DOC: update paper

paper/paper.md

@@ -76,13 +76,13 @@ GraphBin-Tk supports metagenome assemblies generated from three popular metageno
 
 ## Visualisation
 
-The initial MetaCoAG binning result and the refined binning result can be visualised on the assembly graph using the `visualise` subcommand. Users can generate images in different formats such as `png`, `eps`, `pdf` and `svg`, and customise the dimensions of the images. An example is shown in \autoref{fig2} for the Sim-5G+metaSPAdes dataset [@Mallawaarachchi2:2020; @Mallawaarachchi:2021] containing five bacterial species. 
+The initial MetaCoAG binning result and the refined binning result can be visualised on the assembly graph using the `visualise` subcommand  (\autoref{fig1}). Users can generate images in different formats such as `png`, `eps`, `pdf` and `svg`, and customise the dimensions of the images. An example is shown in \autoref{fig2} for the Sim-5G+metaSPAdes dataset [@Mallawaarachchi2:2020; @Mallawaarachchi:2021] containing five bacterial species. 
 
 ![Visualisation of the assembly graph with the initial binning result from MetaCoAG (left) and final binning result from GraphBin (right) for the Sim-5G+metaSPAdes dataset. The five colours represent the five bins and the white nodes represent unbinned contigs.\label{fig2}](visualisation.svg){width=100%}
 
 ## Evaluation
 
-Finally, the produced binning results can be evaluated using the `evaluate` subcommand by providing the ground truth bins of contigs. This evaluation is possible only for simulated or mock metagenomes where the ground truth genomes of contigs are known. GraphBin-Tk uses the four common metrics 1) precision, 2) recall, 3) F1-score and 4) Adjusted Rand Index (ARI) that have been used in previous binning studies [@Alneberg:2014; @Meyer:2018; @Mallawaarachchi1:2020]. These metrics are calculates as follows. The binning result is denoted as a $K \times S$ matrix with $K$ number of bins and $S$ number of ground truth taxa. In this matrix, the element $a_{ks}$ denotes the number of contigs binned to the $k^{th}$ bin and belongs to the $s^{th}$ taxa. $U$ denotes the number of unbinned contigs and $N$ denotes the total number of contigs. Following are the equations used to calculate the evaluation metrics.
+Finally, the produced binning results can be evaluated using the `evaluate` subcommand by providing the ground truth bins of contigs  (\autoref{fig1}). This evaluation is possible only for simulated or mock metagenomes where the ground truth genomes of contigs are known. GraphBin-Tk uses the four common metrics 1) precision, 2) recall, 3) F1-score and 4) Adjusted Rand Index (ARI) that have been used in previous binning studies [@Alneberg:2014; @Meyer:2018; @Mallawaarachchi1:2020]. These metrics are calculates as follows. The binning result is denoted as a $K \times S$ matrix with $K$ number of bins and $S$ number of ground truth taxa. In this matrix, the element $a_{ks}$ denotes the number of contigs binned to the $k^{th}$ bin and belongs to the $s^{th}$ taxa. $U$ denotes the number of unbinned contigs and $N$ denotes the total number of contigs. Following are the equations used to calculate the evaluation metrics.
 
 __Precision__ = $\frac{\sum_{k}max_s \{a_{ks}\}}{\sum_{k}\sum_{s}a_{ks}}$