expand the conclusion with the last suggested change of reviewer vH7P

Author: durandg12

algo-curve.qmd

@@ -1245,13 +1245,13 @@ Finally, comparing scenarios 3 & 4 with scenarios 1 & 2, we see that multiplying
 
 # Conclusion {#sec-conclusion}
 
-In conclusion, we effectively introduced a new algorithm to compute a curve of confidence upper bounds, much faster than the previous alternative, with one power of $m$ less in the complexity.
+In conclusion, we effectively introduced a new algorithm to compute a curve of confidence upper bounds for the false discoveries, or, equivalently, for the FDP, that is much faster than the previous alternative, with one power of $m$ less in the complexity. This algorithm can be applied as soon as the confidence upper bound is built according to the JER framework, when the reference family exhibit a forest structure.
 
-To develop new confidence upper bounds methodology and test them on simulations, it was previously not conceivable to replicate experiments a sufficient number of times while computing whole curves. For instance, in the simulation study of @MR4178188, the number of replications chosen was 10 and the whole curve was not computed, only ten values along the curve were computed, for an `m` set to 12800, that is 0.078% of the curve had been computed. Now, simulation studies with an adequate number of replications and 100% of the curve become feasible.
+To develop new confidence upper bound methods and test them on simulations, it was previously not conceivable to replicate experiments a sufficient number of times while computing whole curves. For instance, in the simulation study of @MR4178188, the number of replications chosen was 10 and the whole curve was not computed, only ten values along the curve were computed, for an `m` set to 12800, that is 0.078% of the curve had been computed. Now, simulation studies with an adequate number of replications and 100% of the curve become feasible.
 
 A lot of work remains to be done on the `sanssouci` package. For example, to make the data format of a forest structure $(R_k)_{k\in\cK}$ less convoluted and more user-friendly is an interesting project. Another one would be to implement inside the package the methods of the paper @blain22notip, which are currently only available in the Python language [@10.5555/1593511], and the methods of the paper @JMLR:v25:23-1025.
 
-Other current works include the development of new reference families with theoretical JER control that could better account for realistic models, such as models with dependence between the $p$-values, see for example @perrot2023selective, or models with discreteness.
+Other current works include the development of new reference families with theoretically proven JER control that could better account for realistic models, such as models with dependence between the $p$-values, see for example @perrot2023selective, or models with discreteness.
 
 # Proofs {#sec-proofs}