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Previous issue date: 2013-03-08 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / 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 / Nesta tese, abordamos duas tem?ticas de ampla relev?ncia pr?tica e conceitual no
estudo de Redes Complexas. A primeira est? associada com a caracteriza??o topol?gica
das redes enquanto que a segunda diz respeito aos processos din?micos que ocorrem sobre
elas. Com rela??o a primeira linha de estudo, inicialmente elaboramos um modelo
para o crescimento de redes, onde a liga??o preferencial inclui: (i) conectividade e (ii)
homofilia (liga??es entre s?tios de caracter?sticas similares s?o mais prov?veis). A partir
disso, observamos que a competi??o entre estes dois aspectos leva a um heterog?neo padr?o
de conex?es, com as propriedades topol?gicas da rede exibindo resultados bastante
interessantes. Em particular, destacamos que existe uma regi?o onde as caracter?sticas dos
s?tios desempenham um papel importante n?o apenas para a taxa com que eles obt?m
liga??es, mas tamb?m para o n?mero de liga??es que ocorrem entre s?tios com caracter?sticas
similares e dissimilares. Por fim, investigamos a propaga??o de epidemias sobre
a topologia da rede elaborada, considerando que sua dissemina??o segue as regras do
Processo de Contato. Usando simula??es de Monte Carlo, mostramos que a competi??o
entre os estados (doente/saud?vel) dos s?tios induz a uma transi??o entre uma fase ativa
(presen?a de doentes) e outra inativa (aus?ncia de doentes). Neste contexto, estimamos
o ponto cr?tico da transi??o de fase atrav?s do cumulante de Binder e da raz?o entre momentos
do par?metro de ordem. Em seguida, utilizando an?lises de escala de tamanho
finito, determinamos os expoentes cr?ticos associados com esta transi??o
| Identifer | oai:union.ndltd.org:IBICT/oai:repositorio.ufrn.br:123456789/16618 |
| Date | 08 March 2013 |
| Creators | Almeida, Maur?cio Lopes de |
| Contributors | CPF:07416407400, http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4783310Y1, Mohan, Madras Viswanathan Gandhi, CPF:04295882755, http://lattes.cnpq.br/1995273890709490, Silva J?nior, Raimundo, CPF:72106310463, http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4790590E2, Moreira, Andr? Auto, CPF:46142193300, http://lattes.cnpq.br/4417117445512655, Mendes, Gabriel Alves, CPF:04410109979, http://lattes.cnpq.br/0040137813382875, Silva, Luciano Rodrigues da |
| Publisher | Universidade Federal do Rio Grande do Norte, Programa de P?s-Gradua??o em F?sica, UFRN, BR, F?sica da Mat?ria Condensada; Astrof?sica e Cosmologia; F?sica da Ionosfera |
| Source Sets | IBICT Brazilian ETDs |
| Language | Portuguese |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, info:eu-repo/semantics/doctoralThesis |
| Format | application/pdf |
| Source | reponame:Repositório Institucional da UFRN, instname:Universidade Federal do Rio Grande do Norte, instacron:UFRN |
| Rights | info:eu-repo/semantics/openAccess |
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