Made available in DSpace on 2015-03-26T13:35:10Z (GMT). No. of bitstreams: 1 texto completo.pdf: 2430887 bytes, checksum: 46c97cae3636842e90c00b8d31b6f16a (MD5) Previous issue date: 2009-02-09 / Fundação de Amparo a Pesquisa do Estado de Minas Gerais / The dramatic resurgence and emergence of epidemic dengue and dengue hemorragic fever in the last two decades neatly define a global pandemic. The dispersion of dengue viruses combines local infections of humans bited by infective mosquitoes inside a city with long-range transmissions to non-infective vectors that feed the blood of infected people arriving from other urban areas. In the present work a cellular automata model for dengue epidemic is proposed and investigated through large-scale computer simulations. The model takes into account the main features concerning the population dynamics of mosquitoes and humans and the disease transmission cycle. Furthermore, the model is defined on a scale-free network in which each node is a square lattice in order to properly describe the environment as urban centers interconnected through a national transportation system. A nonzero epidemic threshold is found and it is approached with a power law behavior by the density of infected individuals, as observed in the small-world network of Watts and Strogatz. Also, it is studied the importance of three parameters for the dengue spreading: the diffusivity of the mosquitoes, the probability of a mosquito bites humans, and the travel's probability of people between two interconnected cities. Finally, maps of infected individuals are obtained in order to caracterise the epidemic spreading. / O dramático ressurgimento e a emergência da epidemia de dengue e dengue hemorrágica nas últimas duas décadas claramente definem uma pandemia global. A dispersão do vírus da dengue combina infecções locais dos seres humanos picados por mosquitos infectados dentro de uma cidade com transmissões de longo alcance por vetores não-infecciosos que se alimentam do sangue de pessoas infectadas provenientes de outras zonas urbanas. No presente trabalho um modelo de autômatos celulares para epidemias de dengue é proposto e investigado através de siulação por computador, em larga escala. O modelo leva em conta as principais características relativas à dinâmica das populações de mosquitos e seres humanos e o ciclo de transmissão da doença. Além disso, o modelo é definido em uma rede livre de escala, em que cada nó é uma rede quadrada, a fim de descrever adequadamente o meio ambiente como os centros urbanos interligados através do sistema de transporte nacional. Um limiar epidêmico diferente de zero é encontrado e é aproximado com um comportamento tipo lei de potência pela densidade de indivíduos infectados, como observado na rede mundo-pequeno de Watts-Strogatz. Também, é estudada a importância de três parâmetros na dispersão da dengue: a difusividade do mosquito, a probabilidade do mosquito picar um ser humano, e a probabilidade de viagem de pessoas entre duas cidades conectadas. Por fim, mapas de indivíduos infectados são obtidos a fim de caracterizar a difusão da epidemia.

Le but de cette thèse est d'étudier la distribution des tailles des répétitions au sein d'un même génome, ainsi que la distribution des tailles des appariements obtenus en comparant différents génomes. Ces distributions présentent d'importantes déviations par rapport aux prédictions des modèles probabilistes existants. Étonnamment, les déviations observées sont distribuées selon une loi de puissance. Afin d'étudier ce phénomène, nous avons développé des modèles mathématiques prenant en compte des mécanismes évolutifs plus complexes, et qui expliquent les distributions observées. Nous avons aussi implémenté des modèles d'évolution de séquences in silico générant des séquences ayant les mêmes propriétés que les génomes étudiés. Enfin, nous avons montré que nos modèles permettent de tester la qualité des génomes récemment séquencés, et de mettre en évidence la prévalence de certains mécanismes évolutifs dans les génomes eucaryotes. / In this thesis, we study the length distribution of maximal exact matches within and between eukaryotic genomes. These distributions strongly deviate from what one could expect from simple probabilistic models and, surprisingly, present a power-law behavior. To analyze these deviations, we develop mathematical frameworks taking into account complex mechanisms and that reproduce the observed deviations. We also implemented in silico sequence evolution models that reproduce these behaviors. Finally, we show that we can use our framework to assess the quality of sequences of recently sequenced genomes and to highlight the importance of unexpected biological mechanisms in eukaryotic genomes.

This thesis examines the urban morphology of fifty cities using spatial syntax analysis. The analysis compares the urban street networks of European, USA, Islamic and East Asian cities. Street connectivity was the main metric and natural roads were the basis for the analysis. The aim of the study was to analyze determine how sensitive space syntax methods are for uncovering the hierarchical patterns of urban street networks and examining their scale-free and small-world properties. Street data was collected from OpenStreetMap. ArcGIS 10 with the Axwoman extension was used to study the hierarchical levels of street networks. Matlab provided the platform to examine the scale-free property of street data. Pajek software was used to measure the small-world behavior. Based on the hierarchical representation, the fifty sample cities were classified into different groups and their scale-free and small-world properties were studied. From a traditionally morphological perspective, it was found that some cities in Europe have a close-knit cellular and organic urban morphology. Cities in the USA exhibit gridiron patterns on the whole. Some Islamic cities have special urban structure with houses grouped around the cul-de-sac lanes. Several of the East Asian cities studied also have grid forms. According to the space syntax analysis, urban street networks that have a connectivity value greater than the average value were less than 40%. The results showed that for most cities, the street connectivity distribution follows a power-law distribution and exhibits scale-free properties. Urban street networks of all sample cities were found to have a small-world property. Space syntax cannot detect all of the morphological patterns recognized in traditional morphological studies. The method can, however, efficiently quantify the spatial configuration of a large sample. Space syntax’s topological and scaling metrics thus provide a way to compare urban street networks. These metrics can thus help classify cities according to their street patterns but also contribute to an understanding of human behavior within and thus the design of urban spaces. For example, an urban street network with a small-world property could have high efficiency for traffic flows at local and global levels and should be considered in further study.

Rather than being randomly wired together, the components of complex network systems are recently reported to represent a scale-free architecture, in which the node degree distribution follows power-law. While social networks are scale-free, it is natural to utilize their structural properties in some social network applications. As a result, this dissertation explores social network architectures, and in turn, leverages these architectures to facilitate some influence and information propagation applications. Social network architectures are analyzed in two different aspects. The first aspect focuses on the node degree snowballing effects (i.e., degree growth effects) in social networks, which is based on an age-sensitive preferential attachment model. The impact of the initial links is explored, in terms of accelerating the node degree snowballing effects. The second aspect focuses on Nested Scale-Free Architectures (NSFAs) for social networks. The scale-free architecture is a classic concept, which means that the node degree distribution follows the power-law distribution. `Nested' indicates that the scale-free architecture is preserved when low-degree nodes and their associated connections are iteratively removed. NSFA has a bounded hierarchy. Based on the social network structure, this dissertation explores two influence propagation applications for the Social Influence Maximization Problem (SIMP). The first application is a friend recommendation strategy with the perspective of social influence maximization. For the system provider, the objective is to recommend a fixed number of new friends to a given user, such that the given user can maximize his/her social influence through making new friends. This problem is proved to be NP-hard by reduction from the SIMP. A greedy friend recommendation algorithm with an approximation ratio of $1-e^{-1}$ is proposed. The second application studies the SIMP with the crowd influence, which is NP-hard, monotone, non-submodular, and inapproximable in general graphs. However, since user connections in Online Social Networks (OSNs) are not random, approximations can be obtained by leveraging the structural properties of OSNs. The modularity, denoted by $\Delta$, is proposed to measure to what degree this problem violates the submodularity. Two approximation algorithms are proposed with ratios of $\frac{1}{\Delta+2}$ and $1-e^{-1/(\Delta+1)}$, respectively. Beside the influence propagation applications, this dissertation further explores three different information propagation applications. The first application is a social network quarantine strategy, which can eliminate epidemic outbreaks with minimal isolation costs. This problem is NP-hard. An approximation algorithm with a ratio of 2 is proposed through utilizing the problem properties of feasibility and minimality. The second application is a rating prediction scheme, called DynFluid, based on the fluid dynamics. DynFluid analogizes the rating reference among the users in OSNs to the fluid flow among containers. The third application is an information cascade prediction framework: given the social current cascade and social topology, the number of propagated users at a future time slot is predicted. To reduce prediction time complexities, the spatiotemporal cascade information (a larger size of data) is decomposed to user characteristics (a smaller size of data) for subsequent predictions. All these three applications are based on the social network structure. / Computer and Information Science

Le calcul des valeurs propres intervient dans des modèles de maladies d’épidémiques et pourrait être utilisé comme un allié des campagnes de vac- cination dans les actions menées par les organisations de soins de santé. La modélisation épidémique peut être considérée, par analogie, comme celle des viruses d’ordinateur qui dépendent de l’état de graphe sous-jacent à un moment donné. Nous utilisons PageRank comme méthode pour étudier la propagation de l’épidémie et d’envisager son calcul dans le cadre de phé- nomène petit-monde. Une mise en œuvre parallèle de méthode multiple de "implicitly restar- ted Arnoldi method" (MIRAM) est proposé pour calculer le vecteur propre dominant de matrices stochastiques issus de très grands réseaux réels. La grande valeur de "damping factor" pour ce problème fait de nombreux algo- rithmes existants moins efficace, tandis que MIRAM pourrait être promet- teuse. Nous proposons également dans cette thèse un générateur de graphe parallèle qui peut être utilisé pour générer des réseaux synthétisés distri- bués qui présentent des structures "scale-free" et petit-monde. Ce générateur pourrait servir de donnée pour d’autres algorithmes de graphes également. MIRAM est mis en œuvre dans le cadre de trilinos, en ciblant les grandes données et matrices creuses représentant des réseaux sans échelle, aussi connu comme les réseaux de loi de puissance. Hypergraphe approche de partitionnement est utilisé pour minimiser le temps de communication. L’al- gorithme est testé sur un grille national de Grid5000. Les expériences sur les très grands réseaux tels que Twitter et Yahoo avec plus de 1 milliard de nœuds sont exécutées. Avec notre mise en œuvre parallèle, une accélération de 27× est satisfaite par rapport au solveur séquentiel / The eigenvalue equation intervenes in models of infectious disease prop- agation and could be used as an ally of vaccination campaigns in the ac- tions carried out by health care organizations. The epidemiological model- ing techniques can be considered by analogy, as computer viral propagation which depends on the underlying graph status at a given time. We point out PageRank as method to study the epidemic spread and consider its calcula- tion in the context of small-world phenomenon. A parallel implementation of multiple implicitly restarted Arnoldi method (MIRAM) is proposed for calculating dominant eigenpair of stochastic matrices derived from very large real networks. Their high damp- ing factor makes many existing algorithms less efficient, while MIRAM could be promising. We also propose in this thesis a parallel graph gen- erator that can be used to generate distributed synthesized networks that display scale-free and small-world structures. This generator could serve as a testbed for graph related algorithms. MIRAM is implemented within the framework of Trilinos, targeting big data and sparse matrices representing scale-free networks, also known as power law networks. Hypergraph partitioning approach is employed to minimize the communication overhead. The algorithm is tested on a nation wide cluster of clusters Grid5000. Experiments on very large networks such as twitter and yahoo with over 1 billion nodes are conducted. With our parallel implementation, a speedup of 27× is met compared to the sequential solver

Este trabalho explora o uso da Análise de Redes Sociais (ARS) como ferramenta de grande valor, aquela que perpassa pelas mais variadas disciplinas, como protagonista do estudo em alguns casos, como coadjuvante em outros. Para a Ciência da Informação, a ARS vem sendo empregada em estudos bibliométricos, procurando responder a questionamentos que intrigam pesquisadores da área ou de outros segmentos do conhecimento. Assim, a ARS ocupa seu espaço como o objeto principal dos estudos, enfatizando-a como ferramenta e, também, pelo seu uso direto em pesquisas nas quais aparece, frequentemente em conjunto com a estatística. Dessa forma, a ARS é empregada, pensando em Ciência da Informação, em ambos os papéis: como protagonista, nas frentes que abordam sua história, seus métodos e suas métricas, e, como coadjuvante, contribuindo na análise de redes de coautoria através de suas métricas de centralidade, mostrando a fluência das informações, determinando a posição de autores com relação à colaboração e seus comportamentos em rede para áreas como a Ciência da Informação, a Educação e a Sociologia. Os gráficos e tabelas foram elaborados com o apoio dos programas Microsoft Excel e, fundamentalmente para as redes de interesse, o programa de uso livre Pajek. Este último, alimentado por programas em VBScript, possibilitou, através de seus recursos de geração de imagens representativas das redes, a confecção dos gráficos e o cálculo dos indicadores para cada uma das três redes. Para a obtenção dos dados de entrada, foram utilizados os mecanismos de busca pela expressão \"Social Networks\" nas bases ASSIA (Sociologia), ERIC (Educação) e LISA (Ciência da Informação) e, com o uso de seus mecanismos internos, a massa foi exportada e empregada como exemplo de bases viabilizando a aplicação e verificação da metodologia proposta nos moldes dos estudos realizados. / This dissertation explores the use of Social Network Analysis (SNA) as a valuable tool, which runs through the most varied disciplines, as a protagonist in same study cases, as an adjunct in other cases. For the Information Science, the SNA has been used in bibliometric studies, trying to answer questions that intrigue researchers in this field or other segments of knowledge. So, the SNA occupies its place as the main object of the studies, emphasizing it as a tool and also for its direct use in researches in which it appears, often in conjunction with the statistics. Thus, the SNA is used, concerning the Information Science, in both roles: as the protagonist, foremost addressing its history, its methods and metrics, and, as an adjunct, contributing for the analysis of networks of co-authorship through its centrality metrics, showing the flow of information, determining the position of the authors, related to their collaboration and their behaviors on the network, for areas of study such as Information Science, Education and Sociology. The graphs and charts were elaborated with the support of Microsoft Excel program and, fundamentally to the networks of interest, the program of free use called Pajek. The latter, powered by VBScript programs, enabled, through its resources of generating representative network images, the elaboration of the graphs and the calculation of the indicators for each one of the three networks. To obtain the input data, search engines were used by the expression \"Social Networks\" in ASSIA (Sociology), ERIC (Education) and LISA (Information Science) bases and, using its internal mechanisms, the mass was exported and used as an example of bases enabling the application and verification of the proposed methodology along the lines of the studies.

In this dissertation, I propose that network theory offers a useful frame for informing mathematics education. Mathematical understanding, like the discipline of formal mathematics within which it is subsumed, possesses attributes characteristic of complex systems. As the techniques of network theorists are often used to explore such forms, a network model provides a novel and productive way to interpret individual comprehension of mathematics. A network structure for mathematical understanding can be found in cognitive mechanisms presented in the theory of embodied mathematics described by Lakoff and Nez. Specifically, conceptual domains are taken as the nodes of a network and conceptual metaphors as the connections among them. Examination of this metaphoric network of mathematics reveals the scale-free topology common to complex systems. Patterns of connectivity in a network determine its dynamic behavior. Scale-free systems like mathematical understanding are inherently vulnerable, for cascading failures, where misunderstanding one concept can lead to the failure of many other ideas, may occur. Adding more connections to the metaphoric network decreases the likelihood of such a collapse in comprehension. I suggest that an individuals mathematical understanding may be made more robust by ensuring each concept is developed using metaphoric links that supply patterns of thought from a variety of domains. Ways of making this a focus of classroom instruction are put forth, as are implications for curriculum and professional development. A need for more knowledge of metaphoric connections in mathematics is highlighted. To exemplify how such research might be carried out, and with the intent of substantiating ideas presented in this dissertation, I explore a small part of the proposed metaphoric network around the concept of EXPONENTIATION. Using collaborative discussion, individual interviews and literature, a search for representations that provide varied ways of making sense of EXPONENTIATION is carried out. Examination of the physical and mathematical roots of these conceptualizations leads to the identification of domains that can be linked to EXPONENTIATION.

People relate with one another in space and through imagined and technologically mediated networks. This thesis is concerned with the relationship between these two types of social connections – spatial and network. Spatial connections structure collectives of people in the same place at the same time. Network connections structure relations between people without regard to place or time. Spatial connections are complex, but rigid by nature, while network connections are simple, but flexible. Essential articulations emerge between these two connection types. These articulations create and evolve contemporary socio-spatial systems such as the city, its many places, and groups of people therein. However, the basic human experience of these systems remains largely polarized between spatial and network social practices to the disadvantage of human agency. This thesis proposes a teleodynamic, socio-spatial interaction model for the articulation of these social practices in human agency architecture. The model is a mobile experience design that functions through people with ‘smart’ mobile devices. It connects them with one another in public place and to global information and communication networks simultaneously. Sociological study informs the model’s design – constraints and conditions for the connection extents and integrity of social interaction. The model supports self-organizing circular relationships between human interaction dynamics and their trace structures based on a methodology for emergence in complex systems. It effects the emergence of the aforementioned socio-spatial, human agency architecture, with great flexibility. The model and architecture together serve to better articulate contemporary spatial and network social practices to the benefit of human agency in urban space.

People relate with one another in space and through imagined and technologically mediated networks. This thesis is concerned with the relationship between these two types of social connections – spatial and network. Spatial connections structure collectives of people in the same place at the same time. Network connections structure relations between people without regard to place or time. Spatial connections are complex, but rigid by nature, while network connections are simple, but flexible. Essential articulations emerge between these two connection types. These articulations create and evolve contemporary socio-spatial systems such as the city, its many places, and groups of people therein. However, the basic human experience of these systems remains largely polarized between spatial and network social practices to the disadvantage of human agency. This thesis proposes a teleodynamic, socio-spatial interaction model for the articulation of these social practices in human agency architecture. The model is a mobile experience design that functions through people with ‘smart’ mobile devices. It connects them with one another in public place and to global information and communication networks simultaneously. Sociological study informs the model’s design – constraints and conditions for the connection extents and integrity of social interaction. The model supports self-organizing circular relationships between human interaction dynamics and their trace structures based on a methodology for emergence in complex systems. It effects the emergence of the aforementioned socio-spatial, human agency architecture, with great flexibility. The model and architecture together serve to better articulate contemporary spatial and network social practices to the benefit of human agency in urban space.

Δίκτυα που εμφανίζουν μόνιμα μια συγκεκριμένη ιδιότητα ανεξάρτητα από το μέγεθος και την πυκνότητά τους ονομάζονται ανεξάρτητα από την κλίμακα (scale-free). Σε πολλά πραγματικά δίκτυα αυτή η ιδιότητα ταυτίζεται με την κατανομή των βαθμών των κόμβων σύμφωνα με τον νόμο της δύναμης με εκθέτη στο διάστημα [2..4]. Η εργασία παρουσιάζει τρία στατικά μοντέλα κατασκευής scale-free δικτύων με την παραπάνω ιδιότητα, βασισμένα στο δυναμικό μοντέλο Barabási-Albert, και επιχειρεί να προσεγγίσει πειραματικά τον χρωματικό τους αριθμό. / Networks that exhibit a certain quality irrespective of their size and density are called scale-free. In many real-life networks this quality coincides with a power-law distribution of the nodes' degree with exponent ranging in [2..4]. This work presents three static models for constructing scale-free networks, based on the dynamic Barabási-Albert model, and attempts to experimentally approximate their chromatic number.