the expert's parameter vector is close to the true task related feature vector, the learner can exploit the expert's knowledge in the early steps of the algorithm and reduce the regret with high probability. A generalization would be to investigate feature vectors that are close in a subspace. We address this idea within the concept of meta learning, where an agent sequentially interacts with multiple tasks sampled from a common meta distribution. Under the assumption of a low-dimensional subspace structure in the meta distribution, we propose a framework to estimate the subspace with projection matrices and exploit it as prior information within an OFUL and Thompson sampling based algorithm. With each task the agent interacts with, it improves its estimation of the projections for exploitation in future tasks. Theoretical guarantees are provided with an emphasis on an improvement on the regret bound with respect to the dimensionality. In a clustered setting, we assume that tasks are grouped in clusters such that only tasks of the same cluster share the same feature vector. When the number of clusters is lower than the number of dimensions, it can be interpreted as a special case of the low-dimensional subspace setting. We explore the general clustered setting in a multi-task framework, where an agent interacts with a fixed number of tasks in parallel. The agent has access to a graph, where each node is associated with a different task. We introduce a network lasso based bandit algorithm that exploits the given graph such that it implicitly learns the cluster structure. Theoretical bounds show that, with a well suited graph, this approach offers significant improvements over other baselines. Finally, we address dynamic environments or piecewise-stationary settings, where the agent typically discards all collected data points upon detecting changes in the environment and retrains its model from scratch. Instead, we propose an algorithm that only discards data points directly associated with the environmental change and retains the rest. We show that intelligent transfer of data from previous segments can reduce exploration after each change and increase overall reward. This dissertation thus proposes multiple algorithms for transferring information in several multi-armed bandit settings with the purpose of optimizing exploration. We provide both theoretical guarantees and empirical evaluations showcasing significant improvements over existing methods. 2026-06-12T00:00:00Z http://hdl.handle.net/10900/180527 Empirical Likelihood Estimators for Robust and Causal Learning Kremer, Heiner Stephan Some of the central problems in robust and causal machine learning, including learning under covariate shifts and instrumental variable regression, can be expressed as conditional moment restrictions (CMR). By restricting the conditional expectation of a signed error metric, models identified via CMR exhibit robustness against shifts in the distribution of the conditioning variable. In practice, this generally results in an ill-posed problem, as it requires the solution of an over-identified infinite-dimensional system of equations. For the unconditional case, empirical likelihood estimators have emerged as general and powerful tools to address over-identified moment restriction problems. These methods learn a model along with an approximation of the population distribution by means of minimizing a φ-divergence constrained by the moment restrictions. The main goal of this work is to advance the state-of-the art in CMR estimation by extending and refining the idea of empirical likelihood estimation in several directions. First, we generalize the classical framework to conditional moment restrictions using a functional formulation, that leverages modern machine learning models. Then, we extend the principle to alternative distributional distance notions based on kernel methods and optimal transport. The resulting estimators exhibit superior small sample properties and robustness against data corruptions at training time and adversarial attacks at test time, respectively. Finally, drawing inspiration from the close relation between empirical likelihood estimation and distributionally robust optimization (DRO), we provide an application of kernel-based DRO on chance-constrained programming. 2026-06-09T00:00:00Z