found if only (sub-)mm datapoints are used.\
Instead of using the three parameters describing the distribution of the intensity of the radiation field U of the @Draine2007 model (the minimal radiation field $\rm U_{min}$, the maximal one $\rm U_{max}$, and the slope of the assumed power-law distribution between these two values $\alpha$), we considered only the mean intensity of the radiation field $\langle U \rangle$ for simplicity. The other parameters derived from the fit and used in this paper are the bolometric infrared luminosity integrated between 8 and 1000$\mu$m (L$_{\rm IR}$) and the dust mass (M$_d$). The SFR is derived from L$_{\rm IR}$ using the @Kennicutt1998 conversion factor ($1 \times 10^{-10}$$\rm M_\odot \, yr^{-1} \, L_\odot^{-1}$ after conversion from Salpeter to Chabrier IMF), since the dust-obscured star formation vastly dominates the unobscured component at z$<$4 given the mass-scale considered [@Heinis2013; @Heinis2014; @Pannella2014]. The sSFR is computed using the later SFR and the mean stellar mass extracted from the @Ilbert2013 catalog. The uncertainties on the derived physical parameters presented in the various figures and tables of this paper are the uncertainties on the average values. The dispersion of physical properties inside a population is difficult to measure by stacking and we 