{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/newton-okounkov-bodies-of-chemical-reaction","title":"Newton-Okounkov bodies of chemical reaction systems","arxiv_id":"2203.03840","date":"2022-03-08","proceeding":null,"authors":["Nida Obatake","Elise Walker"],"abstract":"Despite their noted potential in polynomial-system solving, there are few concrete examples of Newton-Okounkov bodies arising from applications. Accordingly, in this paper, we introduce a new application of Newton-Okounkov body theory to the study of chemical reaction networks, and compute several examples. An important invariant of a chemical reaction network is its maximum number of positive steady states, which is realized as the maximum number of positive real roots of a parametrized polynomial system. Here, we introduce a new upper bound on this number, namely the `Newton-Okounkov body bound' of a chemical reaction network. Through explicit examples, we show that the Newton-Okounkov body bound of a network gives a good upper bound on its maximum number of positive steady states. We also compare this Newton-Okounkov body bound to a related upper bound, namely the mixed volume of a chemical reaction network, and find that it often achieves better bounds.","url_abs":"https://arxiv.org/abs/2203.03840v1","url_pdf":"https://arxiv.org/pdf/2203.03840v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"newton-okounkov-bodies-of-chemical-reaction","repo_url":"https://github.com/eliseawalker/nobodies-for-chemicalrxns","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}