Reconstructing propagation networks with natural diversity and identifying hidden sources

@article{Shen2014ReconstructingPN,
  title={Reconstructing propagation networks with natural diversity and identifying hidden sources},
  author={Zhesi Shen and Wen-Xu Wang and Ying Fan and Zengru Di and Ying-Cheng Lai},
  journal={Nature Communications},
  year={2014},
  volume={5}
}
Our ability to uncover complex network structure and dynamics from data is fundamental to understanding and controlling collective dynamics in complex systems. Despite recent progress in this area, reconstructing networks with stochastic dynamical processes from limited time series remains to be an outstanding problem. Here we develop a framework based on compressed sensing to reconstruct complex networks on which stochastic spreading dynamics take place. We apply the methodology to a large… 

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References

SHOWING 1-10 OF 74 REFERENCES

Network Reconstruction Based on Evolutionary-Game Data via Compressive Sensing

Based on compressive sensing, an efficient approach to reconstructing complex networks under game-based interactions from small amounts of data is developed, demonstrating that the extremely challenging problem of reverse engineering of complex networks can be addressed even when the underlying dynamical processes are governed by realistic, evolutionary-game type of interactions in discrete time.

Time-series–based prediction of complex oscillator networks via compressive sensing

This work demonstrates that the network-reconstruction problem can be casted into the form X=G·a, where the vector X and matrix G are determined by the time series and a is a sparse vector to be estimated that contains all nonzero power series coefficients in the mathematical functions of all existing couplings among the nodes.

Detecting hidden nodes in complex networks from time series.

The paradigm for detecting hidden nodes is expected to find applications in a variety of fields where identifying hidden or black-boxed objects based on a limited amount of data is of interest.

Hierarchical structure and the prediction of missing links in networks

This work presents a general technique for inferring hierarchical structure from network data and shows that the existence of hierarchy can simultaneously explain and quantitatively reproduce many commonly observed topological properties of networks.

On the Convexity of Latent Social Network Inference

This work considers contagions propagating over the edges of an unobserved social network, and presents a maximum likelihood approach based on convex programming with a l1-like penalty term that encourages sparsity to identify the optimal network that best explains the observed data.

Multiscale, resurgent epidemics in a hierarchical metapopulation model.

This work introduces a class of metapopulation models in which homogeneous mixing holds within local contexts, and that these contexts are embedded in a nested hierarchy of successively larger domains and allow diseases to spread stochastically.

Thresholds for epidemic spreading in networks

It is conjecture that on quenched scale-rich networks the threshold of generic epidemic models is vanishing or finite depending on the presence or absence of a steady state.

Revealing network connectivity from response dynamics.

  • M. Timme
  • Mathematics
    Physical review letters
  • 2007
This work considers networks of coupled phase oscillators and explicitly study their long-term stationary response to temporally constant driving, finding good predictions of the actual connectivity even for formally underdetermined problems.

Statistical mechanics of complex networks

A simple model based on these two principles was able to reproduce the power-law degree distribution of real networks, indicating a heterogeneous topology in which the majority of the nodes have a small degree, but there is a significant fraction of highly connected nodes that play an important role in the connectivity of the network.

Noise bridges dynamical correlation and topology in coupled oscillator networks.

Noise leads to a general, one-to-one correspondence between the dynamical correlation and the connections among oscillators for a variety of node dynamics and network structures, enabling an accurate prediction of the full network topology based solely on measuring the dynamicals correlation.
...