The number of energetically stable structures that a system of N
particles can form grows exponentially with N. Stabilizing any one
structure over all others is thus a challenging problem. We
consider a system of N spherical colloidal particles that...
Suppose a large number of voters have each rated or compared a
small subset of a large number of alternatives, how could we rank
the alternatives based on these data? The rank aggregation problem
is fraught with famous difficulties --- Arrow's...
Computation of cycles representing classes of homology groups is
a fundamental problem arising in applications such as
parameterization, feature identification, topology simplification,
and data analysis. Variations of the classical Smith Normal...
Topological defects pervade a wide range of physical systems,
from superconductors to smectic liquid crystals. The behavior and
interactions of such singularities impart many materials with a
wealth of rich behavior. Just as flux vortices in the...