Lorentz时空中的嵌入图
Embedding Graphs in Lorentzian Spacetime
摘要：
网络分析的几何方法将简单定义的模型与强大的描述能力相结合。在这项工作中，我们提供了一种方法嵌入到闵可夫斯基时空使用多维标度（MDS）的有向无环图。首先，我们概括了经典的MDS算法，定义只为度量与欧几里德签名，流形的任何度量签名。然后，我们使用这种一般的方法来开发一种算法，用于具有因果结构的网络，允许它们嵌入洛伦兹流形。通过计算闵可夫斯基时空中因果集和引用网络的嵌入来证明该方法。最后，我们提出了一些应用在引文分析，如论文推荐，识别缺失的引文和拟合引用模型的数据使用这种几何方法。
英文摘要：
Geometric approaches to network analysis combine simply defined models with great descriptive power. In this work we provide a method for embedding directed acyclic graphs into Minkowski spacetime using Multidimensional scaling (MDS). First we generalise the classical MDS algorithm, defined only for metrics with a Euclidean signature, to manifolds of any metric signature. We then use this general method to develop an algorithm to be used on networks which have causal structure allowing them to be embedded in Lorentzian manifolds. The method is demonstrated by calculating embeddings for both causal sets and citation networks in Minkowski spacetime. We finally suggest a number of applications in citation analysis such as paper recommendation, identifying missing citations and fitting citation models to data using this geometric approach.
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