Tuesday, April 19, 2011

The Hierarchy of Neural Complexity

Sporns says that "brain connectivity is organized on a hierarchy of scales from local circuits of neurons to modules of functional brain systems" (258). His use of the word hierarchy presents me with some problems as I have for the last few years contrasted hierarchical structures with network structures. In general, I have assumed that hierarchies were rigid, closed, traced, arboreal structures (to use terms from Deleuze and Guattari) while networks were flexible, scaleable, open, mapped, rhizomatic structures. Hierarchies admit only sanctioned, homogenous nodes within its structure and then fix them into a well-defined place with well-defined relationships to all other nodes; whereas,  networks admit heterogenous nodes within its open structure and allow nodes to develop relationships with any or all other nodes for any reason. For me, then, hierarchies and networks are not the same, and I cringe just a bit each time Sporns uses the term hierarchy to describe an aspect of neural networking.

But I think I have a resolution to my concern. I don't think Sporns is using hierarchy as I do; rather, he is describing various physical and functional layers of the brain and how they interact. As he says: "A recurrent theme in studies of collective behavior in complex networks, from epidemic to brain models, is its dependence on the network's multiscale architecture, its nested levels of clustered communities" (261). He is not so much describing a pyramidal structure as an onion structure. He's talking about layers enclosing layers enclosing layers and so on. This might be a mere quibble over visual metaphors but for his concepts of heterogenous coupling and multiscale dynamics, and some others like them. These principles prevent Sporns' neural hierarchies from calcifying into rigid hierarchies, as I have used the term. Indeed, heterogenous coupling in neurophysiology reminds me much of Deleuze and Guattari's first principle of the rhizome given in the first chapter of their book A Thousand Plateaus (1988): "any point of a rhizome can be connected to anything other, and must be. This is very different from the tree or root, which plots a point, fixes an order" (7). I think Deleuze and Guattari would be most comfortable with Sporns' concept of heterogenous coupling as very rhizomatic.

Sporns also talks about the brain's metastability, or tendency toward chaotic itinerancy:
the itinerant or roaming motion of the trajectory of a high-dimensional system among varieties of ordered states. Chaotic itineracy is found in a number of physical systems that are globally coupled, that are far from equilibrium, or that engage in turbulent flow. … It has also been observed in brain recordings … and neural network models … Over time, systems exhibiting chaotic itineracy alternate between ordered low-dimensional motion within a dynamically unstable "attractor ruin" and high-dimensional chaotic transitions. System variables are coherently coupled, their dynamics slow down during ordered motion, and they transiently lose coherence as the system trajectory rapidly moves between attractor ruins. (263, 264)
This chaotic itinerancy of neural networks with their roaming motions and trajectories and their constant transitions between coherent couplings and incoherent chaos is strongly reminiscent of another characteristic of rhizomes: the principle of asignifying rupture. Deleuze and Guattari say of asignifying ruptures:
Every rhizome contains lines of segmentarity according to which it is stratified, territorialized, organized, signified, attributed, etc., as well as lines of deterritorialization down which it constantly flees. There is a rupture in the rhizome whenever segmentary lines explode into a line of flight, but the line of flight is part of the rhizome.
Rhizomatic structures, then, deterritorialize and reterritorialize only to deterritorialize again. If I understand what Sporns is saying, then it seems that neural networks have a chaotic itinerancy that is at least a Rorschach of asignifying ruptures. Perhaps, Deleuze and Guattari's asignifying ruptures have deterritorialized and reterritorialized as chaotic itinerancy.

Seems possible. Anyway, chaotic itinerancy seems to fit nicely with D&G's whole idea about nomadology and motion in reality. Anyone know for sure?
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