用平方根逼近法估计无穷小量generator
Estimation of the infinitesimal generator by square-root approximation
摘要：
对于分子过程的分析，时间尺度的估计，即，转换率非常重要。从数学的观点来看，估计分子构象之间的转换速率是一个不变的子空间投影问题。将作用在函数空间上的某个无穷小生成元投影到一个低维率矩阵上。该投影可以分两步进行。首先将无穷小生成元离散化，然后逼近不变子空间，并将其用于子空间投影。在我们的方法中，离散化将基于构象空间的Voronoi镶嵌。我们将证明，离散化的无穷小生成元可以简单地近似为Voronoi细胞的玻尔兹曼权重的几何平均值。因此，分子结构的势能面与构象变化的跃迁速率之间存在着直接的相关性。我们提出了一个二维扩散过程和丙氨酸二肽的结果。
英文摘要：
For the analysis of molecular processes, the estimation of time-scales, i.e., transition rates, is very important. Estimating the transition rates between molecular conformations is -- from a mathematical point of view -- an invariant subspace projection problem. A certain infinitesimal generator acting on function space is projected to a low-dimensional rate matrix. This projection can be performed in two steps. First, the infinitesimal generator is discretized, then the invariant subspace is approxi-mated and used for the subspace projection. In our approach, the discretization will be based on a Voronoi tessellation of the conformational space. We will show that the discretized infinitesimal generator can simply be approximated by the geometric average of the Boltzmann weights of the Voronoi cells. Thus, there is a direct correla-tion between the potential energy surface of molecular structures and the transition rates of conformational changes. We present results for a 2d-diffusion process and Alanine dipeptide.
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