Yeah, I read that as well. I found the paper: https://www.biorxiv.org/content/biorxiv/early/2018/12/20/503243.full.pdf https://www.biorxiv.org/content/biorxiv/

Yeah, I read that as well. I found the paper: https://www.biorxiv.org/content/biorxiv/early/2018/12/20/503243.full.pdf https://www.biorxiv.org/content/biorxiv/early/2018/12/20/503... "Avalanches were analyzed in terms of size (S, the number of spikes), and duration (D, time) (Fig 1A), and power law exponents were fit to the two distributions. In critical systems, the exponents of the two distributions can be used to predict the mean avalanche size (<S>) observed at a given duration (i.e. the distributions scale together). When <S> is plotted against avalanche duration, the difference between the empirically derived best-fit exponent and the predicted exponent serves as a compact measure of the deviation from criticality (Deviation from Criticality Coefficient, “DCC”, Fig 1B)." Recap. There are several matters that are at times conflated. + Define an order parameter which "significantly changes" (undergoes a phase transition). + Define a control parameter that drives the system through those different regimes. + Establish that there is a critical point (not just a "region"). + Define properties at the critical point that are scale-free (or having "all scales"). + Define this critical point as an attractor in a dynamical system sense. (The system gets infinitely close to it given enough time.) They show however that the system has an attractor "near" the phase transition. Moreover, do not really establish that this is a critical phase transition. They establish "nearness" w.r.t. the critical phase transition by fitting two power laws (size vs duration) according to an expected exponent relation (a-1)/(t-1). They see this as a quantitative measure of nearness. In other words, their nearness measure depends on their definition of criticality. A lot of these studies talk about "near-critical" states. However, that doesn't always make mathematical sense. PS: If you think, ah, you just have to have the control parameter as an output of a system with as input a value that defines the criticality of the system, yeah, that might work. However, the real interesting systems do not use this type of macroscopic information, but have local processes leading to the same results.