Dokumente Fakultät für Mathematik und Informatik (inkl. GAUSS) nach Erscheinungsdatum
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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 ... -
Computational Complexity Meets Statistical Efficiency: From Change Point Estimation to Monotonicity Testing
(2025-04-04)In the Information Age, statistical efficiency and computational tractability have become equally important. In this dissertation, we propose two novel statistical procedures: the Fast and Optimal Monotonicity Test (FOMT) ... -
Deep Probabilistic Priors for Solving Inverse Problems
(2025-03-20)Inverse problems are problems where causal sources are inferred from observed effects. They are ubiquitous in science and engineering. Examples include image reconstruction from neural responses, feature visualizations of ... -
Higher Order Unfitted Space-Time Finite Element Methods for Moving Domain Problems
(2025-01-13)Finite Element methods are a well-established tool for simulating the behaviour of systems from various applications stemming from physics, engineering, and other sciences. In recent years, Unfitted Finite Element methods ... -
Domain decomposition for optimal transport and localized optimality conditions
(2024-12-19)Optimal transport (OT) is a fundamental tool in the study of the space of probability measures. Several algorithmic breakthroughs, such as the Sinkhorn algorithm, have allowed practicioners to solve the OT problem ... -
Energy-based geometric regularization in three-dimensional inverse obstacle scattering
(2024-12-13)The classic "inverse obstacle scattering problem" in three-dimensions names the challenge of reconstructing 3D-objects from (noisy) far-fied measurements of scattered waves. Like any interesting inverse problem, this ... -
C*-algebras of relatively proper groupoid correspondences
(2024-12-09)The objective of the work is to study C*-algebras associated to relatively proper groupoid correspondences, in particular exploring two constructions and proving that they are isomorphic. We also explore some properties ... -
Aspects of Temporal Patient Similarity in Complex Diseases
(2024-12-09)When comparing patients with complex chronic diseases, such as cancer or Post COVID-19, in Real-World Data (RWD) it is crucial to consider not only their condition at the time point of analysis but also their disease ... -
Statistical Limit Laws for Graph Cuts and Efficient Surrogate Algorithms
(2024-12-05)Graph cuts are a powerful tool that has been used in many applications, from image segmentation and machine learning to network analysis and cluster identification, often in the form of a convex relaxation such as spectral ... -
Microlocal methods in quantum field theory
(2024-11-14)The renormalisation of Feynman diagrams is considered in the context of perturbative algebraic quantum field theory. The construction of Wick polynomials is related to the renormalisation of diagrams with short loops ... -
Privacy-Decision Assisting Techniques
(2024-11-12)In an era where digital communication and content sharing proliferate, managing and protecting users' privacy becomes increasingly challenging and crucial. This particularly intensifies with the fast-paced adoption of ... -
Development of tools to process and analyse precision oncology data in a clinical decision support framework for biomedical research projects in the scope of molecular tumour boards
(2024-11-12)The goal of precision medicine is to tailor treatments to the individual genetic profile of cancer patients, but it faces several challenges. These include the genetic complexity of tumours, the large volume of data generated ... -
Computer Vision for Automated Robotic Device Disassembly: Object Detection, Pose Estimation, and Action Prediction
(2024-11-12)The growth in population and technology has led to an increased demand for electronic products, resulting in a higher volume of end-of-life devices. While recycling these products is critical for reducing environmental ... -
Algorithms for Matching and Analysis Problems on Subsequences
(2024-10-14)The focus of this thesis is on the study of efficient algorithms and computational complexity results for matching and analysis problems on subsequences. The presented results comprise algorithmic solutions and lower ... -
Utilizing HPC Systems to Serve Compute-Intensive Tasks from a Data Lake Managing Sensitive Data
(2024-10-10)Data lakes have been proposed by James Dixon in 2010 to prevent information loss happening during the extract-transform-load process usually employed to ingest data into a data warehouse. Instead, he proposed a schema-on-read ... -
Exploring Stickiness in CAT(κ) Spaces
(2024-10-10)The Fréchet mean is a natural generalization of the expectation to probability distributions on arbitrary metric spaces. In recent years, several seemingly related phenomena were observed for certain distributions on ... -
Novel machine learning solutions for precision medicine - from causal inference to cellular perturbations and interactions
(2024-10-04)Optimal therapy of complex diseases necessitates a shift from one-size-fits-all solutions towards personalized treatment plans. To achieve this, it is crucial to understand the casual effect of medical interventions, such ... -
Higher Currents for the sine-Gordon Model in perturbative Algebraic Quantum Field Theory
(2024-09-19)The main results of this thesis are the establishment of the super-renormalizability by power counting and of the summability of an infinite number of (classically conserved) higher currents for the sine-Gordon model in ...