12,543 research outputs found
Revealing networks from dynamics: an introduction
What can we learn from the collective dynamics of a complex network about its
interaction topology? Taking the perspective from nonlinear dynamics, we
briefly review recent progress on how to infer structural connectivity (direct
interactions) from accessing the dynamics of the units. Potential applications
range from interaction networks in physics, to chemical and metabolic
reactions, protein and gene regulatory networks as well as neural circuits in
biology and electric power grids or wireless sensor networks in engineering.
Moreover, we briefly mention some standard ways of inferring effective or
functional connectivity.Comment: Topical review, 48 pages, 7 figure
Inferring Network Topology from Complex Dynamics
Inferring network topology from dynamical observations is a fundamental
problem pervading research on complex systems. Here, we present a simple,
direct method to infer the structural connection topology of a network, given
an observation of one collective dynamical trajectory. The general theoretical
framework is applicable to arbitrary network dynamical systems described by
ordinary differential equations. No interference (external driving) is required
and the type of dynamics is not restricted in any way. In particular, the
observed dynamics may be arbitrarily complex; stationary, invariant or
transient; synchronous or asynchronous and chaotic or periodic. Presupposing a
knowledge of the functional form of the dynamical units and of the coupling
functions between them, we present an analytical solution to the inverse
problem of finding the network topology. Robust reconstruction is achieved in
any sufficiently long generic observation of the system. We extend our method
to simultaneously reconstruct both the entire network topology and all
parameters appearing linear in the system's equations of motion. Reconstruction
of network topology and system parameters is viable even in the presence of
substantial external noise.Comment: 11 pages, 4 figure
Transition to Reconstructibility in Weakly Coupled Networks
Across scientific disciplines, thresholded pairwise measures of statistical
dependence between time series are taken as proxies for the interactions
between the dynamical units of a network. Yet such correlation measures often
fail to reflect the underlying physical interactions accurately. Here we
systematically study the problem of reconstructing direct physical interaction
networks from thresholding correlations. We explicate how local common cause
and relay structures, heterogeneous in-degrees and non-local structural
properties of the network generally hinder reconstructibility. However, in the
limit of weak coupling strengths we prove that stationary systems with dynamics
close to a given operating point transition to universal reconstructiblity
across all network topologies.Comment: 15 pages, 4 figures, supplementary material include
Disentangling causal webs in the brain using functional Magnetic Resonance Imaging: A review of current approaches
In the past two decades, functional Magnetic Resonance Imaging has been used
to relate neuronal network activity to cognitive processing and behaviour.
Recently this approach has been augmented by algorithms that allow us to infer
causal links between component populations of neuronal networks. Multiple
inference procedures have been proposed to approach this research question but
so far, each method has limitations when it comes to establishing whole-brain
connectivity patterns. In this work, we discuss eight ways to infer causality
in fMRI research: Bayesian Nets, Dynamical Causal Modelling, Granger Causality,
Likelihood Ratios, LiNGAM, Patel's Tau, Structural Equation Modelling, and
Transfer Entropy. We finish with formulating some recommendations for the
future directions in this area
Detecting Directed Interactions of Networks by Random Variable Resetting
We propose a novel method of detecting directed interactions of a general
dynamic network from measured data. By repeating random state variable
resetting of a target node and appropriately averaging over the measurable
data, the pairwise coupling function between the target and the response nodes
can be inferred. This method is applicable to a wide class of networks with
nonlinear dynamics, hidden variables and strong noise. The numerical results
have fully verified the validity of the theoretical derivation
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