Resolution:
## Figure 6.
Convex geometry of the MLMDP used in the THetA algorithm. (Left) For a single cancer genome with normal admixture, the interval count vector
c_{2 }of the cancer genome and tumor purity μ define a collection of rays Cμ, for μ ∈ 0[1]. (Here we show the space Ω_{3,2,3}). (Right) Normalizing these rays, we obtain the parameter , used in the multinomial likelihood. These parameters are embedded in the simplex
Δ_{m }_{- l}(gray triangle with a black outline) because their entries sum to one. (This is the
space .) For a fixed interval count matrix C = (c_{1}, c_{2}) a blue ray (left) defined by Cμ is mapped to the corresponding red/green ray (right) connecting to (right), the normalized columns of C, as described in Theorem 1. For n > 2, hyperplanes are mapped to hyperplanes (see Additional file 1, Figure S2). We show , the maximum likelihood solution when interval counts are not constrained to be integers.
Note that this point is not on any of the rays defined by interval count matrices.
Rays that satisfy the ordering constraint from Theorem 2 are in green. MLMDP: maximum
likelihood mixture decomposition problem
Oesper |