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Dear Jens,
thanks for setting this right.
Best,
Tim
On 11/07/2013 07:53 AM, 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: [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
>>>
>>
>
>
>
- --
- --
Dr Tim Gruene
Institut fuer anorganische Chemie
Tammannstr. 4
D-37077 Goettingen
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