论文标题
牛顿 - 科恩科夫化学反应系统机构
Newton-Okounkov bodies of chemical reaction systems
论文作者
论文摘要
尽管在多项式系统解决方案中具有著名的潜力，但由于应用而引起的牛顿 - 科恩科夫身体的具体例子很少。因此，在本文中，我们在化学反应网络的研究中介绍了牛顿 - 科恩科夫身体理论的新应用，并计算了几个示例。化学反应网络的重要不变是其最大阳性稳态数量，它被认为是参数化多项式系统的最大真实根数。在这里，我们在这个数字上介绍了一个新的上限，即化学反应网络的“牛顿 - 科恩科夫体界”。通过明确的示例，我们表明，网络界限的牛顿 - 科恩科夫身体在其最大阳性稳态数量上具有良好的上限。我们还比较了与相关上限（即化学反应网络的混合体积）结合的这个牛顿 - 科恩科夫的身体，并发现它通常可以实现更好的边界。
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.
