Positron emission tomography (PET) is a non-invasive imaging technique which utilizes positron-emitting radiopharmaceuticals (PERs) to characterize biological processes in tissues of interest. A PET scanner is usually composed of multiple scintillation crystal detectors placed in a ring so as to capture coincident photons from a position annihilation. These detectors require a crystal lookup table (CLUT) to map the detector response to the crystal of interaction. These CLUTs must be accurate, lest events get mapped to the wrong crystal of interaction degrading the final image quality. This work describes an automated algorithm, for CLUT generation, focused around Gaussian Mixture Models (GMM) with Thin Plate Splines (TPS). The algorithm was tested with flood image data collected from 16 detectors. The method maintained at least 99.8% accuracy across all tests. This method is considerably faster than manual techniques and can be adapted to different detector configurations. / February 2016

Bayesian surface smoothing using splines usually proceeds by choosing the smoothness parameter through the use of data driven methods like generalized cross validation. In this methodology, knots of the splines are assumed to lie at the data locations. When anisotropy is present in the data, modeling is done via parametric functions. In the present thesis, we have proposed a non-parametric approach to Bayesian surface smoothing in the presence of anisotropy. We use eigenfunctions generated by thin-plate splines as our basis functions. Using eigenfunctions does away with having to place knots arbitrarily, as is done customarily. The smoothing parameter, the anisotropy matrix, and other parameters are simultaneously updated by a Reversible Jump Markov Chain Monte Carlo (RJMCMC) sampler. Unique in our implementation is model selection, which is again done concurrently with the parameter updates. Since the posterior distribution of the coefficients of the basis functions for any given model order is available in closed form, we are able to simplify the sampling algorithm in the model selection step. This also helps us in isolating the parameters which influence the model selection step. We investigate the relationship between the number of basis functions used in the model and the smoothness parameter and find that there is a delicate balance which exists between the two. Higher values of the smoothness parameter correspond to more number of basis functions being selected. Use of a non-parametric approach to Bayesian surface smoothing provides for more modeling flexibility. We are not constrained by the shape defined by a parametric shape of the covariance as used by earlier methods. A Bayesian approach also allows us to include the results obtained from previous analysis of the same data, if any, as prior information. It also allows us to evaluate pointwise estimates of variability of the fitted surface. We believe that our research also poses many questions for future research.

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Att i förväg försöka förutsäga vilket lag som kommer vinna i en fotbollsmatch har nog de flesta försökt sig på någon gång. Att gissa och att faktiskt försöka att analysera båda lagens förutsättningar är två väldigt olika metoder att komma fram till sitt resultat. I och med att datorkraften de senaste åren kraftigt förbättrats har det också kommit fler och framför allt tyngre matematiska modeller för att skatta utfallet av matcher. I detta examensarbete används Pi-ratingsystemet som går ut på att varje lag får en rating för hur bra man är på hemma- respektive bortaplan. Som en utveckling av den ursprungliga Pi-rating modellen används det i detta arbete tre olika modeller för att prediktera lagens framtida rating. Modellerna som används är enkelt glidande medelvärde, enkel exponentiell utjämning och en ARIMA-modell. En lösning på hur nya lag som inte spelade i ligan föregående år ska behandlas föreslås också. Avslutningsvis diskuteras olika investeringsmetoder som kan användas för att använda resultat från modellerna på marknaden för vadslagning. Resultatet visar att en spelstrategi som utnyttjat Kellys formel ger störst avkastning för kalibreringsdatat. När denna strategi används på matcher utanför kalibreringsåren visar resultatet på en mycket låg vinst och framför allt att vinsten under lång tid är negativ, vilket från en investeringssyn inte är något man önskar. Sammanfattningsvis är denna metod inte i sig själv tillräckligt bra för att ge en säker avkastning men är en bra grund som kan byggas ut för att ta hänsyn till fler faktorer och då ge möjlighet till stabilare och mer långsiktiga vinster. / To predict a soccer game in advance is something that has been done by most people. If the prediction is the result of an advanced mathematical formula or just ha pure guess done on your favorite team is very different. Since the computer power in recent years has greatly improved the number of mathematical approaches has increased and it is especially the computational heavy models that have increased in number. In this thesis the Pi-rating system is used it gives each team a home and away rating that describe how good/bad they are compared to the average competing team. As an extension of the original Pi-rating model, in this thesis time series analysis is used to predict future values of the teams rating, three different methods are tested and they are simple moving average, simple exponential smoothing and an ARIMA-model. A solution to how new teams that did not play in the league last year should be handled is also suggested. Finally a breath discussion and test of different investment methods that can be applied on the final model to be used on the sport betting market. The results show that the greatest returns on the calibration data is achieved when Kelly’s formula is used as an investment method on an ARIMA(0,1,1)-model, but when this strategy is used outside calibration data, the result shows a very low profit and the method  fails to give a stable long term return, which from an investment point of view is not desirable. The conclusion is that this method is not in itself good enough to provide a safe return but is a good foundation that can be expanded to take more factors into account, and then hopefully give bigger and more stable winnings.

Wild canid populations exhibit different anatomical morphologies compared to domesticated dogs in North America. This is particularly important concerning archaeological sites, which may contain early domesticated species, for the proper identification of osteological remains. Previous studies have indicated domestic dogs exhibit a shorter rostrum accompanied by a crowded tooth row; however, none describe the overall complexity of these changes. Consequently, using a landmark-based geometric morphometric analysis, cranial morphological characteristics were examined in North American wild canids: the gray wolf (Canis lupus), coyote (Canis latrans), red wolf (Canis rufus), and the domestic dog (Canis familiaris). The shape and size of the cranium in lateral and ventral views were compared between the three wild species to the group of domesticated dogs. Wild canids clustered separately from the domestic group in all statistical analyses. Results indicate an expansion of the orbital region, a compression of the rostrum, and an overall warping in the shape and orientation of the skull. In domestic species, there is also a downward shift in the frontal portion of the skull accompanied by the braincase assuming a more upward position. This technique successfully depicted how slight changes in isolated areas of the cranium can have an impact on the overall shape and morphology of the skull. We presume these changes in cranial anatomy reflect the recent selective pressures domestic dogs have undergone since diverging from their wild ancestors.

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