Can Occipital Alpha Neurofeedback Influence LTRCs and Deterministic ERPs   without Critical Branching?
  Critical branching is a theoretical interaction in-between simple units, such as neuronal elements of the human brain. Zhigalov, Kaplan, and Palva (2016, Clin. Neurophysiol., 127(8), 2882-2889) revealed that neurofeedback flash stimulation locked to the phase of high-amplitude occipital alpha influences stimulus-locked occipital averages in the alpha-band. This feedback also influences the power scaling of long-range temporal correlations in alpha-band amplitude fluctuations. Seemingly, neurofeedback influences critical branching alongside there being an interaction between ongoing neuronal activity and evoked responses. However, the causal relations between these neuronal long-range temporal correlations, sustained attention, and any avalanche dynamics are called into question. Further, uncorrected concerns include false discovery rate and an objective mathematical error in the precedent (Palva et al., 2013, Proc. Nat. Acad. Sci. U.S.A., 110(9), 3585-3590). An alternative set of illustrative mathematical principles offers a preliminary fit to the effects in the data. That is, neurofeedback influences the deterministic contribution to the single-trial event-related potentials, which each flash evokes, separately from the oscillatory alpha gain that those flashes cause. Accordingly, distinct principles of this neurofeedback-related exponential occipital oscillatory alpha gain and deterministic event-related potential generation produce micro-behaviours with macroscale consequences: neurofeedback causally influences power-scaling of long-range temporal correlations without critical branching. 
Tom Campbell
q-bio.NC nlin.AO physics.bio-ph