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In common shape optimization routines, deformations of the computational mesh
usually suffer from decrease of mesh quality or even destruction of the mesh.
To mitigate this, we propose a theoretical framework using so-called pre-shape
spaces. This gives an opportunity for a unified theory of shape optimization, and of
problems related to parameterization and mesh quality. With this, we stay in the
free-form approach of shape optimization, in contrast to parameterized approaches
that limit possible shapes. The concept of pre-shape derivatives is defined, and
according structure and calculus theorems are derived, which generalize classical
shape optimization and its calculus. Tangential and normal directions are featured
in pre-shape derivatives, in contrast to classical shape derivatives featuring only
normal directions on shapes. Techniques from classical shape optimization and
calculus are shown to carry over to this framework, and are collected in generality
for future reference.
A pre-shape parameterization tracking problem class for mesh quality is in-
troduced, which is solvable by use of pre-shape derivatives. This class allows for
non-uniform user prescribed adaptations of the shape and hold-all domain meshes.
It acts as a regularizer for classical shape objectives. Existence of regularized solu-
tions is guaranteed, and corresponding optimal pre-shapes are shown to correspond
to optimal shapes of the original problem, which additionally achieve the user pre-
scribed parameterization.
We present shape gradient system modifications, which allow simultaneous nu-
merical shape optimization with mesh quality improvement. Further, consistency
of modified pre-shape gradient systems is established. The computational burden
of our approach is limited, since additional solution of possibly larger (non-)linear
systems for regularized shape gradients is not necessary. We implement and com-
pare these pre-shape gradient regularization approaches for a 2D problem, which
is prone to mesh degeneration. As our approach does not depend on the choice of
forms to represent shape gradients, we employ and compare weak linear elasticity
and weak quasilinear p-Laplacian pre-shape gradient representations.
We also introduce a Quasi-Newton-ADM inspired algorithm for mesh quality,
which guarantees sufficient adaption of meshes to user specification during the rou-
tines. It is applicable in addition to simultaneous mesh regularization techniques.
Unrelated to mesh regularization techniques, we consider shape optimization
problems constrained by elliptic variational inequalities of the first kind, so-called
obstacle-type problems. In general, standard necessary optimality conditions cannot
be formulated in a straightforward manner for such semi-smooth shape optimization
problems. Under appropriate assumptions, we prove existence and convergence of
adjoints for smooth regularizations of the VI-constraint. Moreover, we derive shape
derivatives for the regularized problem and prove convergence to a limit object.
Based on this analysis, an efficient optimization algorithm is devised and tested
numerically.
All previous pre-shape regularization techniques are applied to a variational
inequality constrained shape optimization problem, where we also create customized
targets for increased mesh adaptation of changing embedded shapes and active set
boundaries of the constraining variational inequality.
For decades, academics and practitioners aim to understand whether and how (economic) events affect firm value. Optimally, these events occur exogenously, i.e. suddenly and unexpectedly, so that an accurate evaluation of the effects on firm value can be conducted. However, recent studies show that even the evaluation of exogenous events is often prone to many challenges that can lead to diverse interpretations, resulting in heated debates. Recently, there have been intense debates in particular on the impact of takeover defenses and of Covid-19 on firm value. The announcements of takeover defenses and the propagation of Covid-19 are exogenous events that occur worldwide and are economically important, but have been insufficiently examined. By answering open research questions, this dissertation aims to provide a greater understanding about the heterogeneous effects that exogenous events such as the announcements of takeover defenses and the propagation of Covid-19 have on firm value. In addition, this dissertation analyzes the influence of certain firm characteristics on the effects of these two exogenous events and identifies influencing factors that explain contradictory results in the existing literature and thus can reconcile different views.
Broadcast media such as television have spread rapidly worldwide in the last century. They provide viewers with access to new information and also represent a source of entertainment that unconsciously exposes them to different social norms and moral values. Although the potential impact of exposure to television content have been studied intensively in economic research in recent years, studies examining the long-term causal effects of media exposure are still rare. Therefore, Chapters 2 to 4 of this thesis contribute to the better understanding of long-term effects of television exposure.
Chapter 2 empirically investigates whether access to reliable environmental information through television can influence individuals' environmental awareness and pro-environmental behavior. Analyzing exogenous variation in Western television reception in the German Democratic Republic shows that access to objective reporting on environmental pollution can enhance concerns regarding pollution and affect the likelihood of being active in environmental interest groups.
Chapter 3 utilizes the same natural experiment and explores the relationship between exposure to foreign mass media content and xenophobia. In contrast to the state television broadcaster in the German Democratic Republic, West German television regularly confronted its viewers with foreign (non-German) broadcasts. By applying multiple measures for xenophobic attitudes, our findings indicate a persistent mitigating impact of foreign media content on xenophobia.
Chapter 4 deals with another unique feature of West German television. In contrast to East German media, Western television programs regularly exposed their audience to unmarried and childless characters. The results suggest that exposure to different gender stereotypes contained in television programs can affect marriage, divorce, and birth rates. However, our findings indicate that mainly women were affected by the exposure to unmarried and childless characters.
Chapter 5 examines the influence of social media marketing on crowd participation in equity crowdfunding. By analyzing 26,883 investment decisions on three German equity crowdfunding platforms, our results show that startups can influence the success of their equity crowdfunding campaign through social media posts on Facebook and Twitter.
In Chapter 6, we incorporate the concept of habit formation into the theoretical literature on trade unions and contribute to a better understanding of how internal habit preferences influence trade union behavior. The results reveal that such internal reference points lead trade unions to raise wages over time, which in turn reduces employment. Conducting a numerical example illustrates that the wage effects and the decline in employment can be substantial.
Let K be a compact subset of the complex plane. Then the family of polynomials P is dense in A(K), the space of all continuous functions on K that are holomorphic on the interior of K, endowed with the uniform norm, if and only if the complement of K is connected. This is the statement of Mergelyan's celebrated theorem.
There are, however, situations where not all polynomials are required to approximate every f ϵ A(K) but where there are strict subspaces of P that are still dense in A(K). If, for example, K is a singleton, then the subspace of all constant polynomials is dense in A(K). On the other hand, if 0 is an interior point of K, then no strict subspace of P can be dense in A(K).
In between these extreme cases, the situation is much more complicated. It turns out that it is mostly determined by the geometry of K and its location in the complex plane which subspaces of P are dense in A(K). In Chapter 1, we give an overview of the known results.
Our first main theorem, which we will give in Chapter 3, deals with the case where the origin is not an interior point of K. We will show that if K is a compact set with connected complement and if 0 is not an interior point of K, then any subspace Q ⊂ P which contains the constant functions and all but finitely many monomials is dense in A(K).
There is a close connection between lacunary approximation and the theory of universality. At the end of Chapter 3, we will illustrate this connection by applying the above result to prove the existence of certain universal power series. To be specific, if K is a compact set with connected complement, if 0 is a boundary point of K and if A_0(K) denotes the subspace of A(K) of those functions that satisfy f(0) = 0, then there exists an A_0(K)-universal formal power series s, where A_0(K)-universal means that the family of partial sums of s forms a dense subset of A_0(K).
In addition, we will show that no formal power series is simultaneously universal for all such K.
The condition on the subspace Q in the main result of Chapter 3 is quite restrictive, but this should not be too surprising: The result applies to the largest possible class of compact sets.
In Chapter 4, we impose a further restriction on the compact sets under consideration, and this will allow us to weaken the condition on the subspace Q. The result that we are going to give is similar to one of those presented in the first chapter, namely the one due to Anderson. In his article “Müntz-Szasz type approximation and the angular growth of lacunary integral functions”, he gives a criterion for a subspace Q of P to be dense in A(K) where K is entirely contained in some closed sector with vertex at the origin.
We will consider compact sets with connected complement that are -- with the possible exception of the origin -- entirely contained in some open sector with vertex at the origin. What we are going to show is that if K\{0} is contained in an open sector of opening angle 2α and if Λ is some subset of the nonnegative integers, then the span of {z → z^λ : λ ϵ Λ} is dense in A(K) whenever 0 ϵ Λ and some Müntz-type condition is satisfied.
Conversely, we will show that if a similar condition is not satisfied, then we can always find a compact set K with connected complement such that K\{0} is contained in some open sector of opening angle 2α and such that the span of {z → z^λ : λ ϵ Λ} fails to be dense in A(K).
Issues in Price Measurement
(2022)
This thesis focuses on the issues in price measurement and consists of three chapters. Due to outdated weighting information, a Laspeyres-based consumer price index (CPI) is prone to accumulating upward bias. Therefore, chapter 1 introduces and examines simple and transparent revision approaches that retrospectively address the source of the bias. They provide a consistent long-run time series of the CPI and require no additional information. Furthermore, a coherent decomposition of the bias into the contributions of individual product groups is developed. In a case study, the approaches are applied to a Laspeyres-based CPI. The empirical results confirm the theoretical predictions. The proposed revision approaches are adoptable not only to most national CPIs but also to other price-level measures such as the producer price index or the import and export price indices.
Chapter 2 is dedicated to the measurement of import and export price indices. Such indices are complicated by the impact of exchange rates. These indices are usually also compiled by some Laspeyres type index. Therefore, substitution bias is an issue. The terms of trade (ratio of export and import price index) are therefore also likely to be distorted. The underlying substitution bias accumulates over time. The present article applies a simple and transparent retroactive correction approach that addresses the source of the substitution bias and produces meaningful long-run time series of import and export price levels and, therefore, of the terms of trade. Furthermore, an empirical case study is conducted that demonstrates the efficacy and versatility of the correction approach.
Chapter 3 leaves the field of index revision and studies another issue in price measurement, namely, the economic evaluation of digital products in monetary terms that have zero market prices. This chapter explores different methods of economic valuation and pricing of free digital products and proposes an alternative way to calculate the economic value and a shadow price of free digital products: the Usage Cost Model (UCM). The goal of the chapter is, first of all, to formulate a theoretical framework and incorporate an alternative measure of the value of free digital products. However, an empirical application is also made to show the work of the theoretical model. Some conclusions on applicability are drawn at the end of the chapter.
In order to classify smooth foliated manifolds, which are smooth maifolds equipped with a smooth foliation, we introduce the de Rham cohomologies of smooth foliated manifolds. These cohomologies are build in a similar way as the de Rham cohomologies of smooth manifolds. We develop some tools to compute these cohomologies. For example we proof a Mayer Vietoris theorem for foliated de Rham cohomology and show that these cohomologys are invariant under integrable homotopy. A generalization of a known Künneth formula, which relates the cohomologies of a product foliation with its factors, is discussed. In particular, this envolves a splitting theory of sequences between Frechet spaces and a theory of projective spectrums. We also prove, that the foliated de Rham cohomology is isomorphic to the Cech-de Rham cohomology and the Cech cohomology of leafwise constant functions of an underlying so called good cover.
In vielen Branchen und vor allem in großen Unternehmen gehört eine Unterstützung von Geschäftsprozessen durch Workflow-Management-Systeme zum gelebten Alltag. Im Zentrum steht dabei die Steuerung kontrollflussorientierter Abläufe, während Prozesse mit einem Schwerpunkt auf Daten, Informationen und Wissen meist außen vor bleiben. Solche wissensintensive Prozesse (engl.: knowledge intensive processes) (KiPs) sind Untersuchungsgegenstand in vielen aktuellen Studien, welche ein derzeit aktives Forschungsgebiet formen.
Im Vordergrund solcher KiPs steht dabei das durch die mitwirkenden Personen eingebrachte Wissen, welches in einem wesentlichen Maß die Prozessausführung beeinflusst, hierdurch jedoch die Bearbeitung komplexer und meist hoch volatiler Prozesse ermöglicht. Hierbei handelt es sich zumeist um entscheidungsintensive Prozesse, Prozesse zur Wissensakquisition oder Prozesse, die zu einer Vielzahl unterschiedlicher Prozessabläufe führen können.
Im Rahmen dieser Arbeit wird ein Ansatz entwickelt und vorgestellt, der sich der Modellierung, Visualisierung und Ausführung wissensintensiver Prozesse unter Verwendung Semantischer Technologien widmet. Hierzu werden als die zentralen Anforderungen zur Ausführung von KiPs Flexibilität, Adaptivität und Zielorientierung definiert. Daran anknüpfend werden drei zentrale Grundprinzipien der Prozessmodellierung identifiziert, welche in der ersten Forschungsfrage aufgegriffen werden: „Können die drei Grundprinzipien in einem einheitlichen datenzentrierten, deklarativen, semantischen Ansatz (welcher mit ODD-BP bezeichnet wird) kombiniert werden und können damit die zentralen Anforderungen von KiPs erfüllt werden?”
Die Grundlage für ODD-BP bildet ein Metamodell, welches als Sprachkonstrukt fungiert und die Definition der angestrebten Prozessmodelle erlaubt. Darauf aufbauend wird mit Hilfe von Inferenzierungsregeln ein Verfahren entwickelt, welches das Schlussfolgern von Prozesszuständen ermöglicht und somit eine klassische Workflow-Engine überflüssig macht. Zudem wird eine Methodik eingeführt, die für jede in einem Prozess mitwirkende Person eine maßgeschneiderte, adaptive Prozessvisualisierung ermöglicht, um neben dem Freiheitsgrad der Flexibilität auch eine fundierte Prozessunterstützung bei der Ausführung von KiPs leisten zu können. All dies erfolgt innerhalb einer einheitlichen Wissensbasis, die zum einen die Grundlage für eine vollständige semantische Prozessmodellierung bildet und zum anderen die Möglichkeit zur Integration von Expertenwissen eröffnet. Dieses Expertenwissen kann einen expliziten Beitrag bei der Ausführung wissensintensiver Prozesse leisten und somit die Kollaboration von Mensch und Maschine durch Technologien der symbolischen KI ermöglichen. Die zweite Forschungsfrage greift diesen Aspekt auf: „Kann in dem ODD-BP Ansatz ontologisches Wissen so integriert werden, dass dieses in einer Prozessausführung einen Beitrag leistet?”
Das Metamodell sowie die entwickelten Methoden und Verfahren werden in einem prototypischen, generischen System realisiert, welches grundsätzlich für alle Anwendungsgebiete mit KiPs geeignet ist. Zur Validierung des ODD-BP Ansatzes erfolgt eine Ausrichtung auf den Anwendungsfall einer Notrufabfrage aus dem Leitstellenumfeld. Im Zuge der Evaluation wird gezeigt, wie dieser wissensintensive Ablauf von einer flexiblen, adaptiven und zielorientierten Prozessausführung profitiert. Darüber hinaus wird medizinisches Expertenwissen in den Prozessablauf integriert und es wird nachgewiesen, wie dieses zu verbesserten Prozessergebnissen beiträgt.
Wissensintensive Prozesse stellen Unternehmen und Organisationen in allen Branchen und Anwendungsfällen derzeit vor große Herausforderungen und die Wissenschaft und Forschung widmet sich der Suche nach praxistauglichen Lösungen. Diese Arbeit präsentiert mit ODD-BP einen vielversprechenden Ansatz, indem die Möglichkeiten Semantischer Technologien dazu genutzt werden, eine eng verzahnte Zusammenarbeit zwischen Mensch und Maschine bei der Ausführung von KiPs zu ermöglichen. Die zur Evaluation fokussierte Notrufabfrage innerhalb von Leitstellen stellt zudem einen höchst relevanten Anwendungsfall dar, da in einem akuten Notfall in kürzester Zeit Entscheidungen getroffen werden müssen, um weitreichenden Schaden abwenden und Leben retten zu können. Durch die Berücksichtigung umfassender Datenmengen und das Ausnutzen verfügbaren Expertenwissens kann so eine schnelle Lagebewertung mit Hilfe der maschinellen Unterstützung erreicht und der Mensch beim Treffen von richtigen Entscheidungen unterstützt werden.
Modellbildung und Umsetzung von Methoden zur energieeffizienten Nutzung von Containertechnologien
(2021)
Die Nutzung von Cloud-Software und skalierten Web-Apps sowie Web-Services hat in den letzten Jahren extrem zugenommen, was zu einem Anstieg der Hochleistungs-Cloud-Rechenzentren führt. Neben der Verbesserung der Dienste spiegelt sich dies auch im weltweiten Stromverbrauch von Rechenzentren wider, der derzeit etwas mehr als 1% (entspricht etwa 200 TWh) beträgt. Prognosen sagen für die kommenden Jahre einen massiven Anstieg des Stromverbrauchs von Cloud-Rechenzentren voraus. Grundlage dieser Bewegung ist die Beschleunigung von Administration und Entwicklung, die unter anderem durch den Einsatz von Containern entsteht. Als Basis für Millionen von Web-Apps und -Services beschleunigen sie die Skalierung, Bereitstellung und Aktualisierung von Cloud-Diensten.
In dieser Arbeit wird aufgezeigt, dass Container zusätzlich zu ihren vielen technischen Vorteilen Möglichkeiten zur Reduzierung des Energieverbrauchs von Cloud-Rechenzentren bieten, die aus
einer ineffizienten Konfiguration von Containern sowie Container-Laufzeitumgebungen resultieren. Basierend auf einer Umfrage und einer Auswertung geeigneter Literatur werden in einem ersten Schritt wahrscheinliche Probleme beim Einsatz von Containern aufgedeckt. Weiterhin wird die Sensibilität von Administratoren und Entwicklern bezüglich des Energieverbrauchs von Container-Software ermittelt. Aufbauend auf den Ergebnissen der Umfrage und der Auswertung werden anhand von Standardszenarien im Containerumfeld die Komponenten des de facto Standards Docker untersucht. Anschließend wird ein Modell, bestehend aus Messmethodik, Empfehlungen für eine effiziente
Konfiguration von Containern und Tools, beschrieben. Die Messmethodik sollte einfach anwendbar sein und gängige Technologien in Rechenzentren unterstützen. Darüber hinaus geben die Handlungsempfehlungen sowohl Entwicklern als auch Administratoren die Möglichkeit zu entscheiden, welche Komponenten von Docker im Sinne eines energieeffizienten Einsatzes und in Abhängigkeit vom Einsatzszenario der Container genutzt werden sollten und welche weggelassen werden könnten. Die resultierenden Container können im Sinne der Energieeffizienz auf Servern und gleichermaßen auf PCs und Embedded Systems (als Teil von IoT und Edge Cloud) eingesetzt werden und somit nicht nur dem zuvor beschriebenen Problem in der Cloud entgegenwirken.
Die Arbeit beschäftigt sich zudem mit dem Verhalten von skalierten Webanwendungen. Gängige Orchestrierungswerkzeuge definieren statische Skalierungspunkte für Anwendungen, die in den meisten Fällen auf der CPU-Auslastung basieren. Es wird dargestellt, dass dabei weder die tatsächliche Erreichbarkeit noch der Stromverbrauch der Anwendungen berücksichtigt werden. Es wird der Autoscaler des Open-Source-Container-Orchestrierungswerkzeugs Kubernetes betrachtet, der um ein neu entwickeltes Werkzeug erweitert wird. Es wird deutlich, dass eine dynamische Anpassung der Skalierungspunkte durch eine Vorabauswertung gängiger Nutzungsszenarien sowie Informationen über deren Stromverbrauch und die Erreichbarkeit bei steigender Last erreicht werden kann.
Schließlich folgt eine empirische Untersuchung des generierten Modells in Form von drei Simulationen, die die Auswirkungen auf den Energieverbrauch von Cloud-Rechenzentren darlegen sollen.
The Eurosystem's Household Finance and Consumption Survey (HFCS) collects micro data on private households' balance sheets, income and consumption. It is a stylised fact that wealth is unequally distributed and that the wealthiest own a large share of total wealth. For sample surveys which aim at measuring wealth and its distribution, this is a considerable problem. To overcome it, some of the country surveys under the HFCS umbrella try to sample a disproportionately large share of households that are likely to be wealthy, a technique referred to as oversampling. Ignoring such types of complex survey designs in the estimation of regression models can lead to severe problems. This thesis first illustrates such problems using data from the first wave of the HFCS and canonical regression models from the field of household finance and gives a first guideline for HFCS data users regarding the use of replicate weight sets for variance estimation using a variant of the bootstrap. A further investigation of the issue necessitates a design-based Monte Carlo simulation study. To this end, the already existing large close-to-reality synthetic simulation population AMELIA is extended with synthetic wealth data. We discuss different approaches to the generation of synthetic micro data in the context of the extension of a synthetic simulation population that was originally based on a different data source. We propose an additional approach that is suitable for the generation of highly skewed synthetic micro data in such a setting using a multiply-imputed survey data set. After a description of the survey designs employed in the first wave of the HFCS, we then construct new survey designs for AMELIA that share core features of the HFCS survey designs. A design-based Monte Carlo simulation study shows that while more conservative approaches to oversampling do not pose problems for the estimation of regression models if sampling weights are properly accounted for, the same does not necessarily hold for more extreme oversampling approaches. This issue should be further analysed in future research.
Estimation and therefore prediction -- both in traditional statistics and machine learning -- encounters often problems when done on survey data, i.e. on data gathered from a random subset of a finite population. Additional to the stochastic generation of the data in the finite population (based on a superpopulation model), the subsetting represents a second randomization process, and adds further noise to the estimation. The character and impact of the additional noise on the estimation procedure depends on the specific probability law for subsetting, i.e. the survey design. Especially when the design is complex or the population data is not generated by a Gaussian distribution, established methods must be re-thought. Both phenomena can be found in business surveys, and their combined occurrence poses challenges to the estimation.
This work introduces selected topics linked to relevant use cases of business surveys and discusses the role of survey design therein: First, consider micro-econometrics using business surveys. Regression analysis under the peculiarities of non-normal data and complex survey design is discussed. The focus lies on mixed models, which are able to capture unobserved heterogeneity e.g. between economic sectors, when the dependent variable is not conditionally normally distributed. An algorithm for survey-weighted model estimation in this setting is provided and applied to business data.
Second, in official statistics, the classical sampling randomization and estimators for finite population totals are relevant. The variance estimation of estimators for (finite) population totals plays a major role in this framework in order to decide on the reliability of survey data. When the survey design is complex, and the number of variables is large for which an estimated total is required, generalized variance functions are popular for variance estimation. They allow to circumvent cumbersome theoretical design-based variance formulae or computer-intensive resampling. A synthesis of the superpopulation-based motivation and the survey framework is elaborated. To the author's knowledge, such a synthesis is studied for the first time both theoretically and empirically.
Third, the self-organizing map -- an unsupervised machine learning algorithm for data visualization, clustering and even probability estimation -- is introduced. A link to Markov random fields is outlined, which to the author's knowledge has not yet been established, and a density estimator is derived. The latter is evaluated in terms of a Monte-Carlo simulation and then applied to real world business data.