How Neural Domain Activation and Statistical Mechanics Model Interactions in Large Data Corpora (Big Data)

I was enthralled. I could read for only a few pages at a time, I was so overwhelmed with the insights that this book provided.

And I was about twenty-five years old at the time. I had just discovered this book while browsing the stacks as a graduate student at Arizona State (ASU).

The book was The Mindful Brain: Cortical Organization and the Group-Selective Theory of Higher Brain Function, by Vernon Mountcastle and Gerald Edelman. (See The Mindful Brain, pub. 1978, on Amazon, and access the full Mindful Brain text.

Every so often, we have a pivotal moment.

This was one of them.

It was not just Mountcastle and Edelman’s identification of neural cortical columns – and columnar (neural domain) activation as a key part of the brain’s processes. (Particularly exciting since I was modeling domain activations in solid state physics, and thought that the statistical mechanics applied to solid state domains could potentially apply to the neural ones.)

What kept me up at night was the notion of “group selective behavior” in the cortical system.

Recently, one of the faculty members had given a colloquium on group theory; a means of showing how certain behaviors transcend scale. I was fascinated by the potential connection of group theory to brain behavior.

Two decades later, Wolf Singer, with P. König & A.K. Engel, was publishing work on long-range connections and coordinated temporal activity oscillations in the cat visual cortex. (Relation between oscillatory activity and long-range synchronization in cat visual cortex; P König, A K Engel, and W Singer, Proc Natl Acad Sci U S A. Jan 3, 1995; 92(1): 290–294.)

Coherent brain domain activations – and coherent patterns of temporal activity – were now established.

But pervasive, large-scale organization of neural domains – even if mediated by direct neural connections – suggested that statistical mechanics could be involved.

The same statistical mechanics approach to modeling neighboring domain activations in a solid-state substance could potentially describe activity in the brain itself.

What particularly made sense was the fact that we would be modeling neural domains, not just individual neural activations.

Once activated, a neural domain was somewhat persistent – even exhibiting some metastability or hysteresis in its activated state. Also, nearest-neighbor and next-nearest neighbor connections encouraged activation in the solid state model. Might they not do the same, via short-range neural connections, in the cortical system?

In the 1992, I received a Jeffries Trust grant to study this, which led to a first pass on a statistical thermodynamics approach to a new neural network.

More recently, inspired by the potential application of this approach to modeling both groupings of like data in big data corpora, and by the potential of not just modeling neural domain activations, but potentially both influencing these activations and transcribing and interpreting neural domain activation patterns, I returned to the same basic physics.

The approach rests on using the Cluster Variation Method (CVM), which presents the free energy of a system as a function of the usual enthalpy term, and as a somewhat more complex entropy term. Instead of just modeling how many units (or domains) are in state A or state B, the CVM approach models not only their on/off (or A/B) activation, but also their local patterns; A next to A, A next to B, and so on; up to and including local triplet patterns (A-A-A, A-A-B, etc.).

This gives us insight into equilibrium micro-pattern distributions. It also gives us a new tool – a new measure – for describing activation patterns in different systems, ranging from Big Data to cortical column collections.

It’s been almost forty years since Edelman’s and Mountcastle’s insights. They may just now be reaching their fruition.

Related Posts and Technical Reports

• Visualizing Configuration Variables with the 2-D Cluster Variation Method, July 9, 2014.
• Visualizing Configuration Variables with the 1-D Cluster Variation Method, July 9, 2014.
• Analytic Single-Point Solution for Cluster Variation Method Variables (at x! = x2 = 0.5), Dec. 8, 2011.
• The Cluster Variation Method II: 2-D Grid of Zigzag Chains: Basic Theory, Analytic Solution and Free Energy Variable Distributions at Midpoint (x1 = x2 = 0.5), THM TR2014-003 (ajm), July 2014
• The Cluster Variation Method I: 1-D Single Zigzag Chain: Basic Theory, Analytic Solution and Free Energy Variable Distributions at Midpoint (x1 = x2 = 0.5), THM TR2014-002 (ajm), June 2014