First modifications in section 3

[chloroplast13.git] / classEquiv.tex

diff --git a/classEquiv.tex b/classEquiv.tex
index 829a8b48c2d67713624290ab633195b2f586fe4c..f3d3ed13e5f19a1161dcc58dc14fbbae6fa70bc5 100644 (file)
--- 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 $\sim$.
 
 
 %\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:
 (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 
 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 $g_i$ 
 $g_j$  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.
 
 
 equivalence relation whereas $\sim$ is not.
 
 


@@ -51,7 +51,7 @@ the projected  genomes.
 
 \begin{figure}
 \begin{center}
 
 \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}
 \end{center}
 \caption{Size of core and pan genomes w.r.t. the similarity threshold}\label{Fig:sim:core:pan}
 \end{figure}