标题： 顺序可视性图模式 显示英文标题

标题： Sequential visibility-graph motifs

摘要： 可见性算法将时间序列转换为图，并在其拓扑结构中编码动态信息，为基于图论的时间序列分析铺平了道路，并在非线性动力学与网络科学之间建立了一座桥梁。 在本工作中，我们引入并研究了顺序可见性图基序的概念，即出现频率具有特征的小型子结构，这些子结构由n个连续节点组成。 我们发展了一种理论，可以精确地计算与一般确定性和随机动力学类别相关的基序轮廓。 我们发现，这一简单特性确实是一个高度信息丰富且计算高效的特征，能够区分不同的动力学，并对噪声污染具有鲁棒性。 我们最终确认，通过从实验性心率序列中提取基序轮廓，可以在实践中用于无监督学习，从而能够区分冥想状态与其他放松状态。 该通用理论的应用包括对物理、生物和金融时间序列的自动分类和描述。 显示英文摘要

摘要： Visibility algorithms transform time series into graphs and encode dynamical information in their topology, paving the way for graph-theoretical time series analysis as well as building a bridge between nonlinear dynamics and network science. In this work we introduce and study the concept of sequential visibility graph motifs, smaller substructures of n consecutive nodes that appear with characteristic frequencies. We develop a theory to compute in an exact way the motif profiles associated to general classes of deterministic and stochastic dynamics. We find that this simple property is indeed a highly informative and computationally efficient feature capable to distinguish among different dynamics and robust against noise contamination. We finally confirm that it can be used in practice to perform unsupervised learning, by extracting motif profiles from experimental heart-rate series and being able, accordingly, to disentangle meditative from other relaxation states. Applications of this general theory include the automatic classification and description of physical, biological, and financial time series.