共识网络中的边值问题
Boundary value problems in consensus networks
摘要：
本文研究了边界值条件对共识网络的影响。考虑一个网络，其中一些节点保持其估计恒定，而其他节点将其估计与其邻居的估计进行平均。我们分析了这样的网络，并表明，与标准的共识网络，网络估计收敛到一个一般的调和函数的图形。此外，最终值仅取决于边界节点处的值。这在共识网络中具有重要意义-例如，我们表明共识网络对单个恶意节点或单个节点中的一致错误的存在极其敏感。我们还讨论了这一结果在社会和传感器网络中的应用。我们通过一项涉及人类的实验研究，探讨了人类社交网络中边界节点的存在性。最后，对共识网络边值问题的数值研究进行了总结。
英文摘要：
This paper studies the effect of boundary value conditions on consensus networks. Consider a network where some nodes keep their estimates constant while other nodes average their estimates with that of their neighbors. We analyze such networks and show that in contrast to standard consensus networks, the network estimate converges to a general harmonic function on the graph. Furthermore, the final value depends only on the value at the boundary nodes. This has important implications in consensus networks -- for example, we show that consensus networks are extremely sensitive to the existence of a single malicious node or consistent errors in a single node. We also discuss applications of this result in social and sensor networks. We investigate the existence of boundary nodes in human social networks via an experimental study involving human subjects. Finally, the paper is concluded with the numerical studies of the boundary value problems in consensus networks.
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