Neste trabalho, apresentamos um método algébrico para obter formas normais de campos vetoriais reversíveis equivariantes. Adaptamos o método clássico de Belitskii-Elphick, usando ferramentas da teoria invariante para estabelecer fórmulas que consideram as simetrias e antissimetrias como ponto de partida. Mostramos que este método, mesmo sem simetrias, possui uma estreita relação com o método da transversal completa da teoria de singularidades. Com as ferramentas desenvolvidas nesta tese, a forma normal obtida e uma série formal que não depende do cálculo do kernel do chamado operador homológico. Formas normais para duas classes de campos, ressonantes e não ressonantes, são apresentadas, para diferentes representações do grupo \'Z IND. 2\' x \'Z IND. 2\' cuja linearização tem uma parte nilpotente de dimensão 2 e uma parte semi-simples com autovalores puramente imaginários / We give an algebraic method to obtain normal forms of reversible equivariant vector fields. We adapt the classical method by Belitskii-Elphick using tools from invariant theory to establish formulae that take symmetries into account as a starting point. We show that this method, even without symmetries, has a close relation to complete transversal of singularities theory. Applying the method developed in this thesis, the resulting normal form is a formal series which does not depend of the computation of the kernel of the so called homologic operator. Normal forms of two classes of non-resonant and resonant cases are presented, for dierent representations of the group \'Z INT. 2\' x \'Z INT. 2\' - with linearization having a 2 - dimensional nilpotent part and a semisimple part with purely imaginary eigenvalues

Na análise global e local de sistemas dinâmicos assumimos, em geral, que as equações estão numa forma normal. Em presença de simetrias, as equações e o domínio do problema são invariantes pelo grupo formado por estas simetrias; neste caso, o campo de vetores é equivariante pela ação deste grupo. Quando, além das simetrias, temos também ocorrência de anti-simetrias - ou reversibilidades - as equações e o domínio do problema são ainda invariantes pelo grupo formado pelo conjunto de todas as simetrias e anti-simetrias; neste caso, o campo de vetores é reversível-equivariante. Existem muitos modelos físicos onde simetrias e anti-simetrias aparecem naturalmente e cujo efeito pode ser estudado de uma forma sistemática através de teoria de representação de grupos de Lie. O primeiro passo deste processo é colocar a aplicação que modela tal sistema numa forma normal e isto é feito com a dedução a priori da forma geral dos campos de vetores. Esta forma geral depende de dois componentes: da base de Hilbert do anel das funções invariantes e dos geradores do módulo das aplicações reversíveis-equivariantes. Neste projeto, nos concentramos principalmente na aplicação de resultados recentes da literatura para a construção de uma lista de formas gerais de aplicações reversíveisequivariantes sob a ação de diferentes grupos. Além disso, adaptamos ferramentas algébricas da literatura existentes no contexto equivariante para o estudo sistemático de acoplamento de células idênticas no contexto reversível-equivariante / In the global and local analysis of dynamical systems, we assume, in general, that the equations are in a normal form. In presence of symmetries, the equations and the problem domain are invariant under the group formed by these symmetries; in that case, the vector field is equivariant by the action of this group. When, in addition to the symmetries, we have the occurrence of anti-symmetries - or reversibility - the equations and the problem domain are still invariant by the group formed by the set of all symmetries and anti-symmetries; in this case, the vector field is reversible-equivariant. There are many physical models where both symmetries and anti-symmetries occur naturally and whose effect can be studied in a systematic way through group representation theory. The first step of this process is to put the mapping that model the system in a normal form, and this is done with the deduction of the general form of the vector field. This general form depends on two components: the Hilbert basis of the invariant function ring and also the generators of the module of the revesible-equivariants. In this work, we mainly focus on the applications of recent results of the literature to build a list of general forms of reversible-equivariant mappings under the action of different groups. We also adapt algebraic tools of the existing literature in the equivariant context to the systematic study of coupling of identical cells in the reversible-equivariant context

Esteganografia é uma técnica utilizada para ocultar uma informação secreta dentro de outro tipo de informação sem perda de qualidade da informação hospedeira e com o objetivo de extrair a informação posteriormente. Esteganografia reversível permite a exata restauração (sem perda) do sinal hospedeiro original após a extração da informação oculta. Várias ténicas reversíveis têm sido desenvolvidas, mas nenhuma delas parece ser apropriada para imagens binárias. Uma técnica de marca d\'água faz uso de técnicas esteganográficas para inserir informação em uma imagem hospedeira, com o intuito de fazer uma asserção sobre a imagem no futuro. Uma marca d\'água de autenticação (AWT) insere uma informação oculta na imagem com a intenção de detectar qualquer alteração acidental ou maliciosa na imagem. Uma AWT normalmente usa criptografia de chave secreta ou chave pública para computar a assinatura de autenticação da imagem, inserindo-a na própria imagem. JBIG2 é um padrão internacional para compressão de imagens binárias (com ou sem perda). Ele decompõe a imagem em várias regiões (texto, meio-tom e genérica) e codifica cada região usando o método mais apropriado. A criação de AWTs seguras para imagens binárias comprimidas é um importante problema prático. Porém, parece que nenhuma AWT para JBIG2 já foi proposta. Este trabalho propõe algumas técnicas esteganográficas para arquivos JBIG2. Então, estas técnicas são usadas para criar AWTs para imagens codificadas como JBIG2. As imagens marcadas são visualmente agradáveis, sem ruídos do tipo sal-e-pimenta. Este trabalho também propõe uma técnica esteganográfica reversível para imagens binárias. A técnica proposta seleciona um conjunto de pixels de baixa visibilidade e utiliza o algoritmo de Golomb para comprimir as previsões desses pixels. Então, a informação comprimida e a informação a ser oculta são inseridas na imagem. Imagens marcadas com a técnica proposta possuem excelente qualidade visual, pois apenas pixels de baixa visibilidade são modificados. Então, a técnica proposta é utilizada para autenticar imagens binárias e documentos de maneira reversível. / Data-hiding is a technique to hide secret information inside another group of information data, without loss of quality of the host information, and the means to extract the secret information afterwards. Reversible data-hiding enable the exact restoration (lossless) of the original host signal after extracting the embedded information. Several reversible data hiding techniques have been developed, but none of them seems to be appropriate for binary images. A watermarking technique makes use of data-hiding to insert some information into the host image, in order to make a posterior assertion about the image. An authentication watermarking technique (AWT) inserts hidden data into an image in order to detect any accidental or malicious alteration to the image. AWT normally makes use of secret- or publickey cryptographic ciphers to compute the authentication signature of the image, and inserts it into the image itself. JBIG2 is an international standard for compressing bilevel images in both lossy and lossless modes. JBIG2 decomposes the image into several regions (text, halftone and generic) and encodes each one using the most appropriate method. The creation of secure AWTs for compressed binary images is an important practical problem. However, it seems that no AWT for JBIG2 has ever been proposed. This work proposes some data-hiding techniques for JBIG2 files. Then, these techniques are used to design AWTs for JBIG2-encoded images. The resulting watermarked images are visually pleasant, without visible salt and pepper noise. This work also proposes a reversible data hiding technique for binary images. The proposed technique selects a set of low-visibility pixels and uses Golomb codes to compress the predictions of these pixels. Then, this compressed data and the net payload data are embedded into the image. Images watermarked by the proposed technique have excellent visual quality, because only low-visibility pixels are flipped. Then, the proposed data hiding is used to reversibly authenticate binary images and documents.

Neste trabalho, apresentamos um método algébrico para obter formas normais de campos vetoriais reversíveis equivariantes. Adaptamos o método clássico de Belitskii-Elphick, usando ferramentas da teoria invariante para estabelecer fórmulas que consideram as simetrias e antissimetrias como ponto de partida. Mostramos que este método, mesmo sem simetrias, possui uma estreita relação com o método da transversal completa da teoria de singularidades. Com as ferramentas desenvolvidas nesta tese, a forma normal obtida e uma série formal que não depende do cálculo do kernel do chamado operador homológico. Formas normais para duas classes de campos, ressonantes e não ressonantes, são apresentadas, para diferentes representações do grupo \'Z IND. 2\' x \'Z IND. 2\' cuja linearização tem uma parte nilpotente de dimensão 2 e uma parte semi-simples com autovalores puramente imaginários / We give an algebraic method to obtain normal forms of reversible equivariant vector fields. We adapt the classical method by Belitskii-Elphick using tools from invariant theory to establish formulae that take symmetries into account as a starting point. We show that this method, even without symmetries, has a close relation to complete transversal of singularities theory. Applying the method developed in this thesis, the resulting normal form is a formal series which does not depend of the computation of the kernel of the so called homologic operator. Normal forms of two classes of non-resonant and resonant cases are presented, for dierent representations of the group \'Z INT. 2\' x \'Z INT. 2\' - with linearization having a 2 - dimensional nilpotent part and a semisimple part with purely imaginary eigenvalues

Esteganografia é uma técnica utilizada para ocultar uma informação secreta dentro de outro tipo de informação sem perda de qualidade da informação hospedeira e com o objetivo de extrair a informação posteriormente. Esteganografia reversível permite a exata restauração (sem perda) do sinal hospedeiro original após a extração da informação oculta. Várias ténicas reversíveis têm sido desenvolvidas, mas nenhuma delas parece ser apropriada para imagens binárias. Uma técnica de marca d\'água faz uso de técnicas esteganográficas para inserir informação em uma imagem hospedeira, com o intuito de fazer uma asserção sobre a imagem no futuro. Uma marca d\'água de autenticação (AWT) insere uma informação oculta na imagem com a intenção de detectar qualquer alteração acidental ou maliciosa na imagem. Uma AWT normalmente usa criptografia de chave secreta ou chave pública para computar a assinatura de autenticação da imagem, inserindo-a na própria imagem. JBIG2 é um padrão internacional para compressão de imagens binárias (com ou sem perda). Ele decompõe a imagem em várias regiões (texto, meio-tom e genérica) e codifica cada região usando o método mais apropriado. A criação de AWTs seguras para imagens binárias comprimidas é um importante problema prático. Porém, parece que nenhuma AWT para JBIG2 já foi proposta. Este trabalho propõe algumas técnicas esteganográficas para arquivos JBIG2. Então, estas técnicas são usadas para criar AWTs para imagens codificadas como JBIG2. As imagens marcadas são visualmente agradáveis, sem ruídos do tipo sal-e-pimenta. Este trabalho também propõe uma técnica esteganográfica reversível para imagens binárias. A técnica proposta seleciona um conjunto de pixels de baixa visibilidade e utiliza o algoritmo de Golomb para comprimir as previsões desses pixels. Então, a informação comprimida e a informação a ser oculta são inseridas na imagem. Imagens marcadas com a técnica proposta possuem excelente qualidade visual, pois apenas pixels de baixa visibilidade são modificados. Então, a técnica proposta é utilizada para autenticar imagens binárias e documentos de maneira reversível. / Data-hiding is a technique to hide secret information inside another group of information data, without loss of quality of the host information, and the means to extract the secret information afterwards. Reversible data-hiding enable the exact restoration (lossless) of the original host signal after extracting the embedded information. Several reversible data hiding techniques have been developed, but none of them seems to be appropriate for binary images. A watermarking technique makes use of data-hiding to insert some information into the host image, in order to make a posterior assertion about the image. An authentication watermarking technique (AWT) inserts hidden data into an image in order to detect any accidental or malicious alteration to the image. AWT normally makes use of secret- or publickey cryptographic ciphers to compute the authentication signature of the image, and inserts it into the image itself. JBIG2 is an international standard for compressing bilevel images in both lossy and lossless modes. JBIG2 decomposes the image into several regions (text, halftone and generic) and encodes each one using the most appropriate method. The creation of secure AWTs for compressed binary images is an important practical problem. However, it seems that no AWT for JBIG2 has ever been proposed. This work proposes some data-hiding techniques for JBIG2 files. Then, these techniques are used to design AWTs for JBIG2-encoded images. The resulting watermarked images are visually pleasant, without visible salt and pepper noise. This work also proposes a reversible data hiding technique for binary images. The proposed technique selects a set of low-visibility pixels and uses Golomb codes to compress the predictions of these pixels. Then, this compressed data and the net payload data are embedded into the image. Images watermarked by the proposed technique have excellent visual quality, because only low-visibility pixels are flipped. Then, the proposed data hiding is used to reversibly authenticate binary images and documents.

Metallic nanoparticles are unique materials for optical, electronic, catalytic, and sensing applications. Due to the vast flexibility in controlling the surface chemistry of these particles through functionalization there is a great deal of interest in using metallic nanoparticles as building blocks in the development of more complex nanostructures through the use of a 'bottom-up' approach. Using self assembly techniques, one can exploit spontaneous chemical interactions to build complex constructs on the nanometer scale. Towards this end, gold nanorods have been synthesized and modified with various polymers, inorganic oxides and organic ligands to establish principles for self-assembly of these unique nanomaterials. Gold nanorods are of great interest due to their strong optical absorption in the visible and near infrared regions, which can be tuned through material preparation and modification of the surrounding environment. This thesis focuses on investigating approaches for both irreversible and reversible self-assembly of gold nanorods. Techniques such as dynamic light scattering (DLS), ultraviolet-visible (UV) spectroscopy, transmission electron microscopy (TEM), and polarization modulation infrared reflection absorbance spectroscopy (PM-IRRAS) were used to characterize the colloidal particles and gold surfaces. A novel contribution of this work is the successful demonstration of end-to-end linking of gold nanorods in a rapid and reversible manner using a pH responsive polypeptide.

The reversible oxidation of cysteine by reactive oxygen species (ROS) is both a mechanism for cellular protein signaling as well as a cause of cellular injury and death through the generation of oxidative stress. The study of cysteine oxidation is complicated by the methodology currently available to isolate and enrich oxidized-cysteine containing proteins. We sought to simplify this process by reducing the time needed to process samples and reducing sample loss and contamination risk. We accomplished this by eliminating precipitation steps needed for the protocol by (a) introducing an in-solution NEM-quenching step prior to reduction and (b) replacing soluble dithiothreitol reductant with a series of newly-developed high-capacity polyacrylamide-based solid-phase reductants that could be easily separated from the lysate through centrifugation. These modifications, collectively called resin-assisted reduction and capture (RARC), reduced the time needed to perform the RAC method from 2-3 days to 4-5 hours, while the overall quality and quantity of previously-oxidized cysteines captured was increased. In order to demonstrate the RARC method’s utility in studying complex cellular oxidants, the optimized methodology was used to study cysteine oxidation caused by the redox-active metals arsenic, cadmium, and chromium. As(III), Cr(VI), and Cd(II) were all found to increase cysteine oxidation significantly, with As(III) and Cd(II) inducing more oxidation than Cr(VI) following a 24-hour exposure to cytotoxic concentrations. Label-free proteomic analysis and western blotting of RARC-isolated oxidized proteins found a high degree of commonality between the proteins oxidized by these metals, with cytoskeletal, translational, stress response, and metabolic proteins all being oxidized. Several previously-unreported redox-active cysteines were also identified. These results indicate that cysteine oxidation by As(III), Cr(VI), and Cd(II) may play a significant role in these metals’ cytotoxicity and demonstrates the utility of the RARC method as a strategy for studying reversible cysteine oxidation by oxidants in oxidative signaling and disease. The RARC method is a simplification and improvement upon the current state of the art which decreases the barrier of entry to studying cysteine oxidation, allowing more researchers to study this modification. We predict that the RARC methodology will be critical in expanding our understanding of reactive cysteines in cellular function and disease.

Ces travaux de thèse portent sur l’élaboration et l’étude des propriétés thermomécaniques de polymères dynamiques incorporant des dérivés borés. Tout en appliquant ce concept sur une variété d’architectures macromoléculaires : copolymères fonctionnels, briques di- et tri-fonctionelles, deux réactivités distinctes du bore ont été étudiées et exploitées. Une large gamme de méthodes de caractérisation a été utilisée pour mener à bien ce projet : spectroscopies FTIR et RMN sous différents stimuli, ainsi que de nombreuses analyses thermiques et mécaniques. Dans un premier temps, nous avons considéré la formation de paires de Lewis frustrées entre des acides de Lewis (organoboranes) et des bases de Lewis (amines et phosphines) stériquement encombrés, cette interaction pouvant être fortement modulée par la participation d’un troisième composé tels que des molécules de gaz. Ainsi, nous avons été capables de former des réseaux dynamiques réticulables de façon réversible avec le dioxyde de carbone. Dans un second temps, nous avons mis en évidence une nouvelle réactivité dans les esters boroniques cycliques impliquant une ouverture de cycle à haute température, assistée par la présence de nucléophiles. Cette réaction a été mise à profit pour former des polymères réticulés dynamiquement, pouvant atteindre des températures de transition vitreuse jusqu’à 220°C et dé-réticulables par dilution avec un bon solvant du polymère (apolaire). Cette réactivité a été appliquée à une variété de polymères accessibles par copolymérisation radicalaire (styrène, éthylène, acétate de vinyle, acrylate de butyle) ou par post-fonctionnalisation de polymères commerciaux (polybutadiène) / This thesis focuses on the development and study of thermomechanical properties of dynamic polymers incorporating borylated derivatives. While applying this concept to a variety of macromolecular architectures: functional copolymers, di- and tri-functional bricks, two distinct reactivities of boron have been explored. A wide range of characterization methods has been used to carry out this project: FTIR and NMR spectroscopies under numerous stimuli, as well as many thermal and mechanical analyses. In a first step, we considered the formation of Frustrated Lewis Pairs between Lewis acids (organoboranes) and Lewis bases (amines and phosphines) sterically hindered, as this interaction can be strongly modulated by the participation of a third compound such as gas molecules. Thus, we have been able to form dynamic networks reversibly crosslinkable with carbon dioxide. In a second step, we demonstrated a new reactivity in cyclic boronic esters involving a ring-opening at high temperature, assisted by the presence of nucleophiles. This reaction has been used to form dynamically crosslinked polymers, which can reach glass transition temperatures up to 220°C and de-crosslinkable by dilution in a good (apolar) polymer solvent. This reactivity has been applied to a variety of polymers accessible by radical copolymerization (styrene, ethylene, vinyl acetate, butyl acrylate) or by post-functionalization of commercial polymers (polybutadiene)

L'accès à de nouvelles techniques de synthèse simples permettant l'obtention d'architectures macromoléculaires complexes et bien définies demeure un enjeu permanent. Les réactions de couplage dites " click " permettent de relever en parti ce défi et dans cette catégorie, les γ-thiolactones sont apparues comme un nouvel outil important. Dans ce contexte, nous avons développé un nouveau procédé de synthèse de mono- et bis(γ-thiolactones) fonctionnelles basé sur la chimie radicalaire des xanthates, permettant l'accès à une bibliothèque de thiolactones porteuses de groupements fonctionnels divers. La réactivité de ces molécules a été testée au travers de la réaction amine-thiol-ène avec la fonctionnalisation d'extrémités de chaînes polymères et la polymérisation par étapes. Un exemple d'utilisation de ces polymères est présenté avec la stabilisation de nanoparticule de gadolinium en milieu aqueux. Enfin, une série de thiolactones portant des groupements susceptibles de jouer le rôle d'amorceurs et d'agents de contrôle en polymérisation radicalaire par désactivation réversible ont permis l'obtention de polymères fonctionnalisés thiolactone en bout de chaîne. Ces polymères ont par la suite été utilisés dans des réactions de modifications post-polymérisation permettant l'incorporation de groupements possédant des propriétés de fluorescences par exemple. / The development of simple synthetic protocols allowing the construction of complex and well-defined macromolecular architectures remains an ongoing challenge. The so-called "click" coupling reactions make it partially possible. Among these reactions, the use of γ-thiolactones has emerged as a new important tool. In this context, we have developed a new procedure for the synthesis of functional mono- and bis(γ-thiolactones) based on the radical chemistry of xanthates, allowing access to a library of thiolactones bearing various groups. The reactivity of these molecules was tested with the amine-thiol-ene conjugation for the functionalization of polymer chain-ends and step-growth polymerization. An application of these functionalized polymers was presented with the stabilization of gadolinium nanoparticles in water. Finally, a series of thiolactone-functional initiators or control agents for reversible-deactivation radical polymerization techniques allowed us to obtain thiolactone-terminated polymers. These polymers were then used for post-polymerization modification reactions with the incorporation of a new fluorescent group for example.

This thesis is dedicated to the development of statistical and computational methods for the analysis of DNA sequences and gene expression time series.<br /><br />First we study a parsimonious Markov model called Mixture Transition Distribution (MTD) model which is a mixture of Markovian transitions. The overly high number of constraints on the parameters of this model hampers the formulation of an analytical expression of the Maximum Likelihood Estimate (MLE). We propose to approach the MLE thanks to an EM algorithm. After comparing the performance of this algorithm to results from the litterature, we use it to evaluate the relevance of MTD modeling for bacteria DNA coding sequences in comparison with standard Markovian modeling.<br /><br />Then we propose two different approaches for genetic regulation network recovering. We model those genetic networks with Dynamic Bayesian Networks (DBNs) whose edges describe the dependency relationships between time-delayed genes expression. The aim is to estimate the topology of this graph despite the overly low number of repeated measurements compared with the number of observed genes. <br /><br />To face this problem of dimension, we first assume that the dependency relationships are homogeneous, that is the graph topology is constant across time. Then we propose to approximate this graph by considering partial order dependencies. The concept of partial order dependence graphs, already introduced for static and non directed graphs, is adapted and characterized for DBNs using the theory of graphical models. From these results, we develop a deterministic procedure for DBNs inference. <br /><br />Finally, we relax the homogeneity assumption by considering the succession of several homogeneous phases. We consider a multiple changepoint<br />regression model. Each changepoint indicates a change in the regression model parameters, which corresponds to the way an expression level depends on the others. Using reversible jump MCMC methods, we develop a stochastic algorithm which allows to simultaneously infer the changepoints location and the structure of the network within the phases delimited by the changepoints. <br /><br />Validation of those two approaches is carried out on both simulated and real data analysis.