Timeline for Weak submodularity for consecutive indices
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
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| Oct 25, 2020 at 16:21 | comment | added | Charles Pehlivanian | Apologies, you are right on all counts. I replayed everything by hand the calculations are all easily reproducible. Thanks again. | |
| Oct 25, 2020 at 2:23 | vote | accept | Charles Pehlivanian | ||
| Oct 25, 2020 at 2:16 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Oct 25, 2020 at 2:16 | comment | added | Iosif Pinelis | @CharlesPehlivanian : Why are saying this? The substitution R3->R2 was made into dif, which latter is the difference between the left- and right-hand sides of (2). See the pdf image of the updated Mathematica notebook at u.pcloud.link/publink/… . I have now also rechecked (3) manually -- took me 5 or 10 minutes. | |
| Oct 25, 2020 at 0:39 | comment | added | Iosif Pinelis | @CharlesPehlivanian : I did the routine algebraic calculations with Mathematica, rather than by hand; see the pdf image of the Mathematica notebook at u.pcloud.link/publink/… I think these calculations are doable by hand. Otherwise, you can use Mathematica or any other commercial or freely available computer algebra system to check the calculations. | |
| Oct 24, 2020 at 17:26 | vote | accept | Charles Pehlivanian | ||
| Oct 24, 2020 at 17:26 | |||||
| Oct 24, 2020 at 17:17 | comment | added | Charles Pehlivanian | Sorry, how do you get to $\frac{\left(R_1-R_2\right){}^2 t_1^2 t_3}{\left(t_1+t_2\right) \left(t_1+t_2+t_3\right)}\ge0,$ with $R_2 = R_3$? | |
| Oct 21, 2020 at 17:16 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Oct 21, 2020 at 17:12 | comment | added | Iosif Pinelis | I took the derivative in $R_3$, as I wrote, and it is manifestly $\ge0$ when expressed in terms of $R_j$' s (and $t_j$'s). | |
| Oct 21, 2020 at 16:19 | vote | accept | Charles Pehlivanian | ||
| Oct 24, 2020 at 17:19 | |||||
| Oct 21, 2020 at 16:19 | comment | added | Charles Pehlivanian | Yes, $F(\emptyset) = 0$ can be assumed, thanks. So $F$ is submodular for intervals but not in general. "...that the derivative in $s_3$..." maybe?, otherwise it's messy. | |
| Oct 21, 2020 at 15:54 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Oct 21, 2020 at 14:14 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Oct 21, 2020 at 13:53 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Oct 21, 2020 at 13:36 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Oct 21, 2020 at 13:30 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Oct 21, 2020 at 13:22 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |