Fakultät für Mathematik und Informatik (inkl. GAUSS): Recent submissions
Now showing items 21-40 of 531
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An Integration Theorem for Representations of the Tangent Algebroid
(2024-02-09)This dissertation investigates representations of Lie groupoids and Lie algebroids and the connection between them. Lie groupoids and Lie algebroids are differential-geometric generalisations of Lie groups and Lie ... -
Toward Trustworthiness of Deep Learning Models for 12-Lead ECGs
(2024-01-31)A 12-lead electrocardiogram (ECG), a common examination tool in cardiology, represents the electrical activity of the heart as waveforms. Predictions and classifications with deep learning (DL) algorithms show great potential ... -
A Multi-Layered Identity and Access Management Solution for Establishment of Scalable Federated Identity
(2023-12-22)Federated identity management (FIM) systems are defined as a group of organizations (entities) that have agreed to establish trust relationships and share identity information to enable seamless access to resources across ... -
Adaptive numerical methods for optimal and branched transport problems
(2023-11-20)Optimal transport is an area of mathematical research that has been gaining popularity in recent years in various application fields such as economics, statistics or machine learning. Two important factors behind its ... -
Improving the analysis of aeroacoustic measurements through machine learning
(2023-11-20)This thesis focuses on improving the analysis of aeroacoustic imaging methods using automated data processing and machine learning. Imaging methods result in beamforming maps that are challenging to explore manually since ... -
Diophantine problems: inequalities and abelian varieties
(2023-11-10)In this thesis we consider the density of rational points near manifolds and a bound for the torsion on a simple abelian variety of type IV over a number field. In the first part the main result is an asymptotic for the ... -
Service-Differentiated Cooperative Routing in the Internet of Things
(2023-11-06)The IPv6 Routing Protocol for Low-power and Lossy Networks (RPL) was designed to operate with different Internet of Things (IoT) applications ranging from regular, to critical, to alarm/sporadic. That is due to its ability ... -
Cyclotomic Norm Diophantine Equations
(2023-10-25)In this thesis, I consider two Diophantine norm equations. For the equation of the Nagell-Ljunggren equation $\frac{x^p-1}{x-1} = p^e y^q$ with distinct odd prime exponents $p, q$, I show that, for $p > 3$, it has no ... -
A Wasserstein-like Distance on Vector Fields
(2023-10-06)We introduce a new distance on the space of vector fields over a Riemannian manifold that is motivated by the construction and properties of the Wasserstein distance. The construction relies on a particular metric on the ... -
Rational points and lines on cubic hypersurfaces
(2023-10-02)We study the solubility of cubic diophantine equations. In the first chapter, we discuss the convergence of the singular series of a cubic form, which is a central object in the study of the solutions of the associated ... -
Mathematics of Biomolecular Structure Experiments
(2023-09-29)One of the main objectives of structural biology is to understand the complicated three-dimensional structure of biomolecules, and thus provide meaningful links between structure and functionality. There is a wide range ... -
Twisted equivariant K-theory and equivariant T-duality
(2023-09-18)This thesis is about two things: twisted equivariant K-theory and equivariant topological T-duality. First, we prove a fixed point decomposition theorem for twisted equivariant K-theory, generalising a result of Atiyah and ... -
Weakly Regular Hyperbolic Boundary Value Problems of Real Type
(2023-09-11)In this thesis, we derive energy estimates for weakly regular hyperbolic boundary value problems of real type, for which the Lopatinskii condition degenerates in a specific way in the so-called hyperbolic region. Such ... -
Scalable and Reliable Framework to Detect and Mitigate DDoS Attack in OpenFlow-based SDN Network
(2023-08-10)Software-defined networking in recent years has come into the sight of so many network designers as a successor to traditional networking. Unlike traditional networks where control and data planes engage together within a ... -
A Central Limit Theorem for Functions on Weighted Sparse Inhomogeneous Random Graphs
(2023-07-13)We prove a central limit theorem for a certain class of functions on weighted sparse inhomogeneous random graphs. The proof uses a perturbative form of Stein's method and relies on a careful analysis of the local structure ... -
Aspect-based Document Similarity for Literature Recommender Systems
(2023-06-20)Literature recommendation systems assist readers in the discovery of relevant documents. Content-based systems recommend documents similar to the currently viewed document. However, the simple distinction between similar ... -
Propagation of polarization sets for systems of generalized transverse type and for systems of MHD type
(2023-06-16)Polarization sets were introduced by Dencker (1982) as a refinement of wavefront sets to the vector-valued case. He also clarified the propagation of polarization sets when the characteristic variety of the pseudodifferential ... -
Surface waves as Fourier integral operators with complex phase
(2023-06-16)This thesis studies linear hyperbolic boundary value problems that admit surface waves as solutions. Surface waves are related to a specific type of weakly regular hyperbolic boundary value problems, where the precise ... -
Learning-based Biomimetic Strategies for Developing Control Schemes for Lower Extremity Rehabilitation Robotic Devices
(2023-06-16)Lower limb disabilities caused by factors such as amputation, neuromuscular impairment, and traumatic injury can significantly impact mobility and quality of life. To restore impaired functionality, individuals may use ... -
Diophantine problems over global fields and a conjecture of Artin over function fields
(2023-05-26)This thesis considers three diophantine problems over different global fields and Artin's primitive root conjecture over function fields. In the first chapter, which is a joint project with Christian Bernert, the main ...