复杂网络关键节点评估快速算法研究及在蛋白质功能预测中的应用

With the rapid development of complex networks, as one of the most important research areas, the study of essential nodes has crucial applications in the real world. There are two starting points for identifying the essential nodes. The first one is based on network security, and the second one is for retrieving biology information. However, most researches only apply to undirected networks, while many important real-world networks are directed. More importantly, with the increasing of the scale of the complex networks and the data sources involved, some classical technologies are inefficient and even infeasible in practice. Based on matrix functions and projection techniques for large sparse matrix computations, we aim to study novel techniques for assessing essential nodes of complex networks. Firstly, we propose fast algorithms and new criterion for evaluating essential nodes of large scale and directed networks. Secondly, we present efficient algorithms for evolving networks. Finally, we shed light on how to effectively solve the ProteinRank problem that arises in protein function prediction. The goal of this project is to offer novel and efficient numerical methods for large matrix function problems from identifying essential nodes of directed complex networks, and to improve the accuracy and reliability of the results of predicting protein functions when no candidates are available; so that we can retrieve key information from the complicated social networks and biology data sources.

随着复杂网络研究的兴起，作为复杂网络的重要研究内容之一，关键节点识别技术在现实世界中具有重要的应用价值。复杂网络关键节点识别的出发点主要有两个：一是基于网络安全；二是对生物信息的认识和探索。但是，目前的关键节点识别技术大多都是针对"无向网络"，而许多真实网络属于"有向网络"。而且，随着复杂网络规模及网络数据的海量剧增，一些经典的评估方法已经不能够满足实际问题的需要。 本项目基于矩阵函数与大规模稀疏矩阵投影类技术研究新的复杂网络关键节点评估技术，提出大规模复杂有向网络关键节点评估快速算法与新度量标准、"动态网络"关键节点评估快速算法，以及基于分子生物网络的"蛋白质等级"问题的快速算法。旨在为复杂有向网络关键节点评估中的大规模矩阵函数计算问题提供新的快速算法，并在没有参照对象的情况下提高大规模蛋白质功能预测的准确性与可靠性，从而能够从纷繁复杂的社会网络与生物网络数据中快速有效地获取关键的信息。

我们已经顺利完成该面上基金项目的任务。给出了基因等级问题的Jacobi预条件共轭梯度(PCG)算法；求解ProteinRank问题的加速Arnoldi算法； PageRank问题的最小不可约Markov链的新收敛性理论；求解多位移、多右端线性方程组灵活预条件、谱压缩自适应块Krylov子空间算法；进行了复杂网络分析中大规模矩阵函数与大规模特征值相关问题的研究；观察白藜芦醇(Res)对高脂饮食诱导肾损伤小鼠肾组织单核细胞趋化蛋白1(MCP-1)及转化生长因子β1(TGF-β1)表达的影响，并探讨其肾脏保护机制。项目在研期间，申请人在国际知名杂志，如：SIAM Journal on Matrix Analysis and Applications，Pattern Recognition，Data Mining and Knowledge Discovery，Journal of Scientific Computing，Advances in Computational Mathematics，Numerical Linear Algebra with Applications，Linear Algebra and its Applications 上发表学术论文多篇，并被国内外同行、专家多次引用。