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Many NP-hard optimization problems that originate from classical graph theory, such as the maximum stable set problem and the maximum clique problem, have been extensively studied over the past decades and involve the choice of a subset of edges or vertices. There usually exist combinatorial methods that can be applied to solve them directly in the graph.
The most simple method is to enumerate feasible solutions and select the best. It is not surprising that this method is very slow oftentimes, so the task is to cleverly discard fruitless search space during the search. An alternative method to solve graph problems is to formulate integer linear programs, such that their solution yields an optimal solution to the original optimization problem in the graph. In order to solve integer linear programs, one can start with relaxing the integer constraints and then try to find inequalities for cutting off fractional extreme points. In the best case, it would be possible to describe the convex hull of the feasible region of the integer linear program with a set of inequalities. In general, giving a complete description of this convex hull is out of reach, even if it has a polynomial number of facets. Thus, one tries to strengthen the (weak) relaxation of the integer linear program best possible via strong inequalities that are valid for the convex hull of feasible integer points.
Many classes of valid inequalities are of exponential size. For instance, a graph can have exponentially many odd cycles in general and therefore the number of odd cycle inequalities for the maximum stable set problem is exponential. It is sometimes possible to check in polynomial time if some given point violates any of the exponentially many inequalities. This is indeed the case for the odd cycle inequalities for the maximum stable set problem. If a polynomial time separation algorithm is known, there exists a formulation of polynomial size that contains a given point if and only if it does not violate one of the (potentially exponentially many) inequalities. This thesis can be divided into two parts. The first part is the main part and it contains various new results. We present new extended formulations for several optimization problems, i.e. the maximum stable set problem, the nonconvex quadratic program with box
constraints and the p-median problem. In the second part we modify a very fast algorithm for finding a maximum clique in very large sparse graphs. We suggest and compare three alternative versions of this algorithm to the original version and compare their strengths and weaknesses.
Semantic-Aware Coordinated Multiple Views for the Interactive Analysis of Neural Activity Data
(2024)
Visualizing brain simulation data is in many aspects a challenging task. For one, data used in brain simulations and the resulting datasets is heterogeneous and insight is derived by relating all different kinds of it. Second, the analysis process is rapidly changing while creating hypotheses about the results. Third, the scale of data entities in these heterogeneous datasets is manifold, reaching from single neurons to brain areas interconnecting millions. Fourth, the heterogeneous data consists of a variety of modalities, e.g.: from time series data to connectivity data, from single parameters to a set of parameters spanning parameter spaces with multiple possible and biological meaningful solutions; from geometrical data to hierarchies and textual descriptions, all on mostly different scales. Fifth, visualizing includes finding suitable representations and providing real-time interaction while supporting varying analysis workflows. To this end, this thesis presents a scalable and flexible software architecture for visualizing, integrating and interacting with brain simulations data. The scalability and flexibility is achieved by interconnected services forming in a series of Coordinated Multiple View (CMV) systems. Multiple use cases are presented, introducing views leveraging this architecture, extending its ecosystem and resulting in a Problem Solving Environment (PSE) from which custom-tailored CMV systems can be build. The construction of such CMV system is assisted by semantic reasoning hence the term semantic-aware CMVs.
The formerly communist countries in Central and Eastern Europe (transitional economies in Europe and the Soviet Union – for example, East Germany, Czech Republic, Hungary, Lithuania, Poland, Russia) and transitional economies in Asia – for example, China, Vietnam had centrally planned economies, which did not allow entrepreneurship activities. Despite the political-socioeconomic transformations in transitional economies around 1989, they still had an institutional heritage that affects individuals’ values and attitudes, which, in turn, influence intentions, behaviors, and actions, including entrepreneurship.
While prior studies on the long-lasting effects of socialist legacy on entrepreneurship have focused on limited geographical regions (e.g., East-West Germany, and East-West Europe), this dissertation focuses on the Vietnamese context, which offers a unique quasi-experimental setting. In 1954, Vietnam was divided into the socialist North and the non-socialist South, and it was then reunified under socialist rule in 1975. Thus, the intensity of differences in socialist treatment in North-South Vietnam (about 21 years) is much shorter than that in East-West Germany (about 40 years) and East-West Europe (about 70 years when considering former Soviet Union countries).
To assess the relationship between socialist history and entrepreneurship in this unique setting, we survey more than 3,000 Vietnamese individuals. This thesis finds that individuals from North Vietnam have lower entrepreneurship intentions, are less likely to enroll in entrepreneurship education programs, and display lower likelihood to take over an existing business, compared to those from the South of Vietnam. The long-lasting effect of formerly socialist institutions on entrepreneurship is apparently deeper than previously discovered in the prominent case of East-West Germany and East-West Europe as well.
In the second empirical investigation, this dissertation focuses on how succession intentions differ from others (e.g., founding, and employee intentions) regarding career choice motivation, and the effect of three main elements of the theory of planned behavior (e.g., entrepreneurial attitude, subjective norms, and perceived behavioral control) in transition economy – Vietnam context. The findings of this thesis suggest that an intentional founder is labeled with innovation, an intentional successor is labeled with roles motivation, and an intentional employee is labeled with social mission. Additionally, this thesis reveals that entrepreneurial attitude and perceived behavioral control are positively associated with the founding intention, whereas there is no difference in this effect between succession and employee intentions.
The harmonic Faber operator
(2018)
P. K. Suetin points out in the beginning of his monograph "Faber Polynomials and Faber Series" that Faber polynomials play an important role in modern approximation theory of a complex variable as they are used in representing analytic functions in simply connected domains, and many theorems on approximation of analytic functions are proved with their help [50]. In 1903, the Faber polynomials were firstly discovered by G. Faber. It was Faber's aim to find a generalisation of Taylor series of holomorphic functions in the open unit disc D in the following way. As any holomorphic function in D has a Taylor series representation f(z)=\sum_{\nu=0}^{\infty}a_{\nu}z^{\nu} (z\in\D) converging locally uniformly inside D, for a simply connected domain G, Faber wanted to determine a system of polynomials (Q_n) such that each function f being holomorphic in G can be expanded into a series
f=\sum_{\nu=0}^{\infty}b_{\nu}Q_{\nu} converging locally uniformly inside G. Having this goal in mind, Faber considered simply connected domains bounded by an analytic Jordan curve. He constructed a system of polynomials (F_n) with this property. These polynomials F_n were named after him as Faber polynomials. In the preface of [50], a detailed summary of results concerning Faber polynomials and results obtained by the aid of them is given. An important application of Faber polynomials is e.g. the transfer of known assertions concerning polynomial approximation of functions belonging to the disc algebra to results of the approximation of functions being continuous on a compact continuum K which contains at least two points and has a connected complement and being holomorphic in the interior of K. In this field, the Faber operator denoted by T turns out to be a powerful tool (for an introduction, see e.g. D. Gaier's monograph). It
assigns a polynomial of degree at most n given in the monomial basis \sum_{\nu=0}^{n}a_{\nu}z^{\nu} with a polynomial of degree at most n given in the basis of Faber polynomials \sum_{\nu=0}^{n}a_{\nu}F_{\nu}. If the Faber operator is continuous with respect to the uniform norms, it has a unique continuous extension to an operator mapping the disc algebra onto the space of functions being continuous on the whole compact continuum and holomorphic in its interior. For all f being element of the disc algebra and all polynomials P, via the obvious estimate for the uniform norms ||T(f)-T(P)||<= ||T|| ||f-P||, it can be seen that the original task of approximating F=T(f) by polynomials is reduced to the polynomial approximation of the function f. Therefore, the question arises under which conditions the Faber operator is continuous and surjective. A fundamental result in this regard was established by J. M. Anderson and J. Clunie who showed that if the compact continuum is bounded by a rectifiable Jordan curve with bounded boundary rotation and free from cusps, then the Faber operator with respect to the uniform norms is a topological isomorphism. Now, let f be a harmonic function in D. Similar as above, we find that f has a uniquely determined representation f=\sum_{\nu=-\infty}^{\infty}a_{\nu}p_{\nu}
converging locally uniformly inside D where p_{n}(z)=z^{n} for n\in\N_{0} and p_{-n}(z)=\overline{z}^{n} for n\in\N}. One may ask whether there is an analogue for harmonic functions on simply connected domains G. Indeed, for a domain G bounded by an analytic Jordan curve, the conjecture that each function f being harmonic in G has a uniquely determined representation f=\sum_{\nu= \infty}^{\infty}b_{\nu}F_{\nu} where F_{-n}(z)=\overline{F_{n}(z\)} for n\inN, converging locally uniformly inside G, holds true. Let now K be a compact continuum containing at least two points and having a connected complement. A main component of this thesis will be the examination of the harmonic Faber operator mapping a harmonic polynomial given in the basis of the harmonic monomials \sum_{\nu=-n}^{n}a_{\nu}p_{\nu} to a harmonic polynomial given as \sum_{\nu=-n}^{n}a_{\nu}F_{\nu}.
If this operator, which is based on an idea of J. Müller, is continuous with respect to the uniform norms, it has a unique continuous extension to an operator mapping the functions being continuous on \partial\D onto the continuous functions on K being
harmonic in the interior of K. Harmonic Faber polynomials and the harmonic Faber operator will be the objects accompanying us throughout
our whole discussion. After having given an overview about notations and certain tools we will use in our consideration in the first chapter, we begin our studies with an introduction to the Faber operator and the harmonic Faber operator. We start modestly and consider domains bounded by an analytic Jordan curve. In Section 2, as a first result, we will show that, for such a domain G, the harmonic Faber operator has a unique continuous extension to an operator mapping the space of the harmonic functions in D onto the space
of the harmonic functions in G, and moreover, the harmonic Faber
operator is an isomorphism with respect to the topologies of locally
uniform convergence. In the further sections of this chapter, we illumine the behaviour of the (harmonic) Faber operator on certain function spaces. In the third chapter, we leave the situation of compact continua bounded by an analytic Jordan curve. Instead we consider closures of domains bounded by Jordan curves having a Dini continuous curvature. With the aid of the concept of compact operators and the Fredholm alternative, we are able to show that the harmonic Faber operator is a topological isomorphism. Since, in particular, the main result of the third chapter holds true for closures K of domains bounded by analytic Jordan curves, we can make use of it to obtain new results concerning the approximation of functions being continuous on K and harmonic in the interior of K by harmonic polynomials. To do so, we develop techniques applied by L. Frerick and J. Müller in [11] and adjust them to our setting. So, we can transfer results about the classic Faber operator to the harmonic Faber operator. In the last chapter, we will use the theory of harmonic Faber polynomials
to solve certain Dirichlet problems in the complex plane. We pursue
two different approaches: First, with a similar philosophy as in [50],
we develop a procedure to compute the coefficients of a series \sum_{\nu=-\infty}^{\infty}c_{\nu}F_{\nu} converging uniformly to the solution of a given Dirichlet problem. Later, we will point out how semi-infinite programming with harmonic Faber polynomials as ansatz functions can be used to get an approximate solution of a given Dirichlet problem. We cover both approaches first from a theoretical point of view before we have a focus on the numerical implementation of concrete examples. As application of the numerical computations, we considerably obtain visualisations of the concerned Dirichlet problems rounding out our discussion about the harmonic Faber polynomials and the harmonic Faber operator.
Despite significant advances in terms of the adoption of formal Intellectual Property Rights (IPR) protection, enforcement of and compliance with IPR regulations remains a contested issue in one of the world's major contemporary economies—China. The present review seeks to offer insights into possible reasons for this discrepancy as well as possible paths of future development by reviewing prior literature on IPR in China. Specifically, it focuses on the public's perspective, which is a crucial determinant of the effectiveness of any IPR regime. It uncovers possible differences with public perspectives in other countries and points to mechanisms (e.g., political, economic, cultural, and institutional) that may foster transitions over time in both formal IPR regulation and in the public perception of and compliance with IPR in China. On this basis, the review advances suggestions for future research in order to improve scholars' understanding of the public's perspective of IPR in China, its antecedents and implications.
This dissertation investigates corporate acquisition decisions that represent important corporate development activities for family and non-family firms. The main research objective of this dissertation is to generate insights into the subjective decision-making behavior of corporate decision-makers from family and non-family firms and their weighting of M&A decision-criteria during the early pre-acquisition target screening and selection process. The main methodology chosen for the investigation of M&A decision-making preferences and the weighting of M&A decision criteria is a choice-based conjoint analysis. The overall sample of this dissertation consists of 304 decision-makers from 264 private and public family and non-family firms from mainly Germany and the DACH-region. In the first empirical part of the dissertation, the relative importance of strategic, organizational and financial M&A decision-criteria for corporate acquirers in acquisition target screening is investigated. In addition, the author uses a cluster analysis to explore whether distinct decision-making patterns exist in acquisition target screening. In the second empirical part, the dissertation explores whether there are differences in investment preferences in acquisition target screening between family and non-family firms and within the group of family firms. With regards to the heterogeneity of family firms, the dissertation generated insights into how family-firm specific characteristics like family management, the generational stage of the firm and non-economic goals such as transgenerational control intention influences the weighting of different M&A decision criteria in acquisition target screening. The dissertation contributes to strategic management research, in specific to M&A literature, and to family business research. The results of this dissertation generate insights into the weighting of M&A decision-making criteria and facilitate a better understanding of corporate M&A decisions in family and non-family firms. The findings show that decision-making preferences (hence the weighting of M&A decision criteria) are influenced by characteristics of the individual decision-maker, the firm and the environment in which the firm operates.
Official business surveys form the basis for national and regional business statistics and are thus of great importance for analysing the state and performance of the economy. However, both the heterogeneity of business data and their high dynamics pose a particular challenge to the feasibility of sampling and the quality of the resulting estimates. A widely used sampling frame for creating the design of an official business survey is an extract from an official business register. However, if this frame does not accurately represent the target population, frame errors arise. Amplified by the heterogeneity and dynamics of business populations, these errors can significantly affect the estimation quality and lead to inefficiencies and biases. This dissertation therefore deals with design-based methods for optimising business surveys with respect to different types of frame errors.
First, methods for adjusting the sampling design of business surveys are addressed. These approaches integrate auxiliary information about the expected structures of frame errors into the sampling design. The aim is to increase the number of sampled businesses that are subject to frame errors. The element-specific frame error probability is estimated based on auxiliary information about frame errors observed in previous samples. The approaches discussed consider different types of frame errors and can be incorporated into predefined designs with fixed strata.
As the second main pillar of this work, methods for adjusting weights to correct for frame errors during estimation are developed and investigated. As a result of frame errors, the assumptions under which the original design weights were determined based on the sampling design no longer hold. The developed methods correct the design weights taking into account the errors identified for sampled elements. Case-number-based reweighting approaches, on the one hand, attempt to reconstruct the unknown size of the individual strata in the target population. In the context of weight smoothing methods, on the other hand, design weights are modelled and smoothed as a function of target or auxiliary variables. This serves to avoid inefficiencies in the estimation due to highly scattering weights or weak correlations between weights and target variables. In addition, possibilities of correcting frame errors by calibration weighting are elaborated. Especially when the sampling frame shows over- and/or undercoverage, the inclusion of external auxiliary information can provide a significant improvement of the estimation quality. For those methods whose quality cannot be measured using standard procedures, a procedure for estimating the variance based on a rescaling bootstrap is proposed. This enables an assessment of the estimation quality when using the methods in practice.
In the context of two extensive simulation studies, the methods presented in this dissertation are evaluated and compared with each other. First, in the environment of an experimental simulation, it is assessed which approaches are particularly suitable with regard to different data situations. In a second simulation study, which is based on the structural survey in the services sector, the applicability of the methods in practice is evaluated under realistic conditions.
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.
Computer simulation has become established in a two-fold way: As a tool for planning, analyzing, and optimizing complex systems but also as a method for the scientific instigation of theories and thus for the generation of knowledge. Generated results often serve as a basis for investment decisions, e.g., road construction and factory planning, or provide evidence for scientific theory-building processes. To ensure the generation of credible and reproducible results, it is indispensable to conduct systematic and methodologically sound simulation studies. A variety of procedure models exist that structure and predetermine the process of a study. As a result, experimenters are often required to repetitively but thoroughly carry out a large number of experiments. Moreover, the process is not sufficiently specified and many important design decisions still have to be made by the experimenter, which might result in an unintentional bias of the results.
To facilitate the conducting of simulation studies and to improve both replicability and reproducibility of the generated results, this thesis proposes a procedure model for carrying out Hypothesis-Driven Simulation Studies, an approach that assists the experimenter during the design, execution, and analysis of simulation experiments. In contrast to existing approaches, a formally specified hypothesis becomes the key element of the study so that each step of the study can be adapted and executed to directly contribute to the verification of the hypothesis. To this end, the FITS language is presented, which enables the specification of hypotheses as assumptions regarding the influence specific input values have on the observable behavior of the model. The proposed procedure model systematically designs relevant simulation experiments, runs, and iterations that must be executed to provide evidence for the verification of the hypothesis. Generated outputs are then aggregated for each defined performance measure to allow for the application of statistical hypothesis testing approaches. Hence, the proposed assistance only requires the experimenter to provide an executable simulation model and a corresponding hypothesis to conduct a sound simulation study. With respect to the implementation of the proposed assistance system, this thesis presents an abstract architecture and provides formal specifications of all required services.
To evaluate the concept of Hypothesis-Driven Simulation Studies, two case studies are presented from the manufacturing domain. The introduced approach is applied to a NetLogo simulation model of a four-tiered supply chain. Two scenarios as well as corresponding assumptions about the model behavior are presented to investigate conditions for the occurrence of the bullwhip effect. Starting from the formal specification of the hypothesis, each step of a Hypothesis-Driven Simulation Study is presented in detail, with specific design decisions outlined, and generated inter- mediate data as well as final results illustrated. With respect to the comparability of the results, a conventional simulation study is conducted which serves as reference data. The approach that is proposed in this thesis is beneficial for both practitioners and scientists. The presented assistance system allows for a more effortless and simplified execution of simulation experiments while the efficient generation of credible results is ensured.
This work deals with the current support landscape for Social Entrepreneurship (SE) in the DACH region. It provides answers to the questions of which actors support SE, how and why they do so, and which social ventures are supported. In addition, there is a focus on the motives for supporting SE as well as the decision-making process while selecting social ventures. In both cases, it is examined whether certain characteristics of the decision-maker and the organization influence the weighting of motives and decision-making criteria. More precise, the gender of the decision-maker as well as the kind of support by the organization is analyzed. The concrete examples of foundations and venture philanthropy organizations (VPOs) will give a deeper look at the SE support motives and decision-making behavior. In a quantitative empirical data collection, by means of an online survey, decision-makers from SE supporting organizations in the DACH region were asked to participate in a conjoint experiment and to fill in a questionnaire. The results illustrate a positive development of the SE support landscape in the German-speaking area as well as the heterogeneity of the organizational types, the financial and non-financial support instruments and the supported social ventures. Regarding the motives for SE-support, a general endeavor to change and to create an impact has proven to be particularly important at the organizational and the individual level. At the individual level female and male decision-makers have subtle differences in their motives to promote SE. Robustness checks by analyzing certain subsamples provide information about that. Individuals from foundations and VPOs, on the other hand, hardly differ from each other, even though here individuals with a rather social background face individuals with a business background. At the organizational level crucial differences can be identified for the motives, depending on the nature of the organization's support, and again comparing foundations with VPOs. Especially for the motives 'financial interests', 'reputation' and 'employee development' there are big differences between the considered groups. Eventually, by means of cluster analysis and still with respect to the support motives, two types of decision-makers could be determined on both the individual and the organizational level.
In terms of the decision-making behavior, and the weighting of certain decision-making criteria respectively, it has emerged that it is worthwhile having a closer look: The 'importance of the social problem' and the 'authenticity of the start-up team' are consistently the two most important criteria when it comes to selecting social ventures for supporting them. However, comparing male and female decision-makers, foundations and VPOs, as well as the two groups of financially and non-financially supporting organizations, there are certain specifics which are highly relevant for SE practice. Here as well a cluster analysis uncovered patterns of criteria weighting by identifying three different types of decision-makers.
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.
We consider a linear regression model for which we assume that some of the observed variables are irrelevant for the prediction. Including the wrong variables in the statistical model can either lead to the problem of having too little information to properly estimate the statistic of interest, or having too much information and consequently describing fictitious connections. This thesis considers discrete optimization to conduct a variable selection. In light of this, the subset selection regression method is analyzed. The approach gained a lot of interest in recent years due to its promising predictive performance. A major challenge associated with the subset selection regression is the computational difficulty. In this thesis, we propose several improvements for the efficiency of the method. Novel bounds on the coefficients of the subset selection regression are developed, which help to tighten the relaxation of the associated mixed-integer program, which relies on a Big-M formulation. Moreover, a novel mixed-integer linear formulation for the subset selection regression based on a bilevel optimization reformulation is proposed. Finally, it is shown that the perspective formulation of the subset selection regression is equivalent to a state-of-the-art binary formulation. We use this insight to develop novel bounds for the subset selection regression problem, which show to be highly effective in combination with the proposed linear formulation.
In the second part of this thesis, we examine the statistical conception of the subset selection regression and conclude that it is misaligned with its intention. The subset selection regression uses the training error to decide on which variables to select. The approach conducts the validation on the training data, which oftentimes is not a good estimate of the prediction error. Hence, it requires a predetermined cardinality bound. Instead, we propose to select variables with respect to the cross-validation value. The process is formulated as a mixed-integer program with the sparsity becoming subject of the optimization. Usually, a cross-validation is used to select the best model out of a few options. With the proposed program the best model out of all possible models is selected. Since the cross-validation is a much better estimate of the prediction error, the model can select the best sparsity itself.
The thesis is concluded with an extensive simulation study which provides evidence that discrete optimization can be used to produce highly valuable predictive models with the cross-validation subset selection regression almost always producing the best results.
Die vorgelegte Dissertation trägt den Titel Regularization Methods for Statistical Modelling in Small Area Estimation. In ihr wird die Verwendung regularisierter Regressionstechniken zur geographisch oder kontextuell hochauflösenden Schätzung aggregatspezifischer Kennzahlen auf Basis kleiner Stichproben studiert. Letzteres wird in der Fachliteratur häufig unter dem Begriff Small Area Estimation betrachtet. Der Kern der Arbeit besteht darin die Effekte von regularisierter Parameterschätzung in Regressionsmodellen, welche gängiger Weise für Small Area Estimation verwendet werden, zu analysieren. Dabei erfolgt die Analyse primär auf theoretischer Ebene, indem die statistischen Eigenschaften dieser Schätzverfahren mathematisch charakterisiert und bewiesen werden. Darüber hinaus werden die Ergebnisse durch numerische Simulationen veranschaulicht, und vor dem Hintergrund empirischer Anwendungen kritisch verortet. Die Dissertation ist in drei Bereiche gegliedert. Jeder Bereich behandelt ein individuelles methodisches Problem im Kontext von Small Area Estimation, welches durch die Verwendung regularisierter Schätzverfahren gelöst werden kann. Im Folgenden wird jedes Problem kurz vorgestellt und im Zuge dessen der Nutzen von Regularisierung erläutert.
Das erste Problem ist Small Area Estimation in der Gegenwart unbeobachteter Messfehler. In Regressionsmodellen werden typischerweise endogene Variablen auf Basis statistisch verwandter exogener Variablen beschrieben. Für eine solche Beschreibung wird ein funktionaler Zusammenhang zwischen den Variablen postuliert, welcher durch ein Set von Modellparametern charakterisiert ist. Dieses Set muss auf Basis von beobachteten Realisationen der jeweiligen Variablen geschätzt werden. Sind die Beobachtungen jedoch durch Messfehler verfälscht, dann liefert der Schätzprozess verzerrte Ergebnisse. Wird anschließend Small Area Estimation betrieben, so sind die geschätzten Kennzahlen nicht verlässlich. In der Fachliteratur existieren hierfür methodische Anpassungen, welche in der Regel aber restriktive Annahmen hinsichtlich der Messfehlerverteilung benötigen. Im Rahmen der Dissertation wird bewiesen, dass Regularisierung in diesem Kontext einer gegen Messfehler robusten Schätzung entspricht - und zwar ungeachtet der Messfehlerverteilung. Diese Äquivalenz wird anschließend verwendet, um robuste Varianten bekannter Small Area Modelle herzuleiten. Für jedes Modell wird ein Algorithmus zur robusten Parameterschätzung konstruiert. Darüber hinaus wird ein neuer Ansatz entwickelt, welcher die Unsicherheit von Small Area Schätzwerten in der Gegenwart unbeobachteter Messfehler quantifiziert. Es wird zusätzlich gezeigt, dass diese Form der robusten Schätzung die wünschenswerte Eigenschaft der statistischen Konsistenz aufweist.
Das zweite Problem ist Small Area Estimation anhand von Datensätzen, welche Hilfsvariablen mit unterschiedlicher Auflösung enthalten. Regressionsmodelle für Small Area Estimation werden normalerweise entweder für personenbezogene Beobachtungen (Unit-Level), oder für aggregatsbezogene Beobachtungen (Area-Level) spezifiziert. Doch vor dem Hintergrund der stetig wachsenden Datenverfügbarkeit gibt es immer häufiger Situationen, in welchen Daten auf beiden Ebenen vorliegen. Dies beinhaltet ein großes Potenzial für Small Area Estimation, da somit neue Multi-Level Modelle mit großem Erklärungsgehalt konstruiert werden können. Allerdings ist die Verbindung der Ebenen aus methodischer Sicht kompliziert. Zentrale Schritte des Inferenzschlusses, wie etwa Variablenselektion und Parameterschätzung, müssen auf beiden Levels gleichzeitig durchgeführt werden. Hierfür existieren in der Fachliteratur kaum allgemein anwendbare Methoden. In der Dissertation wird gezeigt, dass die Verwendung ebenenspezifischer Regularisierungsterme in der Modellierung diese Probleme löst. Es wird ein neuer Algorithmus für stochastischen Gradientenabstieg zur Parameterschätzung entwickelt, welcher die Informationen von allen Ebenen effizient unter adaptiver Regularisierung nutzt. Darüber hinaus werden parametrische Verfahren zur Abschätzung der Unsicherheit für Schätzwerte vorgestellt, welche durch dieses Verfahren erzeugt wurden. Daran anknüpfend wird bewiesen, dass der entwickelte Ansatz bei adäquatem Regularisierungsterm sowohl in der Schätzung als auch in der Variablenselektion konsistent ist.
Das dritte Problem ist Small Area Estimation von Anteilswerten unter starken verteilungsbezogenen Abhängigkeiten innerhalb der Kovariaten. Solche Abhängigkeiten liegen vor, wenn eine exogene Variable durch eine lineare Transformation einer anderen exogenen Variablen darstellbar ist (Multikollinearität). In der Fachliteratur werden hierunter aber auch Situationen verstanden, in welchen mehrere Kovariate stark korreliert sind (Quasi-Multikollinearität). Wird auf einer solchen Datenbasis ein Regressionsmodell spezifiziert, dann können die individuellen Beiträge der exogenen Variablen zur funktionalen Beschreibung der endogenen Variablen nicht identifiziert werden. Die Parameterschätzung ist demnach mit großer Unsicherheit verbunden und resultierende Small Area Schätzwerte sind ungenau. Der Effekt ist besonders stark, wenn die zu modellierende Größe nicht-linear ist, wie etwa ein Anteilswert. Dies rührt daher, dass die zugrundeliegende Likelihood-Funktion nicht mehr geschlossen darstellbar ist und approximiert werden muss. Im Rahmen der Dissertation wird gezeigt, dass die Verwendung einer L2-Regularisierung den Schätzprozess in diesem Kontext signifikant stabilisiert. Am Beispiel von zwei nicht-linearen Small Area Modellen wird ein neuer Algorithmus entwickelt, welche den bereits bekannten Quasi-Likelihood Ansatz (basierend auf der Laplace-Approximation) durch Regularisierung erweitert und verbessert. Zusätzlich werden parametrische Verfahren zur Unsicherheitsmessung für auf diese Weise erhaltene Schätzwerte beschrieben.
Vor dem Hintergrund der theoretischen und numerischen Ergebnisse wird in der Dissertation demonstriert, dass Regularisierungsmethoden eine wertvolle Ergänzung der Fachliteratur für Small Area Estimation darstellen. Die hier entwickelten Verfahren sind robust und vielseitig einsetzbar, was sie zu hilfreichen Werkzeugen der empirischen Datenanalyse macht.
In the modeling context, non-linearities and uncertainty go hand in hand. In fact, the utility function's curvature determines the degree of risk-aversion. This concept is exploited in the first article of this thesis, which incorporates uncertainty into a small-scale DSGE model. More specifically, this is done by a second-order approximation, while carrying out the derivation in great detail and carefully discussing the more formal aspects. Moreover, the consequences of this method are discussed when calibrating the equilibrium condition. The second article of the thesis considers the essential model part of the first paper and focuses on the (forward-looking) data needed to meet the model's requirements. A large number of uncertainty measures are utilized to explain a possible approximation bias. The last article keeps to the same topic but uses statistical distributions instead of actual data. In addition, theoretical (model) and calibrated (data) parameters are used to produce more general statements. In this way, several relationships are revealed with regard to a biased interpretation of this class of models. In this dissertation, the respective approaches are explained in full detail and also how they build on each other.
In summary, the question remains whether the exact interpretation of model equations should play a role in macroeconomics. If we answer this positively, this work shows to what extent the practical use can lead to biased results.
This dissertation deals with consistent estimates in household surveys. Household surveys are often drawn via cluster sampling, with households sampled at the first stage and persons selected at the second stage. The collected data provide information for estimation at both the person and the household level. However, consistent estimates are desirable in the sense that the estimated household-level totals should coincide with the estimated totals obtained at the person-level. Current practice in statistical offices is to use integrated weighting. In this approach consistent estimates are guaranteed by equal weights for all persons within a household and the household itself. However, due to the forced equality of weights, the individual patterns of persons are lost and the heterogeneity within households is not taken into account. In order to avoid the negative consequences of integrated weighting, we propose alternative weighting methods in the first part of this dissertation that ensure both consistent estimates and individual person weights within a household. The underlying idea is to limit the consistency conditions to variables that emerge in both the personal and household data sets. These common variables are included in the person- and household-level estimator as additional auxiliary variables. This achieves consistency more directly and only for the relevant variables, rather than indirectly by forcing equal weights on all persons within a household. Further decisive advantages of the proposed alternative weighting methods are that original individual rather than the constructed aggregated auxiliaries are utilized and that the variable selection process is more flexible because different auxiliary variables can be incorporated in the person-level estimator than in the household-level estimator.
In the second part of this dissertation, the variances of a person-level GREG estimator and an integrated estimator are compared in order to quantify the effects of the consistency requirements in the integrated weighting approach. One of the challenges is that the estimators to be compared are of different dimensions. The proposed solution is to decompose the variance of the integrated estimator into the variance of a reduced GREG estimator, whose underlying model is of the same dimensions as the person-level GREG estimator, and add a constructed term that captures the effects disregarded by the reduced model. Subsequently, further fields of application for the derived decomposition are proposed such as the variable selection process in the field of econometrics or survey statistics.
The German Mittelstand is closely linked to the success of the German economy. Mittelstand firms, thereof numerous Hidden Champions, significantly contribute to Germany’s economic performance, innovation, and export strength. However, the advancing digitalization poses complex challenges for Mittelstand firms. To benefit from the manifold opportunities offered by digital technologies and to defend or even expand existing market positions, Mittelstand firms must transform themselves and their business models. This dissertation uses quantitative methods and contributes to a deeper understanding of the distinct needs and influencing factors of the digital transformation of Mittelstand firms. The results of the empirical analyses of a unique database of 525 mid-sized German manufacturing firms, comprising both firm-related information and survey data, show that organizational capabilities and characteristics significantly influence the digital transformation of Mittelstand firms. The results support the assumption that dynamic capabilities promote the digital transformation of such firms and underline the important role of ownership structure, especially regarding family influence, for the digital transformation of the business model and the pursuit of growth goals with digitalization. In addition to the digital transformation of German Mittelstand firms, this dissertation examines the economic success and regional impact of Hidden Champions and hence, contributes to a better understanding of the Hidden Champion phenomenon. Using quantitative methods, it can be empirically proven that Hidden Champions outperform other mid-sized firms in financial terms and promote regional development. Consequently, the results of this dissertation provide valuable research contributions and offer various practical implications for firm managers and owners as well as policy makers.
This thesis addresses three different topics from the fields of mathematical finance, applied probability and stochastic optimal control. Correspondingly, it is subdivided into three independent main chapters each of which approaches a mathematical problem with a suitable notion of a stochastic particle system.
In Chapter 1, we extend the branching diffusion Monte Carlo method of Henry-Labordère et. al. (2019) to the case of parabolic PDEs with mixed local-nonlocal analytic nonlinearities. We investigate branching diffusion representations of classical solutions, and we provide sufficient conditions under which the branching diffusion representation solves the PDE in the viscosity sense. Our theoretical setup directly leads to a Monte Carlo algorithm, whose applicability is showcased in two stylized high-dimensional examples. As our main application, we demonstrate how our methodology can be used to value financial positions with defaultable, systemically important counterparties.
In Chapter 2, we formulate and analyze a mathematical framework for continuous-time mean field games with finitely many states and common noise, including a rigorous probabilistic construction of the state process. The key insight is that we can circumvent the master equation and reduce the mean field equilibrium to a system of forward-backward systems of (random) ordinary differential equations by conditioning on common noise events. We state and prove a corresponding existence theorem, and we illustrate our results in three stylized application examples. In the absence of common noise, our setup reduces to that of Gomes, Mohr and Souza (2013) and Cecchin and Fischer (2020).
In Chapter 3, we present a heuristic approach to tackle stochastic impulse control problems in discrete time. Based on the work of Bensoussan (2008) we reformulate the classical Bellman equation of stochastic optimal control in terms of a discrete-time QVI, and we prove a corresponding verification theorem. Taking the resulting optimal impulse control as a starting point, we devise a self-learning algorithm that estimates the continuation and intervention region of such a problem. Its key features are that it explores the state space of the underlying problem by itself and successively learns the behavior of the optimally controlled state process. For illustration, we apply our algorithm to a classical example problem, and we give an outlook on open questions to be addressed in future research.
Zeitgleich mit stetig wachsenden gesellschaftlichen Herausforderungen haben im vergangenen Jahrzehnt Sozialunternehmen stark an Bedeutung gewonnen. Sozialunternehmen verfolgen das Ziel, mit unternehmerischen Mitteln gesellschaftliche Probleme zu lösen. Da der Fokus von Sozialunternehmen nicht hauptsächlich auf der eigenen Gewinnmaximierung liegt, haben sie oftmals Probleme, geeignete Unternehmensfinanzierungen zu erhalten und Wachstumspotenziale zu verwirklichen.
Zur Erlangung eines tiefergehenden Verständnisses des Phänomens der Sozialunternehmen untersucht der erste Teil dieser Dissertation anhand von zwei Studien auf der Basis eines Experiments das Entscheidungsverhalten der Investoren von Sozialunternehmen. Kapitel 2 betrachtet daher das Entscheidungsverhalten von Impact-Investoren. Der von diesen Investoren verfolgte Investmentansatz „Impact Investing“ geht über eine reine Orientierung an Renditen hinaus. Anhand eines Experiments mit 179 Impact Investoren, die insgesamt 4.296 Investitionsentscheidungen getroffen haben, identifiziert eine Conjoint-Studie deren wichtigste Entscheidungskriterien bei der Auswahl der Sozialunternehmen. Kapitel 3 analysiert mit dem Fokus auf sozialen Inkubatoren eine weitere spezifische Gruppe von Unterstützern von Sozialunternehmen. Dieses Kapitel veranschaulicht auf der Basis des Experiments die Motive und Entscheidungskriterien der Inkubatoren bei der Auswahl von Sozialunternehmen sowie die von ihnen angebotenen Formen der nichtfinanziellen Unterstützung. Die Ergebnisse zeigen unter anderem, dass die Motive von sozialen Inkubatoren bei der Unterstützung von Sozialunternehmen unter anderem gesellschaftlicher, finanzieller oder reputationsbezogener Natur sind.
Der zweite Teil erörtert auf der Basis von zwei quantitativ empirischen Studien, inwiefern die Registrierung von Markenrechten sich zur Messung sozialer Innovationen eignet und mit finanziellem und sozialem Wachstum von sozialen Startups in Verbindung steht. Kapitel 4 erörtert, inwiefern Markenregistrierungen zur Messung von sozialen Innovationen dienen können. Basierend auf einer Textanalyse der Webseiten von 925 Sozialunternehmen (> 35.000 Unterseiten) werden in einem ersten Schritt vier Dimensionen sozialer Innovationen (Innovations-, Impact-, Finanz- und Skalierbarkeitsdimension) ermittelt. Darauf aufbauend betrachtet dieses Kapitel, wie verschiedene Markencharakteristiken mit den Dimensionen sozialer Innovationen zusammenhängen. Die Ergebnisse zeigen, dass insbesondere die Anzahl an registrierten Marken als Indikator für soziale Innovationen (alle Dimensionen) dient. Weiterhin spielt die geografische Reichweite der registrierten Marken eine wichtige Rolle. Aufbauend auf den Ergebnissen von Kapitel 4 untersucht Kapitel 5 den Einfluss von Markenregistrierungen in frühen Unternehmensphasen auf die weitere Entwicklung der hybriden Ergebnisse von sozialen Startups. Im Detail argumentiert Kapitel 5, dass sowohl die Registrierung von Marken an sich als auch deren verschiedene Charakteristiken unterschiedlich mit den sozialen und ökonomischen Ergebnissen von sozialen Startups in Verbindung stehen. Anhand eines Datensatzes von 485 Sozialunternehmen zeigen die Analysen aus Kapitel 5, dass soziale Startups mit einer registrierten Marke ein vergleichsweise höheres Mitarbeiterwachstum aufweisen und einen größeren gesellschaftlichen Beitrag leisten.
Die Ergebnisse dieser Dissertation weiten die Forschung im Social Entrepreneurship-Bereich weiter aus und bieten zahlreiche Implikationen für die Praxis. Während Kapitel 2 und 3 das Verständnis über die Eigenschaften von nichtfinanziellen und finanziellen Unterstützungsorganisationen von Sozialunternehmen vergrößern, schaffen Kapitel 4 und 5 ein größeres Verständnis über die Bedeutung von Markenanmeldungen für Sozialunternehmen.
In this thesis, we consider the solution of high-dimensional optimization problems with an underlying low-rank tensor structure. Due to the exponentially increasing computational complexity in the number of dimensions—the so-called curse of dimensionality—they present a considerable computational challenge and become infeasible even for moderate problem sizes.
Multilinear algebra and tensor numerical methods have a wide range of applications in the fields of data science and scientific computing. Due to the typically large problem sizes in practical settings, efficient methods, which exploit low-rank structures, are essential. In this thesis, we consider an application each in both of these fields.
Tensor completion, or imputation of unknown values in partially known multiway data is an important problem, which appears in statistics, mathematical imaging science and data science. Under the assumption of redundancy in the underlying data, this is a well-defined problem and methods of mathematical optimization can be applied to it.
Due to the fact that tensors of fixed rank form a Riemannian submanifold of the ambient high-dimensional tensor space, Riemannian optimization is a natural framework for these problems, which is both mathematically rigorous and computationally efficient.
We present a novel Riemannian trust-region scheme, which compares favourably with the state of the art on selected application cases and outperforms known methods on some test problems.
Optimization problems governed by partial differential equations form an area of scientific computing which has applications in a variety of areas, ranging from physics to financial mathematics. Due to the inherent high dimensionality of optimization problems arising from discretized differential equations, these problems present computational challenges, especially in the case of three or more dimensions. An even more challenging class of optimization problems has operators of integral instead of differential type in the constraint. These operators are nonlocal, and therefore lead to large, dense discrete systems of equations. We present a novel solution method, based on separation of spatial dimensions and provably low-rank approximation of the nonlocal operator. Our approach allows the solution of multidimensional problems with a complexity which is only slightly larger than linear in the univariate grid size; this improves the state of the art for a particular test problem problem by at least two orders of magnitude.
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.