Kinetic transition networks (KTNs) of local minima and transition states are able to capture the dynamics of numerous systems in chemistry, biology, and materials science. However, extracting observables is numerically challenging for large networks and generally will be sensitive to additional computational discovery. To have any measure of convergence for observables, these sensitivities must be regularly calculated. We present a matrix formulation of the discrete path sampling framework for KTNs, deriving expressions for branching probabilities, transition rates, and waiting times. Using the concept of the quasi-stationary distribution, a clear hierarchy of expressions for network observables is established, from exact results to steady-state approximations. We use these results in combination with the graph transformation method to derive the sensitivity, with respect to perturbations of the known KTN, giving explicit terms for the pairwise sensitivity and discussing the pathwise sensitivity. These results provide guidelines for converging the network, with respect to additional sampling, focusing on the estimates obtained for the overall rate coefficients between product and reactant states. We demonstrate this procedure for transitions in the double-funnel landscape of the 38-atom Lennard-Jones cluster.

中文翻译：

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动力学转化网络的定义，计算和收敛的可观察性

局部极小值和过渡态的动力学过渡网络（KTN）能够捕获化学，生物学和材料科学中众多系统的动力学。但是，对于大型网络而言，提取可观测值在数值上具有挑战性，并且通常对其他计算发现很敏感。为了对可观察物进行收敛，必须定期计算这些敏感度。我们提出了KTN离散路径采样框架的矩阵表述，推导了分支概率，转换率和等待时间的表达式。使用准平稳分布的概念，建立了网络可观测表达式的清晰层次，从精确结果到稳态近似。我们将这些结果与图形变换方法结合使用，以得出关于已知KTN扰动的灵敏度，为成对灵敏度给出明确的术语，并讨论路径灵敏度。这些结果提供了关于收敛网络的指导原则（针对额外的采样），重点是针对产物和反应物状态之间的总体速率系数所获得的估计值。我们演示了此过程的过渡在38原子Lennard-Jones群集的双漏斗景观中。着重于对产物和反应物状态之间的总速率系数的估计。我们演示了此过程的过渡在38原子Lennard-Jones群集的双漏斗景观中。着重于对产物和反应物状态之间的总速率系数的估计。我们演示了此过程的过渡在38原子Lennard-Jones群集的双漏斗景观中。