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Carnival of Mathematics #197 – Math ∩ Programming

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Welcome to 197 Carnival of Mathematics!

197 is an inappropriate number, as can be seen from the Wikipedia page Who currently says he has “Indistinguishable, excessive, Or Irrelevant Examples. “Some pervert. It is also a Repfigit, That is, if you start a Fibonacci sequence with the digits 1, 9, 7, and then continue with , Then 197 appears in sequence. indeed: 1, 9, 7, 17, 33, 57, 107, 197,…

Untie the knot

Kennan Crane et al have introduced a new paper that can dissolve tangled curves quickly, and can do things like create Hilbert-type space-fill curves on surfaces. It’s a long thread with lots of links to videos and reading materials, covering energy functions, functional analysis, Sobolev methods and a custom internal product.

Folding triangular equilateral triangles

Dave Richson presents an orderly technique for folding equilateral triangles using paper only and no measurements. Answers in the thread show the geometric series converging to the correct angle of 60 degrees.

Shots were fired at UMAP and t-SNE

Lior Pechter et al. Learn what structure types are maintained by dimensional reduction techniques like UMAP (which I also used in a previous article) by comparing against a genomic data set with an understandable structure. They make some big claims about how UMAP and t-SNE destroy an important structure, and they show how to invent the dimension reduction plot so that it looks like an elephant even when there is no elephant structure in the data.

I’m not an expert, but perhaps the best case scenario for UMAP enthusiasts would be that their analysis only applies when you go from very high dimensions to 2 just so you can draw a picture. But if you stop, say,  sqrt n Dimensions, you may still retain much of the significant structure. Either way, they make a compelling pitch for Johnson-Lindenstrauss’ random linear reductions, which I also covered here. Their paper Found in biorXiv.

Study the strainer

Ben Peters Jones took on Grant Sanderson’s mathematical video challenge and released a series of videos exploring the Strait of Erotostans.

Additional submissions

Be sure to submit fun math you will find in September to The next caravan Moderator!

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