Morphological inversion of complex diffusion.

Area of Science:

• Network science
• Complex systems analysis
• Mathematical modeling

Background:

• Many real-world phenomena, including epidemics and neural cascades, spread via diffusion processes on networks.
• Identifying the initial source node is critical for understanding and mitigating these spreading events.
• Existing methods for origin detection often rely on specific network properties or forward models.

Purpose of the Study:

• To develop a novel method for detecting the origin of diffusion on complex networks.
• To provide a universally applicable approach for identifying triggering nodes regardless of the diffusion model.
• To improve upon existing algorithms in accuracy and applicability.

Main Methods:

• Definition of a new morphological operator tailored for detecting diffusion origins.
• Application of the operator to the final state of a complex network to infer the initial node.
• Comparative analysis against distance (closeness) and Jordan centrality algorithms.

Main Results:

• The proposed morphological operator effectively detects the origin of diffusive fronts.
• The method demonstrates superior performance compared to distance and Jordan centrality algorithms.
• The approach is model-agnostic, applicable to various diffusion processes.

Conclusions:

• A novel morphological operator offers a robust solution for identifying the origin of diffusion on complex networks.
• This method enhances our ability to pinpoint causal origins in diverse systems, from epidemics to infrastructure failures.
• The model-agnostic nature of the operator broadens its applicability across scientific and engineering domains.