next up previous contents
Next:  Old (obsolete) version's documentation Up:  Pathology of GraphEnt calculations, Previous:  My native Patterson function   Contents


 My GraphEnt mFoexp(i$ \phi$) map looks noiser than the conventional.

Do not blame the MaxEnt principle for this : it is all due to bad coding and unjustified approximations on my side. The story for those of you that are interested goes as follows : as discussed on page [*], GraphEnt attempts to approximate the structure factor probability locus with a 2D Gaussian. As was said, this is OK for all cases with the exception of the most interesting (and dangerous) one, ie. when you have a strong reflection with an uncertain phase. In that case, GraphEnt will still try to approximate the pdf with a 2D Gaussian, but because the locus goes around the phase circle, the Gaussian will end-up somewhere near the origin of the complex plane. In other words, a strong reflection with uncertain phase will be effectively be treated as a weak reflection with a very large standard deviation, as shown in the comparative diagram below :

\scalebox {0.1}{\includegraphics{/usr/people/glykos/progs/maxent/doc/fig/pdf_comp.ps2}}

The pdf on the left is what the data tell us, the pdf on the right is how the reflection is treated by GraphEnt. Several ad hockeries have been invented in an attempt to by-pass the problem, but not unexpectedly, all turned-out to be rather unsuccessful. These include the keywords PHASeless, SWITch and EXFOm. Instead of writing about it, I thought I should better show some real-life examples : The following maps are all 2mFo - DFc maps calculated for a 4-$ \alpha$-helical bundle phased only from an incomplete poly-Ala model (ie. without any information about side-chains). Data between 8 and 2Å resolution have been used for this calculation, and the currently available model (including side-chains) is shown superimposed on all maps. The R and Rfree for the refined poly-Ala model used for the calculation were 0.411 and 0.418, and the overall mean figure of merit was 0.573.

Default calculation, Conventional map :

\scalebox {1.0}{\includegraphics{/usr/people/glykos/progs/maxent/doc/fig/FOMseries_simple_conv.ps}}

Default calculation, GraphEnt map :

\scalebox {1.0}{\includegraphics{/usr/people/glykos/progs/maxent/doc/fig/FOMseries_simple_max.ps}}

Reflections with FOM<0.5 treated as PHASeless, GraphEnt map :

\scalebox {1.0}{\includegraphics{/usr/people/glykos/progs/maxent/doc/fig/FOMseries_phaseless_05.ps}}

Just before the default run reaches convergence, SWITch to phase-less mode, GraphEnt map :

\scalebox {1.0}{\includegraphics{/usr/people/glykos/progs/maxent/doc/fig/FOMseries_switch.ps}}

My interpretation of these figures, is that at least for the case considered in this example, calculation of the GraphEnt maps was a waste of CPU time. Having said that, when the phases are better known ( ie. towards the end of the refinement), the GraphEnt maps start again looking better than the conventional synthesis, but this is not very useful17.



Footnotes

... useful17
The reason that the GraphEnt map is becoming better from the conventional near the end of the refinement is, of course, that the higher the FOMs, the better the approximation that GraphEnt does, the closer we get to calculating a MaxEnt map.

next up previous contents
Next:  Old (obsolete) version's documentation Up:  Pathology of GraphEnt calculations, Previous:  My native Patterson function   Contents
NMG, March 2000