**On relating aspects of tropical geometry, cluster algebras, and zonotopal algebras**

*Brodsky, Sarah*
(2016)

Each chapter of this dissertation touches upon subjects which at first glance may not seem related. Upon subtle inspection, aspects of tropical geometry, cluster algebras, and zonotopal algebra all...

**A selection of stochastic processes emanating from natural sciences**

*Wilke Berenguer, Maite Isabel*
(2016)

The thesis consists of three independent parts: Part 1: Percolation. Chapter 1 is concerned with the topic of Lipschitz Percolation. Classic results are stated in Section 1.1 before moving on to th...

**Intersection graphs and geometric objects in the plane**

*Hoffmann, Udo*
(2016)

In this thesis, we consider several aspects of representations of graphs in the plane. We consider mainly intersection and visibility representations of graphs. In both kind of representations, the...

**Some relations between stochastic and deterministic differential equations**

*Leimbach, Matti*
(2016)

Stochastic differential equations (SDEs) have been subject of extensive research ever since the foundation was laid by Kiyoshi Itô in his brilliant work from 1944. We investigate some relations b...

**Singular SPDEs and related topics**

*Cannizzaro, Giuseppe*
(2016)

The focus of this thesis is on singular Stochastic Partial Differential Equations (SPDEs). We present two works that, in different directions, explore the possibilities offered by the paracontroll...

**Sparse recovery from Fourier measurements using compactly supported shearlets**

*Ma, Jackie Ken Yip*
(2016)

The main topic of this thesis is to study the sampling and reconstruction problem of signals that have a sparse structure. We thereby consider different models. First, we study the sampling and rec...

**On linear-quadratic control theory of implicit difference equations**

*Bankmann, Daniel*
(2016)

In this master’s thesis we adapt recent results on optimal control of continuous-time linear differential-algebraic equations to the discrete-time case of implicit difference equations. First, we a...

**Handling critical tasks online**

*Schewior, Kevin*
(2016)

In this thesis, we study two fundamental online optimization problems in which tasks arrive over time and require to be processed either immediately or until a certain deadline. The goal is to fini...

**Rough paths, probability and related topics**

*Shekhar, Atul*
(2016)

In the first part, we prove a deterministic Doob-Meyer type result for rough paths. In the probabilistic setting, the Doob-Meyer theorem says that the martingale part and bounded variation part ...

**Variational methods for discrete surface parameterization**

*Sechelmann, Stefan*
(2016)

Based on the notion of discrete conformal equivalence we investigate discrete uniformization of Riemann surfaces. We generalize the concept from triangulations to cyclic nets, i.e., meshes with fac...

**Infinitesimal deformations of discrete surfaces**

*Lam, Wai Yeung*
(2016)

We introduce Möbius invariant objects - discrete holomorphic quadratic differentials to connect discrete complex analysis, discrete integrable systems and geometric rigidity. Discrete holomorphic q...

**Shearlets on bounded domains and analysis of singularities using compactly supported shearlets**

*Petersen, Philipp Christian*
(2016)

In this thesis we discuss and extend the theory of shearlet systems. These systems were introduced by Guo, Kutyniok, Labate, Lim and Weiss, and have found a multitude of applications in signal- and...

**New importance sampling based algorithms for compensating dataset shifts**

*Vanck, Thomas*
(2016)

Usually, the classic machine learning considers two datasets X1,X2 which have been sampled i.i.d. from distributions p1 and p2. There, it is assumed that p1 = p2. Due to this assumption, models tha...

**Dewetting of thin solid films**

*Dziwnik, Marion*
(2016)

This dissertation is devoted to the mathematical study of solid state dewetting and deals with various mathematical topics such as phase field modeling, the derivation of corresponding sharp interf...

**On the mixing time of the face flip– and up/down Markov chain for some families of graphs**

*Heldt, Daniel*
(2016)

This dissertation studies two natural Markov chains, each living on a family of finite distributive lattices and some related results on the enumeration of lattice paths. In the first part of this...

**Semi-monic operator functions**

*Kallus, Paul Peter*
(2016)

Main objects of the thesis are semi-monic functions with Banach algebra coefficients. Three topics relating to these functions are discussed: We prove a Perron-Frobenius type result relating to the...

**Variational formulas for immersions into 3-manifolds**

*Chubelaschwili, David*
(2016)

In this thesis we introduce the S-theory. We apply the S-theory to variational problems of immersed Riemann surfaces, Elasticity theory and Spin theory. From classical mechanics it is known that ...

**On interpolation and approximation problems in numerical linear algebra**

*Sète, Olivier*
(2016)

This doctoral thesis is on interpolation and approximation problems in the complex plane which are motivated by questions in numerical linear algebra. In the first part of this thesis, we consider ...

**Complexity and algorithms in matching problems under preferences**

*Cseh, Agnes*
(2016)

In dieser Arbeit fokussieren wir uns auf Matching- und Flussprobleme auf Instanzen mit Präferenzen. Es werden Märkte mit Hilfe von kombinatorischer Optimierung durch Graphen modelliert. Während Her...

**The Hermite-Biehler method and functions generating the Pólya frequency sequences**

*Dyachenko, Alexander*
(2016)

Under the Hermite-Biehler method we understand the approach to problems of stability, which exploits a deep relation between Hurwitz-stable functions and mappings of the upper half of the complex p...