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An Introduction to the Dynamics of Compact Group Automorphisms after Klaus Schmidt
Item type: Bachelor Thesis
Ceglie, Levin (2026)
This thesis provides an introduction to the theory of algebraic dynamical systems based on the work of Klaus Schmidt. We begin by establishing fundamental dynamical properties through the lens of actions of countable groups on compact metrizable groups by continuous automorphisms, which we call quasi-algebraic actions. Specifically, we introduce the notions of topological transitivity, ergodicity, mixing, and expansiveness, and illustrate them through four running examples. With these foundations in place, we explore the rigidity of quasi-algebraic actions, structural constraints imposed by dynamical conditions, and provide a spectral characterization of ergodicity and mixing. The culmination of this work is an "algebraic dictionary" that establishes a correspondence between algebraic Z^d-actions and countable modules over a Laurent polynomial ring, translating dynamical properties into algebraic ones and providing a unified framework for their study.
Towards Operational Earthquake Forecasting in Europe: ETAS and Beyond
Item type: Doctoral Thesis
Han, Marta (2026)
Earthquakes are one of the most unpredictable and devastating natural hazards. Because they cannot be prevented, a primary motivation of seismological research is to anticipate their occurrence to mitigate risk and inform civil protection. Within the spectrum of seismic risk mitigation, Operational Earthquake Forecasting (OEF) occupies a middle ground: while earthquake early warning provides seconds of notice, and long-term hazard and risk assessments evaluate probabilities over decades to inform building codes, OEF provides time-dependent probabilities over days to weeks, with the goal of eventually serving as a dynamic trigger for civil preparedness. The overarching objective of this thesis is to develop OEF as a harmonised, pan-European framework. To achieve this, we deployed a series of Epidemic-Type Aftershock Sequence (ETAS) models across a continent-wide domain. Scaling these models across such a large and heterogeneous region required addressing both methodological biases and computational bottlenecks. First, we developed a harmonised baseline forecasting model for Europe. To address spatial variations in long-term hazard, we modified the standard parameter inversion procedure to incorporate background seismicity from the 2020 European Seismic Hazard Model (ESHM20). This equips the purely data-driven model with the memory of historic seismotectonic potential, ensuring long-term forecasting stability in regions that appear quiet but remain highly hazardous. We also applied the $b$-positive method to account for short-term catalogue incompleteness and explore adjusted productivity terms. Testing demonstrates the success of this approach: ETAS models explicitly fitted to the European domain significantly outperform both time-independent benchmarks and time-dependent models calibrated on global datasets. Second, we addressed the geometric over-simplification of the model's spatial triggering kernel. Standard ETAS models distribute aftershocks isotropically, neglecting true fault geometry and the resulting observed anisotropy. By introducing directional information and replacing the circular kernel with a data-driven elliptic one, we successfully captured spatial anisotropy. Evaluations on European catalogues revealed that this geometric correction improves spatial forecasting capability and reduces bias in the estimated ETAS parameters, specifically in the productivity law. To address the high degree of inter-sequence variability, we evaluated dynamic productivity updating strategies during ongoing sequences. While these real-time updates improved forecasts in certain scenarios, they yielded inconsistent results in others. This underlines that accounting for sequence-specific productivity is needed, but also demonstrates the need for more advanced forecasting approaches to tackle this variability. Finally, we tackled the challenges of integrating these models into a real-time operational pipeline. Our results demonstrate that applying a spatially uniform magnitude distribution limits forecasting accuracy. Pseudo-prospective testing over a seven-year period proved that a spatially variable $b$-value model significantly improves the forecasting of weekly seismicity rates. Furthermore, we evaluated the computational resources required for real-time simulation, demonstrating that practical speed-up methods reduce simulation times but incur penalties to forecasting skill. To complete the operational framework, we outlined the system's integration into an automated pipeline. This includes incorporating a `floating' CSEP architecture for truly prospective evaluation, as well as discussing the necessary translation of probabilistic outputs into actionable risk communication.
Single-nucleotide-resolution genomic maps of temozolomide-induced DNA adducts in glioblastoma
Item type: Doctoral Thesis
Kubitschek, Jasmina (2026)
Temozolomide (TMZ) is widely used for glioblastoma (GBM) therapy and functions by inducing DNA alkylation. Tumor cell killing is driven by repair pathways that eventually lead to apoptosis in fast replicating cells. While the combination of TMZ and radiother-apy improves overall survival by synergistically increasing DNA damage burden, treatment responses are typically transient, and most patients experience tumor re-lapse, which remains the major cause of mortality. To improve GBM therapy outcomes, a key challenge is linking individual patient characteristics to treatment outcomes. For TMZ specifically, this requires understanding the genome-wide distribution of induced DNA lesions and their relationship to repair capacities. Chapter 1 introduces GBM biology and current treatment strategies, with a focus on TMZ-induced DNA damage and repair. The roles of repair pathways are discussed in the context of therapy response, resistance, and relapse, highlighting the need for DNA damage mapping approaches. Chapter 2 describes the development of O6-MeG-seq, a method to map O6-methylguanine (O6-MeG) across the genome at single-nucleotide resolution. Applica-tion of this method in a GBM-derived cell line revealed that O6-MeG formation occurs in characteristic sequence contexts that closely resemble TMZ-associated mutational signatures observed in patients, confirming O6-MeG as the precursor for mutations. O6-methylguanine-DNA methyltransferase (MGMT) expression reduced overall lesion abundance but did not alter O6-MeG distribution with respect to sequence context or gene expression, suggesting that lesion patterns are primarily driven by damage for-mation. These results provide high-resolution insight into the interplay between O6-MeG formation and repair, highlighting the potential of O6-MeG-seq to elucidate how repair capacity and gene regulation influence drug resistance and secondary cancer risk. Chapter 3 covers mapping TMZ-induced DNA lesions through recognition by human alkyladenine-DNA glycosylase (hAAG). Click-code-seq (CCS) was expanded to include different glycosylases with distinct substrate specificities to enable comparison of DNA damage maps. Oxidative damage maps generated by two structurally different glyco-sylases were highly concordant across sequence context, base composition, and strand bias, confirming the biological relevance of CCS-generated maps. Mapping with hAAG revealed distinct alkylation patterns associated with transcriptional activity, including enrichment of lesions on the non-transcribed strand of expressed genes. These find-ings highlight the role of transcription-coupled repair in shaping alkylation damage landscapes and demonstrate that glycosylase selection critically influences the inter-pretation of DNA damage maps. Chapter 4 explores the development of single-cell DNA damage mapping with single-nucleotide resolution and the potential integration of transcriptomic profiling in the same cell. Proof-of-concept experiments adapting CCS for nuclei yielded sequencing-ready libraries and demonstrate feasibility. However, protocol refinements are needed to improve lesion specificity and reduce technical noise. Chapter 5 provides a conclusion and outlook on the work presented in this thesis. The developed methods enable linking TMZ-induced DNA lesion distributions to biological processes such as DNA repair and transcription. Integrating DNA damage mapping with advanced tumor models may improve the understanding of GBM evolution under therapy and support the development of more effective and personalized treatment strategies. In summary, this thesis establishes and applies a systematic mapping framework for TMZ-induced lesions in human genome. These approaches provide new insights into how TMZ-related DNA lesions are distributed and establish a foundation for future studies to investigate how they contribute to GBM therapy response.
Only Project Once: Projection-Adaptive Loss for Exact Constraint Satisfaction
Item type: Other Publication
Aebersold, Tim; Massoudi, Soheyl; Fuge, Mark (2026)
Precise constraint satisfaction is a prerequisite to deploying learned models in many areas, motivating methods that repair raw neural predictions with a repair procedure. Current methods unroll multiple repair steps in training and softly penalize constraint violations that remain after the unroll. This is compute- and memory-intensive, lacks robustness when the repair fails to converge, and surrenders most of the constraint satisfaction work to the repair. Our central finding is that, contrary to common practice, a single detached projection step suffices in training. We accomplish this with a Projection-Adaptive Loss (PAL), which uses the constraint residual after this single step to adaptively weigh constraint penalties on the raw prediction. In experiments, PAL is the only method that retains virtually perfect feasibility on extremely nonlinear constraints, and matches or outperforms current methods on synthetic and engineering benchmarks. Because it only requires a single detached projection step, PAL trains 2.5x faster than the canonical repair-based method (DC3) on its own ACOPF benchmark. PAL can also be trained when constraints are expensive to evaluate (e.g., via neural surrogates), a setting where current unrolled methods are memory-intractable.