ektrules said:
Is it known, or widely believed, that the cortex is a scale-free network? I.E. Do a large percentage of neurons have a small number of connections to other neurons, and do a small percentage of neurons have a large number of connections to other neurons?
I certainly believe this is probable
. And various arguments have been made along these lines.
There is the fact that integration takes place over so many scales, from the neuron, to the microcircuit, to the cortical column, to the cortical area, to the cortical lobe. It has the look of scale-free, powerlaw, connection. Though this can't be easily proven because there is always the question of whether structures like columns are "really there", or what we find because they are what we are looking for.
Another line of argument suggestive of scale-free structure is literature on the expansion of the brain from primates to humans. Structures like the prefrontal and striatum are argued to have been scaled up according to a simple powerlaw rather than because the higher areas have had preferential selection. So instead of prefrontal getting a special push in humans, it is just powerlaw larger as part of the whole brain being bigger.
I haven't kept track of recent developments in this area, but I am sure you will find many who would take the hypothesis seriously. Scalefree networks are another way of talking about nested hierarchical structure, and that was the normal way neurologists thought about brain organisation (unless they were cognitive phrenology types rather than dynamicists).
[edit: oh, on your particular point about neuron connections, I don't think it works out that way. Neurons generally all make similar numbers of connections for their class. But there are different classes of neurons, so for example the Purkinje cells of the cerebellum are massively connected compared to cortical pyramidal cells. But then every Purkinje cell has millions of synapses. And the reason relates to the particular job they have to do.
Where scale-free would show would be in the distance of each neurons connections more likely. Many local ones, and far fewer distant ones.
And then also in the various classes of neurons. So modulatory neurons like those producing dopamine in the substantia nigra would be at one extreme for the distances they cover across the brain. While other classes, like a hippocampal pyramidal cell, would only connect pretty locally.
Generally scalefree architecture is what we expect from systems that have self-organised complexity. So as a baseline view, it seems a good lens with which to approach the complex organisation of the brain.]
