摘要翻译：
为一般动力系统的轨迹寻找正确的编码是一项复杂的任务：符号序列需要保持系统轨迹的不变性。在理论上，当得到生成马尔可夫划分(GMP)时，就可以找到这个问题的解决方案。生成马尔可夫划分只有在不稳定流形和稳定流形都已知且精度无限时才被定义。然而，这些流形通常形成高度卷积的欧几里得集，是先验未知的，而且，正如在任何现实世界的实验中所发生的那样，测量是在有限的时间跨度内以有限的分辨率进行的。如果系统是由相互作用的动力单元组成的网络，即高维复杂系统，任务就变得更加复杂。在这里，我们解决了这一问题，并通过定义一种方法来近似构造任何复杂系统的有限分辨率和有限时间轨迹的GMPs。我们在耦合映射网络上严格地测试了我们的方法，将它们的轨迹编码成符号序列。我们证明了这些序列是最优的，因为它们最小化了信息损失和添加的任何虚假信息。因此，我们的方法允许我们从观测数据近似地计算复杂系统的不变概率测度。因此，我们可以有效地定义适用于广泛复杂现象的复杂性度量，例如从不同大脑区域测量的脑电信号来表征大脑活动，或者从不同地球区域测量的温度异常来表征气候变化。
---
英文标题：
《Entropy-based Generating Markov Partitions for Complex Systems》
---
作者：
Nicol\'as Rubido, Celso Grebogi, Murilo S. Baptista
---
最新提交年份：
2017
---
分类信息：

一级分类：Physics        物理学
二级分类：Chaotic Dynamics        混沌动力学
分类描述：Dynamical systems, chaos, quantum chaos, topological dynamics, cycle expansions, turbulence, propagation
动力系统，混沌，量子混沌，拓扑动力学，循环展开，湍流，传播
--
一级分类：Electrical Engineering and Systems Science        电气工程与系统科学
二级分类：Signal Processing        信号处理
分类描述：Theory, algorithms, performance analysis and applications of signal and data analysis, including physical modeling, processing, detection and parameter estimation, learning, mining, retrieval, and information extraction. The term "signal" includes speech, audio, sonar, radar, geophysical, physiological, (bio-) medical, image, video, and multimodal natural and man-made signals, including communication signals and data. Topics of interest include: statistical signal processing, spectral estimation and system identification; filter design, adaptive filtering / stochastic learning; (compressive) sampling, sensing, and transform-domain methods including fast algorithms; signal processing for machine learning and machine learning for signal processing applications; in-network and graph signal processing; convex and nonconvex optimization methods for signal processing applications; radar, sonar, and sensor array beamforming and direction finding; communications signal processing; low power, multi-core and system-on-chip signal processing; sensing, communication, analysis and optimization for cyber-physical systems such as power grids and the Internet of Things.
信号和数据分析的理论、算法、性能分析和应用，包括物理建模、处理、检测和参数估计、学习、挖掘、检索和信息提取。“信号”一词包括语音、音频、声纳、雷达、地球物理、生理、（生物）医学、图像、视频和多模态自然和人为信号，包括通信信号和数据。感兴趣的主题包括：统计信号处理、谱估计和系统辨识；滤波器设计；自适应滤波/随机学习；（压缩）采样、传感和变换域方法，包括快速算法；用于机器学习的信号处理和用于信号处理应用的机器学习；网络与图形信号处理；信号处理中的凸和非凸优化方法；雷达、声纳和传感器阵列波束形成和测向；通信信号处理；低功耗、多核、片上系统信号处理；信息物理系统的传感、通信、分析和优化，如电网和物联网。
--
一级分类：Physics        物理学
二级分类：Data Analysis, Statistics and Probability        数据分析、统计与概率
分类描述：Methods, software and hardware for physics data analysis: data processing and storage; measurement methodology; statistical and mathematical aspects such as parametrization and uncertainties.
物理数据分析的方法、软硬件：数据处理与存储；测量方法；统计和数学方面，如参数化和不确定性。
--

---
英文摘要：
  Finding the correct encoding for a generic dynamical system's trajectory is a complicated task: the symbolic sequence needs to preserve the invariant properties from the system's trajectory. In theory, the solution to this problem is found when a Generating Markov Partition (GMP) is obtained, which is only defined once the unstable and stable manifolds are known with infinite precision and for all times. However, these manifolds usually form highly convoluted Euclidean sets, are \emph{a priori} unknown, and, as it happens in any real-world experiment, measurements are made with finite resolution and over a finite time-span. The task gets even more complicated if the system is a network composed of interacting dynamical units, namely, a high-dimensional complex system. Here, we tackle this task and solve it by defining a method to approximately construct GMPs for any complex system's finite-resolution and finite-time trajectory. We critically test our method on networks of coupled maps, encoding their trajectories into symbolic sequences. We show that these sequences are optimal because they minimise the information loss and also any spurious information added. Consequently, our method allows us to approximately calculate the invariant probability measures of complex systems from observed data. Thus, we can efficiently define complexity measures that are applicable to a wide range of complex phenomena, such as the characterisation of brain activity from EEG signals measured at different brain regions or the characterisation of climate variability from temperature anomalies measured at different Earth regions.
---
PDF链接：
https://arxiv.org/pdf/1711.09072