The use of permutation representations in structural computations in large finite matrix groups

We determine the minimal degree permutation representations of all finite groups with trivial soluble radical, and describe applications to structural computations in large finite matrix groups that use the output of the CompositionTree algorithm. We also describe how this output can be used to help find an effective base and strong generating set for such groups. We have implemented the resulting algorithms in Magma, and we report on their performance

Mind maps and machine learning: An automation framework for qualitative research in entrepreneurship education

Entrepreneurship Education researchers often measure entrepreneurial motivation of college students. It is important for stakeholders, such as policymakers and educators, to assert if entrepreneurship education can encourage students to become entrepreneurs, as well as to understand factors that influence entrepreneurial motivation. For that purpose, researchers have used different methods and instruments to measure students\u27 entrepreneurial motivation. Most of these methods are quantitative, e.g., closed-ended surveys, whereas qualitative methods, e.g., open-ended surveys, are rarely used. Mind maps are an attractive qualitative survey tool because they capture the individual\u27s reflections, thoughts, and experiences. For Entrepreneurship Education, mind maps can be utilized to measure students\u27 entrepreneurial motivation. However, qualitative analysis of mind maps in business studies has been manually performed through human coding, which is time-consuming and labor-intensive, and of questionable reliability when more than one person does the analysis. This dissertation provides a novel automation framework to address these challenges with an interdisciplinary solution that integrates deductive and inductive qualitative content analysis approaches with the computational power of machine learning algorithms and statistical Natural Language Processing to automate the analysis of mind maps. The framework includes four sequential steps: selecting a qualitative content analysis approach, collecting and preprocessing mind maps, automating the analysis, and validating the reliability and model evaluation. Experimentation and hypotheses testing for the automation framework are performed. The results show that the performance of classification models when applied to the automated deductive analysis of mind maps, and the performance of Structural Topic Model when applied to the automated inductive analysis of mind maps, are similar to that of manual mind maps analysis. The utility of mind map topology in the process automation is evaluated. Findings indicate that even though inserting mind map topology as features into the dataset positively affects performance, the improvement is not statistically significant. On the other hand, treating nodes as the unit of analysis while applying Structural Topic Model to automate inductive analysis generates latent topics that follow a similar pattern to manual analysis. This study examines the feasibility of applying the automation framework to Entrepreneurship Education research. Text classification algorithms and STM are used for the first time to automate the analysis of mind maps, and STM is applied for the first time in Entrepreneurship Education research. The automation framework offers a unique and advanced qualitative research design that can be employed by EE researchers to benefit the EE best practices. The automation framework can enhance EE qualitative research by extracting textual statistical inference, shortening labor and time required by the analysis, and measuring entrepreneurial motivations with machine learning and Natural Language Processing techniques

Finding "small' matrices P,Q such that PDQ = S

Given an integer matrix A, there is a unique matrix S of a particular form, called the Smith Normal Form, and non-unique unimodular matrices P and Q such that PAQ = S. It is often the case that these matrices P and Q will be used for further calculation, and as such it is desirable to find P and Q with small entries. In this thesis we address the problem of finding such P and Q with small entries, in particular in the case where A is a diagonal matrix, which arises as a final step in many published algorithms. Heuristic algorithms are developed which appear to do well in practice and some theory is developed to explain this behaviour. We also give an account of the implementation of an alternative algorithm which bypasses this intermediary diagonal form. The basic theoretical development of this is work by Storjohan

Players Unleashed ! Modding The Sims and the Culture of Gaming

The author of this hugely informative study explores the question of what happens when players practise and negotiate computer code, various ideologies, and the game itself by modding (modifying a game) in the context of The Sims, the bestselling computer game of all time.Sihvonen examines the technical and material specificities of The Sims mods, as well as their cultural context. Viewed as a manifestation of participatory culture, modding makes PC games ultimately malleable: players reconfigure the game by creating new content, altering the code and changing the behaviours of the game engine. Using a semiotic framework, Sihvonen suggests a signification process that includes representation, interpretation, investigation and experimentation with the game system and rules. From its historical roots in the shoot’em up games, the author bares the fascinating evolution and dynamics of modding, where gender stereotypes, the thrills of hacking and living the Sims’ American Dream intersect with the aesthetic and operational dimensions of modding

Combinatorial structures in quantum information

This work is an exploration of how graphs and permutations can be applied in the context of quantum information processing. In Chapter 2 we consider problems about the permutations of the subsystems of a quantum system. Explicitly, we attempt to understand the problem of determining if two quantum states of N qubits are isomorphic: if one can be obtained from the other by permuting its subsystems. We show that the well known graph isomorphism problem is a special case of state isomorphism. We also show that the complement of state isomorphism, the problem of determining if two states are not isomorphic, can be verified by a quantum interactive proof system, and that this proof system can be made statistical zero knowledge. We also consider the complexity of isomorphism problems for stabilizer states, and mixed states. In Chapter 3 we work with a special class of quantum states called grid states, in an effort to develop a toy model for mixed state entanglement. The key idea with grid states is that they can be represented by what we call a grid-labelled graph, literally, a graph forced to have vertices on a two dimensional grid. We show that whether or not a grid state is entangled can sometimes be determined solely from the structural properties of its corresponding grid-labelled graph. We use the grid state framework to build families of bound entangled states, suggesting that even in this restricted setting detecting entanglement is non-trivial and will require more than a single entanglement criterion