@PhDThesis{Campanharo:2011:DuAAn,
author = "Campanharo, Andriana Susana Lopes de Oliveira",
title = "Dualidade entre a an{\'a}lise de s{\'e}ries temporais e de redes
complexas",
school = "Instituto Nacional de Pesquisas Espaciais (INPE)",
year = "2011",
address = "S{\~a}o Jos{\'e} dos Campos",
month = "2011-03-29",
keywords = "sistemas complexos, redes complexas, an{\'a}lise de s{\'e}ries
temporais, complex systems, complex networks, time series
analysis.",
abstract = "Recentemente, diversos mapeamentos de s{\'e}ries temporais em
redes complexas foram propostos com o intuito de utilizar
t{\'e}cnicas de caracteriza{\c{c}}{\~a}o de redes complexas
para a an{\'a}lise de s{\'e}ries temporais. Embora esses
mapeamentos demonstrem que s{\'e}ries temporais com
din{\^a}micas distintas resultam em redes complexas com
diferentes topologias, ainda n{\~a}o se sabe dizer como tais
propriedades topol{\'o}gicas est{\~a}o relacionadas com as
s{\'e}ries originais. Nesta tese, prop{\~o}e-se um mapeamento de
uma s{\'e}rie temporal em uma rede complexa com uma
opera{\c{c}}{\~a}o inversa aproximada, tornando
poss{\'{\i}}vel a utiliza{\c{c}}{\~a}o de
estat{\'{\i}}sticas em redes complexas para a
caracteriza{\c{c}}{\~a}o de s{\'e}ries temporais e vice-versa.
Como prova deste conceito, um conjunto de s{\'e}ries temporais
{\'e} gerado, variando de peri{\'o}dica {\`a} aleat{\'o}ria e
demonstra-se que o mapeamento proposto ret{\'e}m a maior parte da
informa{\c{c}}{\~a}o embutida na s{\'e}rie temporal (ou rede)
ap{\'o}s a aplica{\c{c}}{\~a}o do mesmo e de seu inverso. Os
resultados obtidos sugerem que a an{\'a}lise de redes complexas
pode ser utilizada na distin{\c{c}}{\~a}o de regimes
din{\^a}micos em s{\'e}ries temporais e, talvez o mais
importante, a an{\'a}lise de s{\'e}ries temporais pode fornecer
um conjunto de ferramentas {\'u}teis para a
caracteriza{\c{c}}{\~a}o de redes complexas de uma forma
totalmente original. ABSTRACT: Recently, several mappings from a
time series to a network have been proposed with the intent of
using network metrics to characterize time series. Although these
mappings demonstrate that different time series result in networks
with distinct topological properties, it remains unclear how these
topological properties relate to the original time series. Here,
it was proposed an intuitive mapping from a time series to a
network with an approximate inverse operation, making it possible
to use network statistics to characterize time series and time
series statistics to characterize networks. As a proof of concept,
an ensemble of time series ranging from periodic to random were
generated and confirm that the proposed mapping retains much of
the information encoded in the original time series and networks
after repeated application of the mapping and its inverse. The
results obtained in this thesis suggest that network analysis can
be used to distinguish different dynamic regimes in time series
and, perhaps more importantly, time series analysis can provide a
powerful set of tools that augment the traditional network
analysis toolkit to quantify networks in new and useful ways.",
committee = "Silva, Jos{\'e} Demisio Sim{\~o}es da (presidente) and Ramos,
Fernando Manuel (orientador) and Carvalho, Solon Ven{\^a}ncio de
and Velho, Haroldo Fraga de Campos and Castro, Joaquim Jos{\'e}
Barroso de and Costa, Luciano da Fontoura and Viana, Ricardo
Luiz",
copyholder = "SID/SCD",
englishtitle = "Duality between time series and network analysis",
language = "pt",
pages = "100",
ibi = "8JMKD3MGP7W/39AQPCB",
url = "http://urlib.net/ibi/8JMKD3MGP7W/39AQPCB",
targetfile = "publicacao.pdf",
urlaccessdate = "30 abr. 2024"
}