11 citations · 12 across the 7 of their papers we have counts for
8 papers
Inductive construction of path homology chains and the structure of
Matthew Burfitt, Tyrone Cutler
Path homology plays a central role in digraph topology and GLMY theory more generally. Unfortunately, the computation of the path homology of a digraph is a two-step process, a…
Computing singular simplicial homologies of digraphs and quivers
Matthew Burfitt, Jie Wu, Stephen S. -T. Yau +1
The dynamics of large complex systems are predominately modeled through pairwise interactions, the principle underlying structure being a network of the form of a digraph or quiver…
Inductive construction of path homology chains
Matthew Burfitt, Tyrone Cutler
Path homology plays a central role in digraph topology and GLMY theory more general. Unfortunately, the computation of the path homology of a digraph is a two-step process, and…
The cohomology of the free loop spaces of
Matthew I. Burfitt, Jelena Grbić
We study the cohomology of the free loop space of , the simplest example of a complete flag manifolds and an important homogeneous space. Through this enhanced analysi…
On the complexity of zero-dimensional multiparameter persistence
Jacek Brodzki, Matthew Burfitt, Mariam Pirashvili
Multiparameter persistence is a natural extension of the well-known persistent homology, which has attracted a lot of interest. However, there are major theoretical obstacles preve…
A numerical measure of the instability of Mapper-type algorithms
Francisco Belchí, Jacek Brodzki, Matthew Burfitt +1
Mapper is an unsupervised machine learning algorithm generalising the notion of clustering to obtain a geometric description of a dataset. The procedure splits the data into possib…
The cohomology of free loop spaces of rank 2 flag manifolds
Matthew I. Burfitt, Jelena Grbić
A complete flag manifold is the quotient of a Lie group by its maximal torus. The rank of a flag manifold is the dimension of the maximal torus of the Lie group. The rank 2 complet…
The cohomology of free loop spaces of homogeneous spaces
Matthew Burfitt
The free loops space of a space has become an important object of study particularly in the case when is a manifold.The study of free loop spaces is motivated in parti…