Dear all,
thank you for your reply. I would summarize my concerns and opinions,
so
far:
1) for QTLS (non-merohedral twinning - non intersecting lattices) I think one
should consider the variables as independent and random and it is possible to
recover the true intensities of a unique lattice from the stronger diffracting
one (see for example Jenni & Ban, 2009, Acta D65, 101-111). Hence, the
quadratic formula (reported fomr Jens Kaiser) can be applied;
2) for TLS (merohedral twinning - perfectly overlapping spots) I think one
should not consider the two variable independent since they are related by
alpha (see the formulas I reported in my first message). In this case, I think
the right formula should be that reported by Tim Grune, that as far as I know
overestimates the true error but in this case the quadratic is not applicable.
Therefore, one would be prone to conclude that the uncertainties associated to
merohedral-twinned crystals are higher than regular crystals or non-merohedral
crystals. What's your opinion about?
In data mercoledì 6 novembre 2013 23:29:01, Jens Kaiser ha scritto:
> 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#Simplification)
> > > 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: herman.schreu...@sanofi.com
> > > > > Inviato: 06/11/2013, 17:25 A: CCP4BB@JISCMAIL.AC.UK 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:CCP4BB@JISCMAIL.AC.UK] Im Auftrag
> > > > > von Fulvio Saccoccia Gesendet: Mittwoch, 6. November 2013 16:58 An:
> > > > > CCP4BB@JISCMAIL.AC.UK 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
