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Dear Roman and Benjamin,
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<div class="">I don’t understand your comments about Friedel Symmetry. In my understanding, Friedel Symmetry is referring to the fact that any Fourier voxel (h,k,l) with values (AMP,PHA) has a Friedel-related voxel (-h,-k,-l) on the other side of the 3D Fourier
space, which is complex conjugated to the first one, meaning (AMP,-PHA). As this usually applies to Fourier space, most software packages only save one half of the Fourier volume, since the other half is anyway the same, except the complex conjugation. </div>
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<div class="">There are very rare cases, where Friedel symmetry does not uphold, such as in dynamical electron diffraction, but these are probably not what you refer to. </div>
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<div class="">So, what do you refer to by saying the below?</div>
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<div class="">Benjamin:</div>
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<blockquote type="cite" class="">3) Neither presentation seemed to reflect friedel symmetry. While your choice of cone axis could result in asymmetric sampling, I find this curious. Comments? </blockquote>
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<div class="">Roman:</div>
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<div class="">The cones are chosen such that they cover the whole Fourier Space but in opposite directions they are not necessarily exactly the same (there is no symmetry in the cone distribution). So the choice of cone angles is not symmetrical.</div>
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<div class="">Or, do you refer to another type of symmetry?</div>
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<div class="">Henning.</div>
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<div class=""><span class="Apple-style-span" style="color: rgb(102, 102, 153); font-family: 'Stone Sans SC ITC TT'; font-size: 11px; ">Henning Stahlberg, PhD</span></div>
<div class=""><font class="Apple-style-span" color="#666699" face="'Stone Sans SC ITC TT'" size="3"><span class="Apple-style-span" style="font-size: 11px; ">Prof. for Structural Biology, C-CINA, Biozentrum, University Basel</span></font></div>
<div class=""><font class="Apple-style-span" color="#666699" face="'Stone Sans SC ITC TT'" size="3"><span class="Apple-style-span" style="font-size: 11px; ">Mattenstrasse 26 | D-BSSE | WRO-1058 | CH-4058 Basel | Switzerland</span></font></div>
<div class=""><font class="Apple-style-span" color="#666699" face="'Stone Sans SC ITC TT'" size="3"><span class="Apple-style-span" style="font-size: 11px; "><a href="http://c-cina.org" class="">http://c-cina.org</a> | Tel. +41-61-387 32 62</span></font></div>
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<blockquote type="cite" class="">
<div class="">On Sep 7, 2015, at 11:30, <a href="mailto:R.I.Koning@lumc.nl" class="">
R.I.Koning@lumc.nl</a> wrote:</div>
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<div class="">Dear Benjamin,</div>
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<div class="">Different spatial sampling, including under sampling, is definitely an issue. I am not sure what you mean with concern, but it is something to keep in mind. You have to understand the limiting factor in the data and the measurements in order to
not over interpret any data. Doing concial FSC on tomographic data is definitely not a perfect “resolution” measurement criterion (is there is any). I would not put any emphasis on the actual values that originate from the individual cones. However, I hope
we showed that can be useful when one want to compare similar data or reconstruction techniques in a relative and qualitative manner.</div>
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<div class="">We did try other than 200 cones and this number is optimised for spatial distribution against signal to noise. </div>
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<div class="">Interesting though to scale the resolution relatively. I am not sure I understand what would be 1 then. It probably does not matter since the power is in the relative values anyway. Only maybe when one has a subtomogram average with more data
than from one tomogram the values might be somewhat more meaningful. </div>
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<div class="">I am not sure if I understand you last remark. The cones are chosen such that they cover the whole Fourier Space but in opposite directions they are not necessarily exactly the same (there is no symmetry in the cone distribution). So the choice
of cone angles is not symmetrical.</div>
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<div class=""><font class="Apple-style-span"><font class="Apple-style-span" face="Calibri">Best regards,</font></font></div>
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<div class=""><font class="Apple-style-span"><font class="Apple-style-span" face="Calibri">Roman</font></font></div>
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<b class=""><span lang="EN-US" style="font-size: 10pt; font-family: Arial, sans-serif; color: gray;" class="">Dr. R.I.Koning (Roman)<o:p class=""></o:p></span></b></div>
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<span style="font-weight:bold" class="">From: </span>Benjamin Himes <<a href="mailto:himes.benjamin@gmail.com" class="">himes.benjamin@gmail.com</a>><br class="">
<span style="font-weight:bold" class="">Date: </span>Sunday 6 September 2015 15:30<br class="">
<span style="font-weight:bold" class="">To: </span>Roman Koning <<a href="mailto:r.i.koning@lumc.nl" class="">r.i.koning@lumc.nl</a>><br class="">
<span style="font-weight:bold" class="">Cc: </span>"<a href="mailto:3dem@ncmir.ucsd.edu" class="">3dem@ncmir.ucsd.edu</a>" <<a href="mailto:3dem@ncmir.ucsd.edu" class="">3dem@ncmir.ucsd.edu</a>><br class="">
<span style="font-weight:bold" class="">Subject: </span>RE: [3dem] Anisotropic resolution<br class="">
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<div dir="ltr" class="">Dear Roman & Misha,</div>
<div dir="ltr" class="">Thank you both for pointing out your respective papers regarding the subdivision of Fourier space by shells & cones in order to estimate resolution anisotropy.</div>
<div dir="ltr" class="">Follow up questions:</div>
<div dir="ltr" class="">1) are you concerned with the effect of undersampling an already sparse transform (particularly in the case of the tomogram work?)</div>
<div dir="ltr" class="">Roman - you report use of 200 cones. Did you try other numbers, and what did you observe; I would guess the overall pattern to be very similar with different "resolution" values?</div>
<div dir="ltr" class="">2) both papers reference resolution comparing in either pixel^-1 or nm^-1. Depending on your answer to question 1, do you think this is appropriate, or would a relative measure (scale the highest to 1) perhaps be a better representation.</div>
<div dir="ltr" class="">3) Neither presentation seemed to reflect friedel symmetry. While your choice of cone axis could result in asymmetric sampling, I find this curious. Comments?
</div>
<div dir="ltr" class="">Thanks again! </div>
<div dir="ltr" class="">Benjamin Himes<br class="">
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<div dir="ltr" class="">Dear Benjamin,</div>
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<div dir="ltr" class="">We recently published a paper on how to measure the anisotropy in electron tomograms (<a href="http://www.ncbi.nlm.nih.gov/pubmed/25843950" class="">http://www.ncbi.nlm.nih.gov/pubmed/25843950</a>). Though we did not test this on subtomogram
averages it might be useful to have a look at the paper (in case you did not do that yet).</div>
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<div dir="ltr" class="">Best regards,</div>
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<div dir="ltr" class="">Roman</div>
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<div dir="ltr" class=""><b class="">Dr. R.I.Koning (Roman)</b></div>
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<div dir="ltr" class="">Department of Cell Biology, Leiden University Medical Center</div>
<div dir="ltr" class="">Postal Zone S1-P, P.O.Box 9600, 2300 RC Leiden, The Netherlands</div>
<div dir="ltr" class=""><b class="">visiting address</b>: Einthovenweg 20, Building 2, zone S1-P, room R-90-20</div>
<div dir="ltr" class=""><b class="">tel.</b> (31) 71 526 9296<b class=""> fax.</b><a href="tel:%28%2B31%29%2071%20526%208270" class=""> (+31) 71 526 8270</a><b class=""> mail.</b><a href="mailto:r.i.koning@lumc.nl" class=""> r.i.koning@lumc.nl</a><b class="">
web.</b><a href="http://electronmicroscopy.lumc.nl/" class=""> electronmicroscopy.lumc.nl</a></div>
<div class=""> <br class="webkit-block-placeholder">
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<div dir="ltr" class="">Netherlands Centre for Electron Nanoscopy, Institute Biology Leiden, Leiden University</div>
<div dir="ltr" class=""><b class="">visiting address:</b> Einsteinweg 55, 2333 RC Leiden, The Netherlands, room 05.11</div>
<div dir="ltr" class=""><b class="">tel.</b> (31) 71 527 1423<b class=""> mail.</b><a href="mailto:r.i.koning@biology.leidenuniv.nl" class=""> r.i.koning@biology.leidenuniv.nl</a><b class=""> web.</b><a href="http://www.necen.nl/" class=""> www.necen.nl</a></div>
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<div dir="ltr" class=""><b class="">From:</b> 3dem [mailto:<a href="mailto:3dem-bounces@ncmir.ucsd.edu" class="">3dem-bounces@ncmir.ucsd.edu</a>]<b class=""> On Behalf Of</b> Benjamin Himes<br class="">
<b class="">Sent:</b> maandag 24 augustus 2015 15:44<br class="">
<b class="">To:</b><a href="mailto:3dem@ncmir.ucsd.edu" class=""> 3dem@ncmir.ucsd.edu</a><br class="">
<b class="">Subject:</b> [3dem] Anisotropic resolution</div>
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<div dir="ltr" class="">Dear colleagues,</div>
<div dir="ltr" class="">I hate to stir the pot on the resolution discussion, however, I have a question regarding any progress on analyzing the anisotropy potentially present in a 3d em map.</div>
<div dir="ltr" class="">Aside from some discussion on 3d ssnr, particularly by P.P. and a recent paper on 3d covariance estimation from J.F. Has anybody tried to implement a concrete way of assessing this issue?</div>
<div dir="ltr" class="">I am particularly concerned with maps generated from subTomogram averaging and classification: even with an angular distribution that is well sampled, I am concerned about the fact that cumulative dose, and increased sample thickness
on tilting create a situation where the individual projections do not have equivalent SNR and therefore a simple plot of angular distributions would not accurately reflect the quality of the sampling in Fourier space.</div>
<div dir="ltr" class="">It seems a 3d SSNR might work, but the interpretation of such a plot, beyond its "potato" like quality, even in terms of the eigenvalues of the principle axes is not immediately clear to me.</div>
<div dir="ltr" class="">Many thanks,</div>
<div dir="ltr" class="">Benjamin Himes</div>
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