## Doctoral Thesis

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- Interactive Visualizations Supporting Minimal Cut Set Analysis II (2016)
- The Context and Its Importance: In safety and reliability analysis, the information generated by Minimal Cut Set (MCS) analysis is large. The Top Level event (TLE) that is the root of the fault tree (FT) represents a hazardous state of the system being analyzed. MCS analysis helps in analyzing the fault tree (FT) qualitatively-and quantitatively when accompanied with quantitative measures. The information shows the bottlenecks in the fault tree design leading to identifying weaknesses of the system being examined. Safety analysis (containing the MCS analysis) is especially important for critical systems, where harm can be done to the environment or human causing injuries, or even death during the system usage. Minimal Cut Set (MCS) analysis is performed using computers and generating a lot of information. This phase is called MCS analysis I in this thesis. The information is then analyzed by the analysts to determine possible issues and to improve the design of the system regarding its safety as early as possible. This phase is called MCS analysis II in this thesis. The goal of my thesis was developing interactive visualizations to support MCS analysis II of one fault tree (FT). The Methodology: As safety visualization-in this thesis, Minimal Cut Set analysis II visualization-is an emerging field and no complete checklist regarding Minimal Cut Set analysis II requirements and gaps were available from the perspective of visualization and interaction capabilities, I have conducted multiple studies using different methods with different data sources (i.e., triangulation of methods and data) for determining these requirements and gaps before developing and evaluating visualizations and interactions supporting Minimal Cut Set analysis II. Thus, the following approach was taken in my thesis: 1- First, a triangulation of mixed methods and data sources was conducted. 2- Then, four novel interactive visualizations and one novel interaction widget were developed. 3- Finally, these interactive visualizations were evaluated both objectively and subjectively (compared to multiple safety tools) from the point of view of users and developers of the safety tools that perform MCS analysis I with respect to their degree in supporting MCS analysis II and from the point of non-domain people using empirical strategies. The Spiral tool supports analysts with different visions, i.e., full vision, color deficiency protanopia, deuteranopia, and tritanopia. It supports 100 out of 103 (97%) requirements obtained from the triangulation and it fills 37 out of 39 (95%) gaps. Its usability was rated high (better than their best currently used tools) by the users of the safety and reliability tools (RiskSpectrum, ESSaRel, FaultTree+, and a self-developed tool) and at least similar to the best currently used tools from the point of view of the CAFTA tool developers. Its quality was higher regarding its degree of supporting MCS analysis II compared to the FaultTree+ tool. The time spent for discovering the critical MCSs from a problem size of 540 MCSs (with a worst case of all equal order) was less than a minute while achieving 99.5% accuracy. The scalability of the Spiral visualization was above 4000 MCSs for a comparison task. The Dynamic Slider reduces the interaction movements up to 85.71% of the previous sliders and solves the overlapping thumb issues by the sliders provides the 3D model view of the system being analyzed provides the ability to change the coloring of MCSs according to the color vision of the user provides selecting a BE (i.e., multi-selection of MCSs), thus, can observe the BEs' NoO and provides its quality provides two interaction speeds for panning and zooming in the MCS, BE, and model views provide a MCS, a BE, and a physical tab for supporting the analysis starting by the MCSs, the BEs, or the physical parts. It combines MCS analysis results and the model of an embedded system enabling the analysts to directly relate safety information with the corresponding parts of the system being analyzed and provides an interactive mapping between the textual information of the BEs and MCSs and the parts related to the BEs. Verifications and Assessments: I have evaluated all visualizations and the interaction widget both objectively and subjectively, and finally evaluated the final Spiral visualization tool also both objectively and subjectively regarding its perceived quality and regarding its degree of supporting MCS analysis II.

- The Bootstrap for the Functional Autoregressive Model FAR(1) (2016)
- Functional data analysis is a branch of statistics that deals with observations \(X_1,..., X_n\) which are curves. We are interested in particular in time series of dependent curves and, specifically, consider the functional autoregressive process of order one (FAR(1)), which is defined as \(X_{n+1}=\Psi(X_{n})+\epsilon_{n+1}\) with independent innovations \(\epsilon_t\). Estimates \(\hat{\Psi}\) for the autoregressive operator \(\Psi\) have been investigated a lot during the last two decades, and their asymptotic properties are well understood. Particularly difficult and different from scalar- or vector-valued autoregressions are the weak convergence properties which also form the basis of the bootstrap theory. Although the asymptotics for \(\hat{\Psi}{(X_{n})}\) are still tractable, they are only useful for large enough samples. In applications, however, frequently only small samples of data are available such that an alternative method for approximating the distribution of \(\hat{\Psi}{(X_{n})}\) is welcome. As a motivation, we discuss a real-data example where we investigate a changepoint detection problem for a stimulus response dataset obtained from the animal physiology group at the Technical University of Kaiserslautern. To get an alternative for asymptotic approximations, we employ the naive or residual-based bootstrap procedure. In this thesis, we prove theoretically and show via simulations that the bootstrap provides asymptotically valid and practically useful approximations of the distributions of certain functions of the data. Such results may be used to calculate approximate confidence bands or critical bounds for tests.

- Integrality of representations of finite groups (2016)
- Since the early days of representation theory of finite groups in the 19th century, it was known that complex linear representations of finite groups live over number fields, that is, over finite extensions of the field of rational numbers. While the related question of integrality of representations was answered negatively by the work of Cliff, Ritter and Weiss as well as by Serre and Feit, it was not known how to decide integrality of a given representation. In this thesis we show that there exists an algorithm that given a representation of a finite group over a number field decides whether this representation can be made integral. Moreover, we provide theoretical and numerical evidence for a conjecture, which predicts the existence of splitting fields of irreducible characters with integrality properties. In the first part, we describe two algorithms for the pseudo-Hermite normal form, which is crucial when handling modules over ring of integers. Using a newly developed computational model for ideal and element arithmetic in number fields, we show that our pseudo-Hermite normal form algorithms have polynomial running time. Furthermore, we address a range of algorithmic questions related to orders and lattices over Dedekind domains, including computation of genera, testing local isomorphism, computation of various homomorphism rings and computation of Solomon zeta functions. In the second part we turn to the integrality of representations of finite groups and show that an important ingredient is a thorough understanding of the reduction of lattices at almost all prime ideals. By employing class field theory and tools from representation theory we solve this problem and eventually describe an algorithm for testing integrality. After running the algorithm on a large set of examples we are led to a conjecture on the existence of integral and nonintegral splitting fields of characters. By extending techniques of Serre we prove the conjecture for characters with rational character field and Schur index two.

- Development of nano/micro hybrid susceptor sheet for induction heating applications (2016)
- Thermoplastic composite materials are being widely used in the automotive and aerospace industries. Due to the limitations of shape complexity, different components need to be joined. They can be joined by mechanical fasteners, adhesive bonding or both. However, these methods have several limitations. Components can be joined by fusion bonding due to the property of thermoplastics. Thermoplastics can be melted on heating and regain their shape on cooling. This property makes them ideal for joining through fusion bonding by induction heating. Joining of non-conducting or non-magnetic thermoplastic composites needs an additional material that can generate heat by induction heating. Polymers are neither conductive nor electromagnetic so they don’t have inherent potential for inductive heating. A susceptor sheet having conductive materials (e.g. carbon fiber) or magnetic materials (e.g. nickel) can generate heat during induction. The main issues related with induction heating are non-homogeneous and uncontrolled heating. In this work, it was observed that to generate heat with a susceptor sheet depends on its filler, its concentration, and its dispersion. It also depends on the coil, magnetic field strength and coupling distance. The combination of different fillers not only increased the heating rate but also changed the heating mechanism. Heating of 40ºC/ sec was achieved with 15wt.-% nickel coated short carbon fibers and 3wt.-% multiwalled carbon nanotubes. However, only nickel coated short carbon fibers (15wt-.%) attained the heating rate of 24ºC/ sec. In this study, electrical conductivity, thermal conductivity and magnetic properties testing were also performed. The results also showed that electrical percolation was achieved around 15wt.-% in fibers and (13- 6)wt.-% with hybrid fillers. Induction heating tests were also performed by making parallel and perpendicular susceptor sheet as fibers were uni-directionally aligned. The susceptor sheet was also tested by making perforations. The susceptor sheet showed homogeneous and fast heating, and can be used for joining of non-conductive or non-magnetic thermoplastic composites.

- Verification & Performance Measurement for Transport Protocol Parallel Routing of an AUTOSAR Gateway System (2016)
- A wide range of methods and techniques have been developed over the years to manage the increasing complexity of automotive Electrical/Electronic systems. Standardization is an example of such complexity managing techniques that aims to minimize the costs, avoid compatibility problems and improve the efficiency of development processes. A well-known and -practiced standard in automotive industry is AUTOSAR (Automotive Open System Architecture). AUTOSAR is a common standard among OEMs (Original Equipment Manufacturer), suppliers and other involved companies. It was developed originally with the goal of simplifying the overall development and integration process of Electrical/Electronic artifacts from different functional domains, such as hardware, software, and vehicle communication. However, the AUTOSAR standard, in its current status, is not able to manage the problems in some areas of the system development. Validation and optimization process of system configuration handled in this thesis are examples of such areas, in which the AUTOSAR standard offers so far no mature solutions. Generally, systems developed on the basis of AUTOSAR must be configured in a way that all defined requirements are met. In most cases, the number of configuration parameters and their possible settings in AUTOSAR systems are large, especially if the developed system is complex with modules from various knowledge domains. The verification process here can consume a lot of resources to test all possible combinations of configuration settings, and ideally find the optimal configuration variant, since the number of test cases can be very high. This problem is referred to in literature as the combinatorial explosion problem. Combinatorial testing is an active and promising area of functional testing that offers ideas to solve the combinatorial explosion problem. Thereby, the focus is to cover the interaction errors by selecting a sample of system input parameters or configuration settings for test case generation. However, the industrial acceptance of combinatorial testing is still weak because of the deficiency of real industrial examples. This thesis is tempted to fill this gap between the industry and the academy in the area of combinatorial testing to emphasizes the effectiveness of combinatorial testing in verifying complex configurable systems. The particular intention of the thesis is to provide a new applicable approach to combinatorial testing to fight the combinatorial explosion problem emerged during the verification and performance measurement of transport protocol parallel routing of an AUTOSAR gateway. The proposed approach has been validated and evaluated by means of two real industrial examples of AUTOSAR gateways with multiple communication buses and two different degrees of complexity to illustrate its applicability.

- Centimeter-Level Accuracy Path Tracking Control of Tractors and Actively Steered Implements (2015)
- Accurate path tracking control of tractors became a key technology for automation in agriculture. Increasingly sophisticated solutions, however, revealed that accurate path tracking control of implements is at least equally important. Therefore, this work focuses on accurate path tracking control of both tractors and implements. The latter, as a prerequisite for improved control, are equipped with steering actuators like steerable wheels or a steerable drawbar, i.e. the implements are actively steered. This work contributes both new plant models and new control approaches for those kinds of tractor-implement combinations. Plant models comprise dynamic vehicle models accounting for forces and moments causing the vehicle motion as well as simplified kinematic descriptions. All models have been derived in a systematic and automated manner to allow for variants of implements and actuator combinations. Path tracking controller design begins with a comprehensive overview and discussion of existing approaches in related domains. Two new approaches have been proposed combining the systematic setup and tuning of a Linear-Quadratic-Regulator with the simplicity of a static output feedback approximation. The first approach ensures accurate path tracking on slopes and curves by including integral control for a selection of controlled variables. The second approach, instead, ensures this by adding disturbance feedforward control based on side-slip estimation using a non-linear kinematic plant model and an Extended Kalman Filter. For both approaches a feedforward control approach for curved path tracking has been newly derived. In addition, a straightforward extension of control accounting for the implement orientation has been developed. All control approaches have been validated in simulations and experiments carried out with a mid-size tractor and a custom built demonstrator implement.

- Model-based Design of Embedded Systems by Desynchronization (2016)
- In this thesis we developed a desynchronization design flow in the goal of easing the de- velopment effort of distributed embedded systems. The starting point of this design flow is a network of synchronous components. By transforming this synchronous network into a dataflow process network (DPN), we ensures important properties that are difficult or theoretically impossible to analyze directly on DPNs are preserved by construction. In particular, both deadlock-freeness and buffer boundedness can be preserved after desyn- chronization. For the correctness of desynchronization, we developed a criteria consisting of two properties: a global property that demands the correctness of the synchronous network, as well as a local property that requires the latency-insensitivity of each local synchronous component. As the global property is also a correctness requirement of synchronous systems in general, we take this property as an assumption of our desyn- chronization. However, the local property is in general not satisfied by all synchronous components, and therefore needs to be verified before desynchronization. In this thesis we developed a novel technique for the verification of the local property that can be carried out very efficiently. Finally we developed a model transformation method that translates a set of synchronous guarded actions – an intermediate format for synchronous systems – to an asynchronous actor description language (CAL). Our theorem ensures that one passed the correctness verification, the generated DPN of asynchronous pro- cesses (or actors) preserves the functional behavior of the original synchronous network. Moreover, by the correctness of the synchronous network, our theorem guarantees that the derived DPN is deadlock-free and can be implemented with only finitely bounded buffers.

- Monoids as Storage Mechanisms (2016)
- Automata theory has given rise to a variety of automata models that consist of a finite-state control and an infinite-state storage mechanism. The aim of this work is to provide insights into how the structure of the storage mechanism influences the expressiveness and the analyzability of the resulting model. To this end, it presents generalizations of results about individual storage mechanisms to larger classes. These generalizations characterize those storage mechanisms for which the given result remains true and for which it fails. In order to speak of classes of storage mechanisms, we need an overarching framework that accommodates each of the concrete storage mechanisms we wish to address. Such a framework is provided by the model of valence automata, in which the storage mechanism is represented by a monoid. Since the monoid serves as a parameter to specifying the storage mechanism, our aim translates into the question: For which monoids does the given (automata-theoretic) result hold? As a first result, we present an algebraic characterization of those monoids over which valence automata accept only regular languages. In addition, it turns out that for each monoid, this is the case if and only if valence grammars, an analogous grammar model, can generate only context-free languages. Furthermore, we are concerned with closure properties: We study which monoids result in a Boolean closed language class. For every language class that is closed under rational transductions (in particular, those induced by valence automata), we show: If the class is Boolean closed and contains any non-regular language, then it already includes the whole arithmetical hierarchy. This work also introduces the class of graph monoids, which are defined by finite graphs. By choosing appropriate graphs, one can realize a number of prominent storage mechanisms, but also combinations and variants thereof. Examples are pushdowns, counters, and Turing tapes. We can therefore relate the structure of the graphs to computational properties of the resulting storage mechanisms. In the case of graph monoids, we study (i) the decidability of the emptiness problem, (ii) which storage mechanisms guarantee semilinear Parikh images, (iii) when silent transitions (i.e. those that read no input) can be avoided, and (iv) which storage mechanisms permit the computation of downward closures.

- Hecke algebras of type A: Auslander--Reiten quivers and branching rules (2016)
- 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.

- Getting Ready to Read: Promoting Children´s Emergent Literacy Through Shared Book Reading in a German Context (2016)
- 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.