Unraveling the mesoscale organization induced by network-driven processes

Area of Science:

• Complex Systems Science
• Network Science
• Dynamical Systems Theory

Background:

• Complex systems exhibit emergent patterns from interactions between dynamics and networks.
• Existing topological or dynamical descriptors alone are insufficient to capture this interplay.
• Dynamics-specific approaches limit the understanding of general principles.

Purpose of the Study:

• To develop a novel metric, Jacobian distance, to uncover latent geometry in network-driven processes.
• To analyze the interplay between network topology and dynamical processes.
• To assess the metric's utility in diverse applications, including human brain networks.

Main Methods:

• Computation of Jacobian distance for nonlinear dynamical models on synthetic and real-world networks.
• Analytical and computational analysis of network-driven latent geometry.
• Explanation of structure-function mismatches using the Jacobian matrix spectrum.

Main Results:

• Jacobian distance captures spatiotemporal perturbation spreading, revealing inherent network geometry.
• Process-driven latent geometry depends on both dynamics and network topology.
• Mismatches between functional and topological organization are explained by the Jacobian matrix spectrum.

Conclusions:

• Jacobian distance provides a unified approach to understanding complex systems.
• The metric reveals potential discrepancies between functional and topological network organization.
• Jacobian distance offers significant advantages over traditional methods for analyzing human brain networks, linking structure and function.