Research focuses on direct methods solutions to the crystallographic phase problem for biological macromolecules, in particular on mathematical and computational approaches to overcoming the limitations of the conventional theoretical hypotheses of [1] uniform random distributions of [2] independent atoms [3] at rest or with equal mean-square atomic displacements about the mean atomic positions.  These hypotheses are simplifying idealizations employed for formulating the probabilistic direct methods theory that has been so powerfully successful in phasing crystal structures with  N < ~100  independent non-hydrogen atoms.  Biomacromolecular crystal structures, with  N > ~1000,  violate all three hypotheses: [1] Protein crystals have non-uniform structures in which on the order of half the unit cell volume is occupied by solvent molecules, mostly water, much of it liquid-like, with a lower average electron density in the solvent regions, where  <r_solv > ~ 0.33 e Å^-3,  than in the protein regions, where  < r_prot > ~ 0.44 e Å^-3.  [2] Protein crystals seldom diffract to atomic resolution,  d_min = l/(2sinu_max) ~1 Å,  and must, therefore, be interpreted in terms of molecular or functional groups of atoms of known structure, viz., main-chain peptide groups and amino acid side-chain groups with mean diameters of  ~3 Å.  And [3] protein crystals are soft crystals with broad distributions of large-amplitude, anisotropic mean-square atomic displacements due to disorder and/or thermal vibration, typically with mean root-mean-square atomic displacements and root-mean-square deviations from the mean of perhaps 0.5 Å or more, even at T ≈ 100 K  cryotemperatures.