Not all nodes in a network are created equal. Differences and similarities exist at both individual node and group levels. Disentangling single node from group properties is crucial for network modeling and structural inference. Based on unbiased generative probabilistic exponential random graph models and employing distributive message passing techniques, we present an efficient algorithm that allows one to separate the contributions of individual nodes and groups of nodes to the network structure. This leads to improved detection accuracy of latent class structure in real world data sets compared to models that focus on group structure alone. Furthermore, the inclusion of hitherto neglected group specific effects in models used to assess the statistical significance of small subgraph (motif) distributions in networks may be sufficient to explain most of the observed statistics. We show the predictive power of such generative models in forecasting putative gene-disease associations in the Online Mendelian Inheritance in Man (OMIM) database. The approach is suitable for both directed and undirected uni-partite as well as for bipartite networks.
Coarse-Graining of Microscopic Dynamics into Mesoscopic Transient Potential Model
我们表明，一个介观粗粒度的动力学模型，其中包括瞬态电位可以正式从底层的微观动力学模型。作为微观动力学模型，我们采用过阻尼Langevin方程。利用路径概率和Onsager-Machlup型作用量，我们计算了粗粒介观自由度的路径概率。介观自由度的作用可以通过引入瞬态势来简化。介观自由度的动力学方程可以简单地用带有瞬态势的朗之万方程来描述。作为一个简单的和易于分析的近似，我们引入了额外的自由度表示的瞬态电位的状态。然后，我们近似地表示系统的动力学的LETP和瞬态电位的动力学模型的组合。所得动力学模型具有与响应粒子动力学（RaPiD）类型模型相同的动力学结构[W. J. Briels，软物质5，4401（2009）]和多链滑动弹簧型模型[T. Uneyama和Y. Masubuchi，J.Chem.Phys.137，154902（2012）]。作为示范，我们应用我们的粗粒化方法与LETP在过冷液体中的单粒子动力学，并比较的结果与分子动力学模拟和其他粗粒化模型的LETP。
Institute for Functional Intelligent Materials, National University of Singapore（新加坡国立大学功能智能材料研究所）；National University of Singapore（新加坡国立大学）；Peking University（北京大学）；AI for Science Institute, Beijing（北京AI for Science Institute）
