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For some optimization problems on a graph \(G=(V,E)\), one can give a general formulation: Let \(c\colon E \to \mathbb{R}_{\geq 0}\) be a cost function on the edges and \(X \subseteq 2^E\) be a set of (so-called feasible) subsets of \(E\), one aims to minimize \(\sum_{e\in S} c(e)\) among all feasible \(S\in X\). This formulation covers, for instance, the shortest path problem by choosing \(X\) as the set of all paths between two vertices, or the minimum spanning tree problem by choosing \(X\) to be the set of all spanning trees. This bachelor thesis deals with a parametric version of this formulation, where the edge costs \(c_\lambda\colon E \to \mathbb{R}_{\geq 0}\) depend on a parameter \(\lambda\in\mathbb{R}_{\geq 0}\) in a concave and piecewise linear manner. The goal is to investigate the worst case minimum size of a so-called representation system \(R\subseteq X\), which contains for each scenario \(\lambda\in\mathbb{R}_{\geq 0}\) an optimal solution \(S(\lambda)\in R\). It turns out that only a pseudo-polynomial size can be ensured in general, but smaller systems have to exist in special cases. Moreover, methods are presented to find such small systems algorithmically. Finally, the notion of a representation system is relaxed in order to get smaller (i.e. polynomial) systems ensuring a certain approximation ratio.

The main theme of this thesis is the interplay between algebraic and tropical intersection
theory, especially in the context of enumerative geometry. We begin by exploiting
well-known results about tropicalizations of subvarieties of algebraic tori to give a
simple proof of Nishinou and Siebert’s correspondence theorem for rational curves
through given points in toric varieties. Afterwards, we extend this correspondence
by additionally allowing intersections with psi-classes. We do this by constructing
a tropicalization map for cycle classes on toroidal embeddings. It maps algebraic
cycle classes to elements of the Chow group of the cone complex of the toroidal
embedding, that is to weighted polyhedral complexes, which are balanced with respect
to an appropriate map to a vector space, modulo a naturally defined equivalence relation.
We then show that tropicalization respects basic intersection-theoretic operations like
intersections with boundary divisors and apply this to the appropriate moduli spaces
to obtain our correspondence theorem.
Trying to apply similar methods in higher genera inevitably confronts us with moduli
spaces which are not toroidal. This motivates the last part of this thesis, where we
construct tropicalizations of cycles on fine logarithmic schemes. The logarithmic point of
view also motivates our interpretation of tropical intersection theory as the dualization
of the intersection theory of Kato fans. This duality gives a new perspective on the
tropicalization map; namely, as the dualization of a pull-back via the characteristic
morphism of a logarithmic scheme.

Urban quality of life is currently conceptualized in principally economic terms. As the decline in manufacturing activities, the rise of the service and knowledge economy, the growing importance of accessibility and globalizing processes continue to reconfigure the economic competition between cities, quality of life enters the discourse primarily as a means to attract high-skilled workers and improve the city’s economic prospects. Local governments increasingly seek partnerships with local and foreign capital, reorganizing institutions and tasks to attract capital, including the “selling of place”, strengthening place promotion and marketing efforts. The rhetoric clearly welcomes wealthy, creative, high-skilled people, disadvantaged and low skilled groups receive less attention in the making of places. Especially with respect to inner city areas, high quality of life is promoted as spaces for ‘clean’ and convenient consumption with positive atmospheres and shiny images.
Yet, a plethora of theoretical engagements with urban everyday live reminds us that, while on the one hand, variety of jobs, quality of public spaces, range of shops and services, cultural facilities and public transport are important place characteristics, more subjective aspects such as safe neighbourhoods, well-being, community prospects, social cohesion, happiness, satisfaction and social and spatial justice are equally crucial determinants of urban quality of life. These elements of urban quality of life – and how they are experienced by diverse formations of urban inhabitants – seem to be absent from, if not at odds with, the dominant discourse in rankings, policy and practice. Urban life, social cohesion and complexity are at risk in the dynamics of modernization and adaptation strategies of cities. Gentrification, the occupation of inner-city districts by hyper-rich people, segregation and displacement of lower and middle classes can be observed as a consequence of these long-lasting strategies.
Well-known sociologists and geographers from the UK and Germany have presented their insights on the matter and debate theoretical and empirical attempts to capture the dynamics of urban processes in shaping the quality of life.

Requirements-Aware, Template-Based Protocol Graphs for Service-Oriented Network Architectures
(2016)

Rigidness of the Internet causes its architectural design issues such as interdependencies among the layers, no cross-layer information exchange, and applications dependency on the underlying protocols implementation.
G-Lab (i.e., http://www.german-lab.de/) is a research project for Future Internet Architecture (FIA), which focuses on problems of the Internet such as rigidness, mobility, and addressing. Where the focus of ICSY (i.e., www.icsy) was on providing the flexibility in future network architectures. An approach so-called Service Oriented Network Architecture (SONATE) is proposed to compose the protocols dynamically. SONATE is based on principles of the service-oriented architecture (SOA), where protocols are decomposed in software modules and later they are put together on demand to provide the desired service.
This composition of functionalities can be performed at various time-epochs (e.g., run-time, design-time, deployment-time). However, these epochs have trade-off in terms of the time-complexity (i.e., required setup time) and the provided flexibility. The design-time is the least time critical in comparison to other time phases, which makes it possible to utilize human-analytical capability. However, the design-time lacks the real-time knowledge of requirements and network conditions, what results in inflexible protocol graphs, and they cannot be changed at later stages on changing requirements. Contrary to the design-time, the run-time is most time critical where an application is waiting for a connection to be established, but at the same time it has maximum information to generate a protocol graph suitable to the given requirements.
Considering limitations above of different time-phases, in this thesis, a novel intermediate functional composition approach (i.e., Template-Based Composition) has been presented to generate requirements aware protocol graphs. The template-based composition splits the composition process across different time-phases to exploit the less time critical nature and human-analytical availability of the design-time, ability to instantaneously deploy new functionalities of the deployment time and maximum information availability of the run-time. The approach is successfully implemented , demonstrated and evaluated based on its performance to know the implications for the practical use.

When designing autonomous mobile robotic systems, there usually is a trade-off between the three opposing goals of safety, low-cost and performance.
If one of these design goals is approached further, it usually leads to a recession of one or even both of the other goals.
If for example the performance of a mobile robot is increased by making use of higher vehicle speeds, then the safety of the system is usually decreased, as, under the same circumstances, faster robots are often also more dangerous robots.
This decrease of safety can be mitigated by installing better sensors on the robot, which ensure the safety of the system, even at high speeds.
However, this solution is accompanied by an increase of system cost.
In parallel to mobile robotics, there is a growing amount of ambient and aware technology installations in today's environments - no matter whether in private homes, offices or factory environments.
Part of this technology are sensors that are suitable to assess the state of an environment.
For example, motion detectors that are used to automate lighting can be used to detect the presence of people.
This work constitutes a meeting point between the two fields of robotics and aware environment research.
It shows how data from aware environments can be used to approach the abovementioned goal of establishing safe, performant and additionally low-cost robotic systems.
Sensor data from aware technology, which is often unreliable due to its low-cost nature, is fed to probabilistic methods for estimating the environment's state.
Together with models, these methods cope with the uncertainty and unreliability associated with the sensor data, gathered from an aware environment.
The estimated state includes positions of people in the environment and is used as an input to the local and global path planners of a mobile robot, enabling safe, cost-efficient and performant mobile robot navigation during local obstacle avoidance as well as on a global scale, when planning paths between different locations.
The probabilistic algorithms enable graceful degradation of the whole system.
Even if, in the extreme case, all aware technology fails, the robots will continue to operate, by sacrificing performance while maintaining safety.
All the presented methods of this work have been validated using simulation experiments as well as using experiments with real hardware.

Synapses play a central role in the information propagation in the nervous system. A better understanding of synaptic structures and processes is vital for advancing nervous disease research. This work is part of an interdisciplinary project that aims at the quantitative examination of components of the neuromuscular junction, a synaptic connection between a neuron and a muscle cell.
The research project is based on image stacks picturing neuromuscular junctions captured by modern electron microscopes, which permit the rapid acquisition of huge amounts of image data at a high level of detail. The large amount and sheer size of such microscopic data makes a direct visual examination infeasible, though.
This thesis presents novel problem-oriented interactive visualization techniques that support the segmentation and examination of neuromuscular junctions.
First, I introduce a structured data model for segmented surfaces of neuromuscular junctions to enable the computational analysis of their properties. However, surface segmentation of neuromuscular junctions is a very challenging task due to the extremely intricate character of the objects of interest. Hence, such problematic segmentations are often performed manually by non-experts and thus requires further inspection.
With NeuroMap, I develop a novel framework to support proofreading and correction of three-dimensional surface segmentations. To provide a clear overview and to ease navigation within the data, I propose the surface map, an abstracted two-dimensional representation using key features of the surface as landmarks. These visualizations are augmented with information about automated segmentation error estimates. The framework provides intuitive and interactive data correction mechanisms, which in turn permit the expeditious creation of high-quality segmentations.
While analyzing such segmented synapse data, the formulation of specific research questions is often impossible due to missing insight into the data. I address this problem by designing a generic parameter space for segmented structures from biological image data. Furthermore, I introduce a graphical interface to aid its exploration, combining both parameter selection as well as data representation.

This Ph.D. project as a landscape research practice focuses on the less widely studied aspects of urban agriculture landscape and its application in recreation and leisure, as well as landscape beautification. I research on the edible landscape planning and design, its criteria, possibilities, and traditional roots for the particular situation of Iranian cities and landscapes. The primary objective is preparing a conceptual and practical framework for Iranian professions to integrate the food landscaping into the new greenery and open spaces developments. Furthermore, finding the possibilities of synthesis the traditional utilitarian gardening with the contemporary pioneer viewpoints of agricultural landscapes is the other significant proposed achievement.
Finished tasks and list of achieved results:
• Recognition the software and hardware principles of designing the agricultural landscape based on the Persian gardens
• Multidimensional identity of agricultural landscape in Persian gardens
• Principles of architectural integration and the characteristics of the integrative landscape in Persian gardens
• Distinctive characteristics of agricultural landscape in Persian garden
• Introducing the Persian and historical gardens as the starting point for reentering the agricultural phenomena into the Iranian cities and landscape
• Assessment the structure of Persian gardens based on the new achievements and criteria of designing the urban agriculture
• Investigate the role of Persian gardens in envisioning the urban agriculture in
Iranian cities’ landscape.

Reading as a cultural skill is acquired over a long period of training. This thesis supports the idea that reading is based on specific strategies that result from modification and coordination of earlier developed object recognition strategies. The reading-specific processing strategies are considered to be more analytic compared to object recognition strategies, which are described as holistic. To enable proper reading skills these strategies have to become automatized. Study 1 (Chapter 4) examined the temporal and visual constrains of letter recognition strategies. In the first experiment two successively presented stimuli (letters or non-letters) had to be classified as same or different. The second stimulus could either be presented in isolation or surrounded by a shape, which was either similar (congruent) or different (incongruent) in its geometrical properties to the stimulus itself. The non-letter pairs were presented twice as often as the letter pairs. The results demonstrated a preference for the holistic strategy also in letters, even if the non- letter set was presented twice as often as the letter set, showing that the analytic strategy does not replace the holistic one completely, but that the usage of both strategies is task-sensitive. In Experiment 2, we compared the Global Precedence Effect (GPE) for letters and non-letters in central viewing, with the global stimulus size close to the functional visual field in whole word reading (6.5◦ of visual angle) and local stimuli close to the critical size for fluent reading of individual letters (0.5◦ of visual angle). Under these conditions, the GPE remained robust for non-letters. For letters, however, it disappeared: letters showed no overall response time advantage for the global level and symmetric congruence effects (local-to-global as well as global-to-local interference). These results indicate that reading is based on resident analytic visual processing strategies for letters. In Study 2 (Chapter 5) we replicated the latter result with a large group of participants as part of a study in which pairwise associations of non-letters and phonological or non-phonological sounds were systematically trained. We investigated whether training would eliminate the GPE also for non-letters. We observed, however, that the differentiation between letters and non-letter shapes persists after training. This result implies that pairwise association learning is not sufficient to overrule the process differentiation in adults. In addition, subtle effects arising in the letter condition (due to enhanced power) enable us to further specify the differentiation in processing between letters and non-letter shapes. The influence of reading ability on the GPE was examined in Study 3 (Chapter 6). Children with normal reading skills and children with poor reading skills were instructed to detect a target in Latin or Hebrew Navon letters. Children with normal reading skills showed a GPE for Latin letters, but not for Hebrew letters. In contrast, the dyslexia group did not show GPE for either kind of stimuli. These results suggest that dyslexic children are not able to apply the same automatized letter processing strategy as children with normal reading skills do. The difference between the analytic letter processing and the holistic non-letter processing was transferred to the context of whole word reading in Study 4 (Chapter 7). When participants were instructed to detect either a letter or a non-letter in a mixed character string, for letters the reaction times and error rates increased linearly from the left to the right terminal position in the string, whereas for non-letters a symmetrical U-shaped function was observed. These results suggest, that the letter-specific processing strategies are triggered automatically also for more word-like material. Thus, this thesis supports and expands prior results of letter-specific processing and gives new evidences for letter-specific processing strategies.

This work introduces a promising concept for the preparation of new nano-sized receptors. Mixed monolayer protected gold nanoparticles (AuNPs) for low molecular weight compounds were prepared featuring functional groups on their surfaces. It has been shown that these AuNPs can engage in interactions with peptides in aqueous media. Quantitative binding information was obtained from DOSY-NMR titrations indicating that nanoparticles containing a combination of three orthogonal functional groups are more efficient in binding to dipeptides than mono or difunctionalised analogues. The strategy is highly modular and easily allows adapting the receptor selectivity to a
given substrate by varying the type, number, and ratio of binding sites on the nanoparticle
surface.

This thesis presents a novel, generic framework for information segmentation in document images.
A document image contains different types of information, for instance, text (machine printed/handwritten), graphics, signatures, and stamps.
It is necessary to segment information in documents so that to process such segmented information only when required in automatic document processing workflows.
The main contribution of this thesis is the conceptualization and implementation of an information segmentation framework that is based on part-based features.
The generic nature of the presented framework makes it applicable to a variety of documents (technical drawings, magazines, administrative, scientific, and academic documents) digitized using different methods (scanners, RGB cameras, and hyper-spectral imaging (HSI) devices).
A highlight of the presented framework is that it does not require large training sets, rather a few training samples (for instance, four pages) lead to high performance, i.e., better than previously existing methods.
In addition, the presented framework is simple and can be adapted quickly to new problem domains.
This thesis is divided into three major parts on the basis of document digitization method (scanned, hyper-spectral imaging, and camera captured) used.
In the area of scanned document images, three specific contributions have been realized.
The first of them is in the domain of signature segmentation in administrative documents.
In some workflows, it is very important to check the document authenticity before processing the actual content.
This can be done based on the available seal of authenticity, e.g., signatures.
However, signature verification systems expect pre-segmented signature image, while signatures are usually a part of document.
To use signature verification systems on document images, it is necessary to first segment signatures in documents.
This thesis shows that the presented framework can be used to segment signatures in administrative documents.
The system based on the presented framework is tested on a publicly available dataset where it outperforms the state-of-the-art methods and successfully segmented all signatures, while less than half of the found signatures are false positives.
This shows that it can be applied for practical use.
The second contribution in the area of scanned document images is segmentation of stamps in administrative documents.
A stamp also serves as a seal for documents authenticity.
However, the location of stamp on the document can be more arbitrary than a signature depending on the person sealing the document.
This thesis shows that a system based on our generic framework is able to extract stamps of any arbitrary shape and color.
The evaluation of the presented system on a publicly available dataset shows that it is also able to segment black stamps (that were not addressed in the past) with a recall and precision of 83% and 73%, respectively.
%Furthermore, to segment colored stamps, this thesis presents a novel feature set which is based on intensity gradient, is able to extract unseen, colored, arbitrary shaped, textual as well as graphical stamps, and outperforms the state-of-the-art methods.
The third contribution in the scanned document images is in the domain of information segmentation in technical drawings (architectural floorplans, maps, circuit diagrams, etc.) containing usually a large amount of graphics and comparatively less textual components. Further, as in technical drawings, text is overlapping with graphics.
Thus, automatic analysis of technical drawings uses text/graphics segmentation as a pre-processing step.
This thesis presents a method based on our generic information segmentation framework that is able to detect the text, which is touching graphical components in architectural floorplans and maps.
Evaluation of the method on a publicly available dataset of architectural floorplans shows that it is able to extract almost all touching text components with precision and recall of 71% and 95%, respectively.
This means that almost all of the touching text components are successfully extracted.
In the area of hyper-spectral document images, two contributions have been realized.
Unlike normal three channels RGB images, hyper-spectral images usually have multiple channels that range from ultraviolet to infrared regions including the visible region.
First, this thesis presents a novel automatic method for signature segmentation from hyper-spectral document images (240 spectral bands between 400 - 900 nm).
The presented method is based on a part-based key point detection technique, which does not use any structural information, but relies only on the spectral response of the document regardless of ink color and intensity.
The presented method is capable of segmenting (overlapping and non-overlapping) signatures from varying backgrounds like, printed text, tables, stamps, logos, etc.
Importantly, the presented method can extract signature pixels and not just the bounding boxes.
This is substantial when signatures are overlapping with text and/or other objects in image. Second, this thesis presents a new dataset comprising of 300 documents scanned using a high-resolution hyper-spectral scanner. Evaluation of the presented signature segmentation method on this hyper-spectral dataset shows that it is able to extract signature pixels with the precision and recall of 100% and 79%, respectively.
Further contributions have been made in the area of camera captured document images. A major problem in the development of Optical Character Recognition (OCR) systems for camera captured document images is the lack of labeled camera captured document images datasets. In the first place, this thesis presents a novel, generic, method for automatic ground truth generation/labeling of document images. The presented method builds large-scale (i.e., millions of images) datasets of labeled camera captured / scanned documents without any human intervention. The method is generic and can be used for automatic ground truth generation of (scanned and/or camera captured) documents in any language, e.g., English, Russian, Arabic, Urdu. The evaluation of the presented method, on two different datasets in English and Russian, shows that 99.98% of the images are correctly labeled in every case.
Another important contribution in the area of camera captured document images is the compilation of a large dataset comprising 1 million word images (10 million character images), captured in a real camera-based acquisition environment, along with the word and character level ground truth. The dataset can be used for training as well as testing of character recognition systems for camera-captured documents. Various benchmark tests are performed to analyze the behavior of different open source OCR systems on camera captured document images. Evaluation results show that the existing OCRs, which already get very high accuracies on scanned documents, fail on camera captured document images.
Using the presented camera-captured dataset, a novel character recognition system is developed which is based on a variant of recurrent neural networks, i.e., Long Short Term Memory (LSTM) that outperforms all of the existing OCR engines on camera captured document images with an accuracy of more than 95%.
Finally, this thesis provides details on various tasks that have been performed in the area closely related to information segmentation. This includes automatic analysis and sketch based retrieval of architectural floor plan images, a novel scheme for online signature verification, and a part-based approach for signature verification. With these contributions, it has been shown that part-based methods can be successfully applied to document image analysis.

Buses not arriving on time and then arriving all at once - this phenomenon is known from
busy bus routes and is called bus bunching.
This thesis combines the well studied but so far separate areas of bus-bunching prediction
and dynamic holding strategies, which allow to modulate buses’ dwell times at stops to
eliminate bus bunching. We look at real data of the Dublin Bus route 46A and present
a headway-based predictive-control framework considering all components like data
acquisition, prediction and control strategies. We formulate time headways as time series
and compare several prediction methods for those. Furthermore we present an analytical
model of an artificial bus route and discuss stability properties and dynamic holding
strategies using both data available at the time and predicted headway data. In a numerical
simulation we illustrate the advantages of the presented predictive-control framework
compared to the classical approaches which only use directly available data.

Stochastic Network Calculus (SNC) emerged from two branches in the late 90s:
the theory of effective bandwidths and its predecessor the Deterministic Network
Calculus (DNC). As such SNC’s goal is to analyze queueing networks and support
their design and control.
In contrast to queueing theory, which strives for similar goals, SNC uses in-
equalities to circumvent complex situations, such as stochastic dependencies or
non-Poisson arrivals. Leaving the objective to compute exact distributions behind,
SNC derives stochastic performance bounds. Such a bound would, for example,
guarantee a system’s maximal queue length that is violated by a known small prob-
ability only.
This work includes several contributions towards the theory of SNC. They are
sorted into four main contributions:
(1) The first chapters give a self-contained introduction to deterministic net-
work calculus and its two branches of stochastic extensions. The focus lies on the
notion of network operations. They allow to derive the performance bounds and
simplifying complex scenarios.
(2) The author created the first open-source tool to automate the steps of cal-
culating and optimizing MGF-based performance bounds. The tool automatically
calculates end-to-end performance bounds, via a symbolic approach. In a second
step, this solution is numerically optimized. A modular design allows the user to
implement their own functions, like traffic models or analysis methods.
(3) The problem of the initial modeling step is addressed with the development
of a statistical network calculus. In many applications the properties of included
elements are mostly unknown. To that end, assumptions about the underlying
processes are made and backed by measurement-based statistical methods. This
thesis presents a way to integrate possible modeling errors into the bounds of SNC.
As a byproduct a dynamic view on the system is obtained that allows SNC to adapt
to non-stationarities.
(4) Probabilistic bounds are fundamentally different from deterministic bounds:
While deterministic bounds hold for all times of the analyzed system, this is not
true for probabilistic bounds. Stochastic bounds, although still valid for every time
t, only hold for one time instance at once. Sample path bounds are only achieved by
using Boole’s inequality. This thesis presents an alternative method, by adapting
the theory of extreme values.
(5) A long standing problem of SNC is the construction of stochastic bounds
for a window flow controller. The corresponding problem for DNC had been solved
over a decade ago, but remained an open problem for SNC. This thesis presents
two methods for a successful application of SNC to the window flow controller.

This thesis investigates the electromechanic coupling of dielectric elastomers for the static and dynamic case by numerical simulations. To this end, the fundamental equations of the coupled field problem are introduced and the discretisation procedure for the numerical implementation is described. Furthermore, a three field formulation is proposed and implemented to treat the nearly incompressible behaviour of the elastomer. Because of the reduced electric permittivity of the material, very high electric fields are required for actuation purposes. To improve the electromechanic coupling a heterogeneous microstructure consisting of an elastomer matrix with barium titanate inclusions is proposed and studied.

We propose a multiscale model for tumor cell migration in a tissue network. The system of equations involves a structured population model for the tumor cell density, which besides time and
position depends on a further variable characterizing the cellular state with respect to the amount
of receptors bound to soluble and insoluble ligands. Moreover, this equation features pH-taxis and
adhesion, along with an integral term describing proliferation conditioned by receptor binding. The
interaction of tumor cells with their surroundings calls for two more equations for the evolution of
tissue fibers and acidity (expressed via concentration of extracellular protons), respectively. The
resulting ODE-PDE system is highly nonlinear. We prove the global existence of a solution and
perform numerical simulations to illustrate its behavior, paying particular attention to the influence
of the supplementary structure and of the adhesion.

An Adaptive and Dynamic Simulation Framework for Incremental, Collaborative Classifier Fusion
(2016)

Abstract. To investigate incremental collaborative classifier fusion techniques, we have developed a comprehensive simulation framework. It is highly flexible and customizable, and can be adapted to various settings and scenarios. The toolbox is realized as an extension to the NetLogo multi-agent based simulation environment using its comprehensive Java- API. The toolbox has been integrated in two di↵erent environments, one for demonstration purposes and another, modeled on persons using re- alistic motion data from Zurich, who are communicating in an ad hoc fashion using mobile devices.

Mixed-signal systems combine analog circuits with digital hardware and software systems. A particular challenge is the sensitivity of analog parts to even small deviations in parameters, or inputs. Parameters of circuits and systems such as process, voltage, and temperature are never accurate; we hence model them as uncertain values (‘uncertainties’). Uncertain parameters and inputs can modify the dynamic behavior and lead to properties of the system that are not in specified ranges. For verification of mixed- signal systems, the analysis of the impact of uncertainties on the dynamical behavior plays a central role.
Verification of mixed-signal systems is usually done by numerical simulation. A single numerical simulation run allows designers to verify single parameter values out of often ranges of uncertain values. Multi-run simulation techniques such as Monte Carlo Simulation, Corner Case simulation, and enhanced techniques such as Importance Sampling or Design-of-Experiments allow to verify ranges – at the cost of a high number of simulation runs, and with the risk of not finding potential errors. Formal and symbolic approaches are an interesting alternative. Such methods allow a comprehensive verification. However, formal methods do not scale well with heterogeneity and complexity. Also, formal methods do not support existing and established modeling languages. This fact complicates its integration in industrial design flows.
In previous work on verification of Mixed-Signal systems, Affine Arithmetic is used for symbolic simulation. This allows combining the high coverage of formal methods with the ease-of use and applicability of simulation. Affine Arithmetic computes the propagation of uncertainties through mostly linear analog circuits and DSP methods in an accurate way. However, Affine Arithmetic is currently only able to compute with contiguous regions, but does not permit the representation of and computation with discrete behavior, e.g. introduced by software. This is a serious limitation: in mixed-signal systems, uncertainties in the analog part are often compensated by embedded software; hence, verification of system properties must consider both analog circuits and embedded software.
The objective of this work is to provide an extension to Affine Arithmetic that allows symbolic computation also for digital hardware and software systems, and to demonstrate its applicability and scalability. Compared with related work and state of the art, this thesis provides the following achievements:
1. The thesis introduces extended Affine Arithmetic Forms (XAAF) for the representation of branch and merge operations.
2. The thesis describes arithmetic and relational operations on XAAF, and reduces over-approximation by using an LP solver.
3. The thesis shows and discusses ways to integrate this XAAF into existing modeling languages, in particular SystemC. This way, breaks in the design flow can be avoided.
The applicability and scalability of the approach is demonstrated by symbolic simulation of a Delta-Sigma Modulator and a PLL circuit of an IEEE 802.15.4 transceiver system.

Combining ultracold atomic gases with the peculiar properties of Rydberg excited atoms gained a lot of theoretical and experimental attention in recent years. Embedded in the ultracold gas, an interaction between the Rydberg atom and the surrounding ground state atoms arises through the scattering of the Rydberg electron from an intruding perturber atom. This peculiar interaction gives rise to a plenitude of previously unobserved effects. Within the framework of the present thesis, this interaction is studied in detail for Rydberg \(P\)-states in rubidium.
Due to their long lifetime, atoms in Rydberg states are subject to scattering with the surrounding ground state atoms in the ultracold cloud. By measuring their lifetime as a function of the ground state atom flux, we are able to obtain the total inelastic scattering cross section as well as the partial cross section for associative ionisation. The fact that the latter is three orders of magnitude larger than the size of the formed molecular
ion indicates the presence of an efficient mass transport mechanism that is mediated by the Rydberg–ground state interaction. The immense acceleration of the collisional process shows a close analogy to a catalytic process. The increase of the scattering cross section renders associative ionisation an important process that has to be considered for experiments in dense ultracold systems.
The interaction of the Rydberg atom with a ground state perturber gives rise to a highly oscillatory potential that supports molecular bound states. These so-called ultralong-range Rydberg molecules are studied with high resolution time-of-flight spectroscopy, where we are able to determine the binding energies and lifetimes of the molecular states between the two fine structure split \(25P\)-states. Inside an electric field, we observe a broadening of the
molecular lines that indicates the presence of a permanent electric dipole moment, induced by the mixing with high angular momentum states. Due to the mixing of the ground state atom’s hyperfine states by the molecular interaction, we are able to observe a spin-flip of the perturber upon creation of a Rydberg molecule. Furthermore, an incidental near-degeneracy in the underlying level scheme of the \(25P\)-state gives rise to highly entangled states between the Rydberg fine structure state and the perturber’s hyperfine structure. These mechanisms can be used to manipulate the quantum state of a remote particle over distances that exceed by far the typical contact interaction range.
Apart from the ultralong-range Rydberg molecules that predominantly consist of only one low angular momentum state, a class of Rydberg molecules is predicted to exist that strongly mixes the high angular momentum states of the degenerate hydrogenic manifolds. These states, the so-called trilobite- and butterfly Rydberg molecules, show very peculiar properties that cannot be observed for conventional molecules. Here we present the first experimental observation of butterfly Rydberg molecules. In addition to an extensive spectroscopy that reveals the binding energy, we are also able to observe the rotational structure of these exotic molecules. The arising pendular states inside an electric field allow us, in comparison to the model of a dipolar rotor, to extract the precise bond
length and dipole moment of the molecule. With the information obtained in the present study, it is possible to photoassociate butterfly molecules with a selectable bond length, vibrational state, rotational state, and orientation inside an electric field.
By shedding light on various previously unrevealed aspects, the experiments presented in this thesis significantly deepen our knowledge on the Rydberg–ground state interaction and the peculiar effects arising from it. The obtained spectroscopic information on Rydberg molecules and the changed reaction dynamics for molecular ion creation will surely provide valuable data for quantum chemical simulations and provide necessary data to plan future experiments. Beyond that, our study reveals that the hyperfine interaction in Rydberg molecules and the peculiar properties of butterfly states provide very promising new ways to alter the short- and long-range interactions in ultracold many-body systems. In this sense the investigated Rydberg–ground state interaction not only lies right at
the interface between quantum chemistry, quantum many-body systems, and Rydberg physics, but also creates many new and fascinating possibilities by combining these fields.

Knowing the extent to which we rely on technology one may think that correct programs are nowadays the norm. Unfortunately, this is far from the truth. Luckily, possible reasons why program correctness is difficult often come hand in hand with some solutions. Consider concurrent program correctness under Sequential Consistency (SC). Under SC, instructions of each program's concurrent component are executed atomically and in order. By using logic to represent correctness specifications, model checking provides a successful solution to concurrent program verification under SC. Alas, SC’s atomicity assumptions do not reflect the reality of hardware architectures. Total Store Order (TSO) is a less common memory model implemented in SPARC and in Intel x86 multiprocessors that relaxes the SC constraints. While the architecturally de-atomized execution of stores under TSO speeds up program execution, it also complicates program verification. To be precise, due to TSO’s unbounded store buffers, a program’s semantics under TSO might be infinite. This, for example, turns reachability under SC (a PSPACE-complete task) into a non-primitive-recursive-complete problem under TSO. This thesis develops verification techniques targeting TSO-relaxed programs. To be precise, we present under- and over-approximating heuristics for checking reachability in TSO-relaxed programs as well as state-reducing methods for speeding up such heuristics. In a first contribution, we propose an algorithm to check reachability of TSO-relaxed programs lazily. The under-approximating refinement algorithm uses auxiliary variables to simulate TSO’s buffers along instruction sequences suggested by an oracle. The oracle’s deciding characteristic is that if it returns the empty sequence then the program’s SC- and TSO-reachable states are the same. Secondly, we propose several approaches to over-approximate TSO buffers. Combined in a refinement algorithm, these approaches can be used to determine safety with respect to TSO reachability for a large class of TSO-relaxed programs. On the more technical side, we prove that checking reachability is decidable when TSO buffers are approximated by multisets with tracked per address last-added-values. Finally, we analyze how the explored state space can be reduced when checking TSO and SC reachability. Intuitively, through the viewpoint of Shasha-and-Snir-like traces, we exploit the structure of program instructions to explain several state-space reducing methods including dynamic and cartesian partial order reduction.

A vehicles fatigue damage is a highly relevant figure in the complete vehicle design process.
Long term observations and statistical experiments help to determine the influence of differnt parts of the vehicle, the driver and the surrounding environment.
This work is focussing on modeling one of the most important influence factors of the environment: road roughness. The quality of the road is highly dependant on several surrounding factors which can be used to create mathematical models.
Such models can be used for the extrapolation of information and an estimation of the environment for statistical studies.
The target quantity we focus on in this work ist the discrete International Roughness Index or discrete IRI. The class of models we use and evaluate is a discriminative classification model called Conditional Random Field.
We develop a suitable model specification and show new variants of stochastic optimizations to train the model efficiently.
The model is also applied to simulated and real world data to show the strengths of our approach.

Dual-Pivot Quicksort and Beyond: Analysis of Multiway Partitioning and Its Practical Potential
(2016)

Multiway Quicksort, i.e., partitioning the input in one step around several pivots, has received much attention since Java 7’s runtime library uses a new dual-pivot method that outperforms by far the old Quicksort implementation. The success of dual-pivot Quicksort is most likely due to more efficient usage of the memory hierarchy, which gives reason to believe that further improvements are possible with multiway Quicksort.
In this dissertation, I conduct a mathematical average-case analysis of multiway Quicksort including the important optimization to choose pivots from a sample of the input. I propose a parametric template algorithm that covers all practically relevant partitioning methods as special cases, and analyze this method in full generality. This allows me to analytically investigate in depth what effect the parameters of the generic Quicksort have on its performance. To model the memory-hierarchy costs, I also analyze the expected number of scanned elements, a measure for the amount of data transferred from memory that is known to also approximate the number of cache misses very well. The analysis unifies previous analyses of particular Quicksort variants under particular cost measures in one generic framework.
A main result is that multiway partitioning can reduce the number of scanned elements significantly, while it does not save many key comparisons; this explains why the earlier studies of multiway Quicksort did not find it promising. A highlight of this dissertation is the extension of the analysis to inputs with equal keys. I give the first analysis of Quicksort with pivot sampling and multiway partitioning on an input model with equal keys.

By using Gröbner bases of ideals of polynomial algebras over a field, many implemented algorithms manage to give exciting examples and counter examples in Commutative Algebra and Algebraic Geometry. Part A of this thesis will focus on extending the concept of Gröbner bases and Standard bases for polynomial algebras over the ring of integers and its factors \(\mathbb{Z}_m[x]\). Moreover we implemented two algorithms for this case in Singular which use different approaches in detecting useless computations, the classical Buchberger algorithm and a F5 signature based algorithm. Part B includes two algorithms that compute the graded Hilbert depth of a graded module over a polynomial algebra \(R\) over a field, as well as the depth and the multigraded Stanley depth of a factor of monomial ideals of \(R\). The two algorithms provide faster computations and examples that lead B. Ichim and A. Zarojanu to a counter example of a question of J. Herzog. A. Duval, B. Goeckner, C. Klivans and J. Martin have recently discovered a counter example for the Stanley Conjecture. We prove in this thesis that the Stanley Conjecture holds in some special cases. Part D explores the General Neron Desingularization in the frame of Noetherian local domains of dimension 1. We have constructed and implemented in Singular and algorithm that computes a strong Artin Approximation for Cohen-Macaulay local rings of dimension 1.

Integrating Security Concerns into Safety Analysis of Embedded Systems Using Component Fault Trees
(2016)

Nowadays, almost every newly developed system contains embedded systems for controlling system functions. An embedded system perceives its environment via sensors, and interacts with it using actuators such as motors. For systems that might damage their environment by faulty behavior usually a safety analysis is performed. Security properties of embedded systems are usually not analyzed at all. New developments in the area of Industry 4.0 and Internet of Things lead to more and more networking of embedded systems. Thereby, new causes for system failures emerge: Vulnerabilities in software and communication components might be exploited by attackers to obtain control over a system. By targeted actions a system may also be brought into a critical state in which it might harm itself or its environment. Examples for such vulnerabilities, and also successful attacks, became known over the last few years.
For this reason, in embedded systems safety as well as security has to be analyzed at least as far as it may cause safety critical failures of system components.
The goal of this thesis is to describe in one model how vulnerabilities from the security point of view might influence the safety of a system. The focus lies on safety analysis of systems, so the safety analysis is extended to encompass security problems that may have an effect on the safety of a system. Component Fault Trees are very well suited to examine causes of a failure and to find failure scenarios composed of combinations of faults. A Component Fault Tree of an analyzed system is extended by additional Basic Events that may be caused by targeted attacks. Qualitative and quantitative analyses are extended to take the additional security events into account. Thereby, causes of failures that are based on safety as well as security problems may be found. Quantitative or at least semi-quantitative analyses allow to evaluate security measures more detailed, and to justify the need of such.
The approach was applied to several example systems: The safety chain of the off-road robot RAVON, an adaptive cruise control, a smart farming scenario, and a model of a generic infusion pump were analyzed. The result of all example analyses was that additional failure causes were found which would not have been detected in traditional Component Fault Trees. In the analyses also failure scenarios were found that are caused solely by attacks, and that are not depending on failures of system components. These are especially critical scenarios which should not happen in this way, as they are not found in a classical safety analysis. Thus the approach shows its additional benefit to a safety analysis which is achieved by the application of established techniques with only little additional effort.

We propose and analyze a multiscale model for acid-mediated tumor invasion
accounting for stochastic effects on the subcellular level.
The setting involves a PDE of reaction-diffusion-taxis type describing the evolution of the tumor cell density,
the movement being directed towards pH gradients in the local microenvironment,
which is coupled to a PDE-SDE system characterizing the
dynamics of extracellular and intracellular proton concentrations, respectively.
The global well-posedness of the model is shown and
numerical simulations are performed in order to illustrate the solution behavior.

Software defined radios can be implemented on general purpose processors (CPUs), e.g. based on a PC. A processor offers high flexibility: It can not only be used to process the data samples, but also to control receiver functions, display a waterfall or run demodulation software. However, processors can only handle signals of limited bandwidth due to their comparatively low processing speed. For signals of high bandwidth the SDR algorithms have to be implemented as custom designed digital circuits on an FPGA chip. An FPGA provides a very high processing speed, but also lacks flexibility and user interfaces. Recently the FPGA manufacturer Xilinx has
introduced a hybrid system on chip called Zynq, that combines both approaches. It features a dual ARM Cortex-A9 processor and an FPGA, that offer the flexibility of a processor with the processing speed of an FPGA on a single chip. The Zynq is therefore very interesting for use in SDRs. In this paper the
application of the Zynq and its evaluation board (Zedboard) will be discussed. As an example, a direct sampling receiver has been implemented on the Zedboard using a high-speed 16 bit ADC with 250 Msps.

This thesis is concerned with a phase field model for martensitic transformations in metastable austenitic steels. Within the phase field approach an order parameter is introduced to indicate whether the present phase is austenite or martensite. The evolving microstructure is described by the evolution of the order parameter, which is assumed to follow the time-dependent Ginzburg-Landau equation. The elastic phase field model is enhanced in two different ways to take further phenomena into account. First, dislocation movement is considered by a crystal plasticity setting. Second, the elastic model for martensitic transformations is combined with a phase field model for fracture. Finite element simulations are used to study the single effects separately which contribute to the microstructure formation.

The biodiversity of the cyanobacterial lichen flora of Vietnam is chronically understudied. Previous studies often neglected the lichens that inhabit lowlands especially outcrops and sand dunes that are common habitats in Vietnam.
A cyanolichen collection was gathered from lowlands of central and southern Vietnam to study their diversity and distribution. At the same time, cultured photobionts from those lichens were used for olyphasic taxonomic approach.
A total of 66 cyanolichens were recorded from lowland regions in central and southern of Vietnam, doubles the number of cyanolichens for Vietnam. 80% of them are new records for Vietnam in which a new species Pyrenopsis melanophthalma and two new unidentified lichinacean taxa were described.
A notably floristic segregation by habitats was indicated in the communities. Saxicolous Lichinales dominated in coastal outcrops that corresponded to 56% of lichen species richness. Lecanoralean cyanolichens and basidiolichens were found in the lowland forests. Precipitation correlated negatively to species richness in this study, indicating a competitive relationship.
Eleven cyanobacterial strains including 8 baeocyte-forming members of the genus Chroococcidiopsis and 3 heterocyte-forming species of the genera Nostoc and Scytonema were successfully isolated from lichens.
Phylogenetic and morphological analyses indicated that Chroococcidiopsis was the unique photobiont in Peltula. New mophological characters were found in two Chroococcidiopsis strains: (1) the purple content of cells in one photobiont strain that was isolated from a new lichinacean taxon, and (2) the pseudofilamentous feature by binary division from a strain that was isolated from Porocyphus dimorphus.
With respect to heterocyte-forming cyanobiont, Scytonema was confirmed as the photobiont in the ascolichen Heppia lutosa applying the polyphasic method. The genus Scytonema in the basidiolichens Cyphellostereum was morphologically examinated in lichen thalli. For the first time the intracellular haustorial system of basidiolichen genus Cyphellostereum was noted and investigated.
Phylogenetic analysis of photobiont strains Nostoc from Pannaria tavaresii and Parmeliella brisbanensis indicated that a high selectivity occurred in Parmeliella brisbanensis that were from different regions of the world, while low photobiont selectivity occurred among Pannaria tavaresii samples from different geographical regions.
The herewith presented dissertation is therefore an important contribution to the lichen flora of Vietnam and a significant improvement of the actual knowledge about cyanolichens in this country.

The mechanical properties of semi-crystalline polymers depend extremely on their
morphology, which is dependent on the crystallization during processing. The aim of
this research is to determine the effect of various nanoparticles on morphology
formation and tensile mechanical properties of polypropylene under conditions
relevant in polymer processing and to contribute ultimately to the understanding of
this influence.
Based on the thermal analyses of samples during fast cooling, it is found that the
presence of nanoparticle enhances the overall crystallization process of PP. The results
suggest that an increase of the nucleation density/rate is a dominant process that
controls the crystallization process of PP in this work, which can help to reduce the
cycle time in the injection process. Moreover, the analysis of melting behaviors
obtained after each undercooling reveals that crystal perfection increases significantly
with the incorporation of TiO2 nanoparticles, while it is not influenced by the SiO2
nanoparticles.
This work also comprises an analysis of the influence of nanoparticles on the
microstructure of injection-molded parts. The results clearly show multi-layers along
the wall thickness. The spherulite size and the degree of crystallinity continuously
decrease from the center to the edge. Generally both the spherulite size and the degree
of crystallinity decrease with higher the SiO2 loading. In contrast, an increase in the
degree of crystallinity with an increasing TiO2 nanoparticle loading was detected.
The tensile properties exhibit a tendency to increase in the tensile strength as the core
is reached. The tensile strength decreases with the addition of nanoparticles, while the
elongation at break of nanoparticle-filled PP decreases from the skin to the core. With
increasing TiO2 loading, the elongation at break decreases.

Distributed systems are omnipresent nowadays and networking them is fundamental for the continuous dissemination and thus availability of data. Provision of data in real-time is one of the most important non-functional aspects that safety-critical networks must guarantee. Formal verification of data communication against worst-case deadline requirements is key to certification of emerging x-by-wire systems. Verification allows aircraft to take off, cars to steer by wire, and safety-critical industrial facilities to operate. Therefore, different methodologies for worst-case modeling and analysis of real-time systems have been established. Among them is deterministic Network Calculus (NC), a versatile technique that is applicable across multiple domains such as packet switching, task scheduling, system on chip, software-defined networking, data center networking and network virtualization. NC is a methodology to derive deterministic bounds on two crucial performance metrics of communication systems:
(a) the end-to-end delay data flows experience and
(b) the buffer space required by a server to queue all incoming data.
NC has already seen application in the industry, for instance, basic results have been used to certify the backbone network of the Airbus A380 aircraft.
The NC methodology for worst-case performance analysis of distributed real-time systems consists of two branches. Both share the NC network model but diverge regarding their respective derivation of performance bounds, i.e., their analysis principle. NC was created as a deterministic system theory for queueing analysis and its operations were later cast in a (min,+)-algebraic framework. This branch is known as algebraic Network Calculus (algNC). While algNC can efficiently compute bounds on delay and backlog, the algebraic manipulations do not allow NC to attain the most accurate bounds achievable for the given network model. These tight performance bounds can only be attained with the other, newly established branch of NC, the optimization-based analysis (optNC). However, the only optNC analysis that can currently derive tight bounds was proven to be computationally infeasible even for the analysis of moderately sized networks other than simple sequences of servers.
This thesis makes various contributions in the area of algNC: accuracy within the existing framework is improved, distributivity of the sensor network calculus analysis is established, and most significantly the algNC is extended with optimization principles. They allow algNC to derive performance bounds that are competitive with optNC. Moreover, the computational efficiency of the new NC approach is improved such that this thesis presents the first NC analysis that is both accurate and computationally feasible at the same time. It allows NC to scale to larger, more complex systems that require formal verification of their real-time capabilities.

Gröbner bases are one of the most powerful tools in computer algebra and commutative algebra, with applications in algebraic geometry and singularity theory. From the theoretical point of view, these bases can be computed over any field using Buchberger's algorithm. In practice, however, the computational efficiency depends on the arithmetic of the coefficient field.
In this thesis, we consider Gröbner bases computations over two types of coefficient fields. First, consider a simple extension \(K=\mathbb{Q}(\alpha)\) of \(\mathbb{Q}\), where \(\alpha\) is an algebraic number, and let \(f\in \mathbb{Q}[t]\) be the minimal polynomial of \(\alpha\). Second, let \(K'\) be the algebraic function field over \(\mathbb{Q}\) with transcendental parameters \(t_1,\ldots,t_m\), that is, \(K' = \mathbb{Q}(t_1,\ldots,t_m)\). In particular, we present efficient algorithms for computing Gröbner bases over \(K\) and \(K'\). Moreover, we present an efficient method for computing syzygy modules over \(K\).
To compute Gröbner bases over \(K\), starting from the ideas of Noro [35], we proceed by joining \(f\) to the ideal to be considered, adding \(t\) as an extra variable. But instead of avoiding superfluous S-pair reductions by inverting algebraic numbers, we achieve the same goal by applying modular methods as in [2,4,27], that is, by inferring information in characteristic zero from information in characteristic \(p > 0\). For suitable primes \(p\), the minimal polynomial \(f\) is reducible over \(\mathbb{F}_p\). This allows us to apply modular methods once again, on a second level, with respect to the
modular factors of \(f\). The algorithm thus resembles a divide and conquer strategy and
is in particular easily parallelizable. Moreover, using a similar approach, we present an algorithm for computing syzygy modules over \(K\).
On the other hand, to compute Gröbner bases over \(K'\), our new algorithm first specializes the parameters \(t_1,\ldots,t_m\) to reduce the problem from \(K'[x_1,\ldots,x_n]\) to \(\mathbb{Q}[x_1,\ldots,x_n]\). The algorithm then computes a set of Gröbner bases of specialized ideals. From this set of Gröbner bases with coefficients in \(\mathbb{Q}\), it obtains a Gröbner basis of the input ideal using sparse multivariate rational interpolation.
At current state, these algorithms are probabilistic in the sense that, as for other modular Gröbner basis computations, an effective final verification test is only known for homogeneous ideals or for local monomial orderings. The presented timings show that for most examples, our algorithms, which have been implemented in SINGULAR [17], are considerably faster than other known methods.

In retail, assortment planning refers to selecting a subset of products to offer that maximizes profit. Assortments can be planned for a single store or a retailer with multiple chain stores where demand varies between stores. In this paper, we assume that a retailer with a multitude of stores wants to specify her offered assortment. To suit all local preferences, regionalization and store-level assortment optimization are widely used in practice and lead to competitive advantages. When selecting regionalized assortments, a tradeoff between expensive, customized assortments in every store and inexpensive, identical assortments in all stores that neglect demand variation is preferable.
We formulate a stylized model for the regionalized assortment planning problem (APP) with capacity constraints and given demand. In our approach, a 'common assortment' that is supplemented by regionalized products is selected. While products in the common assortment are offered in all stores, products in the local assortments are customized and vary from store to store.
Concerning the computational complexity, we show that the APP is strongly NP-complete. The core of this hardness result lies in the selection of the common assortment. We formulate the APP as an integer program and provide algorithms and methods for obtaining approximate solutions and solving large-scale instances.
Lastly, we perform computational experiments to analyze the benefits of regionalized assortment planning depending on the variation in customer demands between stores.

Interconnected, autonomously driving cars shall realize the vision of a zero-accident, low energy mobility in spite of a fast increasing traffic volume. Tightly interconnected medical devices and health care systems shall ensure the health of an aging society. And interconnected virtual power plants based on renewable energy sources shall ensure a clean energy supply in a society that consumes more energy than ever before. Such open systems of systems will play an essential role for economy and society.
Open systems of systems dynamically connect to each other in order to collectively provide a superordinate functionality, which could not be provided by a single system alone. The structure as well as the behavior of an open system of system dynamically emerge at runtime leading to very flexible solutions working under various different environmental conditions. This flexibility and adaptivity of systems of systems are a key for realizing the above mentioned scenarios.
On the other hand, however, this leads to uncertainties since the emerging structure and behavior of a system of system can hardly be anticipated at design time. This impedes the indispensable safety assessment of such systems in safety-critical application domains. Existing safety assurance approaches presume that a system is completely specified and configured prior to a safety assessment. Therefore, they cannot be applied to open systems of systems. In consequence, safety assurance of open systems of systems could easily become a bottleneck impeding or even preventing the success of this promising new generation of embedded systems.
For this reason, this thesis introduces an approach for the safety assurance of open systems of systems. To this end, we shift parts of the safety assurance lifecycle into runtime in order to dynamically assess the safety of the emerging system of system. We use so-called safety models at runtime for enabling systems to assess the safety of an emerging system of system themselves. This leads to a very flexible runtime safety assurance framework.
To this end, this thesis describes the fundamental knowledge on safety assurance and model-driven development, which are the indispensable prerequisites for defining safety models at runtime. Based on these fundamentals, we illustrate how we modularized and formalized conventional safety assurance techniques using model-based representations and analyses. Finally, we explain how we advanced these design time safety models to safety models that can be used by the systems themselves at runtime and how we use these safety models at runtime to create an efficient and flexible runtime safety assurance framework for open systems of systems.

This thesis is concerned with interest rate modeling by means of the potential approach. The contribution of this work is twofold. First, by making use of the potential approach and the theory of affine Markov processes, we develop a general class of rational models to the term structure of interest rates which we refer to as "the affine rational potential model". These models feature positive interest rates and analytical pricing formulae for zero-coupon bonds, caps, swaptions, and European currency options. We present some concrete models to illustrate the scope of the affine rational potential model and calibrate a model specification to real-world market data. Second, we develop a general family of "multi-curve potential models" for post-crisis interest rates. Our models feature positive stochastic basis spreads, positive term structures, and analytic pricing formulae for interest rate derivatives. This modeling framework is also flexible enough to accommodate negative interest rates and positive basis spreads.

Human forest modification is among the largest global drivers of terrestrial degradation
of biodiversity, species interactions, and ecosystem functioning. One of the most
pertinent components, forest fragmentation, has a long history in ecological research
across the globe, particularly in lower latitudes. However, we still know little how
fragmentation shapes temperate ecosystems, irrespective of the ancient status quo of
European deforestation. Furthermore, its interaction with another pivotal component
of European forests, silvicultural management, are practically unexplored. Hence,
answering the question how anthropogenic modification of temperate forests affects
fundamental components of forest ecosystems is essential basic research that has
been neglected thus far. Most basal ecosystem elements are plants and their insect
herbivores, as they form the energetic basis of the tropic pyramid. Furthermore, their
respective biodiversity, functional traits, and the networks of interactions they
establish are key for a multitude of ecosystem functions, not least ecosystem stability.
Hence, the thesis at hand aimed to disentangle this complex system of
interdependencies of human impacts, biodiversity, species traits and inter-species
interactions.
The first step lay in understanding how woody plant assemblages are shaped by
human forest modification. For this purpose, field investigations in 57 plots in the
hyperfragmented cultural landscape of the Northern Palatinate highlands (SW
Germany) were conducted, censusing > 4,000 tree/shrub individuals from 34 species.
Use of novel, integrative indices for different types of land-use allowed an accurate
quantification of biotic responses. Intriguingly, woody tree/shrub communities reacted
strikingly positive to forest fragmentation, with increases in alpha and beta diversity,
as well as proliferation of heat/drought/light adapted pioneer species. Contrarily,
managed interior forests were homogenized/constrained in biodiversity, with
dominance of shade/cold adapted commercial tree species. Comparisons with recently
unmanaged stands (> 40 a) revealed first indications for nascent conversion to oldgrowth
conditions, with larger variability in light conditions and subsequent
community composition. Reactions to microclimatic conditions, the relationship
between associated species traits and the corresponding species pool, as well as
facilitative/constraining effects by foresters were discussed as underlying mechanisms.
Reactions of herbivore assemblages to forest fragmentation and the subsequent
changes in host plant communities were assessed by comprehensive sampling of >
1,000 live herbivores from 134 species in the forest understory. Diversity was –
similarly to plant communities - higher in fragmentation affected habitats, particularly
in edges of continuous control forests. Furthermore, average trophic specialization
showed an identical pattern. Mechanistically, benefits from microclimatic conditions,
host availability, as well as pronounced niche differentiation are deemed responsible.
While communities were heterogeneous, with no segregation across habitats, (smallforest fragments, edges, and interior of control forests), vegetation diversity, herbivore
diversity, as well as trophic specialization were identified to shape community
composition. This probably reflected a gradient from generalistic/species poor vs.
specialist/species rich herbivore assemblages.
Insect studies conducted in forest systems are doomed to incompleteness
without considering ‘the last biological frontier’, the tree canopies. To access their
biodiversity, relationship to edge effects, and their conservational value, the
arboricolous arthropod fauna of 24 beech (Fagus sylvatica) canopies was sampled via
insecticidal knockdown (‘fogging’). This resulted in an exhaustive collection of > 46,000
specimens from 24 major taxonomic/functional groups. Abundance distributions were
markedly negative exponential, indicating high abundance variability in tree crowns.
Individuals of six pertinent orders were identified to species level, returning > 3,100
individuals from 175 species and 52 families. This high diversity did marginally differ
across habitats, with slightly higher species richness in edge canopies. However,
communities in edge crowns were noticeably more heterogeneous than those in the
forest interior, possibly due to higher variability in environmental edge conditions. In
total, 49 species with protective value were identified, of which only one showed
habitat preferences (for near-natural interior forests). Among them, six species (all
beetles, Coleoptera) were classified as ‘priority species’ for conservation efforts. Hence,
beech canopies of the Northern Palatinate highlands can be considered strongholds of
insect biodiversity, incorporating many species of particular protective value.
The intricacy of plant-herbivore interaction networks and their relationship to
forest fragmentation is largely unexplored, particularly in Central Europe. Illumination
of this matter is all the more important, as ecological networks are highly relevant for
ecosystem stability, particularly in the face of additional anthropogenic disturbances,
such as climate change. Hence, plant-herbivore interaction networks (PHNs) were
constructed from woody plants and their associated herbivores, sampled alive in the
understory. Herbivory verification was achieved using no-choice-feeding assays, as well
as literature references. In total, networks across small forest fragments, edges, and
the forest interior consisted of 696 interactions. Network complexity and trophic niche
redundancy were compared across habitats using a rarefaction-like resampling
procedure. PHNs in fragmentation affected forest habitats were significantly more
complex, as well as more redundant in their realized niches, despite being composed of
relatively more specialist species. Furthermore, network robustness to climate change
was quantified utilizing four different scenarios for climate change susceptibility of
involved plants. In this procedure, remaining herbivores in the network were measured
upon successive loss of their host plant species. Consistently, PHNs in edges (and to a
smaller degree in small fragments) withstood primary extinction of plant species
longer, making them more robust. This was attributed to the high prevalence of
heat/drought-adapted species, as well as to beneficial effects of network topography
(complexity and redundancy). Consequently, strong correlative relationships were
found between realized niche redundancy and climate change robustness of PHNs.
This was both the first time that biologically realistic extinctions (instead of e.g.random extinctions) were used to measure network robustness, and that topographical
network parameters were identified as potential indicators for network robustness
against climate change.
In synthesis, in the light of global biotic degradation due to human forest
modification, the necessity to differentiate must be claimed. Ecosystems react
differently to anthropogenic disturbances, and it seems the particular features present
in Central European forests (ancient deforestation, extensive management, and, most
importantly, high richness in open-forest plant species) cause partly opposed patterns
to other biomes. Lenient microclimates and diverse plant communities facilitate
equally diverse herbivore assemblages, and hence complex and robust networks,
opposed to the forest interior. Therefore, in the reality of extensively used cultural
landscapes, fragmentation affected forest ecosystems, particularly forest edges, can be
perceived as reservoir for biodiversity, and ecosystem functionality. Nevertheless, as
practically all forest habitats considered in this thesis are under human cultivation,
recommendations for ecological enhancement of all forest habitats are discussed.

The Context and Its Importance: In safety and reliability analysis, the information generated by Minimal Cut Set (MCS) analysis is large.
The Top Level event (TLE) that is the root of the fault tree (FT) represents a hazardous state of the system being analyzed.
MCS analysis helps in analyzing the fault tree (FT) qualitatively-and quantitatively when accompanied with quantitative measures.
The information shows the bottlenecks in the fault tree design leading to identifying weaknesses of the system being examined.
Safety analysis (containing the MCS analysis) is especially important for critical systems, where harm can be done to the environment or human causing injuries, or even death during the system usage.
Minimal Cut Set (MCS) analysis is performed using computers and generating a lot of information.
This phase is called MCS analysis I in this thesis.
The information is then analyzed by the analysts to determine possible issues and to improve the design of the system regarding its safety as early as possible.
This phase is called MCS analysis II in this thesis.
The goal of my thesis was developing interactive visualizations to support MCS analysis II of one fault tree (FT).
The Methodology: As safety visualization-in this thesis, Minimal Cut Set analysis II visualization-is an emerging field and no complete checklist regarding Minimal Cut Set analysis II requirements and gaps were available from the perspective of visualization and interaction capabilities,
I have conducted multiple studies using different methods with different data sources (i.e., triangulation of methods and data) for determining these requirements and gaps before developing and evaluating visualizations and interactions supporting Minimal Cut Set analysis II.
Thus, the following approach was taken in my thesis:
1- First, a triangulation of mixed methods and data sources was conducted.
2- Then, four novel interactive visualizations and one novel interaction widget were developed.
3- Finally, these interactive visualizations were evaluated both objectively and subjectively (compared to multiple safety tools)
from the point of view of users and developers of the safety tools that perform MCS analysis I with respect to their degree in supporting MCS analysis II and from the point of non-domain people using empirical strategies.
The Spiral tool supports analysts with different visions, i.e., full vision, color deficiency protanopia, deuteranopia, and tritanopia. It supports 100 out of 103 (97%) requirements obtained from the triangulation and it fills 37 out of 39 (95%) gaps. Its usability was rated high (better than their best currently used tools) by the users of the safety and reliability tools (RiskSpectrum, ESSaRel, FaultTree+, and a self-developed tool) and at least similar to the best currently used tools from the point of view of the CAFTA tool developers. Its quality was higher regarding its degree of supporting MCS analysis II compared to the FaultTree+ tool. The time spent for discovering the critical MCSs from a problem size of 540 MCSs (with a worst case of all equal order) was less than a minute while achieving 99.5% accuracy. The scalability of the Spiral visualization was above 4000 MCSs for a comparison task. The Dynamic Slider reduces the interaction movements up to 85.71% of the previous sliders and solves the overlapping thumb issues by the sliders provides the 3D model view of the system being analyzed provides the ability to change the coloring of MCSs according to the color vision of the user provides selecting a BE (i.e., multi-selection of MCSs), thus, can observe the BEs' NoO and provides its quality provides two interaction speeds for panning and zooming in the MCS, BE, and model views provide a MCS, a BE, and a physical tab for supporting the analysis starting by the MCSs, the BEs, or the physical parts. It combines MCS analysis results and the model of an embedded system enabling the analysts to directly relate safety information with the corresponding parts of the system being analyzed and provides an interactive mapping between the textual information of the BEs and MCSs and the parts related to the BEs.
Verifications and Assessments: I have evaluated all visualizations and the interaction widget both objectively and subjectively, and finally evaluated the final Spiral visualization tool also both objectively and subjectively regarding its perceived quality and regarding its degree of supporting MCS analysis II.

Functional data analysis is a branch of statistics that deals with observations \(X_1,..., X_n\) which are curves. We are interested in particular in time series of dependent curves and, specifically, consider the functional autoregressive process of order one (FAR(1)), which is defined as \(X_{n+1}=\Psi(X_{n})+\epsilon_{n+1}\) with independent innovations \(\epsilon_t\). Estimates \(\hat{\Psi}\) for the autoregressive operator \(\Psi\) have been investigated a lot during the last two decades, and their asymptotic properties are well understood. Particularly difficult and different from scalar- or vector-valued autoregressions are the weak convergence properties which also form the basis of the bootstrap theory.
Although the asymptotics for \(\hat{\Psi}{(X_{n})}\) are still tractable, they are only useful for large enough samples. In applications, however, frequently only small samples of data are available such that an alternative method for approximating the distribution of \(\hat{\Psi}{(X_{n})}\) is welcome. As a motivation, we discuss a real-data example where we investigate a changepoint detection problem for a stimulus response dataset obtained from the animal physiology group at the Technical University of Kaiserslautern.
To get an alternative for asymptotic approximations, we employ the naive or residual-based bootstrap procedure. In this thesis, we prove theoretically and show via simulations that the bootstrap provides asymptotically valid and practically useful approximations of the distributions of certain functions of the data. Such results may be used to calculate approximate confidence bands or critical bounds for tests.

Since the early days of representation theory of finite groups in the 19th century, it was known that complex linear representations of finite groups live over number fields, that is, over finite extensions of the field of rational numbers.
While the related question of integrality of representations was answered negatively by the work of Cliff, Ritter and Weiss as well as by Serre and Feit, it was not known how to decide integrality of a given representation.
In this thesis we show that there exists an algorithm that given a representation of a finite group over a number field decides whether this representation can be made integral.
Moreover, we provide theoretical and numerical evidence for a conjecture, which predicts the existence of splitting fields of irreducible characters with integrality properties.
In the first part, we describe two algorithms for the pseudo-Hermite normal form, which is crucial when handling modules over ring of integers.
Using a newly developed computational model for ideal and element arithmetic in number fields, we show that our pseudo-Hermite normal form algorithms have polynomial running time.
Furthermore, we address a range of algorithmic questions related to orders and lattices over Dedekind domains, including computation of genera, testing local isomorphism, computation of various homomorphism rings and computation of Solomon zeta functions.
In the second part we turn to the integrality of representations of finite groups and show that an important ingredient is a thorough understanding of the reduction of lattices at almost all prime ideals.
By employing class field theory and tools from representation theory we solve this problem and eventually describe an algorithm for testing integrality.
After running the algorithm on a large set of examples we are led to a conjecture on the existence of integral and nonintegral splitting fields of characters.
By extending techniques of Serre we prove the conjecture for characters with rational character field and Schur index two.

Thermoplastic composite materials are being widely used in the automotive and aerospace industries. Due to the limitations of shape complexity, different components
need to be joined. They can be joined by mechanical fasteners, adhesive bonding or
both. However, these methods have several limitations. Components can be joined
by fusion bonding due to the property of thermoplastics. Thermoplastics can be melted on heating and regain their shape on cooling. This property makes them ideal for
joining through fusion bonding by induction heating. Joining of non-conducting or
non-magnetic thermoplastic composites needs an additional material that can generate heat by induction heating.
Polymers are neither conductive nor electromagnetic so they don’t have inherent potential for inductive heating. A susceptor sheet having conductive materials (e.g. carbon fiber) or magnetic materials (e.g. nickel) can generate heat during induction. The
main issues related with induction heating are non-homogeneous and uncontrolled
heating.
In this work, it was observed that to generate heat with a susceptor sheet depends
on its filler, its concentration, and its dispersion. It also depends on the coil, magnetic
field strength and coupling distance. The combination of different fillers not only increased the heating rate but also changed the heating mechanism. Heating of 40ºC/
sec was achieved with 15wt.-% nickel coated short carbon fibers and 3wt.-% multiwalled carbon nanotubes. However, only nickel coated short carbon fibers (15wt-.%)
attained the heating rate of 24ºC/ sec. In this study, electrical conductivity, thermal
conductivity and magnetic properties testing were also performed. The results also
showed that electrical percolation was achieved around 15wt.-% in fibers and (13-
6)wt.-% with hybrid fillers. Induction heating tests were also performed by making
parallel and perpendicular susceptor sheet as fibers were uni-directionally aligned.
The susceptor sheet was also tested by making perforations.
The susceptor sheet showed homogeneous and fast heating, and can be used for
joining of non-conductive or non-magnetic thermoplastic composites.

A wide range of methods and techniques have been developed over the years to manage the increasing
complexity of automotive Electrical/Electronic systems. Standardization is an example
of such complexity managing techniques that aims to minimize the costs, avoid compatibility
problems and improve the efficiency of development processes.
A well-known and -practiced standard in automotive industry is AUTOSAR (Automotive
Open System Architecture). AUTOSAR is a common standard among OEMs (Original Equipment
Manufacturer), suppliers and other involved companies. It was developed originally with
the goal of simplifying the overall development and integration process of Electrical/Electronic
artifacts from different functional domains, such as hardware, software, and vehicle communication.
However, the AUTOSAR standard, in its current status, is not able to manage the problems
in some areas of the system development. Validation and optimization process of system configuration
handled in this thesis are examples of such areas, in which the AUTOSAR standard
offers so far no mature solutions.
Generally, systems developed on the basis of AUTOSAR must be configured in a way that all
defined requirements are met. In most cases, the number of configuration parameters and their
possible settings in AUTOSAR systems are large, especially if the developed system is complex
with modules from various knowledge domains. The verification process here can consume a
lot of resources to test all possible combinations of configuration settings, and ideally find the
optimal configuration variant, since the number of test cases can be very high. This problem is
referred to in literature as the combinatorial explosion problem.
Combinatorial testing is an active and promising area of functional testing that offers ideas
to solve the combinatorial explosion problem. Thereby, the focus is to cover the interaction
errors by selecting a sample of system input parameters or configuration settings for test case
generation. However, the industrial acceptance of combinatorial testing is still weak because of
the deficiency of real industrial examples.
This thesis is tempted to fill this gap between the industry and the academy in the area
of combinatorial testing to emphasizes the effectiveness of combinatorial testing in verifying
complex configurable systems.
The particular intention of the thesis is to provide a new applicable approach to combinatorial
testing to fight the combinatorial explosion problem emerged during the verification and
performance measurement of transport protocol parallel routing of an AUTOSAR gateway. The
proposed approach has been validated and evaluated by means of two real industrial examples
of AUTOSAR gateways with multiple communication buses and two different degrees of complexity
to illustrate its applicability.

In this thesis we developed a desynchronization design flow in the goal of easing the de- velopment effort of distributed embedded systems. The starting point of this design flow is a network of synchronous components. By transforming this synchronous network into a dataflow process network (DPN), we ensures important properties that are difficult or theoretically impossible to analyze directly on DPNs are preserved by construction. In particular, both deadlock-freeness and buffer boundedness can be preserved after desyn- chronization. For the correctness of desynchronization, we developed a criteria consisting of two properties: a global property that demands the correctness of the synchronous network, as well as a local property that requires the latency-insensitivity of each local synchronous component. As the global property is also a correctness requirement of synchronous systems in general, we take this property as an assumption of our desyn- chronization. However, the local property is in general not satisfied by all synchronous components, and therefore needs to be verified before desynchronization. In this thesis we developed a novel technique for the verification of the local property that can be carried out very efficiently. Finally we developed a model transformation method that translates a set of synchronous guarded actions – an intermediate format for synchronous systems – to an asynchronous actor description language (CAL). Our theorem ensures that one passed the correctness verification, the generated DPN of asynchronous pro- cesses (or actors) preserves the functional behavior of the original synchronous network. Moreover, by the correctness of the synchronous network, our theorem guarantees that the derived DPN is deadlock-free and can be implemented with only finitely bounded buffers.

Automata theory has given rise to a variety of automata models that consist
of a finite-state control and an infinite-state storage mechanism. The aim
of this work is to provide insights into how the structure of the storage
mechanism influences the expressiveness and the analyzability of the
resulting model. To this end, it presents generalizations of results about
individual storage mechanisms to larger classes. These generalizations
characterize those storage mechanisms for which the given result remains
true and for which it fails.
In order to speak of classes of storage mechanisms, we need an overarching
framework that accommodates each of the concrete storage mechanisms we wish
to address. Such a framework is provided by the model of valence automata,
in which the storage mechanism is represented by a monoid. Since the monoid
serves as a parameter to specifying the storage mechanism, our aim
translates into the question: For which monoids does the given
(automata-theoretic) result hold?
As a first result, we present an algebraic characterization of those monoids
over which valence automata accept only regular languages. In addition, it
turns out that for each monoid, this is the case if and only if valence
grammars, an analogous grammar model, can generate only context-free
languages.
Furthermore, we are concerned with closure properties: We study which
monoids result in a Boolean closed language class. For every language class
that is closed under rational transductions (in particular, those induced by
valence automata), we show: If the class is Boolean closed and contains any
non-regular language, then it already includes the whole arithmetical
hierarchy.
This work also introduces the class of graph monoids, which are defined by
finite graphs. By choosing appropriate graphs, one can realize a number of
prominent storage mechanisms, but also combinations and variants thereof.
Examples are pushdowns, counters, and Turing tapes. We can therefore relate
the structure of the graphs to computational properties of the resulting
storage mechanisms.
In the case of graph monoids, we study (i) the decidability of the emptiness
problem, (ii) which storage mechanisms guarantee semilinear Parikh images,
(iii) when silent transitions (i.e. those that read no input) can be
avoided, and (iv) which storage mechanisms permit the computation of
downward closures.

Annual Report 2015
(2016)

Annual Report, Jahrbuch AG Magnetismus

The thesis consists of two parts. In the first part we consider the stable Auslander--Reiten quiver of a block \(B\) of a Hecke algebra of the symmetric group at a root of unity in characteristic zero. The main theorem states that if the ground field is algebraically closed and \(B\) is of wild representation type, then the tree class of every connected component of the stable Auslander--Reiten quiver \(\Gamma_{s}(B)\) of \(B\) is \(A_{\infty}\). The main ingredient of the proof is a skew group algebra construction over a quantum complete intersection. Also, for these algebras the stable Auslander--Reiten quiver is computed in the case where the defining parameters are roots of unity. As a result, the tree class of every connected component of the stable Auslander--Reiten quiver is \(A_{\infty}\).\[\]
In the second part of the thesis we are concerned with branching rules for Hecke algebras of the symmetric group at a root of unity. We give a detailed survey of the theory initiated by I. Grojnowski and A. Kleshchev, describing the Lie-theoretic structure that the Grothendieck group of finite-dimensional modules over a cyclotomic Hecke algebra carries. A decisive role in this approach is played by various functors that give branching rules for cyclotomic Hecke algebras that are independent of the underlying field. We give a thorough definition of divided power functors that will enable us to reformulate the Scopes equivalence of a Scopes pair of blocks of Hecke algebras of the symmetric group. As a consequence we prove that two indecomposable modules that correspond under this equivalence have a common vertex. In particular, we verify the Dipper--Du Conjecture in the case where the blocks under consideration have finite representation type.

The present study investigated the effects of two methods of shared book reading on children´s emergent literacy skills, such as language skills (expressive vocabulary and semantic skills) and grapheme awareness, i.e. before the alphabetic phase of reading acquisition (Lachmann & van Leeuwen, 2014) in home and in kindergarten contexts. The two following shared book reading methods were investigated: Method I - literacy enrichment: 200 extra children's books were distributed in kindergartens and children were encouraged every week to borrow a book to take home and read with their parents. Further, a written letter was sent to the parents encouraging them to frequently read the books with their children at home. Method II - teacher training: kindergarten teachers participated in structured training which included formal instruction on how to promote child language development through shared book reading. The training was an adaptation of the Heidelberger Interaktionstraining für pädagogisches Fachpersonal zur Förderung ein- und mehrsprachiger Kinder - HIT (Buschmann & Jooss, 2011). In addition, the effects of the two methods in combination were investigated. Three questions were addressed in the present study: (1) What effect does method I (literacy enrichment), method II (teacher training) and the combination of both methods have on children's expressive vocabulary? (2) What effect does method I (literacy enrichment), method II (teacher training) and the combination of both methods have on children's semantic skills? (3) What effect does method I (literacy enrichment), method II (teacher training) and the combination of both methods have on children's grapheme awareness? Accordingly, 69 children, ranged in age from 3;0 to 4;8 years, were recruited from four kindergartens in the city of Kaiserslautern, Germany. The kindergartens were divided into: kindergarten 1 – Method I (N = 13); kindergarten 2 - Method II (N = 18); kindergarten 3 - Combination of both methods (N = 17); kindergarten 4 - Control group (N = 21). Half of the participants (N = 35) reported having a migration background. All groups were similar in regards to socioeconomic status and literacy activities at home. In a pre- posttest design, children performed three tests: expressive vocabulary (AWSTR, 3-5; Kiese-Himmel, 2005), semantic skills (SETK, 3-5 subtests ESR; Grimm, 2001), and grapheme awareness which is a task developed with the purpose of testing children’s familiarity with grapheme forms. The intervention period had duration of six months. The data analysis was performed using the software IBM SPSS Statistics version 22. Regarding language skills, Method I showed no significant effects on children expressive vocabulary and semantic skills. Method II showed significant effects for children expressive vocabulary. In addition, the children with migration background took more advantage of the method. Regarding semantic skills, no significant effects were found. No significant effects of the combination of both methods in children's language skills were found. For grapheme awareness, however, results showed positive effects for Method I, and Method II, as well as for the combination of both methods. The combination group, as reported by a large effect size, showed to be more effective than Method I and Method II alone. Moreover, the results indicated that in grapheme awareness, all children (in regards to age, gender, with and without migration background) took equal advantage in all three intervention groups. Overall, it can be concluded with the results of the present study, that by providing access to good books, Method I may help parents involve themselves in the active process of their child's literacy skills development. However, in order to improve language skills, access to books alone showed to be not enough. Therefore, it is suggested that access combined with additional support to parents in how to improve their language interactions with their children is highly recommended. In respect to Method II, the present study suggests that shared book reading through professional training is an important tool that supports children´s language development. For grapheme awareness it is concluded that with the combination of the two performed methods, high exposure to shared book reading helps children to informally learn about the surface characteristics of print, acquire some familiarity with the visual characteristics of the letters and learn to differentiate them from other visual patterns. Finally, it is suggested to organizations and institutions as well as to future research, the importance of having more programs that offer different possibilities to children to have more contact with adequate language interaction as well as more experiences with print through shared book reading as showed in the present study.

We propose and study a strongly coupled PDE-ODE-ODE system modeling cancer cell invasion through a tissue network
under the go-or-grow hypothesis asserting that cancer cells can either move or proliferate. Hence our setting features
two interacting cell populations with their mutual transitions and involves tissue-dependent degenerate diffusion and
haptotaxis for the moving subpopulation. The proliferating cells and the tissue evolution are characterized by way of ODEs
for the respective densities. We prove the global existence of weak solutions and illustrate the model behaviour by
numerical simulations in a two-dimensional setting.

Inflation modeling is a very important tool for conducting an efficient monetary policy. This doctoral thesis reviewed inflation models, in particular the Phillips curve models of inflation dynamics. We focused on a well known and widely used model, the so-called three equation new Keynesian model which is a system of equations consisting of a new Keynesian Phillips curve (NKPC), an investment and saving (IS) curve and an interest rate rule.
We gave a detailed derivation of these equations. The interest rate rule used in this model is normally determined by using a Lagrangian method to solve an optimal control problem constrained by a standard discrete time NKPC which describes the inflation dynamics and an IS curve that represents the output gaps dynamics. In contrast to the real world, this method assumes that the policy makers intervene continuously. This means that the costs resulting from the change in the interest rates are ignored. We showed also that there are approximation errors made, when one log-linearizes non linear equations, by doing the derivation of the standard discrete time NKPC.
We agreed with other researchers as mentioned in this thesis, that errors which result from ignoring such log-linear approximation errors and the costs of altering interest rates by determining interest rate rule, can lead to a suboptimal interest rate rule and hence to non-optimal paths of output gaps and inflation rate.
To overcome such a problem, we proposed a stochastic optimal impulse control method. We formulated the problem as a stochastic optimal impulse control problem by considering the costs of change in interest rates and the approximation error terms. In order to formulate this problem, we first transform the standard discrete time NKPC and the IS curve into their high-frequency versions and hence into their continuous time versions where error terms are described by a zero mean Gaussian white noise with a finite and constant variance. After formulating this problem, we use the quasi-variational inequality approach to solve analytically a special case of the central bank problem, where an inflation rate is supposed to be on target and a central bank has to optimally control output gap dynamics. This method gives an optimal control band in which output gap process has to be maintained and an optimal control strategy, which includes the optimal size of intervention and optimal intervention time, that can be used to keep the process into the optimal control band.
Finally, using a numerical example, we examined the impact of some model parameters on optimal control strategy. The results show that an increase in the output gap volatility as well as in the fixed and proportional costs of the change in interest rate lead to an increase in the width of the optimal control band. In this case, the optimal intervention requires the central bank to wait longer before undertaking another control action.

In this thesis, mathematical research questions related to recursive utility and stochastic differential utility (SDU) are explored.
First, a class of backward equations under nonlinear expectations is investigated: Existence and uniqueness of solutions are established, and the issues of stability and discrete-time approximation are addressed. It is then shown that backward equations of this class naturally appear as a continuous-time limit in the context of recursive utility with nonlinear expectations.
Then, the Epstein-Zin parametrization of SDU is studied. The focus is on specifications with both relative risk aversion and elasitcity of intertemporal substitution greater that one. A concave utility functional is constructed and a utility gradient inequality is established.
Finally, consumption-portfolio problems with recursive preferences and unspanned risk are investigated. The investor's optimal strategies are characterized by a specific semilinear partial differential equation. The solution of this equation is constructed by a fixed point argument, and a corresponding efficient and accurate method to calculate optimal strategies numerically is given.

This thesis deals with risk measures based on utility functions and time consistency of dynamic risk measures. It is therefore aimed at readers interested in both, the theory of static and dynamic financial risk measures in the sense of Artzner, Delbaen, Eber and Heath [7], [8] and the theory of preferences in the tradition of von Neumann and Morgenstern [134].
A main contribution of this thesis is the introduction of optimal expected utility (OEU) risk measures as a new class of utility-based risk measures. We introduce OEU, investigate its main properties, and its applicability to risk measurement and put it in perspective to alternative risk measures and notions of certainty equivalents. To the best of our knowledge, OEU is the only existing utility-based risk measure that is (non-trivial and) coherent if the utility function u has constant relative risk aversion. We present several different risk measures that can be derived with special choices of u and illustrate that OEU reacts in a more sensitive way to slight changes of the probability of a financial loss than value at risk (V@R) and average value at risk.
Further, we propose implied risk aversion as a coherent rating methodology for retail structured products (RSPs). Implied risk aversion is based on optimal expected utility risk measures and, in contrast to standard V@R-based ratings, takes into account both the upside potential and the downside risks of such products. In addition, implied risk aversion is easily interpreted in terms of an individual investor's risk aversion: A product is attractive (unattractive) for an investor if its implied risk aversion is higher (lower) than his individual risk aversion. We illustrate this approach in a case study with more than 15,000 warrants on DAX ® and find that implied risk aversion is able to identify favorable products; in particular, implied risk aversion is not necessarily increasing with respect to the strikes of call warrants.
Another main focus of this thesis is on consistency of dynamic risk measures. To this end, we study risk measures on the space of distributions, discuss concavity on the level of distributions and slightly generalize Weber's [137] findings on the relation of time consistent dynamic risk measures to static risk measures to the case of dynamic risk measures with time-dependent parameters. Finally, this thesis investigates how recursively composed dynamic risk measures in discrete time, which are time consistent by construction, can be related to corresponding dynamic risk measures in continuous time. We present different approaches to establish this link and outline the theoretical basis and the practical benefits of this relation. The thesis concludes with a numerical implementation of this theory.

Towards A Non-tracking Web
(2016)

Today, many publishers (e.g., websites, mobile application developers) commonly use third-party analytics services and social widgets. Unfortunately, this scheme allows these third parties to track individual users across the web, creating privacy concerns and leading to reactions to prevent tracking via blocking, legislation and standards. While improving user privacy, these efforts do not consider the functionality third-party tracking enables publishers to use: to obtain aggregate statistics about their users and increase their exposure to other users via online social networks. Simply preventing third-party tracking without replacing the functionality it provides cannot be a viable solution; leaving publishers without essential services will hurt the sustainability of the entire ecosystem.
In this thesis, we present alternative approaches to bridge this gap between privacy for users and functionality for publishers and other entities. We first propose a general and interaction-based third-party cookie policy that prevents third-party tracking via cookies, yet enables social networking features for users when wanted, and does not interfere with non-tracking services for analytics and advertisements. We then present a system that enables publishers to obtain rich web analytics information (e.g., user demographics, other sites visited) without tracking the users across the web. While this system requires no new organizational players and is practical to deploy, it necessitates the publishers to pre-define answer values for the queries, which may not be feasible for many analytics scenarios (e.g., search phrases used, free-text photo labels). Our second system complements the first system by enabling publishers to discover previously unknown string values to be used as potential answers in a privacy-preserving fashion and with low computation overhead for clients as well as servers. These systems suggest that it is possible to provide non-tracking services with (at least) the same functionality as today’s tracking services.

Membrane proteins are generally soluble only in the presence of detergent micelles or other membrane-mimetic systems, which renders the determination of the protein’s molar mass or oligomeric state difficult. Moreover, the amount of bound detergent varies drastically among different proteins and detergents. However, the type of detergent and its concentration have a great influence on the protein’s structure, stability, and functionality and the success of structural and functional investigations and crystallographic trials. Size-exclusion chromatography, which is commonly used to determine the molar mass of water-soluble proteins, is not suitable for detergent-solubilised proteins because
the protein–detergent complex has a different conformation and, thus, commonly exhibits
a different migration behaviour than globular standard proteins. Thus, calibration curves obtained with standard proteins are not useful for membrane-protein analysis. However,
the combination of size-exclusion chromatography with ultraviolet absorbance, static light scattering, and refractive index detection provides a tool to determine the molar mass of protein–detergent complexes in an absolute manner and allows for distinguishing the contributions of detergent and protein to the complex.
The goal of this thesis was to refine the standard triple-detection size-exclusion chromatography measurement and data analysis procedure for challenging membrane-protein samples, non-standard detergents, and difficult solvents such as concentrated denaturant solutions that were thought to elude routine approaches. To this end, the influence of urea on the performance of the method beyond direct influences on detergents and proteins was investigated with the help of the water-soluble bovine serum albumin. On the basis of
the obtained results, measurement and data analysis procedures were refined for different detergents and protein–detergent complexes comprising the membrane proteins OmpLA and Mistic from Escherichia coli and Bacillus subtilis, respectively.
The investigations on mass and shape of different detergent micelles and the compositions of protein–detergent complexes in aqueous buffer and concentrated urea solutions
showed that triple-detection size-exclusion chromatography provides valuable information
about micelle masses and shapes under various conditions. Moreover, it is perfectly suited for the straightforward analysis of detergent-suspended proteins in terms of composition and oligomeric state not only under native but, more importantly, also under denaturing conditions.