Mean field games are critical classes of multi-agent models for efficient analysis of massive populations of interacting agents with numerous applications ranging from economics to crowd motion. Their numerical solutions typically suffer from the curse of dimensionality. Numerical methods for mean field games were usually […]
Molecular dynamics (MD), the numerical integration of the equations of motions of atoms and molecules, is one of the most powerful tools available to materials scientists, chemists, and biologists, because it provides a fully resolved view of the spatio-temporal evolution of materials. Because of its […]
The presence of just a few autonomous vehicles can eliminate the stop-and-go driving of the human drivers in traffic. Under normal circumstances, human drivers naturally create stop-and-go traffic, even in the absence of bottlenecks, lane changes, merges or other disruptions. A small percentage of autonomous […]
By Andrew Papanicolaou The technique of volatility trading has been common practice since the 1970’s. Typically, a long (short) position in volatility included a long (short) position in options. In 2003 there came a more standardized way of trading volatility, as the VIX formula became […]
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