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This study introduces a new maximum entropy framework accounting for signaling delays in collective motion. The method accurately infers coupling strengths and information transfer times, improving models of active units.

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Area of Science:

  • Statistical Physics
  • Complex Systems
  • Active Matter

Background:

  • Maximum entropy methods often assume instantaneous interactions, limiting their applicability to systems with delayed signaling.
  • Existing models struggle with systems like leukocyte coordination where signaling delays are significant.

Purpose of the Study:

  • To develop a maximum entropy framework that incorporates signaling delays in statistical inference.
  • To accurately infer coupling strengths, fields, and information transfer times in systems with delayed interactions.

Main Methods:

  • Developed a path integral approach to the maximum entropy framework.
  • Included time delays in signaling within the statistical inference model.
  • Tested on synthetic non-Markovian trajectories from delayed Heisenberg-Kuramoto and Vicsek models.

Main Results:

  • The new method successfully infers coupling strengths and information transfer times.
  • Demonstrated excellent performance on synthetic datasets with delayed interactions.
  • Showed significant information loss when using equal-time correlations in dendritic migration experiments.

Conclusions:

  • Relaxing the instantaneous interaction assumption is crucial for accurate modeling of many active systems.
  • The developed framework provides a more realistic approach to inferring dynamics in systems with signaling delays.
  • This method offers a significant improvement over traditional methods, particularly in biological systems.