Timeline for Probability that a stick randomly broken in five places can form a tetrahedron
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 12, 2015 at 9:40 | comment | added | VividD | Any chance to buy more RAM? | |
| May 4, 2015 at 13:51 | comment | added | Sasha | @BenjaminDickman As I have already stated in the above comment on Apr. 25, the direct use of quadrature integration of $f(w)$ is bound to fail, because the integrand is discontinuous. I have implemented and attempted to run a hybrid-numeric approach, where $w_1$ is integrated out symbolically for fixed numeric remaining $w_i$. My attempted run of this crashed consuming over 40GB of ram. I have not attempted to rerun this until now. Therefore I did not have any good news updates to post. | |
| May 2, 2015 at 17:12 | comment | added | Benjamin Dickman | ... Still running??? | |
| Apr 5, 2014 at 22:37 | comment | added | Eckhard | Still running?${}$ | |
| Apr 25, 2013 at 9:56 | comment | added | achille hui | @Sasha What a pity, I also want to know more digits. In your way of computing the numerical integral, will it be easier to compute the contribution from the 7 permutations mentioned in leonbloy's update one by one? I suspect the lower probability for a permutation, the more problematic it will be for adaptive quadratures. | |
| Apr 25, 2013 at 4:27 | comment | added | Sasha | Yes, it still does. The function $f(w_1,\ldots,w_5)$ is discontinuous, therefore adaptive numerical quadrature methods run into trouble endlessly subdividing close the boundary. The call I quoted finished in 22 hours, but converged to only 2 significant digits of precision, which is less than what Monte-Carlo gave. I rerun the computation with different settings, which will hopefully improve the matter. Ultimately, I think one would need to resolve to hybrid symbolic-numeric approach, like integrate wrt last variable symbolically. | |
| Apr 25, 2013 at 4:20 | comment | added | Benjamin Dickman | It's still running? | |
| Apr 24, 2013 at 23:59 | history | bounty awarded | CommunityBot | ||
| S Apr 23, 2013 at 20:11 | history | answered | Sasha | CC BY-SA 3.0 | |
| S Apr 23, 2013 at 20:11 | history | made wiki | Post Made Community Wiki by Sasha |