Identifying brain regions that exhibit altered functional connectivity between cognitive or emotional states is a fundamental problem in neuroscience. We propose SpARCD (Spectral Analysis for Revealing Connectivity Differences), a statistical framework for detecting detecting condition-specific patterns of functional connectivity. SpARCD uses distance correlation, a dependence measure sensitive to both linear and nonlinear associations, to construct weighted region-wise connectivity graphs for each condition. A differential operator obtained through spectral filtering is then used to identify connectivity changes via its leading eigenvectors. To assess statistical significance, we develop a permutation-based testing procedure that yields interpretable region-level significance maps. We establish finite-sample validity of the permutation test and derive asymptotic guarantees for the stability of the resulting region rankings. Simulation studies demonstrate improved power relative to conventional edge-wise and univariate approaches, particularly in settings with nonlinear dependence structures. We applied SpARCD to fMRI data from 113 individuals with early-stage PTSD and 42 controls during emotional and neutral task conditions. The method identified distinct connectivity networks associated with visual processing in both PTSD and control participants. Resting-state comparisons between PTSD and control participants highlighted similar visual networks. SpARCD provides a statistically rigorous and computationally efficient framework for comparing high-dimensional connectivity patterns.

翻译：识别在不同认知或情绪状态之间表现出功能连接改变的脑区是神经科学的基本问题。我们提出SpARCD（揭示连接差异的光谱分析），这是一个用于检测功能连接条件特异性模式的统计框架。SpARCD利用距离相关性——一种对线性和非线性关联均敏感的依赖度量——为每种状态构建加权区域间连接图。随后通过光谱滤波获得差分算子，并利用其主导特征向量识别连接变化。为评估统计显著性，我们开发了基于置换的检验程序，可生成可解释的区域级显著性图谱。我们建立了置换检验的有限样本有效性，并推导了区域排序稳定性的渐近保证。仿真研究表明，相比于传统边级和单变量方法，该方法在具有非线性依赖结构的情境中表现出更优的统计功效。我们将SpARCD应用于113名早期PTSD患者和42名对照者在情绪和中性任务态下的fMRI数据。该方法在PTSD和对照参与者中均识别出与视觉处理相关的不同连接网络。PTSD与对照参与者之间的静息态比较凸显了相似的视觉网络。SpARCD为比较高维连接模式提供了一个统计严谨且计算高效的框架。