In this thesis we study sparse classes of graphs and their properties usable for design of algorithms and data structures. Our specific focus is on the con- cepts of bounded expansion and tree-depth, developed in recent years mainly by J. Nešetřil and P. Ossona de Mendez. We first give a brief introduction to the theory as whole and survey tools and results from related areas of parametrised complexity and algorithmic model theory. The main part of the thesis, application of the theory, presents two new dynamic data structures. The first is for keeping a tree-depth decomposition of a graph, the second counts appearances of fixed subgraphs in a given graph. The time and space complexity of operations of both structures is guaranteed to be low when used for sparse graphs. 1

This thesis aims to apply methods of value investing into developing field of algorithmic trading. Firstly, we investigate the effect of several fundamental variables on stock returns using the fixed effects model and portfolio approach. The results confirm that size and book- to-market ratio explain some variation in stock returns that market alone do not capture. Moreover, we observe a significant positive effect of book-to-market ratio and negative effect of size on future stock returns. Secondly, we try to utilize those variables in a trading algorithm. Using the common performance evaluation tools we test several fundamentally based strategies and discover that investing into small stocks with high book-to-market ratio beats the market in the tested period between 2009 and 2015. Although we have to be careful with conclusions as our dataset has some limitations, we believe that there is a market anomaly in the testing period which may be caused by preference of technical strategies over value investing by market participants.

This thesis explores algorithmic thinking development on a high school student level. In the introduction algorithmic thinking as well as current practices of teaching algorithmic thinking are examined. A closer look on programming languages, programming methods and tools which can be utilised to develop algorithmic thinking (such as robotic kits, personal computers and mobile devices with touch screens) follows. After analyzing general properties of these tools one mobile device is selected and its programming possibilities are then explored in the empirical part of this paper. As part of the selected proactive action research a number of activities as well as overall process approach is first designed following by their practical verification in a high school. Final results are summarised as suggestions for improvements for further teaching.

The diploma thesis deals with the development of algorithmic thinking among the lower-secondary students as one of their digital competences. It is based on the principle of algorithmic thinking related to the concept of computational thinking and it searches for the ways how to develop it in pupils. The theoretical part is supported by Skinner's concept of programmed learning and with the help of gamification proposes the research based on the students' observation in one school year in which the competence is developed. The raised issue is solved by setting a complex set of teaching materials and learning activities (both in the digital environment and unplugged activities) and their partial transfer into the teaching to a virtual, algorithmic environment of the specially designed application called Prográmko. The goal of the thesis is the analysis of the possibilities of how to include the gamification and the programmed learning into the practice of the development of algorithmic thinking taught at the lower-secondary schools. The research also evaluates the applicability of the application Prográmko and the proposed set of materials provided with methodological guidelines in the practice.

Student Number : 8109673 - MSc research report - School of Science Education - Faculty of Science / Many students fail the Fundamental Algorithmic Concepts course, in first year Computer Science at the University of the Witwatersrand. To obtain an understanding of why this occurs, the learning styles and learning approaches of the students studying the course and the relationship of these concepts with student grades were researched. A predominately qualitative paradigm was used, supplemented with quantitative data. Two research designs were selected: a survey to get a broad overview of the sample and an ethnographic design to provide an in-depth description of a small group. Existing instruments were used for the survey, namely Felder and Soloman’s Index of Learning Styles and a learning approach diagnostic test that was constructed in South Africa. An interview with open-ended questions was used for the ethnographic research. Contrary to expectations, the results of the study indicated that the adoption of a deep learning approach did not imply success. The findings suggest that a strategic learning approach may be required to achieve good grades. In contrast to other studies, over 65% of the sample population were black students. It was found that black students tend to adopt a deeper learning approach than the rest of the students. From a learning style perspective there was some new evidence to indicate that the more intuitive or global a student was, the deeper the approach the student adopted to learning. A large percentage (over 80%) of the population were visual learners and an unusually high percentage (over 60%) were reflective learners. The lecturer should match the workload and assessment methods with the desired learning approach of the students. The lecturer should also encourage the students to adopt a strategic learning approach where appropriate. In addition, the lecturer should pay particular attention to incorporating teaching styles that accommodate students with visual and active learning style preferences.

L'algèbre géométrique est un outil permettant de représenter et manipuler les objets géométriques de manière générique, efficace et intuitive. A titre d'exemple, l'Algèbre Géométrique Conforme (CGA), permet de représenter des cercles, des sphères, des plans et des droites comme des objets algébriques. Les intersections entre ces objets sont incluses dans la même algèbre. Il est possible d'exprimer et de traiter des objets géométriques plus complexes comme des coniques, des surfaces quadriques en utilisant une extension de CGA. Cependant due à leur représentation requérant un espace vectoriel de haute dimension, les implantations de l'algèbre géométrique, actuellement disponible, n'autorisent pas une utilisation efficace de ces objets. Dans ce manuscrit, nous présentons tout d'abord une implantation de l'algèbre géométrique dédiée aux espaces vectoriels aussi bien basses que hautes dimensions. L'approche suivie est basée sur une solution hybride de code pré-calculé en vue d'une exécution rapide pour des espaces vectoriels de basses dimensions, ce qui est similaire aux approches de l'état de l'art. Pour des espaces vectoriels de haute dimension, nous proposons des méthodes de calculs ne nécessitant que peu de mémoire. Pour ces espaces, nous introduisons un formalisme récursif et prouvons que les algorithmes associés sont efficaces en termes de complexité de calcul et complexité de mémoire. Par ailleurs, des règles sont définies pour sélectionner la méthode la plus appropriée. Ces règles sont basées sur la dimension de l'espace vectoriel considéré. Nous montrons que l'implantation obtenue est bien adaptée pour les espaces vectoriels de hautes dimensions (espace vectoriel de dimension 15) et ceux de basses dimensions. La dernière partie est dédiée à une représentation efficace des surfaces quadriques en utilisant l'algèbre géométrique. Nous étudions un nouveau modèle en algèbre géométrique de l'espace vectoriel $mathbb{R}^{9,6}$ pour manipuler les surfaces quadriques. Dans ce modèle, une surface quadrique est construite par l'intermédiaire de neuf points. Nous montrerons que ce modèle permet non seulement de représenter de manière intuitive des surfaces quadriques mais aussi de construire des objets en utilisant les définitions de CGA. Nous présentons le calcul de l'intersection de surfaces quadriques, du vecteur normal, du plan tangent à une surface en un point de cette surface. Enfin, un modèle complet de traitement des surfaces quadriques est détaillé / Geometric Algebra is considered as a very intuitive tool to deal with geometric problems and it appears to be increasingly efficient and useful to deal with computer graphics problems. The Conformal Geometric Algebra includes circles, spheres, planes and lines as algebraic objects, and intersections between these objects are also algebraic objects. More complex objects such as conics, quadric surfaces can also be expressed and be manipulated using an extension of the conformal Geometric Algebra. However due to the high dimension of their representations in Geometric Algebra, implementations of Geometric Algebra that are currently available do not allow efficient realizations of these objects. In this thesis, we first present a Geometric Algebra implementation dedicated for both low and high dimensions. The proposed method is a hybrid solution that includes precomputed code with fast execution for low dimensional vector space, which is somehow equivalent to the state of the art method. For high dimensional vector spaces, we propose runtime computations with low memory requirement. For these high dimensional vector spaces, we introduce new recursive scheme and we prove that associated algorithms are efficient both in terms of computationnal and memory complexity. Furthermore, some rules are defined to select the most appropriate choice, according to the dimension of the algebra and the type of multivectors involved in the product. We will show that the resulting implementation is well suited for high dimensional spaces (e.g. algebra of dimension 15) as well as for lower dimensional spaces. The next part presents an efficient representation of quadric surfaces using Geometric Algebra. We define a novel Geometric Algebra framework, the Geometric Algebra of $mathbb{R}^{9,6}$ to deal with quadric surfaces where an arbitrary quadric surface is constructed by merely the outer product of nine points. We show that the proposed framework enables us not only to intuitively represent quadric surfaces but also to construct objects using Conformal Geometric Algebra. In the proposed framework, the computation of the intersection of quadric surfaces, the normal vector, and the tangent plane of a quadric surface are provided. Finally, a computational framework of the quadric surfaces will be presented with the main operations required in computer graphics

Artificial Intelligence (AI) systems are increasingly used in society to make decisions that can have direct implications on human lives; credit risk assessments, employment decisions and criminal suspects predictions. As public attention has been drawn towards examples of discriminating and biased AI systems, concerns have been raised about the fairness of these systems. Face recognition systems, in particular, are often trained on non-diverse data sets where certain groups often are underrepresented in the data. The focus of this thesis is to provide insights regarding different aspects that are important to consider in order to mitigate algorithmic bias as well as to investigate the practical implications of bias in AI systems. To fulfil this objective, qualitative interviews with academics and practitioners with different roles in the field of AI and a quantitative online survey is conducted. A practical scenario covering face recognition and gender bias is also applied in order to understand how people reason about this issue in a practical context. The main conclusion of the study is that despite high levels of awareness and understanding about challenges and technical solutions, the academics and practitioners showed little or no awareness of legal aspects regarding bias in AI systems. The implication of this finding is that AI can be seen as a disruptive technology, where organizations tend to develop their own mitigation tools and frameworks as well as use their own moral judgement and understanding of the area instead of turning to legal authorities.

Tillämpningen av dynamisk prissättning har förenklats i och med digitaliseringens framväxt. Med den ökade tillgången till kunddata kan företag idag kartlägga kundernas köpbeteende och genom algoritmer anpassa priserna därefter. Identiska varor och tjänster kan på så sätt prissättas annorlunda. För företaget utgör denna prissättning en möjlighet till ökad lönsamhet, men ur ett kundperspektiv kan detta tänkas skapa känslor av orättvisa och lurendrejeri. Samtidigt har det visat sig vara desto viktigare i en digital miljö att se till kundnöjdhet, eftersom det finns en högre transparens och kunderna har lägre engagemang och lojalitet. Det kan därför ifrågasättas om ett företag i längden tjänar på att använda sig av dynamisk prissättning om den skadar relationen till kunden. Syftet med denna studie är således att undersöka kundattityd kopplat till dynamisk prissättning. För att undersöka kundattityd baseras studien på en modell med komponenterna kundvärde, kundnöjdhet, kvalitet, kundlojalitet, förtroende och rättvisa. Studiens analys grundar sig på empirisk data som samlats in genom virtuella fokusgruppsdiskussioner. Dataunderlaget utgörs av fem fokusgruppsdiskussioner, med totalt 31 deltagare. Studien visar att kundernas attityd till företaget påverkas negativt av dynamisk prissättning. Dock framhäver studien att kundvärdet skapas i andra kvaliteter än pris. Trots en initial negativ inställning påvisas att det finns en viss grad av kundanpassning och utveckling av köpstrategier.

This thesis analyzes the performance and process of constructing portfolios of cryptocurrency pairs based on cointegrated relationships indicated by the Augmented Dickey-Fuller test, Johansen’s test and Phillips Peron’s test. Pairs are tested for cointegration over a 3-month and a 6-month window and then traded over a trading window of the same length. The cryptocurrencies included in the study are 14 cryptocurrencies with the highest market capitalization on April 24th 2019. One trading strategy has been applied on every portfolio following the 3-month and the 6-month methodology with thresholds at 1.75 and stop-losses at 4 standard deviations. The performance of each portfolio is compared with their corresponding buy and hold benchmark. All portfolios outperformed their buy and hold benchmark, with and without transaction costs set to 2%. Following the 3-month methodology was superior to the 6- month method and the portfolios formed through Phillips Peron’s test had the highest return for both window methods.

Os múltiplos trabalhos de sistemas multiagentes musicais realizados nos últimos anos demonstram o interesse crescente na pesquisa de sistemas de composição e de performance musical que utilizem a tecnologia de agentes computacionais, sendo que apresentam um interesse maior por aqueles sistemas que integram técnicas de composição algorítmica, componentes de vida artificial e interatividade. Observamos também que a maioria dos trabalhos existentes apresentam muitas limitações em termos de escopo e flexibilidade, normalmente apresentando codificação musical simbólica e a resolução de um único problema, sendo que a motivação é mais técnica do que musical. Nesse contexto, surgem arcabouços voltados à criação de sistemas multiagentes musicais, como o Ensemble e o Interactive Swarm Orchestra, oferecendo flexibilidade para a modelagem e implementação de sistemas desse tipo, diversificando tanto os tipos de aplicação, tendo um propósito composicional ou performático, como os tipos de codificação musical que podem ser utilizados. Partimos da aparição dessas ferramentas para estudar o agente musical a partir de uma perspectiva interna, focando nos seus raciocínios, que são processos que definem o comportamento do agente no ambiente virtual do sistema e que são fundamentais para determinar e melhorar o seu valor composicional. Os arcabouços estudados se diferenciam por permitir a utilização de áudio como possível formato de codificação musical, o aproveitamento da espacialização sonora e a exploração da interatividade nos aplicativos, seja esta apenas entre agentes computacionais ou entre agentes e usuários humanos. Pretendemos portanto, nessa pesquisa, abordar sistemas com essas características. Através de extensões nos arcabouços e estudos de caso com motivação estética pretendemos dar continuidade a esses projetos e ao mesmo tempo validar e divulgar a sua utilização entre os potenciais usuários das ferramentas, como compositores, músicos interessados em performance e outros entusiastas dos sistemas musicais interativos. / Multiple musical multiagent systems have been developed in the last years proving the increasing interest in composition and musical performance systems that exploit intelligent agents technology. Theres an special focus on systems that integrate algorithmic composition techniques, artificial life and interactivity. We can also observe that most of these existing projects show many flexibility and scope limitations, as they normally use symbolic musical notation and they solve a single issue or scenario, as well as they have a technical motivation rather than a musical one. In that context, some musical multiagent systems frameworks as Ensemble and Interactive Swarm Orchestra emerge, trying to help the modeling and development of this kind of musical systems, diversifying the applications\' types, as they can be composition problems or musical performances, and allowing the inclusion of other kind of musical content communication. Through these new tools we study the musical agent from an internal perspective, focusing on its reasoning components, processes that define the behavior of an agent on its system\'s virtual environment and that are essential to determine and improve its compositional value. The studied frameworks show unique features as they support audio as a possible musical notation format; they exploit sound spatialization and they work with interactivity in their applications, including agent-to-agent or human-to-agent interaction. We will explore this type of systems on this research. Through framework extensions and aesthetics-oriented study cases we pretend to continue these projects and validate them at same time. We also will contact potential users for these tools, as composers and musicians interested in performances or other musical interactive systems enthusiasts.