Exploiting Group Symmetry in Semidefinite Programming Relaxations of the Quadratic Assignment Problem

We consider semidefinite programming relaxations of the quadratic assignment problem, and show how to exploit group symmetry in the problem data. Thus we are able to compute the best known lower bounds for several instances of quadratic assignment problems from the problem library: [R.E. Burkard, S.E. Karisch, F. Rendl. QAPLIB — a quadratic assignment problem library. Journal on Global Optimization, 10: 291–403, 1997]. AMS classification: 90C22, 20Cxx, 70-08

Rapid inverse planning for pressure-driven drug infusions in the brain.

Infusing drugs directly into the brain is advantageous to oral or intravenous delivery for large molecules or drugs requiring high local concentrations with low off-target exposure. However, surgeons manually planning the cannula position for drug delivery in the brain face a challenging three-dimensional visualization task. This study presents an intuitive inverse-planning technique to identify the optimal placement that maximizes coverage of the target structure while minimizing the potential for leakage outside the target. The technique was retrospectively validated using intraoperative magnetic resonance imaging of infusions into the striatum of non-human primates and into a tumor in a canine model and applied prospectively to upcoming human clinical trials