This thesis presents several statistical analysis on a cooperative project with Dr. Pallas and Yuting Mao from Biology Department of Georgia State University. This research concludes the impact of cauterize size of animals’ midbrain on auditory and visual response in brains. Besides some already commonly used statistical analysis method, such as MANOVA and Frequency Test, a unique combination of Permutation Test, Kolmogorov-Smirnov Test and Wilcoxon Rank Sum Test is applied to our non-parametric data. Some simulation results show the Permutation Test we used has very good powers, and fits the need for this study. The result confirms part of the Biology Department’s hypothesis statistically and enhances more complete understanding of the experiments and the potential impact of helping patients with Acquired Brain Injury.

We propose a new method to perform functional principal component analysis (FPCA) for discretely observed functional data by solving successive optimization problems. The new framework can be applied to both regularly and irregularly observed data, and to both dense and sparse data. Our method does not require estimates of the individual sample functions or the covariance functions. Hence, it can be used to analyze functional data with multidimensional arguments (e.g. random surfaces). Furthermore, it can be applied to many processes and models with complicated or nonsmooth covariance functions. In our method, smoothness of eigenfunctions is controlled by directly imposing roughness penalties on eigenfunctions, which makes it more efficient and flexible to tune the smoothness. Efficient algorithms for solving the successive optimization problems are proposed. We provide the existence and characterization of the solutions to the successive optimization problems. The consistency of our method is also proved. Through simulations, we demonstrate that our method performs well in the cases with smooth samples curves, with discontinuous sample curves and nonsmooth covariance and with sample functions having two dimensional arguments (random surfaces), repectively. We apply our method to classification problems of retinal pigment epithelial cells in eyes of mice and to longitudinal CD4 counts data. In the second part of this dissertation, we propose a sparse Fisher’s discriminant analysis method with thresholded linear constraints. Various regularized linear discriminant analysis (LDA) methods have been proposed to address the problems of the LDA in high-dimensional settings. Asymptotic optimality has been established for some of these methods when there are only two classes. A difficulty in the asymptotic study for the multiclass classification is that for the two-class classification, the classification boundary is a hyperplane and an explicit formula for the classification error exists, however, in the case of multiclass, the boundary is usually complicated and no explicit formula for the error generally exists. Another difficulty in proving the asymptotic consistency and optimality for sparse Fisher’s discriminant analysis is that the covariance matrix is involved in the constraints of the optimization problems for high order components. It is not easy to estimate a general high-dimensional covariance matrix. Thus, we propose a sparse Fisher’s discriminant analysis method which avoids the estimation of the covariance matrix, provide asymptotic consistency results and the corresponding convergence rates for all components. To prove the asymptotic optimality, we provide an asymptotic upper bound for a general linear classification rule in the case of muticlass which is applied to our method to obtain the asymptotic optimality and the corresponding convergence rate. In the special case of two classes, our method achieves the same as or better convergence rates compared to the existing method. The proposed method is applied to multivariate functional data with wavelet transformations.

O uso de sistemas denominados Brain Computer Interface, ou simplesmente BCI, para controle de dispositivos tem gerado cada vez mais trabalhos de análise de sinais de EEG, principalmente devido ao fato do desenvolvimento tecnológico dos sistemas de processamento de dados, trazendo novas perspectiva de desenvolvimento de equipamentos que auxiliem pessoas com debilidades motoras. Neste trabalho é abordado o comportamento dos classificadores LDA (Discriminante Linear de Fisher) e o classificador Naive Bayes para classificação de movimento de mão direita e mão esquerda a partir da aquisição de sinais eletroencefalográficos. Para análise destes classificadores foram utilizadas como características de entrada a energia de trechos do sinal filtrados por um passa banda com frequências dentro dos ritmos sensório-motor e também foram utilizadas componentes de energia espectral através do periodograma modificado de Welch. Como forma de pré-processamento também é apresentado o filtro espacial Common Spatial Pattern (CSP) de forma a aumentar a atividade discriminativa entre as classes de movimento. Foram obtidas taxas de acerto de até 70% para a base de dados geradas neste trabalho e de até 88% utilizando a base de dados do BCI Competition II, taxas de acertos compatíveis com outros trabalhos na área. / Brain Computer Interface (BCI) systems usage for controlling devices has increasingly generated research on EEG signals analysis, mainly because the technological development of data processing systems has been offering a new perspective on developing equipment to assist people with motor disability. This study aims to examine the behavior of both Fisher's Linear Discriminant (LDA) and Naive Bayes classifiers in determining both the right and left hand movement through electroencephalographic signals. To accomplish this, we considered as input feature the energy of the signal trials filtered by a band pass with sensorimotor rhythm frequencies; spectral power components from the Welch modified periodogram were also used. As a preprocessing form, the Common Spatial Pattern (CSP) filter was used to increase the discriminative activity between classes of movement. The database created from this study reached hit rates of up to 70% while the BCI Competition II reached hit rates up to 88%, which is consistent with the literature.

O uso de sistemas denominados Brain Computer Interface, ou simplesmente BCI, para controle de dispositivos tem gerado cada vez mais trabalhos de análise de sinais de EEG, principalmente devido ao fato do desenvolvimento tecnológico dos sistemas de processamento de dados, trazendo novas perspectiva de desenvolvimento de equipamentos que auxiliem pessoas com debilidades motoras. Neste trabalho é abordado o comportamento dos classificadores LDA (Discriminante Linear de Fisher) e o classificador Naive Bayes para classificação de movimento de mão direita e mão esquerda a partir da aquisição de sinais eletroencefalográficos. Para análise destes classificadores foram utilizadas como características de entrada a energia de trechos do sinal filtrados por um passa banda com frequências dentro dos ritmos sensório-motor e também foram utilizadas componentes de energia espectral através do periodograma modificado de Welch. Como forma de pré-processamento também é apresentado o filtro espacial Common Spatial Pattern (CSP) de forma a aumentar a atividade discriminativa entre as classes de movimento. Foram obtidas taxas de acerto de até 70% para a base de dados geradas neste trabalho e de até 88% utilizando a base de dados do BCI Competition II, taxas de acertos compatíveis com outros trabalhos na área. / Brain Computer Interface (BCI) systems usage for controlling devices has increasingly generated research on EEG signals analysis, mainly because the technological development of data processing systems has been offering a new perspective on developing equipment to assist people with motor disability. This study aims to examine the behavior of both Fisher's Linear Discriminant (LDA) and Naive Bayes classifiers in determining both the right and left hand movement through electroencephalographic signals. To accomplish this, we considered as input feature the energy of the signal trials filtered by a band pass with sensorimotor rhythm frequencies; spectral power components from the Welch modified periodogram were also used. As a preprocessing form, the Common Spatial Pattern (CSP) filter was used to increase the discriminative activity between classes of movement. The database created from this study reached hit rates of up to 70% while the BCI Competition II reached hit rates up to 88%, which is consistent with the literature.

O uso de sistemas denominados Brain Computer Interface, ou simplesmente BCI, para controle de dispositivos tem gerado cada vez mais trabalhos de análise de sinais de EEG, principalmente devido ao fato do desenvolvimento tecnológico dos sistemas de processamento de dados, trazendo novas perspectiva de desenvolvimento de equipamentos que auxiliem pessoas com debilidades motoras. Neste trabalho é abordado o comportamento dos classificadores LDA (Discriminante Linear de Fisher) e o classificador Naive Bayes para classificação de movimento de mão direita e mão esquerda a partir da aquisição de sinais eletroencefalográficos. Para análise destes classificadores foram utilizadas como características de entrada a energia de trechos do sinal filtrados por um passa banda com frequências dentro dos ritmos sensório-motor e também foram utilizadas componentes de energia espectral através do periodograma modificado de Welch. Como forma de pré-processamento também é apresentado o filtro espacial Common Spatial Pattern (CSP) de forma a aumentar a atividade discriminativa entre as classes de movimento. Foram obtidas taxas de acerto de até 70% para a base de dados geradas neste trabalho e de até 88% utilizando a base de dados do BCI Competition II, taxas de acertos compatíveis com outros trabalhos na área. / Brain Computer Interface (BCI) systems usage for controlling devices has increasingly generated research on EEG signals analysis, mainly because the technological development of data processing systems has been offering a new perspective on developing equipment to assist people with motor disability. This study aims to examine the behavior of both Fisher's Linear Discriminant (LDA) and Naive Bayes classifiers in determining both the right and left hand movement through electroencephalographic signals. To accomplish this, we considered as input feature the energy of the signal trials filtered by a band pass with sensorimotor rhythm frequencies; spectral power components from the Welch modified periodogram were also used. As a preprocessing form, the Common Spatial Pattern (CSP) filter was used to increase the discriminative activity between classes of movement. The database created from this study reached hit rates of up to 70% while the BCI Competition II reached hit rates up to 88%, which is consistent with the literature.

De nos jours plus que jamais, il est nécessaire d’anticiper et de comprendre les réponses évolutives des organismes vivants, face à des habitats instables et hétérogènes. Mais à quel point cela est-il possible ? Reproduire l’ensemble du déroulé d’une trajectoire évolutive nécessite de pouvoir décrire, d’une part, le « matériel » disponible pour s’adapter (c’est-à-dire les effets phénotypiques associés à la variabilité génétique produite), d’autre part, comment agissent les forces évolutives, associées à un contexte écologique, pour aboutir à un certain « assemblage » de ce matériel. Dans sa version la plus simple, ce processus évolutif peut-être décrit par plusieurs cycles d’évènements de mutations-sélection conduisant à l’adaptation d’une population à son environnement. Cette dynamique correspond assez bien à celle qui est décrite par les populations bactériennes dans les expériences d’évolution contrôlées en laboratoire. Parallèlement, les modèles de paysages adaptatifs (phénotypiques), et en particulier le modèle géométrique de Fisher, sont des outils très puissants pour formuler des prédictions générales et quantitativement testables sur ces trajectoires évolutives. Cependant, ils restent très théoriques et ont été largement pensés dans un contexte écologique simplifié. Au cours de cette thèse, nous avons identifié les déterminants (mutationnels et sélectifs) des trajectoires évolutives à long terme de populations bactériennes s’adaptant dans différents contextes environnementaux. Une première partie des résultats est mise en lumière par la validation expérimentale et la reconstruction de la topographie du paysage adaptatif généré par différentes doses d’un antibiotique, le long d’un gradient. Une deuxième partie expérimentale vise à intégrer une composante biotique (une autre bactérie) à ce même contexte environnemental. Les processus évolutifs intervenant au cours d’une coévolution à long terme maintenue par sélection fréquence-dépendante, y sont étudiés. / Today more than ever, it is crucial to anticipate and understand the evolutionary responses of living organisms faced with heterogeneous and unstable habitats. But to what extent is this possible? To reproduce an entire evolutionary trajectory, we must first describe the “material” available for adaptation (e.g. the phenotypic effects associated with the existing and novel genetic variability), and second describe the way evolutionary forces, shaped by the ecological context, result in specific “assemblies” of this material. At its simplest, this evolutionary process can be described by several cycles of mutation-selection events, leading to the adaptation of a population to an environment. This process is reflected in the evolutionary trajectories of bacterial lineages undergoing controlled experimental evolution in the lab. Concurrently, adaptive (phenotypic) landscape models, and especially Fisher’s geometrical model of adaptation, are powerful tools to formulate general predictions, which can then be tested on such evolutionary trajectories. However, they remain highly theoretical, and are widely conceived in a simple ecological context. In this thesis, we identified the (mutational and selective) determinants of the evolutionary trajectories of bacterial lines adapting to various environmental contexts. A first set of results regards evolution along a gradient of antibiotic doses, and their relevance is highlighted by experimental validation and by the reconstruction of the underlying adaptive landscape. A second experimental part integrates a biotic component (another bacteria) to the same environmental context. The evolutionary processes acting throughout the resulting long-term coevolution – maintained by frequency-dependent selection – are studied.

The flood of 2000 caused extensive changes within the riparian landscape of the Sabie River, Kruger National Park (KNP). Changes within the riparian landscape and the removal of vegetation resulted in considerable changes in riparian vegetation characteristics. Open patches created by the flood served as a template for the establishment of new species and the regeneration of existing species, which consequently resulted in a patch mosaic. This memorable event encouraged an investigation into the response of the Sabie River ecosystem to the memorable Large Infrequent Disturbance (LID). Riparian ecosystems are driven by varying combinations of environmental factors, such as water availability, disturbance, herbivory, fire and river morphology. This complexity depicts unique vegetation structure and assemblages of associated plant species. The lack of sufficient knowledge on the role of riparian vegetation in the health assessment of surrounding ecosystems along semi-arid rivers prompted the establishment of the Kruger Rivers Post Flood Research Program (KRPFRP). Research conducted through this monitoring program four years after the 2000 flood, revealed no significant changes in the species composition, although the location and density of many common riparian species have been changed. There was a decrease in species density across the macro channel floor (MCF) and an increase in species density across the macro channel bank (MCB). Furthermore, it was reported that the flood altered the distribution of height classes across the macro channel. In general the riparian vegetation was shorter and bushier four years post-flood. These studies furthermore illustrated that the tree to shrub ratio did not change drastically from pre-flood conditions, although a decrease in the number of shrub individuals was reported. The research presented in this dissertation was designed to further explore changes in woody species composition and structure along the Sabie River, KNP at a post flood temporal interval, i.e. between the last survey in 2004 (by the KRPFRP) and 2010. For data compatibility, the sampling and analytical approach of this study conforms to the approach followed by the KRPFRP. Data were sampled within four preselected belt-transects that form part of the larger KRPFRP. All established woody individuals were counted and measured within each contiguous 10 m x 30 m plot within each of the four belt-transects. Log transformed species composition data were analysed through the application of the Bray Curtis dissimilarity index in combination with Ward’s method of clustering. Statistical significant differences between clusters were tested through the application of the Fisher’s exact relationship test. The MIXED Procedure or PROC MIXED model was used to investigate change within the vegetation structural data. Results obtained through the various analytical methods broadly support the findings of the KRPFRP. No significant change in woody species composition could be detected between 2004 and 2010. However, a change in the density (increase and decrease) of certain species across the MCB and MCF was revealed. Species richness and density increased significantly on the MCF oppose to small changes on the MCB. A significant increase in the total number of shrubs on the MCF contributed to an overall increase in woody density for the entire study area between 2004 and 2010. Shrubs therefore remained the most dominant growth form in both sampling years. Trees decreased across the MCB although the total number of established trees remained unchanged between 2004 and 2010. Riparian vegetation structure is directly linked to species assemblages, hence the continued dominance of shrub species along the Sabie River in the KNP The Sabie River riparian landscape is therefore still characterised by short and multi-stemmed woody individuals ten years after the LID. / Thesis (MSc (Environmental Sciences))--North-West University, Potchefstroom Campus, 2013

The flood of 2000 caused extensive changes within the riparian landscape of the Sabie River, Kruger National Park (KNP). Changes within the riparian landscape and the removal of vegetation resulted in considerable changes in riparian vegetation characteristics. Open patches created by the flood served as a template for the establishment of new species and the regeneration of existing species, which consequently resulted in a patch mosaic. This memorable event encouraged an investigation into the response of the Sabie River ecosystem to the memorable Large Infrequent Disturbance (LID). Riparian ecosystems are driven by varying combinations of environmental factors, such as water availability, disturbance, herbivory, fire and river morphology. This complexity depicts unique vegetation structure and assemblages of associated plant species. The lack of sufficient knowledge on the role of riparian vegetation in the health assessment of surrounding ecosystems along semi-arid rivers prompted the establishment of the Kruger Rivers Post Flood Research Program (KRPFRP). Research conducted through this monitoring program four years after the 2000 flood, revealed no significant changes in the species composition, although the location and density of many common riparian species have been changed. There was a decrease in species density across the macro channel floor (MCF) and an increase in species density across the macro channel bank (MCB). Furthermore, it was reported that the flood altered the distribution of height classes across the macro channel. In general the riparian vegetation was shorter and bushier four years post-flood. These studies furthermore illustrated that the tree to shrub ratio did not change drastically from pre-flood conditions, although a decrease in the number of shrub individuals was reported. The research presented in this dissertation was designed to further explore changes in woody species composition and structure along the Sabie River, KNP at a post flood temporal interval, i.e. between the last survey in 2004 (by the KRPFRP) and 2010. For data compatibility, the sampling and analytical approach of this study conforms to the approach followed by the KRPFRP. Data were sampled within four preselected belt-transects that form part of the larger KRPFRP. All established woody individuals were counted and measured within each contiguous 10 m x 30 m plot within each of the four belt-transects. Log transformed species composition data were analysed through the application of the Bray Curtis dissimilarity index in combination with Ward’s method of clustering. Statistical significant differences between clusters were tested through the application of the Fisher’s exact relationship test. The MIXED Procedure or PROC MIXED model was used to investigate change within the vegetation structural data. Results obtained through the various analytical methods broadly support the findings of the KRPFRP. No significant change in woody species composition could be detected between 2004 and 2010. However, a change in the density (increase and decrease) of certain species across the MCB and MCF was revealed. Species richness and density increased significantly on the MCF oppose to small changes on the MCB. A significant increase in the total number of shrubs on the MCF contributed to an overall increase in woody density for the entire study area between 2004 and 2010. Shrubs therefore remained the most dominant growth form in both sampling years. Trees decreased across the MCB although the total number of established trees remained unchanged between 2004 and 2010. Riparian vegetation structure is directly linked to species assemblages, hence the continued dominance of shrub species along the Sabie River in the KNP The Sabie River riparian landscape is therefore still characterised by short and multi-stemmed woody individuals ten years after the LID. / Thesis (MSc (Environmental Sciences))--North-West University, Potchefstroom Campus, 2013