Healthy brains exhibit a rich dynamic repertoire with flexible and diverse 
spatiotemporal pattern replays across both microscopic and macroscopic scales. 
We hypothesize that the system must operate near a critical regime for the 
functional repertoire to be fully explored, and flexible dynamics to emerge. 
To test this hypothesis, we employ a modular Spiking Neuronal Network model, 
where each group of Leaky Integrate-and-Fire neurons represents a cortical 
region. A learning rule based on Spike-Timing-Dependent Plasticity (STDP) 
is used to encode patterns of activations that propagate between modules. 
The patterns exploit empirical information on the number of white-matter 
fibers between regions. The model [1] displays two distinct dynamical regimes: 
an uncorrelated low-rate state and a strongly correlated state, marked by a 
high Order Parameter value (indicating the similarity of spontaneous activity 
with one of stored patterns). These regimes are separated by either a 
first-order or second-order phase transition, depending on the strength of 
global inhibition and structured connections. When the hysteresis loop shrinks,
a continuous phase transition occurs, and it opens up an extended region with 
high order parameter fluctuations (close a Widom line with maxima of fluctuations).
The model's predictions are compared with empirical data from 
magnetoencephalographic (MEG) recordings in healthy adults.
We show that the structure-function correlation, that is, the coupling 
between structural connectivity and emergent functional observables, is 
maximized in this extended critical region, as well as the correlation 
between the emergent functional observables in the model and those observed 
in the MEG data.
The Levenshtein distance is used to quantify the similarity between the 
sequences of region activations in neural avalanches from both the empirical 
data and the model simulations. Notably a similar repertoire of sequence 
is observed in synthetic data and MEG only when the model operates within 
the critical extended regime.

[1] Role of criticality in the structure-function relationship in the human 
brain, M. Angiolelli S. Scarpetta P. Sorrentino et al., 
accepted in Phys Rev. Res. 2025