Interconnection networks enable fast data communication between components of a digital system. The selection of an appropriate interconnection network and its architecture plays an important role in the development process of the system. The selection of a bad network architecture may significantly delay the communication between components and decrease the overall system performance. There are various interconnection networks available. Most of them are blocking networks. Blocking means that even though a pair of source and target components may be free, a connection between them might still not be possible due to limited capabilities of the network. Moreover, routing algorithms of blocking networks have to avoid deadlocks and livelocks, which typically does only allow poor real-time guarantees for delivering a message. Nonblocking networks can always manage all requests that are coming from their input components and can therefore deliver all messages in guaranteed time, i.e, with strong real-time guarantees. However, only a few networks are nonblocking and easy to implement. The simplest one is the crossbar network which is a comparably simple circuit with also a simple routing algorithm. However, while its circuit depth of O(log(n)) is optimal, its size increases with O(n^2) and quickly becomes infeasible for large networks. Therefore, the construction of nonblocking networks with a quasipolynomial size O(nlog(n)^a) and polylogarithmic depth O(log(n)^b) turned out as a research problem. Benes [Clos53; Bene65] networks were the first non blocking networks having an optimal size of O(nlog(n)) and an optimal depth of O(log(n)), but their routing algorithms are quite complicated and require circuits of depth O(log(n)^2) [NaSa82]. Other nonblocking interconnection networks are derived from sorting networks. Essentially, there are merge-based (MBS) and radix-based (RBS) sorting networks. MBS and RBS networks can be both implemented in a pipelined fashion which leads to a big advantage for their circuit implementation. While these networks are nonblocking and can implement all n! permutations, they cannot directly handle partial permutations that frequently occur in practice since not every input component communicates at every point of time with an output component. For merge-based sorting networks, there is a well known general solution called the Batcher-Banyan network. However, for the larger class of radix-based sorting networks this does not work, and there is only one solution known for a particular permutation network. In this thesis, new nonblocking radix-based interconnection networks are presented. In particular, for a certain permutation network, three routing algorithms are developed and their circuit implementations are evaluated concerning their size, depth, and power consumption. A special extension of these networks allows them to route also partial permutations. Moreover, three general constructions to convert any binary sorter into a ternary split module were presented which is the key to construct a radix-based interconnection network that can cope with partial permutations. The thesis compares also chip designs of these networks with other radix-based sorting networks as well as with the Batcher-Banyan networks as competitors. As a result, it turns out that the proposed radix-based networks are superior and could form the basis of larger manycore architectures.

The neural networks have been extensively used for tasks based on image sensors. These models have, in the past decade, consistently performed better than other machine learning methods on tasks of computer vision. It is understood that methods for transfer learning from neural networks trained on large datasets can reduce the total data requirement while training new neural network models. These methods tend not to perform well when the data recording sensor or the recording environment is unique from the existing large datasets. The machine learning literature provides various methods for prior-information inclusion in a learning model. Such methods employ methods like designing biases into the data representation vectors, enforcing priors or physical constraints on the models. Including such information into neural networks for the image frames and image-sequence classification is hard because of the very high dimensional neural network mapping function and little information about the relation between the neural network parameters. In this thesis, we introduce methods for evaluating the statistically learned data representation and combining these information descriptors. We have introduced methods for including information into neural networks. In a series of experiments, we have demonstrated methods for adding the existing model or task information to neural networks. This is done by 1) Adding architectural constraints based on the physical shape information of the input data, 2) including weight priors on neural networks by training them to mimic statistical and physical properties of the data (hand shapes), and 3) by including the knowledge about the classes involved in the classification tasks to modify the neural network outputs. These methods are demonstrated, and their positive influence on the hand shape and hand gesture classification tasks are reported. This thesis also proposes methods for combination of statistical and physical models with parametrized learning models and show improved performances with constant data size. Eventually, these proposals are tied together to develop an in-car hand-shape and hand-gesture classifier based on a Time of Flight sensor.

Der Leitungsbau hat vor dem Hintergrund der aktuellen ökologischen Herausforderungen und unter dem Aspekt einer umweltgerechten und sicheren Bewirtschaftung des Abwassers nach wie vor einen hohen Stellenwert unter den kommunalen Aufgaben. Nach Erhebungen des Statistischen Bundesamts von 2016 wurden in den letzten Jahren jährlich ca. 4.600 km neue Entwässerungskanäle hergestellt. Dabei sind Baustellen immer ein Eingriff in die Umwelt. Insbesondere der innerstädtische Kanalbau hat erhebliche Auswirkungen auf den Verkehrsfluss. Im urbanen Umfeld und generell bei größeren Tiefenlagen stellt der maschinelle Rohrvortrieb eine Verlegemethode für Abwasserkanäle dar, die gegenüber der offenen Bauweise deutlich reduzierte Einschränkungen für Anwohner und Verkehrsfluss mit sich bringt. Um eine möglichst wirtschaftliche Herstellung von Leitungen zu erreichen, gehen die Bestrebungen hin zu möglichst wenigen Schachtbauwerken. In der Folge werden immer längere Vortriebsstrecken, aber auch immer mehr bogenförmige Trassen mit immer engeren Kurvenradien geplant. Durch eine gekrümmte Trassierung lassen sich insbesondere Schächte vermeiden, die im Wesentlichen dazu dienen, Hindernisse zu umgehen oder nicht geraden Straßenverläufen zu folgen. Um gekrümmten Trassen folgen zu können, müssen sich die Vortriebsrohre gegeneinander abwinkeln. Die Abwinklung führt zu einer Verkleinerung der Kontaktfläche in der Rohrfuge und zu einer Spannungsumlagerung auf die Kurveninnenseite des Rohrspiegels. Die entstehenden Spannungsspitzen können an dieser Stelle zu einer Überbeanspruchung der Rohrwandung führen. Die vorliegende Arbeit entwickelt eine alternative Ausführung der Rohrenden. Diese soll durch eine gelenkige Rohrverbindung die Kontaktfläche zwischen zwei Rohren vergrößern und das Abwinkeln in der Rohrfügung verhindern. Die Gelenkigkeit der Verbindung wird durch die Ausrundung der Rohrenden erreicht. Da die gelenkige Rohrverbindung - aufgrund ihrer Ausrundung - eine grundlegend andere Kinematik aufweist als Rohre mit ebenem Rohrspiegel, werden die Auswirkungen der Ausrundung auf die Geometrie, die Hydraulik und die Statik der neuartigen Rohre untersucht.

As visualization as a field matures, the discussion about the development of a theory of the field becomes increasingly vivid. Despite some voices claiming that visualization applications would be too different from each other to generalize, there is a significant push towards a better understanding of the principles underlying visual data analysis. As of today, visualization is primarily data-driven. Years of experience in the visalization of all kinds of different data accumulated a vast reservoir of implicit knowledge in the community of how to best represent data according to its shape, its format, and what it is meant to express. This knowledge is complemented by knowledge imported to visualization from a variety of other fields, for example psychology, vision science, color theory, and information theory. Yet, a theory of visualization is still only nascent. One major reason for that is the field's too strong focus on the quantitative aspects of data analysis. Although when designing visualizations major design decisions also consider perception and other human factors, the overall appearance of visualizations as of now is determined primarily by the type and format of the data to be visualized and its quantitative attributes like scale, range, or density. This is also reflected by the current approaches in theoretical work on visualization. The models developed in this regard also concentrate primarily on perceptual and quantitative aspects of visual data analysis. Qualitative considerations like the interpretations made by viewers and the conclusions drawn by analysts currently only play a minor role in the literature. This Thesis contributes to the nascent theory of visualization by investigating approaches to the explicit integration of qualitative considerations into visual data analysis. To this end, it promotes qualitative visual analysis, the explicit discussion of the interpretation of artifacts and structures in the visualization, of efficient workflows designed to optimally support an analyst's reasoning strategy and capturing information about insight provenance, and of design methodology tailoring visualizations towards the insights they are meant to provide rather than to the data they show. Towards this aim, three central qualitative principles of visual information encodings are identified during the development of a model for the visual data analysis process that explicitly includes the anticipated reasoning structure into the consideration. This model can be applied throughout the whole life cycle of a visualization application, from the early design phase to the documentation of insight provenance during analysis using the developed visualization application. The three principles identified inspire novel visual data analysis workflows aiming for an insight-driven data analysis process. Moreover, two case studies prove the benefit of following the qualitative principles of visual information encodings for the design of visualization applications. The formalism applied to the development of the presented theoretical framework is founded in formal logics, mathematical set theory, and the theory of formal languages and automata. The models discussed in this Thesis and the findings derived from them are therefore based on a mathematically well-founded theoretical underpinning. This Thesis establishes a sound theoretical framework for the design and description of visualization applications and the prediction of the conclusions an analyst is capable of drawing from working with the visualization. Thereby, it contributes an important piece to the yet unsolved puzzle of developing a visualization theory.

In a recent paper, G. Malle and G. Robinson proposed a modular anologue to Brauer's famous \( k(B) \)-conjecture. If \( B \) is a \( p \)-block of a finite group with defect group \( D \), then they conjecture that \( l(B) \leq p^r \), where \( r \) is the sectional \( p \)-rank of \( D \). Since this conjecture is relatively new, there is obviously still a lot of work to do. This thesis is concerned with proving their conjecture for the finite groups of exceptional Lie type.