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The Borsuk–Ulam theorem forbids 1-1, continuous mappings of the circle onto the real line. Time-of-day must therefore jump discontinuously somewhere as one goes all the way around the world. Hence the need for an International Date Line.
#AlgebraicTopology https://math.hmc.edu/funfacts/why-an-international-date-line/ …Prikaži ovu nit -
Bounty offered: Show that for Abelian groups
$G$ and$H, \bigl[K(G, n), K(H, n)\bigr] \con... https://math.stackexchange.com/q/3519521?atw=1#algebraictopology -
The Hairy Ball theorem or Hedgehog theorem proven by Poincaré in the 19th century states that "you can't comb a hairy ball flat without creating a cowlick". A hairy doughnut is totally combable though!
#AlgebraicTopology#MathTypepic.twitter.com/t3jUVMmb60
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Next week, Friday 1st of March.
@viditnanda will give a talk titled: 'Big Mathematics for Big Data'@UB_Computing@UniOfBuckingham . All welcome.#AppliedTopology#AlgebraicTopology#BigData#BigMathematics#Math#Computingpic.twitter.com/WMEa6uh0p9
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Learnt about cubical complexes today! Might have some applications to
#neuroscience and#AI.#topology#algebraictopology pic.twitter.com/6DEL7lIVvk -
#algebraictopology II. The Fundamental Group §3 Def. of the fundamental group of a space : done コンパクトな曲面の分類定理は和訳じゃなくて日本語でのまとめにしました。証明の準備が終わって、証明本体に入りました。Prikaži ovu nit -
The Hairy Ball theorem or Hedgehog theorem states that there isn't a nonvanishing continuous tangent vector field on even dimensional n-spheres. Or in other words "you can't comb a hairy ball flat without creating a cowlick"
#AlgebraicTopology pic.twitter.com/PjAPtfMZJ3
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@robertghrist and Jakob Hansen outline a program in spectral sheaf theory (an extension of spectral graph theory to cellular sheaves) in their recent paper. https://arxiv.org/abs/1808.01513#AlgebraicTopology@PennSASpic.twitter.com/Ja4Xh5pUKH
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Viewed (==>), the slow ascension to elegance, topology to algebra. Viewed (<==), the realization that abstract nonsense isn’t enough to see what’s really going on. tl;dr
#AlgebraicTopology is amazing pic.twitter.com/SvMWWPKmTC
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Microsoft Research Talks take a deeper dive into some of today's most groundbreaking
#research like Neural Homology Theory. Watch@wgussml's talk on characterizing the capacity of#neuralnetworks using#algebraictopology: https://aka.ms/v30s2w pic.twitter.com/vbeugfgxzs
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I just released my
@MSFTResearch talk on "Neural Homology Theory," work with@rsalakhu!#DeepLearningTheory#AlgebraicTopology Full Talk: https://www.youtube.com/watch?v=QDQ9J5E7Uqk … Paper: http://wguss.ml/dev/nht/empirical/ …pic.twitter.com/IhQK3FToxD -
We just released our paper "On Characterizing the Capacity of Neural Networks using Algebraic Topology" on
#arxiv. Joint work with@rsalakhu!#DeepLearningTheory#AlgebraicTopology Website: http://wguss.ml/dev/nht/empirical/ … Paper: https://arxiv.org/abs/1802.04443 pic.twitter.com/pFTRuC3R2dPrikaži ovu nit -
Bounty offered: On sufficient conditions to ensure
$X/G\cong X/G'\Rightarrow G\cong G'$. https://math.stackexchange.com/q/2378202?atw=1#algebraictopology -
山手線は丸いのか?プログラマのためのトポロジー入門
#algebraictopology https://www.slideshare.net/taketo1024/ss-78032438 …@SlideShareさんから Henri Poincare「"数学とは、異なるものを同じものとみなす技術である"」 これ本質って感じ。 -
Oscar Randal-Williams & Jack Thorne from
@DpmmsCambridge win 2017@LondMathSoc Whitehead prizes for#algebraictopology &#numbertheory -
The human brain can think in 11 dimensions http://bigthink.com/paul-ratner/our-brains-think-in-11-dimensions-discover-scientists …
#BlueBrainProject#neuroscience#AlgebraicTopology#NeuralStructures -
Neuronal findings provide link btw anatomical structure & brain function
#AlgebraicTopology http://bit.ly/2reFWwo http://bit.ly/2rWUcMS -
Cliques of neurons in cavities provide link btw brain structure/function
#AlgebraicTopology http://bit.ly/2reFWwo http://bit.ly/2rWUcMS -
My
@EPFL_en colleague Henry Markram on how multidimensional space might help understand the brain#algebraictopology@StanfordAlumnipic.twitter.com/hCZUFdnrBC
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