In this work we study the wavefront set of a solution u to P u = f , where P is a pseudodifferential operator on a manifold with real-valued homogeneous principal symbol p, when the Hamilton vector field corresponding to p is radial on a Lagrangian submanifold Λ contained in the characteristic set of P. The standard propagation of singularities theorem of… (More)
In this paper we analyze the Feynman wave equation on Lorentzian scattering spaces. We prove that the Feynman propagator exists as a map between certain Banach spaces defined by decay and microlocal Sobolev regularity properties. We go on to show that certain nonlinear wave equations arising in QFT are well-posed for small data in the Feynman setting.
Over 1 million children under the age of 17 in the US have been identified with Autism Spectrum Disorder (ASD). These children struggle to recognize facial expressions, make eye contact, and engage in social interactions. Gaining these skills requires intensive behavioral interventions that are often expensive, difficult to access, and inconsistently… (More)
We have developed a system for automatic facial expression recognition, which runs on Google Glass and delivers real-time social cues to the wearer. We evaluate the system as a behavioral aid for children with Autism Spectrum Disorder (ASD), who can greatly benefit from real-time non-invasive emotional cues and are more sensitive to sensory input than… (More)