O objetivo do presente trabalho foi propor métodos de processamento de sinais e reconhecimento de padrões dos sinais de respostas de sensores de gás, utilizando técnicas e modelos da geometria fractal. Foram analisados e estudados os sinais de resposta de dois tipos de sensores. O primeiro sensor foi um dispositivo de óxido de estanho, cujo princípio de funcionamento baseia-se na mudança da resistividade do filme. Este forneceu sinais de respostas com características ruidosas como resposta à interação com as moléculas de gás. O segundo sensor foi um dispositivo Metal-Óxido-Semicondutor (MOS) com princípio de funcionamento baseado na geração de foto corrente, fornecendo respostas imagens bidimensionais. Para as análises dos sinais ruidosos do sensor de óxido de estanho, foi proposto um método de processamento baseado no modelo do movimento Browniano fracionário. Com este método foi possível a discriminação de gases combustíveis com uma taxa de acerto igual a 100%. Para as análises das respostas do tipo imagem do sensor MOS, foram propostos dois diferentes métodos. O primeiro foi embasado no princípio de compressão fractal de imagens e o segundo método proposto, foi baseado na análise e determinação da dimensão fractal multiescala. Ambos os métodos propostos mostram-se eficazes para a determinação da assinatura, como o reconhecimento, de todos os gases que foram utilizados nos experimentos. Os resultados obtidos no presente trabalho abrem novas fronteiras e perspectivas nos paradigmas de processamento de sinais e reconhecimento de padrões, quando utilizada a teoria da geometria fractal. / The aim of the present work was to propose methods for signal possessing and pattern, recognition from the signals response of gas sensors using models and techniques from the fractal geometry. The data studied and analyzed were obtained from two kinds of sensors. The first sensor was the tin oxide device, which detection principle is based on the resistivity changes of the tin oxide film and it provides noisy signals as response to the gas interaction. The second sensor was a metal-oxide-semiconductor (MOS) device, which has as the working principle the photocurrent generation. This sensor provides two-dimensional images signals. A method using a fractional Brownian motion was proposed to analyze the noise signal from the tin oxide device. The fuel gases discrimination employing this model was 100% successful. Two different methods were proposed to analyze the signal response from the MOS device. The first method was based on the fractal image compression technique and the second one was based on the analysis and determination of the multiscale fractal dimension. Both proposed methods have shown to be efficient tools for signature determination as the pattern recognition of all gases that were used in the experiment. The results obtained in the present work open new frontiers and perspectives inside the paradigms of the signal processing and pattern recognition by using the fractal theory.

Dans le domaine des machines moléculaires, la recherche d'un système produisant un mouvement orienté fait l'objet d'intenses recherches. Des résultats ont déjà été obtenus en ce sens mais n'exploitant pas le mouvement brownien comme le font les systèmes trouvés dans la nature comme la myosine. Nous proposons donc la synthèse d'une roue à rochet avec pour but de mimer ce phénomène, si besoin avec une activation de faible énergie. La première partie de ce travail a consisté en la conception par modélisation de l'équivalent synthétique d'une roue à rochet, basiquement constituée d'une roue crantée et d'un cliquet en vue d'étudier si une telle molécule pourrait produire une rotation orientée. Ce système est constitué d'un motif bishomoinositol fonctionnalisé en tant que roue et d'un cycloadduit de l'anthracène comme cliquet, liés par des bras espaceurs. La synthèse d'un système modèle dans lequel un motif bicyclo[2.2.2]octane joue le rôle de roue simplifiée a été menée afin de valider les différentes stratégies de synthèse. A cette occasion, une méthode alternative de la synthèse du diacide bicyclo[2.2.2]octanoïque a été mise au point ainsi qu'une méthodologie d'estérification compatible avec cet acide ainsi que le diacide 9,10-anthracènedioïque. Nous sommes ainsi parvenus à obtenir le produit de macrolactonisation, avec de possibles application comme roue de nanovéhicules. La synthèse du modèle a été l'occasion de pointer certaines impossibilités synthétiques au niveau des espaceurs (éthers, amides, triazoles, tétrazoles, alcènes) dans le système original. Un nouveau travail de modélisation a permis d'aboutir à une cible accessible synthétiquement conservant le comportement de roue à rochet. Dans cette optique, la synthèse du bishomoinositol fonctionnalisé par des acides en tête de pont a été entreprise par une première voie incluant ces groupements au départ de la synthèse, une seconde voie introduisant ces groupements en fin de séquence. / In the field of molecular machines, systems producing an oriented motion have been intensely looked for. Results, obtained toward this goal, do not exploit Brownian motion whereas it happens in natural systems such as myosin. Hereby we propose the synthesis of a molecular ratchet aiming to mimic this phenomenon or to be able to act as a molecular motor through low energy activation. The first part of this work consisted in the design by modelisation of a synthetic equivalent of a ratchet, basically consisting of a toothed wheel and a pawl. This study aim at determining if such a molecule could produce an oriented motion by simple Brownian motion. This system is consisting of a functionalized bishomoinositol moiety as the wheel and a cycloadduct of anthracene as the pawl, linked by spacers allowing the adjustment of the energy barriers. The synthesis of a model where a bicyclo[2.2.2]octane moiety plays the role of a simplified wheel has been conducted in order to validate various synthetic strategies. This gave the opportunity to develop an alternative method of the synthesis of the bicyclo[2.2.2]octanedicarboxylic diacid as well as an esterification methodology compatible with the bulkiness or low solubility of both partners. The macrolactonization product could be obtained and opens some possible applications as nanovehicle wheels. The synthesis of the model was the occasion to highlight synthetic limitations concerning the spacers (ethers) in the original system. A new series of targets taking into account the synthetic restrictions while keeping the ratchet behavior were designed. The discovery of another synthetic difficulties (amides, triazoles, tetrazoles and alkenes) yielded a single refined target. Toward this goal, the synthesis of the bishomoinositol functionalized in the bridgehead position was engaged in a first pathway including these functions at the beginning of the synthesis, the second way introducing them on the bishomoinositol at the end of the sequence.

Le travail présenté dans cette thèse consiste à modéliser les transports de particules dans un écoulement de Stokes en tenant compte des caractéristiques des particules, du régime d’écoulement de fluide qui les transporte et de l’effet de confinement qui pourrait être lié par exemple à la prise en compte d’une structure d’un milieu poreux. Le phénomène de transport que nous étudions est basé sur le mécanisme d’effet cliquet qui apparaît quand on soumet le système à un pompage alternatif dans le temps. L’étude de la dynamique de la particule est effectuée en utilisant la méthode de continuation qui permet de suivre la solution périodique selon le paramètre désiré et d’identifier les types de bifurcation ainsi que les lieux de ces points critiques. Cette étude nécessite la connaissance de la force de traînée exercée sur la particule et que nous calculons en utilisant la méthode des équations intégrales de frontières. / The work presented in this Phd Thesis is the modelling of particle transport in a Stokes flow taking into account the characteristics of the particle, the regime flow, and the effect of the confinement which could be related for example to the consideration of a porous media structure. The phenomena of the transport is based on the mecansim of ratchet effect which appears when the system is undergoes an alternative pumping. The study of the particle dynamics is performed using the continuation method which allows to follow the periodic solutions according to the desired parameter, to identify the types of bifurcation and critical points. This study requires the knowledge of the drag force exerted on the particle and which we compute using the boundary integral equation.

In the present thesis we deal with several possible approaches to financial de- rivatives pricing. In the first part, we introduce the basic types of derivatives and the methods of trading. Furthermore, we present several models for the valuati- on of specific financial derivative, i.e. options. Firstly we describe Black-Scholes model in detail, which considers that the development of the underlying asset price is governed by Wiener process. Following are the jumps diffusion models that are extension of the Black-Scholes model with jumps. Then we get to jump models, which are based on Lévy processes. Finally, we will deal with the model, which considers that the development of the underlying asset price is governed by fractional Brownian motion with Hurst's coefficient greater than 1/2. All models are suplemented with sample examples. 1

Binding-sites which facilitate the transport of substrates across membranes are ubiquitous in membrane proteins. To understand this fundamental process in cells, we build up a synthetic membrane system consisting of microfluidic channels and colloidal particles. Holographic optical tweezers are used to modulate the potential energy landscape in those channels. We show how to extract the underlying energy potential by analysing local transition probabilities. Our method is applicable both to equilibrium systems and non-equilibrium steady states. Our method offers improved robustness when dealing with fragmented trajectories or small ensembles of data compared to other established approaches, such as probability density function and splitting probability. Meanwhile, we utilise the intensity distribution of the optical traps generated by holographic optical tweezers to estimate energy landscapes featuring high energy barriers where transitions rarely occur. We use this newly developed experimental system to mimic the functionality of membrane protein transporters that are known to alternate their substrate-binding sites between the extracellular and cytosolic side of the membrane. We study particle transport through a channel coupled with an energy well that oscillates its position between the two entrances of the channel deterministically and stochastically. Optimised particle transport across the channel is obtained by adjusting the oscillation frequency. At the optimal oscillation frequency, the translocation rate of particles through the channel is a hundred times higher with respect to free diffusion across the channel. Our findings reveal the effect of time dependent potentials on particle transport across a channel. This work adds a new tool for the investigation of highly controlled membrane transport processes at the micron scale. Our results are relevant for improving our understanding of membrane transport especially for microfluidics application.

This thesis focuses on optimization on a generic objective function based on reflected Brownian motion (RBM). We investigate in several approaches including the partial differential equation approach where we write our objective function in terms of a Hamilton-Jacobi-Bellman equation using the dynamic programming principle and the gradient descent approach where we use two different gradient estimators. We provide extensive numerical results with the gradient descent approach and we discuss the difficulties and future study opportunities for this problem.

The topic of this thesis is the theoretical analysis of theoptomechanical coupling effects in a high-finesse optical cavity, and the experimental realization of such a device.Radiation pressure exerted by light limits the sensitivity of high precision optical measurements. In particular, the sensitivity of interferometric measurements of gravitational wave is limited by the so called standard quantum limit. cavity with a movable mirror. The internal field stored in such cavity can be orders of magnitude greater than the input field, and it's radiation pressure force can change the physical length of the cavity. In turn, any change in the mirror's position changes the phase of the out put field. This optomechanical coupling leads to an intensity-dependent phase shift for thelight equivalent to an optical Kerr effect. Such a device can then be used for squeezing generation or quantum nondemolition measurements.In our experiment, we send a laser beam in to a high-finesse optical cavity with a movable mirror coated on a high Q-factor mechanical resonator. Quantum effects of radiation pressure become therefore, at low temperature, experimentally observable. However, we've shown that the phase of the reflected field is very sensitive to small mirror displacements, which indicate other possible applications of thistype of device like high precision displacements measurements. We've been able to observe the Brownian motion of the moving mirror. We've also used an auxiliary intensity modulated laser beam to optically excite the acoustic modes. We've finally obtained a sensitivity of2x10^(-19) m/sqrt(Hz), in agreement with theoretical prediction.

<p>Behaviour occurs in time, and precise timing in the range of seconds and fractions of seconds is for most living organisms necessary for successful interaction with the environment. Our ability to time discrete actions and to predict events on the basis of prior events indicates the existence of an internal timing mechanism. The nature of this mechanism provides essential constraints on models of the functional organisation of the brain. </p><p>The present work indicates that there are discontinuities in the function of time close to 1 s and 1.4 s, both in the amount of drift in a series of produced intervals (Study I) and in the detectability of drift in a series of sounds (Study II). The similarities across different tasks further suggest that action and perceptual judgements are governed by the same (kind of) mechanism. Study III showed that series of produced intervals could be characterised by different amounts of positive fractal dependency related to the aforementioned discontinuities. </p><p>In conjunction with other findings in the literature, these results suggest that timing of intervals up to a few seconds is strongly dependent on previous intervals and on the duration to be timed. This argues against a clock-counter mechanism, as proposed by scalar timing theory, according to which successive intervals are random and the size of the timing error conforms to Weber's law. </p><p>A functional model is proposed, expressed in an autoregressive framework, which consists of a single-interval timer with error corrective feedback. The duration-specificity of the proposed model is derived from the order of error correction, as determined by a semi-flexible temporal integration span. </p>

<p>The present mini-thesis seeks to explore and investigate the mathematical theory and concepts that underpins the valuation of derivative securities, particularly European plainvanilla options. The main argument that we emphasise is that novel models of option pricing, as is suggested by Hull and White (1987) [1] and others, must account for the discrepancy observed on the implied volatility &ldquo / smile&rdquo / curve. To achieve this we also propose that market volatility be modeled as random or stochastic as opposed to certain standard option pricing models such as Black-Scholes, in which volatility is assumed to be constant.</p>

Behaviour occurs in time, and precise timing in the range of seconds and fractions of seconds is for most living organisms necessary for successful interaction with the environment. Our ability to time discrete actions and to predict events on the basis of prior events indicates the existence of an internal timing mechanism. The nature of this mechanism provides essential constraints on models of the functional organisation of the brain. The present work indicates that there are discontinuities in the function of time close to 1 s and 1.4 s, both in the amount of drift in a series of produced intervals (Study I) and in the detectability of drift in a series of sounds (Study II). The similarities across different tasks further suggest that action and perceptual judgements are governed by the same (kind of) mechanism. Study III showed that series of produced intervals could be characterised by different amounts of positive fractal dependency related to the aforementioned discontinuities. In conjunction with other findings in the literature, these results suggest that timing of intervals up to a few seconds is strongly dependent on previous intervals and on the duration to be timed. This argues against a clock-counter mechanism, as proposed by scalar timing theory, according to which successive intervals are random and the size of the timing error conforms to Weber's law. A functional model is proposed, expressed in an autoregressive framework, which consists of a single-interval timer with error corrective feedback. The duration-specificity of the proposed model is derived from the order of error correction, as determined by a semi-flexible temporal integration span.