-\subsection{Extract Core Genes}
-The goal of this step is trying to extract maximum core genes from sets of genes (\textit{Vectors}) in the local database. The methodology of finding core genes is dividing to three methods: \\
-
-The hypothesis in first method is based on extracting core genes by finding common genes among chloroplast genomes based on extracting gene feature (i.e Gene names, genes counts). Genomes vary in genes counts according to the method of annotation used, so that extracting maximum core genes can be done by constructing Intersection Core Matrix (\textit{ICM}).\\
-While the hypothesis of second method is based on comparing the sequence of reference genes of one annotated genome with other unannotated genomes sequences in Blast database, by using Blastn\cite{Sayers01012011} (nucleotide sequence alignment tool from NCBI). The last method, is based on merge all genes from NCBI and Dogma annotation, then apply a sequence similarity base method (Quality Control test) using Needle-man Wunch algorithm to predict a new genomes. Using predicted genomes to extract core genes using previous methods. Figure \ref{wholesystem}, illustrate the whole system operations.
-
-\begin{figure}[H]
- \centering
- \includegraphics[width=0.7\textwidth]{Whole_system}
- \caption{Total overview of the system pipeline}\label{wholesystem}
-\end{figure}
-
-In the first method, the idea is to collect from each iteration the maximum number of common genes. To do so, the system build an \textit{Intersection core matrix(ICM)}. ICM here is a two dimensional symmetric matrix (considered as a vector space) where each row and column represent a vector for one genome. Each position in ICM stores the \textit{intersection scores}. Intersection Score(IS) is the cardinality number of a core genes comes from intersecting one vector with other vectors in vector space. Taking maximum cardinality from each row and then take the maximum of them will result to select the maximum cardinality in the vector space. Maximum cardinality results to select two genomes with their maximum core. Mathematically speaking, if we have an $n \times m$ vector space matrix where $n=m=\text{number of vectors in local database}$, then lets consider:\\
-
-\begin{equation}
-Score=\max_{i<j}\vert x_i \cap x_j\vert
-\label{Eq1}
-\end{equation}\\
-
-Where $x_i, x_j$ are vectors in the matrix. Generate new core genes is depending on the value of intersecting two vectors, we call it $Score$:\\
-$$\text{New Core} = \begin{cases}
-\text{Ignored} & \text{if $Score=0$;} \\
-\text{new Core id} & \text{if $Score>0$.}
-\end{cases}$$\\
-
-if $Score=0$ then we have \textit{disjoint relation} (i.e no common genes between two genomes). In this case the system ignore the vector that smash the core genes. Otherwise, The system will remove these two vectors from ICM and add new core vector with a \textit{coreID} of them to ICM for the calculation in next iteration. The partial core vectors generated with its values will store in the local database for reused to draw the tree. This process repeat until all vectors treated.
-We observe that ICM will result to be very large because of the huge amount of data that it stores. In addition, this will results to be time and memory consuming for calculating the intersection scores by using just genes names. To increase the speed of calculations, we can calculate the upper triangle scores only and exclude diagonal scores. This will reduce whole processing time and memory to half. The time complexity for this process after enhancement changed from $O(n^2-n)$ to $O(\frac{(n-1).n}{2})$. The Algorithm of construction the vector matrix and extracting the vector of maximum core genes where illustrated in Algorithm \ref{Alg1:ICM}. The output from this step is the maximum core vector with its two vectors to draw it in a tree.\\
+Dogma stands for \textit{Dual Organellar GenoMe Annotator}. It is an
+annotation tool developed at University of Texas in 2004 for plant
+chloroplast and animal mitochondrial genomes. This tool has its own
+database for translating a genome in all six reading frames and
+queries the amino acid sequence database using
+BLAST \cite{altschul1990basic} (\emph{i.e.} Blastx) with various
+parameters. Protein coding genes are identified in an input genome
+using sequence similarity of genes in Dogma database. In addition in
+comparison with NCBI annotation tool, Dogma can produce
+both \textit{Transfer RNAs (tRNA)} and \textit{Ribosomal RNAs (rRNA)},
+verify their start and end positions. Another difference is also that
+there is no gene duplication with Dogma after solving gene
+fragmentation. In fact, genome annotation with Dogma can be the key
+difference when extracting core genes.
+
+The Dogma annotation process is divided into two tasks. First, we
+manually annotate chloroplast genomes using Dogma web tool. The output
+of this step is supposed to be a collection of coding genes files for
+each genome, organized in GeneVision file. The second task is to solve
+the gene duplication problem and therefore we have use two
+methods. The first method, based on gene name, translates each genome
+into a set of genes without duplicates. The second method avoid gene
+duplication through a defragment process. In each iteration, this
+process starts by taking a gene from gene list, searches for gene
+duplication, if a duplication is found, it looks on the orientation of
+the fragment sequence. If it is positive it appends directly the
+sequence to gene files. Otherwise reverse complement operations are
+applied on the sequence, which is then also append to gene files.
+Finally, a check for missing start and stop codons is performed. At
+the end of the annotation process, all the genomes are fully
+annotated, their genes are defragmented, and gene counts are
+available.
+
+\subsection{Core genes extraction}
+
+The goal of this stage is to extract maximum core genes from sets of
+genes. To find core genes, the following methodology is applied.
+
+\subsubsection{Preprocessing}
+
+In order to extract core genomes in a suitable manner, the genomic
+data are preprocessed with two methods: on the one hand a method based
+on gene name and count, and on the other hand a method based on a
+sequence quality control test.
+
+In the first method, we extract a list of genes from each chloroplast
+genome. Then we store this list of genes in the database under genome
+nam and genes counts can be extracted by a specific length command.
+The \textit{Intersection Core Matrix}, described in next subsection,
+is then computed to extract the core genes. The problem with this
+method can be stated as follows: how can we ensure that the gene which
+is predicted in core genes is the same gene in leaf genomes? The
+answer to this problem is that if the sequences of any gene in a
+genome annotated from Dogma and NCBI are similar with respect to a
+given threshold, then we do not have any problem with this
+method. When the sequences are not similar we have a problem, because
+we cannot decide which sequence belongs to a gene in core genes.
+
+The second method is based on the underlying idea: we can predict the
+the best annotated genome by merging the annotated genomes from NCBI
+and Dogma according to a quality test on genes names and sequences. To
+obtain all quality genes of each genome, we consider the following
+hypothesis: any gene will appear in the predicted genome if and only
+if the annotated genes in NCBI and Dogma pass a specific threshold
+of \textit{quality control test}. In fact, the Needle-man Wunch
+algorithm is applied to compare both sequences with respect to a
+threshold. If the alignment score is above the threshold, then the
+gene will be retained in the predicted genome, otherwise the gene is
+ignored. Once the prediction of all genomes is done,
+the \textit{Intersection Core Matrix} is computed on these new genomes
+to extract core genes, as explained in Algorithm \ref{Alg3:thirdM}.
