The modelling power of Itˆo integrals has a far reaching impact on a spectrum of diverse fields. For example, in mathematics of finance, its use has given insights into the relationship between call options and their non-deterministic underlying stock prices; in the study of blood clotting dynamics, its utility has helped provide an understanding of the behaviour of platelets in the blood stream; and in the investigation of experimental psychology, it has been used to build random fluctuations into deterministic models which model the dynamics of repetitive movements in humans. Finding the quadrature for these integrals using continuous groups or Lie groups has to take families of time indexed random variables, known as Wiener processes, into consideration. Adaptations of Sophus Lie’s work to stochastic ordinary differential equations (SODEs) have been done by Gaeta and Quintero [1], Wafo Soh and Mahomed [2], ¨Unal [3], Meleshko et al. [4], Fredericks and Mahomed [5], and Fredericks and Mahomed [6]. The seminal work [1] was extended in Gaeta [7]; the differential methodology of [2] and [3] were reconciled in [5]; and the integral methodology of [4] was corrected and reconciled in [5] via [6]. Symmetries of SODEs are analysed. This work focuses on maintaining the properties of the Weiner processes after the application of infinitesimal transformations. The determining equations for first-order SODEs are derived in an Itˆo calculus context. These determining equations are non-stochastic. Many methods of deriving Lie point-symmetries for Itˆo SODEs have surfaced. In the Itˆo calculus context both the formal and intuitive understanding of how to construct these symmetries has led to seemingly disparate results. The impact of Lie point-symmetries on the stock market, population growth and weather SODE models, for example, will not be understood until these different results are reconciled as has been attempted here. Extending the symmetry generator to include the infinitesimal transformation of the Wiener process for Itˆo stochastic differential equations (SDEs), has successfully been done in this thesis. The impact of this work leads to an intuitive understanding of the random time change formulae in the context of Lie point symmetries without having to consult much of the intense Itˆo calculus theory needed to derive it formerly (see Øksendal [8, 9]). Symmetries of nth-order SODEs are studied. The determining equations of these SODEs are derived in an Itˆo calculus context. These determining equations are not stochastic in nature. SODEs of this nature are normally used to model nature (e.g. earthquakes) or for testing the safety and reliability of models in construction engineering when looking at the impact of random perturbations. The symmetries of high-order multi-dimensional SODEs are found using form invariance arguments on both the instantaneous drift and diffusion properties of the SODEs. We then apply this to a generalised approximation analysis algorithm. The determining equations of SODEs are derived in an It¨o calculus context. A methodology for constructing conserved quantities with Lie symmetry infinitesimals in an Itˆo integral context is pursued as well. The basis of this construction relies on Lie bracket relations on both the instantaneous drift and diffusion operators.

ABSTRACT The focus of this work was the study possible ways to improve the efficiency of solar cells. To this end, the main aim was to investigate the deposition process of Indium Tin Oxide (ITO), Titanium Dioxide (TiO2), multi-layers ITO/TiO2 on quartz SiO2 substrates under different conditions (oxygen pressure, laser fluence and wavelength, and temperature) and later gold nanoparticles by the Reactive Pulsed Laser Ablation Deposition (RPLAD) technique. It was intended to investigate their electrical structural and optical properties under selected conditions for possible application to Dye Sensitised Solar Cells (DSSC). Under optimised conditions, maximum deposition rates of 12nm/min for ITO and 21nm/min for TiO2 thin films were achieved. Rutherford Backscattering Spectrometry (RBS) with 2MeV He+ ions was used to measure the films thickness. Uniform thicknesses over a large area were found to be about 400nm and 800nm for ITO and TiO2 films, respectively. Crystalline properties were studied via x-ray diffraction and Raman spectroscopy. X-ray Diffraction (XRD) analysis revealed that the ITO films are highly orientated nanocrystals with their a-axis normal to the glass substrate surface. The average particle size of the precipitated nanocrystals was calculated to be 10-15nm. The structure of the films was characterised via Atomic Force Microscopy (AFM) imaging of the top surface of the film. The films have a rough surface with average roughness of 26-30nm. Pores were observed with a density of 144 and 125 pores/mm2 and average size of 150 and 110nm for ITO films deposited at 200 and 400°C, respectively. TiO2 films deposited on the prepared ITO films were less crystalline. Annealing was performed at 300 and 500°C for 3 consecutive hours and the XRD results show that the transformation of TiO2 film into anatase phase was almost complete with a crystal size of ~ 6-7nm. Scanning Transmission Electron Microscopy (STEM) of the surfaces was also performed. The TiO2 films deposited onto the prepared ITO films present a relatively high pore size with an average pore diameter of ~ 40nm and excellent uniformity. It is interesting to note that the pores are randomly arranged. The random arrangement of the pores network may actually be beneficial for producing a uniform electrode. In addition, STEM cross-sectional analysis of the films showed a columnar structure but no evidence of voids in the structure. The large surface area produced suggests applications in DSSC. The electrical properties of the films were investigated and an estimation of resistivity and Hall mobility was made. Low values of resistivity and high values of mobility were observed for ITO films. The resistivity of the film increases with increasing thickness while it decreases when increasing the deposition temperature. The lowest value was found to be 1.5x10-6Ωm for ITO films deposited at 400°C. Hall mobility was found to increase with substrate temperature. In this investigation, the highest Hall mobility at room temperature was estimated to be 22.3cm2/Vs under ambient O2 pressure (PO2) of 1Pa and 52.1 and 51.3cm2/Vs for films deposited at 200 and 400°C, respectively. But the best ITO film was deposited at 200°C, since this film combines good resistivity, good Hall mobility and good transmittance. UV-VIS-IR transmission spectra were recorded on a Perkin Elmer Lambda 900. From the transmission data, the energy gap as well as the optical constant was estimated. A high transmission for ITO films in the visible (Vis) range was observed which was above 88% for films produced at room temperature and above 95% for those deposited at 200°C. The transmission for the films produced in oxygen was about 90% above 400nm, whereas it lies between 70 and 80% for films produced in rare gases. An increase in the band gap was observed by increasing the oxygen pressure and substrate temperature for ITO films. Increasing the quartz SiO2 substrate temperature from room temperature to 400 °C resulted in an increase of the transmission of TiO2 films, mostly in the Visible Near Infrared (Vis-NIR) from about 70% to 92%. After annealing at 500°C for 3 consecutive hours, the transmission of TiO2 film further sharply decreases toward shorter wavelengths. Analysis of the transmittance curve of TiO2/Au shows a decrease of about 6% of the transmission in the Ultraviolet Visible (UV-Vis) range. Optical absorption edge analysis showed that the optical density could be used to detect the film growth conditions and to correlate the film structure and the absorption edge. The TiO2 films deposited present a direct band gap at 3.51eV and 3.37eV for TiO2 as deposited and after annealing, respectively, while the indirect band gap was found to be 3.55eV and 3.26eV for TiO2 films as deposited and after annealing, respectively. There was a shift of about 0.1eV between as deposited ITO monolayer films and ITO/TiO2 bilayers deposited at 200°C. A small shift towards shorter wavelengths has been observed for multilayer ITO/TiO2/Au. In this case, the increase of Eg was ascribed to a reduction of the oxygen vacancies with increasing substrate temperature at which the ITO film was deposited. The change in the shape of the fundamental absorption edge is considered to reflect the variation of density and the short range structural modifications undetected by structural characterisations. Enlargement of band-gap energies of semiconductors may be advantageous when used in DSSC to suppress the charge recombination between the reduced electrolytes and the photo-excited holes in the valence band of TiO2 substrates and enhance the open-circuit potential of the cell. When ITO/TiO2 bilayers were annealed before depositing Au, the gap energy remained constant.

Neste trabalho é apresentado o estudo teórico-experimental a respeito das propriedades piezoresistivas de dois tipos de materiais com estrutura amorfa. O primeiro material estudado é o carbono semelhante ao diamante e o segundo é o óxido de estanho dopado com índio. O estudo compreende o levantamento bibliográfico sobre os materiais, projeto teórico e prático de estruturas individuais de testes e piezoresistores configurados em ponte completa, além da realização das caracterizações elétricas, mecânicas e térmicas de acordo com um arranjo experimental proposto. As caracterizações experimentais foram implementadas usando a técnica de flexão de uma viga engastada e a teoria das pequenas deflexões. Os diferentes materiais caracterizados e analisados apresentaram o efeito piezoresistivo e um sinal de sensibilidade mecânica condizente com as características esperadas para estes filmes. Ambos os filmes respondem as variações da temperatura de forma linear e apresentam uma direção de dependência com a temperatura. Os filmes de carbono amorfo hidrogenado livre de dopantes apresentam curvas de corrente e tensão características indicando um mecânismo de condução elétrica complexo devido a sua diversidade de microestruturas e relacionado aos parâmetros de processos de deposição. Os filmes com nitrogênio são mais estáveis termicamente com coeficientes da ordem de - 4900 ppm/ºC. Os resultados encontrados indicam a existência de dois tipos de portadores de cargas responsáveis pela mobilidade média, resistividade e efeito piezoresistivo. Os filmes de óxido de estanho dopado com índio livre e com 5 % e 10 % de oxigênio no plasma apresentam características de diminuição da resistência elétrica com o esforço mecânico e exibem efeitos de piezoresistividade na faixa de - 12 a - 23. Amostras destes filmes com oxigênio apresentaram um fator de sensibilidade mecânica muito baixa e são menos estáveis termicamente que as amostras livres de oxigênio. Os filmes estudados podem ser usados em aplicações envolvendo extensiometria ou mesmo em sensores de pressão piezoresistivos após adequação do processo de deposição e de recozimentos térmicos. / This tesis presents the piezoresistivity theoretical and experimental study for two materials with amorphous structure. The first material is the Diamond Like Carbon and the other is the Indium Tin Oxide. The work includes the bibliographic study, theoretical and practical design of structures for testing individual and piezoresistors configured in bridge, in addition to the completion of the characterizations electrical, mechanical and thermal according to a proposed experimental arrangement. The experimental characterizations have been implemented using the technique of cantilever and the theory of small deflections. The different materials analyzed showed the piezoresistive effect with some order of magnitude and a sign of sensitivity to mechanical stress of tension consistent with the characteristics expected for these types of films. Both films respond to changes in temperature in a very linear and have a direction of dependency with the temperature according to the literature. The films of free doping have curves of current and voltage characteristics for this type of material indicating a mechanism of electric conduction very complex because of its diversity of microstructures and processes related to the parameters of the deposition and films with nitrogen are more thermally stable with coefficients of order of - 4900 ppm/ºC. The results indicate the existence of two types of charge carriers responsible for the average mobility and hence the resistivity and the piezoresistive effect. The films of indium tin oxide free and with some oxygen content in plasma presents characteristics of decreased electrical resistance to mechanical stress and exhibit effects of piezoresistive in the range of - 12 to - 23. Samples of these films with oxygen showed a factor of very low mechanical sensitivity and are less stables to thermal effect the samples free of oxygen. The films studied can be used in certain applications such strain gauges or even in piezoresistive pressure sensors, after adequate process of deposition and thermal annealing.

This thesis consists of three parts. In the first part, we recall some background theory that will be used throughout the thesis. In the second part, we studied the existence and uniqueness of solutions of the stochastic heat equations with Markovian switching. In the third part, we investigate the properties of solutions, such as Feller property, strong Feller property and stability.

Orientador: Sergio Brochsztain / Tese (doutorado) - Universidade Federal do ABC. Programa de Pós-Graduação em Energia, 2014

L’exocytose vésiculaire est une voie physiologique majeure de la communication intercellulaire. Dans ce contexte, le TIRFM (microscopie de fluorescence par réflexion totale interne) et l’ampérométrie sont aujourd'hui les deux méthodes analytiques les plus fréquemment utilisées dans l’étude de l’exocytose. En raison de la complémentarité de ces deux techniques d’analyse pour le suivi de la sécrétion exocytotique, leur combinaison pour suivre la sécrétion exocytotique a d'abord été réalisée par notre groupe en 2011. Ce couplage a permis un enregistrement simultané des signaux fluorescents et ampérométriques avec une bonne résolution spatiale et temporelle. L'inconvénient majeur de ce travail reste le chargement indépendant des sondes optique et électrochimique dans les vésicules de sécrétion, ce qui entraîne la détection d’évènements « orphelins » ampérométriques ou optiques ainsi que la faible efficacité de détection des évènements couplés. Par conséquent, dans cette thèse, nous avons tenté de mettre à profit une sonde unique à la fois fluorescente et électroactive pour suivre l’exocytose par la méthodologie couplée TIRFM/ampérométrie. Ainsi, un analogue de neurotransmetteurs monoamine primaire, la 4-(2-amino-éthyl)-6-chloro-7-hydroxy-2H-1-benzopyran-2-one (nommé 1 dans ce travail), a été synthétisé.1 présente une fluorescence forte, stable et pH-dépendante. Lorsque cette entité est excitée à 405 nm, son intensité de fluorescence est presque doublée de pH 5 (valeur intra-vésiculaire) à 7 (valeur milieu extracellulaire). De plus, des études en voltammétrie ont pu mettre en évidence que 1 est oxydable sur électrode de carbone vitreux, microélectrode à fibre de carbone et ITO (oxyde d’indium dopé à l’étain), montrant ainsi une bonne électroactivité. La pénétration cellulaire dans les vésicules de cellules BON N13 a également été démontrée, prouvant la spécificité de l’interaction entre 1 et ces vésicules équipées d’un transporteur de monoamines primaires (VMAT). L’utilisation de 1 comme sonde unique optique et électrochimique pour le suivi de l'exocytose a ensuite été validée séparément dans des cellules BON N13 par TIRFM et ampérométrie. L’enregistrement simultané par fluorescence et électrochimie en utilisant 1 comme sonde double a ensuite été réalisé dans un microdispositif constitué d’électrodes ITO conductrice et transparente. Nos résultats basés sur la sonde unique 1 montrent qu’elle semble plus adaptée que toutes les stratégies antérieures impliquant deux sondes indépendantes. Les résolutions spatiale et temporelle de cette méthode combinée ont permis d'analyser des sécrétions d’exocytose de cellules marquées par 1. Une analyse ultérieure de ces signaux couplés optique et électrochimique sera à même d’étudier la corrélation entre le comportement du pore de fusion (dynamique d'ouverture/de fermeture, stabilité..) détecté par ampérométrie et le mouvement d'une vésicule en trois dimensions (ancrage, amarrage, fusion puis retrait dans le cytoplasme) détecté par TIRFM. / Vesicular exocytosis is a ubiquitous way for intercellular communications. TIRFM (total internal reflection fluorescence microscopy) and amperometry are nowadays the two most frequently used analytical methods with complementary features for its investigation. The combination of these two analytical techniques to track exocytotic secretions was firstly achieved by our group in 2011 and this new technique was demonstrated to show both high temporal and spatial resolutions by simultaneously recording the fluorescent and amperometric signals. The major disadvantage of this former work was the independent loading of optical and electrochemical probes to the secretory vesicles, which resulted in 'sightless' amperometric or optical signals as well as low coupling efficiency. Therefore, in this thesis, we attempted to develop a unique probe with dual fluorescent/electrochemical characteristics to track exocytotic process by TIRFM/amperometry coupling technique. This is why an analog of biogenic monoamine neurotransmitters, 4-(2-aminoethyl)-6-chloro-7-hydroxy-2H-1-benzopyran-2-one hydrochloride (named as 1 in this work) was synthesized. 1 exhibited bright, stable, pH-dependent fluorescence. When excited at 405 nm, its fluorescence intensity was almost doubled with the increase of pH values from 5 (similar to that in the vesicular lumen) to 7 (similar to the extracellular medium). Furthermore, in voltammetry, 1 was demonstrated to be easily electrooxidized on GCE (glassy carbon electrode), CFE (carbon fiber electrode) and ITO (indium tin oxide) electrodes surfaces, showing good electroactivity. 1 was also shown to penetrate easily into the vesicles of BON N13 cells within 1 hour incubation, testifying its specific affinity with these VMAT-equipped (vesicular monoamine transporter) vesicles. The applications of 1 as optical and electrochemical probes for exocytosis monitoring were then separately validated in BON N13 cells by TIRFM and amperometry measurements, respectively. Simultaneous recording of fluorescent and amperometric information by using 1 dual probes loaded cells was subsequently acquired in a microfabricated device constituted by conductive and transparent ITO electrodes. Our results based on the unique probe 1 for electrochemical and fluorescent detection of exocytotic release seemed more adapted than all the previous works involving independent probes. The high spatial and temporal resolutions of this combined method also allowed analyzing consecutive exocytotic secretions as well as overlapped events in 1-stained cells. Further analysis of these two signals with complementary information will shed more light on the correlation of the fusion pore behavior (opening/closure dynamics, stability…) measured by amperometry and the motion of a secretory vesicle in three dimensions (tethering, docking, fusion and retrieval) detected by TIRFM.

La synchronisation des cellules est importante pour l'analyse des processus moléculaires impliqués dans l'étalement et la motilité. Les interactions électrostatiques entre les cellules et les surfaces ont été étudiées dans le but de synchroniser la première étape de l'adhésion cellulaire. Les cellules Dictyostelium discoideum marquées avec LimE-GFP ont été utilisées pour le suivi en fluorescence des événements de polymérisation de l'actine. Des pics de fluorescence ont été observés pour les cellules individuelles pendant l'étalement en tampon phosphate. Dans une solution de concentration faible (0.17 mM tampon phosphate sucrose) les cellules lévitent au dessous des surfaces conductrices (Indium Tin Oxide, ITO), à cause de la répulsion électrostatique. Un dispositif électrochimique a été construit dans le but d'appliquer un pulse électrique (+2.5 V/Ag,AgCl) sur une surface de ITO pendant 0,1 secondes. Dans ces conditions, l'oxydation de l'eau produit des protons qui réduisent la charge de surface négative de l'ITO et ainsi, les cellules sont attirées simultanément. Ces contacts irréversibles avec la surface déclenchent l'étalement cellulaire. Pour 37 parmi les 47 cellules étudiées (80%), apparaissent des pics de fluorescences successives plus au moins réguliers en temps, montrant une activité de polymérisation de l'actine oscillante. Remarquablement, aucun pic de fluorescence n'apparaît dans les 7 premières secondes d'après l'application du pulse. De plus, 29 des cellules parmi les 37 ont eu le premier pic dans un intervalle de 4 secondes, entre 7,5 et 11,5 secondes après le pulse. Ainsi, nous avons obtenu, pour la première fois, la synchronisation de l'étalement cellulaire d'un groupe de cellules grâce à une méthode électrochimique.

I give explicit estimates of the Lp-norm of a mean zero infinitely divisible random vector taking values in a Hilbert space in terms of a certain mixture of the L2- and Lp-norms of the Levy measure. Using decoupling inequalities, the stochastic integral driven by an infinitely divisible random measure is defined. As a first application utilizing the Lp-norm estimates, computation of Ito Isomorphisms for different types of stochastic integrals are given. As a second application, I consider the discrete time signal-observation model in the presence of an alpha-stable noise environment. Formulation is given to compute the optimal linear estimate of the system state.

L'analyse conjointe du mouvement et des déformations est cruciale dans un grand nombre d'applications de vision par ordinateur. Cette thèse propose d'introduire un filtre stochastique non linéaire afin de suivre une courbe libre dans le temps. L'approche proposée est implémentée à travers un filtre particulaire incluant des mesures colorimétriques caractérisant respectivement la cible et le fond. La dynamique impliquée est formulée sous la forme d'une équation différentielle stochastique. Cela permet d'avoir une représentation continue de la trajectoire de la courbe, et d'être ainsi capable d'en déduire les déformations entre images. La courbe est définie par une courbe de niveau implicite, et la dynamique stochastique s'exprime sur cette dernière. Cela prend la forme d'une équation différentielle stochastique avec un mouvement Brownien de faible dimension. Dans ces modèles d'évolution sont combinés les informations de mouvement locales extraites des images et un modèle d'incertitude de la dynamique. Le filtrage associé proposé pour le suivi de courbes appartient ainsi à la famille des filtrages particulaires conditionnels. Ses capacités sont vérifiées sur différentes séquences contenant des objets fortement déformables.

<p>This research paper aims to understand and analyse the CISG, its history, scope and structure, and to evaluate its impact on SADC.The main ideas that this paper will consider are: what is the CISG / &nbsp / Its history, scope and structure / &nbsp / Its impact on developing countries / &nbsp / Its relevance to developing countries within SADC / and How the implementation of the CISG improved these developing countries within SADC.</p>