  Recently various types of topological Laplacians have been studied from the
perspective of data analysis. The spectral theory of these Laplacians has
significantly extended the scope of algebraic topology and data analysis.
Inspired by the theory of persistent Laplacians and cellular sheaves, this work
develops the theory of persistent sheaf Laplacians for cellular sheaves, and
describes how to construct sheaves for a point cloud where each point is
associated with a quantity that can be devised to embed physical properties. As
a result, the spectra of persistent sheaf Laplacians encode both geometrical
and non-geometrical information of the given point cloud. The theory of
persistent sheaf Laplacians is an elegant method for fusing different types of
data and has huge potential for future development.
