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This article does not have much info. What exactly does exhibit criticality? As correctly stated, all kind of phenomena can exhibit power laws. Avalanches on

This article does not have much info. What exactly does exhibit criticality? As correctly stated, all kind of phenomena can exhibit power laws. Avalanches on a sandpile are sized as a power law. Typical example of self-organized criticality (Per Bak). Back in the day I played with group renormalization theory to prove SOC, but most systems break down if there is loss on a microscopic scale. Intuitively, you need conservation laws on a microscopic scale or the very large events do not happen. This is unlikely the case in a biological system and I won't expect it to be at a critical state, but only hovering around "an interesting area".

pas 7y ago
Hengen said: “Recently, people moved away from measuring simple power laws, which can pop out of random noise, and have started looking at something called the exponent relation. So far, that’s the only true signature of criticality, and it’s the basis of all of our measurements.” They measure neuron activity and spread of firing actions - if I understand correctly without looking at the paper. And they found that thanks to the sophisticated inhibitor neuron network the whole network balances around this mathematical criticality. I guess it means if there were less inhibition then entropically there would be too many firing actions leading to a feedback frenzy, which is obviously not that effective for information processing. And if there were more inhibition then the information wouldn't be able to spread to all the special small parts of the brain, thus making them too specialized. Maybe.
- MrQuincle 7y ago
  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.
- callesgg 7y ago
  Can that be boiled down to something like "the brain is optimised for maximum performance without breaking down." Always being just bellow the activation threshold.
  - pas 7y ago
    I think it's better phrased as that it has active controller feedback loops. If there is room for more specialization, if it can get away with less energy used, less neurons, or some other kind of optimization, then it seems it will do that. And there are loops that work against these to prevent breakdown, forgetting too much, slowing down too much, etc. Of course it's not really known yet what these control system are exactly. (At least I'm not aware we have good data and theories about this aspect of the brain.)

pas 7y ago

Hengen said: “Recently, people moved away from measuring simple power laws, which can pop out of random noise, and have started looking at something called the exponent relation. So far, that’s the only true signature of criticality, and it’s the basis of all of our measurements.” They measure neuron activity and spread of firing actions - if I understand correctly without looking at the paper. And they found that thanks to the sophisticated inhibitor neuron network the whole network balances around this mathematical criticality. I guess it means if there were less inhibition then entropically there would be too many firing actions leading to a feedback frenzy, which is obviously not that effective for information processing. And if there were more inhibition then the information wouldn't be able to spread to all the special small parts of the brain, thus making them too specialized. Maybe.

MrQuincle 7y ago
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.
callesgg 7y ago
Can that be boiled down to something like "the brain is optimised for maximum performance without breaking down." Always being just bellow the activation threshold.
- pas 7y ago
  I think it's better phrased as that it has active controller feedback loops. If there is room for more specialization, if it can get away with less energy used, less neurons, or some other kind of optimization, then it seems it will do that. And there are loops that work against these to prevent breakdown, forgetting too much, slowing down too much, etc. Of course it's not really known yet what these control system are exactly. (At least I'm not aware we have good data and theories about this aspect of the brain.)