Motivated in large part by the possibility of observing signatures of compact extra dimensions, experimental searches for deviations from Newtonian gravity at short distances have improved in sensitivity by many orders of magnitude in the past five years. We review the essential features of the experiments responsible for the current limits on new effects in the range from a few microns to a fe...

In this paper, we develop new test statistics for private hypothesis testing. These statistics are designed specifically so that their asymptotic distributions, after accounting for noise added for privacy concerns, match the asymptotics of the classical (nonprivate) chi-square tests for testing if the multinomial data parameters lie in lower dimensional manifolds (examples include goodness of ...

Chi-square tests are generally used for distinguishing purposes; however when they are combined to simultaneously test several independent variables, extra notation is required. In this study, the chi-square statistics in some previous works is revealed to be computed half of its real value. Therefore, the notion of Multi–Chi-square tests is formulated to avoid possible future confusions. In or...

Sub-mm tests of the gravitational inverse-square law are interesting from several quite different perspectives. This paper discusses work by the Eöt-Wash group performed since the publication of our initial result in February 2001. We find no evidence for short-range Yukawa interactions. Our results provide an upper limit of 200 μm on the size of the largest “extra” dimension, and for the unifi...