21–30 of 32 posts
I failed the class, but learned so many useful things.
I recently saw pictures of social distancing circles drawn on the grass in parks [1]. They were drawn in a square grid. It would be more space-efficient to draw them in a hexagonal packing arrangement. [1] example: https://images.foxtv.com/static.ktvu.com/www.ktvu.com/conten...
I don't think space efficiency is a goal
I recently saw pictures of social distancing circles drawn on the grass in parks [1]. They were drawn in a square grid. It would be more space-efficient to draw them in a hexagonal packing arrangement. [1] example: https://images.foxtv.com/static.ktvu.com/www.ktvu.com/conten...
I don't think space efficiency is a goal
However, in the context of social distancing, 2m is a guideline, but additional distance will reduce your risk more. You can flip the question on its head and ask, if I used larger circles (such as 3m or 4m), is there an arrangement I could use to still fit the people into the area? If so, then using this arrangement should reduce risk further than using an arrangement that can only accommodate 2m circles.
In other words, even if you are below max capacity and meeting the 2m minimum, different arrangements still have different levels of risk of transmission.
Of course, at low enough densities, the gain becomes negligible.
Earlier quoted context omitted.
I don't think space efficiency is a goal
Indeed. Having lots of space between the circles is a better goal, as that way people in motion also maintain distance.
Sphere packings are quite a deep and fascinating area of pure mathemaics. It has close relations to coding theory, lattice theory, number theory, modular forms. John Conway [1] (who recently passed away due to COVID) wrote a famous book about it: Sphere Packings, Lattices and Groups -- which summarizes the subject concisely. A recent (2017) break through, was the proof that the Leech Lattice [2] yields the optimal sp…
Our of curiosity and as a noob to coding theory, what makes a Binary Golay code more useful than say a RS Code or something else more common? The linked wiki article said that given 12 bits, the BG code can encode them as 24 bits with the ability to correct up to 3 bit errors and detect up to 7. If I'm understanding RS codes correctly, an RS code with 12 data and 12 parity bits would be able to correct up to 6 bit er…
> By adding t check symbols to the data, a Reed–Solomon code can detect (but not correct) any combination of up to and including t erroneous symbols, OR locate and correct up to and including ⌊t/2⌋ erroneous symbols at unknown locations
So it looks like you would have to choose between, either:
A) correcting 6 bits OR
B) detecting 12 bit errors.
[1] https://en.wikipedia.org/wiki/Reed%E2%80%93Solomon_error_cor...
Circle packing is one of my favorite applications to display hierarchical data where one dimension defines the radius, like the file size. Other dimensions may alter color or line width. Circle packing is available as an example in D3, highly recommended. https://observablehq.com/@d3/zoomable-circle-packing
So if you have 2 circles depicting files, and one of the files is 3x the size of the other, its circle will have 9x the area and appear 9x larger.
Earlier quoted context omitted.
Our of curiosity and as a noob to coding theory, what makes a Binary Golay code more useful than say a RS Code or something else more common? The linked wiki article said that given 12 bits, the BG code can encode them as 24 bits with the ability to correct up to 3 bit errors and detect up to 7. If I'm understanding RS codes correctly, an RS code with 12 data and 12 parity bits would be able to correct up to 6 bit er…
I am no expert either, but I just checked Wikipedia on Reed-Solomon codes [1]: > By adding t check symbols to the data, a Reed–Solomon code can detect (but not correct) any combination of up to and including t erroneous symbols, OR locate and correct up to and including ⌊t/2⌋ erroneous symbols at unknown locations So it looks like you would have to choose between, either: A) correcting 6 bits OR B) detecting 12 bit e…
if the number of corrupted bits is no more than six, you can reconstruct the original message
if the number of corrupted bits is between 6 and 12, you will detect the corruption
if the number of corrupted bits is larger than 12, you may or may not detect the corruption.
Sphere packings are quite a deep and fascinating area of pure mathemaics. It has close relations to coding theory, lattice theory, number theory, modular forms. John Conway [1] (who recently passed away due to COVID) wrote a famous book about it: Sphere Packings, Lattices and Groups -- which summarizes the subject concisely. A recent (2017) break through, was the proof that the Leech Lattice [2] yields the optimal sp…
Our of curiosity and as a noob to coding theory, what makes a Binary Golay code more useful than say a RS Code or something else more common? The linked wiki article said that given 12 bits, the BG code can encode them as 24 bits with the ability to correct up to 3 bit errors and detect up to 7. If I'm understanding RS codes correctly, an RS code with 12 data and 12 parity bits would be able to correct up to 6 bit er…
Circle packing is one of my favorite applications to display hierarchical data where one dimension defines the radius, like the file size. Other dimensions may alter color or line width. Circle packing is available as an example in D3, highly recommended. https://observablehq.com/@d3/zoomable-circle-packing
Also ported d3s circle packing algorithm to C++ for compilation to WASM
https://github.com/tomlagier/circle-pack
Definitely love how that visualization turns out!
Sphere packings are quite a deep and fascinating area of pure mathemaics. It has close relations to coding theory, lattice theory, number theory, modular forms. John Conway [1] (who recently passed away due to COVID) wrote a famous book about it: Sphere Packings, Lattices and Groups -- which summarizes the subject concisely. A recent (2017) break through, was the proof that the Leech Lattice [2] yields the optimal sp…
I didn't realize he died from COVID complications. That just makes it all the worse.