From: Michel Salomon <salomon@caseb.iut-bm.univ-fcomte.fr>
Date: Mon, 2 Dec 2013 13:02:43 +0000 (+0100)
Subject: I've finished my modifications in section 3
X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/chloroplast13.git/commitdiff_plain/def3c748d0d7f8073ad9a8602822d8f7e0d36a9c?ds=inline;hp=--cc

I've finished my modifications in section 3
---

def3c748d0d7f8073ad9a8602822d8f7e0d36a9c
diff --git a/annotated.tex b/annotated.tex
index c9e00bd..e9e3049 100644
--- a/annotated.tex
+++ b/annotated.tex
@@ -240,36 +240,25 @@ score_{ij}=\vert g_i \cap g_j\vert
 \label{Eq1}
 \end{equation}
 \noindent where $1 \leq i \leq n$, $1 \leq j \leq n$, and $g_i, g_j$ are 
-genomes. The  generation of a new  core gene depends obviously on the
-value of intersection scores $score_{ij}$:
-
-% TO BE CONTINUED
-
-$$
-\text{new Core} = 
-\begin{cases}
-\text{Ignored} & \text{if $\textit{score}=0$;} \\
-\text{new Core id} & \text{if $\textit{Score}>0$.}
-\end{cases}
-$$
-
-if     $\textit{Score}=0$     then     we    have     \textit{disjoint
-relation} \emph{i.e.},  no common genes between two  genomes.  In this
-case  the  system  ignores  the   genome  that  annul  the  core  gene
-size. Otherwise, The system removes these two genomes from ICM and add
-new  core  genome  with a  \textit{coreID}  of  them  to ICM  for  the
-calculation in  next iteration. This  process reduces the size  of ICM
-and repeats until all genomes  are treated \emph{i.e.} ICM has no more
-genomes.  We observe  that ICM is very large because  of the amount of
-data that it stores. This results  to be time and memory consuming for
-calculating  the  intersection  scores.   To  increase  the  speed  of
-calculations, it  is sufficient to  only calculate the  upper triangle
-scores. The time complexity for this process after enhancement is thus
-$O(\frac{n.(n-1)}{2})$.   Algorithm   \ref{Alg1:ICM}  illustrates  the
-construction of  the ICM matrix and  the extraction of  the core genes
-where \textit{GenomeList},  represents the database  where all genomes
-data are stored. At each iteration, it computes the maximum core genes
-with its two genomes parents.
+genomes. The  generation of a new  core gene depends  obviously on the
+value  of the  intersection scores  $score_{ij}$. More  precisely, the
+idea is  to consider a  pair of genomes  such that their score  is the
+largest element in ICM. These two genomes are then removed from matrix
+and the  resulting new  core genome is  added for the  next iteration.
+The ICM is then updated to take into account the new core gene: new IS
+values are computed for it. This process is repeated until no new core
+gene can be obtained.
+
+We  can observe  that  the ICM  is very  large  due to  the amount  of
+data. As a consequence, the  computation of the intersection scores is
+both  time and  memory consuming.  However,  since ICM  is a  symetric
+matrix we can reduce the  computation overhead by considering only its
+triangular  upper part.  The  time complexity  for this  process after
+enhancement is thus $O(\frac{n.(n-1)}{2})$.  Algorithm ~\ref{Alg1:ICM}
+illustrates the construction  of the ICM matrix and  the extraction of
+the  core  genes, where  \textit{GenomeList}  represents the  database
+storing all genomes  data. At each iteration, it  computes the maximum
+core genes with its two genomes parents.
 
 % ALGORITHM HAS BEEN REWRITTEN