12,510 research outputs found
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
Model-free reconstruction of neuronal network connectivity from calcium imaging signals
A systematic assessment of global neural network connectivity through direct
electrophysiological assays has remained technically unfeasible even in
dissociated neuronal cultures. We introduce an improved algorithmic approach
based on Transfer Entropy to reconstruct approximations to network structural
connectivities from network activity monitored through calcium fluorescence
imaging. Based on information theory, our method requires no prior assumptions
on the statistics of neuronal firing and neuronal connections. The performance
of our algorithm is benchmarked on surrogate time-series of calcium
fluorescence generated by the simulated dynamics of a network with known
ground-truth topology. We find that the effective network topology revealed by
Transfer Entropy depends qualitatively on the time-dependent dynamic state of
the network (e.g., bursting or non-bursting). We thus demonstrate how
conditioning with respect to the global mean activity improves the performance
of our method. [...] Compared to other reconstruction strategies such as
cross-correlation or Granger Causality methods, our method based on improved
Transfer Entropy is remarkably more accurate. In particular, it provides a good
reconstruction of the network clustering coefficient, allowing to discriminate
between weakly or strongly clustered topologies, whereas on the other hand an
approach based on cross-correlations would invariantly detect artificially high
levels of clustering. Finally, we present the applicability of our method to
real recordings of in vitro cortical cultures. We demonstrate that these
networks are characterized by an elevated level of clustering compared to a
random graph (although not extreme) and by a markedly non-local connectivity.Comment: 54 pages, 8 figures (+9 supplementary figures), 1 table; submitted
for publicatio
Developmental motifs reveal complex structure in cell lineages
Many natural and technological systems are complex, with organisational structures that exhibit characteristic patterns, but defy concise description. One effective approach to analysing such systems is in terms of repeated topological motifs. Here, we extend the motif concept to characterise the dynamic behaviour of complex systems by introducing developmental motifs, which capture patterns of system growth. As a proof of concept, we use developmental motifs to analyse the developmental cell lineage of the nematode Caenorhabditis elegans, revealing a new perspective on its complex structure. We use a family of computational models to explore how biases arising from the dynamics of the developmental gene network, as well as spatial and temporal constraints acting on development, contribute to this complex organisation
Dynamical Properties of Interaction Data
Network dynamics are typically presented as a time series of network
properties captured at each period. The current approach examines the dynamical
properties of transmission via novel measures on an integrated, temporally
extended network representation of interaction data across time. Because it
encodes time and interactions as network connections, static network measures
can be applied to this "temporal web" to reveal features of the dynamics
themselves. Here we provide the technical details and apply it to agent-based
implementations of the well-known SEIR and SEIS epidemiological models.Comment: 29 pages, 15 figure
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