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#### Faculty / Organisational entity

- Fachbereich Mathematik (40)
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Mechanical ventilation of patients with severe lung injury is an important clinical treatment to ensure proper lung oxygenation and to mitigate the extent of collapsed lung regions. While current imaging technologies such as Computed Tomography (CT) and chest X-ray allow for a thorough inspection of the thorax, they are limited to static pictures and exhibit several disadvantages, including exposure to ionizing radiation and high cost. Electrical Impedance Tomography (EIT) is a novel method to determine functional processes inside the thorax such as lung ventilation and cardiac activity. EIT reconstructs the internal electrical conductivity distribution within the thorax from voltage measurements on the body surface. Conductivity changes correlate with important clinical parameters such as lung volume and perfusion. Current EIT systems and algorithms use simplified or generalized thorax models to solve the reconstruction problem, which reduce image quality and anatomical significance. In this thesis, the development of a clinically relevant workflow to compute sophisticated three-dimensional thorax models from patient-specific CT data is described. The method allows medical experts to generate a multi-material segmentation in an interactive and fast way, while a volumetric mesh is computed automatically from the segmentation. The significantly improved image quality and anatomical precision of EIT images reconstructed with these 3D models is reported, and the impact on clinical applicability is discussed. In addition, three projects concerning quantitative CT (qCT) measurements and multi-modal 3D visualization are presented, which demonstrate the importance and productivity of interdisciplinary research groups including computer scientists and medical experts. The results presented in this thesis contribute significantly to clinical research efforts to pave the way towards improved patient-specific treatments of lung injury using EIT and qCT.

Variational methods in imaging are nowadays developing towards a quite universal and
exible
tool, allowing for highly successful approaches on tasks like denoising, deblurring, inpainting,
segmentation, super-resolution, disparity, and optical flow estimation. The overall structure of such approaches is of the form
D(Ku) + alpha R(u) to min_u
;
where the functional D is a data fidelity term also depending on some input data f and
measuring the deviation of Ku from such and R is a regularization functional. Moreover
K is a (often linear) forward operator modeling the dependence of data on an underlying
image, and alpha is a positive regularization parameter. While D is often smooth and (strictly)
convex, the current practice almost exclusively uses nonsmooth regularization functionals.
The majority of successful techniques is using nonsmooth and convex functionals like the total variation and generalizations thereof, cf. [28, 31, 40], or l_1-norms of coeefficients arising
from scalar products with some frame system, cf. [73] and references therein.
The efficient solution of such variational problems in imaging demands for appropriate algorithms.
Taking into account the specific structure as a sum of two very different terms
to be minimized, splitting algorithms are a quite canonical choice. Consequently this field
has revived the interest in techniques like operator splittings or augmented Lagrangians. In
this chapter we shall provide an overview of methods currently developed and recent results
as well as some computational studies providing a comparison of different methods and also
illustrating their success in applications.
We start with a very general viewpoint in the first sections, discussing basic notations, properties
of proximal maps, firmly non-expansive and averaging operators, which form the basis
of further convergence arguments. Then we proceed to a discussion of several state-of-the
art algorithms and their (theoretical) convergence properties. After a section discussing issues
related to the use of analogous iterative schemes for ill-posed problems, we present some practical convergence studies in numerical examples related to PET and spectral CT reconstruction.

The study addresses the effect of multiple jet passes and other parameters namely feedrate, water pressure and standoff distance in waterjet peening of metallic
surfaces. An analysis of surface integrity was used to evaluate the performance of
different parameters in the process. An increase in the number of jet passes and
pressure leads to a higher roughness and more erosion and also a higher hardness.
In contrast, the feedrate shows a reverse effect on those surface characteristics.
There exists a specific value of standoff distance that results in the maximum surface
roughness, erosion as well as hardness. Analysis of the surface microstructure gave
a good insight into the mechanism material removal process involving initial and
evolved damage. Also, the waterjet peening process was optimized based on the
design of experiment approach. The developed empirical models had shown
reasonable correlations between the measured and predicted responses. A proper selection of waterjet peening parameters can be formulated to be used in practical
works.

This PhD-Thesis deals with the calculation and application of a new class of invariants, that can be used to recognize patterns in tensor fields (i.e. scalar fields, vector fields und matrix fields), and by the composition of scalar fields with delta-functions also to point-clouds.
In the first chapter an overview over already existing invariants is given.
In the second chapter the general definition of the new invariants is given:
starting with a tensor field a set of moment tensor is created via folding in tensor-product manner with different orders of the tensor product of the positional vector. From these, rotational invariant values are calculated via contraction of tensor products. An algorithm to get a complete and independent set of invariants from a given moment tensor set is described. Furthermore methods to make these sets of invariants invariant against translation, rotation, scaling, and affine transformation.
In the third chapter, a method to optimize the calculation of these sets of invariants is described: every invariant can be modeled as undirected graph comprising multiple sub-graphs representing partially contracted tensor products of the moment tensors.
The composition of the sets of invariants is optimized by a clever choice of the decomposition into sub-graphs, all paths creating a hyper-graph of sub-graphs where each node describes a composition step. Finally, C++-source-code is created, which optimized using the symmetry of the different tensors and tensor-products, and a comparison of the effort to other calculation methods of invariants is given.
The fourth chapter describes the application of the invariants to object recognition in point-clouds from 3D-scans. To do this, the invariants of sub-sets of point-clouds are stored for every known object. Afterwards, invariants are calculated from an unknown point-cloud and tried to find them in the database to assign it to one of the known objects. Benchmarks using three 3D-object databases are made testing time and recognition rate.

Three dimensional (3d) point data is used in industry for measurement and reverse engineering. Precise point data is usually acquired with triangulating laser scanners or high precision structured light scanners. Lower precision point data is acquired by real-time structured light devices or by stereo matching with multiple cameras. The basic principle of all these methods is the so-called triangulation of 3d coordinates from two dimensional (2d) camera images.
This dissertation contributes a method for multi-camera stereo matching that uses a system of four synchronized cameras. A GPU based stereo matching method is presented to achieve a high quality reconstruction at interactive frame rates. Good depth resolution is achieved by allowing large disparities between the images. A multi level approach on the GPU allows a fast processing of these large disparities. In reverse engineering, hand-held laser scanners are used for the scanning of complex shaped objects. The operator of the scanner can scan complex regions slower, multiple times, or from multiple angles to achieve a higher point density. Traditionally, computer aided design (CAD) geometry is reconstructed in a separate step after the scanning. Errors or missing parts in the scan prevent a successful reconstruction. The contribution of this dissertation is an on-line algorithm that allows the reconstruction during the scanning of an object. Scanned points are added to the reconstruction and improve it on-line. The operator can detect the areas in the scan where the reconstruction needs additional data.
First, the point data is thinned out using an octree based data structure. Local normals and principal curvatures are estimated for the reduced set of points. These local geometric values are used for segmentation using a region growing approach. Implicit quadrics are fitted to these segments. The canonical form of the quadrics provides the parameters of basic geometric primitives.
An improved approach uses so called accumulated means of local geometric properties to perform segmentation and primitive reconstruction in a single step. Local geometric values can be added and removed on-line to these means to get a stable estimate over a complete segment. By estimating the shape of the segment it is decided which local areas are added to a segment. An accumulated score estimates the probability for a segment to belong to a certain type of geometric primitive. A boundary around the segment is reconstructed using a growing algorithm that ensures that the boundary is closed and avoids self intersections.

In the theory of option pricing one is usually concerned with evaluating expectations under the risk-neutral measure in a continuous-time model.
However, very often these values cannot be calculated explicitly and numerical methods need to be applied to approximate the desired quantity. Monte Carlo simulations, numerical methods for PDEs and the lattice approach are the methods typically employed. In this thesis we consider the latter approach, with the main focus on binomial trees.
The binomial method is based on the concept of weak convergence. The discrete-time model is constructed so as to ensure convergence in distribution to the continuous process. This means that the expectations calculated in the binomial tree can be used as approximations of the option prices in the continuous model. The binomial method is easy to implement and can be adapted to options with different types of payout structures, including American options. This makes the approach very appealing. However, the problem is that in many cases, the convergence of the method is slow and highly irregular, and even a fine discretization does not guarantee accurate price approximations. Therefore, ways of improving the convergence properties are required.
We apply Edgeworth expansions to study the convergence behavior of the lattice approach. We propose a general framework, that allows to obtain asymptotic expansion for both multinomial and multidimensional trees. This information is then used to construct advanced models with superior convergence properties.
In binomial models we usually deal with triangular arrays of lattice random vectors. In this case the available results on Edgeworth expansions for lattices are not directly applicable. Therefore, we first present Edgeworth expansions, which are also valid for the binomial tree setting. We then apply these result to the one-dimensional and multidimensional Black-Scholes models. We obtain third order expansions
for general binomial and trinomial trees in the 1D setting, and construct advanced models for digital, vanilla and barrier options. Second order expansion are provided for the standard 2D binomial trees and advanced models are constructed for the two-asset digital and the two-asset correlation options. We also present advanced binomial models for a multidimensional setting.

Embedded systems, ranging from very simple systems up to complex controllers, may
nowadays have quite challenging real-time requirements. Many embedded systems are reactive
systems that have to respond to environmental events and have to guarantee certain real-time
constrain. Their execution is usually divided into reaction steps, where in each step, the
system reads inputs from the environment and reacts to these by computing corresponding
outputs.
The synchronous Model of Computation (MoC) has proven to be well-suited for the
development of reactive real-time embedded systems whose paradigm directly reflects the
reactive nature of the systems it describes. Another advantage is the availability of formal
verification by model checking as a result of the deterministic execution based on a formal
semantics. Nevertheless, the increasing complexity of embedded systems requires to compensate
the natural disadvantages of model checking that suffers from the well-known state-space
explosion problem. It is therefore natural to try to integrate other verification methods with
the already established techniques. Hence, improvements to encounter these problems are
required, e.g., appropriate decomposition techniques, which encounter the disadvantages
of the model checking approach naturally. But defining decomposition techniques for synchronous
language is a difficult task, as a result of the inherent parallelism emerging from
the synchronous broadcast communication.
Inspired by the progress in the field of desynchronization of synchronous systems by
representing them in other MoCs, this work will investigate the possibility of adapting and use
methods and tools designed for other MoC for the verification of systems represented in the
synchronous MoC. Therefore, this work introduces the interactive verification of synchronous
systems based on the basic foundation of formal verification for sequential programs – the
Hoare calculus. Due to the different models of computation several problems have to be
solved. In particular due to the large amount of concurrency, several parts of the program
are active at the same point of time. In contrast to sequential programs, a decomposition
in the Hoare-logic style that is in some sense a symbolic execution from one control flow
location to another one requires the consideration of several flows here. Therefore, different
approaches for the interactive verification of synchronous systems are presented.
Additionally, the representation of synchronous systems by other MoCs and the influence
of the representation on the verification task by differently embedding synchronous system
in a single verification tool are elaborated.
The feasibility is shown by integration of the presented approach with the established
model checking methods by implementing the AIFProver on top of the Averest system.

This thesis is devoted to the modeling and simulation of Asymmetric Flow Field Flow Fractionation, which is a technique for separating particles of submicron scale. This process is a part of large family of Field Flow Fractionation techniques and has a very broad range of industrial applications, e. g. in microbiology, chemistry, pharmaceutics, environmental analysis.
Mathematical modeling is crucial for this process, as due to the own nature of the process, lab ex- periments are difficult and expensive to perform. On the other hand, there are several challenges for the mathematical modeling: huge dominance (up to 106 times) of the flow over the diffusion, highly stretched geometry of the device. This work is devoted to developing fast and efficient algorithms, which take into the account the challenges, posed by the application, and provide reliable approximations for the quantities of interest.
We present a new Multilevel Monte Carlo method for estimating the distribution functions on a compact interval, which are of the main interest for Asymmetric Flow Field Flow Fractionation. Error estimates for this method in terms of computational cost are also derived.
We optimize the flow control at the Focusing stage under the given constraints on the flow and present an important ingredients for the further optimization, such as two-grid Reduced Basis method, specially adapted for the Finite Volume discretization approach.

For many decades, the search for language classes that extend the
context-free laguages enough to include various languages that arise in
practice, while still keeping as many of the useful properties that
context-free grammars have - most notably cubic parsing time - has been
one of the major areas of research in formal language theory. In this thesis
we add a new family of classes to this field, namely
position-and-length-dependent context-free grammars. Our classes use the
approach of regulated rewriting, where derivations in a context-free base
grammar are allowed or forbidden based on, e.g., the sequence of rules used
in a derivation or the sentential forms, each rule is applied to. For our
new classes we look at the yield of each rule application, i.e. the
subword of the final word that eventually is derived from the symbols
introduced by the rule application. The position and length of the yield
in the final word define the position and length of the rule application and
each rule is associated a set of positions and lengths where it is allowed
to be applied.
We show that - unless the sets of allowed positions and lengths are really
complex - the languages in our classes can be parsed in the same time as
context-free grammars, using slight adaptations of well-known parsing
algorithms. We also show that they form a proper hierarchy above the
context-free languages and examine their relation to language classes
defined by other types of regulated rewriting.
We complete the treatment of the language classes by introducing pushdown
automata with position counter, an extension of traditional pushdown
automata that recognizes the languages generated by
position-and-length-dependent context-free grammars, and we examine various
closure and decidability properties of our classes. Additionally, we gather
the corresponding results for the subclasses that use right-linear resp.
left-linear base grammars and the corresponding class of automata, finite
automata with position counter.
Finally, as an application of our idea, we introduce length-dependent
stochastic context-free grammars and show how they can be employed to
improve the quality of predictions for RNA secondary structures.

In the first part of this thesis we study algorithmic aspects of tropical intersection theory. We analyse how divisors and intersection products on tropical cycles can actually be computed using polyhedral geometry. The main focus is the study of moduli spaces, where the underlying combinatorics of the varieties involved allow a much more efficient way of computing certain tropical cycles. The algorithms discussed here have been implemented in an extension for polymake, a software for polyhedral computations.
In the second part we apply the algorithmic toolkit developed in the first part to the study of tropical double Hurwitz cycles. Hurwitz cycles are a higher-dimensional generalization of Hurwitz numbers, which count covers of \(\mathbb{P}^1\) by smooth curves of a given genus with a certain fixed ramification behaviour. Double Hurwitz numbers provide a strong connection between various mathematical disciplines, including algebraic geometry, representation theory and combinatorics. The tropical cycles have a rather complex combinatorial nature, so it is very difficult to study them purely "by hand". Being able to compute examples has been very helpful
in coming up with theoretical results. Our main result states that all marked and unmarked Hurwitz cycles are connected in codimension one and that for a generic choice of simple ramification points the marked cycle is a multiple of an irreducible cycle. In addition we provide computational examples to show that this is the strongest possible statement.

Safety analysis is of ultimate importance for operating Nuclear Power Plants (NPP). The overall
modeling and simulation of physical and chemical processes occuring in the course of an accident
is an interdisciplinary problem and has origins in fluid dynamics, numerical analysis, reactor tech-
nology and computer programming. The aim of the study is therefore to create the foundations
of a multi-dimensional non-isothermal fluid model for a NPP containment and software tool based
on it. The numerical simulations allow to analyze and predict the behavior of NPP systems under
different working and accident conditions, and to develop proper action plans for minimizing the
risks of accidents, and/or minimizing the consequences of possible accidents. A very large number
of scenarios have to be simulated, and at the same time acceptable accuracy for the critical param-
eters, such as radioactive pollution, temperature, etc., have to be achieved. The existing software
tools are either too slow, or not accurate enough. This thesis deals with developing customized al-
gorithm and software tools for simulation of isothermal and non-isothermal flows in a containment
pool of NPP. Requirements to such a software are formulated, and proper algorithms are presented.
The goal of the work is to achieve a balance between accuracy and speed of calculation, and to
develop customized algorithm for this special case. Different discretization and solution approaches
are studied and those which correspond best to the formulated goal are selected, adjusted, and when
possible, analysed. Fast directional splitting algorithm for Navier-Stokes equations in complicated
geometries, in presence of solid and porous obstales, is in the core of the algorithm. Developing
suitable pre-processor and customized domain decomposition algorithms are essential part of the
overall algorithm amd software. Results from numerical simulations in test geometries and in real
geometries are presented and discussed.

This thesis focuses on dealing with some new aspects of continuous time portfolio optimization by using the stochastic control method.
First, we extend the Busch-Korn-Seifried model for a large investor by using the Vasicek model for the short rate, and that problem is solved explicitly for two types of intensity functions.
Next, we justify the existence of the constant proportion portfolio insurance (CPPI) strategy in a framework containing a stochastic short rate and a Markov switching parameter. The effect of Vasicek short rate on the CPPI strategy has been studied by Horsky (2012). This part of the thesis extends his research by including a Markov switching parameter, and the generalization is based on the B\"{a}uerle-Rieder investment problem. The explicit solutions are obtained for the portfolio problem without the Money Market Account as well as the portfolio problem with the Money Market Account.
Finally, we apply the method used in Busch-Korn-Seifried investment problem to explicitly solve the portfolio optimization with a stochastic benchmark.

The objective of this thesis consists in developing systematic event-triggered control designs for specified event generators, which is an important alternative to the traditional periodic sampling control. Sporadic sampling inherently arising in event-triggered control is determined by the event-triggering conditions. This feature invokes the desire of
finding new control theory as the traditional sampled-data theory in computer control.
Developing controller coupling with the applied event-triggering condition to maximize the control performance is the essence for event-triggered control design. In the design the stability of the control system needs to be ensured with the first priority. Concerning variant control aims they should be clearly incorporated in the design procedures. Considering applications in embedded control systems efficient implementation requires a low complexity of embedded software architectures. The thesis targets at offering such a design to further complete the theory of event-triggered control designs.

Starting from the two-scale model for pH-taxis of cancer cells introduced in [1], we consider here an extension accounting for tumor heterogeneity w.r.t. treatment sensitivity and a treatment approach including chemo- and radiotherapy. The effect of peritumoral region alkalinization on such therapeutic combination is investigated with the aid of numerical simulations.

If an automated system is tasked to provide services such as search or clustering of information on an information repository, the quality of the output depends a lot on the information that is available to the system in machine-readable form. Simple text, for example, is machine-readable only in a very limited sense. Advanced services typically need to derive other representations of the text (e.g., sets of keywords) as input for their core algorithms. Some services might need information that cannot be derived from the resource in question alone, but is available as separate metadata only, such as usage information. Annotations can be used to carry this information.
This thesis focuses on so-called ontology-based annotations. In contrast to other forms of annotations such as Tags (arbitrary strings that users can assign to resources), ontology-based annotations conform to a predefined data structure and class hierarchy. An advantage of this approach is that rich information can be stored in a well-structured way in the annotations; a drawback is that users need to be familiar with the hierarchy and other design decisions of the underlying ontology used for annotations.
Two scenarios are considered in this thesis:
First, a document-based scenario in which text annotations are used to represent both information about the text content and usage and user context information in a multi-user setting with mostly objective annotation criteria; second, a resource-based scenario whose annotation model focuses on multi-user settings with subjective annotation criteria, using (dis-)similarities in user annotations to derive user similarity metrics, and building personalized views from this information.
Finally, the prototypical systems that have been developed throughout this thesis get evaluated, proving the concepts presented in this thesis.

This thesis discusses several applications of computational topology to the visualization
of scalar fields. Scalar field data come from different measurements and simulations. The
intrinsic properties of this kind of data, which make the visualization of it to a complicated
task, are the large size and presence of noise. Computational topology is a powerful tool
for automatic feature extraction, which allows the user to interpret the information contained
in the dataset in a more efficient way. Utilizing it one can make the main purpose of
scientific visualization, namely extracting knowledge from data, a more convenient task.
Volume rendering is a class of methods designed for realistic visual representation of 3D
scalar fields. It is used in a wide range of applications with different data size, noise
rate and requirements on interactivity and flexibility. At the moment there is no known
technique which can meet the needs of every application domain, therefore development
of methods solving specific problems is required. One of such algorithms, designed for
rendering of noisy data with high frequencies is presented in the first part of this thesis.
The method works with multidimensional transfer functions and is especially suited for
functions exhibiting sharp features. Compared with known methods the presented algorithm
achieves better visual quality with a faster performance in presence of mentioned
features. An improvement on the method utilizing a topological theory, Morse theory, and
a topological construct, Morse-Smale complex, is also presented in this part of the thesis.
The improvement allows for performance speedup at a little precomputation and memory
cost.
The usage of topological methods for feature extraction on a real world dataset often
results in a very large feature space which easily leads to information overflow. Topology
simplification is designed to reduce the number of features and allow a domain expert
to concentrate on the most important ones. In the terms of Morse theory features are
represented by critical points. An importance measure which is usually used for removing
critical points is called homological persistence. Critical points are cancelled pairwise
according to their homological persistence value. In the presence of outlier-like noise
homological persistence has a clear drawback: the outliers get a high importance value
assigned and therefore are not being removed. In the second part of this thesis a new
importance measure is presented which is especially suited for data with outliers. This
importance measure is called scale space persistence. The algorithm for the computation
of this measure is based on the scale space theory known from the area of computer
vision. The development of a critical point in scale space gives information about its
spacial extent, therefore outliers can be distinguished from other critical points. The usage
of the presented importance measure is demonstrated on a real world application, crater
identification on a surface of Mars.
The third part of this work presents a system for general interactive topology analysis
and exploration. The development of such a system is motivated by the fact that topological
methods are often considered to be complicated and hard to understand, because
application of topology for visualization requires deep understanding of the mathematical
background behind it. A domain expert exploring the data using topology for feature
extraction needs an intuitive way to manipulate the exploration process. The presented
system is based on an intuitive notion of a scene graph, where the user can choose and
place the component blocks to achieve an individual result. This way the domain expert
can extract more knowledge from given data independent on the application domain. The
tool gives the possibility for calculation and simplification of the underlying topological
structure, Morse-Smale complex, and also the visualization of parts of it. The system also
includes a simple generic query language to acquire different structures of the topological
structure at different levels of hierarchy.
The fourth part of this dissertation is concentrated on an application of computational
geometry for quality assessment of a triangulated surface. Quality assessment of a triangulation
is called surface interrogation and is aimed for revealing intrinsic irregularities
of a surface. Curvature and continuity are the properties required to design a visually
pleasing geometric object. For example, a surface of a manufactured body usually should
be convex without bumps of wiggles. Conventional rendering methods hide the regions
of interest because of smoothing or interpolation. Two new methods which are presented
here: curvature estimation using local fitting with B´ezier patches and computation of reflection
lines for visual representation of continuity, are specially designed for assessment
problems. The examples and comparisons presented in this part of the thesis prove the
benefits of the introduced algorithms. The methods are also well suited for concurrent visualization
of the results from simulation and surface interrogation to reveal the possible
intrinsic relationship between them.

The present work investigated three important constructs in the field of psychology: creativity, intelligence and giftedness. The major objective was to clarify some aspects about each one of these three constructs, as well as some possible correlations between them. Of special interest were: (1) the relationship between creativity and intelligence - particularly the validity of the threshold theory; (2) the development of these constructs within average and above-average intelligent children and throughout grade levels; and (3) the comparison between the development of intelligence and creativity in above-average intelligent primary school children that participated in a special program for children classified as “gifted”, called Entdeckertag (ET), against an age-class- and-IQ matched control group. The ET is a pilot program which was implemented in 2004 by the Ministry for Education, Science, Youth and Culture of the state of Rhineland-Palatinate, Germany. The central goals of this program are the early recognition of gifted children and intervention, based on the areas of German language, general science and mathematics, and also to foster the development of a child’s creativity, social ability, and more. Five hypotheses were proposed and analyzed, and reported separately within five chapters. To analyze these hypotheses, a sample of 217 children recruited from first to fourth grade, and between the ages of six and ten years, was tested for intelligence and creativity. Children performed three tests: Standard Progressive Matrices (SPM) for the assessment of classical intelligence, Test of Creative Thinking – Drawing Production (TCT-DP) for the measurement of classical creativity, and Creative Reasoning Task (CRT) for the evaluation of convergent and divergent thinking, both in open problem spaces. Participants were divided according to two general cohorts: Intervention group (N = 43), composed of children participating in the Entdeckertag program, and a non-intervention group (N = 174), composed of children from the regular primary school. For the testing of the hypotheses, children were placed into more specific groups according to the particular hypothesis that was being tested. It could be concluded that creativity and intelligence were not significantly related and the threshold theory was not confirmed. Additionally, intelligence accounted for less than 1% of the variance within creativity; moreover, scores on intelligence were unable to predict later creativity scores. The development of classical intelligence and classical creativity throughout grade levels also presented a different pattern; intelligence grew increasingly and continually, whereas creativity stagnated after the third grade. Finally, the ET program proved to be beneficial for classical intelligence after two years of attendance, but no effect was found for creativity. Overall, results indicate that organizations and institutions such as schools should not look solely to intelligence performance, especially when aiming to identify and foster gifted or creative individuals.

We develop a framework for shape optimization problems under state equation con-
straints where both state and control are discretized by B-splines or NURBS. In other
words, we use isogeometric analysis (IGA) for solving the partial differential equation and a nodal approach to change domains where control points take the place of nodes and where thus a quite general class of functions for representing optimal shapes and their boundaries becomes available. The minimization problem is solved by a gradient descent method where the shape gradient will be defined in isogeometric terms. This
gradient is obtained following two schemes, optimize first–discretize then and, reversely,
discretize first–optimize then. We show that for isogeometric analysis, the two schemes yield the same discrete system. Moreover, we also formulate shape optimization with respect to NURBS in the optimize first ansatz which amounts to finding optimal control points and weights simultaneously. Numerical tests illustrate the theory.

ABSTRACT
"Spin and orbital contribution to the magnetic moment of transition metal clusters and complexes"
The spin and orbital contributions to the magnetic moments of isolated iron \(Fe_n^+\) \((7 ≤ n ≤ 18)\), cobalt \(Co_n^+\) \((8 ≤ n ≤ 22)\) and nickel \(Ni_n^+\) \((7 ≤ n ≤ 17)\) clusters were investigated. An experimental access to both contributions is possible by the application of x-ray magnetic circular dichroism (XMCD) spectroscopy. XMCD spectroscopy is based on x-ray absorption spectroscopy (XAS). It exploits the fact that for a magnetic sample the resonant absorption cross sections for negative and positive circular polarized x-rays differ for the transition from a spin orbit split ground state to the valence level. The resulting dichroic effects contain the information about the magnetism of the investigated sample. It can be extracted from the experimental spectrum via application of the so called sum rules. However, only the projections of the magnetic moments onto the quantization axis are experimentally accessible which corresponds to the magnetization of the sample.
We developed a method to apply XMCD spectroscopy to isolated clusters in the gas phase. A modified Fourier Transform Ion Cyclotron Resonance (FT-ICR) mass spectrometer was used to record the XA spectra in Total Ion Yield (TIY) mode, i.e. by recording the fragmentation intensity of the clusters in dependence of x-ray energy. The clusters can be considered to be a superparamagnetic ensemble. Thus, the magnetization follows a Langevin curve. The intrinsic magnetic moments can be calculated by Langevin correction of the experimental magnetic moments because the cluster temperature and the magnetic field are known.
The spin and the orbital magnetic moments are enhanced compared to the respective bulk values for all three investigated elements. The enhancement of the orbital contribution is more pronounced, by about a factor 3 - 4 compared to the bulk, than for the spin magnetic moment. However, if compared to the atomic value, both contributions are quenched. The orbital magnetic moment only amounts to about 10 - 15 % of the atomic value while the spin retains about 80 % of its atomic value. If the magnetic moments found for the clusters are put into perspective with respect to the atomic and bulk values by means of scaling laws, it becomes evident that both contributions follow different interpolations between the atomic and bulk value. The spin follows the well-known trend
\(n^{-1/3} = 1/(cluster radius)\) (n = number of atoms per cluster, assumption of a spherical particle). This trend relates to the ratio of surface to inner atoms in spherical particle. Hence, our interpretation is that the spin magnetic moment seems to follow the surface area of the cluster. On the other hand, the orbital magnetic moment follows \(1/n = 1/(cluster volume)\).
First XA spectra recorded with circularly polarized x-rays of a Single Molecule Magnet (SMM) \([Fe_4Ln_2(N_3)_4(Htea)_4(piv_6)]\) (Ln = Gd, Tb; \(H_3tea\) = triethanolamine, Hpiv = pivalic acid) are presented.

This thesis, whose subject is located in the field of algorithmic commutative algebra and algebraic geometry, consists of three parts.
The first part is devoted to parallelization, a technique which allows us to take advantage of the computational power of modern multicore processors. First, we present parallel algorithms for the normalization of a reduced affine algebra A over a perfect field. Starting from the algorithm of Greuel, Laplagne, and Seelisch, we propose two approaches. For the local-to-global approach, we stratify the singular locus Sing(A) of A, compute the normalization locally at each stratum and finally reconstruct the normalization of A from the local results. For the second approach, we apply modular methods to both the global and the local-to-global normalization algorithm.
Second, we propose a parallel version of the algorithm of Gianni, Trager, and Zacharias for primary decomposition. For the parallelization of this algorithm, we use modular methods for the computationally hardest steps, such as for the computation of the associated prime ideals in the zero-dimensional case and for the standard bases computations. We then apply an innovative fast method to verify that the result is indeed a primary decomposition of the input ideal. This allows us to skip the verification step at each of the intermediate modular computations.
The proposed parallel algorithms are implemented in the open-source computer algebra system SINGULAR. The implementation is based on SINGULAR's new parallel framework which has been developed as part of this thesis and which is specifically designed for applications in mathematical research.
In the second part, we propose new algorithms for the computation of syzygies, based on an in-depth analysis of Schreyer's algorithm. Here, the main ideas are that we may leave out so-called "lower order terms" which do not contribute to the result of the algorithm, that we do not need to order the terms of certain module elements which occur at intermediate steps, and that some partial results can be cached and reused.
Finally, the third part deals with the algorithmic classification of singularities over the real numbers. First, we present a real version of the Splitting Lemma and, based on the classification theorems of Arnold, algorithms for the classification of the simple real singularities. In addition to the algorithms, we also provide insights into how real and complex singularities are related geometrically. Second, we explicitly describe the structure of the equivalence classes of the unimodal real singularities of corank 2. We prove that the equivalences are given by automorphisms of a certain shape. Based on this theorem, we explain in detail how the structure of the equivalence classes can be computed using SINGULAR and present the results in concise form. The probably most surprising outcome is that the real singularity type \(J_{10}^-\) is actually redundant.

Researchers and analysts in modern industrial and academic environments are faced with a daunting amount of multivariate data. While there has been significant development in the areas of data mining and knowledge
discovery, there is still the need for improved visualizations and generic solutions. The state-of-the-art in visual analytics and exploratory data visualization is to incorporate more profound analysis methods while focusing on improving interactive abilities, in order to support data analysts in gaining new insights through visual exploration and hypothesis building.
In the research field of exploratory data visualization, this thesis contributes new approaches in dimension reduction that tackle a number of shortcomings in state-of-the-art methods, such as interpretability and ambiguity. By combining methods from several disciplines, we describe how ambiguity can be countered effectively by visualizing coordinate values within a lower-dimensional embedding, thereby focusing on the display of the structural composition of high-dimensional data and on an intuitive depiction of inherent global relationships. We also describe how properties and alignment of high-dimensional manifolds can be analyzed in different levels of detail by means of a self-embedding hierarchy of local projections, each using full degree of freedom, while keeping the global context.
To the application field of air quality research, the thesis provides novel means for the research of aerosol source contributions. Triggered by this particularly challenging application problem, we instigate a new research direction in the area of visual analytics by describing a methodology to model-based visual analysis that (i) allows the scientist to be “in the loop” of computations and (ii) enables him to verify and control the analysis process, in order to steer computations towards physical meaning. Careful reflection of our work in this application has led us to derive key design choices that underlie and transcend beyond application-specific solutions. As a result, we describe a general design methodology to computing parameters of a pre-defined analytical model that map to multivariate data. Core applications areas that can benefit from our approach are within engineering disciplines, such as civil, chemical, electrical, and mechanical engineering, as well as in geology, physics, and biology.

The heart is reported to show a net consumption of lactate. This may contribute up to 15% to the total body lactate disposal. In this work, the consumption of lactate was shown for the first
time on the single cell level with the new FRET-based lactate sensor Laconic.
Research published until today, almost exclusively reports the monocarboxylate transporter 1
(MCT1) as the transporter responsible for myocardial lactate uptake. As this membrane
transporter transports lactate together with H+ in a stoichiometry of 1:1, lactate transport is
coupled to pH regulation. Consequently, interactions of MCT1 and acid/base regulating proteins
(carbonic anhydrases (CAs and sodium bicarbonate co-transporters (NBCs)) are described in
the oocyte expression system, skeletal muscle and cancer cells.
In this work it is shown that activity of extracellular CA increases lactate uptake into mouse
cardiomyocytes by 27% and lactate induced JA/B by 42.8% to 46.2%. This effect is most likely
mediated via NBC/CA interaction because inhibition of extracellular CA reduces HCO3--
dependent acid extruding JA/B by 53.3% to 78.4%. This may link lactate uptake to cellular
respiration. When lactate was applied in medium gassed with 100% N2, lactate induced
acidification was 12.6% faster than in medium gassed with 100% O2. Thus, CO2 produced on
the pathway transferring redox energy from substrates like glucose and lactate to ADP and
phosphate via oxidative phosphorylation, may support further lactate uptake. The findings of
this work suggest an auto regulation of lactate uptake via CO2 release in ventricular mouse
cardiomyocytes.

We consider a network flow problem, where the outgoing flow is reduced by a certain percentage in each node. Given a maximum amount of flow that can leave the source node, the aim is to find a solution that maximizes the amount of flow which arrives at the sink.
Starting from this basic model, we include two new, additional aspects: On the one hand, we are able to reduce the loss at some of the nodes; on the other hand, the exact loss values are not known, but may come from a discrete uncertainty set of exponential size.
Applications for problems of this type can be found in evacuation planning, where one would like to improve the safety of nodes such that the number of evacuees reaching safety is maximized.
We formulate the resulting robust flow problem with losses and improvability as a mixed-integer program for finitely many scenarios, and present an iterative scenario-generation procedure that avoids the inclusion of all scenarios from the beginning. In a computational study using both randomly generated instance and realistic data based on the city of Nice, France, we compare our solution algorithms.

‘Dioxin-like’ (DL) compounds occur ubiquitously in the environment. Toxic responses associated with specific dibenzo-p-dioxins (PCDDs), dibenzofurans (PCDFs), and polychlorinated biphenyls (PCBs) include dermal toxicity, immunotoxicity, liver toxicity, carcinogenicity, as well as adverse effects on reproduction, development, and endocrine functions. Most, if not all of these effects are believed to be due to interaction of these compounds with the aryl hydrocarbon receptor (AhR).
With tetrachlorodibenzo-p-dioxin (TCDD) as representatively most potent congener, a toxic equivalency factor (TEF) concept was employed, in which respective congeners were assigned to a certain TEF-value reflecting the compound’s toxicity relative to TCDD’s.
The EU-project ‘SYSTEQ’ aimed to develop, validate, and implement human systemic TEFs as indicators of toxicity for DL-congeners. Hence, the identification of novel quantifiable biomarkers of exposure was a major objective of the SYSTEQ project.
In order to approach to this objective, a mouse whole genome microarray analysis was applied using a set of seven individual congeners, termed the ‘core congeners’. These core congeners (TCDD, 1-PeCDD, 4-PeCDF, PCB 126, PCB 118, PCB 156, and the non dioxin-like PCB 153), which contribute to approximately 90% of toxic equivalents (TEQs) in the human food chain, were further tested in vivo as well as in vitro. The mouse whole genome microarray revealed a conserved list of differentially regulated genes and pathways associated with ‘dioxin-like’ effects.
A definite data-set of in vitro studies was supposed to function as a fundament for a probable establishment of novel TEFs. Thus, CYP1A induction measured by EROD activity, which represents a sensitive and yet best known marker for dioxin-like effects, was used to estimate potency and efficacy of selected congeners. For this study, primary rat hepatocytes and the rat hepatoma cell line H4IIE were used as well as the core congeners and an additional group of compounds of comparable relevance for the environment: 1,6-HxCDD, 1,4,6-HpCDD, TCDF, 1,4-HxCDF, 1,4,6-HpCDF, PCB 77, and PCB 105.
Besides, a human whole genome microarray experiment was applied in order to gain knowledge with respect to TCDD’s impact towards cells of the immune system. Hence, human primary blood mononuclear cells (PBMCs) were isolated from individuals and exposed to TCDD or to TCDD in combination with a stimulus (lipopolysaccharide (LPS), or phytohemagglutinin (PHA)). A few members of the AhR-gene batterie were found to be regulated, and minor data with respect to potential TCDD-mediated immunomodulatory effects were given. Still, obtained data in this regard was limited due to great inter-individual differences.

In this thesis, we combine Groebner basis with SAT Solver in different manners.
Both SAT solvers and Groebner basis techniques have their own strength and weakness.
Combining them could fix their weakness.
The first combination is using Groebner techniques to learn additional binary clauses for SAT solver from a selection of clauses. This combination is first proposed by Zengler and Kuechlin.
However, in our experiments, about 80 percent Groebner basis computations give no new binary clauses.
By selecting smaller and more compact input for Groebner basis computations, we can significantly
reduce the number of inefficient Groebner basis computations, learn much more binary clauses. In addition,
the new strategy can reduce the solving time of a SAT Solver in general, especially for large and hard problems.
The second combination is using all-solution SAT solver and interpolation to compute Boolean Groebner bases of Boolean elimination ideals of a given ideal. Computing Boolean Groebner basis of the given ideal is an inefficient method in case we want to eliminate most of the variables from a big system of Boolean polynomials.
Therefore, we propose a more efficient approach to handle such cases.
In this approach, the given ideal is translated to the CNF formula. Then an all-solution SAT Solver is used to find the projection of all solutions of the given ideal. Finally, an algorithm, e.g. Buchberger-Moeller Algorithm, is used to associate the reduced Groebner basis to the projection.
We also optimize the Buchberger-Moeller Algorithm for lexicographical ordering and compare it with Brickenstein's interpolation algorithm.
Finally, we combine Groebner basis and abstraction techniques to the verification of some digital designs that contain complicated data paths.
For a given design, we construct an abstract model.
Then, we reformulate it as a system of polynomials in the ring \({\mathbb Z}_{2^k}[x_1,\dots,x_n]\).
The variables are ordered in a way such that the system has already been a Groebner basis w.r.t lexicographical monomial ordering.
Finally, the normal form is employed to prove the desired properties.
To evaluate our approach, we verify the global property of a multiplier and a FIR filter using the computer algebra system Singular. The result shows that our approach is much faster than the commercial verification tool from Onespin on these benchmarks.

Test rig optimization
(2014)

Designing good test rigs for fatigue life tests is a common task in the auto-
motive industry. The problem to find an optimal test rig configuration and
actuator load signals can be formulated as a mathematical program. We in-
troduce a new optimization model that includes multi-criteria, discrete and
continuous aspects. At the same time we manage to avoid the necessity to
deal with the rainflow-counting (RFC) method. RFC is an algorithm, which
extracts load cycles from an irregular time signal. As a mathematical func-
tion it is non-convex and non-differentiable and, hence, makes optimization
of the test rig intractable.
The block structure of the load signals is assumed from the beginning.
It highly reduces complexity of the problem without decreasing the feasible
set. Also, we optimize with respect to the actuators’ positions, which makes
it possible to take torques into account and thus extend the feasible set. As
a result, the new model gives significantly better results, compared with the
other approaches in the test rig optimization.
Under certain conditions, the non-convex test rig problem is a union of
convex problems on cones. Numerical methods for optimization usually need
constraints and a starting point. We describe an algorithm that detects each
cone and its interior point in a polynomial time.
The test rig problem belongs to the class of bilevel programs. For every
instance of the state vector, the sum of functions has to be maximized. We
propose a new branch and bound technique that uses local maxima of every
summand.

The sink location problem is a combination of network flow and location problems: From a given set of nodes in a flow network a minimum cost subset \(W\) has to be selected such that given supplies can be transported to the nodes in \(W\). In contrast to its counterpart, the source location problem which has already been studied in the literature, sinks have, in general, a limited capacity. Sink location has a decisive application in evacuation planning, where the supplies correspond to the number of evacuees and the sinks to emergency shelters.
We classify sink location problems according to capacities on shelter nodes, simultaneous or non-simultaneous flows, and single or multiple assignments of evacuee groups to shelters. Resulting combinations are interpreted in the evacuation context and analyzed with respect to their worst-case complexity status.
There are several approaches to tackle these problems: Generic solution methods for uncapacitated problems are based on source location and modifications of the network. In the capacitated case, for which source location cannot be applied, we suggest alternative approaches which work in the original network. It turns out that latter class algorithms are superior to the former ones. This is established in numerical tests including random data as well as real world data from the city of Kaiserslautern, Germany.

This dissertation focuses on the evaluation of technical and environmental sustainability of water distribution systems based on scenario analysis. The decision support system is created to assist in the decision making-process and to visualize the results of the sustainability assessment for current and future populations and scenarios. First, a methodology is developed to assess the technical and environmental sustainability for the current and future water distribution system scenarios. Then, scenarios are produced to evaluate alternative solutions for the current water distribution system as well as future populations and water demand variations. Finally, a decision support system is proposed using a combination of several visualization approaches to increase the data readability and robustness for the sustainability evaluations of the water distribution system.
The technical sustainability of a water distribution system is measured using the sustainability index methodology which is based on the reliability, resiliency and vulnerability performance criteria. Hydraulic efficiency and water quality requirements are represented using the nodal pressure and water age parameters, respectively. The U.S. Environmental Protection Agency EPANET software is used to simulate hydraulic (i.e. nodal pressure) and water quality (i.e. water age) analysis in a case study. In addition, the environmental sustainability of a water network is evaluated using the “total fresh water use” and “total energy intensity” indicators. For each scenario, multi-criteria decision analysis is used to combine technical and environmental sustainability criteria for the study area.
The technical and environmental sustainability assessment methodology is first applied to the baseline scenario (i.e. the current water distribution system). Critical locations where hydraulic efficiency and water quality problems occur in the current system are identified. There are two major scenario options that are considered to increase the sustainability at these critical locations. These scenarios focus on creating alternative systems in order to test and verify the technical and environmental sustainability methodology rather than obtaining the best solution for the current and future water distribution systems. The first scenario is a traditional approach in order to increase the hydraulic efficiency and water quality. This scenario includes using additional network components such as booster pumps, valves etc. The second scenario is based on using reclaimed water supply to meet the non-potable water demand and fire flow. The fire flow simulation is specifically included in the sustainability assessment since regulations have significant impact on the urban water infrastructure design. Eliminating the fire flow need from potable water distribution systems would assist in saving fresh water resources as well as to reduce detention times.
The decision support system is created to visualize the results of each scenario and to effectively compare these results with each other. The EPANET software is a powerful tool used to conduct hydraulic and water quality analysis but for the decision support system purposes the visualization capabilities are limited. Therefore, in this dissertation, the hydraulic and water quality simulations are completed using EPANET software and the results for each scenario are visualized by combining several visualization techniques in order to provide a better data readability. The first technique introduced here is using small multiple maps instead of the animation technique to visualize the nodal pressure and water age parameters. This technique eliminates the change blindness and provides easy comparison of time steps. In addition, a procedure is proposed to aggregate the nodes along the edges in order to simplify the water network. A circle view technique is used to visualize two values of a single parameter (i.e. the nodal pressure or water age). The third approach is based on fitting the water network into a grid representation which assists in eliminating the irregular geographic distribution of the nodes and improves the visibility of each circle view. Finally, a prototype for an interactive decision support tool is proposed for the current population and water demand scenarios. Interactive tools enable analyzing of the aggregated nodes and provide information about the results of each of the current water distribution scenarios.

Geometric Programming is a useful tool with a wide range of applications in engineering. As in real-world problems input data is likely to be affected by uncertainty, Hsiung, Kim, and Boyd introduced robust geometric programming to include the uncertainty in the optimization process. They also developed a tractable approximation method to tackle this problem. Further, they pose the question whether there exists a tractable reformulation of their robust geometric programming model instead of only an approximation method. We give a negative answer to this question by showing that robust geometric programming is co-NP hard in its natural posynomial form.

Optical character recognition (OCR) of machine printed text is ubiquitously considered as a solved problem. However, error free OCR of degraded (broken and merged) and noisy text is still challenging for modern OCR systems. OCR of degraded text with high accuracy is very important due to many applications in business, industry and large scale document digitization projects. This thesis presents a new OCR method for degraded
text recognition by introducing a combined ANN/HMM OCR approach. The approach
provides significantly better performance in comparison with state-of-the-art HMM based OCR methods and existing open source OCR systems. In addition, the thesis introduces novel applications of ANNs and HMMs for document image preprocessing and recognition of low resolution text. Furthermore, the thesis provides psychophysical experiments to determine the effect of letter permutation in visual word recognition of Latin and Cursive
script languages.
HMMs and ANNs are widely employed pattern recognition paradigms and have been
used in numerous pattern classification problems. This work presents a simple and novel method for combining the HMMs and ANNs in application to segmentation free OCR of degraded text. HMMs and ANNs are powerful pattern recognition strategies and their combination is interesting to improve current state-of-the-art research in OCR. Mostly, previous attempts in combining the HMMs and ANNs were focused on applying ANNs
as approximation of the probability density function or as a neural vector quantizer for HMMs. These methods either require combined NN/HMM training criteria [ECBG-MZM11] or they use complex neural network architecture like time delay or space displacement neural networks [BLNB95]. However, in this work neural networks are used as discriminative feature extractor, in combination with novel text line scanning mechanism, to extract discriminative features from unsegmented text lines. The features are
processed by HMMs to provide segmentation free text line recognition. The ANN/HMM modules are trained separately on a common dataset by using standard machine learning procedures. The proposed ANN/HMM OCR system also realizes to some extent several cognitive reading based strategies during the OCR. On a dataset of 1,060 degraded text lines extracted from the widely used UNLV-ISRI benchmark database [TNBC99], the presented system achieves a 30% reduction in error rate as compared to Google’s Tesseract OCR system [Smi13] and 43% reduction in error as compared to OCRopus OCR system [Bre08], which are the best open source OCR systems available today.
In addition, this thesis introduces new applications of HMMs and ANNs in OCR and document images preprocessing. First, an HMMs-based segmentation free OCR approach is presented for recognition of low resolution text. OCR of low resolution text is quite important due to presence of low resolution text in screen-shots, web images and video captions. OCR of low resolution text is challenging because of antialiased rendering and use of very small font size. The characters in low resolution text are usually joined to each other and they may appear differently at different locations on computer screen. This
work presents the use of HMMs in optical recognition of low resolution isolated characters and text lines. The evaluation of the proposed method shows that HMMs-based OCR techniques works quite well and reaches the performance of specialized approaches for OCR of low resolution text.
Then, this thesis presents novel applications of ANNs for automatic script recognition and orientation detection. Script recognition determines the written script on the page for the application of an appropriate character recognition algorithm. Orientation detection detects and corrects the deviation of the document’s orientation angle from the horizontal direction. Both, script recognition and orientation detection, are important preprocessing steps in developing robust OCR systems. In this work, instead of extracting handcrafted features, convolutional neural networks are used to extract relevant discriminative features for each classification task. The proposed method resulted in more than 95% script recognition accuracy on various multi-script documents at connected component level
and 100% page orientation detection accuracy for Urdu documents.
Human reading is a nearly analogous cognitive process to OCR that involves decoding of printed symbols into meanings. Studying the cognitive reading behavior may help in building a robust machine reading strategy. This thesis presents a behavioral study that deals on how cognitive system works in visual recognition of words and permuted non-words. The objective of this study is to determine the impact of overall word shape
in visual word recognition process. The permutation is considered as a source of shape degradation and visual appearance of actual words can be distorted by changing the constituent letter positions inside the words. The study proposes a hypothesis that reading of words and permuted non-words are two distinct mental level processes, and people use
different strategies in handling permuted non-words as compared to normal words. The hypothesis is tested by conducting psychophysical experiments in visual recognition of words from orthographically different languages i.e. Urdu, German and English. Experimental data is analyzed using analysis of variance (ANOVA) and distribution free rank tests to determine significance differences in response time latencies for two classes of data. The results support the presented hypothesis and the findings are consistent with
the dual route theories of reading.

The classic approach in robust optimization is to optimize the solution with respect to the worst case scenario. This pessimistic approach yields solutions that perform best if the worst scenario happens, but also usually perform bad on average. A solution that optimizes the average performance on the other hand lacks in worst-case performance guarantee.
In practice it is important to find a good compromise between these two solutions. We propose to deal with this problem by considering it from a bicriteria perspective. The Pareto curve of the bicriteria problem visualizes exactly how costly it is to ensure robustness and helps to choose the solution with the best balance between expected and guaranteed performance.
Building upon a theoretical observation on the structure of Pareto solutions for problems with polyhedral feasible sets, we present a column generation approach that requires no direct solution of the computationally expensive worst-case problem. In computational experiments we demonstrate the effectivity of both the proposed algorithm, and the bicriteria perspective in general.

Multilevel Constructions
(2014)

The thesis consists of the two chapters.
The first chapter is addressed to make a deep investigation of the MLMC method. In particular we take an optimisation view at the estimate. Rather than fixing the number of discretisation points \(n_i\) to be a geometric sequence, we are trying to find an optimal set up for \(n_i\) such that for a fixed error the estimate can be computed within a minimal time.
In the second chapter we propose to enhance the MLMC estimate with the weak extrapolation technique. This technique helps to improve order of a weak convergence of a scheme and as a result reduce CC of an estimate. In particular we study high order weak extrapolation approach, which is know not be inefficient in the standard settings. However, a combination of the MLMC and the weak extrapolation yields an improvement of the MLMC.

In the presented work, I evaluate if and how Virtual Reality (VR) technologies can be used to support researchers working in the geosciences by providing immersive, collaborative visualization systems as well as virtual tools for data analysis. Technical challenges encountered in the development of theses systems are identified and solutions for these are provided.
To enable geologists to explore large digital terrain models (DTMs) in an immersive, explorative fashion within a VR environment, a suitable terrain rendering algorithm is required. For realistic perception of planetary curvature at large viewer altitudes, spherical rendering of the surface is necessary. Furthermore, rendering must sustain interactive frame rates of about 30 frames per second to avoid sensory confusion of the user. At the same time, the data structures used for visualization should also be suitable for efficiently computing spatial properties such as height profiles or volumes in order to implement virtual analysis tools. To address these requirements, I have developed a novel terrain rendering algorithm based on tiled quadtree hierarchies using the HEALPix parametrization of a sphere. For evaluation purposes, the system is applied to a 500 GiB dataset representing the surface of Mars.
Considering the current development of inexpensive remote surveillance equipment such as quadcopters, it seems inevitable that these devices will play a major role in future disaster management applications. Virtual reality installations in disaster management headquarters which provide an immersive visualization of near-live, three-dimensional situational data could then be a valuable asset for rapid, collaborative decision making. Most terrain visualization algorithms, however, require a computationally expensive pre-processing step to construct a terrain database.
To address this problem, I present an on-the-fly pre-processing system for cartographic data. The system consists of a frontend for rendering and interaction as well as a distributed processing backend executing on a small cluster which produces tiled data in the format required by the frontend on demand. The backend employs a CUDA based algorithm on graphics cards to perform efficient conversion from cartographic standard projections to the HEALPix-based grid used by the frontend.
Measurement of spatial properties is an important step in quantifying geological phenomena. When performing these tasks in a VR environment, a suitable input device and abstraction for the interaction (a “virtual tool”) must be provided. This tool should enable the user to precisely select the location of the measurement even under a perspective projection. Furthermore, the measurement process should be accurate to the resolution of the data available and should not have a large impact on the frame rate in order to not violate interactivity requirements.
I have implemented virtual tools based on the HEALPix data structure for measurement of height profiles as well as volumes. For interaction, a ray-based picking metaphor was employed, using a virtual selection ray extending from the user’s hand holding a VR interaction device. To provide maximum accuracy, the algorithms access the quad-tree terrain database at the highest available resolution level while at the same time maintaining interactivity in rendering.
Geological faults are cracks in the earth’s crust along which a differential movement of rock volumes can be observed. Quantifying the direction and magnitude of such translations is an essential requirement in understanding earth’s geological history. For this purpose, geologists traditionally use maps in top-down projection which are cut (e.g. using image editing software) along the suspected fault trace. The two resulting pieces of the map are then translated in parallel against each other until surface features which have been cut by the fault motion come back into alignment. The amount of translation applied is then used as a hypothesis for the magnitude of the fault action. In the scope of this work it is shown, however, that performing this study in a top-down perspective can lead to the acceptance of faulty reconstructions, since the three-dimensional structure of topography is not considered.
To address this problem, I present a novel terrain deformation algorithm which allows the user to trace a fault line directly within a 3D terrain visualization system and interactively deform the terrain model while inspecting the resulting reconstruction from arbitrary perspectives. I demonstrate that the application of 3D visualization allows for a more informed interpretation of fault reconstruction hypotheses. The algorithm is implemented on graphics cards and performs real-time geometric deformation of the terrain model, guaranteeing interactivity with respect to all parameters.
Paleoceanography is the study of the prehistoric evolution of the ocean. One of the key data sources used in this research are coring experiments which provide point samples of layered sediment depositions at the ocean floor. The samples obtained in these experiments document the time-varying sediment concentrations within the ocean water at the point of measurement. The task of recovering the ocean flow patterns based on these deposition records is a challenging inverse numerical problem, however.
To support domain scientists working on this problem, I have developed a VR visualization tool to aid in the verification of model parameters by providing simultaneous visualization of experimental data from coring as well as the resulting predicted flow field obtained from numerical simulation. Earth is visualized as a globe in the VR environment with coring data being presented using a billboard rendering technique while the
time-variant flow field is indicated using Line-Integral-Convolution (LIC). To study individual sediment transport pathways and their correlation with the depositional record, interactive particle injection and real-time advection is supported.

Due to the increasing number of natural or man-made disasters, the application of operations research methods in evacuation planning has seen a rising interest in the research community. From the beginning, evacuation planning has been highly focused on car-based evacuation. Recently, also the evacuation of transit depended evacuees with the help of buses has been considered.
In this case study, we apply two such models and solution algorithms to evacuate a core part of the metropolitan capital city Kathmandu of Nepal as a hypothetical endangered region, where a large part of population is transit dependent. We discuss the computational results for evacuation time under a broad range of possible scenarios, and derive planning suggestions for practitioners.

In this paper we propose a procedure to extend classical numerical schemes for
hyperbolic conservation laws to networks of hyperbolic conservation laws. At the
junctions of the network we solve the given coupling conditions and minimize the
contributions of the outgoing numerical waves. This flexible procedure allows
us to also use central schemes at the junctions. Several numerical examples are
considered to investigate the performance of this new approach compared to the
common Godunov solver and exact solutions.

Monte Carlo simulation is one of the commonly used methods for risk estimation on financial markets, especially for option portfolios, where any analytical approximation is usually too inaccurate. However, the usually high computational effort for complex portfolios with a large number of underlying assets motivates the application of variance reduction procedures. Variance reduction for estimating the probability of high portfolio losses has been extensively studied by Glasserman et al. A great variance reduction is achieved by applying an exponential twisting importance sampling algorithm together with stratification. The popular and much faster Delta-Gamma approximation replaces the portfolio loss function in order to guide the choice of the importance sampling density and it plays the role of the stratification variable. The main disadvantage of the proposed algorithm is that it is derived only in the case of Gaussian and some heavy-tailed changes in risk factors.
Hence, our main goal is to keep the main advantage of the Monte Carlo simulation, namely its ability to perform a simulation under alternative assumptions on the distribution of the changes in risk factors, also in the variance reduction algorithms. Step by step, we construct new variance reduction techniques for estimating the probability of high portfolio losses. They are based on the idea of the Cross-Entropy importance sampling procedure. More precisely, the importance sampling density is chosen as the closest one to the optimal importance sampling density (zero variance estimator) out of some parametric family of densities with respect to Kullback - Leibler cross-entropy. Our algorithms are based on the special choices of the parametric family and can now use any approximation of the portfolio loss function. A special stratification is developed, so that any approximation of the portfolio loss function under any assumption of the distribution of the risk factors can be used. The constructed algorithms can easily be applied for any distribution of risk factors, no matter if light- or heavy-tailed. The numerical study exhibits a greater variance reduction than of the algorithm from Glasserman et al. The use of a better approximation may improve the performance of our algorithms significantly, as it is shown in the numerical study.
The literature on the estimation of the popular market risk measures, namely VaR and CVaR, often refers to the algorithms for estimating the probability of high portfolio losses, describing the corresponding transition process only briefly. Hence, we give a consecutive discussion of this problem. Results necessary to construct confidence intervals for both measures under the mentioned variance reduction procedures are also given.

As the complexity of embedded systems continuously rises, their development becomes more and more challenging. One technique to cope with this complexity is the employment of virtual prototypes. The virtual prototypes are intended to represent the embedded system’s properties on different levels of detail like register transfer level or transaction level. Virtual prototypes can be used for different tasks throughout the development process. They can act as executable specification, can be used for architecture exploration, can ease system integration, and allow for pre- and post-silicon software development and verification. The optimization objectives for virtual prototypes and their creation process are manifold. Finding an appropriate trade-off between the simulation accuracy, the simulation performance, and the implementation effort is a major challenge, as these requirements are contradictory.
In this work, two new and complementary techniques for the efficient creation of accurate and high-performance SystemC based virtual prototypes are proposed: Advanced Temporal Decoupling (ATD) and Transparent Transaction Level Modeling (TTLM). The suitability for industrial environments is assured by the employment of common standards like SystemC TLM-2.0 and IP-XACT.
Advanced Temporal Decoupling enhances the simulation accuracy while retaining high simulation performance by allowing for cycle accurate simulation in the context of SystemC TLM-2.0 temporal decoupling. This is achieved by exploiting the local time warp arising in SystemC TLM-2.0 temporal decoupled models to support the computation of resource contention effects. In ATD, accesses to shared resource are managed by Temporal Decoupled Semaphores (TDSems) which are integrated into the modeled shared resources. The set of TDSems assures the correct execution order of shared resource accesses and incorporates timing effects resulting from shared resource access execution and resource conflicts. This is done by dynamically varying the data granularity of resource accesses based on information gathered from the local time warp. ATD facilitates modeling of a wide range of resource and resource access properties like preemptable and non-preemptable accesses, synchronous and asynchronous accesses, multiport resources, dynamic access priorities, interacting and cascaded resources, and user specified schedulers prioritizing simultaneous resource accesses.
Transparent Transaction Level Modeling focuses on the efficient creation of virtual prototypes by reducing the implementation effort and consists of a library and a code generator. The TTLM library adds a layer of convenience functions to ATD comprising various application programming interfaces for inter module communication, virtual prototype configuration and run time information extraction. The TTLM generator is used to automatically generate the structural code of the virtual prototype from the formal hardware specification language IP-XACT.
The applicability and benefits of the presented techniques are demonstrated using an image processing centric automotive application. Compared to an existing cycle accurate SystemC model, the implementation effort can be reduced by approximately 50% using TTLM. Applying ATD, the simulation performance can be increased by a factor of up to five while retaining cycle accuracy.

Glioma is a common type of primary brain tumor, with a strongly invasive potential, often exhibiting nonuniform, highly irregular growth. This makes it difficult to assess
the degree of extent of the tumor, hence bringing about a supplementary challenge for the treatment. It is therefore necessary to understand the
migratory behavior of glioma in greater detail.
In this paper we propose a multiscale model for glioma growth and migration. Our model couples the microscale dynamics (reduced to the binding of surface receptors to the
surrounding tissue) with a kinetic transport equation for the cell density on the mesoscopic level of individual cells. On the latter scale we also include the
proliferation of tumor cells via effects of interaction with the tissue. An adequate parabolic scaling yields a convection-diffusion-reaction equation, for which the coefficients
can be explicitly determined from the information about the tissue obtained by diffusion tensor imaging. Numerical simulations relying on DTI measurements confirm the biological
findings that glioma spreads
along white matter tracts.

We argue that the concepts of resilience in engineering science and robustness in mathematical optimization are strongly related. Using evacuation planning as an example application, we demonstrate optimization techniques to improve solution resilience. These include a direct modelling of the uncertainty for stochastic or robust optimization, as well as taking multiple objective functions into account.

We consider an uncertain traveling salesman problem, where distances between nodes are not known exactly, but may stem from an uncertainty set of possible scenarios. This uncertainty set is given as intervals with an additional bound on the number of distances that may deviate from their expected, nominal value.
A recoverable robust model is proposed, that allows a tour to change a bounded number of edges once a scenario becomes known. As the model contains an exponential number of constraints and variables, an iterative algorithm is proposed, in which tours and scenarios are computed alternately.
While this approach is able to find a provably optimal solution to the robust model, it also needs to solve increasingly complex subproblems. Therefore, we also consider heuristic solution procedures based on local search moves using a heuristic estimate of the actual objective function. In computational experiments, these approaches are compared.
Finally, an alternative recovery model is discussed, where a second-stage recovery tour is not required to visit all nodes of the graph. We show that the previously NP-hard evaluation of a fixed solution now becomes solvable in polynomial time.

The ordered weighted averaging objective (OWA) is an aggregate function over multiple optimization criteria which received increasing attention by the research community over the last decade. Different to the ordered weighted sum, weights are attached to ordered objective functions (i.e., a weight for the largest value, a weight for the second-largest value and so on). As this contains max-min or worst-case optimization as a special case, OWA can also be considered as an alternative approach to robust optimization.
For linear programs with OWA objective, compact reformulations exist, which result in extended linear programs. We present new such reformulation models with reduced size. A computational comparison indicates that these formulations improve solution times.

A new algorithm for optimization problems with three objective functions is presented which computes a representation for the set of nondominated points. This representation is guaranteed to have a desired coverage error and a bound on the number of iterations needed by the algorithm to meet this coverage error is derived. Since the representation does not necessarily contain nondominated points only, ideas to calculate bounds for the representation error are given. Moreover, the incorporation of domination during the algorithm and other quality measures are discussed.

Perceptual grouping is an integral part of visual object recognition. It organizes elements within our visual field according to a set of heuristics (grouping principles), most of which are not well understood. To identify their temporal processing dynamics (i.e., to identify whether they rely on neuronal feedforward or recurrent activation), we introduce the primed flanker task that is based on a firm empirical and theoretical background. In three sets of experiments, participants responded to visual stimuli that were either grouped by (1) similarity of brightness, shape, or size, (2) symmetry and closure, or (3) Good Gestalt. We investigated whether these grouping cues were effective in rapid visuomotor processing (i.e., in terms of response times, error rates, and priming effects) and whether the results met theory-driven indicators of feedforward processing. (1) In the first set of experiments with similarity cues, we varied subjective grouping strength and found that stronger grouping in the targets enhanced overall response times while stronger grouping in the primes enhanced priming effects in motor responses. We also obtained differences between rapid visuomotor processing and the subjective impression with cues of brightness and shape but not with cues of brightness and size. These results show that the primed flanker task is an objective measure for comparing different feedforward-transmitted groupings. (2) In the second set of experiments, we used the task to study grouping by symmetry and grouping by closure that are more complex than similarity cues. We obtained results that were mostly in accordance with a feedforward model. Some other factors (line of view, orientation of the symmetry axis) were irrelevant for processing of symmetry cues. Thus, these experiments suggest that closure and (possibly) viewpoint-independent symmetry cues are extracted rapidly during the first feedforward wave of neuronal processing. (3) In the third set of experiments, we used the task to study grouping by Good Gestalt (i.e., visual completion in occluded shapes). By varying the amount of occlusion, we found that the processing was in accordance with a feedforward model only when occlusion was very limited. Thus, these experiments suggest that Good Gestalt is not extracted rapidly during the first feedforward wave of neuronal processing but relies on recurrent activation. I conclude (1) that the primed flanker task is an excellent tool to identify and compare the processing characteristics of different grouping cues by behavioral means, (2) that grouping strength and other factors are strongly modulating these processing characteristics, which (3) challenges a dichotomous classification of grouping cues based on feedforward vs. recurrent processing (incremental grouping theory, Roelfsema, 2006), and (4) that a focus on temporal processing dynamics is necessary to understand perceptual grouping.

The hypervolume subset selection problem consists of finding a subset, with a given cardinality \(k\), of a set of nondominated points that maximizes the hypervolume indicator. This problem arises in selection procedures of evolutionary algorithms for multiobjective optimization, for which practically efficient algorithms are required. In this article, two new formulations are provided for the two-dimensional variant of this problem.
The first is a (linear) integer programming formulation that can be solved by solving its linear programming relaxation. The second formulation is a \(k\)-link shortest path formulation on a special digraph with the Monge property that can be solved by dynamic programming in \(\mathcal{O}(n(k + \log n))\) time. This improves upon the \(\mathcal{O}(n^2k)\) result of Bader (2009), and matches the recent result of Bringmann et al. (2014), which was developed independently from this work using different techniques. Moreover, it is shown that these bounds may be further improved under mild conditions on \(k\).

This thesis combines mass spectrometric studies on ionic dicarboxylic acids and transition metal cluster adsorbate complexes. IR-MPD spectra of protonated and deprotonated aliphatic and aromatic dicarboxylic acids provide insights in the nature of intramolecular hydrogen bonding. Investigations of their fragmentation behavior are supported by MP2 calculations. Prior work on cobalt transition metal clusters is extended to iron and nickel and three cobalt alloys have been studied.

Minmax regret optimization aims at finding robust solutions that perform best in the worst-case, compared to the respective optimum objective value in each scenario. Even for simple uncertainty sets like boxes, most polynomially solvable optimization problems have strongly NP-hard minmax regret counterparts. Thus, heuristics with performance guarantees can potentially be of great value, but only few such guarantees exist.
A very easy but effective approximation technique is to compute the midpoint solution of the original optimization problem, which aims at optimizing the average regret, and also the average nominal objective. It is a well-known result that the regret of the midpoint solution is at most 2 times the optimal regret. Besides some academic instances showing that this bound is tight, most instances reveal a way better approximation ratio.
We introduce a new lower bound for the optimal value of the minmax regret problem. Using this lower bound we state an algorithm that gives an instance dependent performance guarantee of the midpoint solution for combinatorial problems that is at most 2. The computational complexity of the algorithm depends on the minmax regret problem under consideration; we show that the sharpened guarantee can be computed in strongly polynomial time for several classes of combinatorial optimization problems.
To illustrate the quality of the proposed bound, we use it within a branch and bound framework for the robust shortest path problem. In an experimental study comparing this approach with a bound from the literature, we find a considerable improvement in computation times.

We consider the problem of evacuating an urban area caused by a natural or man-made disaster. There are several planning aspects that need to be considered in such a scenario, which are usually considered separately, due to their computational complexity. These aspects include: Which shelters are used to accommodate evacuees? How to schedule public transport for transit-dependent evacuees? And how do public and individual traffic interact? Furthermore, besides evacuation time, also the risk of the evacuation needs to be considered.
We propose a macroscopic multi-criteria optimization model that includes all of these questions simultaneously. As a mixed-integer programming formulation cannot handle instances of real-world size, we develop a genetic algorithm of NSGA-II type that is able to generate feasible solutions of good quality in reasonable computation times.
We extend the applicability of these methods by also considering how to aggregate instance data, and how to generate solutions for the original instance starting from a reduced solution.
In computational experiments using real-world data modelling the cities of Nice in France and Kaiserslautern in Germany, we demonstrate the effectiveness of our approach and compare the trade-off between different levels of data aggregation.

In this paper we construct a numerical solver for the Saint Venant equations. Special attention
is given to the balancing of the source terms, including the bottom slope and variable cross-
sectional profiles. Therefore a special discretization of the pressure law is used, in order to
transfer analytical properties to the numerical method. Based on this approximation a well-
balanced solver is developed, assuring the C-property and depth positivity. The performance
of this method is studied in several test cases focusing on accurate capturing of steady states.

In 2006 Jeffrey Achter proved that the distribution of divisor class groups of degree 0 of function fields with a fixed genus and the distribution of eigenspaces in symplectic similitude groups are closely related to each other. Gunter Malle proposed that there should be a similar correspondence between the distribution of class groups of number fields and the distribution of eigenspaces in ceratin matrix groups. Motivated by these results and suggestions we study the distribution of eigenspaces corresponding to the eigenvalue one in some special subgroups of the general linear group over factor rings of rings of integers of number fields and derive some conjectural statements about the distribution of \(p\)-parts of class groups of number fields over a base field \(K_{0}\). Where our main interest lies in the case that \(K_{0}\) contains the \(p\)th roots of unity, because in this situation the \(p\)-parts of class groups seem to behave in an other way like predicted by the popular conjectures of Henri Cohen and Jacques Martinet. In 2010 based on computational data Malle has succeeded in formulating a conjecture in the spirit of Cohen and Martinet for this case. Here using our investigations about the distribution in matrixgroups we generalize the conjecture of Malle to a more abstract level and establish a theoretical backup for these statements.

Enhanced information processing of phobic natural images in participants with specific phobias
(2014)

From an evolutionary point of view, it can be assumed that visual processing and rapid detection of potentially dangerous stimuli in the environment (e.g., perilous animals) is highly adaptive for all humans. In the present dissertation, I address three research questions; (1) Is information processing of threatening stimuli enhanced in individuals with specific phobias? (2) Are there any differences between the different types of phobia (e.g., spider phobia vs. snake phobia)? (3) Is the frequently reported attentional bias of individuals with specific phobias - which may contribute to an enhancement in information processing – also detectable in a prior entry paradigm? In Experiments 1 to 3 of the present thesis non-anxious control, spider-fearful, snake-fearful, and blood-injection-injury-fearful participants took part in the study. We applied in each experiment a response priming paradigm which has a strong theoretical (cf. rapid-chase theory; Schmidt, Niehaus, & Nagel, 2006; Schmidt, Haberkamp, Veltkamp et al., 2011) as well as empirical background (cf. Schmidt, 2002). We show that information processing in fearful individuals is indeed enhanced for phobic images (i.e., spiders for spider-fearful participants; injuries for blood-injury-injection(BII)-fearful individuals). However, we found marked differences between the different types of phobia. In Experiment 1 and 2 (Chapter 2 and 3), spiders had a strong and specific influence in the group of spider-fearful individuals: Phobic primes entailed the largest priming effects, and phobic targets accelerated responses, both effects indicating speeded response activation by phobic images. In snake-fearful participants (Experiment 1, Chapter 2), this processing enhancement for phobic material was less pronounced and extended to both snake and spider images. In Experiment 3 (Chapter 4), we demonstrated that early information processing for pictures of small injuries is also enhanced in BII-fearful participants, even though BII fear is unique in that BII-fearful individuals show opposite physiological reactions when confronted with the phobic stimulus compared to individuals with animal phobias. These results show that already fast visuomotor responses are further enhanced in spider- and BII-fearful participants. Results give evidence that responses are based on the first feedforward sweep of neuronal activation proceeding through the visuomotor system. I propose that the additional enhancement in spider- and BII-fearful individuals depend on a specific hardwired binding of elementary features belonging to the phobic object in fearful individuals (i.e., effortless recognition of the respective phobic object via hardwired neuronal conjunctions). I suggest that these hardwired conjunctions developed due to long-term perceptual learning processes. We also investigate the frequently reported attentional bias of phobic individuals and showed that this bias is detectable in temporal order judgments using a prior entry paradigm. I assume that perceptual learning processes might also strengthen the attentional bias, for example, by providing a more salient bottom-up signal that draws attention involuntarily. In sum, I conclude that (1) early information processing of threatening stimuli is indeed enhanced in individuals with specific phobias but that (2) differences between divers types of phobia exist (i.e., spider- and BII-fearful participants show enhanced information of the respective phobic object; though, snake-fearful participants show no specific information processing enhancement of snakes); (3) the frequently reported attentional bias of spider-fearful individuals is also detectable in a prior entry paradigm.