Numerical algebraic geometry is the area devoted to the solution and manipulation of polynomial systems by numerical methods, which are mainly based on continuation. Due to the extreme intrinsic parallelism of continuation, polynomial systems may be successfully dealt with that are much larger than is possible with other methods. Singular solutions require special numerical methods called endga...

This article presents the results of experiments designed to gain insight into the effect of the minimax algorithm on the error of a heuristic evaluation function. Two types of effect of minimax are considered: (a) evaluation accuracy (are the minimax backed-up values more accurate than the heuristic values themselves?), and (b) decision accuracy (are moves played by deeper minimax search bette...

With the dramatic reduction in tobacco use in developed nations, a growing number of public health leaders have called for what they describe as an 'endgame' strategy and the need for new policies to achieve that goal. In moving forward, it is important not to lose sight of the policies that have been the underpinnings of successful tobacco reduction efforts to date, nor should we allow any dis...

BACKGROUND One possible supply-side strategy for the tobacco endgame is a government-mandated 'sinking lid' on tobacco supply (tradeable but decreasing quotas on sales or imports). METHODS We considered literature on quota systems and from a tobacco endgame workshop at the University of Michigan. FINDINGS Likely strengths of the sinking lid strategy include: (1) that it can provide a clear ...