Critical systems exhibit optimal computational properties, suggesting that the possibility that criticality has been evolutionarily selected as a useful trait for our nervous system.
Self-organized criticality as a fundamental property of neural systems 2014
- Self-organized criticality:
- For large finite system, there will be a small region (not a single isolated point) that shows properties of critical systems in an approximate sense.
- Quasi-criticality : our brain, subject to external inputs, cannot reach critical point, can only be close to it.
- Manifold : the critical point is actually a Manifold which has one dimension less than the embedding parameter.
- Self-organized : the control parameter is set by the system itself.
- Critical slowing down : near critical point the recovery from perturbation is slow - the memory of the perturbation is retained for a long time. (analysis by linearization near critical point)
- Power-laws is a typical property of critical system, as seen everywhere in nature.
- Problem : Power-laws in nature can be explained by other mechanisms.
- Scale independence (show similar pattern at all scales), as shown in avalanches. Though, inputs can be processed in parallel, and integrated over the whole system.
- Problem : Avalanches distribution identification is hard.
- Models demonstrate that the self-organization to critical states in the brain is feasible and plausible.
Being Critical of Criticality in the Brain 2012. Friendly explain the problem for beginners, using Ising model.
- communication is optimal at critical point : high dynamic correlation, and high correlation over large distance (large correlation length).
- coupling and variability are balanced to produce long distance communication.
- storage and power are optimized as well.
- power law -> scale free (-> fractal structure, self-similarity).
- power law & artifacts. power law & exponentials.
- power law can be generated by other mechanisms.
- Ising model is equilibrium model, while neural networks are dynamic.
- applying perturbation to Ising model - Barkhausen effect.
- More evidences (
but not strong enough yet ).- The ability to tune the network from a subcritical regime through criticality to supercritical regime (phase transitions).
- The balance between excitation and inhibition can serve as a control parameter.
- The existence of mathematical relationships between the exponents of the power for a system.
- Multiple power laws exist.
- The existence of data collapse within neural data.
- Avalanche shapes (time-size plot) are similar for difference scales.
- The ability to tune the network from a subcritical regime through criticality to supercritical regime (phase transitions).
Emergent complex neural dynamics : the brain at the edge 2010.
Edge of chaos and prediction of computational performance for neural circuit models 2007. (1) shows the edge of chaos predicts quite well those values of circuit parameters that yield maximal computational performance. (2) propose a new method for predicting the computational performance of neural microcircuit models.