The arcsine distribution looks at the fraction of time one player is winning in a fair coin toss game and has been studied for over a hundred years. There has been little further work on how the distribution changes when the coin tosses are not fair or when a player has already won the initial coin tosses or, equivalently, starts with a lead. This thesis will first cover a proof of the arcsine distribution. Then, we explore how the distribution changes when the coin the is unfair. Finally, we will explore the distribution when one person has won the first few flips.

Investeringar i aktier eller aktiefonder kan få ens pengar att växa genom den kumulativa avkastning som genereras. Genom ränta-på-ränta-effekten kan en liten ökning i avkastning från dessa investeringar få en stor effekt över en lång tidsperiod. På grund av detta etablerar många investerare strategier för att försöka uppnå en högre avkastning än den generella aktiemarknaden. Att slå marknaden har historiskt sett varit svårt vilket går i linje med det rådande paradigmet om att marknader är effektiva. Empirisk forskning har dock visat på återupprepande prismönster, som inneburit att det funnits möjligheter att strategiskt och systematiskt investera för att generera en högre riskjusterad avkastning än marknaden. Dessa prismönster kallas för anomalier och när de är tidsbaserade benämns de vanligtvis som kalendereffekter. Syftet med studien var att undersöka huruvida kalendereffekter även varit förekommande på marknader med mindre utvecklade institutioner och begränsad tidigare forskning. Studien är avgränsad till aktiemarknader i Afrika och har ställts i relation till motsvarande marknader i några av västvärldens mest välutvecklade ekonomier. En jämförelse har gjorts för att undersöka vart och vilka kalendereffekter som funnits samt hur resultatet skiljer sig mellan Afrika och västvärlden. Studien omfattar en tidsperiod från år 2000 fram till 2020. Resultatet visar något vanligare och mer signifikanta kalendereffekter på de afrikanska marknaderna men inte någon annan tydlig övergripande skillnad vid jämförelse med de västerländska marknaderna. Långa positioner vid månadsskiftet och efterföljande dagar alternativt vid slutet av handelsveckan har kunnat ge en högre riskjusterad avkastning än den generella marknaden i flera länder. Under tidsperioden finns det således belägg för att överavkastning kunnat uppnåtts på ett flertal afrikanska aktiemarknader genom systematiskt planerade investeringar. / Investments in equities or equity funds can help to make your money grow through the cumulative returns generated. Through compound interest, a small increase in return on these investments can have a large effect over a long period of time, resulting in many investors establishing strategies to achieve a higher return than the general stock market. Beating the market has historically been difficult which supports the prevailing paradigm that markets are efficient. However, empirical research has shown recurring price patterns, implying that there have been opportunities to strategically and systematically invest to generate a higher risk-adjusted return than the market. These price patterns are called anomalies and when time-based, are usually referred to as calendar effects. The purpose of this study was to examine whether calendar effects were also present in markets with less developed institutions and limited previous research. The study is focused on stock markets in Africa, which have been compared to corresponding markets in some of the most developed economies in the Western world. A comparison has been made to examine where and what calendar effects existed and how the results differ between Africa and the Western world. The study covers a period from 2000 to 2020. The results show slightly more common and significant calendar effects in the African markets, but no other clear overall difference was observed when compared with the Western markets. Long positions at the end of the month and subsequent days, alternatively at the end of the trading week, have been able to produce a higher risk-adjusted return than the general market in several countries. Thus, during this time period, there is evidence that excess returns could have been achieved in a number of African stock markets through systematically planned investments.

The purpose of this investigation was to test the theoretical possibility of an investor earning a positive cash return from the activities of the stock market despite effectively holding no position at all in said market. The sample data were the daily returns for the shares of the 780 companies listed on the NASDAQ and the New York Stock Exchange (“NYSE”), which fell within the top 500 listed companies by market capitalisation between 1 January 2005 and 31 December 2017. The reversal strategy’s performance was evaluated using portfolios constructed as quantiles of 100 or 500 shares, respectively, where the investor had the option of implementing the reversal strategy immediately after an information-gathering period closed or a day thereafter. The time intervals used were 1 January 2005 to 29 September 2008 (the day the Dow Jones Industrial Average crashed by 777.68 points), 29 September 2008 to 31 December 2017 and 1 January 2005 to 31 December 2017. Of the 1000 portfolios tested in each time interval, at least 416 had positive average returns in every time interval. Of the portfolios that had positive average returns over the time intervals, at least 66 had statistically significant average returns in every time interval. The best-performing portfolio for the entire sample period was a combination of the best-performing pre-crash and post-crash portfolios - an investor who held that portfolio realised a cumulative return of approximately $61.39 for every $1 invested. The conclusion was that it was theoretically possible for an investor to earn a positive cash return from the market’s activities despite effectively holding no position at all in the market. Consequently, it was concluded that the strong form of Fama’s (1970) Efficient Market Hypothesis was disproved. Future research should include out-of-sample tests, tests that include restrictions on short selling and tests that consider the impact of trading costs on portfolio performance, to render the conclusions of this investigation more practically applicable to investors.

Dans la première partie, on étudie la probabilité de retour des groupes métabéliens de type fini. On donne une caractérisation des tels groupes avec grande probabilité de retour en des termes purement algébriques, à l’aide de la dimension de Krull. Cela nécessite, pour les groupes métabéliens, une variation d’un théorème de Kaloujnine et Krasner qui respecte cette dimension. Au passage, on obtient des bornes inférieures et supérieures sur la probabilité de retour des groupes métabéliens en fonction de la dimension de Krull. La seconde partie concerne les profils isopérimétriques des groupes localement compacts compactement engendrés, qu’on utilise pour caractériser l’existence d’une suite de paires de Følner. On démontre que le profil isopérimétrique augmente lorsqu’on passe au quotient, avec des constantes indépendantes de l’échelle, améliorant une théorème de Tessera. Combinant les deux, on obtient que l’existence de suites de paires de Følner passe au quotient. On montre qu’elle passe au sous-groupe fermé, généralisant un résultat correspondant d’Erschler pour les groupes de type fini. Cela permet d’obtenir une preuve plus auto-contenue du théorème principal de la première partie.La troisième partie est un travail en commun avec Kropholler dans lequel on étudie la structure des groupes résolubles de rang sans torsion infini n’ayant pas de section isomorphe à ZwrZ. On en déduit qu’en présence d’une dimension de Krull, ce type de section est la seule obstruction à la finitude du rang sans torsion. / In the fist part, we study the return probability of finitely generated metabelian groups. We give a characterization of such groups with large return probability in purely algebraic terms, namely the Krull dimension of the group. To do so, we establish, for metabelian groups, a variation of a famous embedding theorem of Kaloujinine and Krasner that respects this dimension. Along the way, we obtain lower and upper bounds on the return probability of metabelian groups according to their dimension.The second part of this thesis deals with isoperimetric profiles of locally compact compactly generated groups, that we use to characterize the existence of sequences of Følner couples. We generalize at a compact scale previous results of Tessera, in particular that they increase when going to a quotient group, so as to state in more generality a result from the first part, namely that the existence of Følner couples goes to a quotient group. We also prove that it goes to a closed subgroup. This allows to obtains a more self-contained proof of the main result of the first part of this thesis.The third part is a joint work with Kropholler in which we study the structure of soluble groups of infinite torsion-free rank with no ZwrZ. As a corollary, we obtain that a finitely generated soluble group with Krull dimension has finite torsion-free rank if and only if it has no ZwrZ.

People who suffer a traumatic brain injury (TBI) experience challenges in returning to work differently and at a rate that surpasses the return to work transition for people who experience other types of disabling injuries. In part, this challenge is a result of a lack of policy structure that promotes the successful return to work transition. The purpose of this ethnographic study was to explore the policy implications of the return to work transition for TBI survivors, address the gap in the literature, and identify key factors that contribute to the success of return-to-work programs in Washington State. A hybrid of Smith's institutional ethnography approach and Foucault's critique of bureaucratic institutions was used as the framework for this study. Data were gathered from 12 interviews and 2 focus groups with TBI survivors who had access to TBI support groups and employers connected to the TBI community. Data were inductively coded and categorized using a comparative analytical method. The study results indicate that an inclusive culture, collaborative communication, TBI-focused knowledge, integrated support, and survivor/employer motivation to interact are key factors in the successful return to work process. This study promotes positive social change by providing information for use in expanding TBI employment policy, TBI employment education, and accommodation practices. The study findings are intended to inform new policies to improve employment post-TBI outcomes for TBI survivors, employers, and their community.

Leaders of youth intervention programs provide a significant social service by redirecting at-risk youth onto a productive path. The standards for youth-serving organizations are inconsistent from 1 organization to another across a wide range of youth-worker training certification programs in the United States. A single-case study was conducted to explore the strategies that 3 leaders of a nonprofit organization located in Minnesota, use to select, collect, and analyze data to assess the effectiveness of training certification programs for youth workers. The 2017-2018 Baldrige Excellence Framework provided the structure for a systems-based evaluation of the client organization; Freeman's stakeholder theory was the conceptual lens for the study. Data were collected from conducting semistructured interviews, reviewing the participating organization's internal documents and performance outcomes, and analyzing open-source resources. Through thematic analysis, 4 key themes emerged: (a) the social return on investment analysis and the overall cost savings by investing in and supporting youth programs, (b) the opportunity to focus research on certification for youth workers, (c) the value of providing training for youth workers, and (d) the opportunity to provide a platform for the youth to share success stories with their community. Specific recommendations stemming from the research findings were to create a state or national recognition standard for youth-worker certifications and to make youth work a paid profession. Implementation of these recommendations may result in positive social change by improving the lives and trajectories of youth.

Regulated deficit irrigation (RDI) is the strategy of reducing irrigation rates during a specific period of growth and development, with the objective of conserving water and managing plant growth while maintaining or improving yield and fruit quality. Mature tart cherry (Prunus cerasus L. 'Montmorency') trees in a commercial orchard were subjected to a range of irrigation deficits from pit hardening to harvest during the 2007 and 2008 seasons. Irrigation treatments replaced from 62% to 96% of ETc, during that period. Midday stem water potential measurements were significantly different among treatments before harvest. However, fresh weight yield at harvest did not differ significantly among irrigation treatments in either year (P-value=0.64). In 2008 the amount of undersized fruit eliminated during packout was significantly higher in the treatments replacing 61% and 68% of ETc than in the control (P-value<0.0001), but only amounted to 2.0% and 1.4% of total yields, respectively. This small increase in undersized fruit did not significantly affect packout. Fruit quality measurements, such as soluble solids concentration and chroma of whole intact fruit, increased with the severity of the irrigation deficit. Visible surface bark damage from mechanical harvesting appeared less severe as deficit levels increased. Return bloom was not significantly affected by irrigation treatments.

The primary objective of this study is to examine U.S. repeat migration for blacks, Hispanics, and whites. It investi gates the relationships and patterns of these different racial/ethnic groups utilizing the National Longitudinal Survey of Youth 1979 (NLSY79). Repeat migration within and across categories of individual characteristics for blacks, Hispanics, and whites, is compared in order to determine if there are differences in the overall rates of repeat migration for these groups, once other factors are controlled. To do this several statistical procedures are utilized, and the results of selected descriptive and logistic analyses are presented. The descriptive statistics control for race/ethnicity and examine patterns within the groups; these findings display important relationships to onward and return migration. The inferential statistical method employed is logistic regression for the sample as a whole, which examines the effects across the groups, and the direction of migration. Where past research has not investigated the complexities of repeat migration in combination with race/ethnicity, there are several notable results from this study. Specifically, this research finds that in terms of onward migration, whites are significantly more likely to move onward than are blacks or Hispanics even after controlling for key socioeconomic factors. Changes in marital status are significantly related to migration, and to the direction of repeat migration; individuals who change from "single to married" are likely to be onward migrants, whereas those who change from "married to single" are likely to be return migrants. This study finds there are differences in rates of return migration by level of education for racial/ethnic groups. Moreover, the relationship between onward migration and employment status is different for Hispanics than blacks and whites.

The primary objective of this study was to examine rice production methods with special emphasis on farm and water irrigation management practices in the different rice farm types of the Guayas Basin of Ecuador. To do this, farmers were divided into eight categories on the basis of farm practices, seasonal farming, irrigation facilities and level of mechanization. Profits per hectare ranged from 4,807 to 762.10 sucres per hectare. Mechanization varied from totally mechanized to total absence of machinery. Year round farming varied to seasonal farming. Average production varied from 110 quintals of hulled rice to 20 quintals per hectare. The preparation of farm budgets for the different types, presented some problems, due to the lack of available records by the small farmers and reluctance to provide data by the large mechanized units. The cost/benefit ratios of changing from one type of farming to another were calculated as well as the labor absorption possibilities for the different types of farming. These could provide a criteria for planification of rice policies in Ecuador.

Microcontrollers and integrated circuits in general have become ubiquitous in the world today. All aspects of our lives depend on them from driving to work, to calling our friends, to checking our bank account balance. People who would do harm to individuals, corporations and nation states are aware of this and for that reason they seek to find or create and exploit vulnerabilities in integrated circuits. This dissertation contains three papers dealing with these types of vulnerabilities. The first paper talks about a vulnerability that was found on a microcontroller, which is a type of integrated circuit. The final two papers deal with hardware trojans. Hardware trojans are purposely added to the design of an integrated circuit in secret so that the manufacturer doesn’t know about it. They are used to damage the integrated circuit, leak confidential information, or in other ways alter the circuit. Hardware trojans are a major concern for anyone using integrated circuits because an attacker can alter a circuit in almost any way if they are successful in inserting one. A known method to prevent hardware trojan insertion is discussed and a type of circuit for which this method does not work is revealed. The discussion of hardware trojans is concluded with a new way to detect them before the integrated circuit is manufactured. Modern deep learning models are used to detect the portions of the hardware trojan called triggers that activate them.