r16229 - /1.3/docs/latex/model-free.tex -- May 11, 2012 - 15:06

Author: bugman
Date: Fri May 11 15:06:24 2012
New Revision: 16229

URL: http://svn.gna.org/viewcvs/relax?rev=16229&view=rev
Log:
A small edit of the "The universal solution" subsection title of the 
model-free chapter.

This is for the relax HTML user manual 
(http://www.nmr-relax.com/manual/Model_free_analysis.html).


Modified:
    1.3/docs/latex/model-free.tex

Modified: 1.3/docs/latex/model-free.tex
URL: 
http://svn.gna.org/viewcvs/relax/1.3/docs/latex/model-free.tex?rev=16229&r1=16228&r2=16229&view=diff
==============================================================================
--- 1.3/docs/latex/model-free.tex (original)
+++ 1.3/docs/latex/model-free.tex Fri May 11 15:06:24 2012
@@ -1052,7 +1052,7 @@
     \subsection{The universal solution $\Univset$}
 \end{latexonly}
 \begin{htmlonly}
-    \subsection{The universal solution U}
+    \subsection{The universal solution $U$}
 \end{htmlonly}
 
 The complex model-free problem, in which the motions of each spin are both 
mathematically and statistically dependent on the diffusion tensor and vice 
versa, was formulated using set theory in \citet{dAuvergneGooley07}.  This 
paper is important for understanding the entire concept of the new protocol 
in relax and for truly grasping the complexity of the model-free problem.  
The solution $\widehat\Univset$ to the model-free problem was derived as an 
element of the universal set $\Univset$, the union of the diverse model-free 
parameter spaces $\Space$.  Each set $\Space$ was constructed from the union 
of the model-free models $\Mfset$ for all spins and the diffusion parameter 
set $\Diffset$.  A single parameter loss on a single spin shifts optimisation 
to a different space $\Space$.  Ever since the seminal work of \citet{Kay89} 
the model-free problem has been tackled by first finding an initial estimate 
of the diffusion tensor and then determining the model-free dynamics of the 
system (see Sections~\ref{sect: Mandel 1995} on page~\pageref{sect: Mandel 
1995} and~\ref{sect: diffusion seeded paradigm} on page~\pageref{sect: 
diffusion seeded paradigm}).  This diffusion seeded paradigm is now highly 
evolved and much theory has emerged to improve this path to the solution 
$\widehat\Univset$.  The technique can, at times, suffer from a number of 
issues including the two minima problem of the spheroid diffusion tensor 
parameter space, the appearance of artificial chemical exchange 
\citep{Tjandra96}, the appearance of artificial nanosecond motions 
\citep{Schurr94}, and the hiding of internal nanosecond motions caused by the 
violation of the rigidity assumption \citep{Orekhov95b, Orekhov99b, 
Orekhov99a}.