New spectral topology method detects ADHD brain signals with 95% confidence

Traditional topological analyses of brain functional connectivity reduce each channel pair to a single scalar (e.g., Pearson correlation), losing frequency-specific synchronization critical for electrophysiology. Researchers from the University of Wisconsin and KAUST introduce a spectral landscape that indexes the persistence landscape by Fourier frequency, building each filtration from a coherence-based distance. This yields a function of both filtration scale and frequency, is Lipschitz-stable in the coherence matrix, and enables a functional two-sample test over chosen frequency bands with known asymptotic properties.

In simulations, the test recovered topological differences at the correct band while holding nominal levels under null. Applied to resting-state EEG from 53 control and 51 ADHD children (ages 7–17), a global test rejected equality of the two groups' cycle topology at the 95% level (p=0.019). Band-by-band follow-up localized differences to the gamma (30–50 Hz) and theta (4–8 Hz) bands, consistent with established roles of these bands in ADHD. The method offers a powerful new tool for frequency-resolved functional connectivity analysis, potentially improving ADHD biomarker discovery and neuroscience research.