Digital ecosystems are one of the most important strategic issues in the current digital economy. Digital ecosystems are dynamic and generative. They evolve as new firms join and as heterogeneous systems are integrated into other systems. These features digital ecosystems determine economic and technological success in the competition among digital platform systems. However, how these ecosystems evolve over time is not yet clearly known. I describe three empirical essays in order to understand the underlying mechanism of the evolution of a digital ecosystem: 1) the underlying architecture of a digital ecosystem, 2) the evolutionary pattern of a digital ecosystem, 3) and the co-evolution of a digital ecosystem. To explore these topics, I focus on the underlying generative structure of the ecosystem and its evolutionary pattern of WordPress, which is the world largest blog platform system. I collected a comprehensive set of information about the WordPress ecosystem including over 23,000 plug-ins from January 2004 to December 2014. To analyze the data, I apply a network approach to capture the generative nature of digital technology that assumes a fractal-like structure in which digital components such as Application Programming Interfaces (API) cluster into groups that generate other groups over time. As such, I can effectively capture the hierarchical structure of a network by exploring the topological structure of sub-networks that represent the fractal-like evolutionary dynamic system mechanism. The network approach, together with the conventional statistical approach, allows me to understand the unique nature of a digital ecosystem that is different from the boundary of a decomposable system, as the generative nature of system-agnostic digital components builds on a developmental combinable system. I also discuss underlying theory, methodology, data, result, and implications and conclude by highlighting the contributions of this study and the direction of future research to further explore the evolution of digital ecosystems. / Business Administration/Management Information Systems

A key attribute of resilience, robustness serves as a predictor of infrastructure system performance under disruptions, thus informing proactive infrastructure risk management. A literature review indicated that previous studies did not consider some key factors that can influence the robustness of Air Transportation Infrastructure Networks (ATIN) and thus their (system-level cascade) systemic risk management processes. In this respect, the current study first assesses existing and then develops a new methodology to quantify the robustness of ATIN. Specifically, based on integrating travel time and flight frequency, the study develops alternative best route and link weight approaches to assess key ATIN robustness measures and relevant operating cost losses (OCL). In order to demonstrate the practical use of the developed methodology, the robustness and the associated OCL of the Canadian Domestic Air Traffic Network are evaluated under random failures (i.e., disruptive events that occur randomly) and targeted threats (i.e., disruptive events that occur deliberately). The analysis results show that the network robustness is influenced by the utilized evaluation approach, especially after 20% of the network components become nonoperational. Overall, the methodology developed within this study is expected to provide ATIN policymakers with the means to quantify the network robustness and OCL, and thus enable ATIN resilience-guided proactive risk management in the face of natural or anthropogenic hazard realizations. / Thesis / Master of Applied Science (MASc)

A teoria do caos estuda o tipo de comportamento, aparentemente aleatório, que apresentam alguns sistemas complexos sensíveis à perturbação dos seus parâmetros, como por exemplo sistemas dinâmicos, fractais, autômatos celulares, entre outros. Os autômatos celulares (ACs) são sistemas dinâmicos discretos que podem apresentar comportamentos caóticos a partir de regras simples. Os ACs tem sido empregados em diversas aplicações principalmente em simulações, mas também tem contribuído no reconhecimento de padrões, processamento de imagens e na Criptografia. A necessidade em transmitir informação de forma mais segura vem crescendo com a necessidade por novos algoritmos criptográficos. Paralelamente, os criptoanalistas vem progredindo constantemente na quebra e na procura de vulnerabilidades destes algoritmos, sendo necessaria a incursão de novas abordagens para atender estes desafios. Neste trabalho é proposto o desenvolvimento e avaliação de algoritmos criptográficos, assim como um novo método de criptoanálise, motivados pela adequação dos ACs caóticos com os princípios de confusão e difusão da Criptografia, seguindo critérios apropriados para a boa construção destes algoritmos, que são sintetizados em três partes: (i) Na proposta do algoritmo de cifra criptográfico baseado no AC caótico, foi sugerida uma estratégia de seleção de ACs em base a combinação de vários critérios como o expoente de Lyapunov, a entropia e a distância de Hamming; visando selecionar um AC apropriado para a geração de números pseudo-aleatórios usados no processo de encriptação/decriptação do algoritmo, o qual é validado por diversos testes de aleatoriedade. (ii) Foi proposto o algoritmo de hash criptográfico baseado numa abordagem híbrida dos ACs e as redes complexas, visando a construção de um algoritmo flexível e de bom desempenho. Os resultados alcançados por ambos os algoritmos criptográficos mostraram-se relevantes quando comparados com o estado da arte, com boas qualidades de segurança e um grande potencial para ser aplicados em problemas reais. (iii) Na proposta do método de criptoanálise foi sugerido traçar equivalências entre os sistemas criptográficos e os ACs caóticos visando explorar e analisar seu comportamento dinâmico, por meio da adaptação do algoritmo do expoente de Lyapunov dos ACs, cujos resultados permitiram encontrar padrões característicos nos modos de operação criptográficos. Os resultados obtidos mostraram que a abordagem dos ACs caóticos para desenvolver os algoritmos pode ser bastante útil em aplicações de Criptografia e Criptoanálise. / Chaos theory studies the apparently random behaviour from some complex systems with highly sensitive to the initial conditions, such as dynamical systems, fractals, cellular automata, among others. Cellular automata (CA) are discrete dynamical systems that may exhibit chaotic behaviour from simple rules. CA have been employed in many multidisciplinary applications, most of them in simulations systems, including pattern recognition, image processing and Cryptography. Nowadays, the development of new cryptographic algorithms is required in order to fulfil the increasing demand for secure transmission of confidential information. These algorithms are intensively analyzed, most of them broken by the cryptanalyst community. We proposed to develop two cryptographic algorithms: a block cipher and a hash function based on chaotic CA and its corresponding evaluation. We also proposed a new cryptanalysis methodology motivated by the strong relationship between the chaotic properties of CA and the cryptographic principles of confusion and diffusion, by following appropriate criteria to the proper design of these algorithms, which are summarized into three parts: (i) To proposed the block cipher proposed it was suggested a methodology to select a suitable CA to Cryptography by means of compounded measures such as the Lyapunov exponent, entropy and Hamming distance. Moreover, this selected CA is employed to generate pseudo-random numbers, which are further used in the encryption/decryption of the proposed block cipher and validated under several randomness tests. The results obtained by this cryptographic algorithm achieved similar and even higher performance when compared to others found in literature. (ii) The cryptographic hash function was developed using an hybrid approach of CA and complex networks, in order to build a flexible algorithm with acceptable performance when compared to conventional hash functions. In general, the results obtained from both cryptographic algorithms showed good security qualities and great potential to be applied in real problems. (iii) To proposed the cryptanalysis methodology it was suggested to draw parallels between cryptographic systems and CA, in order to explore and analise their dynamic behaviour. Hence, upon drawing such parallels, we have a means to adapt the Lyapunov exponent algorithm conceived in the framework of CA. Unexpectedly, the results obtained allow to discriminate among cryptographic modes of operation, which provides significant contributions to the field. Finally, we proved that the chaotic cellular automata approach can be quite useful in applications cryptography and cryptanalysis.

Software engineering projects that utilize inappropriate pathfinding algorithms carry a significant risk of poor runtime performance for customers. Using social network theory, this experimental study examined the impact of algorithms, frameworks, and map complexity on elapsed time and computer memory consumption. The 1,800 2D map samples utilized were computer random generated and data were collected and processed using Python language scripts. Memory consumption and elapsed time results for each of the 12 experimental treatment groups were compared using factorial MANOVA to determine the impact of the 3 independent variables on elapsed time and computer memory consumption. The MANOVA indicated a significant factor interaction between algorithms, frameworks, and map complexity upon elapsed time and memory consumption, F(4, 3576) = 94.09, p < .001, h2 = .095. The main effects of algorithms, F(4, 3576) = 885.68, p < .001, h2 = .498; and frameworks, F(2, 1787) = 720,360.01, p .001, h2 = .999; and map complexity, F(2, 1787) = 112,736.40, p < .001, h2 = .992, were also all significant. This study may contribute to positive social change by providing software engineers writing software for complex networks, such as analyzing terrorist social networks, with empirical pathfinding algorithm results. This is crucial to enabling selection of appropriately fast, memory-efficient algorithms that help analysts identify and apprehend criminal and terrorist suspects in complex networks before the next attack.

Made available in DSpace on 2014-12-17T15:15:01Z (GMT). No. of bitstreams: 1 ThiagoCCN_DISSERT.pdf: 2332508 bytes, checksum: bbc84148d8aa1acc5070a5a68ca8b3b6 (MD5) Previous issue date: 2012-06-29 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / Following the study of Andrade et al. (2009) on regular square lattices, here we investigate the problem of optimal path cracks (OPC) in Complex Networks. In this problem we associate to each site a determined energy. The optimum path is defined as the one among all possible paths that crosses the system which has the minimum cost, namely the sum of the energies along the path. Once the optimum path is determined, at each step, one blocks its site with highest energy, and then a new optimal path is calculated. This procedure is repeated until there is a set of blocked sites forming a macroscopic fracture which connects the opposite sides of the system. The method is applied to a lattice of size L and the density of removed sites is computed. As observed in the work by Andrade et al. (2009), the fractured system studied here also presents different behaviors depending on the level of disorder, namely weak, moderated and strong disorder intensities. In the regime of weak and moderated disorder, while the density of removed sites in the system does not depend of the size L in the case of regular lattices, in the regime of high disorder the density becomes substantially dependent on L. We did the same type of study for Complex Networks. In this case, each new site is connected with m previous ones. As in the previous work, we observe that the density of removed sites presents a similar behavior. Moreover, a new result is obtained, i.e., we analyze the dependency of the disorder with the attachment parameter m / Seguindo a linha do trabalho de Andrade e colaboradores (2009) em redes regulares, n?s investigamos o problema da fratura atrav?s do caminho ?timo (optimal path cracks -OPC) em Redes Complexas. Neste problema n?s associamos para cada s?tio uma determinada energia. O caminho ?timo ? definido como aquele, dentre todos os poss?veis, que atravessa o sistema e tem o menor custo, ou seja, a menor soma das energias ao longo do caminho. Uma vez que o caminho ?timo ? determinado, em cada passo, n?s bloqueamos o s?tio com maior energia e a partir de ent?o um novo caminho ?timo ? calculado. Este procedimento ? repetido at? que existe um conjunto de s?tios bloqueados que forma uma fratura macrosc?pica a qual conecta lados opostos do sistema. O m?todo ? aplicado numa rede de lado L e a densidade de s?tios removidos ? computada. Como observado no trabalho de Andrade e colaboradores, o sistema fraturado que n?s estudamos tamb?m apresenta diferentes comportamentos dependendo do n?vel da desordem, que pode ser fraca, moderada ou forte. No regime de desordem fraca e moderada, a densidade de s?tios removidos no sistema n?o depende do tamanho L no caso de redes regulares, enquanto no regime de desordem forte a densidade se torna substancialmente dependente de L. N?s fizemos o mesmo tipo de estudo para Redes Complexas. Numa rede complexa caso, cada novo s?tio ? conectado a m s?tios que j? est?o presentes na rede. Como no trabalho anterior, n?s observamos que a densidade de s?tios removidos apresenta um comportamento similar. Al?m disso, um novo resultado ? obtido, isto ?, n?s analisamos a depend?ncia da desordem com o par?metro de liga??o m

Nous nous intéressons dans cette thèse à la problématique de recommandation de tags dans les systèmes de partage et de classification sociale des ressources, dits folksonomies. Les utilisateurs annotent les ressources à partager par des tags librement choisis. Or, la liberté de choix de tags les rends ambigus. Nous proposons une nouvelle approche topologique nommé TLTR (Two Level Tag Recommendation)pour la recommandation de tags. TLTR est basée sur une approche originale de compression des graphes. Le graphe d'une folksonomie est compressé en appliquant une méthode de clustering sur chacune des trois composantes d'une folksonomie, à savoir: l'ensemble des utilisateurs, des ressources et des tags. Nous proposons également une méthode de clustering topologique basée sur une approche centrée graine pour la détection des communautés dans les graphes multiplexes. Une approche topologique classique, en occurrence la méthode Folkrank, est appliquée sur le graphe réduit afin de sélectionner les clusters de tags les plus appropriés. Ces clusters sont ensuite utilisés pour construire un autre graphe contextuel extrait du graphe original représentant la folksonomie. La méthode Folkrank est à nouveau appliquée afin de calculer la liste de tags à recommander. Des expérimentations sur des grandes folksonomies, notamment, des jeux de données extraits du système de partage des références bibliographiques Bibsonomy montrent la pertinence de notre approche. / We focus in this thesis on the problem of tag recommendation in social sharing to classification systems called folksonomies. Users of a folksonomy annotate their resources with freely tags chosen. We propose here a new topological approach for tags recommendation called TLTR (Two Level Tag Recommendation). TLTR (Two Level Tag Recommendation) is based on an original approach of graph compression. The graph of a folksonomy is compressed by a clustering each of the three components, namely the set of users, resources and tags. A topological clustering method based on a seed-centered approach for community detection in multiplex graphs is proposed. A classical topological approach, namely Folkrank, is applied to the reduced graph to select the most appropriate clusters of tags. These clusters are then used to build another contextual graph extracted from the original graph representing the folksonomy. Folkrank method is applied again to compute the list of tags to recommend. Experiments on large folksonomy, including, data extracted from references system Bibsonomy show the relevance of our approach.

A teoria do caos estuda o tipo de comportamento, aparentemente aleatório, que apresentam alguns sistemas complexos sensíveis à perturbação dos seus parâmetros, como por exemplo sistemas dinâmicos, fractais, autômatos celulares, entre outros. Os autômatos celulares (ACs) são sistemas dinâmicos discretos que podem apresentar comportamentos caóticos a partir de regras simples. Os ACs tem sido empregados em diversas aplicações principalmente em simulações, mas também tem contribuído no reconhecimento de padrões, processamento de imagens e na Criptografia. A necessidade em transmitir informação de forma mais segura vem crescendo com a necessidade por novos algoritmos criptográficos. Paralelamente, os criptoanalistas vem progredindo constantemente na quebra e na procura de vulnerabilidades destes algoritmos, sendo necessaria a incursão de novas abordagens para atender estes desafios. Neste trabalho é proposto o desenvolvimento e avaliação de algoritmos criptográficos, assim como um novo método de criptoanálise, motivados pela adequação dos ACs caóticos com os princípios de confusão e difusão da Criptografia, seguindo critérios apropriados para a boa construção destes algoritmos, que são sintetizados em três partes: (i) Na proposta do algoritmo de cifra criptográfico baseado no AC caótico, foi sugerida uma estratégia de seleção de ACs em base a combinação de vários critérios como o expoente de Lyapunov, a entropia e a distância de Hamming; visando selecionar um AC apropriado para a geração de números pseudo-aleatórios usados no processo de encriptação/decriptação do algoritmo, o qual é validado por diversos testes de aleatoriedade. (ii) Foi proposto o algoritmo de hash criptográfico baseado numa abordagem híbrida dos ACs e as redes complexas, visando a construção de um algoritmo flexível e de bom desempenho. Os resultados alcançados por ambos os algoritmos criptográficos mostraram-se relevantes quando comparados com o estado da arte, com boas qualidades de segurança e um grande potencial para ser aplicados em problemas reais. (iii) Na proposta do método de criptoanálise foi sugerido traçar equivalências entre os sistemas criptográficos e os ACs caóticos visando explorar e analisar seu comportamento dinâmico, por meio da adaptação do algoritmo do expoente de Lyapunov dos ACs, cujos resultados permitiram encontrar padrões característicos nos modos de operação criptográficos. Os resultados obtidos mostraram que a abordagem dos ACs caóticos para desenvolver os algoritmos pode ser bastante útil em aplicações de Criptografia e Criptoanálise. / Chaos theory studies the apparently random behaviour from some complex systems with highly sensitive to the initial conditions, such as dynamical systems, fractals, cellular automata, among others. Cellular automata (CA) are discrete dynamical systems that may exhibit chaotic behaviour from simple rules. CA have been employed in many multidisciplinary applications, most of them in simulations systems, including pattern recognition, image processing and Cryptography. Nowadays, the development of new cryptographic algorithms is required in order to fulfil the increasing demand for secure transmission of confidential information. These algorithms are intensively analyzed, most of them broken by the cryptanalyst community. We proposed to develop two cryptographic algorithms: a block cipher and a hash function based on chaotic CA and its corresponding evaluation. We also proposed a new cryptanalysis methodology motivated by the strong relationship between the chaotic properties of CA and the cryptographic principles of confusion and diffusion, by following appropriate criteria to the proper design of these algorithms, which are summarized into three parts: (i) To proposed the block cipher proposed it was suggested a methodology to select a suitable CA to Cryptography by means of compounded measures such as the Lyapunov exponent, entropy and Hamming distance. Moreover, this selected CA is employed to generate pseudo-random numbers, which are further used in the encryption/decryption of the proposed block cipher and validated under several randomness tests. The results obtained by this cryptographic algorithm achieved similar and even higher performance when compared to others found in literature. (ii) The cryptographic hash function was developed using an hybrid approach of CA and complex networks, in order to build a flexible algorithm with acceptable performance when compared to conventional hash functions. In general, the results obtained from both cryptographic algorithms showed good security qualities and great potential to be applied in real problems. (iii) To proposed the cryptanalysis methodology it was suggested to draw parallels between cryptographic systems and CA, in order to explore and analise their dynamic behaviour. Hence, upon drawing such parallels, we have a means to adapt the Lyapunov exponent algorithm conceived in the framework of CA. Unexpectedly, the results obtained allow to discriminate among cryptographic modes of operation, which provides significant contributions to the field. Finally, we proved that the chaotic cellular automata approach can be quite useful in applications cryptography and cryptanalysis.

Tesis por compendio / [EN] The study of Complex Systems is one of the scientific fields that has had the highest productivity in recent decades and has not ceased to fascinate the community dedicated to studying its properties. In particular, Network Science has proven to be one of the most prolific areas within Complex Systems. In recent years, his methods have been applied to model multiple phenomena in real life, both naturally generated, such as in biology, and due to the actions and interactions of man, such as social networks or communication networks. Recently, it has been seen how the methods of Network Science can be applied in the context of mathematics, as is the case of Number Theory. One of the most studied cases is networks whose elements are numbers and which are related through the divisibility relation. The main objective of this thesis is to extend these studies to other sets of numbers. On the one hand, we study the divisibility in natural numbers when we obtain these from Pascal matrices of increasing size, which allows us to extract non-sequential sets of numbers with non-constant increments between them. On the other hand, we study the case of the divisibility relation of rational numbers. Cantor's diagonal argument provides a way to order all rational numbers, which allows us to check to what extent some of the properties observed for the divisibility of natural numbers are extensible to a more general context. The thesis is divided into 4 Chapters. Chapter 1 contains a general introduction to the thesis and it is structured into 6 sections. In Sections 1.1 and 1.2, we briefly introduce Network Science, show some application examples, and motivate the study of networks of numbers generated from the divisibility property. In Section 1.3, we define the objectives of this PhD thesis and its scope. In Section 1.4, we present the notion of network, its representations, and some measures that can be calculated on them, such as nodes degrees, their distribution, the assortativity and the clustering coefficients. In another hand, in Section 1.5, we review the best-known network models such as Erdo¿s and Re'nyi random networks, Watts and Strogatz small-world networks, Baraba'si and Albert scale-free networks, and hierarchical networks. Finally, at the end of this Chapter 1, we show in Section 1.6 a review of various studies carried out in order to apply Network Science methods to problems and properties that arise in Number Theory, such as divisibility networks or networks generated from Collatz's Conjecture. or Goldbach's Strong Conjecture. In Chapters 2 and 3, we show the results obtained and that have been published to date. Finally, in Chapter 4, we summarize the conclusions obtained and indicate some related problems that we consider of interest to address in the future. / [ES] El estudio de los Sistemas Complejos es uno de los campos científicos que ha tenido mayor productividad en las últimas décadas y no ha dejado de fascinar a la comunidad que se dedica al estudio de sus propiedades. En particular, la Ciencia de Redes se ha mostrado como una de las áreas más prolíficas dentro de los Sistemas Complejos. En los últimos años, sus métodos han sido aplicados para modelar múltiples fenómenos de la vida real tanto generados de manera natural, como puede ser en el caso de la biología, como debidos a las acciones e interacciones del hombre, como puede ser el caso de las redes sociales o las redes de comunicaciones. Recientemente, se ha visto cómo los métodos de la Ciencia de Redes pueden ser aplicados en el contexto de las matemáticas, como es el caso de la Teoría de Números. Uno de los casos que más se han estudiado es el de las redes cuyos elementos son números y que se relacionan mediante la relación de la divisibilidad. El objetivo principal de esta tesis es extender estos estudios a otros conjuntos de números. Por una parte, estudiamos la divisibilidad en los números naturales cuando obtenemos estos a partir de subconjuntos de números naturales extraídos de matrices de Pascal de orden creciente, lo que nos permite extraer conjuntos de números de manera no secuencial y con incrementos no constantes entre ellos. Por otra parte, estudiamos el caso de la relación de divisibilidad de los números racionales, dado que a partir del argumento diagonal de Cantor se pueden ordenar, lo que nos permite comprobar hasta qué punto algunas de las propiedades observadas para la divisibilidad de los números naturales son extensibles a un contexto más general. La tesis se divide en 4 capítulos. El capítulo 1 contiene una introducción general a la tesis y está estructurado en 6 secciones. En las secciones 1.1 y 1.2, presentamos brevemente la Ciencia de Redes, mostrando algunos ejemplos de aplicación y motivamos el estudio de redes de números generadas a partir de la propiedad de divisibilidad. En la Section 1.3, definimos los objetivos de esta tesis doctoral y su alcance. En la sección 1.4, presentamos la noción de red, sus formas de representación y algunas medidas que se pueden calcular sobre ellas, como son los grados de los nodos, la distribución de estos grados, la asortatividad y los coeficientes de clustering. Por otro lado, en la Sección 1.5, revisamos los modelos de redes más conocidos como son las redes aleatorias de Erdös y Rényi, las redes de pequeño mundo de Watts y Strogatz, las redes libres de escala de Barabási y Albert y las redes jerárquicas. Mostramos en la Sección 1.6, una revisión de diversos estudios realizados con el fin de aplicar métodos de la Ciencia de Redes a problemas y propiedades que surgen en la Teoría de Números, como son las redes de divisibilidad o redes generadas a partir de la Conjetura de Collatz o la Conjetura Fuerte de Goldbach. En los Capítulos 2 y 3, mostramos los resultados obtenidos y que han sido publicados hasta la fecha y, finalmente, en el Capítulo 4, resumimos las conclusiones obtenidas e indicamos algunos problemas relacionados que consideramos de interés abordar en un futuro. / [CAT] L'estudi dels Sistemes Complexos és un dels camps científiques que ha tingut major productivitat en les últimes dècades i no ha deixat de fascinar a la comunitat que es dedica a l'estudi de les seues propietats. En particular, la Ciència de Xarxes s'ha mostrat com una de les àrees més prolífica dins dels Sistemes Complexos. En els últims anys, els seus mètodes han sigut aplicats per a modelar múltiples fenòmens de la vida real tant generats de manera natural, com pot ser en el cas de la biologia, com deguts a les accions i interaccions de l'home, com pot ser el cas de les xarxes socials o les xarxes de comunicacions. Recentment, s'ha vist com els mètodes de la Ciència de Xarxes poden ser aplicats en el context de les matemàtiques, com és el cas de la Teoria de Números. Un dels casos que més s'han estudiat és el de les xarxes els elements de les quals són números i que es relacionen mitjançant la relació de la divisibilitat. L'objectiu principal d'aquesta tesi és estendre aquests estudis a altres conjunts de números. D'una banda, estudiem la divisibilitat en els nombres naturals quan obtenim aquests a partir de matrius de Pascal de grandària creixent, la qual cosa ens permet extraure conjunts de números de manera no sequëncial i amb increments no constants entre ells. D'altra banda, estudiem el cas de la relació de divisibilitat dels nombres racionals, atés que a partir de l'argument diagonal de Cantor es poden ordenar, la qual cosa ens permet comprovar fins a quin punt algunes de les propietats observades per a la divisibilitat dels nombres naturals són extensibles a un context més general. La tesi es troba dividida en 4 Capítols. El capítol 1, conté una introducció general a la tesi i está estructurat en 6 seccions. En les seccions 1.1 i 1.2, presentem breument la Ciència de Xarxes, mostrant alguns exemples d'aplicació i motivem l'estudi de xarxes de números generades a partir de la propietat de divisibilitat. En la Section 1.3, definim els objectius d'aquesta tesi doctoral y el seu abast. En la Secció 1.4, presentem la noció de xarxa, les seves formes de representació i algunes mesures que es poden calcular sobre elles, com són els graus dels nodes, la distribució d'aquests graus, la asortatividad i els coeficients de clustering. En la Sección 1.5, revisem els models de xarxes més coneguts com són les xarxes aleatòries de Erdös i Renyi, les xarxes de xicotet món de Watts i Strogatz, les xarxes lliures d'escala de Barabási i Albert i les xarxes jeràrquiques. Mostrem en la Sección 1.6 una revisió de diversos estudis realitzats amb la finalitat d'aplicar mètodes de la Ciència de Xarxes a problemes i propietats que sorgeixen en la Teoria de Números, com són les xarxes de divisibilitat o xarxes generades a partir de la Conjectura de Collatz o la Conjectura Forta de Goldbach. En els Capítols 2 i 3, vam mostrar els resultats obtinguts i que han sigut publicats fins hui i, finalment, en el Capítol 4, resumim les conclusions obtingudes i indiquem alguns problemes relacionats que considerem d'interés abordar en un futur. / Solares Hernández, PA. (2021). Sets of numbers from complex networks perspective [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/176015 / TESIS / Compendio

Disruptions due to either natural or anthropogenic hazards significantly impact the operation of critical infrastructure networks because they may instigate network-level cascade (i.e., systemic) risks. Therefore, quantifying and enhancing the resilience of such complex dynamically evolving networks ensure minimizing the possibility and consequences of systemic risks. Focusing only on robustness, as one of the key resilience attributes, and on transportation networks, key critical infrastructure, the current study develops a hybrid complex network theoretic-genetic algorithms analysis approach. To demonstrate the developed approach, the robustness of a city transportation network is quantified by integrating complex network theoretic topology measures with a dynamic flow redistribution model. The network robustness is subsequently investigated under different operational measures and the corresponding absorptive capacity thresholds are quantified. Finally, the robustness of the network under different failure scenarios is evaluated using genetic algorithms coupled with k-means clustering to classify the different network components. The hybrid approach developed in the current study is expected to facilitate optimizing potential systemic risk mitigation strategies for critical infrastructure networks under disruptive events. / Thesis / Master of Applied Science (MASc)

Ziel dieser Dissertation ist es, mithilfe zweier Herangehensweisen, das Verständnis der Zusammenhänge verschiedener physikalischer Prozesse des Klimasystems zu verbessern. Im ersten Teil verwende ich Klimanetzwerke zu die gemeinsame Abhängigkeit von Meeresoberflächentemperaturen (SSTs) und Niederschlägen in Hinsicht auf globale charakteristiken und räumlichen Muster untersuchen. In diesem Kontext ist die El Niño Southern Oscillation (ENSO) das wichtigste Phänomen, welches großskalig SSTs und Niederschläge beeinflusst. Durch meine Analyse decke ich kurz und weitreichende Verbindungen auf und zeige deren Abhängigkeit von der jeweiligen ENSO-Phase (El Nino, La Nina, neutrale Phase). Darüber hinaus werden durch die Kombination einer diskreten Wavelet-Transformation mit dem Konzept der gekoppelten Klimanetzwerkanalyse die skalenspezifischen Verbindungen aufgelöst, die bei der ursprünglichen Auflösung der Daten oft übersehen werden. Im zweiten Teil der Arbeit verwende ich Simulationen des COnsortium for Small scale MOdeling (COSMO) Climate Limited-area Modell (CCLM) und untersuche die Auswirkungen des Sobradinho-Stausees. In dieser Arbeit benutzen ich das Flake Modell, um das vertikale Temperaturprofil des Sees zu bestimmen. Durch die Einbettung des Flake Modells in das CCLM konnte ich den Sobradinho-Stausee untersuchen. Dabei simuliere ich zwei verschiedene Szenarien. Die Simulationsergebnisse verifiziere ich mithilfe meteorologischer Daten von Oberflächen- und Satellitenmessungen. Die Ergebnisse zeigen, dass der See sowohl die bodennahe Temperatur als auch Wind- und Luftfeuchtigkeitsmuster der Umgebung beeinflusst. Zudem wird die Luftfeuchtigkeit durch den See erhöht und bewirkt Seewinde. Die Effekte des Sees auf die Luftfeuchtigkeit und temperaturen beschränken sich nicht nur auf die Nähe des Sees, sondern auch auf relativ weit entfernte Gebiete. / This dissertation aims at improving our understanding of the mechanisms of interactions between physical processes within the climate system via two different approaches. In the first part, I have utilized climate networks to understand the mutual interdependence between sea surface temperatures (SST) and precipitation (PCP) in terms of global characteristics and spatial patterns. In this context, the globally most relevant phenomenon is the El Niño Southern Oscillation (ENSO), which strongly affects large-scale SST variability as well as PCP patterns all around the globe. My analysis uncovers both local and remote statistical connections and demonstrates their dependence on the current ENSO phase (El Niño, La Niña or neutral phase). Furthermore by combining time-scale decomposition by means of a discrete wavelet transform with the concept of coupled climate network analysis unravel the scale-specific connections that are often overlooked at the original resolution of the data. In the second part of this thesis, I have focused on simulations with the COnsortium for Small scale MOdeling (COSMO) Climate Limited-area Model (CCLM) and investigate the effects of Lake Sobradinho, a large reservoir in Northeastern Brazil, on the local near-surface atmospheric and boundary layer conditions. In this thesis, the FLake model (Freshwater Lake model) is applied for obtaining the lake’s vertical temperature profile. I have simulated two alternative scenarios. The performance of the simulation is compared with data from surface meteorological stations as well as satellite data. The obtained results demonstrate that the lake affects the near-surface air temperature of the surrounding area as well as its humidity and wind patterns. Moreover, the humidity is significantly increased as a result of the lake’s presence and causes a lake breeze. The observed effects on humidity and air temperature also extend over areas relatively far away from the lake.