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Reconstructing Time-Dependent Dynamics

机译：重建时变动力学

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摘要

The usefulness of the information contained in biomedical data relies heavily on the reliability and accuracy of the methods used for its extraction. The conventional assumptions of stationarity and autonomicity break down in the case of living systems because they are thermodynamically open, and thus constantly interacting with their environments. This leads to an inherent time-variability and results in highly nonlinear, time-dependent dynamics. The aim of signal analysis usually is to gain insight into the behavior of the system from which the signal originated. Here, a range of signal analysis methods is presented and applied to extract information about time-varying oscillatory modes and their interactions. Methods are discussed for the characterization of signals and their underlying nonautonomous dynamics, including time-frequency analysis, decomposition, coherence analysis and dynamical Bayesian inference to study interactions and coupling functions. They are illustrated by being applied to cardiovascular and EEG data. The recent introduction of chronotaxic systems provides a theoretical framework within which dynamical systems can have amplitudes and frequencies which are time-varying, yet remain stable, matching well the characteristics of life. We demonstrate that, when applied in the context of chronotaxic systems, the methods presented facilitate the accurate extraction of the system dynamics over many scales of time and space.
机译：生物医学数据中包含的信息的有用性在很大程度上取决于提取所用方法的可靠性和准确性。在生物系统中，平稳性和自治性的传统假设被打破了，因为它们在热力学上是开放的，因此不断与环境相互作用。这导致固有的时间可变性，并导致高度非线性的，与时间有关的动力学。信号分析的目的通常是深入了解产生信号的系统的行为。在这里，提出了一系列信号分析方法，并将其应用于提取有关时变振荡模式及其相互作用的信息。讨论了表征信号及其潜在非自治动力学的方法，包括时频分析，分解，相干分析和动力学贝叶斯推理，以研究相互作用和耦合函数。通过将其应用于心血管和脑电图数据可以对其进行说明。计时调速系统的最新介绍提供了一个理论框架，其中动力学系统可以具有随时间变化但仍保持稳定，与生活特征相匹配的振幅和频率。我们证明，当在时变系统中应用时，提出的方法有助于在许多时空尺度上准确提取系统动力学。

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