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The focus of this work is to provide and evaluate a novel method for multifield topology-based analysis and visualization. Through this concept, called Pareto sets, one is capable to identify critical regions in a multifield with arbitrary many individual fields. It uses ideas found in graph optimization to find common behavior and areas of divergence between multiple optimization objectives. The connections between the latter areas can be reduced into a graph structure allowing for an abstract visualization of the multifield to support data exploration and understanding.
The research question that is answered in this dissertation is about the general capability and expandability of the Pareto set concept in context of visualization and application. Furthermore, the study of its relations, drawbacks and advantages towards other topological-based approaches. This questions is answered in several steps, including consideration and comparison with related work, a thorough introduction of the Pareto set itself as well as a framework for efficient implementation and an attached discussion regarding limitations of the concept and their implications for run time, suitable data, and possible improvements.
Furthermore, this work considers possible simplification approaches like integrated single-field simplification methods but also using common structures identified through the Pareto set concept to smooth all individual fields at once. These considerations are especially important for real-world scenarios to visualize highly complex data by removing small local structures without destroying information about larger, global trends.
To further emphasize possible improvements and expandability of the Pareto set concept, the thesis studies a variety of different real world applications. For each scenario, this work shows how the definition and visualization of the Pareto set is used and improved for data exploration and analysis based on the scenarios.
In summary, this dissertation provides a complete and sound summary of the Pareto set concept as ground work for future application of multifield data analysis. The possible scenarios include those presented in the application section, but are found in a wide range of research and industrial areas relying on uncertainty analysis, time-varying data, and ensembles of data sets in general.

Novel image processing techniques have been in development for decades, but most
of these techniques are barely used in real world applications. This results in a gap
between image processing research and real-world applications; this thesis aims to
close this gap. In an initial study, the quantification, propagation, and communication
of uncertainty were determined to be key features in gaining acceptance for
new image processing techniques in applications.
This thesis presents a holistic approach based on a novel image processing pipeline,
capable of quantifying, propagating, and communicating image uncertainty. This
work provides an improved image data transformation paradigm, extending image
data using a flexible, high-dimensional uncertainty model. Based on this, a completely
redesigned image processing pipeline is presented. In this pipeline, each
step respects and preserves the underlying image uncertainty, allowing image uncertainty
quantification, image pre-processing, image segmentation, and geometry
extraction. This is communicated by utilizing meaningful visualization methodologies
throughout each computational step.
The presented methods are examined qualitatively by comparing to the Stateof-
the-Art, in addition to user evaluation in different domains. To show the applicability
of the presented approach to real world scenarios, this thesis demonstrates
domain-specific problems and the successful implementation of the presented techniques
in these domains.

Economics of Downside Risk
(2019)

Ever since establishment of portfolio selection theory by Markowitz (1952), the use of Standard deviation as a measure of risk has heavily been criticized. The aim of this thesis is to refine classical portfolio selection and asset pricing theory by using a downside deviation risk measure. It is defined as below-target semideviation and referred to as downside risk.
Downside efficient portfolios maximize expected payoff given a prescribed upper bound for downside risk and, thus, are analogs to mean-variance efficient portfolios in the sense of Markowitz. The present thesis provides an alternative proof of existence of downside efficient portfolios and identifies a sufficient criterion for their uniqueness. A specific representation of their form brings structural similarity to mean-variance efficient portfolios to light. Eventually, a separation theorem for the existence and uniqueness of portfolios that maximize the trade-off between downside risk and return is established.
The notion of a downside risk asset market equilibrium (DRAME) in an asset market with finitely many investors is introduced. This thesis addresses the existence and uniqueness Problem of such equilibria and specifies a DRAME pricing formula. In contrast to prices obtained from the mean-variance CAPM pricing formula, DRAME prices are arbitrage-free and strictly positive.
The final part of this thesis addresses practical issues. An algorithm that allows for an effective computation of downside efficient portfolios from simulated or historical financial data is outlined. In a simulation study, it is revealed in which scenarios downside efficient portfolios
outperform mean-variance efficient portfolios.

The simulation of physical phenomena involving the dynamic behavior of fluids and gases
has numerous applications in various fields of science and engineering. Of particular interest
is the material transport behavior, the tendency of a flow field to displace parts of the
medium. Therefore, many visualization techniques rely on particle trajectories.
Lagrangian Flow Field Representation. In typical Eulerian settings, trajectories are
computed from the simulation output using numerical integration schemes. Accuracy concerns
arise because, due to limitations of storage space and bandwidth, often only a fraction
of the computed simulation time steps are available. Prior work has shown empirically that
a Lagrangian, trajectory-based representation can improve accuracy [Agr+14]. Determining
the parameters of such a representation in advance is difficult; a relationship between the
temporal and spatial resolution and the accuracy of resulting trajectories needs to be established.
We provide an error measure for upper bounds of the error of individual trajectories.
We show how areas at risk for high errors can be identified, thereby making it possible to
prioritize areas in time and space to allocate scarce storage resources.
Comparative Visual Analysis of Flow Field Ensembles. Independent of the representation,
errors of the simulation itself are often caused by inaccurate initial conditions,
limitations of the chosen simulation model, and numerical errors. To gain a better understanding
of the possible outcomes, multiple simulation runs can be calculated, resulting in
sets of simulation output referred to as ensembles. Of particular interest when studying the
material transport behavior of ensembles is the identification of areas where the simulation
runs agree or disagree. We introduce and evaluate an interactive method that enables application
scientists to reliably identify and examine regions of agreement and disagreement,
while taking into account the local transport behavior within individual simulation runs.
Particle-Based Representation and Visualization of Uncertain Flow Data Sets. Unlike
simulation ensembles, where uncertainty of the solution appears in the form of different
simulation runs, moment-based Eulerian multi-phase fluid simulations are probabilistic in
nature. These simulations, used in process engineering to simulate the behavior of bubbles in
liquid media, are aimed toward reducing the need for real-world experiments. The locations
of individual bubbles are not modeled explicitly, but stochastically through the properties of
locally defined bubble populations. Comparisons between simulation results and physical
experiments are difficult. We describe and analyze an approach that generates representative
sets of bubbles for moment-based simulation data. Using our approach, application scientists
can directly, visually compare simulation results and physical experiments.

Destructive diseases of the lung like lung cancer or fibrosis are still often lethal. Also in case of fibrosis in the liver, the only possible cure is transplantation.
In this thesis, we investigate 3D micro computed synchrotron radiation (SR\( \mu \)CT) images of capillary blood vessels in mouse lungs and livers. The specimen show so-called compensatory lung growth as well as different states of pulmonary and hepatic fibrosis.
During compensatory lung growth, after resecting part of the lung, the remaining part compensates for this loss by extending into the empty space. This process is accompanied by an active vessel growing.
In general, the human lung can not compensate for such a loss. Thus, understanding this process in mice is important to improve treatment options in case of diseases like lung cancer.
In case of fibrosis, the formation of scars within the organ's tissue forces the capillary vessels to grow to ensure blood supply.
Thus, the process of fibrosis as well as compensatory lung growth can be accessed by considering the capillary architecture.
As preparation of 2D microscopic images is faster, easier, and cheaper compared to SR\( \mu \)CT images, they currently form the basis of medical investigation. Yet, characteristics like direction and shape of objects can only properly be analyzed using 3D imaging techniques. Hence, analyzing SR\( \mu \)CT data provides valuable additional information.
For the fibrotic specimen, we apply image analysis methods well-known from material science. We measure the vessel diameter using the granulometry distribution function and describe the inter-vessel distance by the spherical contact distribution. Moreover, we estimate the directional distribution of the capillary structure. All features turn out to be useful to characterize fibrosis based on the deformation of capillary vessels.
It is already known that the most efficient mechanism of vessel growing forms small torus-shaped holes within the capillary structure, so-called intussusceptive pillars. Analyzing their location and number strongly contributes to the characterization of vessel growing. Hence, for all three applications, this is of great interest. This thesis provides the first algorithm to detect intussusceptive pillars in SR\( \mu \)CT images. After segmentation of raw image data, our algorithm works automatically and allows for a quantitative evaluation of a large amount of data.
The analysis of SR\( \mu \)CT data using our pillar algorithm as well as the granulometry, spherical contact distribution, and directional analysis extends the current state-of-the-art in medical studies. Although it is not possible to replace certain 3D features by 2D features without losing information, our results could be used to examine 2D features approximating the 3D findings reasonably well.

This thesis addresses several challenges for sustainable logistics operations and investigates (1) the integration of intermediate stops in the route planning of transportation vehicles, which especially becomes relevant when alternative-fuel vehicles with limited driving range or a sparse refueling infrastructure are considered, (2) the combined planning of the battery replacement infrastructure and of the routing for battery electric vehicles, (3) the use of mobile load replenishment or refueling possibilities in environments where the respective infrastructure is not available, and (4) the additional consideration of the flow of goods from the end user in backward direction to the point of origin for the purpose of, e.g., recapturing value or proper disposal. We utilize models and solution methods from the domain of operations research to gain insights into the investigated problems and thus to support managerial decisions with respect to these issues.

Magnetoelastic coupling describes the mutual dependence of the elastic and magnetic fields and can be observed in certain types of materials, among which are the so-called "magnetostrictive materials". They belong to the large class of "smart materials", which change their shape, dimensions or material properties under the influence of an external field. The mechanical strain or deformation a material experiences due to an externally applied magnetic field is referred to as magnetostriction; the reciprocal effect, i.e. the change of the magnetization of a body subjected to mechanical stress is called inverse magnetostriction. The coupling of mechanical and electromagnetic fields is particularly observed in "giant magnetostrictive materials", alloys of ferromagnetic materials that can exhibit several thousand times greater magnitudes of magnetostriction (measured as the ratio of the change in length of the material to its original length) than the common magnetostrictive materials. These materials have wide applications areas: They are used as variable-stiffness devices, as sensors and actuators in mechanical systems or as artificial muscles. Possible application fields also include robotics, vibration control, hydraulics and sonar systems.
Although the computational treatment of coupled problems has seen great advances over the last decade, the underlying problem structure is often not fully understood nor taken into account when using black box simulation codes. A thorough analysis of the properties of coupled systems is thus an important task.
The thesis focuses on the mathematical modeling and analysis of the coupling effects in magnetostrictive materials. Under the assumption of linear and reversible material behavior with no magnetic hysteresis effects, a coupled magnetoelastic problem is set up using two different approaches: the magnetic scalar potential and vector potential formulations. On the basis of a minimum energy principle, a system of partial differential equations is derived and analyzed for both approaches. While the scalar potential model involves only stationary elastic and magnetic fields, the model using the magnetic vector potential accounts for different settings such as the eddy current approximation or the full Maxwell system in the frequency domain.
The distinctive feature of this work is the analysis of the obtained coupled magnetoelastic problems with regard to their structure, strong and weak formulations, the corresponding function spaces and the existence and uniqueness of the solutions. We show that the model based on the magnetic scalar potential constitutes a coupled saddle point problem with a penalty term. The main focus in proving the unique solvability of this problem lies on the verification of an inf-sup condition in the continuous and discrete cases. Furthermore, we discuss the impact of the reformulation of the coupled constitutive equations on the structure of the coupled problem and show that in contrast to the scalar potential approach, the vector potential formulation yields a symmetric system of PDEs. The dependence of the problem structure on the chosen formulation of the constitutive equations arises from the distinction of the energy and coenergy terms in the Lagrangian of the system. While certain combinations of the elastic and magnetic variables lead to a coupled magnetoelastic energy function yielding a symmetric problem, the use of their dual variables results in a coupled coenergy function for which a mixed problem is obtained.
The presented models are supplemented with numerical simulations carried out with MATLAB for different examples including a 1D Euler-Bernoulli beam under magnetic influence and a 2D magnetostrictive plate in the state of plane stress. The simulations are based on material data of Terfenol-D, a giant magnetostrictive materials used in many industrial applications.

Carotenoids are organic lipophilic tetraterpenes ubiquitously present in Nature and found across the three domains of life (Archaea, Bacteria and Eukaryotes). Their structure is characterized by an extensive conjugated double-bond system, which serves as a light-absorbing chromophore, hence determining its colour, and enables carotenoids to absorb energy from other molecules and to act as antioxidant agents. Humans obtain carotenoids mainly via the consumption of fruits and vegetables, and to a smaller extent from other food sources such as fish and eggs. The concentration of carotenoids in the human plasma and tissues has been positively associated with a lower incidence of several chronic diseases including, cancer, diabetes, macular degeneration and cardiovascular conditions, likely due to their antioxidant properties. However, an important aspect of carotenoids, namely β- and α-carotene and β-cryptoxanthin, in human health and development, is their potential to be converted by the body into Vitamin A.
Yet, bioavailability of carotenoids is relatively low (< 30%) and dependent, among others, on dietary factors, such as amount and type of dietary lipids and the presence of dietary fibres. One dietary factor that has been found to negatively impact carotenoid bioaccessibility and cellular uptake in vitro is high concentrations of divalent cations during simulated gastro-intestinal digestion. Nevertheless, the mechanism of action of divalent cations remains unclear. The goal of this thesis was to better understand how divalent cations act during digestion and modulate carotenoid bioavailability. In vitro trials of simulated gastro-intestinal digestion and cellular uptake were run to investigate how varying concentrations of calcium, magnesium and zinc affected the bioaccessibility of both pure carotenoids and carotenoids from food matrices. In order to validate or refute results obtained in vitro, a randomized and double blinded placebo controlled cross-over postprandial trial (24 male participants) was carried out, testing the effect of 3 supplementary calcium doses (0 mg, 500 mg and 1000 mg) on the bioavailability of carotenoids from a spinach based meal. In vitro trials showed that addition of the divalent cations significantly decreased the bioaccessibility of both pure carotenoids (P < 0.001) and those from food matrices (P < 0.01). This effect was dependent on the type of mineral and its concentration. Strongest effects were seen for increasing concentrations of calcium followed by magnesium and zinc. The addition of divalent cations also altered the physico-chemical properties, i.e. viscosity and surface tension, of the digestas. However, the extent of this effect varied according to the type of matrix. The effects on bioaccessibility and physico-chemical properties were accompanied by variations of the zeta-potential of the particles in solution. Taken together, results from the in vitro trials strongly suggested that divalent cations were able to bind bile salts and other surfactant agents, affecting their solubility. The observed i) decrease in macroviscosity, ii) increase in surface tension, and the iii) reduction of the zeta-potential of the digesta, confirmed the removal of surfactant agents from the system, most likely due to precipitation as a result of the lower solubility of the mineral-surfactant complexes. As such, micellarization of carotenoids was hindered, explaining their reduced bioaccessibility. As for the human trial, results showed that there was no significant influence of supplementation with either 500 or 1000 mg of supplemental calcium (in form of carbonate) on the bioavailability of a spinach based meal, as measured by the area-under curve of carotenoid concentrations in the plasma-triacylglycerol rich fraction, suggesting that the in vitro results are not supported in such an in vivo scenario, which may be explained by the initial low bioaccessibility of spinach carotenoids and the dissolution kinetics of the calcium pills. Further investigations are necessary to understand how divalent cations act during in vivo digestion and potentially interact with lipophilic nutrients and food constituents.

Study 1 (Chapter 2) is an empirical case study that concerns the nature of teaching–learning transactions that facilitate self-directed learning in vocational education and training of young adults in England. It addresses in part the concern that fostering the skills necessary for self-directed learning is an important endeavor of vocational education and training in many contexts internationally. However, there is a distinct lack of studies that investigate the extent to which facilitation of self-directed learning is present within vocational education and training in different contexts. An exploratory thematic qualitative analysis of inspectors’ comments within general Further Education college Ofsted inspection reports was conducted to investigate the balance of control of the learning process between teacher and learner within vocational education and training of young adults in England. A clear difference between outstanding and inadequate provision is reported. Inadequate provision was overwhelmingly teacher-directed. Outstanding provision reflected a collaborative relationship between teacher and learner in directing the learning process, despite the Ofsted framework not explicitly identifying the need for learner involvement in directing the learning process. The chapter offers insight into the understanding of how an effective balance of control of learning between teacher and learner may be realized in vocational education and training settings and highlights the need to consider the modulating role of contextual factors.
Following the further research directions outlined in Chapter 2, study 2 (Chapter 3) is a theoretical chapter that addresses the issue that fostering adult learners’ competence to adapt appropriately to our ever-changing world is a primary concern of adult education. The purpose of the chapter is novel and examines whether the consideration of modes of learning (instruction, performance, and inquiry) could assist in the design of adult education that facilitates self-directed learning and enables learners to think and perform adaptively. The concept of modes of learning originated from the typology of Houle (1980). However, to date, no study has reached beyond this typology, especially concerning the potential of using modes of learning in the design of adult education. Specifically, an apparent oversight in adult learning theory is the foremost importance of the consideration of whether inquiry is included in the learning process: its inclusion potentially differentiates the purpose of instruction, the nature of learners’ performance, and the underlying epistemological positioning. To redress this concern, two models of modes of learning are proposed and contrasted. The reinforcing model of modes of learning (instruction, performance, without inquiry) promotes teacher-directed learning. A key consequence of employing this model in adult education is that learners may become accustomed to habitually reinforcing patterns of perceiving, thinking, judging, feeling, and acting—performance that may be rather inflexible and represented by a distinct lack of a perceived need to adapt to social contextual changes: a lack of motivation for self-directed learning. Rather, the adapting model of modes of learning (instruction, performance, with inquiry) may facilitate learners to be adaptive in their performance—by encouraging an enhanced learner sensitivity toward changing social contextual conditions: potentially enhancing learners’ motivation for self-directed learning.
In line with the further research directions highlighted in Chapter 3, concerning the need to consider the nature and treatment of educational experiences that are conductive to learner growth and development, study 3 (Chapter 4) presents a systematic review of the experiential learning theory; a theory that perhaps cannot be uncoupled from self-directed learning theory, especially in regard to understanding the cognitive aspect of self-directed learning, which represents an important direction for further research on self-directed learning. D. A. Kolb’s (1984) experiential learning cycle is perhaps the most scholarly influential and cited model regarding experiential learning theory. However, a key issue in interpreting Kolb’s model concerns a lack of clarity regarding what constitutes a concrete experience, exactly. A systematic literature review was conducted in order to examine: what constitutes a concrete experience and what is the nature of treatment of a concrete experience in experiential learning? The analysis revealed five themes: learners are involved, active, participants; knowledge is situated in place and time; learners are exposed to novel experiences, which involves risk; learning demands inquiry to specific real-world problems; and critical reflection acts as a mediator of meaningful learning. Accordingly, a revision to Kolb’s model is proposed: experiential learning consists of contextually rich concrete experience, critical reflective observation, contextual-specific abstract conceptualization, and pragmatic active experimentation. Further empirical studies are required to test the model proposed. Finally, in Chapter 5 key findings of the studies are summarized, including that the models proposed in Chapters 3 and 4 (Figures 2 and 4, respectively) may be important considerations for further research on self-directed learning.

In this thesis, we deal with the worst-case portfolio optimization problem occuring in discrete-time markets.
First, we consider the discrete-time market model in the presence of crash threats. We construct the discrete worst-case optimal portfolio strategy by the indifference principle in the case of the logarithmic utility. After that we extend this problem to general utility functions and derive the discrete worst-case optimal portfolio processes, which are characterized by a dynamic programming equation. Furthermore, the convergence of the discrete worst-case optimal portfolio processes are investigated when we deal with the explicit utility functions.
In order to further study the relation of the worst-case optimal value function in discrete-time models to continuous-time models we establish the finite-difference approach. By deriving the discrete HJB equation we verify the worst-case optimal value function in discrete-time models, which satisfies a system of dynamic programming inequalities. With increasing degree of fineness of the time discretization, the convergence of the worst-case value function in discrete-time models to that in continuous-time models are proved by using a viscosity solution method.