L'étude de nombreux phénomènes astronomiques repose sur la recherche de périodicités dans des séries temporelles (courbes de lumière ou de vitesse radiale). En raison des contraintes observationnelles, la couverture temporelle des données résultantes est souvent incomplète, présentant des trous périodiques ainsi qu'un échantillonnage irrégulier. L'analyse du contenu fréquentiel de telles séries basée sur le spectre de Fourier s'avère alors inefficace et les méthodes heuristiques de déconvolution de type CLEAN, couramment utilisées en astronomie, ne donnent pas entière satisfaction. Cette thèse s'inscrit dans le formalisme fréquemment rencontré depuis les années 1990 abordant l'analyse spectrale sous la forme d'un problème inverse, le spectre étant discrétisé sur une grille fréquentielle arbitrairement fine. Sa régularisation est alors envisagée en traduisant la nature a priori parcimonieuse de l'objet à reconstruire: nous nous intéressons ici à la recherche de raies spectrales. <br />Une première approche envisagée a trait au domaine de l'optimisation et consiste à minimiser un critère de type moindres carrés, pénalisé par une fonction favorisant les solutions parcimonieuses. La pénalisation par la norme l1 est en particulier étudiée en extension à des variables complexes et s'avère satisfaisante en termes de modélisation. Nous proposons des solutions algorithmiques particulièrement performantes permettant d'envisager une analyse à très haute résolution fréquentielle. <br />Nous étudions ensuite la modélisation probabiliste des amplitudes spectrales sous la forme d'un processus Bernoulli-Gaussien, dont les paramètres sont estimés au sens de la moyenne a posteriori à partir de techniques d'échantillonnage stochastique, permettant d'envisager une estimation totalement non supervisée. L'interprétation probabiliste du résultat ainsi que l'obtention conjointe des variances associées, sont alors d'un intérêt astrophysique majeur, s'interprétant en termes de niveaux de confiance sur les composantes spectrales détectées. Nous proposons dans un premier temps des améliorations de l'algorithme échantillonneur de Gibbs permettant d'accélérer l'exploration de la loi échantillonnée. Ensuite, nous introduisons des variables de décalage fréquentiel à valeur continue, permettant d'augmenter la précision de l'estimation sans trop pénaliser le coût calculatoire associé. <br />Pour chaque méthode proposée, nous illustrons sur des simulations la qualité de l'estimation ainsi que les performances des algorithmes développés. Leur application à un jeu de données issu d'observations astrophysiques est enfin présentée, mettant en évidence l'apport d'une telle méthodologie par rapport aux méthodes d'analyse spectrale habituellement utilisées.

In der Natur und in technischen Anwendungen findet man viele dynamische System mit zeitlicher Verzögerung (delay),zum Beispiel die Mackey-Glass Gleichung, die als Beschreibung vom Aufbau der Blutzelle angewendet wird, und die Ikeda Gleichung, die ein Modell von einem optischen Resonator ist. Hier ist zeitliche Verzögerung τ eine Konstante, aber sie ist nicht immer konstant in der Natur und in der Praxis. Wie sieht das System aus und welche Stabilitätseigenschaften hat es, wenn die Verzögerung schwankt? In dieser Arbeit benutze ich einige einfache diskrete Abbildungen, um die resultierenden Effekte zu untersuchen.

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Climate change is currently a central problem in ecology, with far-reaching effects on species that may be diffcult to quantify. Ectothermic species which rely on environmental cues to complete successive stages of their life history are especially sensitive to temperature changes and so are good indicators of the impacts of climate change on ecosystems. Based on data collected in growth experiments for the alpine butterfly Parnassius smintheus (Rocky Mountain Apollo), a novel mathematical model is presented to study developmental rate in larval insects. The movement of an individual through larval instars is treated as a discrete-time four-outcome Bernoulli process, where class transition and death are assigned temperature-dependent probabilities. Transition and mortality probabilities are estimated using maximum likelihood estimation techniques. This adult emergence model is then integrated into a reproductive success model, and multi-year implications of climate change on the population dynamics of P. smintheus are explored. / Applied Mathematics

The research in distributed algorithms is linked with the developments of statistical inference in wireless sensor networks (WSNs) applications. Typically, distributed approaches process the collected signals from networked sensor nodes. That is to say, the sensors receive local observations and transmit information between each other. Each sensor is capable of combining the collected information with its own observations to improve performance. In this thesis, we propose novel distributed methods for the inference applications using wireless sensor networks. In particular, the efficient algorithms which are not computationally intensive are investigated. Moreover, we present a number of novel algorithms for processing asynchronous network events and robust state estimation. In the first part of the thesis, a distributed adaptive algorithm based on the component-wise EM method for decentralized sensor networks is investigated. The distributed component-wise Expectation-Maximization (EM) algorithm has been designed for application in a Gaussian density estimation. The proposed algorithm operates a component-wise EM procedure for local parameter estimation and exploit an incremental strategy for network updating, which can provide an improved convergence rate. Numerical simulation results have illustrated the advantages of the proposed distributed component-wise EM algorithm for both well-separated and overlapped mixture densities. The distributed component-wise EM algorithm can outperform other EM-based distributed algorithms in estimating overlapping Gaussian mixtures. In the second part of the thesis, a diffusion based EM gradient algorithm for density estimation in asynchronous wireless sensor networks has been proposed. Specifically, based on the asynchronous adapt-then-combine diffusion strategy, a distributed EM gradient algorithm that can deal with asynchronous network events has been considered. The Bernoulli model has been exploited to approximate the asynchronous behaviour of the network. Compared with existing distributed EM based estimation methods using a consensus strategy, the proposed algorithm can provide more accurate estimates in the presence of asynchronous networks uncertainties, such as random link failures, random data arrival times, and turning on or off sensor nodes for energy conservation. Simulation experiments have been demonstrated that the proposed algorithm significantly outperforms the consensus based strategies in terms of Mean-Square- Deviation (MSD) performance in an asynchronous network setting. Finally, the challenge of distributed state estimation in power systems which requires low complexity and high stability in the presence of bad data for a large scale network is addressed. A gossip based quasi-Newton algorithm has been proposed for solving the power system state estimation problem. In particular, we have applied the quasi-Newton method for distributed state estimation under the gossip protocol. The proposed algorithm exploits the Broyden- Fletcher-Goldfarb-Shanno (BFGS) formula to approximate the Hessian matrix, thus avoiding the computation of inverse Hessian matrices for each control area. The simulation results for IEEE 14 bus system and a large scale 4200 bus system have shown that the distributed quasi-Newton scheme outperforms existing algorithms in terms of Mean-Square-Error (MSE) performance with bad data.

The thesis is focused on the properties of the selected plane curves of order higher than two and one transcendent curve. To each curve an overview of its properties which are then derived and described in detail is given. All curves are enriched with their images that are created in mathematical software GeoGebra. In addition, to these images the text links directly to GeoGebra are added, where some interesting features are described and demonstrated.

abstract: In order to verify the dispersive nature of transverse displacement in a beam, a deep understanding of the governing partial differential equation is developed. Using the finite element method and Newmark’s method, along with Fourier transforms and other methods, the aim is to obtain consistent results across each numerical technique. An analytical solution is also analyzed for the Euler-Bernoulli beam in order to gain confidence in the numerical techniques when used for more advance beam theories that do not have a known analytical solution. Three different beam theories are analyzed in this report: The Euler-Bernoulli beam theory, Rayleigh beam theory and Timoshenko beam theory. A comparison of the results show the difference between each theory and the advantages of using a more advanced beam theory for higher frequency vibrations. / Dissertation/Thesis / Masters Thesis Civil Engineering 2016

Made available in DSpace on 2014-06-11T19:24:51Z (GMT). No. of bitstreams: 0 Previous issue date: 2012-09-19Bitstream added on 2014-06-13T19:31:57Z : No. of bitstreams: 1 caire_e_me_rcla.pdf: 1389119 bytes, checksum: ea2e9b574c106bff7f9cf806fe23534b (MD5) / Esta investigação tem como objetivo a história da origem da curva normal identificando a contribuição de Abraham de Moivre na dedução da fórmula para a função densidade de distribuição normal. Serão analisados trechos de obras originais de Abraham de Moivre, Jacob Bernoulli, James Stirling / This research aims at the history of the origin of the normal curve identifying the contribution of Abraham de Moivre in deducing the formula for the density function of normal distribution. Parts of original works of Abraham de Moivre, Jacob Bernoulli, James Stirling will be analysed

Vibration is an inherent phenomenon in dynamic mechanical systems. The work undertaken in this thesis is to identify natural frequencies of a variable length blade. Therefore designers can ensure that natural frequencies will not be close to the frequency (or integer multiples) of the main excitation forces in order to avoid resonance. For a wind turbine blade, the frequency range between 0.5 Hz and 30 Hz is relevant. The turbine blade is approximated by a cantilever, therefore, it is fully constrained where attached to a turbine shaft/hub. Flap-wise, edge-wise and torsional natural frequencies are calculated. The MATLAB program “BEAMANALYSIS.m” has been developed for the finite element analysis of a one dimensional model of the beam. Similarly, a three dimensional model of the beam has been developed in a finite element program Unigraphics NX5. The results found using the MATLAB program are compared with those found with NX5. Satisfactory agreement between the results is found for frequencies up to almost 500 Hz. Additionally, the frequencies one might expect in an experiment are identified. Experimental modal analysis has been performed on a uniform and stepped beam made of mild steel to extract the first five flap-wise natural frequencies. The results found have been compared to numerical results and the exact solution of an Euler-Bernoulli beam. Concurrence is found for the frequency range of interest. Although, some discrepancies exist at higher frequencies (above 500 Hz), finite element analysis proves to be reliable for calculating natural frequencies. Finally, the fixed portion and moveable portion of the variable length blade are approximated respectively by a hollow and a solid beam which can be slid in and out. Ten different configurations of the variable length blade, representing ten different positions of the moveable portion are investigated. A MATLAB program named VARIBLADEANALYSIS.m was developed to predict natural frequencies. Similarly three dimensional models of the variable length blade have been developed in the finite element program Unigraphics NX5. / This work was supported by the Research office of CPUT.

This Thesis deals with the power of a statistical test and the associated problem of determining the appropriate sample size. It should be large enough to meet the requirements of the probabilities of errors of both the first and second kind. The aim of this Thesis is to demonstrate theoretical methods that result in derivation of formulas for minimum sample size determination. For this Thesis, three important probability distributions have been chosen: Normal, Bernoulli, and Exponential.