When atoms arrange themselves in crystals, x-ray crystallography can be used to find them. In nanostructures, atoms are much harder to find.

Essential issues are:

  Loss of signal in the experiments

  Loss of information in those signals

  Increased complexity of the structural solutions

This team is addressing this through a three-pronged attack by developing advanced mathematical, computational, and data analytic approaches.

The problem and recent developments have been reviewed. (1)

A sub-field of Graph Theory, Distance Geometry, has been explored to aid in the solution of nanostructure reconstructions from ensembles of particles (2).