Enregistré dans:
| Auteurs principaux: | , , , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2406.09514 |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866911916763381760 |
|---|---|
| author | Curiel, Maize Farr, Elise Fries, Galileo Puente, Luis David García Hutchins, Julian Hoang, Vuong Nguyen |
| author_facet | Curiel, Maize Farr, Elise Fries, Galileo Puente, Luis David García Hutchins, Julian Hoang, Vuong Nguyen |
| contents | Chemical reaction network theory is a field of applied mathematics concerned with modeling chemical systems, and can be used in other contexts such as in systems biology to study cellular signaling pathways or epidemiology to study the effect of human interaction on the spread of disease. In this paper, we seek to understand a chemical reaction network's equilibrium points through the lens of algebraic geometry by computing the positive part of the steady-state variety defined by polynomial equations arising from the assumption of mass-action kinetics. We provide a systematic classification of positive steady-state varieties produced by 2-species, 2-reaction networks, grounded in combinatorial and algebraic properties. While some (restricted) techniques exist to fully understand the ideal defining the positive steady-state variety, this computation presents a significant challenge in general. Our classification theorems provide a simplification of previous criteria, and aim to provide a foundation for future analysis of larger networks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_09514 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Positive Steady-State Varieties of Small Chemical Reaction Networks Curiel, Maize Farr, Elise Fries, Galileo Puente, Luis David García Hutchins, Julian Hoang, Vuong Nguyen Algebraic Geometry 65H10, 92E20, 12D10 Chemical reaction network theory is a field of applied mathematics concerned with modeling chemical systems, and can be used in other contexts such as in systems biology to study cellular signaling pathways or epidemiology to study the effect of human interaction on the spread of disease. In this paper, we seek to understand a chemical reaction network's equilibrium points through the lens of algebraic geometry by computing the positive part of the steady-state variety defined by polynomial equations arising from the assumption of mass-action kinetics. We provide a systematic classification of positive steady-state varieties produced by 2-species, 2-reaction networks, grounded in combinatorial and algebraic properties. While some (restricted) techniques exist to fully understand the ideal defining the positive steady-state variety, this computation presents a significant challenge in general. Our classification theorems provide a simplification of previous criteria, and aim to provide a foundation for future analysis of larger networks. |
| title | Positive Steady-State Varieties of Small Chemical Reaction Networks |
| topic | Algebraic Geometry 65H10, 92E20, 12D10 |
| url | https://arxiv.org/abs/2406.09514 |