local galaxies? For $f_{\sigma}$=2, and using the scaling relations derived in § \[sec:dynSF\] to estimate the gas mass (Table 1), ($A$=3.4$\times$10$^{-4}$M$_{\odot}$yr$^{-1}$kpc$^{-2}$ and $n$=1.34) we derive a range of cut off masses of M$_{0}$=0.3–30$\times$10$^{9}$M$_{\odot}$ (with a median and error of the sample of $M_{0}$=9$\pm$5$\times$10$^{9}$M$_{\odot}$). This is similar to the mass inferred for the brightest star-forming regions seen in high-resolution images of other high-redshift galaxies [@Elmegreen89; @ElmegreenD07; @Elmegreen09; @Bournaud09; @ForsterSchreiber11; @Genzel11; @Wisnioski11b], and a factor $\sim $1000$\times$ higher than the largest characteristic mass of a star-forming region in the Milky-Way.

In Fig. \[fig:mcut\] we plot our estimates of the the cut off mass versus the clump star-formation densities for the galaxies in our sample [see also @Livermore12a]. We use the H$\alpha$ derived star-formation rate for each clump, corrected for galaxy reddening (note that we do not have reddening estimates for individual clumps and so we assume a factor 2$\times$ uncertainty in their star formation surface density). We also include estimates of the cut off mass and star formation surface density from the SINS survey of $z\sim $2 galaxies from @Genzel11 (with dynamics measured from @ForsterSchreiber09 and @Cresci09), as well as measurements from the lensing samples of @Livermore12a ($z\sim
$1) and @Jones10 ($z\sim 