Re: [ccp4bb] R: [ccp4bb] AW: [ccp4bb] uncertainites associated with intensities from twinned crystals; Sorry for HTML.
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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: 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
>>>
>>
>
>
>
- --
- --
Dr Tim Gruene
Institut fuer anorganische Chemie
Tammannstr. 4
D-37077 Goettingen
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Re: [ccp4bb] R: [ccp4bb] AW: [ccp4bb] uncertainites associated with intensities from twinned crystals; Sorry for HTML.
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
> >
>
Re: [ccp4bb] R: [ccp4bb] AW: [ccp4bb] uncertainites associated with intensities from twinned crystals
-BEGIN PGP SIGNED MESSAGE- Hash: SHA1 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 > - -- Dr Tim Gruene Institut fuer anorganische Chemie Tammannstr. 4 D-37077 Goettingen GPG Key ID = A46BEE1A -BEGIN PGP SIGNATURE- Version: GnuPG v1.4.15 (GNU/Linux) Comment: Using GnuPG with Mozilla - http://enigmail.mozdev.org/ iD8DBQFSewyuUxlJ7aRr7hoRAnP/AJ9biIGWJsHnbcQ4IaG5fusZTN0iOgCfR6bu 3po97EKDH98F881dH3CgD2M= =2QkU -END PGP SIGNATURE-
[ccp4bb] R: [ccp4bb] AW: [ccp4bb] uncertainites associated with intensities from twinned crystals
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
