空间跳跃的精确实现：空间分割跳跃算法
Accurate implementation of leaping in space: The spatial partitioned-leaping algorithm
摘要：
有一个准确的和有效的计算方法，可以占两个离散和随机性质的化学相互作用，以及空间不均匀性和扩散是一个巨大的需求。在生物学和纳米材料科学中尤其如此，在这些领域中，确定性动力学和充分混合的反应体积的常见假设经常被打破。在这篇文章中，我们提出了一个空间版本的分区跳跃算法（PLA），一个多尺度加速随机模拟的方法建立在吉莱斯皮的τ跳跃框架。我们特别注意实现的细节，特别是因为它涉及到时间步长计算过程。我们指出，在这方面已经取得的概念性错误，在以前的实现空间τ跳跃，并说明这些错误的表现形式，通过实际的例子。最后，我们讨论了将有效的精确随机技术，如下一个子体积方法，到一个空间跳跃的框架，并提出可能的解决方案的基本困难。
英文摘要：
There is a great need for accurate and efficient computational approaches that can account for both the discrete and stochastic nature of chemical interactions as well as spatial inhomogeneities and diffusion. This is particularly true in biology and nanoscale materials science, where the common assumptions of deterministic dynamics and well-mixed reaction volumes often break down. In this article, we present a spatial version of the partitioned-leaping algorithm (PLA), a multiscale accelerated-stochastic simulation approach built upon the tau-leaping framework of Gillespie. We pay special attention to the details of the implementation, particularly as it pertains to the time step calculation procedure. We point out conceptual errors that have been made in this regard in prior implementations of spatial tau-leaping and illustrate the manifestation of these errors through practical examples. Finally, we discuss the fundamental difficulties associated with incorporating efficient exact-stochastic techniques, such as the next-subvolume method, into a spatial-leaping framework and suggest possible solutions.
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