419,385 research outputs found
From time series to complex networks: the visibility graph
In this work we present a simple and fast computational method, the
visibility algorithm, that converts a time series into a graph. The constructed
graph inherits several properties of the series in its structure. Thereby,
periodic series convert into regular graphs, and random series do so into
random graphs. Moreover, fractal series convert into scale-free networks,
enhancing the fact that power law degree distributions are related to
fractality, something highly discussed recently. Some remarkable examples and
analytical tools are outlined in order to test the method's reliability. Many
different measures, recently developed in the complex network theory, could by
means of this new approach characterize time series from a new point of view
Azimuthal Anisotropy in High Energy Nuclear Collision - An Approach based on Complex Network Analysis
Recently, a complex network based method of Visibility Graph has been applied
to confirm the scale-freeness and presence of fractal properties in the process
of multiplicity fluctuation. Analysis of data obtained from experiments on
hadron-nucleus and nucleus-nucleus interactions results in values of
Power-of-Scale-freeness-of-Visibility-Graph-(PSVG) parameter extracted from the
visibility graphs. Here, the relativistic nucleus-nucleus interaction data have
been analysed to detect azimuthal-anisotropy by extending the Visibility Graph
method and extracting the average clustering coefficient, one of the important
topological parameters, from the graph. Azimuthal-distributions corresponding
to different pseudorapidity-regions around the central-pseudorapidity value are
analysed utilising the parameter. Here we attempt to correlate the conventional
physical significance of this coefficient with respect to complex-network
systems, with some basic notions of particle production phenomenology, like
clustering and correlation. Earlier methods for detecting anisotropy in
azimuthal distribution, were mostly based on the analysis of statistical
fluctuation. In this work, we have attempted to find deterministic information
on the anisotropy in azimuthal distribution by means of precise determination
of topological parameter from a complex network perspective
Coupling between time series: a network view
Recently, the visibility graph has been introduced as a novel view for
analyzing time series, which maps it to a complex network. In this paper, we
introduce new algorithm of visibility, "cross-visibility", which reveals the
conjugation of two coupled time series. The correspondence between the two time
series is mapped to a network, "the cross-visibility graph", to demonstrate the
correlation between them. We applied the algorithm to several correlated and
uncorrelated time series, generated by the linear stationary ARFIMA process.
The results demonstrate that the cross-visibility graph associated with
correlated time series with power-law auto-correlation is scale-free. If the
time series are uncorrelated, the degree distribution of their cross-visibility
network deviates from power-law. For more clarifying the process, we applied
the algorithm to real-world data from the financial trades of two companies,
and observed significant small-scale coupling in their dynamics
Zero-Parity Stabbing Information
Everett et al. introduced several varieties of stabbing information for the
lines determined by pairs of vertices of a simple polygon P, and established
their relationships to vertex visibility and other combinatorial data. In the
same spirit, we define the ``zero-parity (ZP) stabbing information'' to be a
natural weakening of their ``weak stabbing information,'' retaining only the
distinction among {zero, odd, even>0} in the number of polygon edges stabbed.
Whereas the weak stabbing information's relation to visibility remains an open
problem, we completely settle the analogous questions for zero-parity
information, with three results: (1) ZP information is insufficient to
distinguish internal from external visibility graph edges; (2) but it does
suffice for all polygons that avoid a certain complex substructure; and (3) the
natural generalization of ZP information to the continuous case of smooth
curves does distinguish internal from external visibility
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