The aim of this paper is to investigate the rebinding effect, a phenomenon describing a "short-time memory" which can occur when projecting a Markov process onto a smaller state space. For guaranteeing a correct mapping by the Markov State Model, we assume a fuzzy clustering in terms of membership functions, assigning degrees of membership to each state. The macro states are represented by the membership functions and may be overlapping. The magnitude of this overlap is a measure for the strength of the rebinding effect, caused by the projection and stabilizing the system. A minimal bound for the rebinding effect included in a given system is computed as the solution of an optimization problem. Based on membership functions chosen as a linear combination of Schur vectors, this generalized approach includes reversible as well as non-reversible processes.

翻译：本文的目的是调查约束效应,一种描述在将Markov进程投射到较小国家空间时可能发生的“短暂记忆”的现象。为了保证Markov国家模型的正确映射,我们假定了以成员职能为单位的模糊组合,为每个国家分配了一定的成员资格。宏观国家代表着成员职能,并可能相互重叠。这种重叠的程度是衡量由预测和稳定系统造成的约束效应的强度的一个尺度。对特定系统中包含的约束效应的最低约束值作为优化问题的解决方案来计算。根据Schur矢量的线性组合选择的成员资格功能,这种普遍做法包括可逆和不可逆的过程。