The problem of finding a compact natural representation of brain dynamics and connectivity is addressed using an expansion in terms of physical spatial eigenmodes and their frequency resonances. It is demonstrated that this discrete expansion via the system transfer function enables linear and nonlinear dynamics to be analyzed in compact form in terms of natural dynamic “atoms,” each of which is a frequency resonance of an eigenmode. Because these modal resonances are determined by the system dynamics, not the investigator, they are privileged over widely used phenomenological patterns, and obviate the need for artificial discretizations and thresholding in coordinate space. It is shown that modal resonances participate as nodes of a discrete spectral network, are noninteracting in the linear regime, but are linked nonlinearly by wave-wave coalescence and decay processes. The modal resonance formulation is shown to be capable of speeding numerical calculations of strongly nonlinear interactions. Recent work in brain dynamics, especially based on neural field theory (NFT) approaches, allows eigenmodes and their resonances to be estimated from data without assuming a specific brain model. This means that dynamic equations can be inferred using system identification methods from control theory, rather than being assumed, and resonances can be interpreted as control-systems data filters. The results link brain activity and connectivity with control-systems functions such as prediction and attention via gain control and can also be linked to specific NFT predictions if desired, thereby providing a convenient bridge between physiologically based theories and experiment. Amplitudes of modes and resonances can also be tracked to provide a more direct and temporally localized representation of the dynamics than correlations and covariances, which are widely used in the field. By synthesizing many different lines of research, this work provides a way to link quantitative electrophysiological and imaging measurements, connectivity, brain dynamics, and function. This underlines the need to move between coordinate and spectral representations as required. Moreover, standard theoretical-physics approaches and mathematical methods can be used in place of ad hoc statistical measures such as those based on graph theory of artificially discretized and decimated networks, which are highly prone to selection effects and artifacts.

中文翻译：

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脑动力学和连通性的离散谱本征模共振网络

使用物理空间本征模式及其频率共振的扩展来解决寻找大脑动力学和连通性的紧凑自然表示的问题。已经证明，通过系统传递函数的这种离散扩展能够以自然动态“原子”的紧凑形式分析线性和非线性动力学，每个原子都是本征模式的频率共振。因为这些模态共振是由系统动力学决定的，而不是由研究人员决定的，所以它们优于广泛使用的现象学模式，并且不需要在坐标空间中进行人工离散化和阈值化。结果表明，模态共振作为离散谱网络的节点参与，在线性状态下不相互作用，但通过波-波合并和衰减过程非线性关联。模态共振公式被证明能够加速强非线性相互作用的数值计算。最近在大脑动力学方面的工作，特别是基于神经场理论 (NFT) 方法，允许从数据中估计特征模式及其共振，而无需假设特定的大脑模型。这意味着可以使用控制理论中的系统识别方法来推断动态方程，而不是假设，并且共振可以解释为控制系统数据过滤器。结果将大脑活动和连接与控制系统功能（例如通过增益控制的预测和注意力）联系起来，如果需要，还可以链接到特定的 NFT 预测，从而在生理学理论和实验之间架起了一座方便的桥梁。还可以跟踪模式和共振的幅度，以提供比该领域广泛使用的相关性和协方差更直接和时间局部化的动力学表示。通过综合许多不同的研究领域，这项工作提供了一种将定量电生理和成像测量、连通性、大脑动力学和功能联系起来的方法。这强调需要根据需要在坐标和光谱表示之间移动。此外，可以使用标准的理论物理方法和数学方法来代替临时统计方法，例如基于人工离散化和抽取网络的图论的那些，这些方法很容易受到选择效应和伪影的影响。