Paramotopy: Software for parameter homotopies. It has long been known in the numerical algebraic geometry community that parameter homotopies provide a powerful tool for solving parametrized polynomial systems at a large number of parameter values. Paramotopy is a new software package dedicated to the efficient, parallel processing of a large number of parameter homotopies. Paramotopy makes use of Bertini’s implementation of user-defined homotopies, paired with Boost and other libraries for the efficient handling of large numbers of parameter values and solutions. It was initially developed to solve problems from redundant kinematics - see joint work with D. Brake (North Carolina State University), A. Maciejewski (Colorado State University), and V. Putkaradze (University of Alberta). This talk will include a brief introduction to parameter homotopies, a short tutorial on Paramotopy, and details about an application from biochemistry. In particular, the number of equilibria of a biochemical reaction network depends on the choice of a number of parameter values. With D. Brake, J. Gunawardena (Harvard Medical School), B. Gyori (National University of Singapore), and K-M Nam (Swarthmore College), we have devised a number of methods for better understanding the geography of the parameter space for such problems, with Paramotopy as a key ingredient.

References in zbMATH (referenced in 12 articles , 1 standard article )

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  1. Hao, Wenrui; Zheng, Chunyue: A stochastic homotopy tracking algorithm for parametric systems of nonlinear equations (2021)
  2. Bradford, Russell; Davenport, James H.; England, Matthew; Errami, Hassan; Gerdt, Vladimir; Grigoriev, Dima; Hoyt, Charles; Košta, Marek; Radulescu, Ovidiu; Sturm, Thomas; Weber, Andreas: Identifying the parametric occurrence of multiple steady states for some biological networks (2020)
  3. Bates, Dan; Brake, Danielle; Niemerg, Matt: Paramotopy: parameter homotopies in parallel (2018)
  4. Davenport, James H. (ed.); Kauers, Manuel (ed.); Labahn, George (ed.); Urban, Josef (ed.): Mathematical software -- ICMS 2018. 6th international conference, South Bend, IN, USA, July 24--27, 2018. Proceedings (2018)
  5. Bates, Daniel J.; Newell, Andrew J.; Niemerg, Matthew E.: Decoupling highly structured polynomial systems (2017)
  6. Bates, Daniel J.; Newell, Andrew J.; Niemerg, Matthew: BertiniLab: a MATLAB interface for solving systems of polynomial equations (2016)
  7. Brake, Daniel A.; Bates, Daniel J.; Putkaradze, Vakhtang; Maciejewski, Anthony A.: Workspace multiplicity and fault tolerance of cooperating robots (2016)
  8. Griffin, Zachary A.; Hauenstein, Jonathan D.: Real solutions to systems of polynomial equations and parameter continuation (2015)
  9. Bates, Daniel J.; Davis, Brent; Eklund, David; Hanson, Eric; Peterson, Chris: Perturbed homotopies for finding all isolated solutions of polynomial systems (2014)
  10. Bates, Daniel J.; Niemerg, Matthew: Using monodromy to avoid high precision in homotopy continuation (2014)
  11. Cicoli, Michele; Klevers, Denis; Krippendorf, Sven; Mayrhofer, Christoph; Quevedo, Fernando; Valandro, Roberto: Explicit de Sitter flux vacua for global string models with chiral matter (2014)
  12. He, Yang-Hui; Mehta, Dhagash; Niemerg, Matthew; Rummel, Markus; Valeanu, Alexandru: Exploring the potential energy landscape over a large parameter-space (2013)