Conexão entre as redes complexas e estatística de Kaniadakis e busca eficiente das propriedades críticas do processo epidêmico difusivo 1D

In this work we study a connection between a non-Gaussian statistics, the Kaniadakis statistics, and Complex Networks. We show that the degree distribution P(k)of a scale free-network, can be calculated using a maximization of information entropy in the context of non-gaussian statistics. As an example, a numerical analysis based on the preferential attachment growth model is discussed, as well as a numerical behavior of the Kaniadakis and Tsallis degree distribution is compared. We also analyze the diffusive epidemic process (DEP) on a regular lattice one-dimensional. The model is composed of A (healthy) and B (sick) species that independently diffusive on lattice with diffusion rates DA and DB for which the probabilistic dynamical rule A + B → 2B and B → A. This model belongs to the category of non-equilibrium systems with an absorbing state and a phase transition between active an inactive states. We investigate the critical behavior of the DEP using an auto-adaptive algorithm to find critical points: the method of automatic searching for critical points (MASCP). We compare our results with the literature and we find that the MASCP successfully finds the critical exponents 1/ѵ and 1/zѵ in all the cases DA =DB, DA DB. The simulations show that the DEP has the same critical exponents as are expected from field-theoretical arguments. Moreover, we find that, contrary to a renormalization group prediction, the system does not show a discontinuous phase transition in the regime o DA >DB.

Análises estatísticas em redes complexas: propriedades topológicas, críticas e dinâmicas

In this thesis, we address two issues of broad conceptual and practical relevance in the study of complex networks. The first is associated with the topological characterization of networks while the second relates to dynamical processes that occur on top of them. Regarding the first line of study, we initially designed a model for networks growth where preferential attachment includes: (i) connectivity and (ii) homophily (links between sites with similar characteristics are more likely). From this, we observe that the competition between these two aspects leads to a heterogeneous pattern of connections with the topological properties of the network showing quite interesting results. In particular, we emphasize that there is a region where the characteristics of sites play an important role not only for the rate at which they get links, but also for the number of connections which occur between sites with similar and dissimilar characteristics. Finally, we investigate the spread of epidemics on the network topology developed, whereas its dissemination follows the rules of the contact process. Using Monte Carlo simulations, we show that the competition between states (infected/healthy) sites, induces a transition between an active phase (presence of sick) and an inactive (no sick). In this context, we estimate the critical point of the transition phase through the cumulant Binder and ratio between moments of the order parameter. Then, using finite size scaling analysis, we determine the critical exponents associated with this transition

Contribuições ao estudo das redes complexas: modelo de qualidade

In this work we analyse the implications of using a power law distribution of vertice's quality in the growth dynamics of a network studied by Bianconi anel Barabási. In particular, we start studying the random networks which characterize or are related to some real situations, for instance the tide movement. In this context of complex networks, we investigate several real networks, as well as we define some important concepts in the network studies. Furthermore, we present the first scale-free network model, which was proposed by Barabási et al., and a modified model studied by Bianconi and Barabási, where now the preferential attachment incorporates the different ability (fitness) of the nodes to compete for links. At the end, our results, discussions and conclusions are presented

Dinâmica e estrutura de redes complexas no modelo de afinidade

In this work we elaborate and discuss a Complex Network model which presents connectivity scale free probability distribution (power-law degree distribution). In order to do that, we modify the rule of the preferential attachment of the Bianconi-Barabasi model, including a factor which represents the similarity of the sites. The term that corresponds to this similarity is called the affinity, and is obtained by the modulus of the difference between the fitness (or quality) of the sites. This variation in the preferential attachment generates very interesting results, by instance the time evolution of the connectivity, which follows a power-law distribution ki / ( t t0 )fi, where fi indicates the rate to the site gain connections. Certainly this depends on the affinity with other sites. Besides, we will show by numerical simulations results for the average path length and for the clustering coefficient

Contribuição ao estudo das redes complexas: extensão do modelo de afinidade

Neste trabalho, elaboramos e discutimos uma rede complexa sem escala, ou seja, uma rede cuja distribuição de conectividade segue uma lei de distribuição de potência. Nosso trabalho pode ser resumido da seguinte forma: Para efeito de didática vamos começar com redes aleatórias que estão relacionados com situações reais e artificiais, e depois comentar as redes livres de escala, como proposto por Barabási-Albert (BA). Depois disso, discutimos uma extensão deste modelo, onde Barabasi e Bianconi (BB) incluem a qualidade. Discutimos também o modelo de afinidade, ou seja, (Ver Almeida et al). Finalmente vamos mostrar o nosso modelo, uma extensão do modelo de afinidade dada por e apresentar os resultados correspondentes. Para realizar tal tarefa modificamos a regra de ligação preferencial do modelo de BB colocando um fator que apresenta o grau de probabilidade entre os sítios da rede. Esta quantidade é feita pela diferença entre a qualidade do novo sítio e a qualidade dos anteriores. Este novo parâmetro produz novos resultados interessantes: a distribuição que segue uma lei de especial de potência, expoente apropriado. A evolução temporal da conectividade do sítio também é calculada . Além disso, mostramos também, os resultados que foram obtidos, via simulação numérica, para o menor caminho médio e o coeficiente de agregação da rede gerada pelo nosso modelo, isto é, pelo modelo de afinidade.

Contribuição ao estudo de redes complexas: modelo de afinidade com métrica

Currently the interest in large-scale systems with a high degree of complexity has been much discussed in the scientific community in various areas of knowledge. As an example, the Internet, protein interaction, collaboration of film actors, among others. To better understand the behavior of interconnected systems, several models in the area of complex networks have been proposed. Barabási and Albert proposed a model in which the connection between the constituents of the system could dynamically and which favors older sites, reproducing a characteristic behavior in some real systems: connectivity distribution of scale invariant. However, this model neglects two factors, among others, observed in real systems: homophily and metrics. Given the importance of these two terms in the global behavior of networks, we propose in this dissertation study a dynamic model of preferential binding to three essential factors that are responsible for competition for links: (i) connectivity (the more connected sites are privileged in the choice of links) (ii) homophily (similar connections between sites are more attractive), (iii) metric (the link is favored by the proximity of the sites). Within this proposal, we analyze the behavior of the distribution of connectivity and dynamic evolution of the network are affected by the metric by A parameter that controls the importance of distance in the preferential binding) and homophily by (characteristic intrinsic site). We realized that the increased importance as the distance in the preferred connection, the connections between sites and become local connectivity distribution is characterized by a typical range. In parallel, we adjust the curves of connectivity distribution, for different values of A, the equation P(k) = P0e

Física estatística aplicada a sistemas sociais através do estudo de redes complexas

In this work a study of social networks based on analysis of family names is presented. A basic approach to the mathematical formalism of graphs is developed and then main theoretical models for complex networks are presented aiming to support the analysis of surnames networks models. These, in turn, are worked so as to be drawn leading quantities, such as aggregation coefficient, minimum average path length and connectivity distribution. Based on these quantities, it can be stated that surnames networks are an example of complex network, showing important features such as preferential attachment and small-world character

A Influência da observabilidade e da visualização radial no projeto de sistemas de monitoramento de redes de computadores

Este trabalho apresenta um levantamento dos problemas associados à influência da observabilidade e da visualização radial no projeto de sistemas de monitoramento para redes de grande magnitude e complexidade. Além disso, se propõe a apresentar soluções para parte desses problemas. Através da utilização da Teoria de Redes Complexas, são abordadas duas questões: (i) a localização e a quantidade de nós necessários para garantir uma aquisição de dados capaz de representar o estado da rede de forma efetiva e (ii) a elaboração de um modelo de visualização das informações da rede capaz de ampliar a capacidade de inferência e de entendimento de suas propriedades. A tese estabelece limites teóricos a estas questões e apresenta um estudo sobre a complexidade do monitoramento eficaz, eficiente e escalável de redes

Aninhamento em redes bipartidas

We present a nestedness index that measures the nestedness pattern of bipartite networks, a problem that arises in theoretical ecology. Our measure is derived using the sum of distances of the occupied elements in the adjacency matrix of the network. This index quantifies directly the deviation of a given matrix from the nested pattern. In the most simple case the distance of the matrix element ai,j is di,j = i+j, the Manhattan distance. A generic distance is obtained as di,j = (i¬ + j¬)1/¬. The nestedness índex is defined by = 1 − where is the temperature of the matrix. We construct the temperature index using two benchmarks: the distance of the complete nested matrix that corresponds to zero temperature and the distance of the average random matrix that is defined as temperature one. We discuss an important feature of the problem: matrix occupancy. We address this question using a metric index ¬ that adjusts for matrix occupancy

Estudo de sistemas complexos com interações de longo alcance : percolação, redes e tráfego

In this thesis we investigate physical problems which present a high degree of complexity using tools and models of Statistical Mechanics. We give a special attention to systems with long-range interactions, such as one-dimensional long-range bondpercolation, complex networks without metric and vehicular traffic. The flux in linear chain (percolation) with bond between first neighbor only happens if pc = 1, but when we consider long-range interactions , the situation is completely different, i.e., the transitions between the percolating phase and non-percolating phase happens for pc < 1. This kind of transition happens even when the system is diluted ( dilution of sites ). Some of these effects are investigated in this work, for example, the extensivity of the system, the relation between critical properties and the dilution, etc. In particular we show that the dilution does not change the universality of the system. In another work, we analyze the implications of using a power law quality distribution for vertices in the growth dynamics of a network studied by Bianconi and Barabási. It incorporates in the preferential attachment the different ability (fitness) of the nodes to compete for links. Finally, we study the vehicular traffic on road networks when it is submitted to an increasing flux of cars. In this way, we develop two models which enable the analysis of the total flux on each road as well as the flux leaving the system and the behavior of the total number of congested roads

Influência da filogenia em redes de interações ecológicas

In this thesis we deal with a class of composed networks that are formed by two tree networks, TP and TA, whose end points touches each other through a bipartite network BPA. We explore this network using a functional approach. We are interested in what extend the topology, or the structure, of TX (X = A or P) determines the links of BPA. This composed structure is an useful model in evolutionary biology, where TP and TA are the phylogenetic trees of plants and animals that interact in an ecological community. We use in this thesis two cases of mutualist interactions: frugivory and pollinator networks. We analyse how the phylogeny of TX determines or is correlated with BPA using a Monte Carlo approach. We use the phylogenetic distance among elements that interact with a given species to construct an index κ that quantifies the influence of TX over BPA. The algorithm is based in the assumption that interaction matrices that follows a phylogeny of TX have a total phylogenetic distance smaller than the average distance of an ensemble of Monte Carlo realizations generated by an adequate shuffling data. We find that the phylogeny of animals species has an effect on the ecological matrix that is more marked than plant phylogeny

Fraturas e caminhos ótimos na rede de Barabasi-Albert

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

Arquitetura de controladores fuzzy em redes foundation fieldbus

Foundation Fieldbus Industrial networks are the high standard technology which allows users to create complex control logic and totally decentralized. Although being so advanced, they still have some limitations imposed by their own technology. Attempting to solve one of these limitations, this paper describes how to design a Fuzzy controller in a Foundation Fieldbus network using their basic elements of programming, the functional blocks, so that the network remains fully independent of other devices other than the same instruments that constitute it. Moreover, in this work was developed a tool that aids this process of building the Fuzzy controller, setting the internal parameters of functional blocks and informing how many and which blocks should be used for a given structure. The biggest challenge in creating this controller is exactly the choice of blocks and how to arrange them in order to effectuate the same functions of a Fuzzy controller implemented in other kind of environment. The methodology adopted was to divide each one of the phases of a traditional Fuzzy controller and then create simple structures with the functional blocks to implement them. At the end of the work, the developed controller is compared with a Fuzzy controller implemented in a mathematical program that it has a proper tool for the development and implementation of Fuzzy controllers, obtaining comparatives graphics of performance between both

O Uso das Redes Socais no Âmbito das Bibliotecas Universitárias Federais Brasileiras

Aborda a questão das Redes Sociais Virtuais como ferramenta na comunicação e no repasse de informações nas Bibliotecas Universitárias Federais brasileiras. Objetiva analisar o uso das Redes Sociais como recurso estratégico na comunicação e na melhoria de produtos e serviços no ambiente de bibliotecas universitárias brasileiras, observando suas vantagens e dificuldades de manutenção na visão dos profissionais bibliotecários. A metodologia empregada foi a da pesquisa bibliográfica e estudo de caso, utilizando como universo de pesquisa as Bibliotecas Universitárias Federais do Brasil, com observações e aplicação de questionário como instrumento para coleta de dados. Ressalta ao final que o uso das Redes Sociais torna-se relevante na atual sociedade, como também nas Bibliotecas Universitárias, por possibilitar um repasse de informação mais eficiente e uma comunicação mais ativa e participativa em seus ambientes.

Análise de desempenho sobre redes IEEE 802.3/PM-AH: protoclo multicilos para automação hospitalar

Com a incorporação de conceitos da automação em ambientes hospitalares surge uma série de novos requisitos pertinentes a área médica. Dentre esses requisitos, um que merece destaque é a necessidade do estabelecimento de uma rede de comunicação segura e eficiente entre os elementos do ambiente hospitalar, visto que, os mesmos encontram-se de maneira distribuída. Nesse sentido, existe uma série de protocolos que podem ser utilizados no estabelecimento dessa rede, dentre os quais, um que merece destaque é o PM-AH (Protocolo Multiciclos para Automação Hospitalar) justamente por ser voltado a automatização de ambientes hospitalares tanto no que diz respeito ao cumprimento dos requisitos impostos nesse tipo de ambiente, como pelo fato de ser projetado para funcionar sobre a tecnologia Ethernet, padrão esse que é comumente utilizado pela rede de dados dos hospitais. Em decorrência disso, o presente trabalho aborda uma análise de desempenho comparativa entre redes PM-AH e puramente Ethernet visando atestar a eficiência do primeiro no que diz respeito ao cumprimento dos requisitos impostos pela automação hospitalar