  We investigate some variants of the splitting, reaping, and independence
numbers defined using asymptotic density. Specifically, we give a proof of
Con($\mathfrak{i}<\mathfrak{s}_{1/2}$), Con($\mathfrak{r}_{1/2}<\mathfrak{b}$)
and Con($\mathfrak{i}_*<2^{\aleph_0}$). This answers two questions raised in
arXiv:1808.02442v3. Besides, we prove the consistency of
$\mathfrak{s}_{1/2}^{\infty} < $ non$(\mathcal{E})$ and cov$(\mathcal{E}) <
\mathfrak{r}_{1/2}^{\infty}$, where $\mathcal{E}$ is the $\sigma$-ideal
generated by closed sets of measure zero.
