The NEB molar algebra behind ligation setups — pmol = ng x 1e3 / (650 x bp), three length-keyed ratio bands, and the nM-of-ends floor that gates T4 ligase.
When ABG returns PaO2 in the 50s, the A-a gradient splits hypoventilation from V/Q mismatch, shunt, diffusion block, and low mixed-venous O2 in one equation. PAO2 = FiO2 * (Patm - 47) - PaCO2 / 0.8; A-a = PAO2 - PaO2; normal A-a approximates (Age + 10) / 4 on room air.
A pedigree probability tree is two calculations in one — carrier probability at the parental node, offspring ratios on the leaves. This field guide walks autosomal recessive, autosomal dominant, and X-linked recessive cases and shows where the Mendelian tree breaks down.