Hi Boud,
I put these comments also on shape-univ to stimulate discussion
1) if I understand correctly these functions have nothing to do with the
circles on sky right ?
Me :: 17:16:36
2) these corr. fn. should measure the cross-talk between different angular
scales pesent in the multiply connected univ, but absent in the simply
connected univ. is that right ?
Me :: 17:18:23
3) the fig 1. is still not clear to me. what is the choice of the points you
selected ? seems to me that you focus on scale x1x2 but e.g x1,g14 defines a
different scale is that true ?
Me :: 17:19:30
ad2) absent under GRF (gaussian random field) hypothesis
Me :: 18:57:42
do I understand right that the correction to the corr. fn. due to topology
comes only from the extra correlations from various ang. scales only when at
least one point is fixed at a circle ? then the extra correlation signal
comes from the matched pixel in the matched circle seen at totally different
angle relative to the second direction in the corr. fn. is that right ? in
that case you're looking for an extremly small signal
Me :: 19:00:21
because in case of all other correlations in a corr. fn. calculated for the
hypothesized PDS model, when none of the directions is fixed at some matched
circle any possible images are currently not accessible in the SLS.
Me :: 19:01:17
if this is the case then I don't userstand why you get such a huge discrepancy
between the SCU model and the PDS model
Me :: 19:05:22
-----------------------
above was from gg.
cont. below.
to be honest the paper is rather unclear. I'd propose make lots of wording
changes regarding statistics of CMB field, and regarding maps details.
but this isn't very important at the moment except that it makes for me things
harder to understand.
the paper focus on 3 quite independent points:
1)putting error bars and CLs onto S statistics of the RLCMB04
2) shows again the phase relation
3) does the corr. fn. test
as for (1) I see you haven't change the analysis at since our last talk on
this, so I have the same objections to it as the last time. If you want
corrected GRF simulations of WMAP 3 yr I'm happy to contribute this way.
(these however will not be suitable for Tegmark's map)
(I can easily generate also WMAP1 maps if you like)
basically one simulation should be enough and then you could get your
distributions by calculating S on maps rotated by an 3 random Euler angles,
but for the same orientation of the PDS model.
I disagree (mostly) with the analysis given in sec. amplitude ;(
If you can find "anything" your results is meaningless, and you need change
the approach. btw. do you know that there are the Steven Hawking's initials
in the WMAP data ? does it mean anything ? (sort of close to the galactic
plane and at around l = 50 or so :))
the assessment of the CLs on the fig.2 is not very clear or convincing and
transparent. btw. I'd like to see also -1, -2, -3 sigma contours.
I understand that you get the CDF error function for S stat. but in that case
you should plot S stat. of the WMAP data, not S for individual pairs. I'd
like to see this one too.
if you resolve 3 sigma contour, this means that you need to probe at least
something like 1000 random circles for each alpha, is that right ?
as for (2)
IMHO the phase analysis is very relevant to the amplitude analysis.
However it's already included into S analysis. S has all the info. about the
model that is need. if you'd calculate the S err. fn. from RGF sim. rotated
1000 or 10000 times randomly for the same PDS you'd have it all right IMHO.
In fact showing the S vs phase does not carry any additional information about
the likelihood of the RLCMB04 result.
(of course the best thing to do would be to have 10^4 sims. to assess the
errors but probably it'd be enough to use only Nsim= #of rot./ effective
number of pixels in the 2deg FWHM smoothed maps or so)
as for (3)
the corr. fn. part I'm not sure If full understand so will wait for your
comments and explanations.
pozdr.
Bartek