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

给出了用拓扑计算方法从时间序列数据中进行动力系统Morse分解的数学基础。该理论被成功地应用于生物调控网络模型的时间序列数据和气象学中的全球环流数据。对于生物学应用，我们的Morse分解的动态时间序列分析理论与Fiedler-Mochizuki的调控网络理论相结合，并被用于昼夜节律的基因调控网络模型。我们的Morse分解的动态时间序列分析也被应用于一些关于对流层和平流层的全球环流数据，正确地恢复了气象学家经验观察到的特征压型的转变。

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.