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Section

Definition 2 (Read Assignment): a read belongs to an edge 

LaTeX Math Inline
body$e=(tail,head,mode,T)$
iff each two bases contiguously aligned to the genome 
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body$G[i]G[i+1]$
map to adjacent RNA-coordinates
LaTeX Math Inline
body$R[j]R[j+1]$
within e:
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body$tail_e \leq j < j+1 \leq head_e$
.

Section

Definition 2 requires the read mapping to comply with the annotated exon-intron structure. Specifically, indels of genomic read mappings are considered in a different manner than split-mappings, and discriminated by the description of the alignment. The definition is further extended to match the attributes of specific RNA-Seq experiments, for instance in the case of stranded protocols. All reads r that fulfill Definition 2 are assigned to their corresponding edges e.

Section

Reads can naturally overlap one or multiple adjacent exonic segments

LaTeX Math Inline
body$\left<e,\ldots,e_n\right>$
, i.e. to edges 
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body$e_i$
such that
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body$mode_{e_i}=exonic$
. To this end we extend E by corresponding super-edges se conflating the attributes of atomary exon segments, 
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body$se=(tail_e, head_{e_n}, exonic, \bigcap T_{\{e,...,e_n\}})$
and apply Definition 2 without loss of generality. Note that in the case of split-mappings, exonic segments represented by super-edges can be separated by intermediate intronic edges. Paired-end reads are mapped jointly to super-edges that combine the exonic regions to which each mate is mapping, which in turn can be already super-edges (Fig.2).

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