论文标题
高斯随机嵌入多编码
Gaussian Random Embeddings of Multigraphs
论文作者
论文摘要
本文将线性和环聚合物的高斯随机步行和高斯随机多边形模型概括为由任意的多数$ g $指定的聚合物拓扑。单体位置和边缘位移的概率分布被明确给出，并显示出$ g $的图形laplacian的光谱，以预测配置的几何形状。这为詹姆斯·古特（James-Guth）幻象弹性网络理论提供了新的观点。该模型基于同源性和共同体学理论的思想所激发的线性代数。它为更详细的拓扑聚合物模型提供了强大的理论基础。
This paper generalizes the Gaussian random walk and Gaussian random polygon models for linear and ring polymers to polymer topologies specified by an arbitrary multigraph $G$. Probability distributions of monomer positions and edge displacements are given explicitly and the spectrum of the graph Laplacian of $G$ is shown to predict the geometry of the configurations. This provides a new perspective on the James-Guth-Flory theory of phantom elastic networks. The model is based on linear algebra motivated by ideas from homology and cohomology theory. It provides a robust theoretical foundation for more detailed models of topological polymers.
