Browsing Fakultät für Mathematik und Informatik (inkl. GAUSS) by Issue Date
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Adaptive numerical methods for optimal and branched transport problems
(20231120)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 ... 
Diophantine problems: inequalities and abelian varieties
(20231110)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 ... 
ServiceDifferentiated Cooperative Routing in the Internet of Things
(20231106)The IPv6 Routing Protocol for Lowpower 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
(20231025)In this thesis, I consider two Diophantine norm equations. For the equation of the NagellLjunggren equation $\frac{x^p1}{x1} = p^e y^q$ with distinct odd prime exponents $p, q$, I show that, for $p > 3$, it has no ... 
A Wassersteinlike Distance on Vector Fields
(20231006)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
(20231002)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
(20230929)One of the main objectives of structural biology is to understand the complicated threedimensional structure of biomolecules, and thus provide meaningful links between structure and functionality. There is a wide range ... 
Twisted equivariant Ktheory and equivariant Tduality
(20230918)This thesis is about two things: twisted equivariant Ktheory and equivariant topological Tduality. First, we prove a fixed point decomposition theorem for twisted equivariant Ktheory, generalising a result of Atiyah and ... 
Weakly Regular Hyperbolic Boundary Value Problems of Real Type
(20230911)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 socalled hyperbolic region. Such ... 
Scalable and Reliable Framework to Detect and Mitigate DDoS Attack in OpenFlowbased SDN Network
(20230810)Softwaredefined 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
(20230713)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 ... 
Aspectbased Document Similarity for Literature Recommender Systems
(20230620)Literature recommendation systems assist readers in the discovery of relevant documents. Contentbased systems recommend documents similar to the currently viewed document. However, the simple distinction between similar ... 
Learningbased Biomimetic Strategies for Developing Control Schemes for Lower Extremity Rehabilitation Robotic Devices
(20230616)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 ... 
Propagation of polarization sets for systems of generalized transverse type and for systems of MHD type
(20230616)Polarization sets were introduced by Dencker (1982) as a refinement of wavefront sets to the vectorvalued 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
(20230616)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 ... 
Diophantine problems over global fields and a conjecture of Artin over function fields
(20230526)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 ... 
NovikovShubin Invariants of Nilpotent Lie Groups
(20230525)NovikovShubin invariants are socalled L2invariants of noncompact manifolds. They are defined using the Laplace operators and measure the density of their spectra near zero. This nearzero part of the spectrum is ... 
Interpreting and visualizing the decisions of Deep Neural Networks
(20230420)Machine learning and its associated algorithms involving deep neural networks have gained widespread admiration in the computer vision domain. In this regard, significant progress has been made in automating certain ... 
Concordances in Positive Scalar Curvature and Index Theory
(20230224)We apply the strategy to study of diffeomorphisms via block diffeomorphisms to the world of positive scalar curvature (psc) metrics. For each closed psc manifold, we construct the cubical set of all psc block metrics, the ... 
Highorder Unfitted Discretizations for Partial Differential Equations Coupled with Geometric Flow
(20230217)We consider a moving free boundary problem where a diffusion equation posed on an evolving domain bounded by a smooth surface is coupled with a mean curvature flow of the bounding surface. The evolution velocity of the ...