发现量子图中的隐藏层
Discovering hidden layers in quantum graphs
摘要：
寻找复杂网络中的隐藏层是现代科学中一个重要而又重要的问题。我们探索量子图的框架，以确定多层系统的隐藏部分是否存在，如果存在，那么它们的范围是什么，即，有多少未知层假设所有可用的信息都是波在网络的单层上传播的时间演化，那么仅仅通过观察动态来揭示隐藏的信息确实是可能的。我们提出的证据合成和现实世界的网络，波动力学的频谱可以表达不同的功能，在额外的频率峰值的形式。这些峰值表现出对参与传播的层数的依赖性，从而允许提取所述层数。我们表明，事实上，有足够的观察时间，可以完全重建的行归一化邻接矩阵谱。我们比较我们的主张，机器学习的方法，使用修改后的，多层系统的目的，波包签名方法。
英文摘要：
Finding hidden layers in complex networks is an important and a non-trivial problem in modern science. We explore the framework of quantum graphs to determine whether concealed parts of a multi-layer system exist and if so then what is their extent, i.e., how many unknown layers there are. Assuming that all information available is the time evolution of a wave propagation on a single layer of a network it is indeed possible to uncover that which is hidden by merely observing the dynamics. We present evidence on both synthetic and real-world networks that the frequency spectrum of the wave dynamics can express distinct features in the form of additional frequency peaks. These peaks exhibit dependence on the number of layers taking part in the propagation and thus allowing for the extraction of said number. We show that in fact, with sufficient observation time, one can fully reconstruct the row-normalised adjacency matrix spectrum. We compare our propositions to a machine learning approach using a modified, for the purposes of multi-layer systems, wave packet signature method.
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