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The human being and her behavior is complex. Research has shown serendipity and chance to play a great part in the scientific research praxis, still the complexity of human information retrieval is not fully acknowledged in modern libraries. This master thesis compares two different worldviews; the mechanistic and the organic. This in order to understand why information seeking today is increasingly linear when human information behavior is not. The way people believe the world to work reflects on how libraries and information seeking work. The mechanistic worldview, comparing the world to a machine, is rooted in humanity since the seventeenth century and is still shaping our world and institutions. Today databases and linear searches are pushing physical books off shelves to make room for computers and searching on limiting linear mechanical terms instead of complex human ones. This pattern often occurs without adequate questioning and online information is argued to be even more available to patrons than the physical library.  This thesis uses complexity theory and philosophical method to broaden perspectives and question linear searches in scientific information retrieval. It aims to highlight the importance of complex information retrieval and physical browsing for scientific innovation and creativity. Erdelez's original information encountering method was used to obtain source material for philosophical analysis. Philosophical method and complexity theory is used throughout the text to analyze the linear worldview leading up to a joint argumentative summary at the end of every chapter bringing the text forward.  The thesis contains a field study with semi-structured interviews with librarians at the Picture Collection, New York Public Library. This highlights the value of physical browsing through the strong criticism that arose from patrons when the library wanted to archive the unique and browsable research collection.  The result of the thesis argues that the linear technological development in libraries with less physical collections, librarian encounters, passive information gathering and random information paths without underlying commercial drivers create more like-mindedness instead of innovation. This significantly reducing the possibility of interdisciplinary discoveries. A technical development that at an alarming rate shifts information from being sought by people, to people being sought by information.  This is a two years master’s thesis in Library and Information Science.

The direct and adjoint methods are to linearize the time-averaged solution of bounded dynamical systems about one or more design parameters. Hence, such methods are one way to obtain the gradient necessary in locally optimizing a dynamical system’s time-averaged behavior over those design parameters. However, when analyzing nonlinear systems whose solutions exhibit chaos, standard direct and adjoint sensitivity methods yield meaningless results due to time-local instability of the system. The present work proposes a new method of solving the direct and adjoint linear systems in time, then tests that method’s ability to solve instances of the Lorenz system that exhibit chaotic behavior. Promising results emerge and are presented in the form of a regression analysis across a parametric study of the Lorenz system.

This dissertation investigates uncertainty quantification in dynamic problems. The Advanced Mean Value (AMV) method is used to calculate probabilistic sound power and the sensitivity of elastically supported panels with small uncertainty (coefficient of variation). Sound power calculations are done using Finite Element Method (FEM) and Boundary Element Method (BEM). The sensitivities of the sound power are calculated through direct differentiation of the FEM/BEM/AMV equations. The results are compared with Monte Carlo simulation (MCS). An improved method is developed using AMV, metamodel, and MCS. This new technique is applied to calculate sound power of a composite panel using FEM and Rayleigh Integral. The proposed methodology shows considerable improvement both in terms of accuracy and computational efficiency. In systems with large uncertainties, the above approach does not work. Two Spectral Stochastic Finite Element Method (SSFEM) algorithms are developed to solve stochastic eigenvalue problems using Polynomial chaos. Presently, the approaches are restricted to problems with real and distinct eigenvalues. In both the approaches, the system uncertainties are modeled by Wiener-Askey orthogonal polynomial functions. Galerkin projection is applied in the probability space to minimize the weighted residual of the error of the governing equation. First algorithm is based on inverse iteration method. A modification is suggested to calculate higher eigenvalues and eigenvectors. The above algorithm is applied to both discrete and continuous systems. In continuous systems, the uncertainties are modeled as Gaussian processes using Karhunen-Loeve (KL) expansion. Second algorithm is based on implicit polynomial iteration method. This algorithm is found to be more efficient when applied to discrete systems. However, the application of the algorithm to continuous systems results in ill-conditioned system matrices, which seriously limit its application. Lastly, an algorithm to find the basis random variables of KL expansion for non-Gaussian processes, is developed. The basis random variables are obtained via nonlinear transformation of marginal cumulative distribution function using standard deviation. Results are obtained for three known skewed distributions, Log-Normal, Beta, and Exponential. In all the cases, it is found that the proposed algorithm matches very well with the known solutions and can be applied to solve non-Gaussian process using SSFEM. / Ph. D.

[EN] In this thesis, we consider two problems: we first explore the application of visibility graphs for describing the orbits of a discrete dynamical system that is governed by a fractional version of the logistic equation. We also study how to use this type of graphs to study response time series from the perspective of psychology. The preliminaries and introduction of these visibility graphs are presented in Chapter 1, where we revisit some basic facts from network science related to them. In the first part of this thesis, we analyze a phenomenon of mathematical nature. Wu and Baleanu introduced a fractional discrete dynamical system inspired by the fractional difference logistic equation. In order to study the trajectories of this model under this perspective of network science, in Chapter 2, we first review the most used fractional derivatives (Riemann-Liouville, Caputo, and Gründwald-Letnikov). Later, we show how to consider discrete fractional derivatives. Within our work, we present an alternative way of deducing the governing equation with respect to the one shown by Wu and Baleanu. We revisit the Wu-Baleanu equation in Chapter 3, focused on the visibility graphs of trajectories generated under different values of the scaling factor and the fractional exponent. We also study the existing connections between these parameters and the fitting with the degree distribution of the corresponding visibility graphs. When chaos is present, we link them with the exponent obtained when fitting the degree distribution to a power-law of the form x^(¿¿). With this approach, we provide an integrated vision of the dynamics of a family of fractional discrete dynamical systems that cannot be obtained from single Feigenbaum diagrams computed for each scaling factor and fractional exponent. We also connect the power-law exponent of the degree distribution fitting with the Shannon entropy of the visibility graphs degree distribution. In the second part, we analyze the response times of students to a binary decision task from the perspective of network science. We analyze the properties of the natural visibility graphs associated with their reaction time series. We observe that the degree distribution of these graphs usually fits a power-law distribution p(x) = x^(¿¿). We study the range in which parameter ¿ occurs and the changes of this exponent with respect to the age and gender of the students. Besides, we also study the links between the parameter ¿ and the ex-Gaussian distribution parameters that best fits each subject's response times. Finally, we outline some conclusions and perspectives of future research in both parts in Chapter 6. / [ES] En esta tesis, hemos considerado dos problemas: primero exploramos la aplicación de los grafos de visibilidad para describir las órbitas de un sistema dinámico discreto que está gobernado por una versión fraccionaria de la ecuación logística. Además, también estudiamos cómo usar este tipo de grafos para estudiar series temporales de tiempos de respuesta desde una perspectiva psicológica. Los preliminares, así como una introducción a estos grafos de visibilidad, se presentan en el Capítulo 1, donde revisitamos algunos hechos básicos de la ciencia de redes relacionados con dichos grafos. En la primera parte de esta tesis, analizamos un fenómeno de naturaleza matemática. Wu y Baleanu introdujeron un sistema dinámico discreto fraccionario inspirado en la ecuación logística con derivadas fraccionarias. Con el propósito de estudiar las trayectorias de este modelo desde la perspectiva de la ciencia de redes, en el Capítulo 2, primero revisamos las derivadas fraccionarias más utilizadas (Riemann-Liouville, Caputo y Gründwald-Letnikov). Posteriormente, mostramos cómo considerar derivadas fraccionarias discretas. En nuestro trabajo, presentamos una forma alternativa de deducir la ecuación gobernante con respecto a la presentada por Wu y Baleanu. Revisitamos la ecuación de Wu-Baleanu en el Capítulo 3, centrado en los grafos de visibilidad de trayectorias generadas a partir de distintos valores del factor de escala y del exponente fraccionario. También estudiamos la existencia de conexiones entre estos parámetros y el ajuste de la distribución de los grados de los correspondientes grafos de visibilidad. Cuando el caos está presente, los enlazamos con el exponente obtenido al ajustar la distribución de los grados a una ley de potencias de la forma x^(¿¿). A través de este enfoque, proporcionamos una visión integrada de la dinámica de una familia de sistemas dinámicos discretos fraccionarios que no se pueden obtener a partir de diagramas de Feigenbaum individuales calculados para cada factor de escala y exponente fraccionario. Además, relacionamos el exponente de la ley de potencias del ajuste de la distribución de grados con la entropía de Shannon de la distribución de grados de los grafos de visibilidad. En la segunda parte, analizamos el tiempo de respuesta de un grupo de estudiantes que realizaron una tarea de decisión binaria desde la perspectiva de la ciencia de redes. Estudiamos las propiedades de los grafos de visibilidad natural asociados con sus correspondientes series de tiempos de respuesta. Observamos que la distribución de los grados de estos grafos normalmente sigue una distribución ley de potencias p(x) = x^(¿¿). Analizamos el rango en el cual el parámetro ¿ se mueve y los cambios de este exponente con respecto a la edad y el sexo de los estudiantes. Por otro lado, también estudiamos la relación entre el parámetro ¿ y los parámetros de la distribución ex-Gaussiana que mejor se ajusta al tiempo de respuesta de cada sujeto. Finalmente, destacamos algunas conclusiones y perspectivas de investigación futura en ambas líneas de trabajo en el Capítulo 6. / [CAT] En aquesta tesi, hem considerat dos problemes: primer explorem l'aplicació dels grafs de visibilitat per a descriure les òrbites d'un sistema dinàmic discret que està governat per una versió fraccionària de l'equació logística. A més a més, també estudiem com emprar aquest tipus de grafs per a analitzar sèries temporals de temps de resposta des d'una perspectiva psicològica. Els preliminars, així com una introducció a aquests grafs de visibilitat, es presenten al Capítol 1, on revisitem alguns fets bàsics de la ciència de xarxes relacionats amb ells. En la primera part d'aquesta tesi, analitzem un fenomen de naturalesa matemàtica. Wu i Baleanu van introduir un sistema dinàmic discret fraccionari inspirat en l'equació logística amb derivades fraccionàries. Amb el fi d'estudiar les trajectòries d'aquest model des d'una perspectiva de la ciència de xarxes, en el Capítol 2, primer revisem les derivades fraccionàries més utilitzades (Riemann-Liouville, Caputo i Gründwald-Letnikov). Posteriorment, mostrem com considerar derivades fraccionàries discretes. Al nostre treball, presentem una forma alternativa de deduir l'equació governant respecte a la presentada per Wu i Baleanu. Revisitem l'equació de Wu-Baleanu al Capítol 3, focalitzat en els grafs de visibilitat de trajectòries generades a partir de valors diferents del factor d'escala i de l'exponent fraccionari. També estudiem l'existència de connexions entre aquests paràmetres i l'ajust de la distribució dels graus dels corresponents grafs de visibilitat. Quan el caos hi és, els enllacem amb l'exponent que hem obtés en ajustar la distribució dels graus a una llei de potències de la forma x^(¿¿). Des d'aquesta perspectiva, proporcionem una visió integrada de la dinàmica d'una família de sistemes dinàmics discrets fraccionaris que no es poden obtenir a partir de diagrames de Feigenbaum individuals calculats per a cada factor d'escala i exponent fraccionari. A més a més, relacionem l'exponent de la llei de potències de l'ajust de la distribució de graus amb l'entropia de Shannon de la distribució de graus dels grafs de visibilitat. A la segona part, analitzem el temps de resposta d'un grup d'estudiants que realitzaren una tasca de decisió binària des del punt de vista de la ciència de xarxes. Estudiem les propietats dels grafs de visibilitat natural associats amb les seues corresponents sèries temporals de temps de resposta. Observem que la distribució dels graus d'aquests grafs normalment segueix una distribució llei de potències p(x) = x^(¿¿). Analitzem el rang en què el paràmetre ¿ es mou i els canvis d'aquest exponent respecte a l'edat i el sexe dels estudiants. D'altra banda, també estudiem la relació entre el paràmetre ¿ i els paràmetres de la distribució ex-Gaussiana que millor fita el temps de resposta de cada subjecte. Finalment, destaquem algunes conclusions i perspectives d'investigació futura en ambdues línies de treball en el Capítol 6. / Mira Iglesias, A. (2021). Applications of Visibility Graphs for the representation of Time Series [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/176012

<p>Human Trafficking is the fastest--growing organized criminal activity, second only to drug trafficking. Modeling has given us some sense of the scale of the exploitation, but we do not truly understand the depth and breadth of the behaviors within the system. This research presents chaos theory--driven risk analysis of human trafficking, with the expectation not to predict individual behaviors but to understand the boundaries and patterns of the dynamic system that is human trafficking. Subject matter experts within Six Sigma and risk analysis were consulted to evaluate the application of the traditional Failure Mode Effect Analysis (FMEA) on dynamic systems. This research identified valuable modifications to the traditional FMEA process to better apply to complex, dynamic processes. A dynamic FMEA decouples the generation of failure modes from the RPN score to accommodate the multiple POVs and SME expertise. Application of a dynamic FMEA occurs in two distinct phases: (1) failure modes ranked by their risk to the system and (2) the prioritization of solutions. This allows for broad SME knowledge to identify failure modes in the system but does not require those same SMEs to identify solutions. A discussion is needed regarding the prioritization of solutions. Subject matter experts within anti--trafficking efforts included those working in law, academia, finance, victims’ advocacy, data analysis, and law enforcement, as well as a survivor of sex trafficking. Interviews and thematic analysis identified and ranked high--level human trafficking process steps that include finance, network, transportation, location, product conversion, and law enforcement. Within these steps, major elements of behaviors were identified and included actors, activities, society, structures, government, and media. A vulnerability ranking of these steps of human trafficking gave insight into points of instability that can be used to dismantle the act of human trafficking proactively. The focus when analyzing the risk of human trafficking, therefore, should be on the systems and structures that allow for exploitation to occur in the first place. If those risks and vulnerabilities can be elucidated, true barriers and change can be implemented to destabilize the dynamic system of human trafficking.</p>

京都大学 / 新制・課程博士 / 博士(理学) / 甲第25109号 / 理博第5016号 / 新制||理||1715(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 橋本 幸士, 教授 杉本 茂樹, 教授 田島 治 / 学位規則第4条第1項該当 / Doctor of Agricultural Science / Kyoto University / DFAM

Anomale Diffusion ist ein weitverbreiteter Transportmechanismus, welcher für gewöhnlich mit ensemble-basierten Methoden experimentell untersucht wird. Motiviert durch den Fortschritt in der Einzelteilchenverfolgung, wo typischerweise Zeitmittelwerte bestimmt werden, entsteht die Frage nach der Ergodizität. Stimmen ensemble-gemittelte Größen und zeitgemittelte Größen überein, und wenn nicht, wie unterscheiden sie sich? In dieser Arbeit studieren wir verschiedene stochastische Modelle für anomale Diffusion bezüglich ihres ergodischen oder nicht-ergodischen Verhaltens hinsichtlich der mittleren quadratischen Verschiebung. Wir beginnen unsere Untersuchung mit integrierter Brownscher Bewegung, welche von großer Bedeutung für alle Systeme mit Impulsdiffusion ist. Für diesen Prozess stellen wir die ensemble-gemittelte quadratische Verschiebung und die zeitgemittelte quadratische Verschiebung gegenüber und charakterisieren insbesondere die Zufälligkeit letzterer. Im zweiten Teil bilden wir integrierte Brownsche Bewegung auf andere Modelle ab, um einen tieferen Einblick in den Ursprung des nicht-ergodischen Verhaltens zu bekommen. Dabei werden wir auf einen verallgemeinerten Lévy-Lauf geführt. Dieser offenbart interessante Phänomene, welche in der Literatur noch nicht beobachtet worden sind. Schließlich führen wir eine neue Größe für die Analyse anomaler Diffusionsprozesse ein, die Verteilung der verallgemeinerten Diffusivitäten, welche über die mittlere quadratische Verschiebung hinausgeht, und analysieren mit dieser ein oft verwendetes Modell der anomalen Diffusion, den subdiffusiven zeitkontinuierlichen Zufallslauf. / Anomalous diffusion is a widespread transport mechanism, which is usually experimentally investigated by ensemble-based methods. Motivated by the progress in single-particle tracking, where time averages are typically determined, the question of ergodicity arises. Do ensemble-averaged quantities and time-averaged quantities coincide, and if not, in what way do they differ? In this thesis, we study different stochastic models for anomalous diffusion with respect to their ergodic or nonergodic behavior concerning the mean-squared displacement. We start our study with integrated Brownian motion, which is of high importance for all systems showing momentum diffusion. For this process, we contrast the ensemble-averaged squared displacement with the time-averaged squared displacement and, in particular, characterize the randomness of the latter. In the second part, we map integrated Brownian motion to other models in order to get a deeper insight into the origin of the nonergodic behavior. In doing so, we are led to a generalized Lévy walk. The latter reveals interesting phenomena, which have never been observed in the literature before. Finally, we introduce a new tool for analyzing anomalous diffusion processes, the distribution of generalized diffusivities, which goes beyond the mean-squared displacement, and we analyze with this tool an often used model of anomalous diffusion, the subdiffusive continuous time random walk.

Mon travail de thèse est consacré à l’étude de quelques aspects de la physique quantique des systèmes quantiques à N corps en interaction. Il est orienté vers l’étude des chaînes de spins quantiques. Je me suis intéressé à plusieurs questions relatives aux chaînes de spins quantiques, du point de vue numérique et analytique à la fois. J'aborde en particulier les questions relatives à la structure des fonctions d'onde, la forme de la densité d'états et les propriétés spectrales des Hamiltoniens de chaînes de spins. Dans un premier temps, je présenterais très rapidement les techniques numériques de base pour le calcul des vecteurs et valeurs propres des Hamiltonien de chaînes de spins. Les densités d’états des modèles quantiques constituent des quantités importantes et très simples qui permettent de caractériser les propriétés spectrales des systèmes avec un grand nombre de degrés de liberté. Alors que dans la limite thermodynamique, les densités d'états de la plupart des modèles intégrables sont bien décrites par une loi gaussienne, dans certaines limites de couplage de la chaîne de spins au champ magnétique et pour un nombre de spins N fini sur la chaîne, on observe l’apparition de pics dans la densité d’états. Je montrerais que la connaissance des deux premiers moments du Hamiltonien dans le sous-espace dégénéré associé à chaque pics donne une bonne approximation de la densité d’états. Dans un deuxième temps je m'intéresserais aux propriétés spectrales des Hamiltoniens de chaînes de spins quantiques. L’un des principal résultats sur la statistique spectrale des systèmes quantiques concerne le comportement universel des fluctuations des mesures telles que l’espacement entre valeurs propres consécutives. Ces fluctuations sont bien décrites par la théorie des matrices aléatoires mais la comparaison avec les prédictions de cette théorie nécessite généralement une opération sur le spectre du Hamiltonien appelée unfolding. Dans les problèmes quantiques de N corps, la taille de l’espace de Hilbert croît généralement exponentiellement avec le nombre de particules, entraînant un manque de données pour pouvoir faire une statistique. Ces limitations ont amené l’introduction d’une nouvelle mesure se passant de la procédure d’unfolding basée sur le rapport d’espacements successifs plutôt que les espacements. En suivant l’idée du “surmise” de Wigner pour le calcul de la distribution de l’espacement, je montre comment calculer une approximation de la distribution du rapport d’espacements dans les trois ensembles gaussiens invariants en faisant le calcul pour des matrices 3x3. Les résultats obtenus pour les différents ensembles de matrices aléatoires se sont révélés être en excellent accord avec les résultats numériques. Enfin je m’intéresserais à la structure des fonctions d’ondes fondamentales des modèles de chaînes de spins quantiques. Les fonctions d’onde constituent, avec le spectre en énergie, les objets fondamentaux des systèmes quantiques : leur structure est assez compliquée et n’est pas très bien comprise pour la plupart des systèmes à N corps. En raison de la croissance exponentielle de la taille de l’espace de Hilbert avec le nombre de particules, l’étude des vecteurs propres est une tâche très difficile, non seulement du point de vue analytique mais aussi du point de vue numérique. Je démontrerais en particulier que l’état fondamental de tous les modèles que nous avons étudiés est multifractal avec en général une dimension fractale non triviale. / My thesis is devoted to the study of some aspects of many body quantum interacting systems. In particular we focus on quantum spin chains. I have studied several aspects of quantum spin chains, from both numerical and analytical perspectives. I addressed especially questions related to the structure of eigenfunctions, the level densities and the spectral properties of spin chain Hamiltonians. In this thesis, I first present the basic numerical techniques used for the computation of eigenvalues and eigenvectors of spin chain Hamiltonians. Level densities of quantum models are important and simple quantities that allow to characterize spectral properties of systems with large number of degrees of freedom. It is well known that the level densities of most integrable models tend to the Gaussian in the thermodynamic limit. However, it appears that in certain limits of coupling of the spin chain to the magnetic field and for finite number of spins on the chain, one observes peaks in the level density. I will show that the knowledge of the first two moments of the Hamiltonian in the degenerate subspace associated with each peak give a good approximation to the level density. Next, I study the statistical properties of the eigenvalues of spin chain Hamiltonians. One of the main achievements in the study of the spectral statistics of quantum complex systems concerns the universal behaviour of the fluctuation of measure such as the distribution of spacing between two consecutive eigenvalues. These fluctuations are very well described by the theory of random matrices but the comparison with the theoretical prediction generally requires a transformation of the spectrum of the Hamiltonian called the unfolding procedure. For many-body quantum systems, the size of the Hilbert space generally grows exponentially with the number of particles leading to a lack of data to make a proper statistical study. These constraints have led to the introduction of a new measure free of the unfolding procedure and based on the ratio of consecutive level spacings rather than the spacings themselves. This measure is independant of the local level density. By following the Wigner surmise for the computation of the level spacing distribution, I obtained approximation for the distribution of the ratio of consecutive level spacings by analyzing random 3x3 matrices for the three canonical ensembles. The prediction are compared with numerical results showing excellent agreement. Finally, I investigate eigenfunction statistics of some canonical spin-chain Hamiltonians. Eigenfunctions together with the energy spectrum are the fundamental objects of quantum systems: their structure is quite complicated and not well understood. Due to the exponential growth of the size of the Hilbert space, the study of eigenfunctions is a very difficult task from both analytical and numerical points of view. I demonstrate that the groundstate eigenfunctions of all canonical models of spin chain are multifractal, by computing numerically the Rényi entropy and extrapolating it to obtain the multifractal dimensions.

The significant advances in fiber-optic technology have broadened the optical network\'s reach into end-user business premises and even homes, allowing new services and technologies to be delivered to the customers. The next wave of innovation will certainly generate numerous opportunities provided by the widespread popularity of emerging solutions and applications such as tactile Internet, telemedicine and real time 3-D content generation, making them part of everyday life. Nevertheless, to support such an unprecedented and insatiable demand of data traffic, higher capacity and security, flexible bandwidth allocation and cost-efficiency have become crucial requirements for technologies candidate for future optical access networks. To this aim, optical code-division multiple-access (OCDMA) technology is considered as a prospective candidate, particularly due to features like asynchronous transmissions, flexible as well as conscious bandwidth resource distribution and support to differentiated services at the physical layer, to name but a few. In this context, this thesis proposes new mathematical formalisms for bit error rate, packet throughput and packet delay to assess the performance of flexible OCDMA networks capable of providing multiservice multirate transmissions according to users\' requirements. The proposed analytical formalisms do not require the knowledge a priori of the users\' code sequences, which means that the network performance can be addressed in a simple and straightforward manner using the code parameters only. In addition, the developed analytical formalisms account for a general number of distinct users\' classes as well as general probability of interference among users. Hence, these formalisms can be successfully applied for performance evaluation of flexible OCDMA networks not only under any number of users\' classes in a network, but also for most spreading codes with good correlation properties. The packet throughput expression is derived assuming Poisson, binomial and Markov chain approaches for the composite packet arrivals with the latter defined as benchmark. Then, it is shown via numerical simulation the Poisson-based expression is not appropriate for a reliable throughput estimate when compared to the benchmark (Markov) results. The binomial-based throughput equation, by its turn, provides results as accurate as the benchmark. In addition, the binomial-based throughput is numerically more convenient and computationally more efficient than the Markov chain approach, whereas the Markov-based one is computationally expensive, particularly if the number of users is large. The bit error rate (BER) expressions are derived considering gaussian and binomial distributions for the multiple-access interference and it is shown via numerical simulations that accurate performance of flexible OCDMA networks is only obtained with the binomial-based BER expression. This thesis also proposes and investigates a network architecture for Internet protocol traffic over flexible OCDMA with support to multiservice multirate transmissions, which is independent of the employed spreading code and does not require any new optical processing technology. In addition, the network performance assumes users transmitting asynchronously using receptors based on intensity-modulation direct-detection schemes. Numerical simulations shown that the proposed network performs well when its users are defined with high-weight code or when the channel utilization is low. The BER and packet throughput performance of an OCDMA network that provides multirate transmissions via multicode technique with two codes assigned to each single user is also addressed. Numerical results show that this technique outperforms classical techniques based on multilength code. Finally, this thesis addresses a new breakthrough technology that might lead to higher levels of security at the physical layer of optical networks. This technology consists in the generation of deterministic chaos from a commercial free-running vertical-cavity surface-emitting laser (VCSEL). The chaotic dynamics is generated by means of mechanical strains loaded onto an off-the-shelf quantum-well VCSEL using a simple and easily replicable holder. Deterministic chaos is then achieved, for the first time, without any additional complexity of optical feedback, parameter modulation or optical injection. The simplicity of the proposed system, which is based entirely on low-cost and easily available components, opens the way to the widespread use of commercial and free-running VCSEL devices for chaos-based applications. This off-the-shelf and cost-effective optical chaos generator has the potential for not only paving the way towards new security platforms in optical networks like, for example, successfully hiding the user information in an unpredictable, random-like signal against eventual eavesdroppers, but also for influencing emerging chaos applications initially limited or infeasible due to the lack of low-cost solutions. Furthermore, it leads the way to future realization of emerging applications with high-integrability and -scalability such as two-dimensional arrays of chaotic devices comprising hundreds of individual sources to increase requirements for random bit generation, cryptography or large-scale quantum networks. / Os avanços relacionados a tecnologia fotônica ampliaram o alcance das redes de comunicação óptica tanto em instalações de estabelecimentos comerciais quanto em residências, permitindo que novos serviços e tecnologias fossem entregues aos clientes. A próxima onda de inovação certamente gerará inúmeras oportunidades proporcionadas pela popularidade de soluções emergentes e aplicações como a Internet tátil, a telemedicina e a geração de conteúdo 3-D em tempo real, tornando-os parte da vida cotidiana. No entanto, para suportar a crescente demanda de tráfego atual, uma maior capacidade e segurança, alocação flexível de largura de banda e custo-eficiência tornaram-se requisitos cruciais para as tecnologias candidatas a futuras redes de acesso óptico. Para este fim, a tecnologia de acesso múltiplo por divisão de código óptico (OCDMA) é considerada um candidato em potencial, particularmente devido a características como transmissões assíncronas, distribuição flexível de banda larga e suporte a serviços diferenciados na camada física, para citar apenas alguns. Neste contexto, esta tese propõe novos formalismos matemáticos para a taxa de erro de bits, taxa de transferência de pacotes e atraso de pacotes para avaliar o desempenho de redes OCDMA flexíveis capazes de fornecer transmissões em múltiplas qualidades de serviço (QoS) de acordo com as necessidades dos usuários. Os formalismos analíticos propostos não requerem o conhecimento a priori das sequências de código dos usuários, o que significa que o desempenho da rede pode ser abordado de forma simples e direta usando apenas os parâmetros de código. Além disso, os formalismos analíticos desenvolvidos representam um número geral de classes de usuários distintos, bem como a probabilidade geral de interferência entre os usuários. Portanto, esses formalismos podem ser aplicados com sucesso na avaliação de desempenho de redes OCDMA flexíveis não apenas em qualquer número de classes de usuários em uma rede, mas também para a maioria dos códigos de espalhamento com boas propriedades de correlação. A expressão de taxa de transferência de pacotes é derivada assumindo aproximações de Poisson, binomial e de cadeia de Markov para as chegadas de pacotes compostos, com a última definida como benchmark. Em seguida, é mostrado via simulação numérica que a expressão baseada em Poisson não é apropriada para uma estimativa confiável de taxa de transferência quando comparada aos resultados de benchmark (Markov). A equação de taxa de transferência binomial, por sua vez, fornece resultados tão precisos quanto o benchmark. Além disso, a taxa de transferência binomial é numericamente mais conveniente e computacionalmente eficiente quando comparada com abordagem de Markov, enquanto esta última é computacionalmente dispendiosa, particularmente se o número de usuários é grande. As expressões de taxa de erro de bit (BER) são derivadas considerando distribuições gaussianas e binomiais para a interferência de acesso múltiplo e é mostrado por meio de simulações numéricas que o desempenho exato de redes OCDMA flexíveis é obtido somente com a expressão binomial de BER. Esta tese também propõe e investiga uma arquitetura de rede para o tráfego de protocolo de Internet sobre OCDMA flexível com suporte a transmissões de QoS e de múltiplas taxas, que é independente do código de espalhamento empregado e não requer qualquer nova tecnologia de processamento óptico. Além disso, o desempenho da rede assume que os usuários transmitem de forma assíncrona usando receptores baseados em esquemas de detecção direta de modulação de intensidade. As simulações numéricas mostraram que a rede proposta possui melhor desempenho quando seus usuários são definidos com peso de código alto ou quando a utilização do canal é baixa. O desempenho da BER e da taxa de transferência de pacotes de uma rede OCDMA que fornece transmissões de múltiplas taxas por meio de uma técnica multi-código com dois códigos atribuídos a cada usuário é também abordado. Os resultados numéricos mostram que esta técnica supera as técnicas clássicas baseadas no código de comprimento múltiplo. Finalmente, esta tese aborda uma nova tecnologia que pode levar a níveis mais elevados de segurança na camada física de redes ópticas. Esta tecnologia consiste na geração de caos determinístico a partir de um laser de emissão superficial com cavidade vertical (VCSEL). A dinâmica caótica é gerada através da aplicação de forças mecânicas em um VCSEL comercial usando um suporte simples e facilmente replicável. O caos determinístico é então alcançado, pela primeira vez, sem qualquer complexidade adicional de realimentação óptica, modulação de parâmetros ou injeção óptica. A simplicidade do sistema proposto, o qual se baseia inteiramente em componentes de baixo custo e que são facilmente encontrados, abre o caminho para o uso de dispositivos VCSEL comerciais para aplicações baseadas em caos. Este gerador de caos óptico tem o potencial não só de pavimentar o caminho para novas plataformas de segurança em redes ópticas, como, por exemplo, ocultar com êxito as informações do usuário em um sinal imprevisível e aleatório contra eventuais invasores, como também tem o potencial de influenciar aplicações de caos emergentes inicialmente limitadas ou inviáveis devido à falta de soluções de baixo custo. Além disso, ele conduz o caminho para a realização futura de aplicações emergentes com alta integridade e escalabilidade, tais como matrizes bidimensionais de dispositivos caóticos que compreendem centenas de fontes individuais para aumentar as necessidades de geração de bit aleatória, criptografia ou redes quânticas de grande escala.