Simplicial Complexes: Your Brain as Math Part 2 | Infinite Series

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What is a Simplicial Complex and how can it help us decode the brain’s neurological structure? This is Part 2 in our Your Brain as Math mini-series. Check out part 1 here: https://www.youtube.com/watch?v=M0M3srBoTkY

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Previous Episode
Your Brain as Math - Part 1
https://youtu.be/M0M3srBoTkY

Network Mathematics and Rival Factions
https://www.youtube.com/watch?v=qEKNFOaGQcc

Last episode we saw that your neural network can be modeled as a graph, which -- we’ll show in this episode -- can be viewed as a higher-dimensional simplicial complex. So… what is a simplicial complex??

Written and Hosted by Kelsey Houston-Edwards
Produced by Rusty Ward
Graphics by Ray Lux
Assistant Editing and Sound Design by Mike Petrow
Made by Kornhaber Brown (www.kornhaberbrown.com)

Resources:

Cliques of Neurons Bound into Cavities Provide a Missing Link between Structure and Function
http://journal.frontiersin.org/article/10.3389/fncom.2017.00048/full

The Blue Brain Project:
http://bluebrain.epfl.ch/

Barcodes: The Persistent Topology of Data
https://www.math.upenn.edu/~ghrist/preprints/barcodes.pdf

Network Neuroscience
http://www.nature.com/neuro/journal/v20/n3/full/nn.4502.html

Algebraic Topology
https://www.math.cornell.edu/~hatcher/AT/ATpage.html

Special thanks to Professor Kathryn Hess and Mathematician Florian Frick!

Special thanks to Matthew O'Connor and Yana Chernobilsky who are supporting us on Patreon at the Identity level!

And thanks to Mauricio Pacheco who is supporting us at the Lemma level!