The goal of this paper is to introduce a new algebraic structure for coloring regions in the planar complement of an oriented virtual knot or link diagram that I will refer to as virtual tribrackets. I will begin with an overview of classical knot theory where I introduce knot diagrams and ways of calculating knot invariants. This paper progresses into virtual knots and links, their geometric interpretations as well as their virtual moves, and some invariant examples for the virtual case. This informations allows me to introduce tribrackets, which is a labeling method used to define counting invariants for classical knots and link diagrams. Finally, this paper properly defines and proves the use of virtual tribackets in defining invariants for virtual knots as well as providing examples from [6] which more precisely show that these invariants can distinguish between certain virtual knots.

Syftet med studien har varit att skapa en översikt om vad diagnosen dyskalkyli innebär genom att granska vetenskapliga artiklar ifrån 2011 - 2017. Syftet besvaras genom följande frågeställningar. Hur definieras diagnosen dyskalkyli? Vilka drabbas av dyskalkyli? Vilka samband finns det till andra diagnoser? Vad finns det för kritik mot dyskalkyli? För att få svar på dessa frågor har olika söktjänster använts för att hitta vetenskapligt granskad litteratur. Den litteratur som har använts är till mesta del riktad till grundskolans år. Då forskningen är mycket begränsad består resultatet endast av internationell litteratur. Resultatet visar att de flesta forskarna är överens om att det är en existerande diagnos som behöver specialpedagogiska insatser. Dyskalkyli som begrepp syftar på att det finns en medfödd svårighet att lära sig matematik, som verkar vara ärftligt betingad. Förekomsten av dyskalkyli verkar enligt resultatet vara 3 - 7%. Det finns starka kopplingar till andra diagnoser som dyslexi och ADHD. Följaktligen finns det ett stort behov av fortsatt forskning kring dyskalkyli, både internationellt och nationellt.

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Clearing is keeping track of transactions until they are settled. Standardized derivatives such as options and futures can be cleared through a clearinghouse if you are a clearing member. The clearinghouse step in as an intermediary between trades and manages all occurring counterparty risk. To be able to keep track of all transactions and also monitor members risk exposure a clearinghouse use advanced clearing software. Counterparty risk is mainly handled by collecting collateral from each clearing member, the initial collateral that a clearinghouse require from a member trading with derivatives, is called initial margin. Initial margin is calculated by a risk algorithm incorporated in the clearing software. Cinnober Financial Technology delivers clearing solutions to clearinghouses world wide, software providers to the _nancial industry have high demands on software quality. Ensuring high software quality can be done by performing various types of software testing. The goal of this thesis is to implement an extendable random testing framework that can test risk algorithm implementations that are part of a clearing system under development by Cinnober. By using the implemented framework, we aim to verify if the risk algorithm SPAN calculates fair initial margin amount. We also intend to increase the quality assurance of the risk domain that is responsible for all risk calculations. In this thesis we implement a random testing framework suitable for testing risk algorithms. Furthermore, we implement a framework extension for SPAN that is used to test the SPAN algorithm's initial margin calculations. The implementation consist of two main parts, the _rst being a random generation entity that feeds the clearing system with randomized input data. The second part is a veri_cation entity called test oracle, it is responsible for verifying the SPAN algorithm's calculation results. The random testing framework for risk algorithms was successfully implemented. By running the SPAN extension of the framework, we managed to _nd four issues related to the accuracy of the SPAN algorithm. This discovery led to the conclusion that the current SPAN algorithm implementation does not calculate fair initial margin. It also led to an immediate increase of quality assurance because the issues will be corrected. As a result of the frameworks extensible characteristics, long term quality also increases.

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Corruption is a problem all around the world, but the extent of the problem varies between countries and situations. In this thesis, I focus on how corruption levels can change when they are culturally determined. For this reason, I study the dynamics of the cultural underpinnings: social norms and conventions. The dissertation consists of six papers. In the first paper, I expand a common definition of social norms. The aim of the extension is to capture the fact that the scope of a social norm may be larger than just a single specific situation. I introduce a similarity measure and develop a mathematical model according to which all situations' social norms are interconnected, and affect each other, but those situations that are most similar and most recent have the greatest normative effect on a current situation. Given this model I test the effect of bringing about norm change by temporarily dismantling institutions and then reestablishing them. In the second paper, I show in a mathematical model how it is possible to design fine and reward mechanisms that make it superfluous for individuals to form beliefs about how others will act. Through this mechanism, it should be possible to circumvent the problem that norm change typically will be successful only if it is synchronized across a large part of the population. In the third paper, I and my co-authors, first conducted a survey. The results of which demonstrate that there is a general tendency among people to consider themselves to be less prone to corrupt behavior than the average person. Such an "everyone-is-better-than-average" effect is a well-established phenomenon in social psychology but not previously demonstrated in the corruption domain. We then show in a mathematical model that such systematic biases in estimation of own versus others' corruption make it more difficult to achieve norm change in the direction of less corruption. In the fourth and fifth paper we again consider the "everyone-is-better-than-average" effect and see how in certain value based groups the effect can be reversed. This changes the insight from the third paper slightly. The last paper considers a classic question of how a collective can succeed in collective action when it is risky to be among the first individuals to act. I and my co-author investigate how the collective can benefit from access to a set of signal acts that signal an individual's level of commitment to the collective cause. The problem is modeled as a threshold model where an individual's inclination to conduct a specific act depends on the previous commitment level in the population.

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