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Abstract: In this doctoral dissertation, we address the counting of Hamiltonian cycles in 2-tiled graphs. These graphs are a generalization of the construction of large 2-crossing-critical graphs. We also address the study of the learning process involved in solving unsolved mathematical problems, integrating psychological theories of optimal experience (flow) and deliberate practice into a mathematical framework called the dense challenge domain. The introduction presents fundamental graph theory concepts and an overview of ordinal numbers essential for understanding the core of the dissertation. In the second chapter, known results from relevant related fields are introduced, along with the contributions of the doctoral dissertation. In the third chapter, we address the problem of counting Hamiltonian cycles in 2-tiled graphs. First, we introduce basic concepts such as tile, 2-tile, tiled graphs, and 2-tiled graphs. This is followed by results leading to the characterization of Hamiltonian cycle types in 2-tiled graphs and then the introduction of algorithms that count each type of Hamiltonian cycles. We also demonstrate that if the family of 2-tiles used to construct 2-tiled graphs is finite, the algorithms are efficient. Further, we place large 2-crossing-critical graphs in the context of 2-tiled graphs and adapt the previously introduced algorithms to efficiently count all types of Hamiltonian cycles. To describe 2-crossing-critical graphs, we introduce an alphabet and show that 2-traversing and flanking Hamiltonian cycles can be counted by simply counting the occurrences of certain letters from the introduced alphabet. At the end of the chapter, we extend the counting of traversing Hamiltonian cycles to tiled graphs. We attempt to formally capture the experience of this research work in the fourth chapter. We propose a formal mathematical framework for solving a common challenge in mathematical education: how to effectively use limited time to motivate students for research work. We formalize a theoretical mathematical structure called the dense challenge domain and introduce a structured decision process based on Csikszentmihalyi’s theory of flow, Duckworth’s concept of grit, Snowden’s Cynefin framework from decision theory, and Bokal-Steinbacher’s time usage optimization model. Unlike traditional educational research, which focuses on primary and secondary education, our approach emphasizes fostering mathematical thinking at the research level through optimal psychological experience. We formalize an algorithm for evolving the dense challenge domain, ensuring a balance between perceived skill and levels of challenge. We further prove that large 2-crossing-critical graphs satisfy the conditions of the dense challenge domain, providing a solid mathematical foundation for this methodology. Through three pilot studies, we demonstrate that this approach not only maintains student engagement but also leads to publishable research outcomes.
Keywords: Hamiltonian cycle, 2-crossing-critical graph, 2-tiled graph, research realm, dense challenge domain, psychologically optimal experience, Cynefin framework
Published in DKUM: 24.10.2025; Views: 0; Downloads: 5
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Abstract: This study explores how Business and IT Alignment (BITA) influences business performance (PERFO) and corporate sustainability (SPACS) using a mixed-methods case study of an international manufacturing enterprise. The quantitative analysis (PLS-SEM) indicated BITA affects PERFO indirectly through IT service quality (ITSQ), while remote work (EWORK), despite its relation to BITA, showed no significant impact. BITA strongly predicted SPACS by enhancing employees’ sustainability knowledge, confidence, and willingness to act. Qualitative findings from semi-structured interviews revealed a BITA maturity of 3.3 (on a 5-point scale), highlighting its role in sustainability via better decision-making, process optimization, and IT-enabled transparency. Notable discrepancies between managerial and employee perceptions of BITA maturity were identified. Results suggest successful BITA fosters sustainability-oriented behaviour and IT-driven performance improvements, though continuous reinforcement within organizations is required. The study emphasizes the value of integrating qualitative and quantitative methods for comprehensive insights into BITA's impact.
Keywords: business and IT alignment (BITA), IT service quality (ITSQ), business performance (PERFO), corporate sustainability (SPACS), remote work (EWORK), mixed methods research (MMR), PLS-SEM, organizational maturity, sustainability awareness, case study
Published in DKUM: 29.08.2025; Views: 0; Downloads: 6
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Abstract: Subtle physiological patterns within the human organism, such as molecular fluctuations or systemic adaptations, often remain hidden from direct observation due to the inherent variability and noise within biological samples. The liver, a vital organ essential for systemic regulation and toxicological assessment, presents this challenge due to its heightened activity, which can influence enzyme dynamics and metabolic processes. Unlike direct observation, in vitro liver models offer a more precise means of understanding these trends, providing insights into the organ's (patho)physiology, and serving as a platform for toxicity evaluation. However, current liver models lack essential features required to faithfully replicate the liver's microenvironment, resulting in reduced accuracy in toxicity assessments. Furthermore, while researchers emphasize mechanistic insights, such as the molecular processes governing glucose metabolism and cellular energy production, clinicians focus on tangible health outcomes, like blood glucose levels in patients. This disconnect between the objectives and methodologies of basic researchers and clinicians amplifies this gap, hindering effective translational research. Addressing these challenges, a novel liver cell culture system that resembles the in vivo liver microenvironment with clinical instrumentation has been proposed to enhance current liver models, improving their capacity to emulate in vivo conditions. This study introduces a novel liver cell culture system, utilizing a 96-well plate format incorporating hepatic sinusoidal endothelial cells, hepatic stellate cells, Kupffer cells, and hepatocytes to replicate the liver microenvironment. The model integrates clinical instrumentation, specifically a biochemical analyzer to ensure biomarkers closely align with those observed in clinical diagnostics. This design enables researchers to fine-tune conditions that mimic the liver's microanatomy and physiological responses, enhancing its translational potential for toxicity assessments. The approach involves primary cell culture preparation, supernatant analysis through a clinical biochemistry analyzer, and cell viability assessment using the Membrane Potential Cell Viability Assay (MPCVA) method. Additionally, advanced imaging techniques and data analysis tools are incorporated to refine the model's capabilities and ensure greater translatability to clinical applications.
Keywords: in vitro toxicity, liver (patho)physiology, liver in vitro model, membrane potential cell viability assay, translational research
Published in DKUM: 14.08.2025; Views: 0; Downloads: 8
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Abstract: The article lays out the method of the participatory Oral History project "Multilingual Memory of Migration" against the political background of an unacknowledged Austrian migration history and the political paradigm of monolingualism. The participatory concept engages students in a research process of Austrian migration history, addressing especially (but not exclusively) students with an own migration and multilingual background to conduct intergenerational biographical interviews. By benefitting from the students' language skills and community outreach, the project aims at creating a contribution to a national "archive of migration" as such not institutionalized in Austria.
Keywords: migration, multilingualism, participatory research, oral history, intergenerational interviews
Published in DKUM: 29.07.2025; Views: 0; Downloads: 3
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Abstract: On the basis of the analysis of the general characteristics of alternative schools and the methodology of pedagogical research, the comparison and synthesis of the obtained facts were formed. It is pointed out that in the field of pedagogy, the adoption of (positivist) methodology has become a global trend. It emphasizes the uncritical application of research tools from the corpus of quantitative methodology in research of specific educational problems, as well as in research of alternative schools in which the context of the research is significantly different than the one of the conventional public schools.
Keywords: alternative schools, education, research methodology, social and humanistic sciences, teaching
Published in DKUM: 19.06.2025; Views: 0; Downloads: 33
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