794 citations · 1.8k across the 40 of their papers we have counts for
6 papers · 1 filter
Geometric combinatorics and computational molecular biology: branching polytopes for RNA sequences
Elizabeth Drellich, Andrew Gainer-Dewar, Heather A. Harrington +3
Questions in computational molecular biology generate various discrete optimization problems, such as DNA sequence alignment and RNA secondary structure prediction. However, the op…
Reduction of dimension for nonlinear dynamical systems
Heather A. Harrington, Robert A. Van Gorder
We consider reduction of dimension for nonlinear dynamical systems. We demonstrate that in some cases, one can reduce a nonlinear system of equations into a single equation for one…
Numerical algebraic geometry for model selection and its application to the life sciences
Elizabeth Gross, Brent Davis, Kenneth L. Ho +2
Researchers working with mathematical models are often confronted by the related problems of parameter estimation, model validation, and model selection. These are all optimization…
A roadmap for the computation of persistent homology
Nina Otter, Mason A. Porter, Ulrike Tillmann +2
Persistent homology (PH) is a method used in topological data analysis (TDA) to study qualitative features of data that persist across multiple scales. It is robust to perturbation…
Algebraic Systems Biology: A Case Study for the Wnt Pathway
Elizabeth Gross, Heather A. Harrington, Zvi Rosen +1
Steady state analysis of dynamical systems for biological networks give rise to algebraic varieties in high-dimensional spaces whose study is of interest in their own right. We dem…
Mathematical and Statistical Techniques for Systems Medicine: The Wnt Signaling Pathway as a Case Study
Adam L. MacLean, Heather A. Harrington, Michael P. H. Stumpf +1
The last decade has seen an explosion in models that describe phenomena in systems medicine. Such models are especially useful for studying signaling pathways, such as the Wnt path…