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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.

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

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.

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

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

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.

Towards A Non-tracking Web
(2016)

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

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

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

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

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.