$S$ -Leaping：一种自适应的加速随机模拟算法，桥接$τ$ -leaping和$R$ -leaping
$S$-Leaping: An adaptive, accelerated stochastic simulation algorithm, bridging $τ$-leaping and $R$-leaping
摘要：
我们提出了$S$ -跳跃算法的Gillespie的随机模拟算法的加速，结合了两个主要的加速方法的优点; $τ$ -跳跃和$R$ -跳跃算法。已知这些算法在不同条件下是有效的; $τ$ -跳跃对于非刚性系统或具有部分平衡的系统是有效的，而$R$ -跳跃由于有效的采样过程而在刚性组中表现得更好。然而，即使是系统设置中的微小变化也会严重影响模拟系统的性质，从而降低加速算法的效率。该算法结合了$τ$ -跳跃算法的有效时间步长选择和$R$ -跳跃算法的有效采样过程。$S$ -跳跃在不同的条件下保持其效率，并在大型和刚性组或快速动态系统的情况下，$S$ -跳跃优于这两种方法。我们证明了性能和准确性的$S$跳跃比较$τ$跳跃和$R$跳跃的基准系统，涉及生物反应网络。
英文摘要：
We propose the $S$-leaping algorithm for the acceleration of Gillespie's stochastic simulation algorithm that combines the advantages of the two main accelerated methods; the $τ$-leaping and $R$-leaping algorithms. These algorithms are known to be efficient under different conditions; the $τ$-leaping is efficient for non-stiff systems or systems with partial equilibrium, while the $R$-leaping performs better in stiff system thanks to an efficient sampling procedure. However, even a small change in a system's set up can critically affect the nature of the simulated system and thus reduce the efficiency of an accelerated algorithm. The proposed algorithm combines the efficient time step selection from the $τ$-leaping with the effective sampling procedure from the $R$-leaping algorithm. The $S$-leaping is shown to maintain its efficiency under different conditions and in the case of large and stiff systems or systems with fast dynamics, the $S$-leaping outperforms both methods. We demonstrate the performance and the accuracy of the $S$-leaping in comparison with the $τ$-leaping and $R$-leaping on a number of benchmark systems involving biological reaction networks.
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