Generalize the reduction scheme to structured, networked populations beyond all-to-all mixing

Generalize and validate the effective one-dimensional reduction based on the Doi-Peliti Hamiltonian to structured, networked populations with non-all-to-all interactions; develop a framework that incorporates network topology into the constraint selection and reduced Hamiltonian H⋆ while preserving the ability to characterize fixed points, phase transitions, and fluctuations.

Background

The current development and demonstrations largely address well-mixed (all-to-all) systems. Many real-world systems are structured by network topology, where interactions are not homogeneous and mean-field assumptions break down.

The authors explicitly identify extending their reduction method to networked populations as an open question with potentially large impact due to broad applicability in complex systems with structured interactions.