Timeline for Approximate homology of a large simplicial complex
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 1, 2018 at 21:08 | comment | added | alesia | web.math.ku.dk/~moller/students/brian_brost.pdf seems to have a good state of the art (section 7) | |
| Dec 1, 2018 at 20:21 | comment | added | apg | Do you recommend a reference I can read? | |
| Dec 1, 2018 at 19:03 | comment | added | alesia | yes, that's right | |
| Dec 1, 2018 at 18:55 | comment | added | apg | So you get the exact Betti numbers? And it can work on rapidly expanding complexes? Just there is no guarantee it will reduce the computation time effectively. | |
| Dec 1, 2018 at 18:00 | comment | added | alesia | Actually the volume condition I was mentioning was for a different algorithm that approximates Betti numbers. It shouldn't affect the complex reduction algorithms | |
| Dec 1, 2018 at 17:45 | comment | added | apg | So it may not have too much of an effect, if for example the volume expands from a point rapidly | |
| Dec 1, 2018 at 17:19 | comment | added | alesia | yes, these methods reduce the size of the complex without changing the Betti numbers. They are heuristics though, so it's hard to predict how well they will work on a given example. | |
| Dec 1, 2018 at 13:25 | comment | added | apg | So you can reduce the computation time, without losing information? Like lossless compression? | |
| Nov 28, 2018 at 18:55 | comment | added | alesia | Those reduction methods typically won't change the homotopy type, so they'll give you exact Betti numbers in fact | |
| Nov 28, 2018 at 17:41 | vote | accept | apg | ||
| Nov 28, 2018 at 17:41 | comment | added | apg | OK I will look at this "lossy compression" idea. | |
| Nov 28, 2018 at 2:32 | history | edited | alesia | CC BY-SA 4.0 |
added 16 characters in body
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| Nov 28, 2018 at 1:36 | history | answered | alesia | CC BY-SA 4.0 |