Characterization of complex interdependencies of oscillatory processes from data with extended phase dynamics methods

这是B3项目的延续，其总体目标是利用非线性动力学的最新成果，以推进神经数据的多元分析技术。该项目的重点是相位动力学方程的重建，该重建以不变的方式进行，即独立于所使用的观测值。所得方程完整地描述了非线性神经振子之间的相互作用。该项目的主要任务是扩展在项目第一阶段开发的技术，以覆盖更复杂的设置，并将它们应用于涉及认知的神经活动。将在以下方向进行扩展：(i)将核函数估计等新的统计方法纳入现有框架，以期从非常短和非均匀的数据集获得可靠的模型重建；（ii）通过对这类系统的有效相位动力学描述，扩展方法以涵盖噪声引起的振荡；（iii）对多个相互作用的振荡单元的推广，特别强调非痛苦相互作用的影响；（iv）寻找相互作用中非线性的影响，即使在建模层面上也尚未探索。

This is a continuation of the Project B3 with the overall aim to exploit recent achievements of nonlinear dynamics in order to advance techniques of multivariate analysis of neural data.The key point of the project is reconstruction of the equations of the phase dynamics, which is performed in an invariant way, i.e. independently of the observables used. The obtained equations yield a complete description of interaction between nonlinear neural oscillators. The main task of the project is to extend the techniques, developed in the first stage of the Project, to cover more complex setups, and to apply them to neural activity involved incognition.The extension will be pursued in the following directions: (i) incorporation of new statistical approaches, like kernel function estimation, into the existing framework with the aim to obtain reliable model reconstruction from very short and inhomogeneous data sets; (ii) extension of the method to cover noise-induced oscillations by means of effective phase dynamics descripfion of such systems; (iii) extension for the case of many interacfing oscillating units, with especial emphasis on the effects of non-painwise interaction; (iv) search for the effects of nonlinearity in interaction, what is yet unexplored even on the modeling level.