The phenomenological renormalization group in neuronal models near criticality

Abstract: The phenomenological renormalization group (PRG) has been applied to the study of scaleinvariant phenomena in neuronal data, providing evidence for critical phenomena in the brain. However, it remains unclear how reliably these observed signatures indicate genuine critical behavior, as it is not well established how close to criticality a system must be for them to emerge. Here, we rely on neuronal models with known critical points to investigate under which conditions the PRG procedure yields consistent results. We discuss how the time-binning step of data preprocessing can crucially affect the final results, and propose a data-driven method to adapt the time bin in order to circumvent this issue. Under these conditions, the PRG method only detects scaling behavior in neuronal models within a very narrow range of the critical point, lending credence to the conclusions drawn from PRG results in experimental data.