The previous framework (left) fails to take into account noises of the brain. The brain state transitions were written as point-to-point, the dynamics as deterministic, and the control cost as the ...

We consider the spread of a general epidemic amongst a population consisting of invididuals with differing susceptibilities to the disease. Deterministic and stochastic versions of the basic model are ...

We use asymptotic methods to analyze the effects of discreteness and random noise on a mathematical model of the lithiation/delithiation dynamics of a single electrode nanoparticle. We begin by ...

First, are macro shocks large enough to alter the course of the economy? Second, are they large enough to materially impact economic welfare? Lucas and many others have addressed these issues, but do ...