Identifiability and numerical algebraic geometry. by Daniel J Bates, Jonathan D Hauenstein, Nicolette Meshkat

“…In this work, we use numerical algebraic geometry to determine if a model given by polynomial or rational ordinary differential equations is identifiable or unidentifiable. …”
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Numerical algebraic geometry for model selection and its application to the life sciences by Gross, E, Davis, B, Ho, K, Bates, D, Harrington, H

“…Here, we consider polynomial models (e.g. mass-action chemical reaction networks at steady state) and describe a framework for their analysis based on optimization using numerical algebraic geometry. Specifically, we use probability-one polynomial homotopy continuation methods to compute all critical points of the objective function, then filter to recover the global optima. …”

A numerical algebraic geometry approach to regional stability analysis of polynomial systems by Wampler, Charles, Permenter, Frank Noble, Tedrake, Russell Louis

“…Solutions to this optimization problem are found by solving a polynomial system of equations using techniques from numerical algebraic geometry. This system describes KKT points and singular points not satisfying a regularity condition. …”
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Sampling Algebraic Varieties for Sum of Squares Programs by Cifuentes, Diego Fernando, Parrilo, Pablo A.

“…For arbitrary varieties, we can obtain the required samples by using the tools of numerical algebraic geometry. In this way we connect the areas of SOS optimization and numerical algebraic geometry.…”
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Sampling real algebraic varieties for topological data analysis by Dufresne, E, Edwards, P, Harrington, H, Hauenstein, J

“…The algorithm utilizes methods from numerical algebraic geometry to give formal guarantees about the density of the sampling, and also employs geometric heuristics to reduce the size of the sample. …”

Robustness and parameter geography in post-translational modification systems. by Kee-Myoung Nam, Benjamin M Gyori, Silviana V Amethyst, Daniel J Bates, Jeremy Gunawardena

“…We further use the numerical algebraic geometry tools Bertini, Paramotopy, and alphaCertified to statistically assess the solutions to these equations at ∼109 parameter points in total. …”
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Polynomial systems : graphical structure, geometry, and applications by Cifuentes Pardo, Diego Fernando

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