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.

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.

C-H activations(C-H bond weakening effects) under impact of transition metal atoms are theoretically investigated, two model systems are used, one is CH3MX, the other is n-ButMX, (X=F,Cl,Br,I,H,CN, M include all transition metal atoms from group 4 to group 10).

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

In this paper, we discuss the problem of approximating ellipsoid uncertainty sets with bounded (gamma) uncertainty sets. Robust linear programs with ellipsoid uncertainty lead to quadratically constrained programs, whereas robust linear programs with bounded uncertainty sets remain linear programs which are generally easier to solve. We call a bounded uncertainty set an inner approximation of an ellipsoid if it is contained in it. We consider two different inner approximation problems. The first problem is to find a bounded uncertainty set which sticks close to the ellipsoid such that a shrank version of the ellipsoid is contained in it. The approximation is optimal if the required shrinking is minimal. In the second problem, we search for a bounded uncertainty set within the ellipsoid with maximum volume. We present how both problems can be solved analytically by stating explicit formulas for the optimal solutions of these problems. Further, we present in a computational experiment how the derived approximation techniques can be used to approximate shortest path and network flow problems which are affected by ellipsoidal uncertainty.

Computer Vision (CV) problems, such as image classification and segmentation, have traditionally been solved by manual construction of feature hierarchies or incorporation of other prior knowledge. However, noisy images, varying viewpoints and lighting conditions of images, and clutters in real-world images make the problem challenging. Such tasks cannot be efficiently solved without learning from data. Therefore, many Deep Learning (DL) approaches have recently been successful for various CV tasks, for instance, image classification, object recognition and detection, action recognition, video classification, and scene labeling. The main focus of this thesis is to investigate a purely learning-based approach, particularly, Multi-Dimensional LSTM (MD-LSTM) recurrent neural networks to tackle the challenging CV tasks, classification and segmentation on 2D and 3D image data. Due to the structural nature of MD-LSTM, the network learns directly from raw pixel values and takes the complex spatial dependencies of each pixel into account. This thesis provides several key contributions in the field of CV and DL. Several MD-LSTM network architectural options are suggested based on the type of input and output, as well as the requiring tasks. Including the main layers, which are an input layer, a hidden layer, and an output layer, several additional layers can be added such as a collapse layer and a fully connected layer. First, a single Two Dimensional LSTM (2D-LSTM) is directly applied on texture images for segmentation and show improvement over other texture segmentation methods. Besides, a 2D-LSTM layer with a collapse layer is applied for image classification on texture and scene images and have provided an accurate classification results. In addition, a deeper model with a fully connected layer is introduced to deal with more complex images for scene labeling and outperforms the other state-of-the-art methods including the deep Convolutional Neural Networks (CNN). Here, several input and output representation techniques are introduced to achieve the robust classification. Randomly sampled windows as input are transformed in scaling and rotation, which are integrated to get the final classification. To achieve multi-class image classification on scene images, several pruning techniques are introduced. This framework provides a good results in automatic web-image tagging. The next contribution is an investigation of 3D data with MD-LSTM. The traditional cuboid order of computations in Multi-Dimensional LSTM (MD-LSTM) is re-arranged in pyramidal fashion. The resulting Pyramidal Multi-Dimensional LSTM (PyraMiD-LSTM) is easy to parallelize, especially for 3D data such as stacks of brain slice images. PyraMiD-LSTM was tested on 3D biomedical volumetric images and achieved best known pixel-wise brain image segmentation results and competitive results on Electron Microscopy (EM) data for membrane segmentation. To validate the framework, several challenging databases for classification and segmentation are proposed to overcome the limitations of current databases. First, scene images are randomly collected from the web and used for scene understanding, i.e., the web-scene image dataset for multi-class image classification. To achieve multi-class image classification, the training and testing images are generated in a different setting. For training, images belong to a single pre-defined category which are trained as a regular single-class image classification. However, for testing, images containing multi-classes are randomly collected by web-image search engine by querying the categories. All scene images include noise, background clutter, unrelated contents, and also diverse in quality and resolution. This setting can make the database possible to evaluate for real-world applications. Secondly, an automated blob-mosaics texture dataset generator is introduced for segmentation. Random 2D Gaussian blobs are generated and filled with random material textures. These textures contain diverse changes in illumination, scale, rotation, and viewpoint. The generated images are very challenging since they are even visually hard to separate the related regions. Overall, the contributions in this thesis are major advancements in the direction of solving image analysis problems with Long Short-Term Memory (LSTM) without the need of any extra processing or manually designed steps. We aim at improving the presented framework to achieve the ultimate goal of accurate fine-grained image analysis and human-like understanding of images by machines.

The task of printed Optical Character Recognition (OCR), though considered ``solved'' by many, still poses several challenges. The complex grapheme structure of many scripts, such as Devanagari and Urdu Nastaleeq, greatly lowers the performance of state-of-the-art OCR systems. Moreover, the digitization of historical and multilingual documents still require much probing. Lack of benchmark datasets further complicates the development of reliable OCR systems. This thesis aims to find the answers to some of these challenges using contemporary machine learning technologies. Specifically, the Long Short-Term Memory (LSTM) networks, have been employed to OCR modern as well historical monolingual documents. The excellent OCR results obtained on these have led us to extend their application for multilingual documents. The first major contribution of this thesis is to demonstrate the usability of LSTM networks for monolingual documents. The LSTM networks yield very good OCR results on various modern and historical scripts, without using sophisticated features and post-processing techniques. The set of modern scripts include modern English, Urdu Nastaleeq and Devanagari. To address the challenge of OCR of historical documents, this thesis focuses on Old German Fraktur script, medieval Latin script of the 15th century, and Polytonic Greek script. LSTM-based systems outperform the contemporary OCR systems on all of these scripts. To cater for the lack of ground-truth data, this thesis proposes a new methodology, combining segmentation-based and segmentation-free OCR approaches, to OCR scripts for which no transcribed training data is available. Another major contribution of this thesis is the development of a novel multilingual OCR system. A unified framework for dealing with different types of multilingual documents has been proposed. The core motivation behind this generalized framework is the human reading ability to process multilingual documents, where no script identification takes place. In this design, the LSTM networks recognize multiple scripts simultaneously without the need to identify different scripts. The first step in building this framework is the realization of a language-independent OCR system which recognizes multilingual text in a single step. This language-independent approach is then extended to script-independent OCR that can recognize multiscript documents using a single OCR model. The proposed generalized approach yields low error rate (1.2%) on a test corpus of English-Greek bilingual documents. In summary, this thesis aims to extend the research in document recognition, from modern Latin scripts to Old Latin, to Greek and to other ``under-privilaged'' scripts such as Devanagari and Urdu Nastaleeq. It also attempts to add a different perspective in dealing with multilingual documents.

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.

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.

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.

In this paper, we show the feasibility of low supply voltage for SRAM (Static Random Access Memory) by adding error correction coding (ECC). In SRAM, the memory matrix needs to be powered for data retentive standby operation, resulting in standby leakage current. Particularly for low duty- cycle systems, the energy consumed due to standby leakage current can become significant. Lowering the supply voltage (VDD) during standby mode to below the specified data retention voltage (DRV) helps decrease the leakage current. At these VDD levels errors start to appear, which we can remedy by adding ECC. We show in this paper that addition of a simple single error correcting (SEC) ECC enables us to decrease the leakage current by 45% and leakage power by 72%. We verify this on a large set of commercially available standard 40nm SRAMs.

To continue reducing voltage in scaled technologies, both circuit and architecture-level resiliency techniques are needed to tolerate process-induced defects, variation, and aging in SRAM cells. Many different resiliency schemes have been proposed and evaluated, but most prior results focus on voltage reduction instead of energy reduction. At the circuit level, device cell architectures and assist techniques have been shown to lower Vmin for SRAM, while at the architecture level, redundancy and cache disable techniques have been used to improve resiliency at low voltages. This paper presents a unified study of error tolerance for both circuit and architecture techniques and estimates their area and energy overheads. Optimal techniques are selected by evaluating both the error-correcting abilities at low supplies and the overheads of each technique in a 28nm. The results can be applied to many of the emerging memory technologies.

Magnetic spin-based memory technologies are a promising solution to overcome the incoming limits of microelectronics. Nevertheless, the long write latency and high write energy of these memory technologies compared to SRAM make it difficult to use these for fast microprocessor memories, such as L1- Caches. However, the recent advent of the Spin Orbit Torque (SOT) technology changed the story: indeed, it potentially offers a writing speed comparable to SRAM with a much better density as SRAM and an infinite endurance, paving the way to a new paradigm in processor architectures, with introduction of non- volatility in all the levels of the memory hierarchy towards full normally-off and instant-on processors. This paper presents a full design flow, from device to system, allowing to evaluate the potential of SOT for microprocessor cache memories and very encouraging simulation results using this framework.