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Abstract Due to commonalities in pathophysiology, age-related macular degeneration (AMD) represents a uniquely accessible model to investigate therapies for neurodegenerative diseases, leading us to examine whether pathways of disease progression are shared across neurodegenerative conditions. Here we use single-nucleus RNA sequencing to profile lesions from 11 postmortem human retinas with age-related macular degeneration and 6 control retinas with no history of retinal disease. We create a machine-learning pipeline based on recent advances in data geometry and topology and identify activated glial populations enriched in the early phase of disease. Examining single-cell data from Alzheimer’s disease and progressive multiple sclerosis with our pipeline, we find a similar glial activation profile enriched in the early phase of these neurodegenerative diseases. In late-stage age-related macular degeneration, we identify a microglia-to-astrocyte signaling axis mediated by interleukin-1 β which drives angiogenesis characteristic of disease pathogenesis. We validated this mechanism using in vitro and in vivo assays in mouse, identifying a possible new therapeutic target for AMD and possibly other neurodegenerative conditions. Thus, due to shared glial states, the retina provides a potential system for investigating therapeutic approaches in neurodegenerative diseases. 

We introduce a new intrinsic measure of local curvature on point-cloud data called diffusion curvature. Our measure uses the framework of diffusion maps, including the data diffusion operator, to structure point cloud data and define local curvature based on the laziness of a random walk starting at a point or region of the data. We show that this laziness directly relates to volume comparison results from Riemannian geometry. We then extend this scalar curvature notion to an entire quadratic form using neural network estimations based on the diffusion map of point-cloud data. We show applications of both estimations on toy data, single-cell data and on estimating local Hessian matrices of neural network loss landscapes.