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Area of Science:

  • Network Science
  • Complex Systems
  • Statistical Inference

Background:

  • Prior research focused on reconstructing networks with pairwise interactions.
  • Growing interest in higher-order (many-body) interactions necessitates new reconstruction methods.
  • Observational data requires robust techniques for inferring complex network structures.

Purpose of the Study:

  • To develop a general framework for reconstructing 2-simplicial complexes with two- and three-body interactions.
  • To utilize binary time-series data from discrete-state dynamics for network reconstruction.
  • To improve reconstruction accuracy and computational efficiency.

Main Methods:

  • Combined statistical inference and expectation maximization.
  • Developed a two-step scheme for enhanced accuracy and reduced computational load.
  • Validated using synthetic and real-world 2-simplicial complex data.

Main Results:

  • Successfully reconstructed 2-simplicial complexes with two- and three-body interactions.
  • All network connections were faithfully identified.
  • The full topology of the complexes was accurately inferred.

Conclusions:

  • The proposed framework effectively reconstructs complex networks with higher-order interactions.
  • The method demonstrates robustness against noisy data and stochastic disturbances.
  • Enables detailed topological inference from observational time-series data.