  Betti curves of symmetric matrices were introduced in [3] as a new class of
matrix invariants that depend only on the relative ordering of matrix entries.
These invariants are computed using persistent homology, and can be used to
detect underlying structure in biological data that may otherwise be obscured
by monotone nonlinearities. Here we prove three theorems that fully
characterize the Betti curves of rank 1 symmetric matrices. We then illustrate
how these Betti curve signatures arise in natural data obtained from calcium
imaging of neural activity in zebrafish.
