Hmmmm. "Hess says they tried to shop around the idea to other neuroscience journals first, to avoid the conflict of interest—but didn’t have much luck, since most editors they spoke to had never heard of algebraic topology".

Neuroscience as a field is quite comfortable with 'n-dimensions', given the importance of matrices to data. Let alone the relationship between topology and graph/network theory... It seems highly unlikely that editors would not be at least roughly familiar with algebraic topology. It reads (to me), "Our research is not marketable, because it lacks prescriptive insight, so we published it in our own journal". The conflict of interest statement in the paper is suspect, as the article roughly mentions.

From the abstract: "We propose that the brain processes stimuli by forming increasingly complex functional cliques and cavities". I can't see how this says anything not already well-established, though perhaps differently described - that biological structures in the brain support the use of hierarchical network models at the neuronal IP level.

Anecdotally, I find the 'jargonification' of neuroscience a little disturbing. This reads like false progress. I'm simply an interested lay-person, so I'm open to correction on all the above - but as I see it, additional ways of describing 'what' does not necessarily give a 'how'.