closedGenomes

diff --git a/closedgenomes.tex b/closedgenomes.tex
index 7d84b64488ed26c2a94723ea8e0a9bc2c608453e..bfe1c1be6c2336c547c078bb58f64974af509005 100644 (file)
--- a/closedgenomes.tex
+++ b/closedgenomes.tex
@@ -2,7 +2,7 @@ The approach is further based on the ability to decide how far is each
 genome from each others. To achieve this, we combine XXX metrics which are 
 detailed in this part.
 
-\subsection{Core SNP based metric} 
+\subsection{Core SNP based Metric} 
 Due to the definition of the core genome, for each element $\dot{x}$ 
 in this set, there is a gene $x \in \dot{x}$ in each genome. 
 Let us consider a class 
@@ -33,7 +33,7 @@ without considering the number of SNP it contains.
 
 % plus il y a de diff, plus le nombre est élevé
 
-\subsection{Symmetric Difference based metric}
+\subsection{Symmetric Difference based Metric}
 The third metric consider the symmetric difference $\Delta$ 
 between the two sets $G_1$ and $G_2$ of genes recalled hereafter
 $$
@@ -50,9 +50,23 @@ one.
 This metric is equal to the Hamming distance between the two corresponding  
 vectors of Boolean values.
 
+% plus il y a de diff, plus le nombre est élevé
+
+
 \subsection{}
 
 % 4/ Using EPFL method
-% 5/ On size of the biggest syntheny bloc
-% 6/ On average size of syntheny blocs
-% 7/ On number of syntheny blocs.
+\subsection{Shared Synteny based Metric}
+Given two genomes abstracted as sequences of classes, it is classical
+to computes all the maximum shared synteny chains. 
+
+% Attention ici, moins il y a de diff, plus le nombre est élevé
+There are then three issues with such a set of shared synteny chains:
+\begin{itemize}
+\item let $m_{Y}$ be the metric, which returns the 
+length of the largest chains;
+\item let $m_{\overline{Y}}$ be the metric, which returns the 
+average length of synteny chains;
+\item finally, let $m_{|Y|}$ be the metric, which returns the 
+number of synteny chains.
+\end{itemize}