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CCP4BB  February 2020

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Subject:

AW: [ccp4bb] [3dem] Which resolution?

From:

Jon Hughes <[log in to unmask]>

Reply-To:

Jon Hughes <[log in to unmask]>

Date:

Sun, 23 Feb 2020 22:37:22 +0100

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absolutely.
jon

-----Ursprüngliche Nachricht-----
Von: CCP4 bulletin board <[log in to unmask]> Im Auftrag von Gerard Bricogne
Gesendet: Sonntag, 23. Februar 2020 20:42
An: [log in to unmask]
Betreff: Re: [ccp4bb] [3dem] Which resolution?

Gentlemen,

     Please consider for a moment that by such intemperate language and tone, you are making a topic of fundamental importance to both the MX and the EM communities into a no-go area. This cannot be good for anyone's reputation nor for the two fields in general. It has to be possible to discuss the topic of "resolution" in a dispassionate way, so as to jointly gain an improved and shared understanding of the matter, without feeling implicitly under pressure to support one side or the other. An acrimonious dispute like this one can only be putting people off getting involved in the discussion, which is exactly the opposite of what a thread on a scientific bulletin board should be doing.


     With best wishes,

          Gerard.

--
On Sun, Feb 23, 2020 at 08:15:34AM -0300, Marin van Heel wrote:
> Hi Carlos Oscar and Jose-Maria,
> 
> I choose to answer you guys first, because it will take little of my 
> time to counter your criticism and because I have long since been less 
> than amused by your published, ill-conceived criticism:
> 
> “*Marin, I always suffer with your reference to sloppy statistics. If 
> we take your paper of 2005 where the 1/2 bit criterion was proposed, 
> Eqs. 4 to
> 15 have completely ignored the fact that you are dealing with Fourier 
> components, that are complex numbers, and consequently you have to 
> deal with random variables that have TWO components, which moreover 
> the real and imaginary part are not independent and, in their turn, 
> they are not independent of the nearby Fourier coefficients so that 
> for computing radial averages you would need to account for the correlation among coefficients*”
> 
> I had seen this argumentation against our (2005) paper in your 
> manuscript/paper years back. I was so stunned by the level of 
> misunderstanding expressed in your manuscript that I chose not to 
> spend any time reacting to those statements. Now that you choose to so 
> openly display your thoughts on the matter, I have no other choice 
> than to spell out your errors in public.
> 
> 
> 
> All complex arrays in our 2005 paper are Hermitian (since they are the 
> FTs of real data), and so are all their inner products. In all the 
> integrals over rings one always averages a complex Fourier-space voxel 
> with its Hermitian conjugate yielding *ONE* real value (times two)!  
> Without that Hermitian property, FRCs and FSCs, which are real 
> normalised correlation functions would not even have been possible. I 
> was - and still am - stunned by this level of misunderstanding!
> 
> 
> 
> This is a blatant blunder that you are propagating over years, a 
> blunder that does not do any good to your reputation, yet also a 
> blunder that has probably damaged to our research income. The fact 
> that you can divulgate such rubbish and leave it out there for years 
> for referees to read (who are possibly not as well educated in physics 
> and mathematics) will do – and may already have done – damage to our 
> research.  An apology is appropriate but an apology is not enough.
> 
> 
> 
> Maybe you should ask your granting agencies how to transfer 25% of 
> your grant income to our research, in compensation of damages created 
> by your blunder!
> 
> 
> 
> Success with your request!
> 
> 
> 
> Marin
> 
> 
> 
> PS. You have also missed that our 2005 paper explicitly includes the 
> influence of the size of the object within the sampling box (your: 
> “*they are not independent of the nearby Fourier coefficients*”). I 
> remain flabbergasted.
> 
> On Fri, Feb 21, 2020 at 3:15 PM Carlos Oscar Sorzano 
> <[log in to unmask]>
> wrote:
> 
> > Dear all,
> >
> > I always try to refrain myself from getting into these discussions, 
> > but I cannot resist more the temptation. Here are some more ideas 
> > that I hope bring more light than confusion:
> >
> > - There must be some functional relationship between the FSC and the 
> > SNR, but the exact analytical form of this relationship is unknown 
> > (I suspect that it must be at least monotonic, the worse the SNR, 
> > the worse FSC; but even this is difficult to prove). The 
> > relationship we normally use
> > FSC=SNR/(1+SNR) was derived in a context that does not apply to 
> > CryoEM (1D stationary signals in real space; our molecules are not 
> > stationary), and consequently any reasoning of any threshold based 
> > on this relationship is incorrect (see our review).
> >
> > - Still, as long as we all use the same threshold, the reported 
> > resolutions are comparable to each other. In that regard, I am happy 
> > that we have set 0.143 (although any other number would have served 
> > the purpose) as the standard.
> >
> > - I totally agree with Steve that the full FSC is much more 
> > informative than its crossing with the threshold. Specially, because 
> > we should be much more worried about its behavior when it has high 
> > values than when it has low values. Before crossing the threshold it 
> > should be as high as possible, and that is the "true measure" of 
> > goodness of the map. When it crosses the threshold of 0.143, it has 
> > too low SNR, and by definition, that is a very unstable part of the 
> > FSC, resulting in relatively unstable reports of resolution. We made 
> > some tests about the variability of the FSC (refining random splits 
> > of the dataset), trying to put the error bars that Steve was asking 
> > for, and it turned out to be pretty reproducible (rather low 
> > variance except in the region when it crosses the threshold) as long as the dataset was large enough (which is the current state).
> >
> > - @Marin, I always suffer with your reference to sloppy statistics. 
> > If we take your paper of 2005 where the 1/2 bit criterion was 
> > proposed ( 
> > https://www.sciencedirect.com/science/article/pii/S1047847705001292)
> > , Eqs. 4 to 15 have completely ignored the fact that you are dealing 
> > with Fourier components, that are complex numbers, and consequently 
> > you have to deal with random variables that have two components, 
> > which moreover the real and imaginary part are not independent and, 
> > in their turn, they are not independent of the nearby Fourier 
> > coefficients so that for computing radial averages you would need to 
> > account for the correlation among coefficients ( 
> > https://www.aimspress.com/fileOther/PDF/biophysics/20150102.pdf). 
> > For properly dealing the statistics, at least one needs to carry out 
> > a two-dimensional reasoning, including the complex conjugate 
> > multiplication which is all missing in your derivation, rather than 
> > treating everything as one-dimensional, real valued random 
> > variables. Additionally, embedded in your whole reasoning is the 
> > idea that the expected value of a ratio is the ratio of the expected 
> > values, that is a 0-th order Taylor approximation of the mean of the distribution of a ratio between two random variables.
> > Finally, I always find an extreme difficulty to understand the 1 bit 
> > or 1/2 bit criteria, that is, what is the relationship between the 
> > channel's capacity formula of Shannon (
> > https://en.wikipedia.org/wiki/Shannon%E2%80%93Hartley_theorem) and 
> > our FSC (we do not have any channel through which we are 
> > "transmitting" our volume, although it is true we have a model y=x+n 
> > that is the same as in signal transmission, it is not true that the 
> > average information of a signal is log2(1+SNR); for me, the only 
> > relationship is that the SNR appears in both formulas, FSC and 
> > channel capacity, but that does not automatically make them 
> > comparable and interchangeble). This is not a criticism on your 
> > work. I think the FSC is a very useful tool to measure some 
> > properties of the reconstruction process and the quality of the 
> > dataset (not everything is measured by the FSC) and it also has its 
> > drawbacks (for instance, systematic errors are rewarded by the FSC 
> > as they are reproducible in both halves). Moreover, I think you are 
> > an extremely intelligent person, who I consider a good friend, with 
> > a very good intuition about image processing and who has brought 
> > very interesting ideas and methodologies into the field. Only that 
> > we cannot become crazy about the FSC threshold and the reported resolution, as the most interesting part of the FSC is not when it is low, but when it is high.
> >
> > I hope I can keep refraining myself in the future :-)
> >
> > Cheers, Carlos Oscar
> >
> > On 2/21/20 6:19 PM, Ludtke, Steven J. wrote:
> >
> > I've been steadfastly refusing to get myself dragged in this time, 
> > but with this very sensible statement (which I am largely in 
> > agreement with), I thought I'd throw in one thought, just to stir the pot a little more.
> >
> > This is not a new idea, but I think it is the most sensible strategy 
> > I've heard proposed, and addresses Marin's concerns in a more conventional way.
> > What we are talking about here is the statistical noise present in 
> > the FSC curves themselves. Viewed from the framework of traditional 
> > error analysis and propagation of uncertainties, which pretty much 
> > every scientist should be familiar with since high-school, (and thus 
> > would not be confusing to the non statisticians)  the 'correct' 
> > solution to this issue is not to adjust the threshold, but to present FSC curves with error bars.
> >
> > One can then use a fixed threshold at a level based on expectation 
> > values, and simply produce a resolution value which also has an 
> > associated uncertainty. This is much better than using a variable 
> > threshold and still producing a single number with no uncertainty 
> > estimate!  Not only does this approach account for the statistical 
> > noise in the FSC curve, but it also should stop people from 
> > reporting resolutions as 2.3397 Å, as it would be silly to say 2.3397 +- 0.2.
> >
> > The cross terms are not ignored, but are used in the production of 
> > the error bars. This is a very simple approach, which is certainly 
> > closer to being correct than the fixed threshold without error-bars 
> > approach, and it solves many of the issues we have with resolution 
> > reporting people do.  Of course we still have people who will insist 
> > that 3.2+-0.2 is better than 3.3+-0.2, but there isn't much you can 
> > do about them... (other than beat them over the head with a statistics textbook).
> >
> > The caveat, of course, is that like all propagation of uncertainty 
> > that it is a linear approximation, and the correlation axis isn't 
> > linear, so the typical Normal distributions with linear propagation 
> > used to justify propagation of uncertainty aren't _strictly_ true. 
> > However, the approximation is fine as long as the error bars are 
> > reasonably small compared to the -1 to 1 range of the correlation 
> > axis. Each individual error bar is computed around its expectation 
> > value, so the overall nonlinearity of the correlation isn't a concern.
> >
> >
> >
> >
> > --------------------------------------------------------------------------------------
> > Steven Ludtke, Ph.D. <[log in to unmask]>                      Baylor
> > College of Medicine
> > Charles C. Bell Jr., Professor of Structural Biology
> > Dept. of Biochemistry and Molecular Biology                      (
> > www.bcm.edu/biochem)
> > Academic Director, CryoEM Core                                        (
> > cryoem.bcm.edu)
> > Co-Director CIBR Center                                    (
> > www.bcm.edu/research/cibr)
> >
> >
> >
> > On Feb 21, 2020, at 10:34 AM, Alexis Rohou <[log in to unmask]> wrote:
> >
> > ****CAUTION:*** This email is not from a BCM Source. Only click 
> > links or open attachments you know are safe.*
> > ------------------------------
> > Hi all,
> >
> > For those bewildered by Marin's insistence that everyone's been 
> > messing up their stats since the bronze age, I'd like to offer what 
> > my understanding of the situation. More details in this thread from 
> > a few years ago on the exact same topic:
> > https://mail.ncmir.ucsd.edu/pipermail/3dem/2015-August/003939.html
> > <https://urldefense.proofpoint.com/v2/url?u=https-3A__mail.ncmir.ucs
> > d.edu_pipermail_3dem_2015-2DAugust_003939.html&d=DwMFaQ&c=ZQs-KZ8oxE
> > w0p81sqgiaRA&r=Dk5VoQQ-wINYVssLMZihyC5Dj_sWYKxCyKz9E4Lp3gc&m=UWn2RUC
> > MENrXjn3JLSwlIU6Zmp_JYnRrXesjtsM1u2E&s=CZ3YcAV1LVKXsLT0KjCIRby6j3XPA
> > 6GqZcOVP3nMyK0&e=> 
> > https://mail.ncmir.ucsd.edu/pipermail/3dem/2015-August/003944.html
> > <https://urldefense.proofpoint.com/v2/url?u=https-3A__mail.ncmir.ucs
> > d.edu_pipermail_3dem_2015-2DAugust_003944.html&d=DwMFaQ&c=ZQs-KZ8oxE
> > w0p81sqgiaRA&r=Dk5VoQQ-wINYVssLMZihyC5Dj_sWYKxCyKz9E4Lp3gc&m=UWn2RUC
> > MENrXjn3JLSwlIU6Zmp_JYnRrXesjtsM1u2E&s=oG6lGnei74jC5VVGsfFAdiTpIxrZh
> > s_IH2mH0re5QRM&e=>
> >
> > Notwithstanding notational problems (e.g. strict equations as 
> > opposed to approximation symbols, or omission of symbols to denote 
> > estimation), I believe Frank & Al-Ali and "descendent" papers (e.g. 
> > appendix of Rosenthal & Henderson 2003) are fine. The cross terms 
> > that Marin is agitated about indeed do in fact have an expectation 
> > value of 0.0 (in the ensemble; if the experiment were performed an 
> > infinite number of times with different realizations of noise). I 
> > don't believe Pawel or Jose Maria or any of the other authors really believe that the cross-terms are orthogonal.
> >
> > When N (the number of independent Fouier voxels in a shell) is large 
> > enough, mean(Signal x Noise) ~ 0.0 is only an approximation, but a 
> > pretty good one, even for a single FSC experiment. This is why, in 
> > my book, derivations that depend on Frank & Al-Ali are OK, under the 
> > strict assumption that N is large. Numerically, this becomes 
> > apparent when Marin's half-bit criterion is plotted - asymptotically 
> > it has the same behavior as a constant threshold.
> >
> > So, is Marin wrong to worry about this? No, I don't think so. There 
> > are indeed cases where the assumption of large N is broken. And 
> > under those circumstances, any fixed threshold (0.143, 0.5, whatever) is dangerous.
> > This is illustrated in figures of van Heel & Schatz (2005). Small 
> > boxes, high-symmetry, small objects in large boxes, and a number of 
> > other conditions can make fixed thresholds dangerous.
> >
> > It would indeed be better to use a non-fixed threshold. So why am I 
> > not using the 1/2-bit criterion in my own work? While numerically it 
> > behaves well at most resolution ranges, I was not convinced by 
> > Marin's derivation in 2005. Philosophically though, I think he's 
> > right - we should aim for FSC thresholds that are more robust to the kinds of edge cases mentioned above.
> > It would be the right thing to do.
> >
> > Hope this helps,
> > Alexis
> >
> >
> >
> > On Sun, Feb 16, 2020 at 9:00 AM Penczek, Pawel A < 
> > [log in to unmask]> wrote:
> >
> >> Marin,
> >>
> >> The statistics in 2010 review is fine. You may disagree with 
> >> assumptions, but I can assure you the “statistics” (as you call it) 
> >> is fine. Careful reading of the paper would reveal to you this much.
> >>
> >> Regards,
> >> Pawel
> >>
> >> On Feb 16, 2020, at 10:38 AM, Marin van Heel < 
> >> [log in to unmask]> wrote:
> >>
> >> 
> >>
> >> ***** EXTERNAL EMAIL *****
> >> Dear Pawel and All others ....
> >>
> >> This 2010 review is - unfortunately - largely based on the flawed 
> >> statistics I mentioned before, namely on the a priori assumption 
> >> that the inner product of a signal vector and a noise vector are 
> >> ZERO (an orthogonality assumption).  The (Frank & Al-Ali 1975) 
> >> paper we have refuted on a number of occasions (for example in 
> >> 2005, and most recently in our BioRxiv paper) but you still take 
> >> that as the correct relation between SNR and FRC (and you never cite the criticism...).
> >> Sorry
> >> Marin
> >>
> >> On Thu, Feb 13, 2020 at 10:42 AM Penczek, Pawel A < 
> >> [log in to unmask]> wrote:
> >>
> >>> Dear Teige,
> >>>
> >>> I am wondering whether you are familiar with
> >>>
> >>> Resolution measures in molecular electron microscopy.
> >>> Penczek PA. Methods Enzymol. 2010.
> >>> Citation
> >>>
> >>> Methods Enzymol. 2010;482:73-100. doi: 10.1016/S0076-6879(10)82003-8.
> >>>
> >>> You will find there answers to all questions you asked and much more.
> >>>
> >>> Regards,
> >>> Pawel Penczek
> >>>
> >>>
> >>> Regards,
> >>> Pawel
> >>> _______________________________________________
> >>> 3dem mailing list
> >>> [log in to unmask]
> >>> https://mail.ncmir.ucsd.edu/mailman/listinfo/3dem
> >>> <https://urldefense.proofpoint.com/v2/url?u=https-3A__mail.ncmir.u
> >>> csd.edu_mailman_listinfo_3dem&d=DwMFaQ&c=bKRySV-ouEg_AT-w2QWsTdd9X
> >>> __KYh9Eq2fdmQDVZgw&r=yEYHb4SF2vvMq3W-iluu41LlHcFadz4Ekzr3_bT4-qI&m
> >>> =3-TZcohYbZGHCQ7azF9_fgEJmssbBksaI7ESb0VIk1Y&s=XHMq9Q6Zwa69NL8kzFb
> >>> maLmZA9M33U01tBE6iAtQ140&e=>
> >>>
> >> _______________________________________________
> >> 3dem mailing list
> >> [log in to unmask]
> >> https://mail.ncmir.ucsd.edu/mailman/listinfo/3dem
> >> <https://urldefense.proofpoint.com/v2/url?u=https-3A__mail.ncmir.uc
> >> sd.edu_mailman_listinfo_3dem&d=DwMFaQ&c=ZQs-KZ8oxEw0p81sqgiaRA&r=Dk
> >> 5VoQQ-wINYVssLMZihyC5Dj_sWYKxCyKz9E4Lp3gc&m=UWn2RUCMENrXjn3JLSwlIU6
> >> Zmp_JYnRrXesjtsM1u2E&s=TeEhUNYC5v59HGWMrPQCMaGK5opuX-NIG2mJvGLuiKA&
> >> e=>
> >>
> > _______________________________________________
> > 3dem mailing list
> > [log in to unmask]
> >
> > https://urldefense.proofpoint.com/v2/url?u=https-3A__mail.ncmir.ucsd
> > .edu_mailman_listinfo_3dem&d=DwICAg&c=ZQs-KZ8oxEw0p81sqgiaRA&r=Dk5Vo
> > QQ-wINYVssLMZihyC5Dj_sWYKxCyKz9E4Lp3gc&m=UWn2RUCMENrXjn3JLSwlIU6Zmp_
> > JYnRrXesjtsM1u2E&s=TeEhUNYC5v59HGWMrPQCMaGK5opuX-NIG2mJvGLuiKA&e=
> >
> >
> >
> > _______________________________________________
> > 3dem mailing 
> > [log in to unmask]https://mail.ncmir.ucsd.edu/mailman/listinfo/
> > 3dem
> >
> >
> 
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