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dc.contributor.authorGross, Elizabeth
dc.contributor.authorDavis, Brent
dc.contributor.authorHo, Kenneth L.
dc.contributor.authorBates, Daniel J.
dc.contributor.authorHarrington, Heather A.
dc.date.accessioned2017-05-15T10:35:09Z
dc.date.available2017-05-15T10:35:09Z
dc.date.issued2016-10-12
dc.identifier.citationGross E, Davis B, Ho KL, Bates DJ, Harrington HA (2016) Numerical algebraic geometry for model selection and its application to the life sciences. Journal of The Royal Society Interface 13: 20160256. Available: http://dx.doi.org/10.1098/rsif.2016.0256.
dc.identifier.issn1742-5689
dc.identifier.issn1742-5662
dc.identifier.doi10.1098/rsif.2016.0256
dc.identifier.urihttp://hdl.handle.net/10754/623572
dc.description.abstractResearchers working with mathematical models are often confronted by the related problems of parameter estimation, model validation and model selection. These are all optimization problems, well known to be challenging due to nonlinearity, non-convexity and multiple local optima. Furthermore, the challenges are compounded when only partial data are available. 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. Our approach exploits the geometrical structures relating models and data, and we demonstrate its utility on examples from cell signalling, synthetic biology and epidemiology.
dc.description.sponsorshipE.G., K.L.H., D.J.B. and H.A.H. acknowledge funding from the American Institute of Mathematics (AIM). E.G. was supported by the US National Science Foundation grant DMS-1304167. B.D. was partially supported by NSF DMS-1115668. K.L.H. acknowledges support from NSF DMS-1203554. D.J.B. gratefully acknowledges partial support from NSF DMS-1115668, NSF ACI-1440467, and the Mathematical Biosciences Institute (MBI). H.A.H. gratefully acknowledges funding from AMS Simons Travel Grant, EPSRC Fellowship EP/K041096/1, King Abdullah University of Science and Technology (KAUST) KUK-C1-013-04 and MPH Stumpf Leverhulme Trust Grant.
dc.publisherThe Royal Society
dc.subjectChemical reaction networks
dc.subjectMaximum-likelihood
dc.subjectModel validation
dc.subjectParameter estimation
dc.subjectPolynomial optimization
dc.titleNumerical algebraic geometry for model selection and its application to the life sciences
dc.typeArticle
dc.identifier.journalJournal of The Royal Society Interface
dc.contributor.institutionDepartment of Mathematics, San Jose´ State University, San Jose´, CA 95112, USA
dc.contributor.institutionDepartment of Mathematics, Colorado State University, Fort Collins, CO 80523, USA
dc.contributor.institutionDepartment of Mathematics, Stanford University, Stanford, CA 94305, USA
dc.contributor.institutionMathematical Institute, University of Oxford, Oxford OX2 6GG, UK
kaust.grant.numberKUK-C1-013-04
dc.date.published-online2016-10-12
dc.date.published-print2016-10


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