Mathematics - General

This thesis contributes to the fields of data compression and compressed sensing and their application to imaging mass spectrometry and sporadic communication. Compressed sensing is mainly built on the knowledge that most data is compressible or sparse, meaning that most of its content is...

Network design models have been considered for a long time to solve practical problems from different areas such as transportation planning, distribution network design, or communication networks design, and ever since, these models and the development of efficient solution methods have been a major...

The Fields medalist, Terence Tao, recently emphasized the importance of "hard" (or finitary) analysis and connected the finitisation to the methods we will employ in this thesis: ... The main advantage of working in a finitary setting ... is that the underlying dynamical system...

Networked Control Systems are control systems, where the feedback loop is closed by a communication system. Within the past decades, the effects of the properties of the communication system, like loss, delay, or bandwidth constraints, on the control performance have been studied thoroughly. Since...

This thesis is concerned with the sequential detection of gradual changes in the location of a stochastic process in two different settings: In Chapter 1 we consider a general stochastic process with a linear drift term which exhibits a possible gradual (non-linear) perturbation at...

This work addresses the analysis of a sequential chain of processing steps, which is particularly important for the manufacture of robust product components. In each processing step, the material properties may have changed and distributions of related characteristics, for example, strains, may become inhomogeneous....

These Lecture Notes provide an introduction to classical statistical mechanics. The first part presents classical results, mainly due to L. Boltzmann and J.W. Gibbs, about equilibrium statistical mechanics of continuous systems. Among the topics covered are: kinetic theory of gases, ergodic problem, Gibbsian formalism,...

Many tasks in operations management require the solution of complex optimization problems. Problems in which decisions are taken sequentially over time can be modeled and solved by dynamic programming. Real-world dynamic programming problems, however, exhibit complexity that cannot be handled by conventional solution techniques....

This thesis investigates the role of duality and the use of approximation methods in cooperative optimization and control. Concerning cooperative optimization, a general algorithm for convex optimization in networks with asynchronous communication is presented. Based on the idea of polyhedral approximations, a family of...

The present thesis introduces a new approach for the generation of Ck - approximants of functions defined on closed submanifolds for arbitrary k in N. In case a function on a surface resembles the three coordinates of a topologically equivalent surface in R3, we...

English summary: Today's globalized business environment is characterized by a strong competitive pressure which requires companies to improve their supply chains' effectiveness and efficiency by coordination. However, the organizational structures are more and more characterized by networks containing equal partners which restricts the application...

These Lecture Notes provide an introduction to the theory of finite-dimensional dynamical systems. The first part presents the main classical results about continuous time dynamical systems with a finite number of degrees of freedom. Among the topics covered are: initial value problems, geometrical methods...

Many complex chemical processes are responsible for the proper functioning of the human body. A prime example is the finely structured endoplasmic reticulum, which plays an important role in the metabolisms of human cells. To handle mathematical models that account for this fine structure,...

In this thesis a functorial approach to the category of derived manifolds is developed. We use a similar approach as Demazure and Gabriel did when they described the category of schemes as a full subcategory of the category of sheaves on the big Zariski...

The Boolean satisfiability problem (SAT) and its generalization to variables of higher arities - constraint satisfaction problems (CSP) - can arguably be called the most "natural" of all NP-complete problems. The present work is concerned with their algorithmic treatment. It consists of two parts....

The objective of this thesis is the development of novel model predictive control (MPC) schemes for nonlinear continuous-time systems with and without time-delays in the states which guarantee asymptotic stability of the closed-loop. The most well-studied MPC approaches with guaranteed stability use a control...

This PhD thesis was written at ETH Zurich, in Prof. Dr. Emo Welzl's research group, under the supervision of Dr. Bernd Garnter. It shows two theoretical results that are both related to quadratic programming. The first one concerns the abstract optimization framework of violator...

This thesis contains a comprehensive presentation of fundamental problems and novel mathematical questions in structural dynamics. An introduction to the theory and a motivation of the mathematical models are given in the beginning. The basic principles of the finite element method are introduced and...

In this thesis, we will focus on inverse problems appearing in ultra precise turning processes. Ultra precision turning is widely used to manufacture metallic surfaces with high surface quality. One crucial influencing factor of the surface quality is unbalances leading to vibrations of the...

Das Multi-Ionen Transport und Reaktionsmodell wird fur die Simulation von elektrochemischen Prozessen eingesetzt. Das durch das Modell gegebene System partieller Differentialgleichungen (PDE) wird mit Hilfe einer gemischten Residuen-Distribution und Finiten Elemente Methode diskretisiert und mit dem Newton Verfahren linearisiert. Dabei entstehen eine Reihe linearer...

Steel is an important material in various applications. It has a complex material behaviour which is, in addition to elastic and plastic effects, basically characterised by phase transitions. An important feature in this context is the transformation-induced plasticity, which arises during phase transitions and...

This work deals with theoretical aspects of creating purposeful self-organization in collective autonomous systems. The core of this approach is closely related to a qualitative dynamics of corresponding models and to the reductive synergetic approach. Changes of qualitative dynamics can be associated with, for...

The Godel spacetime is an important cosmological solution of Einstein's field equations of gravitation. Although it does not offer a viable description of the physical universe, it illustrates the theoretical possibility of time travel. This work investigates world models similar to the Godel spacetime...

For over thirty years bound states of gluons are an outstanding problem of both theoretical and experimental physics. Being predicted by Quantum-Chromodynamics their experimental confirmation is one of the foremost goals of large experimental facilities currently under construction like FAIR in Darmstadt. This thesis...

Discrete geometry has been among the fastest growing fields of mathematics in the last decades. One of the most fascinating objects studied in discrete geometry are k-sets. Not only are they extremely difficult to understand but they also play an important role in estimating...

This thesis addresses optimal control of discrete-time switched linear systems with application to networked embedded control systems (NECSs). Part I focuses on optimal control and scheduling of discrete-time switched linear systems. The objective is to simultaneously design a control law and a switching (scheduling)...

In the mathematical theory of viscous incompressible fluids the fundamental model is provided by the incompressible Navier-Stokes equations. For the last 20 years the analysis of the Navier-Stokes equations in the exterior of a moving and rotating obstacle has attracted particular attention. The main...

There is a variety of finite element based methods applicable to the discretization of second order elliptic boundary value problems in mixed form. However, it is expensive to solve the resulting discrete linear system due to its size and its algebraic structure. Hybridization serves...

This thesis focuses on the exploration of polygonal environments with simple agents. The goal is to understand what minimal capabilities such agents need in order to draw a map of their environment. Starting from a very basic agent model, we investigate what extra capabilities...

Lie groups and their "derived objects", Lie algebras, appear in various fields of mathematics and physics. At least since the beginning of the 20th century, and after the famous works of Wilhelm Killing, Elie Cartan, Eugenio Elia Levi, Anatoly Malcev and Igor Ado on...

Combinatorial topology is a field of research that lies in the intersection of geometric topology, combinatorics, algebraic topology and polytope theory. The main objects of interest are piecewise linear topological manifolds where the manifold is given as a simplicial complex with some additional combinatorial...

Several regularization methods for variational inequalities and fixed point problems are studied. Known convergence results especially require some kind of monotonicity of the problem data as well as, especially for Bregman-function-based algorithms, some additional assumption known as the cutting plane property. Unfortunately, these assumptions...

Classical orthogonal polynomials and the related associated functions are real classics in approximation theory. They share a rich history of research that has uncovered their many relationships to topics of fundamental importance. This text develops a new aspect of the so-called connection problem. This...

Adaptivity is a crucial tool in state-of-the-art scientific computing. However, its theoretical foundations are only understood partially and are subject of current research. This self-contained work provides theoretical basics on partial differential equations and finite element discretizations before focusing on adaptive finite element methods...

In this thesis, we will analyze an approach to describe the rotational behaviour of dynamical systems and control systems, namely the concept of rotational factor maps. The general idea is to find a complex-valued map F on the state space that maps the dynamics...

This dissertation demonstrates that graphics processors (GPUs) as representatives of emerging many-core architectures are very well-suited for the fast and accurate solution of large, sparse linear systems of equations, using parallel multigrid methods on heterogeneous compute clusters. Such systems arise for instance in the...

In recent years there has been an increasing interest in the regularization of ill-posed inverse problems for operators mapping between two Banach spaces. This thesis focuses on the case of linear, continuous operators and Banach spaces, which are convex of power type and/or smooth...

Increasing complexity combined with decreasing geometrical sizes in electric circuit design lead to high dimensional dynamical models to be considered by EDA tools. Model order reduction (MOR) has become a popular strategy to decrease the problem's size while preserving its crucial properties. MOR shall...

Modern computer networks or wireless ad-hoc networks offer a wide range of interesting optimization problems. Usual optimization goals are the minimization of the message delay in a Peer-to-Peer system or the minimization of the energy consumption of a wireless network. This thesis presents different...

This book investigates the well-posedness of the mathematical model behind the method "Image Inpainting Based on Coherence Transport". Image inpainting methods serve the purpose of touching up damaged or unwanted elements of a digital picture. The model behind the mentioned method is a Dirichlet...

In a systems theoretic context, the terms 'consensus' and 'synchronization' both describe the property that all individual systems in a group behave asymptotically identical, i.e., output or state trajectories asymptotically converge to a common trajectory. The objective of the present thesis is an improved...

The research of this work is motivated by the Timetable Synchronization Problem in public transport. The problem is formulated as a multi-criteria Quadratic Semi-Assignment Problem (QSAP). This type of problem is known to be NP-hard. Therefore, the real life problem instances are solved with...

There exist very few concepts in computational algebra which are as central to theory and applications as Grobner bases. This thesis describes theory, algorithms and applications for the special case of Boolean polynomials. These parts form the mathematical foundations of the PolyBoRi framework (developed...

We consider the initial boundary value problem for the movement of a rigid body in a viscous incompressible fluid. It is shown that, locally in time, a unique strong solution exists. This result has been known in the case of Newtonian fluids, in Hilbert...

Subject of this work is the analysis of numerical methods for the solution of optimal control problems governed by elliptic partial differential equations. Such problems arise, if one does not only want to simulate technical or physical processes but also wants to optimize them...

Database transformations consist of queries and updates which are two fundamental types of computations in any databases - the first provides the capability to retrieve data and the second is used to maintain databases in light of ever-changing application domains. This dissertation aims to...

General purpose theorem provers provide sophisticated proof methods, and become valuable tools in, e.g. formal software development. Of particular interest here are proof systems with the LCF architecture, developing large theories from a small logical kernel, because this approach simplifies the validation of derived...

This text is primarily concerned with the extension of classical results in algebraic topology and related fields (such as homological algebra) to more general settings. The main subjects covered are the rational homology of H-spaces, simplicial spaces and geometric realisation, a construction of Eilenberg-Mac...

This work presents new achievements and results concerning duality in scalar convex optimization with applications in the theory of maximal monotone operators. Regularity conditions guaranteeing Fenchel and Lagrange duality expressed by means of generalized interiority notions like the quasi interior and the quasi-relative interior,...

In this book, an interdisciplinary approach combining dynamic quantitative measurements with mathematical modelling is used to solve two different problems in molecular immunology. In the first part, structure and function of the gene-regulatory network that controls differentiation of type I T-helper (Th1) cells is...