The analysis of large and complex data sets is one of the most important problems facing the
scientific community, and physics in particular. One response to this challenge has been the …

This paper introduces cellular sheaf theory to graphical methods and reciprocal
constructions in structural engineering. The elementary mechanics and statics of trusses are …

Persistent topological Laplacians constitute a new class of tools in topological data analysis
(TDA), motivated by the necessity to address challenges encountered in persistent …

We set up the theory for a distributed algorithm for computing persistent homology. For this
purpose we develop linear algebra of persistence modules. We present bases of …

A method is presented for the distributed computation of persistent homology, based on an
extension of the generalized Mayer-Vietoris principle to filtered spaces. Cellular cosheaves …

This work extends the theory of reciprocal diagrams in graphic statics to frameworks that are
invariant under finite group actions by utilizing the homology and representation theory of …

Over the past two decades, topological data analysis has emerged as a field of applied
mathematics with new applications and algorithmic developments appearing rapidly. Two …

We expand the toolbox of (co) homological methods in computational topology by applying
the concept of persistence to sheaf cohomology. Since sheaves (of modules) combine …

Topological data analysis seeks to understand and utilize topological features of data, such
as clusters and holes. One such problem is to characterize topological spaces from sampled …

Topological and geometrical methods are known for their capability to reduce noise and
have achieved significant success in analyzing complex biological data. A key method in …