Cortical columns and irreducible subgraphs (ISGs)

I have recently come across a paper by Peter Grindrod titled ‘On human consciousness: A mathematical perspective’ which seems to suggest that there is a link between cortical columns and irreducible (strongly-connected) subgraphs (referred to as ISG’s in his paper):

“The neocortex (the most recently developed part) is differentiated into a number of horizontal layers, and neurons within the different layers connect vertically to form small circuits, called cortical columns. It is these tightly connected columns that are highly suggestive of a massive number of ISGs, with each acting as a multimodal processor, yet integrated more loosely across the surface of the cortex. There is thus some physical evidence for the ‘network of networks’ architecture that is suggested to be efficient here.”

Being a relative newcomer to HTM theory, I am having difficulty parsing the relationship between cortical columns and ISG’s. Would individual nodes, ISG’s or groups of ISG’s represent cortical columns? Also, I am wondering how this ‘network of networks’ architecture might relate/conflict with Numenta’s HTM theory and their views on information processing in the brain?

Edit: Link to the paper -


Thank you for the link to the paper?

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