Thankyou for the reference, but actually it's the wrong paper and anyway
my only contribution to the 'free lunch algorithm' was to name it (in the
title of the paper by Uson et al., Acta Cryst. (2007) D63, 1069-1074). By
that time the method was already being used in ACORN and by the Bari group,
who were the first to describe it in print (Caliandro et al., Acta Cryst.
Acta Cryst. (2005) D61, 556-565). As you correctly say, it only makes sense
in the context of density modification, but under favorable conditions,
i.e. native data to 2A or better, inventing data to a resolution that you
would have liked to collect but didn't can make a dramatic improvement to
a map, as SHELXE has often demonstrated. Hence the name. And of course
there is no such thing as a free lunch!
Best regards, George
On Wed, Oct 12, 2011 at 01:25:12PM -0700, Ethan Merritt wrote:
> On Wednesday, October 12, 2011 01:12:11 pm Edward A. Berry wrote:
> > Tim Gruene wrote:
> > > -----BEGIN PGP SIGNED MESSAGE-----
> > > Hash: SHA1
> > >
> > >
> > > On 10/11/2011 09:58 PM, Ethan Merritt wrote:
> > >> On Tuesday, October 11, 2011 12:33:09 pm Garib N Murshudov wrote:
> > >>> In the limit yes. however limit is when we do not have solution, i.e. when model errors are very large. In the limit map coefficients will be 0 even for 2mFo-DFc maps. In refinement we have some model. At the moment we have choice between 0 and DFc. 0 is not the best estimate as Ed rightly points out. We replace (I am sorry for self promotion, nevertheless: Murshudov et al, 1997) "absent" reflection with DFc, but it introduces bias. Bias becomes stronger as the number of "absent" reflections become larger. We need better way of estimating "unobserved" reflections. In statistics there are few appraoches. None of them is full proof, all of them are computationally expensive. One of the techniques is called multiple imputation.
> > >>
> > >> I don't quite follow how one would generate multiple imputations in this case.
> > >>
> > >> Would this be equivalent to generating a map from (Nobs - N) refls, then
> > >> filling in F_estimate for those N refls by back-transforming the map?
> > >> Sort of like phase extension, except generating new Fs rather than new phases?
> > >
> > > Some people call this the "free-lunch-algorithm" ;-)
> > > Tim
> > >
> > Doesn't work- the Fourier transform is invertable. As someone already said in this
> > thread, if the map was made with coefficients of zero for certain reflections
> > (which is equivalent to omitting those reflections) The back-transform will
> > give zero for those reflections. Unless you do some density modification first.
> > So free-lunch is a good name- there aint no such thing!
> Tim refers to the procedure described in
> Sheldrick, G. M. (2002). Z. Kristallogr. 217, 644–65
> which was later incorporated into shelxe as the Free Lunch Algorithm.
> It does indeed involve a form of density modification.
> Tim is also correct that this procedure is the precedent I had in mind,
> although I had forgotten its clever name.
> Ethan A Merritt
> Biomolecular Structure Center, K-428 Health Sciences Bldg
> University of Washington, Seattle 98195-7742
Prof. George M. Sheldrick FRS
Dept. Structural Chemistry,
University of Goettingen,
D37077 Goettingen, Germany
Tel. +49-551-39-3021 or -3068