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Parkinson’s disease is the world’s fastest-growing neurological disorder. Research to elucidate the mechanisms of Parkinson’s disease and automate diagnostics would greatly improve the treatment of patients with Parkinson’s disease. Current diagnostic methods are expensive and have limited availability. Considering the insidious and preclinical onset and progression of the disease, a desirable screening should be diagnostically accurate even before the onset of symptoms to allow medical interventions. We highlight retinal fundus imaging, often termed a window to the brain, as a diagnostic screening modality for Parkinson’s disease. We conducted a systematic evaluation of conventional machine learning and deep learning techniques to classify Parkinson’s disease from UK Biobank fundus imaging. Our results suggest Parkinson’s disease individuals can be differentiated from age and gender-matched healthy subjects with 68% accuracy. This accuracy is maintained when predicting either prevalent or incident Parkinson’s disease. Explainability and trustworthiness are enhanced by visual attribution maps of localized biomarkers and quantified metrics of model robustness to data perturbations. 

This article presents a new method for accurately enclosing the reachable sets of nonlinear discrete-time systems with unknown but bounded disturbances. This method is motivated by the discrete-time differential inequalities method (DTDI) proposed by Yang and Scott, which exhibits state-of-the-art accuracy at low cost for many problems, but suffers from theoretical limitations that significantly restrict its applicability. The proposed method uses an efficient one-dimensional partitioning scheme to approximate DTDI while avoiding the key technical assumptions that limit it. Numerical result shows that this approach matches the accuracy of DTDI when DTDI is applicable, but, unlike DTDI, is valid for arbitrary systems.