<p>In this dissertation stochastic processes are regarded in the framework of Colombeau-type algebras of generalized functions. Such processes are called Colombeau stochastic processes.The notion of point values of Colombeau stochastic processes in compactly supported generalized points is established. The Colombeau algebra of compactly supported generalized constants is endowed with the topology generated by sharp open balls. The measurability of the corresponding random variables with values in the Colombeau algebra of compactly supported generalized constants is shown.<br />The generalized correlation function and the generalized characteristic function of Colombeau stochastic processes are introduced and their properties are investigated. It is shown that the characteristic function of classical stochastic processes can be embedded into the space of generalized characteristic functions. Examples of generalized characteristic function related to gaussian Colombeau stochastic<br />processes are given. The structural representation of the generalized correlation function which is supported on the diagonal is given. Colombeau stochastic processes with independent values are introduced. Strictly stationary and weakly stationary Colombeau stochastic processes are studied. Colombeau stochastic processes with stationary increments are characterized via their stationarity of the gradient of the process.Gaussian stationary solutions are analyzed for linear stochastic partial differential equations with generalized constant coefficients in the framework of Colombeau stochastic processes.</p> / <p>U disertaciji se stohastički procesi posmatraju u okviru Kolomboove algebre uop&scaron;tenih funkcija. Takve procese nazivamo Kolomboovi stohastički procesi. Pojam vrednosti Kolomboovog stohastičkog procesa u tačkama sa kompaktnim nosačem je uveden. Dokazana je merljivost odgovarajuće slučajne promenljive sa vrednostima u Kolomboovoj algebri uop&scaron;tenih konstanti sa kompaktnim nosačem,&nbsp; snabdevenom topologijom generisanom o&scaron;trim otvorenim loptama. Uop&scaron;tena korelacijska funkcija i uop&scaron;tena karakteristična funkcija Kolomboovog stohastičkog procesa su definisane i njihove osobine su izučavane. Pokazano je da&nbsp; se karakteristična funkcija klasičnog stohastičkog procesa može potopiti u prostor uop&scaron;tenih karakterističnih funkcija. Dati su primeri uop&scaron;tenih karakterističnih funkcija&nbsp; gausovskih Kolomboovih stohastičkih procesa. Data je strukturna reprezentacija uop&scaron;tene korelacijske funkcije sa nosačem na dijagonali. Kolomboovi stohastički procesi sa nezavisnim vrednostima su predstavljeni. Izučavani su strogo stacionarni i&nbsp; slabo stacionarni Kolomboovi stohastički procesi. Kolomboovi stohastički procesi sa stacionarnim prira&scaron;tajima su okarakterisani preko stacionarnosti gradijenta procesa. Gausovska stacionarna re&scaron;enja za linearnu stohastičku parcijalnu diferencijalnu jednačinu sa uop&scaron;tenim konstantnim koeficijentima su analizirana u okvirima Kolomboovih stohastičkih procesa.</p>

Background: Career ending injuries are known to cause negative psychosocial and behavioural outcomes in retired athletes. However, there has been a limited amount of quantitative studies to complement mostly qualitative research. Furthermore, qualitative studies have typically assessed the effects of athletic identity, mental health/mood disturbances, loss, coping mechanisms and social support with minimal research regarding physical body transitions and body-esteem throughout the retirement process. Thus, the purpose of this thesis was to investigate the relationship between affective, behavioural, and cognitive outcomes and athletic retirement (voluntary, involuntary) among elite and competitive athletes. Method: A retrospective mixed method (questionnaire and interview) study was utilized to examine how participants interpreted their experience during the transitional process into retirement. Inclusion criteria consisted of male and female, elite and competitive athletes who have voluntarily or involuntarily (career ending injury) retired, ages 18 and above. Exclusion criteria included non-athletes/recreational athletes, athletes who were able to return to play or retired due to illness, health problems or deselection as well as who were less than 18 years of age. Posters were advertised in sports clubs, fitness centers, sports centers, physiotherapy offices and universities as well as on social media (Facebook and Instagram). The main outcome measures are as follows:1) Athletic Identity Measurement Scale (AIMS); 2) Mood and Feelings Questionnaire (MFQ), 3) Mental Health and 4) COPE Inventory. Semi-structured interviews were conducted with participants from both retirement (voluntary and involuntary) groups. All interviews (telephone, zoom) were recorded, transcribed verbatim and a thematic analysis was implemented to further determine the various themes and subthemes. An independent t-test explored the impacts of body dimensions and coping mechanisms on retirement type. Then a factorial ANOVA was conducted to examine the effects of the dependent variables (mental health, mood disturbances and coping mechanisms) on the main analysis (retirement) and the exploratory (strength of athletic identity) analysis. Results: 50 (26 involuntary and 24 voluntary) questionnaires and eight (four voluntary and four involuntary) interviews were completed by the participants. Results from the quantitative data revealed a borderline main effect of retirement type on both mental health and mood disturbances. An exploratory analysis found retirees who weakly identified with the athletic role were less likely to experience severe mood disturbances and demonstrated higher levels of mental health than retirees who strongly identified with the athletic role. Information from qualitative data suggested participants who involuntarily retired and possessed a strong athletic identity experienced higher levels of mood disturbances (depression, frustrations, loss etc.), lower levels of mental health, identity loss, physical discomfort, negative effects of mind and body dualism as well as utilized maladaptive coping techniques than their counterpart who voluntarily retired or weakly identified with the athletic role. Conclusion: Both retirement types are subjected to various athletic and non-athletic demands and psychosocial effects of athletic retirement however, what sets them apart from experiencing a successful or unsuccessful transition into retirement is the intensity and severity of their emotional reaction to their retirement. Limitations of said study included a decrease in sample size, memory recall bias, the participant’s own bias, limited diversity of the sample population as well as the inability to verify the findings from the interviews. The following study can be implemented to aid researchers, retired or soon to be retired athletes, coaches and athletic personnel to comprehend the diverse areas of athletic retirement. Future research should aim to investigate the impacts of mood disorders, the utilization of psychologist or mental performance consultant during the retirement process as well as the effects of body dimensions in retired athletes. Lastly, a longitudinal study should be employed to examine the athlete’s emotional response and reaction throughout retirement (time of injury, during physiotherapy, post- surgery and recovery). / Graduate

The aim of this thesis is to present new results concerning duality in scalar optimization. We show how the theory can be applied to optimization problems arising in the theory of risk measures, portfolio optimization and machine learning. First we give some notations and preliminaries we need within the thesis. After that we recall how the well-known Lagrange dual problem can be derived by using the general perturbation theory and give some generalized interior point regularity conditions used in the literature. Using these facts we consider some special scalar optimization problems having a composed objective function and geometric (and cone) constraints. We derive their duals, give strong duality results and optimality condition using some regularity conditions. Thus we complete and/or extend some results in the literature especially by using the mentioned regularity conditions, which are weaker than the classical ones. We further consider a scalar optimization problem having single chance constraints and a convex objective function. We also derive its dual, give a strong duality result and further consider a special case of this problem. Thus we show how the conjugate duality theory can be used for stochastic programming problems and extend some results given in the literature. In the third chapter of this thesis we consider convex risk and deviation measures. We present some more general measures than the ones given in the literature and derive formulas for their conjugate functions. Using these we calculate some dual representation formulas for the risk and deviation measures and correct some formulas in the literature. Finally we proof some subdifferential formulas for measures and risk functions by using the facts above. The generalized deviation measures we introduced in the previous chapter can be used to formulate some portfolio optimization problems we consider in the fourth chapter. Their duals, strong duality results and optimality conditions are derived by using the general theory and the conjugate functions, respectively, given in the second and third chapter. Analogous calculations are done for a portfolio optimization problem having single chance constraints using the general theory given in the second chapter. Thus we give an application of the duality theory in the well-developed field of portfolio optimization. We close this thesis by considering a general Support Vector Machines problem and derive its dual using the conjugate duality theory. We give a strong duality result and necessary as well as sufficient optimality conditions. By considering different cost functions we get problems for Support Vector Regression and Support Vector Classification. We extend the results given in the literature by dropping the assumption of invertibility of the kernel matrix. We use a cost function that generalizes the well-known Vapnik's ε-insensitive loss and consider the optimization problems that arise by using this. We show how the general theory can be applied for a real data set, especially we predict the concrete compressive strength by using a special Support Vector Regression problem.

The aim of this thesis is to present new results concerning duality in scalar optimization. We show how the theory can be applied to optimization problems arising in the theory of risk measures, portfolio optimization and machine learning. First we give some notations and preliminaries we need within the thesis. After that we recall how the well-known Lagrange dual problem can be derived by using the general perturbation theory and give some generalized interior point regularity conditions used in the literature. Using these facts we consider some special scalar optimization problems having a composed objective function and geometric (and cone) constraints. We derive their duals, give strong duality results and optimality condition using some regularity conditions. Thus we complete and/or extend some results in the literature especially by using the mentioned regularity conditions, which are weaker than the classical ones. We further consider a scalar optimization problem having single chance constraints and a convex objective function. We also derive its dual, give a strong duality result and further consider a special case of this problem. Thus we show how the conjugate duality theory can be used for stochastic programming problems and extend some results given in the literature. In the third chapter of this thesis we consider convex risk and deviation measures. We present some more general measures than the ones given in the literature and derive formulas for their conjugate functions. Using these we calculate some dual representation formulas for the risk and deviation measures and correct some formulas in the literature. Finally we proof some subdifferential formulas for measures and risk functions by using the facts above. The generalized deviation measures we introduced in the previous chapter can be used to formulate some portfolio optimization problems we consider in the fourth chapter. Their duals, strong duality results and optimality conditions are derived by using the general theory and the conjugate functions, respectively, given in the second and third chapter. Analogous calculations are done for a portfolio optimization problem having single chance constraints using the general theory given in the second chapter. Thus we give an application of the duality theory in the well-developed field of portfolio optimization. We close this thesis by considering a general Support Vector Machines problem and derive its dual using the conjugate duality theory. We give a strong duality result and necessary as well as sufficient optimality conditions. By considering different cost functions we get problems for Support Vector Regression and Support Vector Classification. We extend the results given in the literature by dropping the assumption of invertibility of the kernel matrix. We use a cost function that generalizes the well-known Vapnik's ε-insensitive loss and consider the optimization problems that arise by using this. We show how the general theory can be applied for a real data set, especially we predict the concrete compressive strength by using a special Support Vector Regression problem.

In a Reinforced Concrete (RC) building subjected to lateral loads such as earthquake and wind pressure, the beam to column joints constitute one of the critical regions, especially the exterior ones, and they must be designed and detailed to dissipate large amounts of energy without a significant loss of, strength, stiffness and ductility. This would be achieved when the beam-column joints are designed in such a way that the plastic hinges form at a distance away from the column face and the joint region remain elastic. In existing frames, an easy and practical way to implement this behaviour following the accepted design philosophy of the strong-column weak-beam concept is the use a Fibre Reinforced Plastic (FRP) retrofitting system. In the case of damaged buildings, this can be achieved through a FRP repairing system. In the experimental part of this study, seven scaled down exterior subassemblies were tested under monotonic or cyclic loads. All specimens were designed following the strong-column weak-beam principal. The three categories selected for this investigation included the FRP-repaired and FRP-retrofitted specimens under monotonic loads and FRP-retrofitted specimen under cyclic loads. All repairing/retrofitting was performed using a new technique called a web-bonded FRP system, which was developed for the first time in the current study. On the basis of test results, it was concluded that the FRP repairing/retrofitting system can restore/upgrade the integrity of the joint, keeping/upgrading its strength, stiffness and ductility, and shifting the plastic hinges from the column face toward the beam in such a way that the joint remains elastic. In the analytical part of this study, a closed-form solution was developed in order to predict the physical behaviour of the repaired/retrofitted specimens. Firstly, an analytical model was developed to calculate the ultimate moment capacity of the web-bonded FRP sections considering two failure modes, FRP rupture and tension failure, followed by an extended formulation for estimating the beam-tip displacement. Based on the analytical model and the extended formulation, failure mechanisms of the test specimens were implemented into a computer program to facilitate the calculations. All seven subassemblies were analysed using this program, and the results were found to be in good agreement with those obtained from experimental study. Design curves were also developed to be used by practicing engineers. In the numerical part of this study, all specimens were analysed by a nonlinear finite element method using ANSYS software. Numerical analysis was performed for three purposes: to calculate the first yield load of the specimens in order to manage the tests; to investigate the ability of the web-bonded FRP system to relocate the plastic hinge from the column face toward the beam; and to calibrate and confirm the results obtained from the experiments. It was concluded that numerical analysis using ANSYS could be considered as a practical tool in the design of the web-bonded FRP beam-column joints.

Derek Parfit är kanske en av vår tids mest kända moralfilosofer. Parfit inleder sin första bok Reasons and Persons med att ställa frågan: vad har vi mest skäl att göra? Hans fråga berör vad som egentligen har betydelse, en fråga som han fortsätter att beröra i sin andra bok On What Matters. Filosofen Toby Ord argumenterar i sin bok The Precipice för att den utmaning som definierar vår tid, och bör ha en central prioritering, är utmaningen att skydda mänskligheten emot så kallade existentiella risker. En existentiell risk är en typ av risk som hotar att förstöra, eller förhindra, mänsklighetens långsiktiga potential. Ord menar att vi idag befinner oss vid en kritisk tidpunkt i mänsklighetens historia som kan vara helt avgörande för om det ens kommer existera en framtid för mänskligheten. Men om vi bör skydda mänskligheten emot existentiella risker, så kan en lämplig följdfråga vara i vilken ordning vi bör prioritera olika existentiella risker. Den svenske filosofen Nick Bostrom har liksom Ord länge förespråkat att existentiella risker bör tas på allvar. Han menar att preventiva åtgärder bör vidtas. I sin bok Superintelligens argumenterar Bostrom, både omfattande och väl, för att den existentiella risk som kan te sig som mest brådskande, och kanske allvarligast, är artificiell intelligens. Bostrom menar att vi har goda skäl att tro att utveckling av artificiell intelligens kan eskalera till den grad att mänsklighetens öde kan hamna bortom vår egen kontroll. Det han syftar på är att människan just nu är den dominerande agenten på jorden och därför innehar en stor kontroll, men att så inte alltid behöver vara fallet. Bostroms tes kunde te sig som okonventionell då den presenterades, men kan även te sig så idag vid en första anblick. Han har dock fått explicit medhåll av personer som Bill Gates, Stephen Hawking, Elon Musk, Yuval Noah Harari och Max Tegmark, som antingen håller med eller resonerar i liknande banor. Även jag själv finner Bostroms antaganden välgrundade. Slutsatsen som många drar är därför att vi bör betrakta artificiell intelligens som en existentiell risk som ska prioriteras högt. Jag kommer dock i denna text att argumentera för tesen att vi inte bör betrakta artificiell intelligens som en existentiell risk. Tesen följer från en invändning som jag kommer att kalla för AI-paradoxen. Det tycks enligt invändningen som att artificiell intelligens inte kan leda till en existentiell katastrof givet vissa premisser som flera i debatten om artificiell intelligens tycks acceptera. Texten i uppsatsen är strukturerad på följande sätt. I avsnitt 2 kommer jag att återge det övergripande argumentet som cirkulerar i debatten om artificiell intelligens som ett hot. I avsnittet kommer jag också förklara några viktiga termer och begrepp. I avsnitt 3 börjar jag med att titta på den första premissen i argumentet, samt resonera om dess rimlighet. I avsnitt 4 går jag sedan vidare till den andra premissen i argumentet och gör samma sak med den. Väl i avsnitt 5 så väljer jag att presentera min egen idé som jag kallar för AI-paradoxen, vilket är en invändning mot argumentet. I avsnitt 6 diskuterar jag sedan AI-paradoxens implikationer. Avslutningsvis, i avsnitt 7, så ger jag en övergripande sammanfattning och en slutsats, samt några sista reflektioner. / Derek Parfit is perhaps one of the most famous moral philosophers of our time. Parfit begins his first book Reasons and Persons by asking the question: what do we have most reason to do? His question touches upon what really matters, a question he continues to touch upon in his second book On What Matters. The philosopher Toby Ord argues in his book The Precipice that the challenge that defines our time, and should have a central priority, is the challenge of safeguarding humanity from so-called existential risks. An existential risk is a type of risk that threatens to destroy, or prevent, humanity’s longterm potential. Ord means that today we are at a critical time in the history of humanity that can be absolutely decisive for whether there will even exist a future for humanity. But if we are to safeguard humanity from existential risks, then an appropriate question may be in what order we should prioritize different existential risks. The Swedish philosopher Nick Bostrom, like Ord, has long advocated that existential risks should be taken seriously. He believes that preventive measures should be taken. In his book Superintelligence Bostrom argues, both extensively and well, that the existential risk that may seem most urgent, and perhaps most severe, is artificial intelligence. Bostrom believes that we have good reason to believe that the development of artificial intelligence can escalate to the point that the fate of humanity can end up beyond our own control. What he is referring to is that humans are currently the dominant agent on earth and therefore has great control, but that this does not always have to be the case. Bostrom's thesis may have seemed unconventional when it was presented, but it can also seem so today at first glance. However, he has been explicitly supported by people like Bill Gates, Stephen Hawking, Elon Musk, Yuval Noah Harari and Max Tegmark, who either agree or reason similarly. I myself also find Bostrom's assumptions well-founded. The conclusion that many draw is therefore that we should regard artificial intelligence as an existential risk that should be given a high priority. However, in this text I will argue for the thesis that we should not regard artificial intelligence as an existential risk. The thesis follows from an objection of my own, which I call the AI ​​paradox. According to the objection, it seems that artificial intelligence cannot lead to an existential catastrophe given certain premises that many in the debate about artificial intelligence as a threat seem to accept. The text in the essay is structured as follows. In section 2 I will present the main argument circulating in the debate about artificial intelligence as a threat. In the section I will also explain some important terms and concepts. In section 3 I begin by looking at the first premise in the argument, and also reason about its plausibility. In section 4 I proceed to the second premise in the argument and examine it similarly. Once in section 5 I choose to present my own idea, which I call the AI ​​paradox, which is an objection to the argument. In section 6 I discuss the implications of the AI ​​paradox. Finally, in section 7, I give an overall summary and a conclusion, as well as some last reflections.