  The contribution of $O^{2-}$ ions to antiferromagnetism in
$La_{2-x}Ae_xCuO_4$ ($Ae = Sr, Ba)$ is highly sensitive to doped holes. In
contrast, the contribution of $Cu^{2+}$ ions to antiferromagnetism in
$Nd_{2-x}Ce_xCuO_{4+y}$ is much less sensitive to doped electrons. The
difference causes the precarious and, respectively, robust antiferromagnetic
phase of these cuprates. The same sensitivities affect the doping dependence of
the incommensurability of density waves, $\delta (x)$. In the hole-doped
compounds this gives rise to a doping offset for magnetic and charge density
waves, $\delta_{m,c}^p(x) \propto \sqrt{x-x_{0p}^N}$. Here $x_{0p}^N$ is the
doping concentration where the N\'{e}el temperature vanishes, $T_N(x_{0p}^N) =
0$. No such doping offset occurs for density waves in the electron-doped
compound. Instead, excess oxygen (necessary for stability in crystal growth) of
concentration $y$ causes a different doping offset in the latter case,
$\delta_{m,c}^n(x) \propto \sqrt{x- 2y}$. The square-root formulas result from
the assumption of superlattice formation through partitioning of the $CuO_2$
plane by pairs of itinerant charge carriers. Agreement of observed
incommensurability $\delta(x)$ with the formulas is very good for the
hole-doped compounds and reasonable for the electron-doped compound. The
deviation in the latter case may be caused by residual excess oxygen.
