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In this thesis, we deal with the finite group of Lie type \(F_4(2^n)\). The aim is to find information on the \(l\)-decomposition numbers of \(F_4(2^n)\) on unipotent blocks for \(l\neq2\) and \(n\in \mathbb{N}\) arbitrary and on the irreducible characters of the Sylow \(2\)-subgroup of \(F_4(2^n)\).
S. M. Goodwin, T. Le, K. Magaard and A. Paolini have found a parametrization of the irreducible characters of the unipotent subgroup \(U\) of \(F_4(q)\), a Sylow \(2\)-subgroup of \(F_4(q)\), of \(F_4(p^n)\), \(p\) a prime, for the case \(p\neq2\).
We managed to adapt their methods for the parametrization of the irreducible characters of the Sylow \(2\)-subgroup for the case \(p=2\) for the group \(F_4(q)\), \(q=p^n\). This gives a nearly complete parametrization of the irreducible characters of the unipotent subgroup \(U\) of \(F_4(q)\), namely of all irreducible characters of \(U\) arising from so-called abelian cores.
The general strategy we have applied to obtain information about the \(l\)-decomposition numbers on unipotent blocks is to induce characters of the unipotent subgroup \(U\) of \(F_4(q)\) and Harish-Chandra induce projective characters of proper Levi subgroups of \(F_4(q)\) to obtain projective characters of \(F_4(q)\). Via Brauer reciprocity, the multiplicities of the ordinary irreducible unipotent characters in these projective characters give us information on the \(l\)-decomposition numbers of the unipotent characters of \(F_4(q)\).
Sadly, the projective characters of \(F_4(q)\) we obtained were not sufficient to give the shape of the entire decomposition matrix.

The design of the fifth generation (5G) cellular network should take account of the emerging services with divergent quality of service requirements. For instance, a vehicle-to-everything (V2X) communication is required to facilitate the local data exchange and therefore improve the automation level in automated driving applications. In this work, we inspect the performance of two different air interfaces (i.e., LTE-Uu and PC5) which are proposed by the third generation partnership project (3GPP) to enable the V2X communication. With these two air interfaces, the V2X communication can be realized by transmitting data packets either over the network infrastructure or directly among traffic participants. In addition, the ultra-high reliability requirement in some V2X communication scenarios can not be fulfilled with any single transmission technology (i.e., either LTE-Uu or PC5). Therefore, we discuss how to efficiently apply multi-radio access technologies (multi-RAT) to improve the communication reliability. In order to exploit the multi-RAT in an efficient manner, both the independent and the coordinated transmission schemes are designed and inspected. Subsequently, the conventional uplink is also extended to the case where a base station can receive data packets through both the LTE-Uu and PC5 interfaces. Moreover, different multicast-broadcast single-frequency network (MBSFN) area mapping approaches are also proposed to improve the communication reliability in the LTE downlink. Last but not least, a system level simulator is implemented in this work. The simulation results do not only provide us insights on the performances of different technologies but also validate the effectiveness of the proposed multi-RAT scheme.

Asynchronous concurrency is a wide-spread way of writing programs that
deal with many short tasks. It is the programming model behind
event-driven concurrency, as exemplified by GUI applications, where the
tasks correspond to event handlers, web applications based around
JavaScript, the implementation of web browsers, but also of server-side
software or operating systems.
This model is widely used because it provides the performance benefits of
concurrency together with easier programming than multi-threading. While
there is ample work on how to implement asynchronous programs, and
significant work on testing and model checking, little research has been
done on handling asynchronous programs that involve heap manipulation, nor
on how to automatically optimize code for asynchronous concurrency.
This thesis addresses the question of how we can reason about asynchronous
programs while considering the heap, and how to use this this to optimize
programs. The work is organized along the main questions: (i) How can we
reason about asynchronous programs, without ignoring the heap? (ii) How
can we use such reasoning techniques to optimize programs involving
asynchronous behavior? (iii) How can we transfer these reasoning and
optimization techniques to other settings?
The unifying idea behind all the results in the thesis is the use of an
appropriate model encompassing global state and a promise-based model of
asynchronous concurrency. For the first question, We start from refinement
type systems for sequential programs and extend them to perform precise
resource-based reasoning in terms of heap contents, known outstanding
tasks and promises. This extended type system is known as Asynchronous
Liquid Separation Types, or ALST for short. We implement ALST in for OCaml
programs using the Lwt library.
For the second question, we consider a family of possible program
optimizations, described by a set of rewriting rules, the DWFM rules. The
rewriting rules are type-driven: We only guarantee soundness for programs
that are well-typed under ALST. We give a soundness proof based on a
semantic interpretation of ALST that allows us to show behavior inclusion
of pairs of programs.
For the third question, we address an optimization problem from industrial
practice: Normally, JavaScript files that are referenced in an HTML file
are be loaded synchronously, i.e., when a script tag is encountered, the
browser must suspend parsing, then load and execute the script, and only
after will it continue parsing HTML. But in practice, there are numerous
JavaScript files for which asynchronous loading would be perfectly sound.
First, we sketch a hypothetical optimization using the DWFM rules and a
static analysis.
To actually implement the analysis, we modify the approach to use a
dynamic analysis. This analysis, known as JSDefer, enables us to analyze
real-world web pages, and provide experimental evidence for the efficiency
of this transformation.

Motivation: Mathematical models take an important place in science and engineering.
A model can help scientists to explain dynamic behavior of a system and to understand
the functionality of system components. Since length of a time series and number of
replicates is limited by the cost of experiments, Boolean networks as a structurally simple
and parameter-free logical model for gene regulatory networks have attracted interests
of many scientists. In order to fit into the biological contexts and to lower the data
requirements, biological prior knowledge is taken into consideration during the inference
procedure. In the literature, the existing identification approaches can only deal with a
subset of possible types of prior knowledge.
Results: We propose a new approach to identify Boolean networks fromtime series data
incorporating prior knowledge, such as partial network structure, canalizing property,
positive and negative unateness. Using vector form of Boolean variables and applying
a generalized matrix multiplication called the semi-tensor product (STP), each Boolean
function can be equivalently converted into a matrix expression. Based on this, the
identification problem is reformulated as an integer linear programming problem to
reveal the system matrix of Boolean model in a computationally efficient way, whose
dynamics are consistent with the important dynamics captured in the data. By using
prior knowledge the number of candidate functions can be reduced during the inference.
Hence, identification incorporating prior knowledge is especially suitable for the case of
small size time series data and data without sufficient stimuli. The proposed approach is
illustrated with the help of a biological model of the network of oxidative stress response.
Conclusions: The combination of efficient reformulation of the identification problem
with the possibility to incorporate various types of prior knowledge enables the
application of computational model inference to systems with limited amount of time
series data. The general applicability of thismethodological approachmakes it suitable for
a variety of biological systems and of general interest for biological and medical research.

The core muscles play a central role in stabilizing the head during headers in soccer. The objective of this study was to examine the influence of a fatigued core musculature on the acceleration of the head during jump headers and run headers. Acceleration of the head was measured in a pre-post-design in 68 soccer players (age: 21.5 ± 3.8 years, height: 180.0 ± 13.9 cm, weight: 76.9 ± 8.1 kg). Data were recorded by means of a telemetric 3D acceleration sensor and with a pendulum header. The treatment encompassed two exercises each for the ventral, lateral, and dorsal muscle chains. The acceleration of the head between pre- and post-test was reduced by 0.3 G (p = 0.011) in jump headers and by 0.2 G (p = 0.067) in run headers. An additional analysis of all pretests showed an increased acceleration in run headers when compared to stand headers (p < 0.001) and jump headers (p < 0.001). No differences were found in the sub-group comparisons: semi-professional vs. recreational players, offensive vs. defensive players. Based on the results, we conclude that the acceleration of the head after fatiguing the core muscles does not increase, which stands in contrast to postulated expectations. More tests with accelerated soccer balls are required for a conclusive statement.

The complexity of modern real-time systems is increasing day by day. This inevitable rise in complexity predominantly stems from two contradicting requirements, i.e., ever increasing demand for functionality, and required low cost for the final product. The development of modern multi-processors and variety of network protocols and architectures have enabled such a leap in complexity and functionality possible. Albeit, efficient use of these multi-processors and network architectures is still a major problem. Moreover, the software design and its development process needs improvements in order to support rapid-prototyping for ever changing system designs. Therefore, in this dissertation, we provide solutions for different problems faced in the development and deployment process of real-time systems. The contributions presented in this thesis enable efficient utilization of system resources, rapid design & development and component modularity & portability.
In order to ease the certification process, time-triggered computation model is often used in distributed systems. However, time-triggered scheduling is NP-hard, due to which the process of schedule generation for complex large systems becomes convoluted. Large scheduler run-times and low scalability are two major problems with time-triggered scheduling. To solve these problems, we present a modular real-time scheduler based on a novel search-tree pruning technique, which consumes less time (compared to the state-of-the-art) in order to schedule tasks on large distributed time-triggered systems. In order to provide end-to-end guarantees, we also extend our modular scheduler to quickly generate schedules for time-triggered network traffic in large TTEthernet based networks. We evaluate our schedulers on synthetic but practical task-sets and demonstrate that our pruning technique efficiently reduces scheduler run-times and exhibits adequate scalability for future time-triggered distributed systems.
In safety critical systems, the certification process also requires strict isolation between independent components. This isolation is enforced by utilizing resource partitioning approach, where different criticality components execute in different partitions (each temporally and spatially isolated from each other). However, existing partitioning approaches use periodic servers or tasks to service aperiodic activities. This approach leads to utilization loss and potentially leads to large latencies. On the contrary to the periodic approaches, state-of-the-art aperiodic task admission algorithms do not suffer from problems like utilization loss. However, these approaches do not support partitioned scheduling or mixed-criticality execution environment. To solve this problem, we propose an algorithm for online admission of aperiodic tasks which provides job execution flexibility, jitter control and leads to lower latencies of aperiodic tasks.
For safety critical systems, fault-tolerance is one of the most important requirements. In time-triggered systems, modes are often used to ensure survivability against faults, i.e., when a fault is detected, current system configuration (or mode) is changed such that the overall system performance is either unaffected or degrades gracefully. In literature, it has been asserted that a task-set might be schedulable in individual modes but unschedulable during a mode-change. Moreover, conventional mode-change execution strategies might cause significant delays until the next mode is established. In order to address these issues, in this dissertation, we present an approach for schedulability analysis of mode-changes and propose mode-change delay reduction techniques in distributed system architecture defined by the DREAMS project. We evaluate our approach on an avionics use case and demonstrate that our approach can drastically reduce mode-change delays.
In order to manage increasing system complexity, real-time applications also require new design and development technologies. Other than fulfilling the technical requirements, the main features required from such technologies include modularity and re-usability. AUTOSAR is one of these technologies in automotive industry, which defines an open standard for software architecture of a real-time operating system. However, being an industrial standard, the available proprietary tools do not support model extensions and/or new developments by third-parties and, therefore, hinder the software evolution. To solve this problem, we developed an open-source AUTOSAR toolchain which supports application development and code generation for several modules. In order to exhibit the capabilities of our toolchain, we developed two case studies. These case studies demonstrate that our toolchain generates valid artifacts, avoids dirty workarounds and supports application development.
In order to cope with evolving system designs and hardware platforms, rapid-development of scheduling and analysis algorithms is required. In order to ease the process of algorithm development, a number of scheduling and analysis frameworks are proposed in literature. However, these frameworks focus on a specific class of applications and are limited in functionality. In this dissertation, we provide the skeleton of a scheduling and analysis framework for real-time systems. In order to support rapid-development, we also highlight different development components which promote code reuse and component modularity.

Arctic, Antarctic and alpine biological soil crusts (BSCs) are formed by adhesion of soil particles to exopolysaccharides (EPSs) excreted by cyanobacterial and green algal communities, the pioneers and main primary producers in these habitats. These BSCs provide and inﬂuence many ecosystem services such as soil erodibility, soil formation and nitrogen (N) and carbon (C) cycles. In cold environments degradation rates are low and BSCs continuously increase soil organic C; therefore, these soils are considered to be CO2 sinks. This work provides a novel, nondestructive and highly comparable method to investigate intact BSCs with a focus on cyanobacteria and green algae and their contribution to soil organic C. A new terminology arose,basedonconfocallaserscanningmicroscopy(CLSM) 2-D biomaps, dividing BSCs into a photosynthetic active layer (PAL) made of active photoautotrophic organisms and a photosynthetic inactive layer (PIL) harbouring remnants of cyanobacteria and green algae glued together by their remaining EPSs. By the application of CLSM image analysis (CLSM–IA) to 3-D biomaps, C coming from photosynthetic activeorganismscouldbevisualizedasdepthproﬁleswithC peaks at 0.5 to 2mm depth. Additionally, the CO2 sink character of these cold soil habitats dominated by BSCs could be highlighted, demonstrating that the ﬁrst cubic centimetre of soil consists of between 7 and 17% total organic carbon, identiﬁed by loss on ignition.

In this thesis we integrate discrete dividends into the stock model, estimate
future outstanding dividend payments and solve different portfolio optimization
problems. Therefore, we discuss three well-known stock models, including
discrete dividend payments and evolve a model, which also takes early
announcement into account.
In order to estimate the future outstanding dividend payments, we develop a
general estimation framework. First, we investigate a model-free, no-arbitrage
methodology, which is based on the put-call parity for European options. Our
approach integrates all available option market data and simultaneously calculates
the market-implied discount curve. We illustrate our method using stocks
of European blue-chip companies and show within a statistical assessment that
the estimate performs well in practice.
As American options are more common, we additionally develop a methodology,
which is based on market prices of American at-the-money options.
This method relies on a linear combination of no-arbitrage bounds of the dividends,
where the corresponding optimal weight is determined via a historical
least squares estimation using realized dividends. We demonstrate our method
using all Dow Jones Industrial Average constituents and provide a robustness
check with respect to the used discount factor. Furthermore, we backtest our
results against the method using European options and against a so called
simple estimate.
In the last part of the thesis we solve the terminal wealth portfolio optimization
problem for a dividend paying stock. In the case of the logarithmic utility
function, we show that the optimal strategy is not a constant anymore but
connected to the Merton strategy. Additionally, we solve a special optimal
consumption problem, where the investor is only allowed to consume dividends.
We show that this problem can be reduced to the before solved terminal wealth
problem.

A fast numerical method for an advanced electro-chemo-mechanical model is developed which is able to capture phase separation processes in porous materials. This method is applied to simulate lithium-ion battery cells, where the complex microstructure of the electrodes is fully resolved. The intercalation of ions into the popular cathode material LFP leads to a separation into lithium-rich and lithium-poor phases. The large concentration gradients result in high mechanical stresses. A phase-field method applying the Cahn-Hilliard equation is used to describe the diffusion. For the sake of simplicity, the linear elastic case is considered. Numerical tests for fully resolved three-dimensional granular microstructures are discussed in detail.

The Power and Energy Student Summit (PESS) is designed for students, young professionals and PhD-students in the field of power engineering. PESS offers the possibility to gain first experience in presentation, publication and discussion with a renowned audience of specialists. Therefore, the conference is accompanied and supervised by established scientists and experts. The venue changes every year. In 2018, the University of Kaiserslautern held the eighth PESS conference. This document presents the submissions of this conference.