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first transform the observations of each variable into ranks, referred to as dCov and HHG, respectively. We note that the power of the original dCov and HHG was fairly similar to the power of their distribution-free variants, see Appendix I. 

We examine complex bivariate relationships depicted in Figure 4. Most of these sce- narios were collected from the literature illustrating the performance of other meth- ods. Specifically, the first two rows were examined in Newton (2009), the next two rows are similar to the relationships examined in Reshef et al. (2011), and the Heav- isine and Doppler examples in the last row were used extensively in the literature on denoising, see e.g., Donoho and Johnstone (1995). In all but the 4 Independent Clouds setup, there is dependence. The 4 Independent Clouds setup allows us to 

