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Perfect Fowl
Funnily enough, one of the papers I had in mind relies heavily on the graph Laplacian to solve the Laplace equation on a graph. This is particularly useful when one wishes to work on spatial domains in which nodes are non-uniformly distributed w.r.t to the range, such as the complex logarithmic mapping of visual coordinates in human vision. A lot of recent vision work has involved graph theoretic discrete calculus methods. It's a super interesting field but not my area of expertise by any means. So I might ask you questions from time to time, if you don't mind answering them?
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