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Phoenix666 writes:

The conventional view of the brain is that the gray matter is primarily involved in information processing and cognition, while white matter transmits information between different parts of the brain. The structure of white matter—the connectome—is essentially the brain's wiring diagram.

This structure is poorly understood, but there are several high-profile projects to study it. This work shows that the connectome is much more complex than originally thought. The human brain contains some 10¹⁰ neurons linked by 10¹⁴ synaptic connections. Mapping the way this link together is a tricky business, not least because the structure of the network depends on the resolution at which it is examined.

[...] understanding this structure over vastly different scales is one of the great challenges of neuroscience; but one that is hindered by a lack of appropriate mathematical tools.

Today, that looks set to change thanks to the mathematical field of algebraic topology, which neurologists are gradually coming to grips with for the first time. This discipline has traditionally been an arcane pursuit for classifying spaces and shapes. Now Ann Sizemore at the University of Pennsylvania and a few pals show how it is beginning to revolutionize our understanding of the connectome.

I had always hoped algebraic topology would finally unlock the secrets to untangling my fishing line, but figuring out how the brain works is useful, too.

arXiv.org hosts both an abstract and Full Paper (pdf).

Original Submission