Statistical Inverse Problem and its Applications to Complex Systems

本研究以回馈系统理论为基础，探讨脑功能或工程植物等复杂系统的统计逆问题。由于在上个世纪对脑活动的定位有了很好的理解，因此脑中相关区域的活动对于理解更高级的脑功能感兴趣，即，语言、认知、视觉等活动的研究是世纪的一个重要课题，在研究之初，脑磁图（magnetoencephalography，MEG）的时间序列数据似乎很难解决这些问题，因为大脑中存在着许多并行的活动处理过程。然而，重复的电刺激或声音刺激会使大脑产生周期性的活动，这些活动被称为诱发磁场。然后，利用基于时间结构的独立分量分析方法，将特定的脑诱发磁场从脑背景磁场中分离出来。一个例子是听觉诱发场，另一个是体感诱发场。在选择诱发脑磁图后，我们可以通过基于反馈系统理论的辨识方法来检测脑磁图时间序列数据中包含的动力学。也就是说，可观测通道之间的传递函数被识别，并获得其脉冲响应。它们给我们大脑区域之间的动力。在该方法的框架中的高斯性是重要的，以获得平稳的时间序列数据，因为它是观察到的不仅MEG数据，但也波动的中子数的核电厂。

In this research statistical inverse problem on complex systems such as brain functions or engineering plants is examined by using the identification method based on feedback system theory. Since the localization of brain activities was well understood in the last century, activities of associated regions in brain are interested for understanding of higher order brain functions, i.e., language, recognition, vision activities, in the present century.At the beginning of research, it seemed to be difficult to attack such topics for time series data of magnetoencephalography (MEG), since there are many parallel processing of activities in brain. However, repeated electrical or sound stimuli give periodical activities in brain, and they are called by the evoked magnetic field. Then, we could separate particular evoked magnetic fields from background magnetic fields of brain by using the independent component analysis based on temporal structure. One example is the auditory evoked field, and the other is the somatosensory evoked field. After selection of evoked MEG we can examine dynamics included in MEG time series data by the identification method based on feedback system theory. That is, transfer functions between observable channels were identified, and their impulse responses were obtained. They give us dynamics between regions of brains. The Gaussianity in the framework of the method was important to obtain the stationarity of time series data, since it is observed in not only MEG data but also fluctuations of neutron number of nuclear power plants.