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We interpret G with each edge colored by read mappings as a = flow network, considering the read volume assigned to every (super-) edge a= s a flux created by the expression of the underlying supporting transcripts= T.Consequently, given an edge the contribution of the supporti= ng transcripts to the flux observed along e can be described by a lin= ear equation
(Equation 1)
where fi represents a factor that expresses= the fraction of the respective transcript expression ti<= /em> observed between taile and head= e. In the trivial case, fi<= /sub> corresponds to the proportion of the interval [tail= e; heade] in comparison to the enti= re length of the processed transcript. The correction factor in Eq.= 1 is to compensate for divergence from the expectation created by stochasti= cal sampling intrinsic to RNA-Seq experiments.
The crux of the flux is that an RNA-Seq experiment provides a series of = observations on the underlying expression level ti= sub> along the transcript body. Following tradition in transportation probl= ems, we model all of these observations as a system of linear equations by = inferring Equation 1 on all . Subsequently, the linear equations spanned = by a locus are resolved by the objective function
(Equation 2)
Solving the linear program (Eq.2) imposed by a locus intrinsically provi= des an estimate for the expression level ti of= all alternative transcripts that are annotated.