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In the ground vehicle industry it is often an important task to simulate full vehicle models based on the wheel forces and moments, which have been measured during driving over certain roads with a prototype vehicle. The models are described by a system of differential algebraic equations (DAE) or ordinary differential equations (ODE). The goal of the simulation is to derive section forces at certain components for a durability assessment. In contrast to handling simulations, which are performed including more or less complex tyre models, a driver model, and a digital road profile, the models we use here usually do not contain the tyres or a driver model. Instead, the measured wheel forces are used for excitation of the unconstrained model. This can be difficult due to noise in the input data, which leads to an undesired drift of the vehicle model in the simulation.

We prove a general monotonicity result about Nash flows in directed networks and use it for the design of truthful mechanisms in the setting where each edge of the network is controlled by a different selfish agent, who incurs costs when her edge is used. The costs for each edge are assumed to be linear in the load on the edge. To compensate for these costs, the agents impose tolls for the usage of edges. When nonatomic selfish network users choose their paths through the network independently and each user tries to minimize a weighted sum of her latency and the toll she has to pay to the edges, a Nash flow is obtained. Our monotonicity result implies that the load on an edge in this setting can not increase when the toll on the edge is increased, so the assignment of load to the edges by a Nash flow yields a monotone algorithm. By a well-known result, the monotonicity of the algorithm then allows us to design truthful mechanisms based on the load assignment by Nash flows. Moreover, we consider a mechanism design setting with two-parameter agents, which is a generalization of the case of one-parameter agents considered in a seminal paper of Archer and Tardos. While the private data of an agent in the one-parameter case consists of a single nonnegative real number specifying the agent's cost per unit of load assigned to her, the private data of a two-parameter agent consists of a pair of nonnegative real numbers, where the first one specifies the cost of the agent per unit load as in the one-parameter case, and the second one specifies a fixed cost, which the agent incurs independently of the load assignment. We give a complete characterization of the set of output functions that can be turned into truthful mechanisms for two-parameter agents. Namely, we prove that an output function for the two-parameter setting can be turned into a truthful mechanism if and only if the load assigned to every agent is nonincreasing in the agent's bid for her per unit cost and, for almost all fixed bids for the agent's per unit cost, the load assigned to her is independent of the agent's bid for her fixed cost. When the load assigned to an agent is continuous in the agent's bid for her per unit cost, it must be completely independent of the agent's bid for her fixed cost. These results motivate our choice of linear cost functions without fixed costs for the edges in the selfish routing setting, but the results also seem to be interesting in the context of algorithmic mechanism design themselves.

This thesis is devoted to two main topics (accordingly, there are two chapters): In the first chapter, we establish a tropical intersection theory with analogue notions and tools as its algebro-geometric counterpart. This includes tropical cycles, rational functions, intersection products of Cartier divisors and cycles, morphisms, their functors and the projection formula, rational equivalence. The most important features of this theory are the following: - It unifies and simplifies many of the existing results of tropical enumerative geometry, which often contained involved ad-hoc computations. - It is indispensable to formulate and solve further tropical enumerative problems. - It shows deep relations to the intersection theory of toric varieties and connected fields. - The relationship between tropical and classical Gromov-Witten invariants found by Mikhalkin is made plausible from inside tropical geometry. - It is interesting on its own as a subfield of convex geometry. In the second chapter, we study tropical gravitational descendants (i.e. Gromov-Witten invariants with incidence and "Psi-class" factors) and show that many concepts of the classical Gromov-Witten theory such as the famous WDVV equations can be carried over to the tropical world. We use this to extend Mikhalkin's results to a certain class of gravitational descendants, i.e. we show that many of the classical gravitational descendants of P^2 and P^1 x P^1 can be computed by counting tropical curves satisfying certain incidence conditions and with prescribed valences of their vertices. Moreover, the presented theory is not restricted to plane curves and therefore provides an important tool to derive similar results in higher dimensions. A more detailed chapter synopsis can be found at the beginning of each individual chapter.

One approach to multi-criteria IMRT planning is to automatically calculate a data set of Pareto-optimal plans for a given planning problem in a first phase, and then interactively explore the solution space and decide for the clinically best treatment plan in a second phase. The challenge of computing the plan data set is to assure that all clinically meaningful plans are covered and that as many as possible clinically irrelevant plans are excluded to keep computation times within reasonable limits. In this work, we focus on the approximation of the clinically relevant part of the Pareto surface, the process that consititutes the first phase. It is possible that two plans on the Parteto surface have a very small, clinically insignificant difference in one criterion and a significant difference in one other criterion. For such cases, only the plan that is clinically clearly superior should be included into the data set. To achieve this during the Pareto surface approximation, we propose to introduce bounds that restrict the relative quality between plans, so called tradeoff bounds. We show how to integrate these trade-off bounds into the approximation scheme and study their effects.

Interactive visualization of large structured and unstructured data sets is a permanent challenge for scientific visualization. Large data sets are for example created by magnetic resonance imaging (MRI), computed tomography (CT), Computational fluid dynamics (CFD) finite element method (FEM), and computer aided design (CAD). For visualizing those data sets not only accelerated rasterization by means of using specialized hardware i.e. graphics cards is of interest, but also ray casting, as it is perfectly suited for scientific visualization. Ray casting does not only support many rendering modes (e.g., opaque rendering, semi transparent rendering, iso surface rendering, maximum intensity projection, x-ray, absorption emitter model, ...) for which it allows the creation of high quality images, but it also supports many primitives (e.g., not only triangles but also spheres, curved iso surfaces, NURBS, implicit functions, ...). It furthermore scales basically linear to the amount of processor cores used and - this makes it highly interesting for the visualization of large data sets - it scales for static scenes sublinear to data size. Interactive ray casting is currently not widely used within the scientifc visualization community. This is mainly based on historical reasons, as just a few years ago no applicable interactive ray casters for commodity hardware did exist. Interactive scientific visualization has only been possible by using graphics cards or specialized and/or expensive hardware. The goal of this work is to broaden the possibilies for interactive scientific visualization, by showing that interactive CPU based ray casting is today feasible on commodity hardware and that it may efficiently be used together with GPU based rasterization. In this thesis it is first shown that interactive CPU based ray casters may efficiently be integrated into already existing OpenGL frameworks. This is achieved through an OpenGL friendly interface that supports multiple threads and single instruction multiple data (SIMD) operations. For the visualization of rectilinear (and not necessarily cartesian) grids are new implicit kd-trees introduced. They have fast construction times, low memory requirements, and allow ontoday's commodity desktop machines interactive iso surface ray tracing and maximum intensity projection of large scalar fields. A new interactive SIMD ray tracing technique for large tetrahedral meshes is introduced. It is very portable and general and is therefore suited for portation upon different (future) hardware and for usage upon several applications. The thesis ends with a real life commercial application which shows that CPU-based ray casting has already reached the state where it may outperform GPU-based rasterization for scientific visualization.

Within this thesis we present a novel approach towards the modeling of strong discontinuities in a three dimensional finite element framework for large deformations. This novel finite element framework is modularly constructed containing three essential parts: (i) the bulk problem, ii) the cohesive interface problem and iii) the crack tracking problem. Within this modular design, chapter 2 (Continuous solid mechanics) treats the behavior of the bulk problem (i). It includes the overall description of the continuous kinematics, the required balance equations, the constitutive setting and the finite element formulation with its corresponding discretization and required solution strategy for the emerging highly non-linear equations. Subsequently, we discuss the modeling of strong discontinuities within finite element discretization schemes in chapter 3 (Discontinuous solid mechanics). Starting with an extension of the continuous kinematics to the discontinuous situation, we discuss the phantom-node discretization scheme based on the works of Hansbo & Hansbo. Thereby, in addition to a comparison with the extended finite element method (XFEM), importance is attached to the technical details for the adaptive introduction of the required discontinuous elements: The splitting of finite elements, the numerical integration, the visualization and the formulation of geometrical correct crack tip elements. In chapter 4 (The cohesive crack concept), we consider the treatment of cohesive process zones and the associated treatment of cohesive tractions. By applying this approach we are able to merge all irreversible, crack propagation accompanying, failure mechanisms into an arbitrary traction separation relation. Additionally, this concept ensures bounded crack tip stresses and allows the use of stress-based failure criteria for the determination of crack growth. In summary, the use of the discontinuous elements in conjunction with cohesive traction separation allows the mesh-independent computation of crack propagation along pre-defined crack paths. Therefore, this combination is defined as the interface problem (ii) and represents the next building block in the modular design of this thesis. The description and the computation of the evolving crack surface, based on the actual status of a considered specimen is the key issue of chapter 5 (Crack path tracking strategies). In contrast to the two-dimensional case, where tracking the path in a C0-continuous way is straightforward, three-dimensional crack path tracking requires additional strategies. We discuss the currently available approaches regarding this issue and further compare the approaches by means of usual quality measures. In the modular design of this thesis these algorithms represent the last main part which is classified as the crack tracking problem (iii). Finally chapter 6 (Representative numerical examples) verifies the finite element tool by comparisons of the computational results which experiments and benchmarks of engineering fracture problems in concrete. Afterwards the finite element tool is applied to model folding induced fracture of geological structures.

2,3,7,8-Tetrachlorodibenzo-p-dioxin (TCDD) is a highly toxic and persistent organic pollutant, which is ubiquitously found in the environment. The prototype dioxin compound was classified as a human carcinogen by the International Agency for Research on Cancer. TCDD acts as a potent liver tumor promoter in rats, which is one of the major concerns related to TCDD exposure. There is extensive evidence, that TCDD exerts anti-estrogenic effects via arylhydrocarbon receptor (AhR)-mediated induction of cytochromes P450 and interferes with the estrogen receptor alpha (ERalpha)-mediated signaling pathway. The present work was conducted to shed light on the hypothesis that enhanced activation of estradiol metabolism by TCDD-induced enzymes, mainly CYP1A1 and CYP1B1, leads to oxidative DNA damage in liver cells. Furthermore, the possible modulation by 17beta-estradiol (E2) was investigated. The effects were examined using four different AhR-responsive species- and sex-specific liver cell models, rat H4II2 and human HepG2 hepatoma cell lines as well as rat primary hepatocytes from male and female Wistar rats. The effective induction of CYP1A1 and CYP1B1 by TCDD was demonstrated in all liver cell models. Basal and TCDD-induced expression of CYP1B1, which is a key enzyme in stimulating E2 metabolism via the more reactive formation of the genotoxic 4-hydroxyestradiol, was most pronounced in rat primary hepatocytes. CYP-dependent induction of reactive oxygen species (ROS) was only observed in rodent cells. E2 induced ROS only in primary rat hepatocytes, which was associated with a weak CYP1B1 mRNA induction. Thus, E2 itself was suggested to induce its own metabolism in primary rat hepatocytes, resulting in the redox cycling of catechol estradiol metabolites leading to ROS formation. In this study the role of TCDD and E2 on oxidative DNA damage was investigated for the first time in vitro in the comet assay using liver cells. Both TCDD and E2 were shown to induce oxidative DNA base modifications only in rat hepatocytes. Additionally, direct oxidative DNA-damaging effects of the two main E2 metabolites, 4-hydroxyestradiol and 2-hydroxyestradiol, were only observed in rat hepatocytes and revealed that E2 damaged the DNA to the same extent. However, the induction of oxidative DNA damage by E2 could not completely be explained by the metabolic conversion of E2 via CYP1A1 and CYP1B1 and has to be further investigated. The expression of low levels of endogenous ERalpha mRNA in primary rat hepatocytes and the lack of ERalpha in hepatoma cell lines were identified as crucial. Therefore, the effects of interference of ERalpha with AhR were examined in HepG2 cells, which were transiently transfected with ERalpha. The over-expression of ERalpha led to enhanced AhR-mediated transcriptional activity by E2, suggesting a possible regulation of E2 levels. In turn, TCDD reduced E2-mediated ERalpha signaling, confirming the anti-estrogenic action of TCDD. Such a modulation of the combined effects of TCDD with E2 was not observed in any of the other experiments. Thus, the role of low endogenous ERalpha levels has to be further investigated in transfection experiments using rat primary hepatocytes. Overall, rat primary hepatocyte culture turned out to be the more adaptive cell model to investigate metabolism in the liver, reflecting a more realistic situation of the liver tissue. Nevertheless, during this work a crosstalk between ERalpha and AhR was shown for the first time using human hepatoma cell line HepG2 by transiently transfecting ERalpha.

In this article we prove existence and uniqueness results for solutions to the outer oblique boundary problem for the Poisson equation under very weak assumptions on boundary, coefficients and inhomogeneities. Main tools are the Kelvin transformation and the solution operator for the regular inner problem, provided in [1]. Moreover we prove regularisation results for the weak solutions of both, the inner and the outer problem. We investigate the non-admissible direction for the oblique vector field, state results with stochastic inhomogeneities and provide a Ritz-Galerkinm approximation. The results are applicable to problems from Geomathematics, see e.g. [2] and [3].

Proteins of the intermembrane space of mitochondria are generally encoded by nuclear genes that are synthesized in the cytosol. A group of small intermembrane space proteins lack classical mitochondrial targeting sequences, but these proteins are imported in an oxidation-driven reaction that relies on the activity of two components, Mia40 and Erv1. Both proteins constitute the mitochondrial disulfide relay system. Mia40 functions as an import receptor that interacts with incoming polypeptides via transient, intermolecular disulfide bonds. Erv1 is an FAD-binding sulfhydryl oxidase that activates Mia40 by re-oxidation, but the process how Erv1 itself is re-oxidized has been poorly understood. Here, I show that Erv1 interacts with cytochrome c which provides a functional link between the mitochondrial disulfide relay system and the respiratory chain. This mechanism not only increases the efficiency of mitochondrial inport by the re-oxidation of Erv1 and Mia40 but also prevents the formation of deleterious hydrogen peroxide within the intermembrane space. Thus, the miochondrial disulfide relay system is, analogous to that of the bacterial periplasm, connected to the electron transport chain of the inner membrane, which possibly allows an oxygen-dependend regulation of mitochondrial import rates. In addition, I modeled the structure of Erv1 on the basis of the Saccharomyces cerevisiae Erv2 crystal structure in order to gain insight into the molecular mechanism of Erv1. According to the high degree of sequence homologies, various characteristics found for Erv2 are also valid for Erv1. Finally, I propose a regulatory function of the disulfide relay system on the respiratory chain. The disulfide relay system senses the molecular oxygen levels in mitochondria and, thus, is able to adapt respiratory chain activity in order to prevent wastage of NADH and production of ROS.

The capacitated single-allocation hub location problem revisited: A note on a classical formulation
(2009)

Denote by G = (N;A) a complete graph where N is the set of nodes and A is the set of edges. Assume that a °ow wij should be sent from each node i to each node j (i; j 2 N). One possibility is to send these °ows directly between the corresponding pairs of nodes. However, in practice this is often neither e±cient nor costly attractive because it would imply that a link was built between each pair of nodes. An alternative is to select some nodes to become hubs and use them as consolidation and redistribution points that altogether process more e±ciently the flow in the network. Accordingly, hubs are nodes in the graph that receive tra±c (mail, phone calls, passengers, etc) from di®erent origins (nodes) and redirect this tra±c directly to the destination nodes (when a link exists) or else to other hubs. The concentration of tra±c in the hubs and its shipment to other hubs lead to a natural decrease in the overall cost due to economies of scale.