### Abstract

Original language | English |
---|---|

Article number | 201702697 |

Journal | Proceedings of the National Academy of Sciences of the United States of America |

Number of pages | 6 |

ISSN | 0027-8424 |

DOIs | |

Publication status | Published - 2017 |

Externally published | Yes |

### Keywords

- Polynomial dynamical systems
- Partition refinement
- Aggregation

### Cite this

*Proceedings of the National Academy of Sciences of the United States of America*, [201702697]. https://doi.org/10.1073/pnas.1702697114

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*Proceedings of the National Academy of Sciences of the United States of America*. https://doi.org/10.1073/pnas.1702697114

**Maximal aggregation of polynomial dynamical systems.** / Cardelli, Luca; Tribastone, Mirco; Tschaikowski, Max; Vandin, Andrea.

Research output: Contribution to journal › Journal article › Research › peer-review

TY - JOUR

T1 - Maximal aggregation of polynomial dynamical systems

AU - Cardelli, Luca

AU - Tribastone, Mirco

AU - Tschaikowski, Max

AU - Vandin, Andrea

PY - 2017

Y1 - 2017

N2 - Ordinary differential equations (ODEs) with polynomial derivatives are a fundamental tool for understanding the dynamics of systems across many branches of science, but our ability to gain mechanistic insight and effectively conduct numerical evaluations is critically hindered when dealing with large models. Here we propose an aggregation technique that rests on two notions of equivalence relating ODE variables whenever they have the same solution (backward criterion) or if a self-consistent system can be written for describing the evolution of sums of variables in the same equivalence class (forward criterion). A key feature of our proposal is to encode a polynomial ODE system into a finitary structure akin to a formal chemical reaction network. This enables the development of a discrete algorithm to efficiently compute the largest equivalence, building on approaches rooted in computer science to minimize basic models of computation through iterative partition refinements. The physical interpretability of the aggregation is shown on polynomial ODE systems for biochemical reaction networks, gene regulatory networks, and evolutionary game theory.

AB - Ordinary differential equations (ODEs) with polynomial derivatives are a fundamental tool for understanding the dynamics of systems across many branches of science, but our ability to gain mechanistic insight and effectively conduct numerical evaluations is critically hindered when dealing with large models. Here we propose an aggregation technique that rests on two notions of equivalence relating ODE variables whenever they have the same solution (backward criterion) or if a self-consistent system can be written for describing the evolution of sums of variables in the same equivalence class (forward criterion). A key feature of our proposal is to encode a polynomial ODE system into a finitary structure akin to a formal chemical reaction network. This enables the development of a discrete algorithm to efficiently compute the largest equivalence, building on approaches rooted in computer science to minimize basic models of computation through iterative partition refinements. The physical interpretability of the aggregation is shown on polynomial ODE systems for biochemical reaction networks, gene regulatory networks, and evolutionary game theory.

KW - Polynomial dynamical systems

KW - Partition refinement

KW - Aggregation

U2 - 10.1073/pnas.1702697114

DO - 10.1073/pnas.1702697114

M3 - Journal article

JO - Proceedings of the National Academy of Sciences of the United States of America

JF - Proceedings of the National Academy of Sciences of the United States of America

SN - 0027-8424

M1 - 201702697

ER -