反应网络的符号敏感性：一种代数方法
Sign-sensitivities for reaction networks: an algebraic approach
摘要：
本文提出了一个代数框架来研究由常微分方程系统建模的反应网络的符号灵敏度。具体来说，我们研究的符号的衍生物的浓度在网络中的稳定状态相对于一个小扰动的参数向量。我们提供了一个封闭的公式的衍生物，可容纳共同的扰动，并说明其形式与众多的例子。我们认为，从数学上讲，研究系统对总量变化的响应是不合理的，人们应该考虑初始条件的扰动。我们找到了一个基于符号的标准来确定，而不计算灵敏度，符号是否依赖于系统的稳态和参数。这是基于所谓的内射网络的早期结果。最后，我们解决系统的多个稳定状态和稳定的稳定状态的限制。
英文摘要：
This paper presents an algebraic framework to study sign-sensitivities for reaction networks modeled by means of systems of ordinary differential equations. Specifically, we study the sign of the derivative of the concentrations of the species in the network at steady state with respect to a small perturbation on the parameter vector. We provide a closed formula for the derivatives that accommodates common perturbations, and illustrate its form with numerous examples. We argue that, mathematically, the study of the response to the system with respect to changes in total amounts is not well posed, and that one should rather consider perturbations with respect to the initial conditions. We find a sign-based criterion to determine, without computing the sensitivities, whether the sign depends on the steady state and parameters of the system. This is based on earlier results of so-called injective networks. Finally, we address systems with multiple steady states and the restriction to stable steady states.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
