This bachelor thesis shows a way to classify second order symmetric tensors in the Lorentz metric. Some basic prerequisite about indefinite and definite algebra is introduced, such as the Jordan form, indefinite inner products, the Segre type, and the Minkowski space. There are also some results concerning the invariant 2-spaces of a symmetric tensor and a different approach on how to classify second order symmetric tensor.

We consider an SDE driven by a Lévy noise on a foliated manifold, whose trajectories stay on compact leaves. We determine the effective behavior of the system subject to a small smooth transversal perturbation of positive order epsilon. More precisely, we show that the average of the transversal component of the SDE converges to the solution of a deterministic ODE, according to the average of the perturbing vector field with respect to the invariant measures on the leaves (of the unpertubed system) as epsilon goes to 0. In particular we give upper bounds for the rates of convergence. The main results which are proved for pure jump Lévy processes complement the result by Gargate and Ruffino for Stratonovich SDEs to Lévy driven SDEs of Marcus type.

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Functional magnetic resonance imaging (fMRI) is a prime example of multi-disciplinary research. Without the beautiful physics of MRI, there wouldnot be any images to look at in the first place. To obtain images of goodquality, it is necessary to fully understand the concepts of the frequencydomain. The analysis of fMRI data requires understanding of signal pro-cessing, statistics and knowledge about the anatomy and function of thehuman brain. The resulting brain activity maps are used by physicians,neurologists, psychologists and behaviourists, in order to plan surgery andto increase their understanding of how the brain works. This thesis presents methods for real-time fMRI and non-parametric fMRIanalysis. Real-time fMRI places high demands on the signal processing,as all the calculations have to be made in real-time in complex situations.Real-time fMRI can, for example, be used for interactive brain mapping.Another possibility is to change the stimulus that is given to the subject, inreal-time, such that the brain and the computer can work together to solvea given task, yielding a brain computer interface (BCI). Non-parametricfMRI analysis, for example, concerns the problem of calculating signifi-cance thresholds and p-values for test statistics without a parametric nulldistribution. Two BCIs are presented in this thesis. In the first BCI, the subject wasable to balance a virtual inverted pendulum by thinking of activating theleft or right hand or resting. In the second BCI, the subject in the MRscanner was able to communicate with a person outside the MR scanner,through a virtual keyboard. A graphics processing unit (GPU) implementation of a random permuta-tion test for single subject fMRI analysis is also presented. The randompermutation test is used to calculate significance thresholds and p-values forfMRI analysis by canonical correlation analysis (CCA), and to investigatethe correctness of standard parametric approaches. The random permuta-tion test was verified by using 10 000 noise datasets and 1484 resting statefMRI datasets. The random permutation test is also used for a non-localCCA approach to fMRI analysis.

The objective of this master thesis is to identify “key-drivers” embedded in customer satisfaction data. The data was collected by a large transportation sector corporation during five years and in four different countries. The questionnaire involved several different sections of questions and ranged from demographical information to satisfaction attributes with the vehicle, dealer and several problem areas. Various regression, correlation and cooperative game theory approaches were used to identify the key satisfiers and dissatisfiers. The theoretical and practical advantages of using the Shapley value, Canonical Correlation Analysis and Hierarchical Logistic Regression has been demonstrated and applied to market research.

I have with this thesis sought to understand how chick lit could be useful in the classroom in the teaching of Swedish B-course in high school. Based on the model of critical literacy I am arguing that this genre would help to meet the objectives of the policy documents which, among other things, are to critically examine and analyze various types of texts. I have found that some of these texts could be used for analyzing and critically examine the ideological dimensions of texts and cultural heritage by the model of critical literacy, and also as a counterweight to the more traditional teaching of the canonical literature as a literary historical stuff that students should learn. I have also wanted to create a basis for discussions about literature in the classroom based on the chick lit genre. To do this I have, based on three themes and questions from the model of critical literacy, tried to focus on issues that might emerge from the ideological analysis and critical review. The model aims to deconstruct norms of society, and in the work of chick lit, I wanted to show how you could deconstruct norms around gender.

Human activities, such as agricultural activity, housing construction, forest logging, etc., play an important role in vegetation changes. Any disturbance to the ecosystem by a severe change in landscape patterns may reduce the survival capacity of certain plant species. In recent years, many studies have used a geographic information system to establish spatial data on vegetation changes; this information includes both the plant species and their spatial structure. Therefore, the aim of this study is to investigate the trends and patterns of vegetation changes and the degree of correlation with the particular environmental features at Wangan Island and Chimei Island in the Penghu Islands, from 1979 to 2009. Both islands have very similar natural features, including geographic location, natural environment, and economic development, but the spatial structures of the land use type are different. The study makes use of geographic information systems, detrended correspondence analysis, canonical correspondence analysis and landscape ecological indicators as study tools. The results are expected to promote our understanding of the spatial distribution patterns of vegetation types and plant species. The results can be divided into three areas. First, both islands follow the same trend with regard to changes in land cover, but the rates of change are different. And the spatial structure of land use types affects the location of land cover types. Example, the centralized and decentralized villages both impact the distribution of the woodland. The mesh and ring road both impact the location of agricultural land. Second, the grassland plant species are correlated with the environmental factors, but the forest plant species are not. The major woodland specie is Leucaena leucocephala on both islands, whose physiological habits may reduce the degree of the correlation. Third, compared to the two islands, Chimei Island is more significant about that the vegetation types are correlated with the neighboring land use types. Finally, the plant species of the local vegetation types could be predicted by changes in the type of land use. In addition, this study has built a trend scheme of the spatial structure changes on Wangan Island and on Chimei Island, which can be used in the island¡¦s future environmental planning.

In this thesis, we propose an adaptive multicast key management scheme for secure group communications. In a secure communication session, group members could dynamically join and leave the group. Therefore, a multicast key management scheme is required to ensure that only legitimate users will continue to receive the latest information. In the literature, star-based key management schemes and tree-based key management schemes were proposed for secure group communications. In this thesis, we propose a novel canonical-tree-based key management scheme. We evaluate the average rekeying costs of the canonical-tree-based scheme as well as two well-known key management schemes. We find that the leaving probability of group members dominates the relative performance between the star-based scheme and the tree-based scheme. Based on the above observations, we propose an adaptive key management scheme that is superior to both the star-based scheme and the tree-based scheme in a dynamic environment.

The study intended to investigate the phylogeography of mid-altitude species, Japalura brevipes, which is the endemic to Taiwan. I used mitochondrial cytochrome b sequences and morphological characters to investigate the phylogeography. The molecular results showed that there are 16 haplotypes. The length of partial cytochrome b sequences is 617 bp including 84 informative sites, and the mean genetic distance is 5.4%. In phylogenetic analyses, three major clades were found in the phylogenetic trees. Moreover, these clades (north, central-north and south) corresponded to the geographic distribution. Analysis of population genetic structure revealed significant differentiation among populations, and most of the haplotypes were restricted to the locally. The morphological analyses showed that there is no difference between sexes at 18 characters, with the exception of the axilla-groin length and dorsal-crest scales. The Principal Component Analysis and Canonical Discriminate Analysis using 16 morphological characters showed the different results. Principal Component Analysis failed to separate populations. However, Canonical Discriminate Analysis could discriminate the populations of Guanwu, Nanheng, Sihyuantkou and Wuling Farm from others. Phylogeography of J. brevipes belonged to category 1 defined by Avise (2000). I infer refuge effect and dispersal ability hypotheses to explain the genetic structure of J. brevipes.

In this study, the hydrology and physical, chemical and biological variables of a shallow lake system including the Lakes Mogan and Eymir between 1997-2005 were evaluated. In Lake Eymir, a biomanipulation study was conducted between August, 1998 &ndash / December, 1999. Upon biomanipulation, Lake Eymir shifted to clearwater state with submerged vegetation domination during 2000-2003. However, in 2004, the lake shifted back to algae-dominated turbid state since the buffer mechanisms provided by submerged plants were absent. In the summer of 2005, fish kills were observed due to algal bloom. However, due to increasing hydraulic residence time in the lake, internal processes became more important for nutrients. Lake Mogan faces seasonal and interannual water level fluctuations. During the low water levels experienced in 2001 and 2005, which coincided with the high hydraulic residence times, the in-lake phosphorus amount was controlled by internal processes rather than external loading. Moreover, results revealed that hydrology and submerged plants were important in the ecology of Lake Mogan. Furthermore, the relationship between the phytoplankton, zooplankton and the environment in Lakes Eymir and Mogan, which was predicted via Canonical Corresponding Analysis, revealed that nutrients and water transparency were both important for plankton communities. Both the top-down and bottom up effects were valid in Lake Eymir, while only the bottom-up effect and submerged plants were important for Lake Mogan. Finally, the present study provided a good example for the submerged plant dominated clearwater state triggered by biomanipulation, and the impact of hydrology on the ecology of shallow lakes.