State-space reduction and equivalence class sampling for a molecular self-assembly model

Direct simulation of a model with a large state space will generate enormous volumes of data, much of which is not relevant to the questions under study. In this paper, we consider a molecular self-assembly model as a typical example of a large state-space model, and present a method for selectively retrieving ‘target information’ from this model. This method partitions the state space into equivalence classes, as identified by an appropriate equivalence relation. The set of equivalence classes H, which serves as a reduced state space, contains none of the superfluous information of the original model. After construction and characterization of a Markov chain with state space H, the target information is efficiently retrieved via Markov chain Monte Carlo sampling. This approach represents a new breed of simulation techniques which are highly optimized for studying molecular self-assembly and, moreover, serves as a valuable guideline for analysis of other large state-space models.

对大状态空间模型进行直接模拟时，往往会产生海量数据，其中多数与研究关注的问题并无关联。本文以分子自组装模型这一典型大状态空间模型为例，提出了一种可从该模型中选择性检索"目标信息"的方法。该方法通过设定恰当的等价关系，将状态空间划分为若干等价类。作为约简状态空间的等价类集合H，剔除了原模型中的全部冗余信息。在构建并表征状态空间为H的马尔可夫链后，即可通过马尔可夫链蒙特卡洛采样高效获取目标信息。该方法属于一类专为分子自组装研究优化的新型模拟技术，同时也为其他大状态空间模型的分析提供了极具价值的参考范式。