Fakultät für Mathematik und Informatik (inkl. GAUSS)
Recent Submissions
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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 ... -
On Combinatorial Properties of Subsequences
(2024-08-22)A word, also known as string, is a sequence of letters, while a subsequence of a word w is another word u which can be obtained by deleting some of the letters of w. Words in general, and subsequences in particular, play ... -
Mathematical Entity Linking Methods and Applications
(2024-08-15)Entity Linking (EL) is a vital component of Information Retrieval (IR) systems that extract abstract representations from text documents. As such, EL plays a crucial role in various applications such as semantic search, ... -
Analysis of Optical Coherence Tomography Images by Dictionary Learning Methods
(2024-07-17)An accurate analysis of Optical Coherence Tomography (OCT) images plays an important role in the diagnosis of abnormalities within these images. Unfortunately, noise caused by various sources degenerates the quality of the ... -
Divisors on K3 surfaces and Hilbert schemes
(2024-06-27)This thesis consists of three chapters. In the first chapter we study rational curves on K3 surfaces and show that on elliptic K3s there are rational curves whose arithmetic genus tends to infinity. In the second chapter ... -
Action understanding and prediction during inter-agent interaction
(2024-06-17)The utilisation of robotics has seen a significant rise over the years, particularly fuelled by the burgeoning advancements in deep learning and artificial intelligence research and development. Despite this progress, the ... -
Neural Networks for MRI Reconstruction
(2024-06-10)MRI is arguably the most versatile imaging modality for clinical use available today. In recent years, the development of advanced deep-learning-based reconstruction methods has significantly accelerated data acquisition ... -
Simulated Mental Imagery for Image Synthesis and its Application in Robotic Planning
(2024-06-05)The autonomy of robots is a prominent research focus in the field of robotics. A key aspect is endowing robots with the ability to accurately perceive the environment and to plan for specific tasks, which poses a considerable ... -
Towards Personalized Cardiac Modeling of Failing Heart with Engineered Heart Muscle
(2024-05-28)This dissertation investigates the biomechanics of the left ventricle across multiple geometric levels toward personalized cardiac modeling with engineered heart muscle. Firstly, a physics-based model for the EDPVR and ... -
Entwicklung einer Bewertungsmetrik für klinische Entscheidungsunterstützungssysteme (CDSS) in der Kardiologie
(2024-05-17)The topic of clinical decision support systems (CDSS) is currently in a phase of transition in which the multi-layered and comprehensive development approaches from the thematic his-tory are increasingly being used in both ... -
Reduction of Lie and Courant Algebroids and Application to Double Vector Bundles
(2024-05-17)In this thesis we evaluate the reduction procedure of Poisson manifolds and apply it to structures closely related to them such as Lie (bi-)algebroids, Courant algebroids and Lie-Rinehart algebras. Moreover, we apply this ... -
All Ravens are Black—Formalisation and Computational Analysis of Generalising Statements in Natural Language
(2024-05-16)This interdisciplinary thesis reviews and refines the concepts of generalisation and generalising statements (e.g. all ravens are black) as a phenomenon of human cognition and language. The main parts of the thesis target ... -
Development of Advanced Generative Priors for MRI Reconstruction
(2024-05-02)This thesis investigates generative models for parallel compressed magnetic resonance imaging (MRI) reconstruction. The challenges of compressed MRI reconstruction using deep learning are identified, including model ... -
Statistical Optimal Transport and its Entropic Regularization: Compared and Contrasted
(2024-04-26)In recent years, statistical methodology based on optimal transport witnessed a considerable increase in practical and theoretical interest. A central reason for this trend is the ability of optimal transport to compare ... -
Controlling Data Streams of IoT Devices in Smart Homes from a User Perspective
(2024-04-16)Increasingly, humans are surrounded by intelligent devices, such as smart devices, in the Internet of Things (IoT) context. These smart devices are used in various environments, such as smart environments as well as homes. ... -
Generalizations of Quandles to Multi-Linkoids
(2024-04-10)In this thesis, we define the fundamental quandle of knotoids and linkoids and prove that it is invariant under the under forbidden-move and hence encodes only the information of the underclosure of the knotoid. We ...