Novel time-series analysis for dynamics based on topological-computation

给出了用拓扑计算方法对时间序列数据进行动力系统莫尔斯分解的数学基础。 将该理论应用于生物调节网络模型的时间序列数据和气象学中的全球环流数据，并将莫尔斯分解的动力学时间序列分析理论与Fiedler-Mochizuki调节网络理论相结合，并测试了昼夜节律的基因调控网络模型。我们的动态时间-对对流层和平流层的一些全球环流资料也作了莫尔斯分解的系列分析，正确地恢复了气象学家经验观测到的特征气压型的转变。

Mathematical foundation is given for Morse decomposition of dynamical systems from time-series data using topological-computation method. The theory is successfully applied to time-series data from a biological regulatory network model and global circulation data in meteorology.For a biological application, our theory on dynamical time-series analysis for Morse decomposition is combined with the Fiedler-Mochizuki theory on regulatory networks, and is tested for a model of a gene regulatory network of circadian rhythm.Our dynamical time-series analysis for Morse decomposition is also applied to some data on the global circulation in the troposphere and stratosphere, and correctly recovered transition of characteristic pressure patterns which meteorologists empirically observed.