#### Capitalizing on shared expertise:

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#### Sometimes seemingly different problems are in fact linked, and share common mathematical solutions. Matrixing mathematicians and scientists into more than one group creates cross-fertilization. Common questions emerge, and mathematics can be built that serves multiple projects.

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#### Working together, we have seen that advances in such diverse fields as computational harmonic analysis, PDE-based techniques for image segmentation, graph theoretic approaches, dimensional reduction and manifold embedding, diffusion maps and non-linear tensor schemes, sparse and compressed approximation methods, and new approaches to operator decompositions, can be cross-fertilized across challenges at the facilities.

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#### This cross-fertilization is apparent in a node-edge graph showing how different types of mathematics come into play in more than one field, and how mathematics in one particular application can suggest new ideas when attacking a different area.

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Supported by the US Department of Energy Office of Science

Advanced Scientific Computing Research (steven.lee@science.doe.gov)