140,227 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
Networks with time structure from time series
We propose a method of constructing a network, in which its time structure is
directly incorporated, based on a deterministic model from a time series. To
construct such a network, we transform a linear model containing terms with
different time delays into network topology. The terms in the model are
translated into temporal nodes of the network. On each link connecting these
nodes, we assign a positive real number representing the strength of
relationship, or the "distance," between nodes specified by the parameters of
the model. The method is demonstrated by a known system and applied to two
actual time series.Comment: 15 pages, 5 figures, accepted to be published in Physica
Recurrence-based time series analysis by means of complex network methods
Complex networks are an important paradigm of modern complex systems sciences
which allows quantitatively assessing the structural properties of systems
composed of different interacting entities. During the last years, intensive
efforts have been spent on applying network-based concepts also for the
analysis of dynamically relevant higher-order statistical properties of time
series. Notably, many corresponding approaches are closely related with the
concept of recurrence in phase space. In this paper, we review recent
methodological advances in time series analysis based on complex networks, with
a special emphasis on methods founded on recurrence plots. The potentials and
limitations of the individual methods are discussed and illustrated for
paradigmatic examples of dynamical systems as well as for real-world time
series. Complex network measures are shown to provide information about
structural features of dynamical systems that are complementary to those
characterized by other methods of time series analysis and, hence,
substantially enrich the knowledge gathered from other existing (linear as well
as nonlinear) approaches.Comment: To be published in International Journal of Bifurcation and Chaos
(2011
Ambiguities in recurrence-based complex network representations of time series
Recently, different approaches have been proposed for studying basic
properties of time series from a complex network perspective. In this work, the
corresponding potentials and limitations of networks based on recurrences in
phase space are investigated in some detail. We discuss the main requirements
that permit a feasible system-theoretic interpretation of network topology in
terms of dynamically invariant phase-space properties. Possible artifacts
induced by disregarding these requirements are pointed out and systematically
studied. Finally, a rigorous interpretation of the clustering coefficient and
the betweenness centrality in terms of invariant objects is proposed
Horizontal visibility graphs transformed from fractional Brownian motions: Topological properties versus Hurst index
Nonlinear time series analysis aims at understanding the dynamics of
stochastic or chaotic processes. In recent years, quite a few methods have been
proposed to transform a single time series to a complex network so that the
dynamics of the process can be understood by investigating the topological
properties of the network. We study the topological properties of horizontal
visibility graphs constructed from fractional Brownian motions with different
Hurst index . Special attention has been paid to the impact of Hurst
index on the topological properties. It is found that the clustering
coefficient decreases when increases. We also found that the mean
length of the shortest paths increases exponentially with for fixed
length of the original time series. In addition, increases linearly
with respect to when is close to 1 and in a logarithmic form when
is close to 0. Although the occurrence of different motifs changes with ,
the motif rank pattern remains unchanged for different . Adopting the
node-covering box-counting method, the horizontal visibility graphs are found
to be fractals and the fractal dimension decreases with . Furthermore,
the Pearson coefficients of the networks are positive and the degree-degree
correlations increase with the degree, which indicate that the horizontal
visibility graphs are assortative. With the increase of , the Pearson
coefficient decreases first and then increases, in which the turning point is
around . The presence of both fractality and assortativity in the
horizontal visibility graphs converted from fractional Brownian motions is
different from many cases where fractal networks are usually disassortative.Comment: 12 pages, 8 figure
Beyond element-wise interactions: identifying complex interactions in biological processes
Background: Biological processes typically involve the interactions of a number of elements (genes, cells) acting on each others. Such processes are often modelled as networks whose nodes are the elements in question and edges pairwise relations between them (transcription, inhibition). But more often than not, elements actually work cooperatively or competitively to achieve a task. Or an element can act on the interaction between two others, as in the case of an enzyme controlling a reaction rate. We call “complex” these types of interaction and propose ways to identify them from time-series observations.
Methodology: We use Granger Causality, a measure of the interaction between two signals, to characterize the influence of an enzyme on a reaction rate. We extend its traditional formulation to the case of multi-dimensional signals in order to capture group interactions, and not only element interactions. Our method is extensively tested on simulated data and applied to three biological datasets: microarray data of the Saccharomyces cerevisiae yeast, local field potential recordings of two brain areas and a metabolic reaction.
Conclusions: Our results demonstrate that complex Granger causality can reveal new types of relation between signals and is particularly suited to biological data. Our approach raises some fundamental issues of the systems biology approach since finding all complex causalities (interactions) is an NP hard problem
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