Inferring structural complexity from dynamical measures
- 1Department of Biomedical and Clinical Sciences, University of Milan, Milan, Italy
Abstract
Complexity, commonly defined as the coexistence of integration and differentiation, is a fundamental property of thalamocortical networks and is regarded as a prerequisite for adaptive brain function and consciousness. A variety of metrics have been developed to estimate neural complexity from recorded activity and are increasingly employed in both research and clinical settings. Yet, the extent to which these measures reflect specific architectural features of the underlying circuits remains poorly understood. Here, we used Wilson-Cowan mean-field equations to simulate neural dynamics across networks spanning a broad range of architectures. By systematically rewiring connectivity, we generated graded variations in the structural integration-differentiation balance and assessed a panel of complexity measures derived either from spontaneous activity (observational metrics) or from responses to external perturbations (perturbational metrics). Observational measures exhibited markedly heterogeneous behavior: some were primarily sensitive to network integration, others to differentiation, whereas some showed limited sensitivity to architectural manipulations. In contrast, perturbational measures robustly peaked at intermediate rewiring steps and scaled with small-worldness, consistent with architectures that combine local recurrence and distributed communication. Moreover, perturbational metrics proved robust to common-driver confounds and were highest in a wake-like regime near critical instability, declining as sleep-like dynamics became more widespread across the network. Taken together, these findings map widely used empirical complexity measures onto specific network architectures, reveal dynamical factors that can bias observational estimates, and provide guidance for inferring complexity in systems whose internal organization is inaccessible, unconventional, or only partially known, including brain organoids, non-human nervous systems, and synthetic neural networks.
Related
- Inferring Multi-Timescale Neural Dynamics with Switching Linear Dynamical Systems
- Simplifying complexity: the reliability of lidar-derived forest structural complexity metrics for conservation management
- Beyond the uniform: uncovering structural complexity within Adélie penguin colonies
- Restoring structural complexity in temperate forests increases bat and bird diversity
- Leaf economic strategy and stand structural complexity are associated with net woody productivity in a subtropical mixed forest
BibTeX
@misc{gaglioti2026inferring,
title = {{Inferring structural complexity from dynamical measures}},
author = {G. Gaglioti and A. Cattani and T. Nieus and D. Momi and R. Comolatti and L. Dalla Porta and S. Sarasso and M. Massimini},
howpublished = {bioRxiv},
year = {2026},
month = oct,
doi = {10.64898/2026.10.21.760743},
url = {https://www.biorxiv.org/content/10.64898/2026.10.21.760743v1},
note = {CC BY-NC},
}
RIS
TY - UNPB
TI - Inferring structural complexity from dynamical measures
AU - G. Gaglioti
AU - A. Cattani
AU - T. Nieus
AU - D. Momi
AU - R. Comolatti
AU - L. Dalla Porta
AU - S. Sarasso
AU - M. Massimini
PY - 2026
DA - 2026/10/21
PB - bioRxiv
DO - 10.64898/2026.10.21.760743
UR - https://www.biorxiv.org/content/10.64898/2026.10.21.760743v1
AB - Complexity, commonly defined as the coexistence of integration and differentiation, is a fundamental property of thalamocortical networks and is regarded as a prerequisite for adaptive brain function and consciousness. A variety of metrics have been developed to estimate neural complexity from recorded activity and are increasingly employed in both research and clinical settings. Yet, the extent to which these measures reflect specific architectural features of the underlying circuits remains poorly understood. Here, we used Wilson-Cowan mean-field equations to simulate neural dynamics across networks spanning a broad range of architectures. By systematically rewiring connectivity, we generated graded variations in the structural integration-differentiation balance and assessed a panel of complexity measures derived either from spontaneous activity (observational metrics) or from responses to external perturbations (perturbational metrics). Observational measures exhibited markedly heterogeneous behavior: some were primarily sensitive to network integration, others to differentiation, whereas some showed limited sensitivity to architectural manipulations. In contrast, perturbational measures robustly peaked at intermediate rewiring steps and scaled with small-worldness, consistent with architectures that combine local recurrence and distributed communication. Moreover, perturbational metrics proved robust to common-driver confounds and were highest in a wake-like regime near critical instability, declining as sleep-like dynamics became more widespread across the network. Taken together, these findings map widely used empirical complexity measures onto specific network architectures, reveal dynamical factors that can bias observational estimates, and provide guidance for inferring complexity in systems whose internal organization is inaccessible, unconventional, or only partially known, including brain organoids, non-human nervous systems, and synthetic neural networks.
ER -