Communication delays are common in many complex systems. It has been shown that these delays cannot be neglected when they are long enough compared to other timescales in the system. In systems of coupled phase oscillators discrete delays in the coupling give rise to effects such as multistability of steady states. However, variability in the communication times inherent to many processes suggests that the description with discrete delays maybe insufficient to capture all effects of delays. An interesting example of the effects of communication delays is found during embryonic development of vertebrates. A clock based on biochemical reactions inside cells provides the periodicity for the successive and robust formation of somites, the embryonic precursors of vertebrae, ribs and some skeletal muscle. Experiments show that these cellular clocks communicate in order to synchronize their behavior. However, in cellular systems, fluctuations and stochastic processes introduce a variability in the communication times. Here we account for such variability by considering the effects of distributed delays. Our approach takes into account entire intervals of past states, and weights them according to a delay distribution. We find that the stability of the fully synchronized steady state with zero phase lag does not depend on the shape of the delay distribution, but the dynamics when responding to small perturbations about this steady state do. Depending on the mean of the delay distribution, a change in its shape can enhance or reduce the ability of these systems to respond to small perturbations about the phase-locked steady state, as compared to a discrete delay with a value equal to this mean. For synchronized steady states with non-zero phase lag we find that the stability of the steady state can be altered by changing the shape of the delay distribution. We conclude that the response to a perturbation in systems of phase oscillators coupled with discrete delays has a sharper functional dependence on the mean delay than in systems with distributed delays in the coupling. The strong dependence of the coupling on the mean delay time is partially averaged out by distributed delays that take into account intervals of the past.

Communication delays are common in many complex systems. It has been shown that these delays cannot be neglected when they are long enough compared to other timescales in the system. In systems of coupled phase oscillators discrete delays in the coupling give rise to effects such as multistability of steady states. However, variability in the communication times inherent to many processes suggests that the description with discrete delays maybe insufficient to capture all effects of delays. An interesting example of the effects of communication delays is found during embryonic development of vertebrates. A clock based on biochemical reactions inside cells provides the periodicity for the successive and robust formation of somites, the embryonic precursors of vertebrae, ribs and some skeletal muscle. Experiments show that these cellular clocks communicate in order to synchronize their behavior. However, in cellular systems, fluctuations and stochastic processes introduce a variability in the communication times. Here we account for such variability by considering the effects of distributed delays. Our approach takes into account entire intervals of past states, and weights them according to a delay distribution. We find that the stability of the fully synchronized steady state with zero phase lag does not depend on the shape of the delay distribution, but the dynamics when responding to small perturbations about this steady state do. Depending on the mean of the delay distribution, a change in its shape can enhance or reduce the ability of these systems to respond to small perturbations about the phase-locked steady state, as compared to a discrete delay with a value equal to this mean. For synchronized steady states with non-zero phase lag we find that the stability of the steady state can be altered by changing the shape of the delay distribution. We conclude that the response to a perturbation in systems of phase oscillators coupled with discrete delays has a sharper functional dependence on the mean delay than in systems with distributed delays in the coupling. The strong dependence of the coupling on the mean delay time is partially averaged out by distributed delays that take into account intervals of the past.:Abstract i Acknowledgement iii I. INTRODUCTION 1. Coupled Phase Oscillators Enter the Stage 5 1.1. Adjusting rhythms – synchronization . . . . . . . . . . . . . . . . . . 5 1.2. Historical remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3. Reducing variables – phase models . . . . . . . . . . . . . . . . . . . . 9 1.4. The Kuramoto order parameter . . . . . . . . . . . . . . . . . . . . . . 10 1.5. Who talks to whom – coupling topologies . . . . . . . . . . . . . . . . 12 2. Coupled Phase Oscillators with Delay in the Coupling 15 2.1. Communication needs time – coupling delays . . . . . . . . . . . . . . 15 2.1.1. Discrete delays consider one past time . . . . . . . . . . . . . . 16 2.1.2. Distributed delays consider multiple past times . . . . . . . . 17 2.2. Coupled phase oscillators with discrete delay . . . . . . . . . . . . . . 18 2.2.1. Phase locked steady states with no phase lags . . . . . . . . . 18 2.2.2. m-twist solutions: phase-locked steady states with phase lags 21 3. The Vertebrate Segmentation Clock – What Provides the Rhythm? 25 3.1. The clock and wavefront mechanism . . . . . . . . . . . . . . . . . . . 26 3.2. Cyclic gene expression on the cellular and the tissue level . . . . . . 27 3.3. Coupling by Delta-Notch signalling . . . . . . . . . . . . . . . . . . . . 29 3.4. The Delayed Coupling Theory . . . . . . . . . . . . . . . . . . . . . . . 30 3.5. Discrete delay is an approximation – is it sufficient? . . . . . . . . . 32 4. Outline of the Thesis 33 II. DISTRIBUTED DELAYS 5. Setting the Stage for Distributed Delays 37 5.1. Model equations with distributed delays . . . . . . . . . . . . . . . . . 37 5.2. How we include distributed delays . . . . . . . . . . . . . . . . . . . . 38 5.3. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 6. The Phase-Locked Steady State Solution 41 6.1. Global frequency of phase-locked steady states . . . . . . . . . . . . . 41 6.2. Linear stability of the steady state . . . . . . . . . . . . . . . . . . . . 42 6.3. Linear dynamics of the perturbation – the characteristic equation . 43 6.4. Summary and application to the Delayed Coupling Theory . . . . . . 50 7. Dynamics Close to the Phase-Locked Steady State 53 7.1. The response to small perturbations . . . . . . . . . . . . . . . . . . . 53 7.2. Relation between order parameter and perturbation modes . . . . . 54 7.3. Perturbation dynamics in mean-field coupled systems . . . . . . . . 56 7.4. Nearest neighbour coupling with periodic boundary conditions . . . 62 7.4.1. How variance and skewness influence synchrony dynamics . 73 7.4.2. The dependence of synchrony dynamics on the number of oscillators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 7.5. Synchrony dynamics in systems with arbitrary coupling topologies . 88 7.6. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 8. The m-twist Steady State Solution on a Ring 95 8.1. Global frequency of m-twist steady states . . . . . . . . . . . . . . . . 95 8.2. Linear stability of m-twist steady states . . . . . . . . . . . . . . . . . 97 8.3. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 9. Dynamics Approaching the m-twist Steady States 105 9.1. Relation between order parameter and perturbation modes . . . . . 105 9.2. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 10.Conclusions and Outlook 111 vi III. APPENDICES A. 119 A.1. Distribution composed of two adjacent boxcar functions . . . . . . . 119 A.2. The gamma distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 124 A.3. Distribution composed of two Dirac delta peaks . . . . . . . . . . . . 125 A.4. Gerschgorin’s circle theorem . . . . . . . . . . . . . . . . . . . . . . . . 127 A.5. The Lambert W function . . . . . . . . . . . . . . . . . . . . . . . . . . 127 A.6. Roots of unity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 B. Simulation methods 129

Today’s communication network is changing rapidly and radically. Demand for low latency, high reliability and low energy consumption increases as well the variety of characteristics of the connected devices. It is also expected that the number of connected devices will be massive in coming years. Some devices will be connected to the new generation base stations directly, while some of them will be connected through other devices via multi-hops. Reliable communication between these massive devices can be done via re-transmission, repetition of packets several times or via Forward Error Correction (FEC). In re-transmission method, when packets are negatively acknowledged or the sender’s acknowledgment timer expires, packets are re-transmitted. In repetition method, every packet can be send several times. Both aforementioned methods can cause a huge delay, particularly, in multi-hop network. On the contrary of these methods, FEC methods are preferred for low latency applications. Source information are transmitted together with redundant information. Hence, the number of transmissions are reduced comparing to the methods mentioned above. Random Linear Network Coding (RLNC) is a packet level erasure correcting codes which aims to reduce latency. Specifically, source packets are combined and these combinations or coded packets are sent to the destination. Lost packets do no need to be re-sent since another coded packet can be substituted to the lost coded packet. Hence, the feedback mechanism and re-sending process becomes unnecessary. There are many variations of RLNC. One variation is called sliding window RLNC which apples FEC mechanism. This coding scheme achieves low latency via interleaved coded packets in between source packets. Another variation of the RLNC is Fulcrum, which is a versatile code. Fulcrum provides three different decoding options. Received coded packets can be decoded with low, high or middle complexity. This is a very important feature since connected devices will have different computation capabilities and proving a versatile code will allow them flexibility. Although the aforementioned coding schemes are well suited to error prone network, there are still remaining challenges need to be studied. For instance, Fulcrum RLNC has high encoding and decoding complexity which increase the computation time and energy consumption. Moreover, although original Fulcrum RLNC strengths the reliability, it needs to be improved for low latency applications. Another remaining challenges is that recoding strategy of RLNC is not optimal for low latency. Allowing the intermediate nodes to combine received packets is referred as recoding. As described earlier, data packets will pass many hops until they reach destination. Therefore, compute-and-forward paradigm will be preferred rather than store-and-forward. Although recoding capability of RLNC differs it from other coding schemes (Raptor, LT), the conventional way of recoding is not efficient for low latency. Hence, the aim of this thesis is to address the aforementioned remaining challenges. One way to address the remaining challenges is to employ sparsity. In other words, a few source packets can be combined rather than a large set of source packets to generate coded packets. Particularly, a dynamic sparse mechanism is proposed to vary the number of combined source packets during the encoding without a signaling between sender and receiver for Fulcrum RLNC to speed up encoding and decoding process without increasing overhead amount. Then, two different sliding window schemes were integrated into Fulcrum RLNC to make Fulcrum RLNC gain the low latency property. Sending source packets systematically and then spreading sparse coded packets in between systematic source packets can be referred as systematic sparsity. Moreover, different sparse and systematic recoding strategies have been proposed in this thesis to lower the delay and computation time at the intermediate nodes and destination. Finally, one of the proposed recoding strategy has been applied to the vehicle platooning scenario to increase reliability. All proposed coding schemes were analyzed and performed on KODO which is well known network coding library.

In dieser Dissertation werden wir die Wirkung der Verzögerung Kupplung auf Netzwerke von chaotischen erkunden dynamischer Systeme mit dem Rahmen der Master Stabilität Formalismus. Wir werden untersuchen das Phänomen der Verzögerung-verstärkter und Verzögerungen-induzierte stabile Synchronisation in einer willkürlichen Verzögerung gekoppelt Netzwerk von zeitkontinuierlichen dynamischen Systemen. Wir demonstrieren, dass es immer existieren eine erweiterte Regime des stabilen synchronen Zustand als eine Funktion der Kopplungsstärke geeignete Verbindung Verzögerungen, die nicht ohne Verzögerung in die Kupplung beobachtet werden kann. Wir schlagen eine partielle verzögerung Verbindung als eine Kombination von sowohl den momentanen und der komplett Verzögerung Verbindung mit gewissen Gewichten Bestimmung ihrer Beiträgen. Wir werden zeigen, dass die partielle Verzögerung Verbindung beide Grenzfälle des momentanen und der komplett Verzögerung Kupplung am synchronizabilit von Netzwerken übertrifft. Der Rahmen fuer Master Stabilität Formalismus ist mit einem Netzwerk von intrinsischen Zeitverzögerung Systeme, deren Knoten Dynamik durch Verzögerung Differentialgleichungen beschrieben erweitert, zum ersten Mal in der Literatur und veranschaulicht das allgemeine Verhalten des Master-Stabilisierungsfunktion in Netzwerken skalare Zeit Einschaltverzögerung Systeme auf den Synchronisations-Eigenschaften des Netzes. Außerdem untersuchen wir das Zusammenspiel von Lärm und verzögert in das Phänomen der Lärmverstärkter Phasensynchronisierung in beiden unidirektional und bidirektional gekoppelt zeitverzögerung systeme. / In this thesis, we will explore the effect of delay coupling on networks of chaotic dynamical systems using the framework of master stability formalism. We will investigate the phenomenon of delay-enhanced and delay-induced stable synchronization in an arbitrary delay coupled network of time-continuous dynamical systems. We will demonstrate that there always exist an extended regime of stable synchronous state as a function of coupling strength for appropriate coupling delays, which cannot be observed without any delay in the coupling. We will also propose a partial delay coupling as a combination of both the instantaneous and the completely delay coupling with certain weights determining their contributions. We will show that the partial delay coupling outperforms both limiting cases of the instantaneous and the completely delay coupling on the synchronizability of networks. The framework of master stability formalism is extended to a network of intrinsic time-delay systems, whose node dynamics are described by delay differential equations, for the first time in the literature and illustrated the generic behavior of the master stability function in networks of scalar time-delay systems based on the synchronization properties of the network. We also investigate the interplay of noise and delay in the phenomenon of noise-enhanced phase synchronization in both unidirectionally and bidirectionally coupled time-delay systems.

The variability of the thermosphere-ionosphere (T-I) system and its complex behavior is strongly dependent on the continuously changing solar extreme ultraviolet (EUV) and ultraviolet (UV) radiation. The ionospheric electron density (or ion density) is mainly controlled by photoionization, loss by recombination, and transport processes. Transport processes play a significant role in the T-I composition and are responsible for the plasma distribution. The ionospheric response to solar activity has been investigated using total electron content (TEC) and solar EUV observations, as well as various solar proxies. An ionospheric delay of about 1-2 days in the daily TEC on the time scale of 27 days solar rotation period has been reported. It has also been shown that the He-II index is one of the best solar proxies to represent the solar activity at different time scales. The ionospheric delay in relation to solar radiation variations has attracted less attention in the past, especially with respect to its possible mechanisms. However, such studies, are of great importance for a better understanding of the complex interactions between solar radiation and the ionosphere that affect radio communications and navigation systems such as GNSS. Since the T-I region is affected not only by solar radiation, but also by lower atmospheric forcings, geomagnetic activity, and space weather events. Therefore, numerical modeling provides an opportunity to interpret the possible physical mechanism. To shed more light on this issue, a global, 3-D, time-dependent, physics-based numerical model was used in this thesis. It is a comprehensive numerical study to investigate the ionospheric response to solar flux changes during the 27 days solar rotation period. Satellite observations were used for comparison with the model simulations. The average delay for the observed (modeled) TEC is about 17 (16) h againest high-resolution solar EUV flux. The study confirms the capabilities of the model to reproduce the delayed ionospheric response with daily and hourly resolution. These results are in close agreement with previous studies. For the first time, the model simulations were performed to understand the role of eddy diffusion. The study shows that eddy diffusion is an important factor affecting the ionospheric delay and highlights the influence of the lower atmospheric forcing. Eddy diffusion was found to cause a change in thermospheric composition, which induces changes in atomic oxygen by modifying loss and photoionization rates. Atomic oxygen contributes significantly to ionization. Enhanced eddy diffusion leads to a decrease in atomic oxygen ion density and consequently TEC. Therefore, TEC decreases due to enhanced eddy diffusion, showing that the ionospheric delay is reduced. Thus, slow transport leads to maximum ionospheric delay.:Bibliographische Beschreibung Bibliographic Description Acronyms 1 General introduction 1.1 Introduction: Ionospheric delayed response 1.2 Objectives and structure of the thesis 1.3 Model description and data 1.3.1 CTIPe model description 1.3.2 Data 2 Paper 1: Ionospheric delayed response: preliminary results Vaishnav, R., Jacobi, C., Berdermann, J., Schmölter, E., and Codrescu, M.: Ionospheric response to solar EUV variations: Preliminary results 3 Paper 2: Long term trends of ionospheric response to solar EUV variations Vaishnav, R., Jacobi, C., and Berdermann, J.: Long-term trends in the iono- spheric response to solar extreme-ultraviolet variations 4 Paper 3: Comparison between CTIPe model simulations and satellite measurements Vaishnav, R., Schmölter, E., Jacobi, C., Berdermann, J., and Codrescu, M.: Ionospheric response to solar extreme ultraviolet radiation variations: com- parison based on CTIPe model simulations and satellite measurements 5 Paper 4: Role of eddy diffusion in the ionospheric delayed response Vaishnav, R., Jacobi, C., Berdermann, J., Codrescu, M., and Schmölter, E.: Role of eddy diffusion in the delayed ionospheric response to solar flux changes 6 Conclusions 7 Outlook References Acknowledgements Curriculum Vitae Affirmation / Die Veränderungen des Thermosphäre-Ionosphäre (T-I) Systems und dessen Komplexität werden entscheidend durch die sich ständig ändernde extreme ultraviolette (EUV) und ultraviolette (UV) Sonnenstrahlung geprägt. Hierbei wird die ionosphärische Elektronendichte (oder Ionendichte) hauptsächlich durch Photoionisation, Rekombination und Transportprozesse gesteuert. Insbesondere Transportprozesse spielen eine wichtige Rolle für die Zusammensetzung des T-I-Systems und sind für die Plasmaverteilung verantwortlich. Die ionosphärische Reaktion auf Veränderungen der Sonnenaktivität wurde mithilfe des Gesamtelektronengehalts (englisch total electron content, TEC) und Messdaten des solaren EUV-Spektrums sowie solaren Proxys untersucht. Eine ionosphärische Verzögerung von 1 bis 2 Tagen für Tageswerte von TEC wurde für die 27-Tage-Sonnenrotation gefunden. Es wurde auch gezeigt, dass der He-II-Index einer der besten solaren Proxys ist, um die Sonnenaktivität auf verschiedenen Zeitskalen zu beschreiben. Die ionosphärische Verzögerung in Bezug auf Variationen der Sonnenstrahlung wurde in der Vergangenheit wenig Aufmerksamkeit gewidmet. Insbesondere die zugrundenliegenden Mechanismen wurden nicht untersucht. Solche Studien sind jedoch von entscheidender Bedeutung für ein besseres Verständnis der komplexen Wechselwirkungen zwischen Sonnenstrahlung und Ionosphäre, die unteranderem die Leistung von Radiokommunikation und globalen Navigationssystemen beeinflussen. Das T-I-System wird jedoch nicht nur von der solaren EUV-Strahlung kontrolliert. Prozesse der unteren Atmosphäre, geomagnetische Aktivität und Weltraumwettereignisse haben ebenfalls einen Einfluss auf diese Region. Daher bietet sich numerische Modellierung als Möglichkeit für die Interpretation der physikalischen Prozesse an. Zur Klärung der offenen Fragen wurde in dieser Arbeit ein globales, dreidimensionales, zeitabhängiges physikalisches Modell verwendet und eine umfangreiche Studie der ionosphärischen Reaktion auf Veränderungen der Sonnenstrahlungen während der 27-Tage-Sonnenrotation wurde durchgeführt. Hierfür wurden Messdaten von Satellitenmissionen mit den Modellsimulationen verglichen. Im Mittel ergibt sich eine Verzögerung von 16 Stunden aus der Analyse der Messdaten und eine Verzögerung von 17 Stunden aus den Modellsimulationen. Die Studie bestätigt demnach die Fähigkeit des Modells, die verzögerte ionosphärische Reaktion in stündlicher und täglicher Auflösung zu simulieren. Diese Ergebnisse stimmen gut mit vorangegangenen Studien überein. Im Rahmen dieser Arbeit wurden zum ersten Mal Simulationen zum Einfluss der Eddy-Diffusion durchgeführt. Diese Analyse zeigt, dass die Eddy-Diffusion ein wichtiger Faktor für die Ausprägung der ionosphärischen Verzögerung ist und dass der Einfluss von Prozessen der unteren Atmosphäre eine entscheidende Rolle spielt. Es wurde festgestellt, dass die Eddy-Diffusion eine erhebliche Veränderung der thermosphärischen Zusammensetzung verursacht, was wiederum zu Veränderung der Menge des atomaren Sauerstoffs führt. Dies beeinflusst dann die Ionisations- und Verlustrate. Da der atomare Sauerstoff erheblich zur Ionisierung beiträgt. Zunehmender Eddy-Diffusion folgen damit auch verkleinert der atomarer Sauerstoff Ionendichte und TEC. Daher nimmt TEC mit zunehmender Eddy-Diffusion ab und auch die Verzögerung wird kleiner. Andersherum führt ein langsamer Transport zu einem Maximum der ionosphärischen Verzögerung. Diese Dissertation gibt eine umfangreiche Zusammenfassung für das Verständnis der ionosphärischen Verzögerung zu Variationen der solaren EUV-Strahlung. Dafür werden TEC-Messungen mit numerischen Simulationen kombiniert. Weiterhin werden durch Vergleich die besten solaren Proxys für die Beschreibung der solaren Aktivität in T-I-Modellen bestimmt. Dies ist von entscheidender Bedeutung, um den Fokus auf die Verbesserung dieser Modelle zu lenken.:Bibliographische Beschreibung Bibliographic Description Acronyms 1 General introduction 1.1 Introduction: Ionospheric delayed response 1.2 Objectives and structure of the thesis 1.3 Model description and data 1.3.1 CTIPe model description 1.3.2 Data 2 Paper 1: Ionospheric delayed response: preliminary results Vaishnav, R., Jacobi, C., Berdermann, J., Schmölter, E., and Codrescu, M.: Ionospheric response to solar EUV variations: Preliminary results 3 Paper 2: Long term trends of ionospheric response to solar EUV variations Vaishnav, R., Jacobi, C., and Berdermann, J.: Long-term trends in the iono- spheric response to solar extreme-ultraviolet variations 4 Paper 3: Comparison between CTIPe model simulations and satellite measurements Vaishnav, R., Schmölter, E., Jacobi, C., Berdermann, J., and Codrescu, M.: Ionospheric response to solar extreme ultraviolet radiation variations: com- parison based on CTIPe model simulations and satellite measurements 5 Paper 4: Role of eddy diffusion in the ionospheric delayed response Vaishnav, R., Jacobi, C., Berdermann, J., Codrescu, M., and Schmölter, E.: Role of eddy diffusion in the delayed ionospheric response to solar flux changes 6 Conclusions 7 Outlook References Acknowledgements Curriculum Vitae Affirmation

The objective of the International Financial Reporting Standards (IFRS) is to provide useful information to the users of financial statements to assist in making economic decisions. To be useful, information has to be relevant and reliable, but the reliability of information suffers when the guidelines for the reporting of specific issues are not clear and managerial discretion arises. Write-offs are one of those accounting issues that are regularly related to earnings management. By now it is seen as common knowledge that write-offs, especially those on goodwill, do not reflect declines in asset value; rather, they are used as a device to manipulate financial reports. However, there is a striking lack of grounded theoretical research that can confirm this assessment. The aim of this dissertation is to provide valuable analytical and empirical insights on fixed asset write-offs under IFRS. In a first step, the practical implementation of IAS 36 in Europe has to be analyzed, which is best done empirically. Based on the findings from these empirical surveys, the most substantial questions remaining are subject to an in-depth analytical discussion. Since IAS 36 entails different measurement issues that have their origins in finance theory, this dissertation also aims to introduce some basic techniques from theoretical finance to accounting research. Lastly, as the analyses presented in this dissertation do not cover all open questions on fixed asset write-offs, the author hopes to encourage further research on this important topic.

Data marts and caching are two closely related concepts in the domain of multi-dimensional data. Both store pre-computed data to provide fast response times for complex OLAP queries, and for both it must be guaranteed that every query can be completely processed. However, they differ extremely in their update behaviour which we utilise to build a specific data mart extended by cache semantics. In this paper, we introduce a novel cache exploitation concept for data marts - coarse-grained caching - in which the containedness check for a multi-dimensional query is done through the comparison of the expected and the actual cardinalities. Therefore, we subdivide the multi-dimensional data into coarse partitions, the so called cubletets, which allow to specify the completeness criteria for incoming queries. We show that during query processing, the completeness check is done with no additional costs.

The objective of the International Financial Reporting Standards (IFRS) is to provide useful information to the users of financial statements to assist in making economic decisions. To be useful, information has to be relevant and reliable, but the reliability of information suffers when the guidelines for the reporting of specific issues are not clear and managerial discretion arises. Write-offs are one of those accounting issues that are regularly related to earnings management. By now it is seen as common knowledge that write-offs, especially those on goodwill, do not reflect declines in asset value; rather, they are used as a device to manipulate financial reports. However, there is a striking lack of grounded theoretical research that can confirm this assessment. The aim of this dissertation is to provide valuable analytical and empirical insights on fixed asset write-offs under IFRS. In a first step, the practical implementation of IAS 36 in Europe has to be analyzed, which is best done empirically. Based on the findings from these empirical surveys, the most substantial questions remaining are subject to an in-depth analytical discussion. Since IAS 36 entails different measurement issues that have their origins in finance theory, this dissertation also aims to introduce some basic techniques from theoretical finance to accounting research. Lastly, as the analyses presented in this dissertation do not cover all open questions on fixed asset write-offs, the author hopes to encourage further research on this important topic.:1. Analytical and Empirical Analyses on Fixed Asset Write-Offsffs: An Overview... 1 2. Determinants of the Write-Off Decision under IFRS: Evidence from Germany... 20 3. What Drives Companies? An Analysis of Fixed Asset Write-Offs in Europe in the Context of Different Institutional Settings... 60 4. A Critical Analysis of the Requirements of IAS 36 - A Pre-Tax CAPM?... 134 5. A New Perspective on Fixed Asset Write-Offs - When is Earnings Management Optimal... 166

The aim of this thesis is to investigate the dynamical behaviors of spatially extended systems with fluctuating time delays. In recent years, the study of spatially extended systems and systems with fluctuating delays has experienced a fast growth. In ubiquitous natural and laboratory situations, understanding the action of time-delayed signals is a crucial for understanding the dynamical behavior of these systems. Frequently, the length of the delay is found to change with time. Spatially extended systems are widely studied in many fields, such as chemistry, ecology, and biology. Self-organization, turbulence, and related nonlinear dynamic phenomena in spatially extended systems have developed into one of the most exciting topics in modern science. The first part of this thesis considers the discrete system. Diffusively coupled map lattices with a fluctuating delay are used in the study. The uncoupled local dynamics of the considered system are represented by the delayed logistic map. In particular, the influences of diffusive coupling and fluctuating delay are studied. To observe and understand the influences, the results for the considered system are compared with coupled map lattices without delay and with a constant delay as well as with the uncoupled logistic map with fluctuating delays. Identifying different patterns, determining the existence of traveling wave solutions, and specifying the fully synchronized stable state are the focus of this part of the study. The Lyapunov exponent, the master stability function, spectrum analysis, and the structure factor are used to characterize the different states and the transitions between them. The second part examines the continuous system. The delay is introduced into the reactionterm of the Fisher-KPP equation. The focus of this part of study is the time-delay-induced Turing instability in one-component reaction-diffusion systems. Turing instability has previously only been found in multiple-component reaction-diffusion systems. However, this work demonstrates with the help of the stability exponent that fluctuating delay can result in Turing instability in one-component reaction-diffusion systems as well. / Ziel der vorliegenden Arbeit ist die Untersuchung der Einflüsse der zeitlich fluktuierenden Verzögerungen in räumlich ausgedehnten diffusiven Systemen. Durch den Vergleich von Systemen mit konstanter Verzögerung bzw. Systemen ohne räumliche Kopplung erhält man ein tieferes Verständnis und eine bessere Beschreibungsweise der Dynamik des räumlich ausgedehnten diffusiven Systems mit fluktuierenden Verzögerungen. Im ersten Teil werden diskrete Systeme in Form von diffusiven Coupled Map Lattices untersucht. Als die lokale iterierte Abbildung des betrachteten Systems wird die logistische Abbildung mit Verzögerung gewählt. In diesem Teil liegt der Fokus auf Musterbildung, Existenz von Multiattraktoren und laufenden Wellen sowie der Möglichkeit der vollen Synchronisation. Masterstabilitätsfunktion, Lyapunov Exponent und Spektrumsanalyse werden benutzt, um das dynamische Verhalten zu verstehen. Im zweiten Teil betrachten wir kontinuierliche Systeme. Hier wird die Fisher-KPP Gleichung mit Verzögerungen im Reaktionsteil untersucht. In diesem Teil liegt der Fokus auf der Existenz der Turing Instabilität. Mit Hilfe von analytischen und numerischen Berechnungen wird gezeigt, dass bei fluktuierenden Verzögerungen eine Turing Instabilität auch in 1-Komponenten-Reaktions-Diffusionsgleichungen gefunden werden kann

The aim of this thesis is to investigate the dynamical behaviors of spatially extended systems with fluctuating time delays. In recent years, the study of spatially extended systems and systems with fluctuating delays has experienced a fast growth. In ubiquitous natural and laboratory situations, understanding the action of time-delayed signals is a crucial for understanding the dynamical behavior of these systems. Frequently, the length of the delay is found to change with time. Spatially extended systems are widely studied in many fields, such as chemistry, ecology, and biology. Self-organization, turbulence, and related nonlinear dynamic phenomena in spatially extended systems have developed into one of the most exciting topics in modern science. The first part of this thesis considers the discrete system. Diffusively coupled map lattices with a fluctuating delay are used in the study. The uncoupled local dynamics of the considered system are represented by the delayed logistic map. In particular, the influences of diffusive coupling and fluctuating delay are studied. To observe and understand the influences, the results for the considered system are compared with coupled map lattices without delay and with a constant delay as well as with the uncoupled logistic map with fluctuating delays. Identifying different patterns, determining the existence of traveling wave solutions, and specifying the fully synchronized stable state are the focus of this part of the study. The Lyapunov exponent, the master stability function, spectrum analysis, and the structure factor are used to characterize the different states and the transitions between them. The second part examines the continuous system. The delay is introduced into the reactionterm of the Fisher-KPP equation. The focus of this part of study is the time-delay-induced Turing instability in one-component reaction-diffusion systems. Turing instability has previously only been found in multiple-component reaction-diffusion systems. However, this work demonstrates with the help of the stability exponent that fluctuating delay can result in Turing instability in one-component reaction-diffusion systems as well. / Ziel der vorliegenden Arbeit ist die Untersuchung der Einflüsse der zeitlich fluktuierenden Verzögerungen in räumlich ausgedehnten diffusiven Systemen. Durch den Vergleich von Systemen mit konstanter Verzögerung bzw. Systemen ohne räumliche Kopplung erhält man ein tieferes Verständnis und eine bessere Beschreibungsweise der Dynamik des räumlich ausgedehnten diffusiven Systems mit fluktuierenden Verzögerungen. Im ersten Teil werden diskrete Systeme in Form von diffusiven Coupled Map Lattices untersucht. Als die lokale iterierte Abbildung des betrachteten Systems wird die logistische Abbildung mit Verzögerung gewählt. In diesem Teil liegt der Fokus auf Musterbildung, Existenz von Multiattraktoren und laufenden Wellen sowie der Möglichkeit der vollen Synchronisation. Masterstabilitätsfunktion, Lyapunov Exponent und Spektrumsanalyse werden benutzt, um das dynamische Verhalten zu verstehen. Im zweiten Teil betrachten wir kontinuierliche Systeme. Hier wird die Fisher-KPP Gleichung mit Verzögerungen im Reaktionsteil untersucht. In diesem Teil liegt der Fokus auf der Existenz der Turing Instabilität. Mit Hilfe von analytischen und numerischen Berechnungen wird gezeigt, dass bei fluktuierenden Verzögerungen eine Turing Instabilität auch in 1-Komponenten-Reaktions-Diffusionsgleichungen gefunden werden kann