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

使用扩展相动力学方法从数据中表征振荡过程的复杂相互依赖性

基本信息

批准号：
54432586
负责人：
Professor Dr. Arkady Pikovsky
金额：
--
依托单位：
Institut für Physik und Astronomie
依托单位国家：
德国
项目类别：
Research Units
财政年份：
2007
资助国家：
德国
起止时间：
2006-12-31 至 2013-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/54432586?language=en
关键词：
Characterization complex interdependencies oscillatory processes

项目摘要

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.

这是项目B3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变量分析技术。该项目的关键点是以不变的方式（即独立于所使用的观测量）重建相动力学方程。得到的方程产生一个完整的描述非线性神经振荡器之间的相互作用。该项目的主要任务是扩展项目第一阶段开发的技术，以涵盖更复杂的设置，并将其应用于涉及认知的神经活动。扩展将在以下方向进行：（i）采用新的统计方法，如核函数估计，纳入现有框架，目的是从非常短和不均匀的数据集获得可靠的模型重建;（ii）利用系统的有效相动力学方法，将方法推广到噪声诱导的振动，（iii）推广到多个相互作用的振动单元的情况，特别强调非painwise相互作用的影响;（iv）寻找交互作用中的非线性效应，这是甚至在建模水平上尚未探索的。