It is common in regression discontinuity analysis to control for third, fourth, or higher-degree polynomials of the forcing variable. There appears to be a perception that such methods are theoretically justified, even though they can lead to evidently nonsensical results. We argue that controlling for global high-order polynomials in regression discontinuity analysis is a flawed approach with ...

In this paper we present a new algorithm for finding small roots of multivariate polynomials over the integers based on lattice reduction techniques. Our simpler heuristic method is inspired in algorithms for predicting pseudorandom numbers, and it can be considered as another variant of Coppersmith’s method for finding small solutions of integer bivariate polynomials. We also apply the method ...

The forward voltage of GaAlAs semiconductor diode has been measured in the temperature range 50 K 300 K and for current values between 10 nA and 450 μA. The forward voltage as a function of temperature is least-squares fitted and the coefficients are given. The 1st and 2nd order least-squares fitting has high temperature root between 400 K and 950 K. The presence of the high temperature root in...