Scientists have employed a traditional field of
mathematics in an entirely novel approach to investigate the anatomy of human
brains.

They revealed that the brain is filled of
multidimensional geometrical structures that operate in up to 11 dimensions.

We're used to seeing the world in three dimensions,
so this may sound difficult, but the findings of this new study could be the
next important step in understanding the fabric of the human brain - the most
intricate structure we've discovered.

The Blue Brain Project, a Swiss scientific endeavour
dedicated to developing a supercomputer-powered recreation of the human brain,
created its latest brain model.

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 tantalising new picture of
how the brain processes information, but the researchers emphasise that it is
not yet clear what causes the cliques and cavities to form in such specific
ways, and that more research will be required to determine how the complexity
of these multidimensional geometric shapes formed by our neurons correlates
with the complexity of various cognitive tasks.

But this is far from the last we'll hear about
algebraic topology's insights into the most enigmatic of human organs - the
brain.

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