For fans of Algebraic Topology, here is a fascinating practical application in the exploration of brain structure, a good example of apparently arcane math suddenly finding uses in the so-called "real" world...
Science Daily Article:
'Multi-dimensional universe' in brain networks
Wired Article:
The Mind-Boggling Math That (Maybe) Mapped the Brain in 11 Dimensions
Blue Brain Blog Report:
Team Discovers a Multi-Dimensional Universe in Brain Networks
Topology in Neuroscience
The image attempts to illustrate something that can not be imaged – a universe of multi-dimensional structures and spaces. On the left is a digital copy of a part of the neocortex, the most evolved part of the brain. On the right are shapes of different sizes and geometries in an attempt to represent structures ranging from 1D to 7D and beyond. The “black-hole” in the middle is used to symbolise a complex x of multi-dimensional spaces, or cavities.
Blue Brain Project / EPFL © 2005 – 2017.
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Cliques of Neurons Bound into Cavities Provide a Missing Link between Structure and Function
This discovery was made by a team from the Blue Brain Project
a Swiss Brain Research Initiative. They have also provided videos about this research...
The Blue Brain Project also provides some general videos about their research...
Fun video introduction to Algebraic Topology...
And a fun video introduction to Topology in general...
