Exact(60)
Flux per unit length of discrete segment (i, j), (m2/s).
where b i and ξ i are the Burgers vector and the line sense vector of segment i, respectively.
Assuming that the segment i j corresponds to the l-th element of ( tilde{Updelta } ), the state of segment i j is determined by: S_{i,j} = left{ begin{aligned} & 0,;;;;;Upphi (tilde{delta }_{l} ) le p_{i,j} & 1,;;;;;Upphi (tilde{delta }_{l} ) > p_{i,j} end{aligned} right., (5 where ( Upphi ( cdot ) ) is the standard normal distribution function.
We denote the number of points in cluster (segment) i as J i, the 2D coordinates of the j th (j = 1,…J i ) point in segment i as P ij →, and the SIFT vector of the point as S ij →.
The evolutionary process of the segment i (i = 1,..,K) is assumed to follow the HKY model [59].
The values v ij represent gains and losses for segment i and patient j.
S - i is the average property value for segment i along the whole sequence.
Each patient has a different number of segments, which might not have the same initial value; this means that the initial or final value of segment i and patient j can be different from segment i and patient k.
For example, supposing node B, corresponding to segment (i, j), has three child nodes A1, A2 and A3, where A k corresponds to segment (i k, j k ) and i< i1< j1< i2< j2< i3< j3< j.
The latter is calculated based on the read density of segment i (defined in Equation (1)) over all F samples.
For every vertex v i ∈ V\{ s, t}, we assign w i,i = − log(d i + 1), where d i is the average read density of segment i in the F samples: (1) d i = ∑ k = 1 F C i k / (l i - L + 1 ) Here, C i k is the number of reads mapped to segment i from the kth RNA-Seq sample, l i is the length of the segment i and L is the read length.
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