Identifying brain regions that exhibit altered functional connectivity across cognitive or emotional states is a key problem in neuroscience. Existing methods, such as edge-wise testing, seed-based psychophysiological interaction (PPI) analysis, or correlation network comparison, typically suffer from low statistical power, arbitrary thresholding, and limited ability to capture distributed or nonlinear dependence patterns. We propose SpARCD (Spectral Analysis of Revealing Connectivity Differences), a novel statistical framework for detecting differences in brain connectivity between two experimental conditions. SpARCD leverages distance correlation, a dependence measure sensitive to both linear and nonlinear associations, to construct a weighted graph for each condition. It then constructs a differential operator via spectral filtering and uncovers connectivity changes by computing its leading eigenvectors. Inference is achieved via a permutation-based testing scheme that yields interpretable, region-level significance maps. Extensive simulation studies demonstrate that SpARCD achieves superior power relative to conventional edge-wise or univariate approaches, particularly in the presence of complex dependency structures. Application to fMRI data from 113 early PTSD patients performing an emotional face-matching task reveals distinct networks associated with emotional reactivity and regulatory processes. Overall, SpARCD provides a statistically rigorous and computationally efficient framework for comparing high-dimensional connectivity structures, with broad applicability to neuroimaging and other network-based scientific domains.

翻译：识别在不同认知或情感状态下表现出功能连接改变的大脑区域是神经科学中的一个关键问题。现有方法，如逐边检验、基于种子的心理生理交互（PPI）分析或相关网络比较，通常存在统计功效低、阈值设定随意以及捕捉分布式或非线性依赖模式能力有限等问题。我们提出了SpARCD（揭示连接差异的谱分析），这是一种用于检测两种实验条件下大脑连接差异的新型统计框架。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）为每种条件构建加权图。然后，它通过谱滤波构建一个差分算子，并通过计算其前导特征向量来揭示连接变化。推断通过基于置换的检验方案实现，该方案可生成可解释的区域级显著性图谱。大量的模拟研究表明，与传统的逐边或单变量方法相比，SpARCD具有更优的统计功效，尤其是在存在复杂依赖结构的情况下。将其应用于113名早期PTSD患者执行情绪面孔匹配任务的fMRI数据，揭示了与情绪反应性和调节过程相关的不同网络。总体而言，SpARCD为比较高维连接结构提供了一个统计严谨且计算高效的框架，在神经影像学及其他基于网络的科学领域具有广泛的适用性。