t

diff --git a/biblio.bib b/biblio.bib
index 79c455d164928ce310ceae149cb06e91394bc2d4..b141f0545e4b08186ccc0f6fcb65af18888c738e 100644 (file)
--- a/biblio.bib
+++ b/biblio.bib
@@ -52,7 +52,7 @@ pages={1-12}
     doi = {10.1371/journal.pone.0052841}
 }        
 @Article{17623808,
     doi = {10.1371/journal.pone.0052841}
 }        
 @Article{17623808,

-AUTHOR = {Gómez-Valero, Laura and Rocha, Eduardo P C and Latorre, Amparo and Silva, Francisco J}
+AUTHOR = {Gomez-Valero, Laura and Rocha, Eduardo P C and Latorre, Amparo and Silva, Francisco J},

 TITLE = {Reconstructing the ancestor of Mycobacterium leprae: the dynamics of gene loss and genome reduction.},
 JOURNAL = {Genome Res},
 VOLUME = {17},
 TITLE = {Reconstructing the ancestor of Mycobacterium leprae: the dynamics of gene loss and genome reduction.},
 JOURNAL = {Genome Res},
 VOLUME = {17},


@@ -61,5 +61,5 @@ NUMBER = {8},
 PAGES = {1178-85},
 URL = {http://www.biomedsearch.com/nih/Reconstructing-ancestor-Mycobacterium-leprae-dynamics/17623808.html},
 PubMedID = {17623808},
 PAGES = {1178-85},
 URL = {http://www.biomedsearch.com/nih/Reconstructing-ancestor-Mycobacterium-leprae-dynamics/17623808.html},
 PubMedID = {17623808},

-ISSN = {1088-9051},
+ISSN = {1088-9051}

 }
\ No newline at end of file
 }
\ No newline at end of file

diff --git a/classEquiv.tex b/classEquiv.tex
index 5d9f19da719782ac2d4a19a8310ec265264f9316..cdc1280d2bf86f1628f3160b8853d08da090e0b7 100644 (file)
--- a/classEquiv.tex
+++ b/classEquiv.tex
@@ -2,8 +2,8 @@ This step considers as input the set
 $\{((g_1,g_2),r_{12}), (g_1,g_3),r_{13}), (g_{n-1},g{n}),r_{n-1.n})\}$ of 
 $\frac{n(n-1)}{2}$ elements. 
 Each one $(g_i,g_j),r_{ij})$ where $i < j$, 
 $\{((g_1,g_2),r_{12}), (g_1,g_3),r_{13}), (g_{n-1},g{n}),r_{n-1.n})\}$ of 
 $\frac{n(n-1)}{2}$ elements. 
 Each one $(g_i,g_j),r_{ij})$ where $i < j$, 

-is a pair that gives the similarity rate $r_{ij}$ between the genes  
-$g_{i}$ and $g_{j}$ in $G$.
+is a pair that gives the similarity rate $r_{ij}$ between the two genes  
+$g_{i}$ and $g_{j}$.

 
 The first step of this stage consists in building the following non-oriented
 graph furthere denoted as to \emph{similarity graphe}.
 
 The first step of this stage consists in building the following non-oriented
 graph furthere denoted as to \emph{similarity graphe}.


@@ -11,30 +11,29 @@ In this one, the vertices are the genes. There is an edge between
 $g_{i}$ and $g_{j}$ if the rate $r_{ij}$ is greater than a given similarity 
 treeshold $t$.
 
 $g_{i}$ and $g_{j}$ if the rate $r_{ij}$ is greater than a given similarity 
 treeshold $t$.
 

-We then define the relation $\sim \in G \times G $ such that
+We then define the relation $\sim$  such that

 $ x \sim y$ if $x$ and $y$ belong in the same connected component.
 Mathematically speaking, it is obvious that this 
 defines an equivalence relation. 
 $ x \sim y$ if $x$ and $y$ belong in the same connected component.
 Mathematically speaking, it is obvious that this 
 defines an equivalence relation. 

-Let $\dot{x}= \{y \in G | x \sim y\}$
+Let $\dot{x}= \{y  | x \sim y\}$

 denotes the equivalence class to which $x$ belongs.
 denotes the equivalence class to which $x$ belongs.

-All the elements of $G$ which are  equivalent to each other
+All the genes which are  equivalent to each other

 are also elements of the same equivalence class.
 are also elements of the same equivalence class.

-Let us then consider the set of all equivalence classes of $G$ 
-by $\sim$, denoted $X/\sim = \{\dot{x} | x \in G\}$. 
-We then consider the projection $\pi: G \to G/\mathord{\sim}$
+Let us then consider the set of all equivalence classes of the set of genes 
+by $\sim$, denoted $X/\sim = \{\dot{x} | x \textrm{ is a gene}\}$. 

 defined by \pi(x) = \dot{x} 
 defined by \pi(x) = \dot{x} 

-which maps elements of $G$ into their respective equivalence classes by $\sim$.
+which maps each gene  into it respective equivalence classe by $\sim$.

 
 
 
 
 
 
 
 

-For each genome $G=[g_l,\ldot,g{l+m}]$, the second step computes 
+For each genome $[g_l,\ldot,g{l+m}]$, the second step computes 

 the projection of each gene according to $\pi$. 
 the projection of each gene according to $\pi$. 

-Let $G'$ the resulting genome  which is 
+The resulting genome  which is 

 $$
 $$

-G'=[\pi(g_l),\ldot,\pi(g{l+m})]
+[\pi(g_l),\ldot,\pi(g{l+m})]

 $$ 
 $$ 

-is of size $m$.
+is again of size $m$.

 
 Intuitivelly speaking, for two genes $g_i$ and $g_j$ 
 in the same equivalence class, there is path from  $g_i$ and $g_j$.
 
 Intuitivelly speaking, for two genes $g_i$ and $g_j$ 
 in the same equivalence class, there is path from  $g_i$ and $g_j$.


@@ -44,3 +43,13 @@ has produced a gene s.t. the similarity with the previous one
 is greater than $t$. 
 Genes $g_i$ and $g_j$ may thus have a common ancestor.
 
 is greater than $t$. 
 Genes $g_i$ and $g_j$ may thus have a common ancestor.
 

+
+We compute the core genome as follow.
+Each genome is projected according to $\pi$. We then consider the 
+intersection of all the projected genomes which are considered as sets of genes
+and not as sequences of genes.
+This results as the set of all the class representents $\dot{x}$
+such that each geneome has an gene $x$ in  $\dot{x}$.
+The pan genome is computed similarly: the union of all the 
+projected genomes in computed here.
+

diff --git a/main.tex b/main.tex
index b6e9569d476ca4437364c5865f2551750ae96987..4a7c86bf526c2fd788a6af051d56b4d490947bee 100755 (executable)
--- a/main.tex
+++ b/main.tex
@@ -56,8 +56,11 @@
 
 
 \section{First Stage: Genomes as Lists of Homologous Classes}
 
 
 \section{First Stage: Genomes as Lists of Homologous Classes}

+\input{classEquiv}

 
 \section{Second Stage: to Find Closed Genomes}
 
 \section{Second Stage: to Find Closed Genomes}

+\input{closedgenomes}
+

 
 \section{Third Stage: Reconstruction of Ancestral Synteny Blocs for the two Closest Genomes}
 
 
 \section{Third Stage: Reconstruction of Ancestral Synteny Blocs for the two Closest Genomes}