Modelling long-range dependence and critical brain dynamics in brain networks

The primary aim is to develop mathematically principled frameworks that improve the measurement and characterisation of complex neural systems, specifically long-memory structure, critical dynamics, and heavy-tailed nonstationary behaviour in neural time series data. In particular, investigation of the instability of classical long-range dependence estimators outside ideal statistical regimes and its impact on the ambiguity surrounding the critical brain hypothesis. This research ultimately aims to enhance the reliability of neural-dynamics inferences, more clearly differentiate genuine long-range dependence from statistical artefacts, and strengthen the mathematical foundations for interpretable and biologically informed brain network models.