Open Access

According to the cognitive action architecture approach (CAA-A; Schack, 2002, 2004), mental representations play a central role in movement control, as they are hierarchically structured in long-term memory and differentiate due to expertise. By means of structural dimensional analysis - motoric (SDA-M; Schack, 2012), movements are subdivided into basic action concepts (BACs) that are related to each other, to make mental representation structures visible. The method seeks to psychometrically depict the structural dimensions of conceptually ordered motor knowledge, both case-by-case and group-specific, and has been applied to a variety of sports contexts (Land, Volchenkov, Bläsing, & Schack, 2013). Although the examination of mental representations seems promising regarding the gain of insights into the structure of movements, motor learning processes and the relation of cognitive and movement structures, research in the field of educational research has not been conducted so far. Therefore, the aim of this dissertation project is to address the main research question: What influence can the knowledge about mental representation structures of movements have in the context of physical education and the optimization processes of learning and teaching? The research issue, research program and research questions are presented in the general introduction of this thesis (chapter 1). To answer the main research question, three different perspectives are introduced in the main part. The first perspective focuses on the structure of motor skills and the methodological approach to acquiring the mental representation structures. The practical implementation of the SDA-M is discussed in a text-image comparison of questionnaire items (chapter 2). The study aimed at determining an appropriate item format for the use of the SDA-M in the context of physical education. In light of the findings, the use of text or combined items is recommended when applying the SDA-M to children or adolescents. The second perspective focuses on knowledge about the mental representation structure of learners and their execution of the skill. Based on pupils’ mental representation structure, specific instructions are developed that might contribute to the optimization of movement execution (chapter 3). Results revealed that specific instructions based on pupils’ mental representation of a gymnastics skill have a positive impact on their mental representation structure and on their motor performance. The third perspective focuses on knowledge about the mental representation structure of teachers, here represented by sports students, examining its relation with their evaluation of pupils’ movements (chapter 4). Results indicate that more structured mental representations are linked with a more precise performance evaluation. Therefore, a relation between physical education students’ mental representation structure and their evaluation of gymnastics skills can be assumed. Conclusively, in the general discussion, the key findings are highlighted, limitations are discussed and an outlook concerning practical implications and further research is provided (chapter 5). In sum, according to the findings of this dissertation, the acquisition and analysis of the structure of mental representations might constitute an effective means of optimizing the quality of physical education and can be seen as important for improving physical education teacher training as well as motor learning processes in general.

Social media has become an integral part of numerous individuals as well as organizations, with many services being used frequently by a majority of people. Along with its widespread use, the amount of information explodes when people use these services. This demands for efficient tools as well as methods to assist data management and retrieval. Annotating resources by keywords, known as the tagging task, is a solution to improve categorizability and findability of resources. However, tagging is a human, time-consuming task, which requires the user's focus to figure out many keywords in a short moment and manually enter them into the system. To encourage users to tag their resources more correctly and frequently, tag recommendation is adopted into the social tagging systems to suggest relevant keywords for resources. In this thesis, we will address the problem of personalized tag recommendation for images and present ways to solve this problem by combining the advantages of the user relation with the images' content. In order to suggest tags for unobserved images, their visual contents are used to replace the index-based information of the image entity in the tagging relations. Because the limitation of low-level features does not show the "content" of images, we propose to utilize a deep learning based approach to learn high-level visual features concurrently with the scoring-tag estimator. For the tag predictor, a latent factor model or a multi-layer perceptron is selected to compute scores of tags by which the top selected tags are sorted in descending order. As a further development upon our findings, we examine the inside and outside context of images to enhance the accuracy of estimators. Regarding the image-inside context, we are motivated by the fact that objects, such as cars or cats are influential on the user's selection criteria. Regarding the image-outside context, the image's surrounding text contributes to the clarity of the image's content for different users. We consider these contextual features as a supporting part which is combined with the mainly visual representation to enhance the tag recommendation performance. Finally, as an additional technique, transfer learning is also adapted to support the proposed models to overcome the limitations of too small training data and boost up their performance. This thesis demonstrates the usefulness and versatility of deep learning approaches for tag recommendation and highlights the importance of the learned image's content in predicting personalized tags. Directions for future work include semantic enhancements to context-based representation and extensions of the content-aware approaches to different recommendation scenarios.

Number theory is one of the oldest mathematical areas. This is perhaps one of the reasons why there are many connections between number theory and other areas inside mathematics. This thesis is devoted to some of those connections. In the first part of this thesis I describe known connections between number theory and twelve other areas, namely analysis, sequences, applied mathematics (i.e., probability theory and numerical mathematics), topology, graph theory, linear algebra, geometry, algebra, differential geometry, complex analysis, physics and computer science, and algebraic geometry. We will see that the concepts will not only connect number theory with these areas but also yield connections among themselves. In the second part I present some new results in four topics connecting number theory with computer science, graph theory, algebra, and linear algebra and analysis, respectively. [...] In the next topic I determine the neighbourhood of the neighourhood of vertices in some special graphs. This problem can be formulated with generators of subgroups in abelian groups and is a direct generalization of a corresponding result for cyclic groups. In the third chapter I determine the number of solutions of some linear equations over factor rings of principal ideal domains R. In the case R = Z this can be used to bound sums appearing in the circle method. Lastly I investigate the puzzle “Lights Out” as well as variants of it. Of special interest is the question of complete solvability, i.e., those cases in which all starting boards are solvable. I will use various number theoretical tools to give a criterion for complete solvability depending on the board size modulo 30 and show how this puzzle relates to algebraic number theory.

Cartel theory, being the doctrine of the cooperation between entrepreneurs of the same industry, was founded in 1883 by the Austrian Friedrich Kleinwächter. This theory, with its specific concepts, was essentially confined to the German-speaking world until World War I. Other cultural or language areas such as the Anglosphere and the Romanic countries had different terminologies and different insights into the topic: There were theories about syndicates, combinations or trusts. The peculiarities of the respective economic cultures hindered a unification of the terms, their meanings and their underlying theories up to the early 1920s. From the mid-1890s, German cartel theory had undergone several conceptual reforms and outdid its foreign-language counterparts in terms of differentiation. Until about 1910, cartel theory (besides American trust theory) had become the most respected theory on economic unions. After World War I, international cartels became needed. Since 1929, the terminology of German cartel theory became fundamental for the corresponding debates, which had taken place first at the International Economic Conference of the League of Nations in 1927. With the entry into the 1930s, the German cartel doctrine had become a scientific standard worldwide. This recognition makes it clear that German economic science was by no means in every respect ‹backward› in the interwar period, which is the current state of research. Therefore, German economics was better prepared than any other national economic discipline for the development of an ever more organized economy as evoked by the extensive cartelization and state-initiated regulation of the 1930s. So, cartel-related expertise was increasingly used in the policy of the controlled economy of the Third Reich.

This work is rooted in the fields of English Literary Studies, Cultural Studies, and Jewish American Studies. It examines memory representation in exemplary works published around the millennial change by third generation Jewish American writers Jonathan Safran Foer, Shalom Auslander, and Nicole Krauss. The focus lies on the latter’s work. Symbolic characters and objects connected to memory are discerned and analyzed in detail.