小反应网络的混合体积
Mixed volume of small reaction networks
摘要：
化学反应网络的一个重要不变量是它的正稳态的最大数目。然而，这个数字通常很难计算。尽管如此，这个数字有一个上限-即网络的混合体积-很容易计算。此外，最近的工作表明，对于某些生物信号网络，混合体积不会大大超过正稳态的最大数量。继续这条研究路线，我们进一步研究这种超支，并计算小网络的混合体积，这些网络只有几个物种或反应。
英文摘要：
An important invariant of a chemical reaction network is its maximum number of positive steady states. This number, however, is in general difficult to compute. Nonetheless, there is an upper bound on this number -- namely, a network's mixed volume -- that is easy to compute. Moreover, recent work has shown that, for certain biological signaling networks, the mixed volume does not greatly exceed the maximum number of positive steady states. Continuing this line of research, we further investigate this overcount and also compute the mixed volumes of small networks, those with only a few species or reactions.
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