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              <text>This study expands upon the work of Barberis (2012) which discusses the application of Tversky and Kahneman’s updated model of prospect theory in 1992 (cumulative prosepect theory) to the area of repeated bets with win probabilities of close to 0.5, in contexts such as casinos or financial markets. In particular, we look to explore the idea of a ’time inconsistency’ that is abundant in many strategic situations evaluated using cumulative prospect theory. What this refers to is the phenomenon of an agent deciding what their optimal strategy is before entering the situation but then following a different plan of action at future time periods. We explore the impacts of moving away from simple bets by changing some of the underlying principles, such as the effects of generalising the win probability, p, or introducing a random shock to the reward at a random point in time. This allows us to connect Barberis’ work to areas beyond just a casino, such as prices of securities in financial markets. We will do this by exploring the effects on a two-period binomial model but which can be extended.</text>
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              <text>This document is a report/log of my 2024 Undergraduate Research Support Scheme (URSS) project with the University of Warwick. This project was completed under the supervision of Helena Verrill, with the Warwick Mathematics Institute. The project has synergies with projective geometry, graph theory and combinatorics.</text>
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              <text>Murdoch’s The Sovereignty of Good is often interpreted as suggesting that love requires recognizing the individual reality of one’s beloved. However, through a closer reading, I argue that Murdoch’s characterization of love is more nuanced. Specifically, I show that, due to ambiguity in her writing, Murdoch leaves the exact relationship between love and the perception of reality unclear. In this paper, I begin by unpacking this ambiguity. Then, I propose that this ambiguity allows for two possible kinds of interpretations of her view on love: the objective view, and the positive light view. Finally, I argue that the positive light view offers a better interpretation of Murdoch’s position, concluding that love, while rooted in reality, also exceeds it and transcends it.</text>
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              <text>Premenstrual Dysphoric Disorder is characterised by the cyclical nature of psychological and somatic symptoms occurring in the luteal phase of the menstrual cycle that significantly affect the functioning of various aspects of daily life. Controversy, paucity of knowledge and awareness surrounds the research on Premenstrual dysphoric Disorder. It is an under-researched disorder riddled with methodological limitations, lack of diversity in cohort studies, small samples and a lack of systemic reviews, meta-analysis and randomised control trials. A qualitative systematic literature review was conducted and the findings show that there is no universal diagnostic and screening standardised method, nor is there a different nomenclature used to describe the disorder. First-line treatment of the disease differs among professional healthcare bodies. The foundations of Premenstrual dysphoric disorder were always controversial, as seen with its inclusion in the American Psychiatric DSM-5 and the World Health Organisation’s ICD11 caused controversy where psychologists and feminist thinkers alike argued that this is a way of pathologising a natural process, adding to the stigma around women’s emotions being tied to their hormones. The pathophysiology of the disease is still relatively unknown. However, a widely accepted cause is the interaction of reproductive steroids like oestrogen, progesterone and allopregnanolone on central neurotransmitters like serotonin and GABAa receptors and the Hypothalamic-pituitary-ovarian axis. Other possible causes, associations, and co-morbidities are discussed below. There is a hidden figure of those who have PMDD and are unaware or have not received efficient healthcare services, this research highlights the inconsistencies with how healthcare services approach PMDD. There needs to be more precise definitions around premenstrual dysphoric disorder separated from premenstrual syndrome and more education within healthcare systems about the disorder in order to improve patient-provider communication for better experiences and a more accurate clinical picture of the disorder. In addition, a more personalised care for women with PMDD is needed as well as approaching research of the pathophysiology from a psychosomatic perspective.</text>
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              <text>Dynamic environments are a phenomenon within video games that tend to be strictly used in multiplayer settings as it is challenging to create agents that can effectively navigate and take advantage of such a rapidly changing setting. In this paper we will discuss a simple modification to the well-known A* pathfinding algorithm that allows agents to navigate through destructible environments within a 2D setting. Furthermore, we will discuss potential improvements to our solution and alternative methods.</text>
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