Random Notes

• Probability and Integral Geometry
  • Integral symplectic geometry may be useful for coarsening of Hamiltonian systems
  • Likewise for symplectic integrators
• Algorithmic Complexity
  • Sieve interface codifies operations on arbitrary meshes
  • Sieve implementation can use more or less storage to represent different meshes based on their regularity
    • Unstructured meshes use more storage since they are less compressible (covering arrows)
    • Structured meshes use very little storage (extents and mesh sizes only), since they are more compressible
    • There is a short algorithm that reconstructs a full sieve for a structured mesh given its data (above)
    • A locally regular mesh can use a Sieve for superelement relations and a compressed description locally
  • Sieve implementations can and should take advantage of the compressibility of the objects they express
  • What is the optimal compression of general unstructured meshes (tet, hex, etc; work by the CMU crowd)
  • Can we use the Sieve interface to generate a graph complexity estimate?
    • For instance, the amount of storage/work necessary to emulate the sieve could be a complexity measure.