Many interactions with nuclei can be described in terms of convolutions of universal parton distributions. These parton distributions describe the way quarks and gluons distribute themselves within a hadron in terms of the fraction of the total momentum they contribute and their position/momentum transverse to the hadron's collective motion. Over the past decade these distributions have been inferred from matrix elements calculated with Lattice QCD in analogous methods to those used for their extraction from experimental cross sections by solving an integral inverse problem. Beyond the distributions themselves, a different inverse problem can be setup to non-perturbatively infer the scale dependent evolution of the parton pseudo-distributions as an alternative to high order resummation of perturbative calculations. Finally, the Lattice QCD matrix elements can be included as prior information in global analysis of experimental cross sections leading to significantly improved reliability of the distributions in a wider range of the momentum fraction than either independently due to overlapping sensitivity to different regions.