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Neuroscientists have used a classic branch of
maths in a totally new way to peer into the structure of our brains. What
they've discovered is that the brain is full of multi-dimensional geometrical
structures operating in as many as 11 dimensions.

We're used to thinking of the world from a 3-D
perspective, so this may sound a bit tricky, but the results of this new study
could be the next major step in understanding the fabric of the human brain -
the most complex structure we know of.

This latest brain model was produced by a team
of researchers from the Blue Brain Project, a Swiss research initiative devoted
to building a supercomputer-powered reconstruction of the human brain.

The team used algebraic topology, a branch of
mathematics used to describe the properties of objects and spaces regardless of
how they change shape. They found that groups of neurons connect into
'cliques', and that the number of neurons in a clique would lead to its size as
a high-dimensional geometric object.

"We found a world that we had never
imagined. There are tens of millions of these objects even in a small speck of
the brain, up through seven dimensions. In some networks, we even found
structures with up to 11 dimensions." says lead researcher, neuroscientist
Henry Markram from the EPFL institute in Switzerland.

Human brains are estimated to have a
staggering 86 billion neurons, with multiple connections from each cell webbing
in every possible direction, forming the vast cellular network that somehow
makes us capable of thought and consciousness. With such a huge number of
connections to work with, it's no wonder we still don't have a thorough understanding
of how the brain's neural network operates. But the new mathematical framework
built by the team takes us one step closer to one day having a digital brain
model.

To perform the mathematical tests, the team
used a detailed model of the neocortex the Blue Brain Project team published
back in 2015. The neocortex is thought to be the most recently evolved part of
our brains, and the one involved in some of our higher-order functions like
cognition and sensory perception.

After developing their mathematical framework
and testing it on some virtual stimuli, the team also confirmed their results
on real brain tissue in rats. According to the researchers, algebraic topology
provides mathematical tools for discerning details of the neural network both
in a close-up view at the level of individual neurons, and a grander scale of
the brain structure as a whole.

By connecting these two levels, the
researchers could discern high-dimensional geometric structures in the brain,
formed by collections of tightly connected neurons (cliques) and the empty
spaces (cavities) between them.

"We found a remarkably high number and
variety of high-dimensional directed cliques and cavities, which had not been
seen before in neural networks, either biological or artificial," the team
writes in the study.

"Algebraic topology is like a telescope
and microscope at the same time. It can zoom into networks to find hidden
structures, the trees in the forest, and see the empty spaces, the clearings,
all at the same time." says one of the team, mathematician Kathryn Hess
from EPFL.

Those clearings or cavities seem to be
critically important for brain function. When researchers gave their virtual
brain tissue a stimulus, they saw that neurons were reacting to it in a highly
organized manner.

"It is as if the brain reacts to a
stimulus by building [and] then razing a tower of multi-dimensional blocks,
starting with rods (1D), then planks (2D), then cubes (3D), and then more
complex geometries with 4D, 5D, etc. The progression of activity through the
brain resembles a multi-dimensional sandcastle that materializes out of the
sand and then disintegrates." says one of the team, mathematician Ran Levi
from Aberdeen University in Scotland.

These findings provide a tantalizing new
picture of how the brain processes information, but the researchers point out
that it's not yet clear what makes the cliques and cavities form in their
highly specific ways and more work will be needed to determine how the
complexity of these multi-dimensional geometric shapes formed by our neurons
correlates with the complexity of various cognitive tasks.

But this is definitely not the last we'll be
hearing of insights that algebraic topology can give us on this most mysterious
of human organs - the brain.

The study was published in Frontiers of
Computational Neuroscience

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