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A Few Self-Driving Cars Can Dramatically Improve Traffic Flow

Posted on 4/27/18 in Research Articles

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 […]

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Identifying Links Between the S&P500 and VIX Derivatives

Posted on 4/5/16 in Research Articles

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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Overcoming the Curse of Dimensionality for Control Theory

Posted on 10/30/15 in Research Articles

Optimal control problems lead to Hamilton-Jacobi Bellman (HJB) differential equations in many space variables for finding the cost function to be optimized. This beautiful connection has not generally led to effective numerical methods because grid based solutions of partial differential equations in n variables generally […]

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The Kakeya problem

Posted on 6/29/14 in Research Articles

Submitted by Larry Guth (MIT) The Kakeya problem is an open problem in Euclidean geometry, and it was a central theme in the 2014 IPAM long program, Algebraic Techniques for Combinatorial and Computational Geometry. It is elementary to state, but it’s also a model for […]

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Kakeya Figure