论文标题
一种用于测试可逆化学反应网络二项式的理论方法
A Graph Theoretical Approach for Testing Binomiality of Reversible Chemical Reaction Networks
论文作者
论文摘要
我们研究化学反应网络稳态理想的二项式。将速率常数视为不确定的，已经引入了无条件二项式的概念，并且在最近的可逆化学反应网络的最新工作中提出了基于线性代数的算法，该算法具有多项式时间复杂性的上限，该算法在物种和反应的数量上具有多项式时间复杂性上限。在本文中，使用修改版的物种 - 反应图，我们提出了一种基于图理论的算法，该算法通过添加和删除边缘并更改边缘的标签来执行，以测试无条件的二项式。我们已经在枫树中实现了图理论算法以及线性代数，并在生化模型上进行了实验。我们的实验表明，图理论方法的性能与线性代数方法相似或更好，而它的速度大大比groebner基础和量词消除方法快。
We study binomiality of the steady state ideals of chemical reaction networks. Considering rate constants as indeterminates, the concept of unconditional binomiality has been introduced and an algorithm based on linear algebra has been proposed in a recent work for reversible chemical reaction networks, which has a polynomial time complexity upper bound on the number of species and reactions. In this article, using a modified version of species--reaction graphs, we present an algorithm based on graph theory which performs by adding and deleting edges and changing the labels of the edges in order to test unconditional binomiality. We have implemented our graph theoretical algorithm as well as the linear algebra one in Maple and made experiments on biochemical models. Our experiments show that the performance of the graph theoretical approach is similar to or better than the linear algebra approach, while it is drastically faster than Groebner basis and quantifier elimination methods.
