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Single-cell and single-nucleus RNA sequencing are used to reveal heterogeneity in cells, showing a growing potential for precision and personalized medicine. Nevertheless, sustainable drug discovery must be based on a population-level understanding of molecular mechanisms, which calls for a population-scale analysis of this data. This work introduces a sequential target-drug selection model for drug repurposing against Alzheimer’s Disease (AD) targets inferred from snRNA-seq data of AD progression- involving hundreds of thousands of nuclei from multipatient and multiregional studies. We utilize Persistent Sheaf Laplacians (PSL) to facilitate a Protein−Protein Interaction (PPI) analysis inferred from disease related differential gene expression (DEG). We then use an ensemble of machine learning models to predict repurpose- able compounds. We screen the efficacy of different small compounds and further examine their central nervous system relevant ADMET properties, resulting in a list of potential molecular targets as well as pharmaceutical lead candidates for AD treatment. 

Abstract Khovanov homology has been the subject of much study in knot theory and low dimensional topology since 2000. This work introduces a Khovanov Laplacian and a Khovanov Dirac to study knot and link diagrams. The harmonic spectrum of the Khovanov Laplacian or the Khovanov Dirac retains the topological invariants of Khovanov homology, while their non-harmonic spectra reveal additional information that is distinct from Khovanov homology. 

The multiscale topological learning framework, based on persistent topological Laplacians, captures complex interactions and enhances energy prediction accuracy in multi-atom systems.