X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/chloroplast13.git/blobdiff_plain/1e61bcbdaedf0f72f05c3dd365fc11d3a2071330..181fe86127b57e8c7df3e97082134e7a5b7b8618:/classEquiv.tex

diff --git a/classEquiv.tex b/classEquiv.tex
index 829a8b4..f3d3ed1 100644
--- a/classEquiv.tex
+++ b/classEquiv.tex
@@ -14,7 +14,7 @@ $d(x,y)\leqslant T$.
 
 %\noindent $\sim_{d,T}$ is obviously an equivalence relation and when $d=1-\Delta$, where $\Delta$ is the similarity scoring function embedded into the emboss package , we will simply denote $\sim_{d,0.1}$ by $\sim$.
 
-Let be given a \emph{similarity} threshold $T$  and a distance $d$, 
+Let be given a \emph{similarity} threshold $T$  and a distance $d$
 (Needleman-Wunch released by EMBL for instance).
 The method begins by building  an undirected graph 
 between all the DNA~sequences $g$ of the set  of genomes as follows:
@@ -23,10 +23,10 @@ if  $g_i \sim_{d,T} g_j$ is established.
 This graph is further denoted as the ``similarity'' graph.
 
 We thus consider that the pair of two coding sequences 
-$(g_i,g_j)$ belongs in the relation $\mathcal{R}$ if both $g_i$ an,d 
+$(g_i,g_j)$ belongs in the relation $\mathcal{R}$ if both $g_i$ and 
 $g_j$  belong in the same 
 connected component (CC), \textit{i.e.} if there is a path between $g_i$ 
-and $g_j$ in the similarity graph. It is not hard to see this relation is an
+and $g_j$ in the similarity graph. It is not hard to see that this relation is an
 equivalence relation whereas $\sim$ is not.
 
 
@@ -51,7 +51,7 @@ the projected  genomes.
 
 \begin{figure}
 \begin{center}
-\includegraphics[scale=0.4]{stats.png}
+\includegraphics[scale=0.5]{stats.png}
 \end{center}
 \caption{Size of core and pan genomes w.r.t. the similarity threshold}\label{Fig:sim:core:pan}
 \end{figure}