Thesis (M.Sc. (Applied Mathematics)) -- University of Limpopo, 2019 / Functional Itˆo calculus is based on an extension of the classical Itˆo calculus to functionals depending on the entire past evolution of the underlying paths and not only on its current value. The calculus builds on F¨ollmer’s deterministic proof of the Itˆo formula Föllmer (1981) and a notion of pathwise functional derivative recently proposed by Dupire (2019). There are no smoothness assumptions required on the functionals, however, they are required to possess certain directional derivatives which may be computed pathwise, see Cont and Fournié (2013); Schied and Voloshchenko (2016a); Cont (2012). In this project we revise the functional Itô calculus together with the notion of quadratic variation. We compute the pathwise change of variable formula utilizing the functional Itô calculus and the quadratic variation notion. We study the martingale representation for the case of weak derivatives, we allow the vertical operator, rX, to operate on continuous functionals on the space of square-integrable Ft-martingales with zero initial value. We approximate the hedging strategy, H, for the case of path-dependent functionals, with Lipschitz continuous coefficients. We study some hedging strategies on the class of discounted market models satisfying the quadratic variation and the non-degeneracy properties. In the classical case of the Black-Scholes, Greeks are an important part of risk-management so we compute Greeks of the price given by path-dependent functionals. Lastly we show that they relate to the classical case in the form of examples. / NRF and AIMS-SA

Suicide is a worldwide public health issue which has substantial consequences and The World Health Organization (WHO) fears that mental illness will be the largest public health matter in 2030. About 40 times a day Swedish police intervene in suicide cases (polisen.se, 2020) and on Gotland there are both suicide attempts and fulfilled suicide beyond the national average (Public Health Agency, 2020). Since the first quarter of 2020, the education initiative Acute care of suicidal persons" (AOSP) has been conducted in line with a government assignment that the Police Authority has undertaken. This study uses semi-structured interviews to investigate and evaluate the Police Authority's educational efforts and work to prevent suicide on Gotland. Furthermore, the study examines the perceived benefit of the educational initiative AOSP and how the participants experience their self-efficacy to intervene with people who struggle with suicidal behaviour. Previous research shows that qualified and educated police officers will play a crucial role in suicide prevention (Marzano et al., 2016) and police officers' self-efficacy should be strengthened for an effective suicide prevention strategy (Osteen et. Al, 2014). It also appears that factual knowledge combined with practical training generates the best conditions for police officers to handle the encounter with suicidal persons (Isaac et al., 2009). It appears in this study that all interviewees value the education and that the consequences of the education are predominantly good as the participants feel assured in the encounter with mental illness and that in the long run they conduct a better suicide prevention. All informants describe that their self-efficacy to handle the encounter with a suicidal person has been strengthened and that the consequences from the educational initiative in the form of both manifest and latent functions have affected the suicide prevention on Gotland mainly in positive ways.

Live (Direct) Supervision has always been key to training therapists. However, little research has been done to determine which type of direct supervision is most effective in changing therapist behavior. This study compared bug-in-the-ear (BITE), phone-in, and computer assisted (CA) supervision. The purpose of this study was to (a) complete functional analysis of each supervision type via an alternating feedback session, to determine each therapists' most effective form of supervision; (b) determine the effect of using the most-effective form of supervision on the therapists' adherence to treatment protocols during follow-up sessions; (c) determine the effect of therapist adherence on client in-session behaviors, and outcome assessments. Results of the functional analysis indicated that phone-in supervisory feedback was the least effective form of supervision. BITE and CA supervision were both found to be effective for at least one therapist. In follow-up sessions BITE supervision did not create sustained changes in overall adherence. CA feedback appeared to maintain overall therapist adherence. In affecting changes to client behavior and outcome scores BITE supervision gave mixed results. CA supervision created desired changes in client behaviors and outcome assessments. For practitioners in the field, this study demonstrates that client behavior does not improve without therapist intervention. Even when client behavior in session appears to be improving, marital distress may increase. This is especially true when therapist adherence does not improve. This study further demonstrates that when the therapists did not intervene appropriately the clients either worsened, or at best, stayed the same. When the therapists made even small improvements client behavior improved. Improving adherence to treatment protocols will always serve the best interest of the client.

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In this thesis we develop a mathematically rigorous framework of the so-called ''classical limit'' of quantum systems and their semi-classical properties. Our methods are based on the theory of strict, also called C*- algebraic deformation quantization. Since this C*-algebraic approach encapsulates both quantum as classical theory in one single framework, it provides, in particular, an excellent setting for studying natural emergent phenomena like spontaneous symmetry breaking (SSB) and phase transitions typically showing up in the classical limit of quantum theories. To this end, several techniques from functional analysis and operator algebras have been exploited and specialised to the context of Schrödinger operators and quantum spin systems. Their semi-classical properties including the possible occurrence of SSB have been investigated and illustrated with various physical models. Furthermore, it has been shown that the application of perturbation theory sheds new light on symmetry breaking in Nature, i.e. in real, hence finite materials. A large number of physically relevant results have been obtained and presented by means of diverse research papers.

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Ce mémoire présente une analyse tracéologique, c’est-à-dire l’analyse fonctionnelle d’un objet à partir des microtraces d’usure, appliquée à une collection d’incisives de castor issue des sites iroquoiens de la région de Saint-Anicet: McDonald, Droulers et Mailhot-Curran. L’objectif est de mieux comprendre la fonction de ces objets fréquents sur les sites archéologiques iroquoiens, étant donné que la fonction précise est soit inconnue, soit présumée de façon spéculative. Pour répondre à cette question de recherche, l’analyse se déploie en trois volets : expérimental, analytique et comparatif. Le premier permettra d’éclairer la relation entre différentes matières travaillées et les traces laissées sur les outils en incisives de castor, ainsi que les mouvements effectués et la durée d’utilisation. Le deuxième volet aborde la tracéologie des incisives de castor de nos trois sites à l’étude, à partir des résultats des expérimentations. Le troisième volet de l’étude est dédié à la comparaison inter-sites. Ce projet permet de déterminer à quelles activités les outils sur dents de castor des collections ont servi, puis de comprendre les choix qui les sous-tendent. Cela permet donc de mieux comprendre l’humain derrière l’objet. Les résultats des analyses ont permis de démontrer l’utilisation des incisives de castor iroquoiennes comme outils servant à travailler le bois, mais plus spécifiquement comme outils servant à travailler des bois verts, tendres et mi-durs. De plus, il a été confirmé que les incisives de castor à double fonction, ciseau-racloir, sont le résultat d’outils recyclés ou réutilisés qui servaient à des usages divers. / This dissertation presents a traceological analysis, that is to say the functional analysis of an object based on microtraces of wear, applied to a collection of beaver incisors from Iroquoian sites in the Saint-Anicet region. : McDonald, Droulers and Mailhot-Curran. The goal is to better understand the function of these common objects at Iroquoian archaeological sites, given that the precise function is either unknown or speculated speculatively. To answer this research question, the analysis is deployed in three parts: experimental, analytical and comparative. The first will shed light on the relationship between different materials worked and the traces left on beaver incisor tools, as well as the movements made and the duration of use. The second part addresses the traceology of beaver incisors from our three sites under study, based on the results of the experiments. The third part of the study is dedicated to the inter-site comparison. This project makes it possible to determine what activities the beaver tooth tools in the collections were used for, then to understand the choices behind them. This therefore allows us to better understand the human behind the object. The results of the analyzes demonstrated the use of Iroquoian beaver incisors as tools for working wood, but more specifically as tools for working green, soft and semi-hard wood. Furthermore, it was confirmed that the double-function beaver incisors, chisel-scraper, are the result of recycled or reused tools that were used for various purposes.

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