E-Dissertationen: Suche
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Error analysis of regularized and unregularized least-squares regression on discretized function spaces
(2017-01-04)
In this thesis, we analyze a variant of the least-squares regression method which operates on subsets of finite-dimensional vector spaces.
In the first part, we focus on a regression problem which is constrained to ...
In the first part, we focus on a regression problem which is constrained to ...
Plasticity as the Γ-limit of a Dislocation Energy
(2017-07-19)
In this thesis, we derive macroscopic crystal plasticity models from mesoscopic dislocation models by means of Γ-convergence as the interatomic distance tends to zero. Crystal plasticity is the effect of a crystal undergoing ...
An Easton-like Theorem for all Cardinals in ZF
(2020-07-01)
We show that in Zermelo-Fraenkel Set Theory without the Axiom of Choice (ZF), a surjectively modified Continuum Function θ(κ) can take almost arbitrary values on all cardinals. This is in sharp contrast ......
Natural maps in higher Teichmüller theory
(2021-09-17)
In this thesis we consider harmonic maps and barycentric maps in the context of higher Teichmüller theory. We are particularly interested in how these maps can be used to study Hitchin representations. The main results of ...
Algebraic Multigrid for Meshfree Methods
(2020-02-11)
This thesis deals with the development of a new Algebraic Multigrid method (AMG) for the solution of linear systems arising from Generalized Finite Difference Methods (GFDM). In particular, we consider the Finite Pointset ...
Sedimentation of particle suspensions in Stokes flows
(2020-05-14)
In this thesis, we consider problems arising from the physical phenomenon of particle sedimentation. We focus on non-Brownian particles in fluids at zero Reynolds number. Microscopically, the particle
system is described ...
Approximation Algorithms for Traveling Salesman Problems
(2020-04-15)
The traveling salesman problem is the probably most famous problem in combinatorial optimization. Given a graph G and nonnegative edge costs, we want to find a closed walk in G that visits every vertex at least once and ...
Heat flow aspects of synthetic Ricci bounds in the extended Kato class
(2022-01-21)
This thesis studies heat flows acting on different objects on possibly singular spaces that admit synthetic lower Ricci curvature bounds by constants, functions, or signed measures. Geometric properties of such spaces and ......
On the membrane model and the discrete Bilaplacian
(2021-04-26)
This thesis is concerned with the membrane model, an example of a discrete random interface model. This model arises, for example, when studying thermal fluctuations in biomembranes. Mathematically, it is given as a Gibbs ...
Numerical Methods for Optimal Transport and Elastic Shape Optimization
(2019-12-06)
In this thesis, we consider a novel unbalanced optimal transport model incorporating singular sources, we develop a numerical computation scheme for an optimal transport distance on graphs, we propose a simultaneous elastic ...