title: State-space reduction and equivalence class sampling for a molecular self-assembly model.
abstract: 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.
authors: Advanced Institute for Materials Research (AIMR), Tohoku University, Sendai 980-8577, Japan; Japan Science and Technology Agency (PRESTO), Kawaguchi, Saitama 332-0012, Japan.
authors: Daniel M
authors: 0000-0001-9387-728X
authors: DM
authors: Packwood
authors: Advanced Institute for Materials Research (AIMR), Tohoku University, Sendai 980-8577, Japan; California Nanosystems Institute, University of California, Los Angeles, CA 90095, USA; Department of Chemistry and Biochemistry, University of California, Los Angeles, CA 90095, USA; Department of Materials Science and Engineering, University of California, Los Angeles, CA 90095, USA.
authors: Patrick
authors: P
authors: Han
authors: Advanced Institute for Materials Research (AIMR), Tohoku University, Sendai 980-8577, Japan; Department of Applied Chemistry, Graduate School of Science and Engineering, Tokyo Institute of Technology, Tokyo 152-8352, Japan.
authors: Taro
authors: T
authors: Hitosugi
keywords: Markov chain Monte Carlo; model reduction; self-assembly