  Within the context of topological data analysis, the problems of identifying
topological significance and matching signals across datasets are important and
useful inferential tasks in many applications. The limitation of existing
solutions to these problems, however, is computational speed. In this paper, we
harness the state-of-the-art for persistent homology computation by studying
the problem of determining topological prevalence and cycle matching using a
cohomological approach, which increases their feasibility and applicability to
a wider variety of applications and contexts. We demonstrate this on a wide
range of real-life, large-scale, and complex datasets. We extend existing
notions of topological prevalence and cycle matching to include general
non-Morse filtrations. This provides the most general and flexible
state-of-the-art adaptation of topological signal identification and persistent
cycle matching, which performs comparisons of orders of ten for thousands of
sampled points in a matter of minutes on standard institutional HPC CPU
facilities.
