2026/03/30 by Bernd von Mallinckrodt · 1 voice
Earth and Planetary Sciences · Environmental Science · Physics and Astronomy · #Complex Systems and Dynamics #Covariance #Covariance matrix #Earthquake Detection and Analysis #Ecosystem dynamics and resilience #Modular design #Modularity (biology) #Rank (graph theory) #Robustness (evolution) #Structural break #Variance (accounting)
paper · doi:10.5281/zenodo.19338685
published in Zenodo (CERN European Organization for Nuclear Research) (European Organization for Nuclear Research)
openalex publication_date 2026/03/30 · openalex created_date 2026/03/31 · openalex updated_date 2026/07/01
Classical early-warning signals (EWS), such as rising variance and lag-1 autocorrelation, assume critical slowing down as a universal precursor mechanism. These indicators can fail when collapse is driven by structural reorganization rather than proximity to a bifurcation. This work introduces Φ, defined as one minus the normalized effective rank of a covariance matrix estimated via Oracle Approximating Shrinkage (OAS), as a complementary indicator for modular structural compression (M3). In this regime, variance is redistributed across eigenmodes rather than amplified, rendering amplitude-based indicators uninformative. Detection is formalized using a surrogate-based hypothesis test with IAAFT (phase-randomized) null models, combined with duration and slope constraints and explicit suppression guards (p/n < 0.5, baseline stationarity, and confirmed modular structure via correlation-based modularity Q). Φ is not proposed as a universal EWS and is not expected to perform in bifurcation-driven (M1) or noise-amplified (M2) regimes. Its applicability is restricted to multivariate systems in which covariance concentration constitutes the dominant precursor mechanism. early warning signals, structural compression, covariance concentration, effective rank, modularity, complex systems, critical transitions, OAS shrinkage, surrogate data, mechanism dependence