Source: Wired, Jun 2017
Instead of a meaningless pile of data, she saw in Markram’s results an obvious place to apply her abstract math goggles. “Topology is really the mathematics of connectivity in some sense,” she says. “It’s particularly good at taking local information and integrating it to see what global structures emerge.”
For the last two years she’s been converting Blue Brain’s virtual network of connected neurons and translating them into geometric shapes that can then be analyzed systematically. Two connected neurons look like a line segment. Three look like a flat, filled-in triangle. Four look like a solid pyramid. More connections are represented by higher dimensional shapes—and while our brains can’t imagine them, mathematics can describe them.
Using this framework, Hess and her collaborators took the complex structure of the digital brain slice and mapped it across as many as 11 dimensions. It allowed them to take random-looking waves of firing neurons and, according to Hess, watch a highly coordinated pattern emerge. “There’s a drive toward a greater and greater degree of organization as the wave of activity moves through the rat brain,” she says. “At first it’s just pairs, just the edges light up. Then they coordinate more and more, building increasingly complex structures before it all collapses.”
Nanoporous materials are super useful for all sorts of industries—from gas separation to chemical storage to medicine. And the performance of these materials depends on the shape of their pores, something that’s really difficult to quantify. So when scientists are looking for new materials to do certain jobs, they rely almost entirely on visual inspection of the more than 3 million nanoporous materials out there. Hess used algebraic topology to quantify the similarity of pore structures instead, assigning a sort of geometric fingerprint to each one. It’s a computational method chemical engineers can now use to find exactly what they need without having to stare into a microscope for days on end.
Markram is as on-brand now as ever. His signature style is to present ideas too speculative for most scientists to countenance and then find ways to test them despite (and often in spite of) the haters. His latest hypothesis: that those patterns of increasingly complex neuronal structures represent ever richer and more interesting responses to stimuli. He thinks it’s how people learn. Maybe even where they store memories. To find out, Argonne National Laboratory outside of Chicago, Illinois gave him 100 million core hours on their super-super computer to run a year-long simulation to see how those patterns change and evolve over time. At the end of 2017 Markram will pass off that mountain of data to Hess. Then it will be up to the math to decide.