16 papers
Computing Conley-Morse Persistence Barcode Efficiently by Updating Matrix Decompositions
Tamal K. Dey, Andrew Haas, Michał Lipiński
Recent advances in combinatorial dynamical systems that generalize the classic discrete Morse theory have prompted algorithmic studies of combinatorial vector fields. In this regar…
Linked Barcode for Persistence Induced by Filtrations
Tamal K. Dey, Gilberto Gonzalez-Arroyo, Tao Hou
The well-known persistence algorithm summarizes the evolution of homological cycles into what is called a \emph{barcode} while scanning an input simplicial filtration. We show that…
Updating zigzag representatives efficiently
Tamal K. Dey, Tao Hou, Dmitriy Morozov
Computation of zigzag persistence has progressed in recent years, with results showing that complexities of many problems closely align with those in the non-zigzag setting. The ma…
Computing Projective Implicit Representations from Poset Towers
Tamal K. Dey, Florian Russold
A family of simplicial complexes connected by simplicial maps and indexed by a finite poset is called a poset tower. Poset towers subsume multi-parameter filtrations, zigzag fi…
Conley-Morse persistence barcode: a homological signature of combinatorial bifurcations
Tamal K. Dey, MichaÅ LipiÅski, Manuel Soriano-Trigueros
Bifurcation characterizes the qualitative changes in parameterized dynamical systems and is one of the major topics in the field. In this work, we study combinatorial bifurcations…
A Fast Algorithm for Computing Zigzag Representatives
Tamal K. Dey, Tao Hou, Dmitriy Morozov
Zigzag filtrations of simplicial complexes generalize the usual filtrations by allowing simplex deletions in addition to simplex insertions. The barcodes computed from zigzag filtr…