Teoria de Valores Extremos Aplicada a Redes Complexas
Autor(a) principal: | |
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Data de Publicação: | 2013 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Biblioteca Digital de Teses e Dissertações da UEPG |
Texto Completo: | http://tede2.uepg.br/jspui/handle/prefix/905 |
Resumo: | The extreme value theory is a branch of statistics and probability. It deals with the asymptotic distributions of extreme values (maximum or minimum) temporal series. The events which takes the average values removed are classified as extreme events. Examples include natural disasters such as goods, earthquakes or an event that causes a strong impact on society. Considering the scenario of complex networks, some examples of extreme events are congestion in networks of roads, power outages in power transmission networks and web servers congested. Thus, understanding the mechanisms that occur in such events is of great interest, because the prediction of these occurrences can minimize its efects, or even avoid them. Thus, the objectives of this study were: 1) to describe the asymptotic behavior of exceedances of a threshold specified by the generalized extreme value distribution, 2) extend the study to the probability of extreme events in complex networks with random topology, small world and scale free. This work was carried out by simulations of random walk pattern and shorter paths. The results shows that for the nodes, also called vertices or sites with low connectivity (lesser degree) in the networks analyzed, the distribution of excesses is not of exponential type. This implies that this distribution is bounded above. The results for the nodes with higher degree were similar, but only for the scale-free network this behavior does not occur. This is due to the fact that the number of exceedances observed in this case is signicantly smaller than the other. It was checked analytically and numerically simulated by random walk pattern, the probability of extreme event is larger and the average time between them is smaller for nodes with lower degree when compared with nodes with higher degree. The spectrum of eigenvalues of the adjacency matrix of the network, which describes the links between nodes, provides conditions for a good agreement between the analytical results and the simulations. For simulations of random walk for shorter paths it was found that nodes with lower betweenness centralities are more likely to have extreme events. |
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Pinto, Sandro Ely de SouzaCPF:00383353955http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4769629E9Viana, Ricardo LuizCPF:54502659991http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4785888H6Rodrigues Junior, PedroCPF:18575811991http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4789495T0CPF:03490007948http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4250951H3Borges, Rafael Ribaski2017-07-21T19:26:05Z2013-04-162017-07-21T19:26:05Z2013-03-05BORGES, Rafael Ribaski. Teoria de Valores Extremos Aplicada a Redes Complexas. 2013. 116 f. Dissertação (Mestrado em Fisica) - UNIVERSIDADE ESTADUAL DE PONTA GROSSA, Ponta Grossa, 2013.http://tede2.uepg.br/jspui/handle/prefix/905The extreme value theory is a branch of statistics and probability. It deals with the asymptotic distributions of extreme values (maximum or minimum) temporal series. The events which takes the average values removed are classified as extreme events. Examples include natural disasters such as goods, earthquakes or an event that causes a strong impact on society. Considering the scenario of complex networks, some examples of extreme events are congestion in networks of roads, power outages in power transmission networks and web servers congested. Thus, understanding the mechanisms that occur in such events is of great interest, because the prediction of these occurrences can minimize its efects, or even avoid them. Thus, the objectives of this study were: 1) to describe the asymptotic behavior of exceedances of a threshold specified by the generalized extreme value distribution, 2) extend the study to the probability of extreme events in complex networks with random topology, small world and scale free. This work was carried out by simulations of random walk pattern and shorter paths. The results shows that for the nodes, also called vertices or sites with low connectivity (lesser degree) in the networks analyzed, the distribution of excesses is not of exponential type. This implies that this distribution is bounded above. The results for the nodes with higher degree were similar, but only for the scale-free network this behavior does not occur. This is due to the fact that the number of exceedances observed in this case is signicantly smaller than the other. It was checked analytically and numerically simulated by random walk pattern, the probability of extreme event is larger and the average time between them is smaller for nodes with lower degree when compared with nodes with higher degree. The spectrum of eigenvalues of the adjacency matrix of the network, which describes the links between nodes, provides conditions for a good agreement between the analytical results and the simulations. For simulations of random walk for shorter paths it was found that nodes with lower betweenness centralities are more likely to have extreme events.A teoria de valores extremos é um ramo da estatística e probabilidade. Ela trata das distribuições assintóticas de valores extremos (máximos ou mínimos) de séries temporais. Os eventos que assumem valores afastados da média são classificados como eventos extremos. Alguns exemplos são desastres naturais, tais como enchentes, terremotos ou um evento que cause um forte impacto na sociedade. Considerando o cenário de redes complexas, alguns exemplos de eventos extremos são congestionamentos em redes de rodovias, quedas de energia em redes de transmissão e servidores de internet congestionados. Assim, a compreensão dos mecanismos que regem tais eventos é de grande interesse, pois com a previsão de ocorrências destes pode-se minimizar seus efeitos ou até mesmo evitá-los. Com isso, os objetivos deste trabalho foram: 1) descrever o comportamento assintótico das excedências de um valor limite especicado por meio da distribuição de valores extremos generalizada; 2) estender o estudo para a probabilidade de eventos extremos em redes complexas com topologia aleatória, mundo pequeno e escala livre. Este trabalho foi realizado por meio de simulações de caminhada aleatória padrão e por menores caminhos. Os resultados obtidos mostram que para os nós, também denominados vértices ou sítios, com menor conectividade (menor grau) nas redes analisadas, a distribuição dos excessos não é do tipo exponencial. Isto implica que esta distribuição é limitada superiormente. Os resultados para os nós com maior grau foram semelhantes, porém, somente para a rede de escala livre este comportamento não ocorre. Isto se deve ao fato de que o número de excedências observadas neste caso são menores do que nos demais. Foi vericado analiticamente e numericamente por meio de simulações de caminhada aleatória padrão, que a probabilidade de evento extremo é maior e que o tempo médio entre eles é menor para os nós com grau menor, quando comparados com nós com grau maior. O espectro de autovalores da matriz adjacência da rede, a qual descreve as ligações entre os nós, fornece condições para uma boa concordância entre os resultados analíticos e das simulações.Para simulações de caminhada aleatória por menores caminhos verificou-se que os nós com menores centralidades de intermediação são mais propensos a ter eventos extremos.Made available in DSpace on 2017-07-21T19:26:05Z (GMT). No. of bitstreams: 1 Rafael Ribaski Borges.pdf: 2504879 bytes, checksum: b87dbb16266c955866bfc47eef34de30 (MD5) Previous issue date: 2013-03-05Coordenação de Aperfeiçoamento de Pessoal de Nível Superiorapplication/pdfporUNIVERSIDADE ESTADUAL DE PONTA GROSSAPrograma de Pós-Graduação em CiênciasUEPGBRFisicaeventos extremoscaminhada aleatóriaredes complexasextreme eventsrandom walkcomplex networksCNPQ::CIENCIAS EXATAS E DA TERRA::FISICATeoria de Valores Extremos Aplicada a Redes Complexasinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/openAccessreponame:Biblioteca Digital de Teses e Dissertações da UEPGinstname:Universidade Estadual de Ponta Grossa (UEPG)instacron:UEPGORIGINALRafael Ribaski Borges.pdfapplication/pdf2504879http://tede2.uepg.br/jspui/bitstream/prefix/905/1/Rafael%20Ribaski%20Borges.pdfb87dbb16266c955866bfc47eef34de30MD51prefix/9052017-07-21 16:26:05.406oai:tede2.uepg.br:prefix/905Biblioteca Digital de Teses e Dissertaçõeshttps://tede2.uepg.br/jspui/PUBhttp://tede2.uepg.br/oai/requestbicen@uepg.br||mv_fidelis@yahoo.com.bropendoar:2017-07-21T19:26:05Biblioteca Digital de Teses e Dissertações da UEPG - Universidade Estadual de Ponta Grossa (UEPG)false |
dc.title.por.fl_str_mv |
Teoria de Valores Extremos Aplicada a Redes Complexas |
title |
Teoria de Valores Extremos Aplicada a Redes Complexas |
spellingShingle |
Teoria de Valores Extremos Aplicada a Redes Complexas Borges, Rafael Ribaski eventos extremos caminhada aleatória redes complexas extreme events random walk complex networks CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA |
title_short |
Teoria de Valores Extremos Aplicada a Redes Complexas |
title_full |
Teoria de Valores Extremos Aplicada a Redes Complexas |
title_fullStr |
Teoria de Valores Extremos Aplicada a Redes Complexas |
title_full_unstemmed |
Teoria de Valores Extremos Aplicada a Redes Complexas |
title_sort |
Teoria de Valores Extremos Aplicada a Redes Complexas |
author |
Borges, Rafael Ribaski |
author_facet |
Borges, Rafael Ribaski |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Pinto, Sandro Ely de Souza |
dc.contributor.advisor1ID.fl_str_mv |
CPF:00383353955 |
dc.contributor.advisor1Lattes.fl_str_mv |
http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4769629E9 |
dc.contributor.referee1.fl_str_mv |
Viana, Ricardo Luiz |
dc.contributor.referee1ID.fl_str_mv |
CPF:54502659991 |
dc.contributor.referee1Lattes.fl_str_mv |
http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4785888H6 |
dc.contributor.referee2.fl_str_mv |
Rodrigues Junior, Pedro |
dc.contributor.referee2ID.fl_str_mv |
CPF:18575811991 |
dc.contributor.referee2Lattes.fl_str_mv |
http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4789495T0 |
dc.contributor.authorID.fl_str_mv |
CPF:03490007948 |
dc.contributor.authorLattes.fl_str_mv |
http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4250951H3 |
dc.contributor.author.fl_str_mv |
Borges, Rafael Ribaski |
contributor_str_mv |
Pinto, Sandro Ely de Souza Viana, Ricardo Luiz Rodrigues Junior, Pedro |
dc.subject.por.fl_str_mv |
eventos extremos caminhada aleatória redes complexas |
topic |
eventos extremos caminhada aleatória redes complexas extreme events random walk complex networks CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA |
dc.subject.eng.fl_str_mv |
extreme events random walk complex networks |
dc.subject.cnpq.fl_str_mv |
CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA |
description |
The extreme value theory is a branch of statistics and probability. It deals with the asymptotic distributions of extreme values (maximum or minimum) temporal series. The events which takes the average values removed are classified as extreme events. Examples include natural disasters such as goods, earthquakes or an event that causes a strong impact on society. Considering the scenario of complex networks, some examples of extreme events are congestion in networks of roads, power outages in power transmission networks and web servers congested. Thus, understanding the mechanisms that occur in such events is of great interest, because the prediction of these occurrences can minimize its efects, or even avoid them. Thus, the objectives of this study were: 1) to describe the asymptotic behavior of exceedances of a threshold specified by the generalized extreme value distribution, 2) extend the study to the probability of extreme events in complex networks with random topology, small world and scale free. This work was carried out by simulations of random walk pattern and shorter paths. The results shows that for the nodes, also called vertices or sites with low connectivity (lesser degree) in the networks analyzed, the distribution of excesses is not of exponential type. This implies that this distribution is bounded above. The results for the nodes with higher degree were similar, but only for the scale-free network this behavior does not occur. This is due to the fact that the number of exceedances observed in this case is signicantly smaller than the other. It was checked analytically and numerically simulated by random walk pattern, the probability of extreme event is larger and the average time between them is smaller for nodes with lower degree when compared with nodes with higher degree. The spectrum of eigenvalues of the adjacency matrix of the network, which describes the links between nodes, provides conditions for a good agreement between the analytical results and the simulations. For simulations of random walk for shorter paths it was found that nodes with lower betweenness centralities are more likely to have extreme events. |
publishDate |
2013 |
dc.date.available.fl_str_mv |
2013-04-16 2017-07-21T19:26:05Z |
dc.date.issued.fl_str_mv |
2013-03-05 |
dc.date.accessioned.fl_str_mv |
2017-07-21T19:26:05Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
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info:eu-repo/semantics/masterThesis |
format |
masterThesis |
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publishedVersion |
dc.identifier.citation.fl_str_mv |
BORGES, Rafael Ribaski. Teoria de Valores Extremos Aplicada a Redes Complexas. 2013. 116 f. Dissertação (Mestrado em Fisica) - UNIVERSIDADE ESTADUAL DE PONTA GROSSA, Ponta Grossa, 2013. |
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http://tede2.uepg.br/jspui/handle/prefix/905 |
identifier_str_mv |
BORGES, Rafael Ribaski. Teoria de Valores Extremos Aplicada a Redes Complexas. 2013. 116 f. Dissertação (Mestrado em Fisica) - UNIVERSIDADE ESTADUAL DE PONTA GROSSA, Ponta Grossa, 2013. |
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UNIVERSIDADE ESTADUAL DE PONTA GROSSA |
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