Ronald. R. Coifman

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We provide a framework for structural multiscale geometric organization of graphs and subsets of R(n). We use diffusion semigroups to generate multiscale geometries in order to organize and represent complex structures. We show that appropriately selected eigenfunctions or scaling functions of Markov matrices, which describe local transitions, lead to(More)
In the companion article, a framework for structural multiscale geometric organization of subsets of R(n) and of graphs was introduced. Here, diffusion semigroups are used to generate multiscale analyses in order to organize and represent complex structures. We emphasize the multiscale nature of these problems and build scaling functions of Markov matrices(More)
DESIGN: We have developed and applied a unique tuned light source based on a Digital Mirror Device (DMD) (Plain Sight Systems Inc.) which transmits any combination of light frequencies, range 450 nm – 850 nm, transilluminating H&E stained micro-array tissue sections of normal and malignant colon through a Nikon Biophot microscope. Hyper-spectral pictures of(More)
Recovering the three-dimensional structure of proteins is important for understanding their functionality. We describe a spectral graph algorithm for reconstructing the three-dimensional structure of molecules from their cryo-electron microscopy images taken at random unknown orientations. The key idea of the algorithm is designing a sparse operator defined(More)
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