16 citations · 35 across the 5 of their papers we have counts for
7 papers
Morse Theoretic Templates for High Dimensional Homology Computation
Shaun Harker, Konstantin Mischaikow, Kelly Spendlove
We introduce the notion of a template for discrete Morse theory. Templates provide a memory efficient approach to the computation of homological invariants (e.g., homology, persist…
A computational framework for connection matrix theory
Shaun Harker, Konstantin Mischaikow, Kelly Spendlove
The connection matrix is a powerful algebraic topological tool from Conley index theory that captures relationships between isolated invariant sets. Conley index theory is a topolo…
A Comparison Framework for Interleaved Persistence Modules
Shaun Harker, Miroslav Kramar, Rachel Levanger +1
We present a generalization of the induced matching theorem and use it to prove a generalization of the algebraic stability theorem for -indexed pointwise finite-dimens…
Model rejection and parameter reduction via time series
Bree Cummins, Tomas Gedeon, Shaun Harker +1
We show how a graph algorithm for finding matching labeled paths in pairs of labeled directed graphs can be used to perform model validation for a class of dynamical systems includ…
Combinatorial Representation of Parameter Space for Switching Systems
Bree Cummins, Tomas Gedeon, Shaun Harker +2
We describe the theoretical and computational framework for the Dynamic Signatures for Genetic Regulatory Network (DSGRN) database. The motivation stems from urgent need to underst…
Global Dynamics for Steep Sigmoidal Nonlinearities in Two Dimensions
Tomas Gedeon, Shaun Harker, Hiroshi Kokubu +2
We introduce a novel approach to obtaining mathematically rigorous results on the global dynamics of ordinary differential equations. Motivated by models of regulatory networks, we…