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

2017-08-23

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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: /youtube/video/M0M3srBoTkY

Check out Part 3 here: /youtube/video/akgU8nRNIp0

Tweet at us! @pbsinfinite

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Previous Episode

Your Brain as Math - Part 1

/youtube/video/M0M3srBoTkY

Network Mathematics and Rival Factions

/youtube/video/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 Kathryn Hess and 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!


Your Brain as Math - Part 1 | Infinite Series by PBS Infinite Series
/youtube/video/M0M3srBoTkY
Network Mathematics and Rival Factions | Infinite Series by PBS Infinite Series
/youtube/video/qEKNFOaGQcc
Simplicial Complexes
/youtube/video/rlI1KOo1gp4?t=140
Euler Characteristics
/youtube/video/rlI1KOo1gp4?t=284
PBS Infinite Series Mathematician Tai-Danae Bradley and physicist Gabe Perez-Giz offer ambitious content for viewers that are eager to attain a greater understanding of the world around them. Math is pervasive - a robust yet precise language - and with each episode you’ll begin to see the math that underpins everything in this puzzling, yet fascinating, universe. Previous host Kelsey Houston-Edwards is currently working on her Ph.D. in mathematics at Cornell University.
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Infinite Series is creating Math Videos | Patreon patreon.com
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Your Mind Is Eight-Dimensional - Your Brain as Math Part 3 | Infinite Series 276,173 views
/youtube/video/akgU8nRNIp0