论文标题
如何在所有积极时期产生浓度阳性的物种？
How to generate species with positive concentrations for all positive times?
论文作者
论文摘要
鉴于反应（网络），我们正在寻找最小的物种集，从该物种开始，所有物种将在诱导动力学微分方程溶液的存在的所有积极时期都具有阳性浓度。我们提出三种解决问题的算法。第一个实质上检查了物种集的所有可能子集。由于组合爆炸，这显然可以仅适用于几十种物种。第二个是基于对问题的整数编程重新重新制定的。第三个以系统的方式绕过问题的状态空间，并产生所有有利的初始物种的最低集合，也适用于大型系统。所有算法都在很大程度上依赖于Volpert指数的概念，该算法早些时候用于分解整体反应[Kovács\ textit {等，物理化学化学物理学} 2004，6，1236]。分析了与永久性假设的关系，问题解决方案的可能经济或医疗用途，并在最后提出了开放问题。
Given a reaction (network) we are looking for minimal sets of species starting from which all the species will have positive concentrations for all positive times in the domain of existence of the solution of the induced kinetic differential equation. We present three algorithms to solve the problem. The first one essentially checks all the possible subsets of the sets of species. This can obviously work for only a few dozen species because of combinatorial explosion. The second one is based on an integer programming reformulation of the problem. The third one walks around the state space of the problem in a systematic way and produces all the minimal sets of the advantageous initial species, and works also for large systems. All the algorithms rely heavily on the concept of Volpert indices, used earlier for the decomposition of overall reactions [Kovács \textit{et al., Physical Chemistry Chemical Physics} 2004, 6, 1236]. Relations to the permanence hypothesis, possible economic or medical uses of the solution of the problem are analyzed, and open problems are formulated at the end.
