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Explores topological waves for robust signal processing applications, focusing on resistance to perturbations and the design paradigm of topological systems.
Delves into the invariance of domain theorem, proving that a subset homeomorphic to an open subset is open itself, with implications for embeddings and homeomorphisms.
Discusses challenges in comparing non-Euclidean data, proposing a Laplacian-based solution for graph alignment and exploring optimal transport for graph distance computation.
Showcases the advanced applications of the Scanning Tunneling Microscope beyond imaging, including spectroscopy for electronic properties and nanostructure assembly.
