Dear Fulvio and others,
I do not understand this whole discussion. In case of perfectly twinned crystals, it is impossible to derive a detwinned F1 and F2 from two independent, but otherwise identical measurements. In this case, the only signal is noise, and one could as well use a random generator to get the detwinned data. It makes perfectly sense to me that in this case the theoretical error would be infinite. In practical terms, since in case of twinning intensities and not structure factors are added, the error cannot be larger than twice the largest of the two measurements plus twice the error for that measurement. There might be a formula to properly calculate this error.
My 2 cents,
Herman
-----Ursprüngliche Nachricht-----
Von: CCP4 bulletin board [mailto:[log in to unmask]] Im Auftrag von Jens Kaiser
Gesendet: Donnerstag, 7. November 2013 08:29
An: [log in to unmask]
Betreff: Re: [ccp4bb] [ccp4bb] AW: [ccp4bb] uncertainites associated with intensities from twinned crystals; Sorry for HTML.
Tassos,
I'm no expert either, and there are caveats for using this formula on correlated magnitudes. But I would assume that the intensities of twin related reflections should be independent from each other (that's my understanding of the sigmoid cumulative intensity distribution of twins). Thus, I think the simple Gaussian error propagation should be applicable to uncertainty estimates in detwinned intensities.
Cheers,
Jens
On Thu, 2013-11-07 at 08:09 +0100, Anastassis Perrakis wrote:
> Dear Jens,
>
>
> That formula for error propagation is correct for independent
> measurements.
> Does this assumption stand true for Intensities in twinning? I am no
> expert, but I would think not.
>
>
> Tassos
>
> On 7 Nov 2013, at 7:53, Jens Kaiser wrote:
>
> > Fulvio, Tim,
> > error propagation is correct, but wrongly applied in Tim's
> > example.
> > s_f= \sqrt{ \left(\frac{\partial f}{\partial {x} }\right)^2 s_x^2 +
> > \left(\frac{\partial f}{\partial {y} }\right)^2 s_y^2 +
> > \left(\frac{\partial f}{\partial {z} }\right)^2 s_z^2 + ...} (see
> > http://en.wikipedia.org/wiki/Propagation_of_uncertainty#Simplificati
> > on) The uncertainty in a derived magnitude is always larger than any
> > individual uncertainty, so no subtraction, anytime. Furthermore, in
> > Tim's example you could end up with negative sigmas..
> >
> > HTH,
> >
> > Jens
> >
> >
> > On Thu, 2013-11-07 at 04:44 +0100, Tim Gruene wrote:
> > > Dear Fulvio,
> > >
> > > with simple error propagation, the error would be
> > > sigma(I(h1)) = (1-α)sigma(Iobs(h1))-α*sigma(Iobs(h2))/(1-2α)
> > >
> > > would it not?
> > >
> > > Although especially for theoretical aspects you should be
> > > concerned about division by zero.
> > >
> > > Best,
> > > Tim
> > >
> > > On 11/06/2013 05:54 PM, Fulvio Saccoccia wrote:
> > > > Thank you for reply. My question mostly concern a theoretical
> > > > aspect rather than practical one. To be not misunderstood, what
> > > > is the mathematical model that one should apply to be able to
> > > > deal with twinned intensities with their errors? I mean,
> > > > I+_what? I ask this In order to state some general consideration
> > > > on the accuracy about the recovery the true intensities on
> > > > varying of alpha. Thanks Fulvio
> > > >
> > > > Fulvio Saccoccia PhD Dept. of Biochemical Sciences Sapienza
> > > > University of Rome 5, Piazzale A. Moro 00185 phone +39
> > > > 0649910556
> > > >
> > > > ----Messaggio Originale---- Da: [log in to unmask]
> > > > Inviato: 06/11/2013, 17:25 A: [log in to unmask] Oggetto:
> > > > [ccp4bb] AW: [ccp4bb] uncertainites associated with intensities
> > > > from twinned crystals
> > > >
> > > >
> > > > Dear Fulvio, you cannot detwin perfectly twinned data with this
> > > > formula. The term (1-2α) becomes zero, so you are dividing by zero.
> > > > With good refinement programs (ShelX, Refmac), refinement is
> > > > done against twinned data, which is better than to detwin the
> > > > data with the formula you mention.
> > > >
> > > > As I understand it, to get map coefficients, the calculated
> > > > contribution of the twin domain (Fcalc’s) is substracted from
> > > > Fobs (with the appropriate weighting factors), so what you see
> > > > in coot is detwinned electron density. In practical terms, the
> > > > only thing you have to do is to specify the TWIN keyword in Refmac.
> > > >
> > > > Best regards, Herman
> > > >
> > > >
> > > >
> > > > Von: CCP4 bulletin board [mailto:[log in to unmask]] Im
> > > > Auftrag von Fulvio Saccoccia Gesendet: Mittwoch, 6. November 2013 16:58 An:
> > > > [log in to unmask] Betreff: [ccp4bb] uncertainites associated
> > > > with intensities from twinned crystals
> > > >
> > > >
> > > > Dear ccp4 users
> > > >
> > > > a question about the recovering of true intensities from
> > > > merohedral twinned crystal. Providing alpha and the twin
> > > > operator one should be able to recover the intensities from the formulas:
> > > >
> > > >
> > > >
> > > > I(h1) = (1-α)Iobs(h1)-αIobs(h2)/(1-2α)
> > > >
> > > > I(h2) = -αIobs(h1)+(1+α)Iobs(h2)/(1-2α)
> > > >
> > > > as stated in many papers and books*.
> > > >
> > > > However I was wondering about the uncertainties associated to
> > > > these measurements, I mean: for all physical observable an
> > > > uncertainty should be given.
> > > >
> > > > Hence, what is the uncertainty associated to a perfect
> > > > merohedrally twinned crystal (alpha=0.5)? It is clear that in
> > > > this case we drop in a singular value of the above formulas.
> > > >
> > > > Please, let me know your hints or your concerns on the matter.
> > > > Probably there is something that it is not so clear to me.
> > > >
> > > >
> > > >
> > > > Thanks in advance
> > > >
> > > >
> > > >
> > > > Fulvio
> > > >
> > > >
> > > >
> > > >
> > > >
> > > > ref. **(C. Giacovazzo, H. L. Monaco, G. Artioli, D. Viterbo, M.
> > > > Milaneso, G. Ferraris, G. Gilli, P. Gilli, G. Zanotti and M. Catti.
> > > > Fundamentals of Crystallography, 3rd edition. IUCr Texts on
> > > > Crystallography No. 15, IUCr/Oxford University Press, 2011;
> > > > Chandra, N., Acharya, K. R., Moody, P. C. (1999). Acta Cryst. D55.
> > > > 1750-1758)
> > > >
> > > > --
> > > >
> > > > Fulvio Saccoccia, PhD
> > > >
> > > > Dept. of Biochemical Sciences "A. Rossi Fanelli"
> > > >
> > > > Sapienza University of Rome
> > > >
> > > > Tel. +39 0649910556
> > > >
> > >
> >
> >
>
>
