Hi Bernhard,
Thanks for that, but it reinforces my impression (also reinforced offline by
George Sheldrick) that this is something that was floating around at some
point, and no-one ever bothered to put it in a proper publication.
The background is that we've just submitted a paper on a new way to deal with
intensity errors (the paper with all the equations that Word has been giving me
grief over, in the earlier thread) and we wanted to compare it to what people
use now. The French & Wilson treatment is the most common, and this equation
probably comes next out of a number of alternatives that we found, but it would
have been nice to give a reference.
Phil Evans gave me the same derivation (not a surprise, as he seems to have
been the person who put that code in TRUNCATE). The thing that bothers me
about this is that it's not immediately obvious why it's right to solve the
equation
(F+SIGF)^2 == I+SIGI
for SIGF and not
(F-SIGF)^2 == I-SIGI
Both are ways of looking at the effect of a perturbation, but the latter
equation gives a complex value for SIGF when I<SIGI. Phil said something about
the skewness of the probability of the amplitude, when the probability
distribution for the corresponding intensity is an unskewed Gaussian, and maybe
there's some kind of argument for which direction of perturbation is
appropriate for a particular sign for the skewness?
It turns out that an equivalent equation is used in the ADDREF program in the
Xtal package of programs for small molecule crystallography. ADDREF was
written by Syd Hall and George Davenport, so I've been in touch with Syd Hall,
who also can't remember who first came up with this equation, but who feels
that there was more to the derivation than Phil's explanation!
Perhaps it will now remain a mystery, unless someone else on the BB has a
recollection of the origin of this equation decades ago!
Randy
> On 26 May 2015, at 23:51, Bernhard Rupp <b...@ruppweb.org> wrote:
>
> Derivation but no reference except truncate is in BMC page 330 sidebar.
> Probably read the source code or some prog. ref….
> BR
>
> From: CCP4 bulletin board [mailto:CCP4BB@JISCMAIL.AC.UK
> <mailto:CCP4BB@JISCMAIL.AC.UK>] On Behalf Of Jonathan Cooper
> Sent: Tuesday, May 26, 2015 4:33 PM
> To: CCP4BB@JISCMAIL.AC.UK <mailto:CCP4BB@JISCMAIL.AC.UK>
> Subject: [ccp4bb] reference needed for "TRUNCATE NO" equation.
>
> Dear all
>
> I have been asked by Randy for a reference for the following equation which
> appears in Sherwood & Cooper:
>
> http://www.ucl.ac.uk/~rmhajc0/truncate_no.jpg
> <http://www.ucl.ac.uk/~rmhajc0/truncate_no.jpg>
>
> ... or in text form:
>
> sigma(F) = sqrt(I + sigma(I)) - sqrt(I)
>
> It is the equation which TRUNCATE uses to calculate sigma(|F|) if the user
> switches off the French-Wilson treatment, although that is never usually done!
>
> Can anyone shed any light on who derived it and where/whether it has been
> published, etc?
>
> Cheers for now.
>
> Jon Cooper
------
Randy J. Read
Department of Haematology, University of Cambridge
Cambridge Institute for Medical Research Tel: + 44 1223 336500
Wellcome Trust/MRC Building Fax: + 44 1223 336827
Hills Road E-mail: rj...@cam.ac.uk
Cambridge CB2 0XY, U.K. www-structmed.cimr.cam.ac.uk
