  The plasticity of amorphous solids undergoing shear is characterized by
quasi-localized rearrangements of particles. While many models of plasticity
exist, the precise relationship between plastic dynamics and the structure of a
particle's local environment remains an open question. Previously, machine
learning was used to identify a structural predictor of rearrangements, called
"softness." Although softness has been shown to predict which particles will
rearrange with high accuracy, the method can be difficult to implement in
experiments where data is limited and the combinations of descriptors it
identifies are often difficult to interpret physically. Here we address both of
these weaknesses, presenting two major improvements to the standard softness
method. First, we present a natural representation of each particle's observed
mobility, allowing for the use of statistical models which are both simpler and
provide greater accuracy in limited data sets. Second, we employ persistent
homology as a systematic means of identifying simple, topologically-informed,
structural quantities that are easy to interpret and measure experimentally. We
test our methods on two-dimensional athermal packings of soft spheres under
quasi-static shear. We find that the same structural information which predicts
small variations in the response is also predictive of where plastic events
will localize. We also find that excellent accuracy is achieved in athermal
sheared packings using simply a particle's species and the number of nearest
neighbor contacts.
