Dans cette thèse, une nouvelle manière de générer des nombres pseudo-aléatoires est présentée.La proposition consiste à mixer deux générateurs exitants avec des itérations chaotiquesdiscrètes, qui satisfont à la définition de chaos proposée par Devaney. Un cadre rigoureux estintroduit, dans lequel les propriétés topologiques du générateur résultant sont données. Deuxréalisations pratiques d’un tel générateur sont ensuite présentées et évaluées. On montre que lespropriétés statistiques des générateurs fournis en entrée peuvent être grandement améliorées enprocédant ainsi. Ces deux propositions sont alors comparées, en profondeur, entre elles et avecun certain nombre de générateurs préexistants. On montre entre autres que la seconde manièrede mixer deux générateurs est largement meilleure que la première, à la fois en terme de vitesseet de performances.Dans la première partie de ce manuscrit, la fonction d’itérations considérée est la négation vectorielle.Dans la deuxième partie, nous proposons d’utiliser des graphes fortement connexescomme critère de sélection de bonnes fonctions d’itérations. Nous montrons que nous pouvonschanger de fonction sans perte de propriétés pour le générateur obtenu. Finalement, une illustrationdans le domaine de l’information dissimulée est présentée, et la robustesse de l’algorithmede tatouage numérique proposé est évalué. / In this thesis, a new way to generate pseudorandom numbers is presented. The propositionis to mix two exiting generators with discrete chaotic iterations that satisfy the Devaney’sdefinition of chaos. A rigorous framework is introduced, where topological properties of theresulting generator are given, and two practical designs are presented and evaluated. It is shownthat the statistical quality of the inputted generators can be greatly improved by this way, thusfulfilling the up-to-date standards. Comparison between these two designs and existing generatorsare investigated in details. Among other things, it is established that the second designedtechnique outperforms the first one, both in terms of performance and speed.In the first part of this manuscript, the iteration function embedded into chaotic iterations isthe vectorial Boolean negation. In the second part, we propose a method using graphs havingstrongly connected components as a selection criterion.We are thus able to modify the iterationfunction without deflating the good properties of the associated generator. Simulation resultsand basic security analysis are then presented to evaluate the randomness of this new family ofpseudorandom generators. Finally, an illustration in the field of information hiding is presented,and the robustness of the obtained data hiding algorithm against attacks is evaluated.

published_or_final_version / Electrical and Electronic Engineering / Doctoral / Doctor of Philosophy

Fractional calculus enables the possibility of using real number powers or complex number powers of the differentiation operator. The fundamental connection between fractional calculus and subordination processes is explored and affords a physical interpretation for a fractional trajectory, that being an average over an ensemble of stochastic trajectories. With an ensemble average perspective, the explanation of the behavior of fractional chaotic systems changes dramatically. Before now what has been interpreted as intrinsic friction is actually a form of non-Markovian dissipation that automatically arises from adopting the fractional calculus, is shown to be a manifestation of decorrelations between trajectories. Nonlinear Langevin equation describes the mean field of a finite size complex network at criticality. Critical phenomena and temporal complexity are two very important issues of modern nonlinear dynamics and the link between them found by the author can significantly improve the understanding behavior of dynamical systems at criticality. The subject of temporal complexity addresses the challenging and especially helpful in addressing fundamental physical science issues beyond the limits of reductionism.

This thesis examines chaotic mixing in wavy-type channels and two-layer shallow water flow. For wavy-type channels, the equations of motion for vortices and fluid particles are derived assuming two-dimensional irrotational, incompressible flow. Instantaneous positions of the vortices and particles are determined using Lagrangian tracking, and are conformally mapped to the physical domain. Unsteady vortex motion is analysed, and vortex-induced chaotic mixing in the channels studied. The dynamics of mixing associated with the evolution of the separation bubble, and the invariant manifolds are examined. Mixing efficiencies of the different channel configurations are compared statistically. Fractal enhancement of productivity is identified in the study of auto-catalytic reaction in the wavy channel. For the two-layer shallow water model, an entropy-correction free Roe type two-layer shallow water solver is developed for a hyperbolic system with non-conservative products and source terms. The scheme is well balanced and satisfies the C-property such that smooth steady solutions are second order accurate. Numerical treatment of the wet-dry front of both layers and the loss of hyperbolicity are incorporated. The solver is tested rigorously on a number of 1D and 2D benchmark test cases. For 2D implementation, a dynamically adaptive quadtree grid generation system is adopted, giving results which are in excellent agreement with those on regular grids at a much lower cost. It is also shown that algebraic balancing cannot be applied directly to a two-layer shallow water flow due to the lack of simultaneous referencing for the still water position for both layers. The adaptive two-layer shallow water solver is applied successfully to flow in an idealised tidal channel and to tidal-driven flow in Tampa Bay, Florida. Finally, chaotic advection and particle mixing is studied for wind-induced recirculation in two-layer shallow water basins, as well as Tampa Bay, Florida.

Le collage suscite un intérêt important pour remplacer les techniques traditionnelles d’assemblage, car il permet d’alléger les structures via une meilleure répartition des contraintes, et également de limiter les contraintes liées à l’assemblage de matériaux différents. Cependant, l’absence de technique de contrôle non destructive robuste de la qualité du collage et plus particulièrement de l’adhésion freine son développement en particulier dans le domaine aéronautique. Dans ce travail une méthode d’inspection ultrasonore d’interfaces collées qui doit révéler des défauts d’adhésion est proposée. Cette technique est validée sur un système représentatif d’applications industrielles, à savoir une liaison entre substrats métalliques liés par un adhésif époxy en film de faible épaisseur. Des défauts ont été introduits au sein de l’interface adhésive (dans l’adhésif ou à l’interface adhésif/substrat) de façon à simuler des défauts rencontrés en environnement industriel. Afin d’améliorer les capacités de détection des méthodes ultrasonores linéaires usuelles, des algorithmes de reconstruction des courbes de dispersion optimisés ont été développés. Cependant, les ondes guidées ne se sont pas montrées suffisamment sensibles à des interfaces faibles dans cette configuration, pour des adhésifs de faible épaisseur et lorsqu’une incertitude des épaisseurs des matériaux est tolérée. Dès lors, des méthodes de contrôle reposant sur l’interaction non-linéaire entre une onde ultrasonore de forte amplitude et un défaut sont proposées car moins système dépendant. Pour détecter et quantifier ces nonlinéarités, des ultrasons suffisamment énergétiques doivent être générés, ce qui implique généralement l’usage de dispositifs électroniques de puissance potentiellement intrinsèquement non-linéaires. Pour contourner ces limitations technologiques, un dispositif dédié est proposé, utilisant des traducteurs alimentés sous tension faible et placés sur un objet réverbérant. L’émission de signaux complexes préalablement établis par étalonnage permet par retournement temporel de concentrer l’énergie acoustique temporellement et spatialement, pour générer des déplacements particulaires ultrasonores de fortes amplitudes à la surface de l’échantillon contrôlé. Pour valider cette approche, le dispositif est utilisé pour contrôler des interfaces collées au sein desquelles différents types de défauts de collage ont été introduits : pollutions (particules de PTFE, démoulant, trace de doigt, etc.), insert. Les échantillons sont finalement testés mécaniquement pour évaluer la sensibilité de la résistance des interfaces à la présence de ces défauts. / Bonding is of great interest to replace traditional assembly techniques, as it makes it possible to lighten structures, through a better distribution of stresses but also to limit the stresses associated with assembling different materials. However, the lack of a robust non-destructive control technique for bonding quality and more particularly adhesion slows down its development, particularly in the aeronautical field. In this work an ultrasonic inspection method of glued interfaces which should reveal defects in adhesion is proposed. This technique is validated on a system representative of industrial applications, metal substrates bonded by a thin film epoxy adhesive. Defects have been introduced into the adhesive interface (in the adhesive or at the adhesive/substrate interface) in order to simulate defects encountered in an industrial environment. In order to improve the detection capabilities of conventional linear ultrasonic guided waves methods, algorithms for reconstructing optimized dispersion curves have been developed. However, the guided waves were not sufficiently sensitive to low interfaces in this configuration, where adhesives are thin, and an uncertainty of material thickness is tolerated. Therefore, control methods based on the non-linear interaction between a high amplitude ultrasonic wave and a defect are proposed. To detect and quantify these non-linearities, sufficiently energetic ultrasound must be generated, which generally involves the use of potentially intrinsically non-linear electronic power devices. To overcome these technological limitations, a dedicated device is proposed, using transducers powered under low voltage and placed on a reverberant object. The emission of complex signals previously established by calibration makes it possible to concentrate acoustic energy temporally and spatially, to generate after time reversal ultrasonic particle movements of high amplitude on the surface of the controlled sample. To validate this approach, the device is used to control glued interfaces in which different types of gluing defects have been introduced: pollution (PTFE particles, release agent, fingerprints, etc.), insert. The samples are finally mechanically tested to assess the sensitivity of the interface resistance to the presence of these defects.

Metodologias de sequenciamento do genoma total para investigação de diferentes tipos de câncer detectaram recentemente uma nova classe de alterações caóticas de DNA, denominada Chromothripsis. Este fenômeno de instabilidade genômica é relativamente comum em tumores de Osteossarcoma (OS), mas existem poucos estudos que expliquem esta conexão ou abordem suas causas e consequências. A presente tese iniciou-se com a re-análise de microarrays de dez amostras de OS pediátrico, previamente processadas pelo nosso laboratório, para avaliar a variação de número de cópias de DNA (CNVs). Usando ferramentas de detecção de padrões característicos de Chromothripsis (CTLPs), encontramos 3 amostras de OS com Chromothripsis , que afetaram quatro cromossomos (2, 10, 14 e 20). As amostras com presença de Chromothripsis tiveram uma media de 468 CNVs/amostra, enquanto o grupo sem o fenômeno teve uma média de 255 CNVs/amostra. Após essa avaliação de CNVs, comparamos os níveis de expressão de RNA entre duas amostras com a presença e quatro tumores com ausência de Chromothripsis. Cerca de 171 genes estão presentes em regiões de CNVs diferentes entre os grupos avaliados. Destes, a maioria (77 genes) são relacionados com funções de comunicação celular e ao ciclo celular. Um grupo de 43 genes foi relacionado às vias de processo metabólico (principalmente associado ao metabolismo do RNA) e 27 genes associados à organização do componente celular ou biogênese. Tumores com Chromothripsis possuiam 4 genes do sistema imune menos expressos (CADM1; CLEC4A; CCR1; CD164) e 12 estavam superexpressos (IL32, LAT, BCL3, FCAR, RFX1, ILIB, CXCL1, SPON2, CCR6, IL6, SEMA3C, GEM). Os genes pouco expressos também têm um papel na via de adesão celular. A adesão celular está associada à progressão do câncer e metástase. Em seguida, re-analisamos as CNVs de 82 amostras de OS e 35 linhagens celulares de OS, usando microarrays disponíveis em bancos de dados públicos (GEO e arrayexpress), para identificar potenciais regiões cromossômicas comumente envolvidas em alterações caóticas no número de cópias de DNA, especialmente CTLPs. Identificamos Chromothripsis em 27 amostras (11 tumores e 16 linhagens), afetando 17 cromossomos diferentes. Os cromossomos 2, 8 e 12 foram alvos frequentes de Chromothripsis em OS. Em seguida, foram analisados dados de sequenciamento WGS de 12 tumores de OS disponíveis no banco de dados online dbGaP. Fizemos a avaliação da variação de número de cópias para caracterizar detalhadamente as alterações caóticas e identificar asregiões cromossômicas alvo envolvidas nas regiões de alterações caóticas no número de cópias do DNA. Encontramos CTPLs em 7 (58%) das 12 amostras de OS analisadas, usando dados de sequenciamento total. Foram encontrados 12 cromossomos diferentes afetados pelo fenômeno de alteração caótica. CTPLs foram detectadas em 62,5% das amostras de pacientes que faleceram em decorrência deste tumor. Os cromossomos 1, 3 e 7 foram um pouco mais afetados por Chromothripsis nas amostras disponibilizadas pelo dbGaP. Além disso, os cromossomos 2 e 12 também foram afetados por Chromothripsis nessas amostras. Cerca de 700 genes/tumor foram encontrados nas regiões de CTLPs. Um total de 101 genes foram localizados em regiões de alteração de número de cópias que distinguem os grupos com e sem Chromothripsis. Estes genes estão relacionados com vias de processo celular (45 genes - os quais 17 estão associados à comunicação celular) e processo metabólico (22 genes - os quais 19 estão associados ao processo metabólico primário). Nós também comparamos os níveis de expressão gênica das amostras disponíbilizadas pelo dbGap, em que foram avaliados dados de expressão de 6 amostras de RNA de OS com Chromothripsis e de 3 amostras de RNA de OS sem Chromothripsis . Diferentes algoritmos e ferramentas foram utilizadas para avaliação de RNA. Nós analisamos os dados de expressão por dois diferentes mecanismos: EdgeR e Nexus Expression. Ambos mostraram menor expressão de RNA nas vias de comunicação celular e processo metabólico primário em amostras com Chromothripsis. Os genes com regulação negativa da resposta do sistema imunológico foram encontrados em ambas ferramentas (COL8A1, CCL25). Para estudar os cromossomos envolvidos na formação de micronúcleos na linhagem celular U2OS, foram investigados erros na divisão celular induzidos por drogas (durante a anáfase). Esta etapa foi realizada durante o período de doutorado sanduíche, no Barts Cancer Institute, em Londres-UK. Os cromossomos com erros durante a anáfase foram contados por meio da técnica de FISH centromérica. Os cromossomos mais comumente encontrados com erros foram Chr2, Chr6, Chr11 e Chr12. Estes dados corroboram a ideia de que alguns cromossomos são mais suscetíveis a erros de divisão celular e colaboram para maiores índices de CTPLs em certos tumores. O fenômeno Chromothripsis parece estar presente em pelo menos 30% dos tumores de osteossarcoma e pode estar contribuindo para o fenótipo mais agressivo deste tumor ósseo. / Whole genome sequencing methods applied to a number of human cancers have detected a new class of chaotic DNA alterations in tumors called Chromothripsis. This mechanism of genomic instability is relatively common in the human bone tumor osteosarcoma (OS), but there are few studies in this tumor addressing either its causes or consequences. In this thesis we initially re-analyzed the DNA copy number data using newer software designed to detect signatures of Chromothripsis-like Patterns (CTLPs) using ten OS samples previously studied by our laboratory. We found three of the osteosarcomas had Chromothripsis signatures that affected four chromosomes (2, 10, 14 and 20). The osteosarcomas with Chromothripsis had a median of 468 copy number abnormalities per tumor compared to 255 for OS tumors without Chromothripsis. Next, we compared global RNA expression levels from two OS samples with Chromothripsis to four tumors without Chromothripsis to determine the types of gene expression differences associated with this process. We found that 171 genes mapped to regions of Chromothripsis with the majority (77 genes) mainly having functions related to cellular communication and cell cycle. There were 43 genes that were related to metabolic process (mainly associated with RNA metabolism) and 27 genes with cellular component organization or biogenesis. Also, there were four genes associated with the immune system that were underexpressed (CADM1; CLEC4A; CCR1; CD164) and 12 were overexpressed (IL32, LAT, BCL3, FCAR, RFX1, ILIB, CXCL1, SPON2, CCR6, IL6, SEMA3C, GEM) in the Chromothripsis tumors. Interestingly, all the genes underexpressed also have a role in cell adhesion pathway. Cell adhesion is associated with cancer progression and metastasis. We then reanalyzed DNA copy number data from 82 OS tumors and 35 OS cell lines using microarrays datasets available in public databanks (GEO and arrayexpress), to identify potential chromosomal regions commonly involved in chaotic DNA copy number alterations, especially CTLPs. We found Chromothripsis in 27 OS samples (11 tumors and 16 cell lines), affecting 17 different chromosomes. Chromosomes 2, 8 and 12 were frequent targets of Chromothripsis in OS. Sequentially, the DNA copy number alterations were analyzed using whole genome sequence data of 12 OS tumors available from dbGaP databank to characterize chaotic alterations in detail and identify the target chromosomal regions involved in Chromothripsis. We found Chromothripsis patterns in 7 (58%) of the 12 OS samples analyzed using whole genome sequence data. In total there were12 different chromosomes involved affecting 62.5% of samples from patients that died from OS. Chromosomes 1, 2, 3, 7 and 12 were slightly more often Chromothripsis target locations. Nearly 700 genes per tumor were found in the CTLPs regions. A total of 101 genes were located in regions of copy number change that distinguished the group of OS with Chromothripsis in comparison to OS without Chromothripsis. These genes are related with cellular process (45 genes - which 17 are associated with cell communication) and metabolic process (22 genes - which 19 are associated with primary metabolic process). We were also able to compare the RNA levels from the dbGap samples when expression data was available: comparing 6 OS RNA samples with Chromothripsis to 3 OS RNA samples without Chromothripsis. Both the EdgeR and Nexus Expression pipelines showed downregulation in cell communication pathway and primary metabolic process in samples with Chromothripsis. Genes downregulated of immune system response pathway were found in both pipeline (COL8A1, CCL25). To study the chromosomes involved in micronucleus formation in the OS cell line U2OS, errors in cell division induced by drugs during the anaphase were evaluated during the sandwich period at Barts Cancer Institute in London-UK. The lagging chromosomes were counted and the most common chromosomes with errors were Chr2, Chr6, Chr11, and Chr12. These data provide further support to the idea that some chromosomes are more susceptible to cell division errors and corroborate with the chromosomes affected by CTPLs in some tumors.

Neste trabalho investiga-se o emprego de técnicas de estimação em sistemas de modulação digital que utilizam sinais caóticos. Inicialmente, aspectos básicos das teorias de sistemas não-lineares e de modulações digitais são revisitados seguidos de técnicas recentemente propostas de modulações digitais caóticas com receptores por correlação coerente, não-coerente e diferencial: o CSK (Chaos Shift Keying), o DCSK (Differential Chaos Shift Keying) e algumas de suas variantes, em especial o FM-DCSK (Frequency Modulated DCSK). Nessa descrição, utiliza-se a notação de equivalente passa-baixas de tempo discreto para facilitar a comparação com modulações digitais convencionais. Deduz-se o limite de Cramér-Rao para a estimação da condição inicial de órbitas caóticas em função de propriedades estatísticas do mapa que as gerou e descrevem-se dois estimadores para elas: o MLE (Maximum Likelihood Estimator) que se aplica a mapas com densidade invariante uniforme e o algoritmo de Viterbi para o qual se apresenta uma generalização a fim de aplicá-lo a uma classe maior de mapas. Por apresentar ganho de estimação maior na faixa de relação sinal-ruído de interesse, este último é utilizado em propostas de sistemas de modulação digital que utilizam estimação de órbitas para detectar o símbolo enviado: o ML-CSK (Maximum Likelihood CSK) modificado para poder usar mapas com densidade invariante não-uniforme, empregando um ou dois mapas e o ML-DCSK (Maximum Likelihood DCSK). Por simulação, avaliou-se o desempenho em termos de taxa de erro desses sistemas sob ruído branco aditivo gaussiano. / In this work, we investigate the use of estimation techniques to digital modulation systems that use chaotic signals. Initially, basic aspects of nonlinear systems and digital modulation theory are reviewed followed by currently proposed techniques of chaotic digital modulation with coherent, noncoherent and differential correlation receivers: CSK (Chaos Shift Keying), DCSK (Differential Chaos Shift Keying) and some of its variants in special FM-DCSK (Frequency Modulated DCSK). These systems are described using a discrete-time lowpass equivalent model to facilitate comparison with conventional digital modulation systems. We derive Cramér-Rao lower bounds for the estimation of the initial condition of chaotic orbits as a function of the statistical properties of the chaos generating map and describe two chaotic orbits estimators: the MLE (Maximum Likelihood Estimator) that applies only to maps with uniform invariant density and the Viterbi algorithm for which a generalization is presented that allows its application to a broader class of maps. Because of the larger estimation gains attained in the signal-to-noise ratio range of interest, the latter is used in proposed digital modulation systems that use orbit estimation to detect the transmitted symbol: ML-CSK (Maximum Likelihood CSK) modified to allow maps with nonuniform invariant density using one map or two maps and ML-DCSK (Maximum Likelihood DCSK). The performance of these systems in terms of symbol error rate is accessed via simulation under additive white gaussian noise perturbations.

A geometric model of a reinjected cuspidal horseshoe is constructed, that resembles the standard horseshoe, but where the set of points that escape are now reinjected and contribute to richer dynamics. We show it is observed in the unfolding of a three-dimensional vector field possessing an inclination-flip homoclinic orbit with a resonant hyperbolic equilibrium. We use techniques from classical dynamical systems theory and rigorous computational symbolic dynamics with algebraic topology to show that for suitable parameters the flow contains a strange attractor. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2016. / FAU Electronic Theses and Dissertations Collection

In this thesis we will discuss connections between Hamiltonian systems with a periodic kick and planar diffeomorphisms. After a brief overview of Hamiltonian theory we will focus, as an example, on derivations of the Hâenon map that can be obtained by considering kicked Hamiltonian systems. We will conclude with examples of Hâenon maps of interest. / by Zalmond C. Barney. / Thesis (M.S.)--Florida Atlantic University, 2011. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2011. Mode of access: World Wide Web.

Systems with time delays have a broad range of applications not only in control systems but also in many other disciplines such as mathematical biology, financial economics, etc. The time delays cause more complex behaviours of the systems. It requires more sophisticated analysis due to the infinite dimensional structure of the space spaces. In this thesis we investigate stability properties associated with output functions of delay systems. Our primary target is the equivalent Lyapunov characterization of input-tooutput stability (ios). A main approach used in this work is the Lyapuno Krasovskii functional method. The Lyapunov characterization of the so called output-Lagrange stability is technically the backbone of this work, as it induces a Lyapunov description for all the other output stability properties, in particular for ios. In the study, we consider two types of output functions. The first type is defined in between Banach spaces, whereas the second type is defined between Euclidean spaces. The Lyapunov characterization for the first type of output maps provides equivalence between the stability properties and the existence of the Lyapunov-Krasovskii functionals. On the other hand, as a special case of the first type, the second type output renders flexible Lyapunov descriptions that are more efficient in applications. In the special case when the output variables represent the complete collection of the state variables, our Lyapunov work lead to Lyapunov characterizations of iss, complementing the current iss theory with some novel results. We also aim at understanding how output stability are affected by the initial data and the external signals. Since the output variables are in general not a full collection of the state variables, the overshoots and decay properties may be affected in different ways by the initial data of either the state variables or just only the output variables. Accordingly, there are different ways of defining notions on output stability, making them mathematically precisely. After presenting the definitions, we explore the connections of these notions. Understanding the relation among the notions is not only mathematically necessary, it also provides guidelines in system control and design. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2017. / FAU Electronic Theses and Dissertations Collection