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An important application is the problem of assessing functional connectivity based on functional magnetic resonance imaging (fMRI), where one aims to determine the similarity of fMRI time courses that are recorded on anatomically separated brain regions. In the functional brain connectivity literature, the static temporal Pearson correlation has been the prevailing measure for functional connectivity. However, recent research has revealed temporally changing patterns of functional connectivity, leading to the study of dynamic functional connectivity. This motivates new similarity measures for pairs of random curves that reflect the dynamic features of functional similarity. Specifically, we introduce gradient synchronization measures in a general setting. These similarity measures are based on the concordance and discordance of the gradients between paired smooth random functions. Asymptotic normality of the proposed estimates is obtained under regularity conditions. We illustrate the proposed synchronization measures via simulations and an application to resting-state fMRI signals from the Alzheimer\u2019s Disease Neuroimaging Initiative and they are found to improve discrimination between subjects with different disease status.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkad140","type":"journal-article","created":{"date-parts":[[2024,1,22]],"date-time":"2024-01-22T18:02:33Z","timestamp":1705946553000},"page":"694-713","source":"Crossref","is-referenced-by-count":3,"title":["Gradient synchronization for multivariate functional data, with application to brain connectivity"],"prefix":"10.1093","volume":"86","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0566-6130","authenticated-orcid":false,"given":"Yaqing","family":"Chen","sequence":"first","affiliation":[{"name":"Department of Statistics, Rutgers University , New Brunswick, New Jersey 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