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- Shaun Harker, Konstantin Mischaikow, Marian Mrozek, Vidit Nanda
- Foundations of Computational Mathematics
- 2014

We provide explicit and efficient reduction algorithms based on discrete Morse theory to simplify homol-ogy computation for a very general class of complexes. A set-valued map of top-dimensional cells between such complexes is a natural discrete approximation of an underlying (and possibly unknown) continuous function, especially when the evaluation of that… (More)

Two implementations of a homology algorithm based on the Forman's discrete Morse theory combined with the coreduction method are presented. Their efficiency is compared with other implementations of homology algorithms.

- Justin Bush, Marcio Gameiro, +4 authors Paweł Pilarczyk
- Chaos
- 2012

We discuss an algorithmic framework based on efficient graph algorithms and algebraic-topological computational tools. The framework is aimed at automatic computation of a database of global dynamics of a given m-parameter semidynamical system with discrete time on a bounded subset of the n-dimensional phase space. We introduce the mathematical background,… (More)

- ARNAUD GOULLET, SHAUN HARKER, KONSTANTIN MISCHAIKOW, WILLIAM D. KALIES, DINESH KASTI
- 2014

We present an efficient algorithm for constructing piecewise constant Lyapunov functions for dynamics generated by a continuous nonlinear map defined on a compact metric space. We provide a memory efficient data structure for storing nonuniform grids on which the Lyapunov function is defined and give bounds on the complexity of the algorithm for both time… (More)

- Justin Bush, Wes Cowan, Shaun Harker, Konstantin Mischaikow
- SIAM J. Applied Dynamical Systems
- 2016

- Bree Cummins, Tomás Gedeon, Shaun Harker, Konstantin Mischaikow, Kafung Mok
- SIAM J. Applied Dynamical Systems
- 2016

- Tomáš Gedeon, Shaun Harker, Hiroshi Kokubu, Konstantin Mischaikow, Hiroe Oka
- Physica D. Nonlinear phenomena
- 2017

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 including regulatory network models of relevance to systems biology. In particular, we extract a partial order of events describing local minima and local maxima of observed quantities… (More)

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