ArticleJournal of the Royal Society, Interface2016
Numerical algebraic geometry for model selection and its application to the life sciences.
Article in Journal of the Royal Society, Interface, 2016. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 6 papers.
What it found
Each row is one number read from the abstract, on the scale the paper reported it, with its interval. Left of the dashed line favours the treatment, right favours the comparator. Under each row is the sentence it came from. New to these charts? A ten-minute tutorial.
The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.
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Trials whose registry record cites this paper, or whose number appears in the abstract. A trial that started after this paper was published is citing it as background, not reporting it.
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Who cites it
6 citing papers in PubMed.
- Maximum Likelihood Estimation for Unrooted 3-Leaf Trees: An Analytic Solution for the CFN Model.Bulletin of mathematical biology · 2024Article
- HOMOTOPY CONTINUATION FOR THE SPECTRA OF PERSISTENT LAPLACIANS.Foundations of data science (Springfield, Mo.) · 2021Article
- IDENTIFYING THE NUMBER OF COMPONENTS IN GAUSSIAN MIXTURE MODELS USING NUMERICAL ALGEBRAIC GEOMETRY.Journal of algebra and its applications · 2020Article
- Inferring reaction network structure from single-cell, multiplex data, using toric systems theory.PLoS computational biology · 2019Article
- Maximum Likelihood Estimation of Symmetric Group-Based Models via Numerical Algebraic Geometry.Bulletin of mathematical biology · 2019Article
- Dynamics of Posttranslational Modification Systems: Recent Progress and Future Directions.Biophysical journal · 2018Review
Corrections and comments
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Authors and funding
5 authors.
Funding
No grant is acknowledged in the PubMed record.
Abstract
Researchers 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.
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Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.