One of the great aims of statistics, the science of collecting, analyzing, and interpreting data, is to protect against the probability of falsely rejecting an accepted claim, or hypothesis, given observed data stemming from some experiment. This is generally known as protecting against a Type I Error, or controlling the Type I Error rate. The extension of this protection against Type I Errors to the situation where thousands upon thousands of hypotheses are examined simultaneously is known as multiple hypothesis testing. This dissertation presents an improvement to an existing multiple hypothesis testing approach, the Focus Level method, specific to gene set testing (a branch of genomics) on Gene Ontology graphs. This improvement resolves a long standing computational difficulty of the Focus Level method, providing more than a 15.000-fold increase in computational efficiency. This dissertation also presents a solution to a multiple testing problem in genetics where a specific approach to mapping genes underlying quantitative traits of interest requires a multiplicity adjustment approach that both corrects for the number of tests while also ensuring logical consistency. The power advantage of the solution is demonstrated over the current standard approach to the problem. A side issue of this model framework led to the development of a new bivariate approach to quantitative trait marker detection, which is presented herein. The overall contribution of this dissertation to the statistics literature is that it provides novel solutions that meet real needs of practitioners in genetics and genomics with the aim of ensuring both that truth is discovered and that discoveries are actually true.

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Sector-Wise Golden Angle (SWIG) is a novel approach that was developed to address the limitations associated with Golden Angle radial imaging, commonly used for high temporal resolution flow measurements. Golden angle radial imaging is a time-efficient method that effectively reduces motion sensitivity. However, binned or retrospectively gated imaging where multiple heartbeats are utilized to acquire a single time series may lead to uneven coverage of k- space, ultimately resulting in poor image quality. In contrast, SWIG restricts the radial profiles to a sector of k-space per heartbeat, ensuring even distributions of spokes during retrospectively gated acquisitions. One drawback of SWIG is the loss of ability to reconstruct real-time images. The combination of sorted and unsorted acquisition simultaneously holds significant potential and could be applied in various domains. The goal of the thesis work was to design a trajectory that combines radial and spiral k-space sampling, enabling hybrid real-time and retrospectively gated imaging. The objective was to obtain an image series with comparable quality to a SWIG readout while retaining the ability to reconstruct a low-resolution real-time image series from the same data. To evaluate the hybrid trajectory, the numerical phantom XCAT was used to generate synthetic MRI images. Binned images were sampled using a hybrid-SWIG method, yielding similar image quality to a conventional SWIG image series, with the added benefit of being able to reconstruct a low-resolution real-time image series. Although the current method was only evaluated in a numerical phantom and may require additional adjustment to be suitable for a real MRI scanner, the results show that it is possible to combine radial and spiral imaging in a single readout.

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Social entrepreneurship and related concepts have received an increasing amount of attention during the last years. Social entrepreneurship is characterized by ventures with a social mission, seeking to address societal challenges and needs. The social goal is the primary goal of the business activities whereas generating economic profit is not the main objective, yet still possible. Social entrepreneurship is often seen as a powerful tool for creating sustainable development, a fundamental goal of many businesses, countries and organizations today. Just like any other firm, social entrepreneurs need finance in order to exist. This thesis seeks to examine how Swedish social entrepreneurs finance their businesses. A questionnaire was sent out to Swedish social entrepreneurs and the results suggest that Swedish social entrepreneurs to a large extent rely on governmental funds and support, personal resources and internally generated capital. Access to the traditional banking system seems to be limited compared to traditional entrepreneurs. There seems to be a gap between the demand and supply of external capital since the majority of the respondents believe that they have a limited access to external capital. 60 per cent of the respondents reported a positive economic result in the last fiscal year. Furthermore, the majority of the respondents want to expand their businesses in the future but the largest obstacles seem to be lack of financing and political aspects. The respondents hope for, among other things, an improved attitude towards social entrepreneurship in general, more financing and increased collaboration with Swedish municipalities. Altogether the results highlight the role of the government in supporting and promoting this type of firms in Sweden.

Neural networks are regarded as state of the art within many areas of machine learning, however due to their growing complexity and size, a question regarding their trustability and understandability has been raised. Thus, neural networks are often being considered a "black-box". This has lead to the emersion of evaluation methods trying to decipher these complex networks. Two of these methods, layer-wise relevance propagation (LRP) and sensitivity analysis (SA), are used to generate heatmaps, which presents pixels in the input image that have an impact on the classification. In this report, the aim is to do a usability-analysis by evaluating and comparing these methods to see how they can be used in order to understand a particular classification. The method used in this report is to iteratively distort image regions that were highlighted as important by the two heatmapping-methods. This lead to the findings that distorting essential features of an image according to the LRP heatmaps lead to a decrease in classification score, while distorting inessential features of an image according to the combination of SA and LRP heatmaps lead to an increase in classification score. The results corresponded well with the theory of the heatmapping-methods and lead to the conclusion that a combination of the two evaluation methods is advocated for, to fully understand a particular classification. / Neurala nätverk betraktas som den senaste tekniken i många områden inom maskininlärning, dock har deras pålitlighet och förståelse ifrågasatts på grund av deras växande komplexitet och storlek. Således, blir neurala nätverk ofta sedda som en "svart låda". Detta har lett till utvecklingen  av evalueringsmetoder som ämnar att tolka dessa komplexa nätverk. Två av dessa metoder, layer-wise relevance propagation (LRP) och sensitivity analysis (SA), används för att generera färgdiagram som visar pixlar i indata-bilden som har en påverkan på klassificeringen. I den här rapporten, är målet att göra en användarbarhets-analys genom att utvärdera och jämföra dessa metoder för att se hur de kan användas för att förstå en specifik klassificering. Metoden som används i denna rapport är att iterativt förvränga bilder genom att följa de två färgdiagrams-metoderna. Detta ledde till insikterna att förvrängning av väsentliga delar av bilden, vilket framgick ur LRP färgdiagrammen, tydligt minskade sannolikheten för klassen. Det framkom även att förvrängning av oväsentliga delar, som framgick genom att kombinera SA och LRP färgdiagrammen, ökade sannolikheten för klassen. Resultaten stämde väl överens med teorin och detta ledde till slutsatsen att en kombination av metoderna rekommenderas för att förstå en specifik klassificering.

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Hydropower plays an important role in the Swedish power system and is a valuable renewable energy source with great ability for regulation. It is, therefore, crucial to plan and optimize hydropower in a way that is effective. In this project, the Skellefte River is modeled with the software Spine. The focus is on applying a piece-wise linear function to describe the electricity production, instead of a simpler linear one, and optimizing the profit. The results of the optimization indicate that the piece-wise linear function gives accurate values on the electricity production. This work has also further contributed to the development of Spine. / Vattenkraft spelar en viktig roll i det svenska elsystemet och är en värdefull förnybar energikälla med stor regleringsförmåga. Det är därför avgörande att planera och optimera vattenkraft på ett effektivt sätt. I detta projekt modelleras Skellefteälven med programvaran Spine. Fokus ligger på att tillämpa en styckvis linjär funktion för att beskriva elproduktionen istället för att använda en enklare linjär funktion. Modellen optimeras efter pris. Resultaten av optimeringen indikerar att den styckvis linjära funktionen ger korrekta värden på elproduktionen. Detta arbete har också bidragit till den fortsatta utvecklingen av Spine. / Kandidatexjobb i elektroteknik 2022, KTH, Stockholm

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