Criticality in the Brain
What is criticality? (Physics p.o.v.)
Upon stumbling across this article, for those unfamiliar with this line of work, this is probably the first thought that pops in mind: What exactly is criticality? After all, the discussion afterwards would be pointless if such a critical word is not defined properly. Criticality is the transition between ordered and chaotic states. It is an emergent property that is commonly observed in many systems, but unfortunately it is still unclear how it came to be. Simply put, it is a global phenomenon of a system that has different characteristics from the local interactions in which it arose from (for a more detailed definition and explanation, see [1]). Still, despite its lack of a clear definition, there are some characteristics that points toward the system being in a critical state, as we can see in the following example.
Consider an Ising model, i.e. a magnet. Each unit (each site in the lattice) has binary states, spin up and spin down. The abundance of spin ups and downs in each spin’s neighborhood determines its state in the next time step. For low temperature, the spins tend to organize themselves into the same state. For high temperatures, the thermal energy is so high that the spins don’t converge to a certain state, instead they fluctuate around noisily. Between this regime or order and disorder, then, is the critical state. Such a state has two characteristics: (a) it is often characterized by event sizes following power laws. For example, when measuring the correlation of two units as a function of distance, we can observe a power law relationship for the critical state, whereas in the sub- and super-critical state, the correlations remain low and almost constant over different distances. (b) There is a sharp peak between phase transitions. For example, if the correlation length is plotted against temperature, we can observe a sharp peak when the critical temperature is reached (see [2]).
There are of course stricter defining characteristics (as systems not operating in the critical state can still exhibit such behaviors), but for the purpose of the current article, these would be sufficient.
What does criticality imply in neuroscience?
In Dr.Begg’s 2003 paper [3], they claimed to have observed a new mode of activity – neuronal avalanches. These avalanches are found to have propagations of activities obeying power laws and have branching parameters that indicate criticality. In his subsequent work, he showed further proofs of neural networks operating in the critical regime with more power laws and exponent relations (the “stricter” characteristics).
There are still arguments about it, but say the brain does operate in critical states. How is this important? Some studies show that criticality provides optimal information transfer, information storage, computational power and more. This further implies not operating in such a region might result in neuropathologies.
Written by: Pei-Hsien Liu
References
[1] Kivelson, Sophia, and Steven A Kivelson. “Defining Emergence in Physics.” Npj Quantum Materials, vol. 1, no. 1, 2016, doi:10.1038/npjquantmats.2016.24.
[2] Beggs, John. “The Criticality Hypothesis.” 2013 ISB Symposium. 2013 ISB Symposium, www.youtube.com/watch?v=quwJKgzyNaI&fbclid=IwAR1znJwj_aGR5M1cT5-u2hyZbbWJOFkRkcHIR661J_Qa8v0ekoEj2ItCvio.
[3] Beggs, John M., and Dietmar Plenz. “Neuronal Avalanches in Neocortical Circuits.” The Journal of Neuroscience, vol. 23, no. 35, Mar. 2003, pp. 11167–11177., doi:10.1523/jneurosci.23-35-11167.2003.
Upon stumbling across this article, for those unfamiliar with this line of work, this is probably the first thought that pops in mind: What exactly is criticality? After all, the discussion afterwards would be pointless if such a critical word is not defined properly. Criticality is the transition between ordered and chaotic states. It is an emergent property that is commonly observed in many systems, but unfortunately it is still unclear how it came to be. Simply put, it is a global phenomenon of a system that has different characteristics from the local interactions in which it arose from (for a more detailed definition and explanation, see [1]). Still, despite its lack of a clear definition, there are some characteristics that points toward the system being in a critical state, as we can see in the following example.
Consider an Ising model, i.e. a magnet. Each unit (each site in the lattice) has binary states, spin up and spin down. The abundance of spin ups and downs in each spin’s neighborhood determines its state in the next time step. For low temperature, the spins tend to organize themselves into the same state. For high temperatures, the thermal energy is so high that the spins don’t converge to a certain state, instead they fluctuate around noisily. Between this regime or order and disorder, then, is the critical state. Such a state has two characteristics: (a) it is often characterized by event sizes following power laws. For example, when measuring the correlation of two units as a function of distance, we can observe a power law relationship for the critical state, whereas in the sub- and super-critical state, the correlations remain low and almost constant over different distances. (b) There is a sharp peak between phase transitions. For example, if the correlation length is plotted against temperature, we can observe a sharp peak when the critical temperature is reached (see [2]).
There are of course stricter defining characteristics (as systems not operating in the critical state can still exhibit such behaviors), but for the purpose of the current article, these would be sufficient.
What does criticality imply in neuroscience?
In Dr.Begg’s 2003 paper [3], they claimed to have observed a new mode of activity – neuronal avalanches. These avalanches are found to have propagations of activities obeying power laws and have branching parameters that indicate criticality. In his subsequent work, he showed further proofs of neural networks operating in the critical regime with more power laws and exponent relations (the “stricter” characteristics).
There are still arguments about it, but say the brain does operate in critical states. How is this important? Some studies show that criticality provides optimal information transfer, information storage, computational power and more. This further implies not operating in such a region might result in neuropathologies.
Written by: Pei-Hsien Liu
References
[1] Kivelson, Sophia, and Steven A Kivelson. “Defining Emergence in Physics.” Npj Quantum Materials, vol. 1, no. 1, 2016, doi:10.1038/npjquantmats.2016.24.
[2] Beggs, John. “The Criticality Hypothesis.” 2013 ISB Symposium. 2013 ISB Symposium, www.youtube.com/watch?v=quwJKgzyNaI&fbclid=IwAR1znJwj_aGR5M1cT5-u2hyZbbWJOFkRkcHIR661J_Qa8v0ekoEj2ItCvio.
[3] Beggs, John M., and Dietmar Plenz. “Neuronal Avalanches in Neocortical Circuits.” The Journal of Neuroscience, vol. 23, no. 35, Mar. 2003, pp. 11167–11177., doi:10.1523/jneurosci.23-35-11167.2003.
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