by Olivier Lévêque -
Number of replies: 1

Dear all,

Tomorrow, you will receive your project grades: the max for the project is 50 points (same as for the midterm), but some of you (the nearly ex-aequo winners of the competition) receive a +10 points bonus. Besides, no team got below 40 points for the project, so please, do not worry too much about this!

Here is more detailed info, about the grading first: our more detailed evaluation criteria are:

- your answers to the 2 theoretical questions

- quality of the text and the graphs presented

- there was no coefficient beta in this study (or if you want, beta=1 is fixed: there is no choice)

- the Metropolis step can be optimized (which allows then to consider larger values of N in practice)

- the originality of initiatives taken by some of the groups

And here are more comments about the conclusions you were expected to reach:

- As many of you found out, there is not much difference between the performance of Metropolis / Houdayer / mixed Metropolis-Houdayer on the long run. What has been observed in general is that Houdayer gets to the equilibrium in less steps (but each step costs actually more...)

- Focusing now on the graph representing the overlap (after convergence and using Metropolis, say) with respect to the parameter r : observe first that nothing guarantees that the Metropolis algorithm will be able to reach the critical point r_c. The theoretical result says that as N grows large, recovery should be impossible beyond this critical point, but before this point, who knows? In particular, it is not true that the overlap should tend to 1 as soon as r<r_c. The optimal overlap will actually be increasing continuously from 0 to 1 as r decreases (and again, nothing guarantees that the Metropolis algo will reach this optimal curve). Some of the groups concluded on the contrary that the overlap tends to 0 as N increase, and this for all values of r. This is probably due to the fact that you did not increase (or did not increase enough) the number of Monte-Carlo steps as N increases, leading to a poorer performance of the algorithm, that needs more time to converge as N gets large.

That's it for the comments on the project; please recall the Q&A session at 10 AM this Wednesday in INM 10.

All the best,

Nicolas and Olivier