The work is situated within the theory of slice analysis, a generalization of complex analysis for hypercomplex numbers, considering function of both quaternionic and Clifford variables, in both one and several variables. %We first characterize some partial slice sets of The primary focus of the thesis is on the harmonic and polyharmonic properties of slice regular functions. We derive explicit formulas for the iteration of the Laplacian on slice regular functions, proving that their degree of harmonicity increases with the dimension of the algebra. Consequently, we present Almansi-type decompositions for slice functions in several variables. Additionally, using the harmonic properties of the partial spherical derivatives and their connection with the Dirac operator in Clifford analysis, we achieve a generalization of the Fueter and Fueter-Sce theorems in the several variables context. Finally, we establish that regular polynomials of sufficiently low degree are the unique slice regular functions in the kernel of the iteration of the Laplacian, whose power is less than Sce index.

This thesis is an account of our study of two branches of dynamical systems theory, namely the mean and pointwise ergodic theory. In our work on mean ergodic theorems, we investigate the spectral theory of integrable actions of a locally compact abelian group on a locally convex vector space. We start with an analysis of various spectral subspaces induced by the action of the group. This is applied to analyse the spectral theory of operators on the space generated by measures on the group. We apply these results to derive general Tauberian theorems that apply to arbitrary locally compact abelian groups acting on a large class of locally convex vector spaces which includes Fr echet spaces. We show how these theorems simplify the derivation of Mean Ergodic theorems. Next we turn to the topic of pointwise ergodic theorems. We analyse the Transfer Principle, which is used to generate weak type maximal inequalities for ergodic operators, and extend it to the general case of -compact locally compact Hausdor groups acting measure-preservingly on - nite measure spaces. We show how the techniques developed here generate various weak type maximal inequalities on di erent Banach function spaces, and how the properties of these function spaces in- uence the weak type inequalities that can be obtained. Finally, we demonstrate how the techniques developed imply almost sure pointwise convergence of a wide class of ergodic averages. Our investigations of these two parts of ergodic theory are uni ed by the techniques used - locally convex vector spaces, harmonic analysis, measure theory - and by the strong interaction of the nal results, which are obtained in greater generality than hitherto achieved. / PhD (Mathematics), North-West University, Potchefstroom Campus, 2014

This thesis is an account of our study of two branches of dynamical systems theory, namely the mean and pointwise ergodic theory. In our work on mean ergodic theorems, we investigate the spectral theory of integrable actions of a locally compact abelian group on a locally convex vector space. We start with an analysis of various spectral subspaces induced by the action of the group. This is applied to analyse the spectral theory of operators on the space generated by measures on the group. We apply these results to derive general Tauberian theorems that apply to arbitrary locally compact abelian groups acting on a large class of locally convex vector spaces which includes Fr echet spaces. We show how these theorems simplify the derivation of Mean Ergodic theorems. Next we turn to the topic of pointwise ergodic theorems. We analyse the Transfer Principle, which is used to generate weak type maximal inequalities for ergodic operators, and extend it to the general case of -compact locally compact Hausdor groups acting measure-preservingly on - nite measure spaces. We show how the techniques developed here generate various weak type maximal inequalities on di erent Banach function spaces, and how the properties of these function spaces in- uence the weak type inequalities that can be obtained. Finally, we demonstrate how the techniques developed imply almost sure pointwise convergence of a wide class of ergodic averages. Our investigations of these two parts of ergodic theory are uni ed by the techniques used - locally convex vector spaces, harmonic analysis, measure theory - and by the strong interaction of the nal results, which are obtained in greater generality than hitherto achieved. / PhD (Mathematics), North-West University, Potchefstroom Campus, 2014

Les protéines-G hétérotrimériques, constituées des sous-unités α, β et γ, sont les premières actrices de la transduction du signal en interagissant directement avec les Récepteurs Couplés aux protéines-G (RCPG). Les protéines-G ont la capacité de lier soit une molécule de GDP lorsqu'elles sont inactives, soit une molécule de GTP quand elles sont activées par un RCPG. Cet échange de nucléotide va conduire à la dissociation de l'hétérotrimère avec d'une part la sous-unité α seule, et d'autre part le complexe βγ. Chacune de ces entités va ensuite propager le signal dans le compartiment intracellulaire. Les travaux effectués au cours de cette thèse ont pour but de mieux comprendre la dynamique des protéines-G hétérotrimériques et de leurs récepteurs par des techniques de mécanique moléculaire incluant la Dynamique Moléculaire (DM) et l'Analyse de Modes Normaux (AMN). Dans un premier temps une AMN nous a permis de décrire les possibles mouvements de larges amplitudes des protéine-G. Nous avons à l'occasion de cette étude mis au point une méthode de sélection de Modes Normaux (MN) pertinents que nous avons appelés modes représentatifs. Nous avons également développé une méthode d'extraction de ligand (ici le GDP) le long de ces MN. Ceci nous a permis de montrer qu'un mouvement concerté de toute la sous-unité α pouvait permettre l'ouverture de la poche et la sortie du GDP. Dans un deuxième temps, nous avons affiné nos résultats en reconstruisant des profils d'énergie libre le long de plusieurs chemins de sortie possibles pour le GDP. Ainsi nous avons pu proposer un mécanisme fin de sortie du ligand et plusieurs résidus clés impliqués dans cette sortie. Nous avons également étudié le processus de dissociation de l'hétérotrimère par la technique de la Dynamique Moléculaire Dirigée. Il a été possible, à l'issue de cette étude, de proposer un mécanisme à l'échelle moléculaire de la séparation des sous-unités α et βγ. Pour finir, nous avons également étudié le macro-complexe RCPG : protéine-G. Deux études traitent des mécanismes d'activation et de couplage des protéines-G à son récepteur. Nous avons notamment montré que l'hétérotrimère de protéine-G contraint très fortement les mouvements du récepteur. Un mouvement très largement retrouvé dans le complexe ainsi que dans plusieurs autres RCPGs dont les structures sont connues a été proposé comme étant le mouvement d'activation des RCPG une fois complexés à leurs protéines partenaires. / Heterotrimeric G-proteins, constituted of α, β and γ subunits are the first actresses of the intra-cellular signal transduction and interact directly with G-protein Coupled Receptors (GPCR). The heterotrimer is able to bind either a GDP molecule (inactive state) or a GTP molecule (active state). The nucleotide exchange is triggered by the interaction with an activated GPCR and leads to the dissociation of the whole heterotrimer into two independant entities : α and tightly bound βγ subunits. Both subunits further propagate the signal into the intracellular compartment. Goals of the present work were to better understand the mechanics of G-proteins and GPCR by combining several molecular mechanics techniques such as Molecular Dynamics (MD) and Normal Mode Analysis (NMA).Firstly, we described large amplitude motions of the whole G-protein heterotrimer. In this study we developped a method to select relevant Normal Modes (NM), we called representative NM. We also developped a method which consists to extract a ligand (in our case the GDP) out of its binding pocket along computed NM. With these two new methods, we showed that a concerted motion of the α subunit would promote the opening of the pocket and the release of the GDP.Secondly, to refine our results, we performed free energy profiles reconstructions along several putative exit pathways of the GDP. Thus, we proposed for the first time a fine-tuned mechanism of GDP exit at the molecular scale and putative key-residues. We proposed also a molecular scale mechanism for the dissociation of the heterotrimeric G-protein through the use of the Targeted Molecular Dynamics (TMD). Finally we were interested in the study of the GPCR:G-protein complex. We performed two studies related to the activation and to the coupling of the macro-complex. We showed that G-protein constrain drastically the GPCR motions. One over-represented motion in the complex that was also retrieved in other crystallized structures of several different GPCRs thus suggested that this motion could be the putative activation motion of a GPCR when complexed to its favorite protein partners.

La recherche menée dans cette thèse a pour but de développer une analyse harmonique pour des fonctions définies sur les sommets d'un graphe orienté. À l'ère du déluge de données, de nombreuses données sont sous forme de graphes et données sur ce graphe. Afin d'analyser d'exploiter ces données de graphes, nous avons besoin de développer des méthodes mathématiques et numériquement efficientes. Ce développement a conduit à l'émergence d'un nouveau cadre théorique appelé le traitement de signal sur graphe dont le but est d'étendre les concepts fondamentaux du traitement de signal classique aux graphes. Inspirées par l'aspect multi échelle des graphes et données sur graphes, de nombreux constructions multi-échelles ont été proposé. Néanmoins, elles s'appliquent uniquement dans le cadre non orienté. L'extension d'une analyse harmonique sur graphe orienté bien que naturelle, s'avère complexe. Nous proposons donc une analyse harmonique en utilisant l'opérateur de marche aléatoire comme point de départ de notre cadre. Premièrement, nous proposons des bases de type Fourier formées des vecteurs propres de l'opérateur de marche aléatoire. De ces bases de Fourier, nous en déterminons une notion fréquentielle en analysant la variation de ses vecteurs propres. La détermination d'une analyse fréquentielle à partir de la base des vecteurs de l'opérateur de marche aléatoire nous amène aux constructions multi-échelles sur graphes orientés. Plus particulièrement, nous proposons une construction en trames d'ondelettes ainsi qu'une construction d'ondelettes décimées sur graphes orientés. Nous illustrons notre analyse harmonique par divers exemples afin d'en montrer l'efficience et la pertinence. / The research conducted in this thesis aims to develop a harmonic analysis for functions defined on the vertices of an oriented graph. In the era of data deluge, much data is in the form of graphs and data on this graph. In order to analyze and exploit this graph data, we need to develop mathematical and numerically efficient methods. This development has led to the emergence of a new theoretical framework called signal processing on graphs, which aims to extend the fundamental concepts of conventional signal processing to graphs. Inspired by the multi-scale aspect of graphs and graph data, many multi-scale constructions have been proposed. However, they apply only to the non-directed framework. The extension of a harmonic analysis on an oriented graph, although natural, is complex. We, therefore, propose a harmonic analysis using the random walk operator as the starting point for our framework. First, we propose Fourier-type bases formed by the eigenvectors of the random walk operator. From these Fourier bases, we determine a frequency notion by analyzing the variation of its eigenvectors. The determination of a frequency analysis from the basis of the vectors of the random walk operator leads us to multi-scale constructions on oriented graphs. More specifically, we propose a wavelet frame construction as well as a decimated wavelet construction on directed graphs. We illustrate our harmonic analysis with various examples to show its efficiency and relevance.

This thesis aims to provide new insights into the importance of decomposing aggregate time series data using the Maximum Overlap Discrete Wavelet Transform. In particular, the analysis throughout this thesis involves decomposing aggregate financial time series data at hand into approximation (low-frequency) and detail (high-frequency) components. Following this, information and hidden relations can be extracted for different investment horizons, as matched with the detail components. The first study examines the ability of different GARCH models to forecast stock return volatility in eight international stock markets. The results demonstrate that de-noising the returns improves the accuracy of volatility forecasts regardless of the statistical test employed. After de-noising, the asymmetric GARCH approach tends to be preferred, although that result is not universal. Furthermore, wavelet de-noising is found to be more important at the key 99% Value-at-Risk level compared to the 95% level. The second study examines the impact of fourteen macroeconomic news announcements on the stock and bond return dynamic correlation in the U.S. from the day of the announcement up to sixteen days afterwards. Results conducted over the full sample offer very little evidence that macroeconomic news announcements affect the stock-bond return dynamic correlation. However, after controlling for the financial crisis of 2007-2008 several announcements become significant both on the announcement day and afterwards. Furthermore, the study observes that news released early in the day, i.e. before 12 pm, and in the first half of the month, exhibit a slower effect on the dynamic correlation than those released later in the month or later in the day. While several announcements exhibit significance in the 2008 crisis period, only CPI and Housing Starts show significant and consistent effects on the correlation outside the 2001, 2008 and 2011 crises periods. The final study investigates whether recent returns and the time-scaled return can predict the subsequent trading in ten stock markets. The study finds little evidence that recent returns do predict the subsequent trading, though this predictability is observed more over the long-run horizon. The study also finds a statistical relation between trading and return over the long-time investment horizons of [8-16] and [16-32] day periods. Yet, this relation is mostly a negative one, only being positive for developing countries. It also tends to be economically stronger during bull-periods.

Made available in DSpace on 2017-07-10T19:24:19Z (GMT). No. of bitstreams: 1 Clovis_Cechim_MC.pdf: 6987482 bytes, checksum: c33db297dd7ec8aaf8bfde9e1e56c2cc (MD5) Previous issue date: 2016-02-04 / Sugarcane has been cropped and produced in Brazil for a long time, so, it deserves mention because it makes the country as the largest producer, with also representativeness in sugar and ethanol production. The knowledge of reliable estimates concerning their cropped areas is essential for Brazilian agribusiness, as they help in determining prices to producers by power plants as well as allow establishing logistics flow of production. The cropped areas estimates are made by official agencies. Therefore, in order to reduce this subjectivity, geotechnology use comes as an alternative since it has been widely used in mappings agricultural crops. Thus, this study aimed at developing a methodology for mapping sugarcane crop in Paraná State with satellite images as LANDSAT, IRS and spectrum-temporal series of vegetation indexes from MODIS sensor, for 2010/2011 to 2014/2015 harvesting season. The carried out mappings indicated a strong positive correlation concerning Canasat and official IBGE. The developed method was based on Fuzzy ARTMAP classification and was efficient to map and estimate the sugarcane cropped area using vegetation index in Paraná State. / A cana-de-açúcar como cultura cultivada e produzida no Brasil merece destaque, pois torna o País o maior produtor mundial, com representatividade também na produção de açúcar e etanol. O conhecimento de estimativas confiáveis de suas áreas cultivadas é imprescindível para o agronegócio brasileiro, por auxiliar na determinação dos preços aos produtores pelas usinas e permitir estabelecer a logística de escoamento da produção. As estimativas de área cultivada são realizadas de forma subjetiva pelos órgãos oficiais. Com a finalidade de diminuir tal subjetividade, surge como alternativa o uso de geotecnologias, as quais têm sido muito utilizadas em mapeamentos de culturas agrícolas. Diante disto, o objetivo deste trabalho foi o desenvolvimento de uma metodologia para o mapeamento da cultura de cana-de-açúcar para o Estado do Paraná usando imagens dos satélites LANDSAT, IRS e de séries espectro-temporais de índices de vegetação, provenientes do sensor MODIS, para as safras de 2010/2011 a 2014/2015. O mapeamento da cultura foi realizado a partir do modelo de classificação supervisionada Fuzzy ARTMAP, tendo como variáveis de entrada, termos harmônicos de amplitude e fase e as métricas fenológicas da cultura. Os mapeamentos realizados indicaram forte correlação positiva com relação aos dados do Canasat e oficiais IBGE. O método desenvolvido com base na classificação Fuzzy ARTMAP demonstrou ser eficiente para mapear e estimar a área cultivada da cultura de cana-de-açúcar utilizando índices de vegetação no Estado do Paraná.

Made available in DSpace on 2017-05-12T14:47:35Z (GMT). No. of bitstreams: 1 Clovis_Cechim_MC.pdf: 6987482 bytes, checksum: c33db297dd7ec8aaf8bfde9e1e56c2cc (MD5) Previous issue date: 2016-02-04 / Sugarcane has been cropped and produced in Brazil for a long time, so, it deserves mention because it makes the country as the largest producer, with also representativeness in sugar and ethanol production. The knowledge of reliable estimates concerning their cropped areas is essential for Brazilian agribusiness, as they help in determining prices to producers by power plants as well as allow establishing logistics flow of production. The cropped areas estimates are made by official agencies. Therefore, in order to reduce this subjectivity, geotechnology use comes as an alternative since it has been widely used in mappings agricultural crops. Thus, this study aimed at developing a methodology for mapping sugarcane crop in Paraná State with satellite images as LANDSAT, IRS and spectrum-temporal series of vegetation indexes from MODIS sensor, for 2010/2011 to 2014/2015 harvesting season. The carried out mappings indicated a strong positive correlation concerning Canasat and official IBGE. The developed method was based on Fuzzy ARTMAP classification and was efficient to map and estimate the sugarcane cropped area using vegetation index in Paraná State. / A cana-de-açúcar como cultura cultivada e produzida no Brasil merece destaque, pois torna o País o maior produtor mundial, com representatividade também na produção de açúcar e etanol. O conhecimento de estimativas confiáveis de suas áreas cultivadas é imprescindível para o agronegócio brasileiro, por auxiliar na determinação dos preços aos produtores pelas usinas e permitir estabelecer a logística de escoamento da produção. As estimativas de área cultivada são realizadas de forma subjetiva pelos órgãos oficiais. Com a finalidade de diminuir tal subjetividade, surge como alternativa o uso de geotecnologias, as quais têm sido muito utilizadas em mapeamentos de culturas agrícolas. Diante disto, o objetivo deste trabalho foi o desenvolvimento de uma metodologia para o mapeamento da cultura de cana-de-açúcar para o Estado do Paraná usando imagens dos satélites LANDSAT, IRS e de séries espectro-temporais de índices de vegetação, provenientes do sensor MODIS, para as safras de 2010/2011 a 2014/2015. O mapeamento da cultura foi realizado a partir do modelo de classificação supervisionada Fuzzy ARTMAP, tendo como variáveis de entrada, termos harmônicos de amplitude e fase e as métricas fenológicas da cultura. Os mapeamentos realizados indicaram forte correlação positiva com relação aos dados do Canasat e oficiais IBGE. O método desenvolvido com base na classificação Fuzzy ARTMAP demonstrou ser eficiente para mapear e estimar a área cultivada da cultura de cana-de-açúcar utilizando índices de vegetação no Estado do Paraná.

<p>U ovoj doktorskoj disertaciji je predstavljena je nova metoda za<br />detekciju propada napona, zasnovana na Rekurentnoj<br />neuronskoj mreži i analizi u harmonijskom domenu. Metoda je<br />namenjena za primenu u savremenim distributivnim mrežama<br />koje sadrže obnovljive izvore, i u skladu sa tim je optimizovana i<br />testirana. Pametna metoda postiže izuzetne rezultate u brzini<br />detekcije, sa prosečnim vremenom detekcije manjim od 1 ms, uz<br />izuzetnu pouzdanost (preko 97%). U doktorskoj disertaciji<br />dokazana je i druga hipoteza, a to je da je moguće predvideti<br />dubinu propada algoritmom zasnovanim na harmonijskoj analizi.</p> / <p>In this PhD thesis, a novel method for the detection of voltage dips<br />(sags), based on the Recurrent Neural Network and analysis in the<br />frequency domain, is presented. The method is intended for use in<br />the modern distribution grids that contains renewable sources, and<br />accordingly it is optimized and tested. The smart method achieves<br />exceptional results in detection speed, with an average detection<br />time of less than 1 ms and with high reliability (over 97%). In the<br />PhD thesis, another hypothesis is proved, which claims that is<br />possible to predict the depth of dip with algorithm based on the<br />harmonic analysis.</p>

In PDEs with nontrivial Lie symmetry algebras, the Lie symmetry naturally yield Fourier and Laplace transforms of fundamental solutions. Applying this fact we discuss the semidirect product of the metaplectic group and the Heisenberg group, then induce a representation our group and use it to investigate the invariant solutions of a general differential equation of the form .