Temporal heterogeneity shapes diffusion dynamics in complex networks.

Area of Science:

• Complex systems science
• Network science
• Theoretical physics

Background:

• Real-world network diffusion often deviates from simple Markovian models due to temporal heterogeneity.
• Understanding these deviations is crucial for modeling phenomena like social contagion and neural dynamics.

Purpose of the Study:

• To develop a general theoretical framework for network diffusion that incorporates temporal heterogeneity.
• To provide analytical tools for predicting the impact of local timing on global network dynamics.

Main Methods:

• Incorporation of node-specific waiting-time distributions using renewal processes.
• Formulation of network dynamics in the Laplace domain.
• Derivation of closed-form expressions linking local temporal statistics to spectral properties.

Main Results:

• Analytical bounds on relaxation times, mixing behavior, and sensitivity to temporal perturbations.
• Quantitative criteria for predicting the propagation of local timing alterations to global dynamics.
• Validation through numerical simulations and empirical analysis of α-synuclein spreading.

Conclusions:

• The proposed framework offers a unified foundation for studying non-Markovian diffusion in networks.
• Gamma-based temporal kernels significantly improve model accuracy compared to memoryless models.
• The findings have broad implications for diverse spreading processes in biological and social systems.