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Updated: Mar 12, 2026

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Inferring propagation paths for sparsely observed perturbations on complex networks.

Francesco Alessandro Massucci1, Jonathan Wheeler1, Raúl Beltrán-Debón2

  • 1Departament d'Enginyeria Química, Universitat Rovira i Virgili, Tarragona 43007, Catalonia, Spain.

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Inferring perturbation propagation paths in complex systems is challenging with sparse data. A probabilistic model using belief propagation accurately estimates node perturbation probabilities, improving upon shortest path methods.

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Area of Science:

  • Complex systems analysis
  • Network science
  • Computational biology

Background:

  • Perturbations propagate through interaction networks in complex systems.
  • Observing these perturbations is often limited by sparse temporal and spatial data.
  • Inferring propagation paths under sparsity is a significant challenge across disciplines.

Purpose of the Study:

  • To develop a method for inferring perturbation propagation paths in complex systems with sparse observations.
  • To move beyond traditional shortest path analyses for perturbation inference.
  • To provide fast and accurate estimates of node perturbation probabilities.

Main Methods:

  • Developed a simple and general probabilistic model.
  • Solved the model using belief propagation.
  • Applied the method to infer perturbation paths from sparse data.

Main Results:

  • The probabilistic model successfully infers perturbation propagation paths.
  • Belief propagation provided fast and accurate estimates of node perturbation probabilities.
  • The approach surpasses traditional shortest path methods in accuracy and scope.

Conclusions:

  • A probabilistic approach using belief propagation is effective for inferring perturbation paths in sparse complex systems.
  • This method offers a significant advancement for analyzing perturbation dynamics in various scientific fields.
  • Accurate perturbation probability estimation is achievable even with limited observational data.