1. Fixing $\nu$ : As showed you in the meeting, we have so much fracturing in the sigma_sm = 2 map (due to noise). Therefore, to get the halo mass function right for large masses, we need to go to much lower $\nu$ values, but it would cause over-counting in mid-mass range. So, basically we may need to look at this figure only as a discriminator for \nu < -2.0 . Right ?


2. To find a rough a cut, for $\nu$, we can go back to our noise argument, the one we used in the text to roughly find a range for \nu before introducing the halo mass function. It is checking the ratio of the pdf for the pure-noise map and the mock maps (Figure 2 in the draft). If we again use the choose the 1/100 ratio , we find $\nu$ = -2.45 for map smoothed with sigma_sm = 2 cMpc/h.

3. After fixing \nu, we use the same method to constrain the \kappa, i.e. minimizing the error in M_tomo. The dashed line roughly shows the \kappa which we get the same error as we got in the maps smoothed with sigma_sm = 4 cMpc/h, i.e. 0.45 dex. With the same argument we brought in the text, one would not go to more significant \kappa values since we loose more structures. So, we fix \kappa = -3.0.

4. The new parameter set (-2.45,-3.0) slightly differ from what we chose previously (-2.75,-3.25), but I will show the conclusion does not change in the next step:

5. Now, we look into the M_desc vs M_tomo plot. It is basically the same as the figure we have in the draft. It shows the majority of the new watersheds are significant, but it is too noisy. So, we find the same thing as before and it seems the exact choice of \nu and \kappa does not matter much.