Triangular linear systems are fundamental in numerical linear algebra. A triangular linear system has a straight-forward and efficient solution strategy, namely forward substitution for lower triangular systems and backward substitution for upper triangular systems. Triangular systems, or, more generally, systems of triangular type occur frequently in algorithms for more complex problems. This thesis addresses three systems that involve linear systems of triangular type. The first system concerns quasi-triangular matrices. Quasi-triangular matrices are block triangular with 1-by-1 and 2-by-2 blocks on the diagonal. Quasi-triangular systems arise in the computation of eigenvectors from the real Schur form for the non-symmetric eigenvalue problem. This thesis contributes two algorithms for the eigenvector computation, which solve shifted quasi-triangular linear systems in an efficient and scalable way. The second system addresses scaled triangular linear systems. During the solution of a triangular linear system, the entries of the solution can grow. This growth can exceed the representable range of floating-point numbers. Such an overflow can be avoided by solving a scaled triangular system. The solution is scaled prior to every operation that would otherwise result in an overflow. After scaling, the operations can be executed safely. This thesis analyzes the scalability of a recently developed tiled, robust solver for scaled triangular systems, which ensures that at no point in the computation the overflow threshold is exceeded. The third system tackles the scaled continuous-time triangular Sylvester equation, which couples two quasi-triangular matrices. The solution process is prone to overflow. This thesis contributes a robust, tiled solver and demonstrates its practicability. These three systems can be addressed with a variation of forward or backward substitution. Compared to the highly optimized and scalable implementations of standard forward and backward substitution available in HPC libraries,the existing implementations of these three systems run at a smaller fraction of the peak performance. This thesis presents techniques to improve on the performance and robustness of the implementations of the three systems.

Context: The context of this research is to detect and track humans in an underwater environment using deep learning algorithms which can, in turn, reduce the deaths caused due to accidental drowning. Objectives: This study first investigates to find the suitable deep learning algorithms that can be used to detect objects and then an experiment is performed with the chosen algorithms to state the possibility to detect humans in an underwater environment and then evaluate the performance of algorithms. Methods: Firstly, a Literature review is used to find suitable deep learning algorithms and then based on findings an experiment is performed to evaluate the chosen deep learning algorithms. Results: Results from the literature review showed evidence that Faster RCNN and SSD are suitable algorithms and the experimental results showed that Faster RCNN performed better than SSD in detecting humans in an underwater environment. Conclusions: Analyzing the results obtained and considering the real world scenario this thesis is aiming at, it can be concluded that Faster RCNN is the algorithm of choice to detect and track humans in an underwater environment.

Modeling and analysis of imperfection in network data is essential in many applications such as protein–protein interaction networks, ad-hoc networks and social influence networks. In the study of imperfect network data, three issues have to be considered: first the type of imperfection, second the aspects of networks such as existence of nodes/edges or attributes of nodes/edges in which imperfection occurs and third the theory that has been used to represent imperfection. This thesis, first, reviews the different types of imperfection and consolidates the meaning of the terms used in literature. Second, it discusses network aspects and theories through which imperfect network data is represented and analyzed. Amongst all, the most applied model is uncertainty about existence of edges which is represented using probability theory, called probabilistic networks. Third, this thesis surveys queries and algorithms which have been applied over probabilistic networks. Fourth and the main focus of this dissertation is to look deeply at nodes' local properties in probabilistic networks. In our first contribution we have shown that two nodes with the same expected degree can have different properties. In this work we have highlighted the role of other summary information of degree distribution such as variance and skewness in addition to the expected value. In our second contribution, we have introduced two possible definitions of probabilistic ego networks and we have studied the concepts of degree, ego betweenness and ego closeness. One of the main applications of the proposed local properties could be in the sparsification process, in which a network's edges and the probability of the edges are altered, but nodes' local properties are preserved.

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Den här rapporten redovisar och diskuterar resultatet av ett kandidatarbete. Arbetet som utförts var uppdraget Plattform för maskininlärning och visualisering av trafikdata med Institutionen för datavetenskap som kund och Östgötatrafiken som behovsägare och referenspartner. Östgötatrafiken är idag intresserade av maskininlärningsmöjligheter inom trafikområdet och efterfrågar en plattform som möjliggör presentation samt analys av trafikdata med hjälp av maskininlärning. Uppdragets syfte var att utveckla en produkt som passade Östgötatrafikens önskemål för att visualisera trafikdata i Linköping och Norrköping. Projektet utfördes av sju studenter som studerade på Linköpings universitet som en del av kursen TDDD96 Kandidatprojekt i programvaruutveckling och resulterade i webbapplikationen Chronos. Chronos är ett system byggt enligt en treskiktad klient-server-arkitektur där klienten är en webbsida byggd i JavaScript med React och servern är byggd i Python med Flask och Flask-SQLAlchemy. Klienten har kontroller för filtrering av data och visualisering av trafikdata sker på en Leaflet-karta. De data som visualiseras på kartan hämtas automatiskt från Trafiklab, som tillhandahåller API:er för kollektivtrafiken i Sverige, för att bygga en databas med historisk trafikdata. Visualisering av data sker genom att visa bilder av bussarnas hastigheter över en vald tidsperiod. Rapporten innehåller även individuella bidrag från varje gruppmedlem.

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