2024
Identifying Nonlinear Dynamics with High Confidence from Sparse Data.
SIAM J. Appl. Dyn. Syst., March, 2024
MORALS: Analysis of High-Dimensional Robot Controllers via Topological Tools in a Latent Space.
Proceedings of the IEEE International Conference on Robotics and Automation, 2024
2023
Computing the Conley Index: A Cautionary Tale.
SIAM J. Appl. Algebra Geom., December, 2023
Data-Efficient Characterization of the Global Dynamics of Robot Controllers with Confidence Guarantees.
Proceedings of the IEEE International Conference on Robotics and Automation, 2023
2022
Experimental guidance for discovering genetic networks through hypothesis reduction on time series.
PLoS Comput. Biol., October, 2022
Extending Combinatorial Regulatory Network Modeling to Include Activity Control and Decay Modulation.
SIAM J. Appl. Dyn. Syst., September, 2022
Global analysis of regulatory network dynamics: equilibria and saddle-node bifurcations.
CoRR, 2022
Morse Graphs: Topological Tools for Analyzing the Global Dynamics of Robot Controllers.
Proceedings of the Algorithmic Foundations of Robotics XV, 2022
2021
Equilibria and their Stability in Networks with Steep Sigmoidal Nonlinearities.
SIAM J. Appl. Dyn. Syst., 2021
Computing Linear Extensions for Polynomial Posets Subject to Algebraic Constraints.
SIAM J. Appl. Algebra Geom., 2021
Rational design of complex phenotype via network models.
PLoS Comput. Biol., 2021
Mapping parameter spaces of biological switches.
PLoS Comput. Biol., 2021
A computational framework for connection matrix theory.
J. Appl. Comput. Topol., 2021
Extracting Global Dynamics of Loss Landscape in Deep Learning Models.
CoRR, 2021
2020
Conley Index Approach to Sampled Dynamics.
SIAM J. Appl. Dyn. Syst., 2020
Contractibility of a persistence map preimage.
J. Appl. Comput. Topol., 2020
2019
A comparison framework for interleaved persistence modules.
J. Appl. Comput. Topol., 2019
2018
Model Rejection and Parameter Reduction via Time Series.
SIAM J. Appl. Dyn. Syst., 2018
Identifying robust hysteresis in networks.
PLoS Comput. Biol., 2018
2017
Topological Signals of Singularities in Ricci Flow.
Axioms, 2017
Database of Dynamic Signatures Generated by Regulatory Networks (DSGRN).
Proceedings of the Computational Methods in Systems Biology, 2017
2016
Combinatorial Representation of Parameter Space for Switching Networks.
SIAM J. Appl. Dyn. Syst., 2016
Conley-Morse Databases for the Angular Dynamics of Newton's Method on the Plane.
SIAM J. Appl. Dyn. Syst., 2016
Lattice Structures for Attractors II.
Found. Comput. Math., 2016
2014
Discrete Morse Theoretic Algorithms for Computing Homology of Complexes and Maps.
Found. Comput. Math., 2014
Coarse Dynamics for Coarse Modeling: An Example From Population Biology.
Entropy, 2014
Complex contagions on noisy geometric networks.
CoRR, 2014
2013
Rigorous A Posteriori Computation of (Un)Stable Manifolds and Connecting Orbits for Analytic Maps.
SIAM J. Appl. Dyn. Syst., 2013
Morse Theory for Filtrations and Efficient Computation of Persistent Homology.
Discret. Comput. Geom., 2013
2011
Rigorous Numerics for Symmetric Connecting Orbits: Even Homoclinics of the Gray-Scott Equation.
SIAM J. Math. Anal., 2011
2010
Global smooth solution curves using rigorous branch following.
Math. Comput., 2010
Modeling Complexity of Physiological Time Series In-Silico.
Proceedings of the BIOSIGNALS 2010, 2010
2009
A Database Schema for the Analysis of Global Dynamics of Multiparameter Systems.
SIAM J. Appl. Dyn. Syst., 2009
2008
Efficient Morse Decompositions of Vector Fields.
IEEE Trans. Vis. Comput. Graph., 2008
Validated continuation over large parameter ranges for equilibria of PDEs.
Math. Comput. Simul., 2008
2007
Vector Field Editing and Periodic Orbit Extraction Using Morse Decomposition.
IEEE Trans. Vis. Comput. Graph., 2007
Validated Continuation for Equilibria of PDEs.
SIAM J. Numer. Anal., 2007
Structure of the Attractor of the Cahn-hilliard equation on a Square.
Int. J. Bifurc. Chaos, 2007
2006
Vector field design on surfaces.
ACM Trans. Graph., 2006
On the detection of simple points in higher dimensions using cubical homology.
IEEE Trans. Image Process., 2006
Rigorous Computations of Homoclinic Tangencies.
SIAM J. Appl. Dyn. Syst., 2006
Coronary vessel trees from 3D imagery: A topological approach.
Medical Image Anal., 2006
2005
Feature-based surface parameterization and texture mapping.
ACM Trans. Graph., 2005
Rigorous Numerics for Global Dynamics: A Study of the Swift-Hohenberg Equation.
SIAM J. Appl. Dyn. Syst., 2005
Graph Approach to the Computation of the Homology of Continuous Maps.
Found. Comput. Math., 2005
An Algorithmic Approach to Chain Recurrence.
Found. Comput. Math., 2005
Coronary vessel cores from 3D imagery: a topological approach.
Proceedings of the Medical Imaging 2005: Image Processing, 2005
2004
A Rigorous Numerical Method for the Global Analysis of Infinite-Dimensional Discrete Dynamical Systems.
SIAM J. Appl. Dyn. Syst., 2004
2003
Competing Species near a Degenerate Limit.
SIAM J. Math. Anal., 2003
2002
Analysis of blood vessel topology by cubical homology.
Proceedings of the 2002 International Conference on Image Processing, 2002
2001
Rigorous Numerics for Partial Differential Equations: The Kuramoto-Sivashinsky Equation.
Found. Comput. Math., 2001
Cubical homology and the topological classification of 2D and 3D imagery.
Proceedings of the 2001 International Conference on Image Processing, 2001
1998
Chaos in the Lorenz equations: A computer assisted proof. Part II: Details.
Math. Comput., 1998