Parsimony: suppressing artificial detail Since the 2DSA algorithm never actually applies a model with a full regularly spaced high-resolution grid, the traditional regularization methods, such as Tikhonov or maximum-entropy regularization described above, do not seem to be easily applicable. In fact, Brookes et al. (2009) express the view that the fit of c(s, f r ) with a high-resolution grid in conjunction with regularization suffers from ''lack of resolution,'' and ''produces unnecessarily broad molecular weight distributions.'' We believe that, if prior Fig. 5 Contour plots of the size-and-shape distributions calculated with different models for the IgG data shown in Fig. 1 . The color temperature (blue to red) indicates increasing height of the peaks. (a) For comparison, this panel shows the same distribution as shown in Fig. 1c , calculated with the high-resolution grid of 10 9 100 (f r , s)values. b Distribution obtained in stage (I) by merging the distributions calculated sequentially and independently with different lowresolution grid of 10 9 10 (f r , s)-values, each translated by D 2 s = 0.1505 S. One example for the low-resolution grid analysis is shown in Fig. 3 . All low-resolution grids are chosen such that they are evenly spaced subgrids of the high-resolution grid, and such that, by joining the grid points of (f r , s)-values of all the low-resolution grids, the high-resolution grid of a is obtained. c A new grid is defined in stage (II) by joining all grid points from the entire sequence of lowresolution grids that yielded positive contributions to the fit. This is the set of grid points for which b displays nonzero populations of the distribution. In a secondary analysis, a fit to this irregular grid is performed, and the results are shown as a contour plot. Although the smallest differences Ds and Df r in this secondary grid are the same as those of the high-resolution grid, it considers only a small subset of the points from the high-resolution grid. This causes the deviations from the exact results in a and those in c. d Illustration of the grid points used in c, showing as black crosses all points that yielded positive contributions in any of the first-stage low-resolution fits. For comparison, solid circles are the grid points that make positive contributions in the exact direct high-resolution analysis of a. Blue circles indicate those that coincide with grid points in the Demeler scheme, and red circles indicate those that are populated in the exact solution but not found in the grid of the Demeler scheme knowledge about the sharpness of the expected c(s, f r ) peaks is available, this can be inserted with a Bayesian refinement of the Tikhonov regularization as we have reported for SV analysis (Brown et al. 2007 ) and implemented in SEDFIT.