Implement / Recommend the fast-exchange CPMG RD equation

Issue: in fast exchange (kex >> Δν = Δω / (2π)), the quantities PA*PB and 
Δω are correlated, and sometimes although neither quantity can be defined 
independently, the quantity ΦexX = PA*PB*ΔωX^2 = PA*(1-PA)*ΔωX^2 , where X 
refers to the X nucleus, can be well-defined (Luz, 1963; Ishima, 1999).

Goal 1 (Optimal) for fast-exchange and correlation of PA*PB and Δω^2
 "These parameters are correlated an amount X, and therefore one can only know each of them to an amount Y (or with confidence Z). Therefore the fast exchange equation is recommended, with interpretation of Φex instead of each parameter individually."

 Calculate X, Y, and Z.

Goal 2
 Fit the RD group with the fast exchange equation and use χ2 statistics to determine which model is more appropriate (all timescales Carver-Richards-Jones (CRJ) eqn, or fast exchange)

To program
 This will likely be somewhat complicated, but here is a relatively simple solution

  (1) Edit the FitResult.m file to allow for the fast exchange equation to be used in the function fit_me(), as an option instead of CRJ eqn.

  (2) Store fitting results in the same data structures as used for the CRJ results (e.g., resultsMatrix)

   EXCEPT there should be another vector that designates WHAT equation was used for each fit, and what the meaning of each parameter number is.

Programming difficulty
 High

Time required
 Large (40-60 hrs?)

ISSUES
  What is the fast-exchange approximation for MQ RD, where Δω = ΔωH + ΔωX? Is Φex = PA*PB*(ΔωΗ+ΔωX)^2?

Original issue reported on code.google.com by ian.klec...@gmail.com on 11 Sep 2011 at 10:24

rachitshah86 / guardd

Implement / Recommend the fast-exchange CPMG RD equation #19