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
