Magnetic nanoparticles have received extensive attention in the biomedical research, e.g. as prospective contrast agents for T2-weighted magnetic resonance imaging. The ability of a contrast agent to enhance the relaxation rate of 1 H in its vicinity is quantified by relaxivity. The main aim of this thesis is to evaluate the transversal re- laxivity of ε-Fe2−x Alx O3 nanoparticles coated with amorphous silica or citrate - its dependence on external magnetic field, temperature and thickness of silica coating - by means of nuclear magnetic resonance. The aluminium content x = 0.23(1) was determined from XRF, the material was further characterised by XRPD, Möss- bauer spectroscopy, DLS, TEM and magnetic measurements. The size of magnetic cores was ∼ 21 nm, the thickness of silica coating ∼ 6,10,17 and 21 nm. Magne- tization of the ε-Fe2−x Alx O3 nanoparticles increased by ∼ 30 % when compared to ε-Fe2O3. The saturating dependence of relaxivity on external magnetic field and on the linear decrease with increase of thickness of silica coating contravene the theo- retical model of motional averaging regime (MAR); nevertheless, the temperature dependence acquired in 0.47 T and 11.75 T may be explained by MAR. In compari- son to ε-Fe2O3 nanoparticles, the relaxivity of examined samples was higher for par-...

In risk management one important aspect is the allocation of total portfolio risk into its components. This can be done by measuring each components' risk contribution relative to the total risk, taking into account the covariance between components. The measurement procedure is straightforward under assumptions of elliptical distributions but not under the commonly used multivariate log-normal distributions. Two portfolio strategies are considered, the "buy and hold" and the "constant mix" strategy. The profits and losses of the components of a generic portfolio strategy are defined in order to enable a proper definition of risk contribution for the constant mix strategy. Then kernel estimation of risk contribution is performed for both portfolio strategies using Monte Carlo simulation. Further, applications for asset and risk management with risk contributions are discussed in the context of life insurance. / En viktig aspekt inom riskhantering är tilldelning av total portföljrisk till tillångsportföljens beståndsdelar. Detta kan åstadkommas genom att mäta riskbidrag, som även kan ta hänsyn till beroenden mellan risktillgångar. Beräkning av riskbidrag är enkel vid antagande om elliptiska fördelningar så som multivariat normalfördelning, men inte vid antagande om multivariat log-normalfördelning där analytiska formler saknas. Skillnaden mellan riskbidragen inom två portföljstrategier undersöks. Dessa strategier är "buy and hold" och "constant mix" (konstant ombalansering). Tilldelning av resultaten hos de olika beståndsdelarna med en generisk portföljstrategi härleds för att kunna definiera riskbidrag för "constant mix" portföljstrategin. "Kernel estimering" används för att estimera riskbidrag genom simulering. Vidare diskuteras applikationer för tillgångs- och riskhantering inom ramen för livförsäkringsbolag.

In this dissertation an overview on the real representation of quaternions in distribution theory is given. The density functions of the p-variate and matrix-variate quaternion normal distributions are derived from first principles, while that of the quaternion Wishart distribution is derived from the real associated Wishart distribution via the characteristic function. Applications of this theory in hypothesis testing is presented, and the density function of Wilks's statistic is derived for quaternion Wishart matrices. / Dissertation (MSc)--University of Pretoria, 2010. / Statistics / unrestricted

In this discusses four different approaches used during a statistics tutorial of a group of first year undergraduates studying computer science related degrees at the University of Westminster UK. The four approaches were each implemented in an attempt to keep the students interested in the statistics topics delivered. It was found that “Chalk and Talk” (i.e. board work) was not the best form of imparting knowledge to the students of the group as determined by student analysing feedback forms and generally observing student behaviour and listening to student comments over a number of years delivering statistics topics. The duration of each tutorial was two hours. The teaching strategies adopted were: a) A class quiz. b) Group explanation of material to members of the individual’s group. c) Group explanation of material to members of the entire class. d) Students teaching at the front of the class. Each of the methods will now be discussed with the relative merits and defects included for a comparison. It was found that each method worked better at the end of each module when the students were more familiar with the topics introduced on the module.

Autonomous vehicles in the recent era are robust vehicles that have the capability to drive themselves without human involvement using sensors and Simultaneous Localization and Mapping algorithms, which helps the vehicle gain an understanding of its environment while driving with the help of laser scanners (Velodyne), IMU and GPS to collect data and solidify the foundation for locating itself in an unknown environment. Various methods were studied and have been tested for increasing the efficiency of registration and optimization over the years but the implementation of the NDT library for mapping and localization have been found to be fast and more accurate as compared to conventional methods. The objective of this thesis is to ascertain a robust method of pose estimation of the vehicle by combining data from the laser sensor, with the data from the IMU and GPS receiver on the vehicle. The initial estimate prediction of the position is achieved by generating a 3D map using the Normal Distribution Transform and estimating the position using the NDT localization algorithm and the GPS data collected by driving the vehicle in an external environment. The results presented explain and verify the hypothesis being stated and shows the comparison of the localization algorithm implemented with the GPS receiver data available on the vehicle while driving. / Autonoma fordon har på senare tid utvecklats till robusta fordon som kan köra sig själva utan hjälp av en människa, detta har möjliggjorts genom användandet av sensorer och algoritmer som utför lokalisering och kartläggning samtidigt (SLAM). Dessa sensorer och algoritmer hjälper fordonet att förstå dess omgivning medan det kör och tillsammans med laser skanners (Velodyne), IMU'er och GPS läggs grunden för att kunna utföra lokalisering i en okänd miljö. Ett flertal metoder har studerats och testats för att förbättra effektiviteten av registrering och optimering under åren men implementationen av NDT biblioteket för kartläggning och lokalisering har visat sig att vara snabbt och mer exakt jämfört med konventionella metoder. Målet med detta examensarbete är att hitta en robust metod för uppskatta pose genom att kombinera data från laser sensorn, en uppskattning av den ursprungliga positionen som fås genom att generera en 3D karta med hjälp av normalfördelningstransformen och GPS data insamlad från körningar i en extern miljö. Resultaten som presenteras beskriver och verifierar den hypotes som läggs fram och visar jämförelsen av den implementerade lokaliseringsalgoritmen med GPS data tillgänglig på fordonet under körning.

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Based on an application in the field of server consolidation, we consider the one-dimensional cutting stock problem with nondeterministic item lengths. After a short introduction to the general topic we investigate the case of normally distributed item lengths in more detail. Within this framework, we present two lower bounds as well as two heuristics to obtain upper bounds, where the latter are either based on a related (ordinary) cutting stock problem or an adaptation of the first fit decreasing heuristic to the given stochastical context. For these approximation techniques, dominance relations are discussed, and theoretical performance results are stated. As a main contribution, we develop a characterization of feasible patterns by means of one linear and one quadratic inequality. Based on this, we derive two exact modeling approaches for the nondeterministic cutting stock problem, and provide results of numerical simulations.

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Collected data may simultaneously be of low sample size and high dimension. Such data exhibit some geometric regularities consisting of a single observation being a rotation on a sphere, and a pair of observations being orthogonal. This thesis investigates these geometric properties in some detail. Background is provided and various approaches to the result are discussed. An approach based on the mean value theorem is eventually chosen, being the only candidate investigated that gives explicit convergence bounds. The bounds are tested employing Monte Carlo simulation and found to be adequate. / Data som insamlas kan samtidigt ha en liten stickprovsstorlek men vara högdimensionell. Sådan data uppvisar vissa geometriska mönster som består av att en enskild observation är en rotation på en sfär, och att ett par av observationer är rätvinkliga. Den här uppsatsen undersöker dessa geometriska egenskaper mer detaljerat. En bakgrund ges och olika typer av angreppssätt diskuteras. Till slut väljs en metod som baseras på medelvärdessatsen eftersom detta är den enda av de undersökta metoderna som ger explicita konvergensgränser. Gränserna testas sedermera med Monte Carlo-simulering och visar sig stämma.