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Our goal is to approximate energy forms on suitable fractals by discrete graph energies and certain metric measure spaces, using the notion of quasi-unitary equivalence. Quasi-unitary equivalence generalises the two concepts of unitary equivalence and norm resolvent convergence to the case of operators and energy forms defined in varying Hilbert spaces.
More precisely, we prove that the canonical sequence of discrete graph energies (associated with the fractal energy form) converges to the energy form (induced by a resistance form) on a finitely ramified fractal in the sense of quasi-unitary equivalence. Moreover, we allow a perturbation by magnetic potentials and we specify the corresponding errors.
This aforementioned approach is an approximation of the fractal from within (by an increasing sequence of finitely many points). The natural step that follows this realisation is the question whether one can also approximate fractals from outside, i.e., by a suitable sequence of shrinking supersets. We partly answer this question by restricting ourselves to a very specific structure of the approximating sets, namely so-called graph-like manifolds that respect the structure of the fractals resp. the underlying discrete graphs. Again, we show that the canonical (properly rescaled) energy forms on such a sequence of graph-like manifolds converge to the fractal energy form (in the sense of quasi-unitary equivalence).
From the quasi-unitary equivalence of energy forms, we conclude the convergence of the associated linear operators, convergence of the spectra and convergence of functions of the operators – thus essentially the same as in the case of the usual norm resolvent convergence.
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.
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.
Many combinatorial optimization problems on finite graphs can be formulated as conic convex programs, e.g. the stable set problem, the maximum clique problem or the maximum cut problem. Especially NP-hard problems can be written as copositive programs. In this case the complexity is moved entirely into the copositivity constraint.
Copositive programming is a quite new topic in optimization. It deals with optimization over the so-called copositive cone, a superset of the positive semidefinite cone, where the quadratic form x^T Ax has to be nonnegative for only the nonnegative vectors x. Its dual cone is the cone of completely positive matrices, which includes all matrices that can be decomposed as a sum of nonnegative symmetric vector-vector-products.
The related optimization problems are linear programs with matrix variables and cone constraints.
However, some optimization problems can be formulated as combinatorial problems on infinite graphs. For example, the kissing number problem can be formulated as a stable set problem on a circle.
In this thesis we will discuss how the theory of copositive optimization can be lifted up to infinite dimension. For some special cases we will give applications in combinatorial optimization.
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.
Entrepreneurial ventures are associated with economic growth, job creation, and innovation. Most entrepreneurial ventures need external funding to succeed. However, they often find it difficult to access traditional forms of financing, such as bank loans. To overcome this hurdle and to provide entrepreneurial ventures with badly-needed external capital, many types of entrepreneurial finance have emerged over the past decades and continue to emerge today. Inspired by these dynamics, this postdoctoral thesis contains five empirical studies that address novel questions regarding established (e.g., venture capital, business angels) and new types of entrepreneurial finance (i.e., initial coin offerings).
With two-thirds to three-quarters of all companies, family firms are the most common firm type worldwide and employ around 60 percent of all employees, making them of considerable importance for almost all economies. Despite this high practical relevance, academic research took notice of family firms as intriguing research subjects comparatively late. However, the field of family business research has grown eminently over the past two decades and has established itself as a mature research field with a broad thematic scope. In addition to questions relating to corporate governance, family firm succession and the consideration of entrepreneurial families themselves, researchers mainly focused on the impact of family involvement in firms on their financial performance and firm strategy. This dissertation examines the financial performance and capital structure of family firms in various meta-analytical studies. Meta-analysis is a suitable method for summarizing existing empirical findings of a research field as well as identifying relevant moderators of a relationship of interest.
First, the dissertation examines the question whether family firms show better financial performance than non-family firms. A replication and extension of the study by O’Boyle et al. (2012) based on 1,095 primary studies reveals a slightly better performance of family firms compared to non-family firms. Investigating the moderating impact of methodological choices in primary studies, the results show that outperformance holds mainly for large and publicly listed firms and with regard to accounting-based performance measures. Concerning country culture, family firms show better performance in individualistic countries and countries with a low power distance.
Furthermore, this dissertation investigates the sensitivity of family firm performance with regard to business cycle fluctuations. Family firms show a pro-cyclical performance pattern, i.e. their relative financial performance compared to non-family firms is better in economically good times. This effect is particularly pronounced in Anglo-American countries and emerging markets.
In the next step, a meta-analytic structural equation model (MASEM) is used to examine the market valuation of public family firms. In this model, profitability and firm strategic choices are used as mediators. On the one hand, family firm status itself does not have an impact on firms‘ market value. On the other hand, this study finds a positive indirect effect via higher profitability levels and a negative indirect effect via lower R&D intensity. A split consideration of family ownership and management shows that these two effects are mainly driven by family ownership, while family management results in less diversification and internationalization.
Finally, the dissertation examines the capital structure of public family firms. Univariate meta-analyses indicate on average lower leverage ratios in family firms compared to non-family firms. However, there is significant heterogeneity in mean effect sizes across the 45 countries included in the study. The results of a meta-regression reveal that family firms use leverage strategically to secure their controlling position in the firm. While strong creditor protection leads to lower leverage ratios in family firms, strong shareholder protection has the opposite effect.
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.
Entrepreneurship has become an essential phenomenon all over the world because it is a major driving force behind the economic growth and development of a country. It is widely accepted that entrepreneurship development in a country creates new jobs, pro-motes healthy competition through innovation, and benefits the social well being of individuals and societies. The policymakers in both developed and developing countries focus on entrepreneurship because it helps to alleviate impediments to economic development and social welfare. Therefore, policymakers and academic researchers consider the promotion of entrepreneurship as essential for the economy and research-based support is needed for further development of entrepreneurship activities.
The impact of entrepreneurial activities on economic and social development also varies from country to country. The effect of entrepreneurial activities on economic and social development also varies from country to country because the level of entrepreneur-ship activities also varies from one region to another or one country to another. To under-stand these variations, policymakers have investigated the determinants of entrepreneur-ship at different levels, such as the individual, industry, and country levels. Moreover, entrepreneurship behavior is influenced by various personal and environmental level factors. However, these personal-level factors cannot be separated from the surrounding environment.
The link between religion and entrepreneurship is well established and can be traced back to Weber (1930). Researchers have analyzed the relationship between religion and entrepreneurship from various perspectives, and the research related to religion and entrepreneurship is diversified and scattered across disciplines. This dissertation tries to explain the link between religion and entrepreneurship, specifically Islamic religion and entrepreneurship. Technically this dissertation comprises three parts. The first part of this dissertation consists of two chapters that discuss the definition and theories of entrepreneurship (Chapter 2) and the theoretical relationship between religion and entrepreneur-ship (Chapter 3).
The second part of this dissertation (Chapter 4) provides an overview of the field with a purpose to gain a better understanding of the field’s current state of knowledge to bridge the different views and perspectives. In order to provide an overview of the field, a systematic literature search leading to a descriptive overview of the field based on 270 articles published in 163 journals Subsequently, bibliometric methods are used to identify thematic clusters, the most influential authors and articles, and how they are connected.
The third part of this dissertation (Chapter 5) empirically evaluates the influence of Islamic values and Islamic religious practices on entrepreneurship intentions within the Islamic community. Using the theory of planned behavior as a theoretical lens, we also take into account that the relationship between religion and entrepreneurial intentions can be mediated by individual’s attitude towards entrepreneurship. A self-administrative questionnaire was used to collect the responses from a sample of 1895 Pakistani university students. A structured equation modeling was adopted to perform a nuanced assessment of the relationship between Islamic values and practices and entrepreneurship intentions and to account for mediating effect of attitude towards entrepreneurship.
The research on religion and entrepreneurship has increased sharply during the last years and is scattered across various academic disciplines and fields. The analysis identifies and characterize the most important publications, journals, and authors in the area and map the analyzed religions and regions. The comprehensive overview of previous studies allows us to identify research gaps and derive avenues for future research in a substantiated way. Moreover, this dissertation helps the research scholars to understand the field in its entirety, identify relevant articles, and to uncover parallels and differences across religions and regions. Besides, the study reveals a lack of empirical research related to specific religions and specific regions. Therefore, scholars can take these regions and religions into consideration when conducting empirical research.
Furthermore, the empirical analysis about the influence of Islamic religious values and Islamic religious practices show that Islamic values served as a guiding principle in shaping people’s attitudes towards entrepreneurship in an Islamic community; they had an indirect influence on entrepreneurship intention through attitude. Similarly, the relationship between Islamic religious practices and the entrepreneurship intentions of students was fully mediated by the attitude towards entrepreneurship. Furthermore, this dissertation contributes to prior research on entrepreneurship in Islamic communities by applying a more fine-grained approach to capture the link between religion and entrepreneurship. Moreover, it contributes to the literature on entrepreneurship intentions by showing that the influence of religion on entrepreneurship intentions is mainly due to religious values and practices, which shape the attitude towards entrepreneurship and thereby influence entrepreneurship intentions in religious communities. The entrepreneur-ship research has put a higher emphasis on assessing the influence of a diverse set of con-textual factors. This dissertation introduces Islamic values and Islamic religious practices as critical contextual factors that shape entrepreneurship in countries that are characterized by the Islamic religion.
Nonlocal operators are used in a wide variety of models and applications due to many natural phenomena being driven by nonlocal dynamics. Nonlocal operators are integral operators allowing for interactions between two distinct points in space. The nonlocal models investigated in this thesis involve kernels that are assumed to have a finite range of nonlocal interactions. Kernels of this type are used in nonlocal elasticity and convection-diffusion models as well as finance and image analysis. Also within the mathematical theory they arouse great interest, as they are asymptotically related to fractional and classical differential equations.
The results in this thesis can be grouped according to the following three aspects: modeling and analysis, discretization and optimization.
Mathematical models demonstrate their true usefulness when put into numerical practice. For computational purposes, it is important that the support of the kernel is clearly determined. Therefore nonlocal interactions are typically assumed to occur within an Euclidean ball of finite radius. In this thesis we consider more general interaction sets including norm induced balls as special cases and extend established results about well-posedness and asymptotic limits.
The discretization of integral equations is a challenging endeavor. Especially kernels which are truncated by Euclidean balls require carefully designed quadrature rules for the implementation of efficient finite element codes. In this thesis we investigate the computational benefits of polyhedral interaction sets as well as geometrically approximated interaction sets. In addition to that we outline the computational advantages of sufficiently structured problem settings.
Shape optimization methods have been proven useful for identifying interfaces in models governed by partial differential equations. Here we consider a class of shape optimization problems constrained by nonlocal equations which involve interface-dependent kernels. We derive the shape derivative associated to the nonlocal system model and solve the problem by established numerical techniques.