模糊置换时间不可逆性用于复杂系统的非平衡分析
Fuzzy permutation time irreversibility for nonequilibrium analysis of complex system
AI总结：
本研究提出模糊置换时间不可逆性（fpTIR），通过负指数函数度量向量差异，有效量化复杂系统非平衡特性，并在心跳分析中优于传统方法，支持衰老和疾病的复杂性丧失理论。
摘要：
置换时间不可逆性是量化复杂系统非平衡特性的重要方法；然而，序数模式是时间结构的粗粒化替代方案，无法准确表示详细的结构信息。本研究旨在通过基于负指数函数测量向量元素之间的差异，提出一种模糊置换时间不可逆性（fpTIR）。构建向量的幅度置换并计算其隶属度；然后，测量前向和后向序列之间概率分布的差异，以得到fpTIR。为了比较和测量系统的复杂性，计算香农熵作为模糊置换概率分布中的平均信息量，即模糊置换熵（fPEn）。根据替代理论，使用逻辑斯蒂、埃农和一阶自回归系统生成模式序列以验证fpTIR，随后将其用于分析来自PhysioNet数据库的充血性心力衰竭患者以及健康老年人和年轻参与者的心跳数据。结果表明，fpTIR有效测量了系统的非平衡特性，从而提高了心跳分析的准确性。然而，在分析概率分布时，fpTIR和fPEn在混沌序列中表现出差异，甚至在心跳数据中得出相反的结果，其中fpTIR的结果与衰老和疾病中复杂性丧失的理论一致。总体而言，fpTIR准确表征了序列的结构，并增强了复杂系统非平衡分析的准确性，为从非平衡动力学和熵复杂性的角度探索复杂系统提供了理论基础。
英文摘要：
Permutation time irreversibility is an important method to quantify nonequilibrium characteristics of complex systems; however, ordinal pattern is a coarse-graining alternative of temporal structure and cannot accurately represent detailed structural information. This study aims to propose a fuzzy permutation time irreversibility (fpTIR) by measuring the difference between vector elements based on a negative exponential function. The amplitude permutation of vector is constructed and its membership degree is calculated; then, the difference in probability distribution between the forward and backward sequences is measured for fpTIR. To compare and measure the system's complexity, the Shannon entropy is calculated as the average amount of information in the fuzzy permutation probability distribution, i.e., fuzzy permutation entropy (fPEn). According to the surrogate theory, mode series are generated using logistic, Henon, and first-order autoregressive systems to verify the fpTIR, which is then used to analyze the heartbeats of patients with congestive heart failure and healthy elderly and young participants from the PhysioNet database. Results suggest that the fpTIR effectively measures the system's nonequilibrium characteristics, thus improving the accuracy of heartbeat analysis. However, in analyzing probability distributions, the fpTIR and fPEn exhibit discrepancies in the chaotic series and even opposite results in the heartbeats, wherein the results of fpTIR are consistent with the theory of complexity loss in aging and disease. Overall, the fpTIR accurately characterizes the structure of the sequences and enhances the accuracy of the nonequilibrium analysis of complex systems, providing a theoretical basis for exploring complex systems from the perspectives of nonequilibrium dynamics and entropy complexity.
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