Segments, extremities, and copy number profiles for genomes. (A) A diploid reference genome r containing two pairs of homologous chromosomes: A Chromosomes are dark blue and dark green, and the homologous B Chromosomes are light blue and light green. Chromosomes are partitioned into consecutive segments labeled 1 through 12. (B, top) Reference genome r is a collection of concatenations of segments; the “flat” end of segment j corresponds to the tail extremity j^t, whereas the “pointy” end of each segment j corresponds to the head extremity j^h. Dashed lines correspond to reference adjacencies between adjacent extremities. The set $\mathcal{T}\left(\mathrm{R}\right)=\{1_{\mathrm{A}}^t,1_{\mathrm{B}}^t,5_{\mathrm{A}}^h,5_{\mathrm{B}}^h,6_{\mathrm{A}}^t,6_{\mathrm{B}}^t,{12}_{\mathrm{A}}^h,{12}_{\mathrm{B}}^h\}$ of extremities is the telomere set. (Bottom) The diploid segment copy number profile C_R = (a, b) for the genome R with colors (dark/light blue/green) corresponding to A/B labeled segments. (C, top) A derived genome g obtained via multiple large-scale rearrangements from the reference genome R. Red dashed lines correspond to novel adjacencies, for example, $\{3_{\mathrm{A}}^h,7_{\mathrm{B}}^h\}$. (Bottom) The diploid segment copy number profile C_G = (a, b) for the genome g with colors (dark/light blue/green) corresponding to A/B labeled segments. The set $\mathcal{T}(\mathrm{G})$ of telomeres in the derived genome G is identical to the set $\mathcal{T}\left(\mathrm{R}\right)$ of telomeres in the reference genome R.