Dokumente Fakultät für Mathematik und Informatik (inkl. GAUSS) nach Erscheinungsdatum
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Achieving Scalable AI Inference in a Unified Cloud and HPC Environment by Employing System of Systems Architecture Design
(2025-12-04)Providing access to AI powered services commonly requires access to powerful compute infrastructure equipped with hardware accelerators such as GPUs. The recent rise of LLMs further emphasized this need and already caused ... -
Graph Neural Networks for Spatial Data Analysis: Theoretical Results and Applications
(2025-12-02)Overall, this thesis explores the advantages and challenges of spatial data prediction tasks with Graph Neural Networks (GNN). Kriging, the best linear unbiased predictor presents a great number of advantages over other ... -
Nonlinear Parsimonious Modeling with Information Filtering Networks: Theory and Practice
(2025-11-06)This thesis offers a comprehensive exploration and methodological advancement of Information Filtering Networks (IFNs), emphasizing Triangulated Maximally Filtered Graphs (TMFG), Local-Global (LoGo) models, and their ... -
A real effective version of the Freĭman-Scourfield Theorem
(2025-11-04)We study the solvability of a Diophantine equation with mixed real exponents for sufficiently large natural numbers. The connection to a condition on the sum over the reciprocals of the exponents was first shown by Freĭman ... -
Classifying spaces for quasi-topological groups
(2025-10-24)This thesis provides a quick introduction into quasi-topological spaces, first introduced by Spanier. It then constructs notions of numerable principal G-bundles in the quasi-topological case and constructs a quasi-topological ... -
Towards Resilient Energy Systems - Probabilistic Deep Learning for Forecasting and Control under Uncertainty
(2025-10-09)The integration of variable renewable energy source (RES) and the electrification of end-use sectors introduce significant uncertainty into energy systems, challenging traditional deterministic modeling and operational ... -
Evaluation of Contradictions as a Data Quality Measure for Real-world and Clinical Research Data
(2025-10-07)In health research discourse, there is the assumption that a controlled, planned clinical research naturally produces cleaner datasets, while real-world data suffers from quality deficiencies due to its spontaneous collection ... -
Mathematical Background of Parallel Magnetic Resonance Imaging
(2025-10-07)We provide mathematical analyses of reconstruction methods in parallel Magnetic Resonance Imaging (pMRI). We start with a discussion of the mathematical model and then discuss multiple methods such as SENSE, (AUTO-)SMASH, ... -
Spatial Random Graphs: Studying dependence structures in spatial data
(2025-10-02)Spatial random graphs provide a powerful framework for analyzing the relations and interactions governed by an underlying spatial structure. Such graphs can be used not only to model and analyze observed networks, but also ... -
Newton-type Methods
(2025-09-17)Newton’s method has long been enjoying its position as the algorithm of choice for solving nonlinear equations and unconstrained optimization problems. In classical Euclidean settings, under strong smoothness assumptions, ... -
Enabling Trustworthy Transition from Centralized to Decentralized Identity Management Systems
(2025-09-16)As the digital landscape grows in scale and complexity, identity management has become critical to ensure security and trust. Meanwhile, the growing concerns over privacy, user autonomy, and centralized control have exposed ... -
Temporal and spatial discretizations of Brownian motion on Riemannian manifolds
(2025-09-02)This thesis studies temporal and spatial discretizations of Brownian motion and diffusion processes on Riemannian manifolds. Geodesic random walks serve as temporal discretizations of diffusion processes and converge to ... -
Optimal Transport Based Methods for Analyzing Co-localization and Statistical Dependence
(2025-07-31)This dissertation develops optimal transport-based methodologies to advance statistical dependency analysis and co-localization studies, with applications in biological imaging. First, we introduce transport dependency, a ... -
Big Data Infrastructure for Analysing Digitalized Library Collections
(2025-07-31)Digital Humanities (DH) represents an interdisciplinary field at the intersection of digital technologies and the study of the humanities. A variety of projects fall under the umbrella of DH, including digital archives, ... -
Deformations of Ideals in Lie Algebroids
(2025-07-31)In this dissertation, we address the deformation problem of ideals in Lie algebras and its generalization(s) in the context of Lie algebroids. Lie ideals lie at the heart of the representation theory of Lie algebras, as ... -
A Cross-Cultural Investigation of Privacy Perceptions Regarding Concerns, Responsibility, and Understandability
(2025-07-01)In today's data driven world, individuals' data is collected almost constantly. Whether it is apps on mobile phones or social media sites, companies collect, store, and process their users' data in order to enhance their ... -
Enhancing Transparency and Control in Voice-Controlled Digital Assistants: Identifying Privacy Risks, Understanding User Expectations, and Developing Mitigation Strategies
(2025-06-27)Voice assistants have become an integral part of modern smart environments, extending beyond smartphones to cars, smart speakers, and robots, enabling hands-free control of various devices. Their widespread adoption has ... -
Advancing Explainable AI in Medicine: Novel Frameworks for Robustness, Evaluation, and Human-Centered Interpretability
(2025-06-23)The advancement of artificial intelligence (AI) has led to its increasing usage in various fields, including medicine, where AI models, particularly deep neural networks (DNNs), have shown great performance. However, ... -
Simulation-Based Data Fusion and Tracking
(2025-05-15)Autonomous systems ranging from self-driving cars and driver assistance systems, over autonomous vacuum cleaners to unmanned aerial vehicles rely on accurate perception of their surroundings to navigate and interact with ... -
The Minimal Hypersurface Method to Obstruct Positive Scalar Curvature via the Classification of 3-Manifolds
(2025-05-05)In 1979, Schoen and Yau developed a method using descending chains of minimal hypersurfaces to obstruct psc for manifolds initially up to dimension 7. Recent results on regularity for minimal hypersurfaces extend the ...