Presidential Lectures

While autism clearly involves altered function of the central nervous system, the neuropathology of the disorder remains controversial. This is due in part,to the enormous complexity of the disorder, which likely has many causes and many biological trajectories. It is also due to the fact that few neuroimaging studies involve very young children or severely affected individuals. This lack of information is compounded by the fact that findings at the magnetic resonance imaging (MRI) level of analysis cannot be confirmed and extended to the cellular level due to a lack of postmortem brains.

Integral equation methods play an important role in the numerical simulation of electromagnetic scattering. They are easy to employ in complex geometry and impose the desired radiation conditions at infinity without the need for artificial numerical boundaries. Two of the obstacles faced by current forward simulation tools are “low-frequency breakdown” and the lack of easy to use high order quadrature rules for complicated surfaces. In this talk, I will review the relevant background material, discuss a new mathematical formalism for scattering from perfect conductors and briefly describe a new quadrature technique that yields easily implementable high order rules for singular and weakly singular integrals. The scheme, denoted QBX (quadrature by expansion) is compatible with fast hierarchical algorithms such as the fast multipole method.

New evidence of exoplanets reveals a higher-than-expected occurrence of potentially habitable worlds in our galactic neighborhood. What does this evidence tell us about life on other planets? How can we search for signs of life on other planets?