13,256 research outputs found
Recurrence networks - A novel paradigm for nonlinear time series analysis
This paper presents a new approach for analysing structural properties of
time series from complex systems. Starting from the concept of recurrences in
phase space, the recurrence matrix of a time series is interpreted as the
adjacency matrix of an associated complex network which links different points
in time if the evolution of the considered states is very similar. A critical
comparison of these recurrence networks with similar existing techniques is
presented, revealing strong conceptual benefits of the new approach which can
be considered as a unifying framework for transforming time series into complex
networks that also includes other methods as special cases.
It is demonstrated that there are fundamental relationships between the
topological properties of recurrence networks and the statistical properties of
the phase space density of the underlying dynamical system. Hence, the network
description yields new quantitative characteristics of the dynamical complexity
of a time series, which substantially complement existing measures of
recurrence quantification analysis
Modeling the Internet
We model the Internet as a network of interconnected Autonomous Systems which
self-organize under an absolute lack of centralized control. Our aim is to
capture how the Internet evolves by reproducing the assembly that has led to
its actual structure and, to this end, we propose a growing weighted network
model driven by competition for resources and adaptation to maintain
functionality in a demand and supply ``equilibrium''. On the demand side, we
consider the environment, a pool of users which need to transfer information
and ask for service. On the supply side, ASs compete to gain users, but to be
able to provide service efficiently, they must adapt their bandwidth as a
function of their size. Hence, the Internet is not modeled as an isolated
system but the environment, in the form of a pool of users, is also a
fundamental part which must be taken into account. ASs compete for users and
big and small come up, so that not all ASs are identical. New connections
between ASs are made or old ones are reinforced according to the adaptation
needs. Thus, the evolution of the Internet can not be fully understood if just
described as a technological isolated system. A socio-economic perspective must
also be considered.Comment: Submitted to the Proceedings of the 3rd International Conference
NEXT-SigmaPh
Exact results of the limited penetrable horizontal visibility graph associated to random time series and its application
The limited penetrable horizontal visibility algorithm is a new time analysis
tool and is a further development of the horizontal visibility algorithm. We
present some exact results on the topological properties of the limited
penetrable horizontal visibility graph associated with random series. We show
that the random series maps on a limited penetrable horizontal visibility graph
with exponential degree distribution ,
independent of the probability distribution from which the series was
generated. We deduce the exact expressions of the mean degree and the
clustering coefficient and demonstrate the long distance visibility property.
Numerical simulations confirm the accuracy of our theoretical results. We then
examine several deterministic chaotic series (a logistic map, the
Hnon map, the Lorentz system, and an energy price chaotic system)
and a real crude oil price series to test our results. The empirical results
show that the limited penetrable horizontal visibility algorithm is direct, has
a low computational cost when discriminating chaos from uncorrelated
randomness, and is able to measure the global evolution characteristics of the
real time series.Comment: 23 pages, 12 figure
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