Search for: All records

We provide new proofs based on the Myers–Steenrod theorem to confirm that travel time data, travel time difference data and the broken scattering relations determine a simple Riemannian metric on a disc up to the natural gauge of a boundary fixing diffeomorphism. Our method of the proof leads to a Lipschitz-type stability estimate for the first two data sets in the class of simple metrics. 

Abstract Alzheimer's disease is the leading cause of dementia. The long progression period in Alzheimer's disease provides a possibility for patients to get early treatment by having routine screenings. However, current clinical diagnostic imaging tools do not meet the specific requirements for screening procedures due to high cost and limited availability. In this work, we took the initiative to evaluate the retina, especially the retinal vasculature, as an alternative for conducting screenings for dementia patients caused by Alzheimer's disease. Highly modular machine learning techniques were employed throughout the whole pipeline. Utilizing data from the UK Biobank, the pipeline achieved an average classification accuracy of 82.44%. Besides the high classification accuracy, we also added a saliency analysis to strengthen this pipeline's interpretability. The saliency analysis indicated that within retinal images, small vessels carry more information for diagnosing Alzheimer's diseases, which aligns with related studies.