QUOTE
The Brain—is wider than the Sky—
For—put them side by side—
The one the other will contain
With ease—and you—beside—The Brain is deeper than the sea—
For—hold them—Blue to Blue—
The one the other will absorb—
As sponges—Buckets—do—
—Emily Dickinson, c. 1862
How neurons work together - in just a paragraph.
The right pressure, changes into steam. For a moment it is both a flowing liquid and individual molecules zipping around through the air. Neurons can act that way too, firing synchronously and then breaking off to improvise by themselves. Just at this transition, they are paradoxically both independent and interdependent with all other neurons. Right here, near what we will call the critical point, information flows easily, computations are most facile, and the brain is exquisitely sensitive to inputs. Here, intricate patterns of waves, oscillations, and avalanches of activity arise most readily. Slip too far below this point, and neurons fall into the abyss of silence. Nudge above it, and they get swept up into the fatal storm of seizures. Right around the critical point there is a narrow passage that opens to an expanse of complexity and emergence that is wider than the sky and deeper than the sea.
The bigger the network, the closer you need to be at the critical point.
→ Scale-freeness and other criticality properties can already be reached under a finite setting by being close enough.
Then however, phyiscal models don’t exaclty match → “quasicriticality”.
Generally, the window you can be in is extremely narrow. Slight perturbations in stimulus intensity, jitter in spike times, … can push neuronal networks off he critical point, and there are active processes to homeostatically keep the newtork at the critical point.
Scale-free free properties (and universality) are usually described by extremely simple models of basic interaction dynamics.
If it werent so, i.e. the specifics of each different layer would play a role in the dynamics, then it would likely not show the same behavior across different scales.
The model should not just be independent of scale, but also other specifics like species, type of neurotransmitter, cell types, … or even type of the substrate, …
Not all brain regions are operate at a critical point, and others only under specific circumstances (e.g. some visual regions only when visual input is provided)!
3 Phases:
Periodic (ordered): Low firing thresholds → exploding activity → brought down by refractory period → repeat.
Complex (critical): Intermediate thresholds → complex activity → mix of periodic and random activity
Disordered (chaotic): High thresholds → random activity
→ Only the interactions between the neurons matter.
Stopped at: The branching model: Fractal Copies of Avalanches.
References
book
critical state
scale-free
neural branching factor
emergence
ubiquity - book
dialectical materialism
the brain - high level facts and resources