- Nov 2022
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www.researchgate.net www.researchgate.net
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Think of "data" as thevegetables grown in this garden
Since next example states local data is like an "apple", and global data is like "all apples from one tree", replace "vegetables" with "produce".
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watermark.silverchair.com watermark.silverchair.com
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Introduction to Daniel Rosiak's spectacular "Sheaf Theory through Examples" available open access from MIT Direct Press: https://doi.org/10.7551/mitpress/12581.003.0003
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docdrop.org docdrop.org
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okay so remind you what is a sheath so a sheep is something that allows me to 00:05:37 translate between physical sources or physical realms of data and physical regions so these are various 00:05:49 open sets or translation between them by taking a look at restrictions overlaps 00:06:02 and then inferring
Fixed typos in transcript:
Just generally speaking, what can I do with this sheaf-theoretic data structure that I've got? Okay, [I'll] remind you what is a sheaf. A sheaf is something that allows me to translate between physical sources or physical realms of data [in the left diagram] and the data that are associated with those physical regions [in the right diagram]
So these [on the left] are various open sets [an example being] simplices in a [simplicial complex which is an example of a] topological space.
And these [on the right] are the data spaces and I'm able to make some translation between [the left and the right diagrams] by taking a look at restrictions of overlaps [a on the left] and inferring back to the union.
So that's what a sheaf is [regarding data structures]. It's something that allows me to make an inference, an inferential machine.
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