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Monte Carlo simulations are embarrassingly parallel in nature, so having a parallel and efficient random number generator becomes crucial. To have a parallel generator with uncorrelated processors, parallelization methods are implemented together with a binary tree mapping. Although, this method has considerable advantages, because of the constraints arising from the binary tree structure, a situation defined as problem of falling off the tree occurs. In this thesis, a new spawning method that is based on binary tree traversal and new spawn processor appointment is proposed to use when falling off the tree problem is encountered. With this method, it is seen that, spawning operation becomes more costly but the independency of parallel processors is guaranteed. In Monte Carlo simulations, random number generation time should be unperceivable when compared with the execution time of the whole simulation. That is why / linear congruential generators with Mersenne prime moduli are used. In highly branching Monte Carlo simulations, cost of parameterization also gains importance and it becomes reasonable to consider other types of primes or other parallelization methods that provide different balance between parameterization cost and random number generation cost. With this idea in mind, in this thesis, for improving performance of linear congruential generators, two approaches are proposed. First one is using Sophie-Germain primes as moduli and second one is using a hybrid method combining both parameterization and splitting techniques. Performance consequences of Sophie-Germain primes over Mersenne primes are shown through graphics. It is observed that for some cases proposed approaches have better performance consequences.

Digital urban tree registers serve many porposes and facilitate the administration, care and management of urban trees within a city or municipality. Currently, mapping of urban tree stands is carried out manually with methods which are both laborious and time consuming. The aim of this study is to establish a way of operation based on the use of existing LiDAR data and othophotos to automatically detect individual trees. By using the extensions LIDAR Analyst and Feature Analyst for ArcMap a tree extraction was performed. This was carried out over the extent of the city district committee area of Östermalm in the city of Stockholm, Sweden. The results were compared to the city’s urban tree register and validated by calculating its Precision and Recall. This showed that FeatureAnalyst generated the result with the highest accuracy. The derived trees were represented by polygons which despite their high accuracy make the result unsuitable for detecting individual tree positions. Even though the use of LIDAR Analyst resulted in a less precise tree mapping result, individual tree positions were detected satisfactory. This especially in areas with more sparse, regular tree stands. The study concludes that the use of both tools complement each other and compensate the shortcomings of the other. FeatureAnalyst maps an acceptable tree coverage while LIDAR Analyst more accurately identifies individual tree positions. Thus, a combination of the two results could be used for individual tree mapping. / Digitala urbana trädregister tjänar många syften och underlättar för städer och kommuner att administrera, sköta och hantera sina park- och gatuträd. Dagens kartering av urbana trädbestånd sker ofta manuellt med metoder vilka är både arbetsintensiva och tidskrävande. Denna studie syftar till att utveckla ett arbetssätt för att med hjälp av befintliga LiDAR-data och ortofoton automatiskt kartera individuella träd. Med hjälp av tilläggen LIDAR Analyst och FeatureAnalyst för ArcMap utfördes en trädkartering över Östermalms stadsdelsnämndsområde i Stockholms stad. Efter kontroll mot stadens träddatabas och validering av resultatet genom beräknandet av Precision och Recall konstaterades att användningen av FeatureAnalyst resulterade i det bästa trädkarteringsresultatet. Dessa träd representeras av polygoner vilket medför att resultatet trots sin goda täckning inte lämpar sig för identifierandet av enskilda trädpositioner. Även om användningen av LIDAR Analyst resulterade i ett mindre precist karteringsresultat erhölls goda positionsbestämmelser för enskilda träd, främst i områden med jämna, glesa trädbestånd. Slutsatsen av detta är att användandet av de båda verktygen kompenserar varandras tillkortakommanden där FeatureAnalyst ger en godtagbar trädtäckning medan LIDAR Analyst bättre identifierar enskilda trädpositioner. En kombination av de båda resultaten skulle alltså kunna användas i trädkarteringssyfte.