3,716 research outputs found
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
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
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
Model-free inference of direct network interactions from nonlinear collective dynamics
The topology of interactions in network dynamical systems fundamentally
underlies their function. Accelerating technological progress creates massively
available data about collective nonlinear dynamics in physical, biological, and
technological systems. Detecting direct interaction patterns from those
dynamics still constitutes a major open problem. In particular, current
nonlinear dynamics approaches mostly require to know a priori a model of the
(often high dimensional) system dynamics. Here we develop a model-independent
framework for inferring direct interactions solely from recording the nonlinear
collective dynamics generated. Introducing an explicit dependency matrix in
combination with a block-orthogonal regression algorithm, the approach works
reliably across many dynamical regimes, including transient dynamics toward
steady states, periodic and non-periodic dynamics, and chaos. Together with its
capabilities to reveal network (two point) as well as hypernetwork (e.g., three
point) interactions, this framework may thus open up nonlinear dynamics options
of inferring direct interaction patterns across systems where no model is
known.Comment: 10 pages, 7 figure
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