Many biological materials are hierarchically structured which means that they are designed from the nano- to the macro-scale in a sometimes self-similar way. There are lots of papers published including very detailed descriptions of these structures at all length scales--however, investigations of mechanical properties are most often focused on either nano-indentation or bulk mechanical testing...

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This supplemental document presents details concerning analytical derivations that support the theorems made in the main text " Spectral Compressed Sensing via Structured Matrix Completion " , accepted to the 30th International Conference on Machine Learning (ICML 2013). One can find here the detailed proof of Theorems 1-3.

The challenge for nanoscale modeling and simulation is to bridge the length and time scales that are necessary to connect nanostructure of the material with its macroscopic properties. This challenge can only be met by combining the efforts of individual researchers who collectively are expert in a wide range of computational and theoretical techniques. The team we have assembled from the Unive...