EEG functional connectivity as a Riemannian mediator: An application to malnutrition and cognition

Mediation analysis assesses whether an exposure directly produces changes in cognitive behavior or is influenced by intermediate "mediators". Electroencephalographic (EEG) spectral measurements have been previously used as effective mediators representing diverse aspects of brain function. However, it has been necessary to collapse EEG measures onto a single scalar using standard mediation methods. In this article, we overcome this limitation and examine EEG frequency-resolved functional connectivity measures as a mediator using the full EEG cross-spectral tensor (CST). Since CST samples do not exist in Euclidean space but in the Riemannian manifold of positive-definite tensors, we transform the problem, allowing for the use of classic multivariate statistics. Toward this end, we map the data from the original manifold space to the Euclidean tangent space, eliminating redundant information to conform to a "compressed CST." The resulting object is a matrix with rows corresponding to frequencies and columns to cross spectra between channels. We have developed a novel matrix mediation approach that leverages a nuclear norm regularization to determine the matrix-valued regression parameters. Furthermore, we introduced a global test for the overall CST mediation and a test to determine specific channels and frequencies driving the mediation. We validated the method through simulations and applied it to our well-studied 50+-year Barbados Nutrition Study dataset by comparing EEGs collected in school-age children (5-11 years) who were malnourished in the first year of life with those of healthy classmate controls. We hypothesized that the CST mediates the effect of malnutrition on cognitive performance. We can now explicitly pinpoint the frequencies (delta, theta, alpha, and beta bands) and regions (frontal, central, and occipital) in which functional connectivity was altered in previously malnourished children, an improvement to prior studies. Understanding the specific networks impacted by a history of postnatal malnutrition could pave the way for developing more targeted and personalized therapeutic interventions. Our methods offer a versatile framework applicable to mediation studies encompassing matrix and Hermitian 3D tensor mediators alongside scalar exposures and outcomes, facilitating comprehensive analyses across diverse research domains.

Dispersal synchronizes giant kelp forests

Spatial synchrony is the tendency for population fluctuations to be correlated among different locations. This phenomenon is a ubiquitous feature of population dynamics and is important for ecosystem stability, but several aspects of synchrony remain unresolved. In particular, the extent to which any particular mechanism, such as dispersal, contributes to observed synchrony in natural populations has been difficult to determine. To address this gap, we leveraged recent methodological improvements to determine how dispersal structures synchrony in giant kelp (Macrocystis pyrifera), a global marine foundation species that has served as a useful system for understanding synchrony. We quantified population synchrony and fecundity with satellite imagery across 11 years and 880 km of coastline in southern California, USA, and estimated propagule dispersal probabilities using a high-resolution ocean circulation model. Using matrix regression models that control for the influence of geographic distance, resources (seawater nitrate), and disturbance (destructive waves), we discovered that dispersal was an important driver of synchrony. Our findings were robust to assumptions about propagule mortality during dispersal and consistent between two metrics of dispersal: (1) the individual probability of dispersal and (2) estimates of demographic connectivity that incorporate fecundity (the number of propagules dispersing). We also found that dispersal and environmental conditions resulted in geographic clusters with distinct patterns of synchrony. This study is among the few to statistically associate synchrony with dispersal in a natural population and the first to do so in a marine organism. The synchronizing effects of dispersal and environmental conditions on foundation species, such as giant kelp, likely have cascading effects on the spatial stability of biodiversity and ecosystem function.

Identifying Imaging Markers for Predicting Cognitive Assessments Using Wasserstein Distances Based Matrix Regression

Alzheimer's disease (AD) is a severe type of neurodegeneration which worsens human memory, thinking and cognition along a temporal continuum. How to identify the informative phenotypic neuroimaging markers and accurately predict cognitive assessment are crucial for early detection and diagnosis Alzheimer's disease. Regression models are widely used to predict the relationship between imaging biomarkers and cognitive assessment, and identify discriminative neuroimaging markers. Most existing methods use different matrix norms as the similarity measures of the empirical loss or regularization to improve the prediction performance, but ignore the inherent geometry of the cognitive data. To tackle this issue, in this paper we propose a novel robust matrix regression model with imposing Wasserstein distances on both loss function and regularization. It successfully integrate Wasserstein distance into the regression model, which can excavate the latent geometry of cognitive data. We introduce an efficient algorithm to solve the proposed new model with convergence analysis. Empirical results on cognitive data of the ADNI cohort demonstrate the great effectiveness of the proposed method for clinical cognitive predication.

svt: Singular Value Thresholding in MATLAB

Many statistical learning methods such as matrix completion, matrix regression, and multiple response regression estimate a matrix of parameters. The nuclear norm regularization is frequently employed to achieve shrinkage and low rank solutions. To minimize a nuclear norm regularized loss function, a vital and most time-consuming step is singular value thresholding, which seeks the singular values of a large matrix exceeding a threshold and their associated singular vectors. Currently MATLAB lacks a function for singular value thresholding. Its built-in svds function computes the top r singular values/vectors by Lanczos iterative method but is only efficient for sparse matrix input, while aforementioned statistical learning algorithms perform singular value thresholding on dense but structured matrices. To address this issue, we provide a MATLAB wrapper function svt that implements singular value thresholding. It encompasses both top singular value decomposition and thresholding, handles both large sparse matrices and structured matrices, and reduces the computation cost in matrix learning algorithms.