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.

Objective Our study investigated body image representations in female patients with anorexia nervosa and healthy controls using a size estimation with pictures of their own body. We also explored a method to reduce body image distortions through right hemispheric activation. Method Pictures of participants’ own bodies were shown on the left or right visual fields for 130 ms after presentation of neutral, positive, or negative word primes, which could be self-relevant or not, with the task of classifying the picture as “thinner than”, “equal to”, or “fatter than” one’s own body. Subsequently, activation of the left- or right hemispheric through right- or left-hand muscle contractions for 3 min., respectively. Finally, participants completed the size estimation task again. Results The distorted “fatter than” body image was found only in patients and only when a picture of their own body appeared on the right visual field (left hemisphere) and was preceded by negative self-relevant words. This distorted perception of the patients’ body image was reduced after left-hand muscle contractions (right hemispheric activation). Discussion To reduce body image distortions it is advisable to find methods that help anorexia nervosa patients to increase their self-esteem. The body image distortions were ameliorated after right hemispheric activation. A related method to prevent distorted body-image representations in these patients may be Eye Movement Desensitization and Reprocessing (EMDR) therapy.

Academic achievement is a central outcome in educational research, both in and outside higher education, has direct effects on individual’s professional and financial prospects and a high individual and public return on investment. Theories comprise cognitive as well as non-cognitive influences on achievement. Two examples frequently investigated in empirical research are knowledge (as a cognitive determinant) and stress (as a non-cognitive determinant) of achievement. However, knowledge and stress are not stable, what raises questions as to how temporal dynamics in knowledge on the one hand and stress on the other contribute to achievement. To study these contributions in the present doctoral dissertation, I used meta-analysis, latent profile transition analysis, and latent state-trait analysis. The results support the idea of knowledge acquisition as a cumulative and long-term process that forms the basis for academic achievement and conceptual change as an important mechanism for the acquisition of knowledge in higher education. Moreover, the findings suggest that students’ stress experiences in higher education are subject to stable, trait-like influences, as well as situational and/or interactional, state-like influences which are differentially related to achievement and health. The results imply that investigating the causal networks between knowledge, stress, and academic achievement is a promising strategy for better understanding academic achievement in higher education. For this purpose, future studies should use longitudinal designs, randomized controlled trials, and meta-analytical techniques. Potential practical applications include taking account of students’ prior knowledge in higher education teaching and decreasing stress among higher education students.

External capital plays an important role in financing entrepreneurial ventures, due to limited internal capital sources. An important external capital provider for entrepreneurial ventures are venture capitalists (VCs). VCs worldwide are often confronted with thousands of proposals of entrepreneurial ventures per year and must choose among all of these companies in which to invest. Not only do VCs finance companies at their early stages, but they also finance entrepreneurial companies in their later stages, when companies have secured their first market success. That is why this dissertation focuses on the decision-making behavior of VCs when investing in later-stage ventures. This dissertation uses both qualitative as well as quantitative research methods in order to provide answer to how the decision-making behavior of VCs that invest in later-stage ventures can be described. Based on qualitative interviews with 19 investment professionals, the first insight gained is that for different stages of venture development, different decision criteria are applied. This is attributed to different risks and goals of ventures at different stages, as well as the different types of information available. These decision criteria in the context of later-stage ventures contrast with results from studies that focus on early-stage ventures. Later-stage ventures possess meaningful information on financials (revenue growth and profitability), the established business model, and existing external investors that is not available for early-stage ventures and therefore constitute new decision criteria for this specific context. Following this identification of the most relevant decision criteria for investors in the context of later-stage ventures, a conjoint study with 749 participants was carried out to understand the relative importance of decision criteria. The results showed that investors attribute the highest importance to 1) revenue growth, (2) value-added of products/services for customers, and (3) management team track record, demonstrating differences when compared to decision-making studies in the context of early-stage ventures. Not only do the characteristics of a venture influence the decision to invest, additional indirect factors, such as individual characteristics or characteristics of the investment firm, can influence individual decisions. Relying on cognitive theory, this study investigated the influence of various individual characteristics on screening decisions and found that both investment experience and entrepreneurial experience have an influence on individual decision-making behavior. This study also examined whether goals, incentive structures, resources, and governance of the investment firm influence decision making in the context of later-stage ventures. This study particularly investigated two distinct types of investment firms, family offices and corporate venture capital funds (CVC), which have unique structures, goals, and incentive systems. Additional quantitative analysis showed that family offices put less focus on high-growth firms and whether reputable investors are present. They tend to focus more on the profitability of a later-stage venture in the initial screening. The analysis showed that CVCs place greater importance on product and business model characteristics than other investors. CVCs also favor later-stage ventures with lower revenue growth rates, indicating a preference for less risky investments. The results provide various insights for theory and practice.

Die Dissertation untersucht vergleichend deutsch-japanische fotografische Kriegspropaganda des Zweiten Weltkrieges anhand der zu jener Zeit auflagenstärksten illustrierten Zeitschriften "Illustrierter Beobachter" auf deutscher und "Shashin Shūhō" (Fotografische Wochenzeitung) auf japanischer Seite. Unter Rückgriff auf die ikonographisch-ikonologische Methode des Kunsthistorikers Erwin Panofsky bei gleichzeitiger Bezugnahme auf das Bildverständnis Charles Sanders Peirces werden Muster der bildlichen Darstellung von Kindern und Jugendlichen analysiert, um hierdurch Rückschlüsse zu ziehen auf Gemeinsamkeiten und Unterschiede in der Ausgestaltung der Bildpropaganda beider Länder unmittelbar vor und im Zweiten Weltkrieg (1939-1945), auf allgemeine Tendenzen in der Gestaltung von Propaganda im selben Zeitraum, auf die Organisation und Funktion von Propaganda in radikalnationalistischen Staaten. Gleichzeitig wird durch Einbeziehung der Rezipientensicht die Frage nach Mehrdeutigkeit und, hiermit einhergehend, Wirkungsweise und Wirkungsgrad der Propaganda gestellt. Schwerpunkt der Untersuchung bilden sämtliche publizierten Ausgaben der zweiten Jahreshälften 1938 und 1943.