Fakultät für Mathematik und Informatik (inkl. GAUSS)
Recent Submissions
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Advancing Differentially Private Deep Learning: Algorithmic Improvements and Performance Evaluation
(2026-01-16)In recent years, machine learning and deep learning technologies have been widely applied across various domains. However, the privacy concerns associated with these technologies have become increasingly prominent. In this ... -
Conditional Stability and Instability Estimates for Inverse Random Source Problems
(2026-01-13)This thesis is motivated by the study of passive imaging problems. Such problems can be characterised as scattering problems under uncontrolled incident waves. We focus specifically on inverse random source problems, a ... -
Sums with hyperbolic conditions
(2025-12-18)We develop a generalization of the hyperbola method, a technique used to obtain asymptotic estimates for summations involving a product of variables as a constraint, given that similar sums over rectangular regions can be ... -
Language Modeling and Understanding Through Paraphrase Generation and Detection
(2025-12-18)Language enables humans to share knowledge, reason about the world, and pass on strategies for survival and innovation across generations. At the heart of this process is not just the ability to communicate but also the ... -
Learning the shape of neurons: Representation learning, generative modeling and hierarchical clustering
(2025-12-10)The remarkable diversity of neuronal morphologies has continued to fascinate researchers since Ramón y Cajal's pioneering work in 1911. A neuron's dendritic shape determines the inputs it receives, and, consequently, the ... -
Designing a System for Tracking and Spatio-Temporal Action Classification of Primates
(2025-12-10)Primate researchers in both laboratory settings and natural environments are fundamentally interested in primate behavior. Approaches range from controlled laboratory setups enabling implant-based neuronal recordings to ... -
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 ... -
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, ... -
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 ... -
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 ... -
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 ...