large volume (radius $100 \hmpc$) which contains all the galaxies used in the analysis. Hence, for each basis function we can measure its corresponding bulk flow, $\vB^\alpha(r)$, and once coefficients $a^\alpha$ have been determined from the data by minimization of (\[eq:chi\]) then the  reconstructed bulk, $\vB_{_{\rm ASCE}}(r)$, is readily given by (\[eq:best\]).

Figure \[fig:scatt\] shows scatter plots of the estimated versus true bulk flows of a spherical region of $60 \hmpc$ in radius. For clarity, results from only 400 randomly selected mock catalogues are shown. Blue dots and red plus signs correspond to $\vmle$ and $\vace$, respectively. Because of the anisotropic distribution of the observed galaxies, the methods may not reconstruct the three cartesian components equally well. Hence, $x,y$ and $z$ bulk flow components in Supergalactic coordinates are, respectively, shown in the top, middle and bottom panels. Blue and red lines in each panel are linear regressions of the estimated on true bulk flows. The corresponding mathematical expressions of the regressions are indicated in each panel.

The regularization term in (\[eq:chi\]) naturally tends to underestimate the coefficients $a^\alpha$ and subsequently the reconstructed bulk flow. However, the agreement between the  reconstructed and the true bulk flows seen in figure (\[fig:scatt\]) clearly 