  Let $Q$ be an acyclic quiver and $w \geq 1$ be an integer. Let
$\mathsf{C}_{-w} (\mathbf{k} Q)$ be the $(-w)$-cluster category of $\mathbf{k}
Q$. We show that there is a bijection between simple-minded collections in
$\mathsf{D}^b (\mathbf{k} Q)$ lying in a fundamental domain of $\mathsf{C}_{-w}
(\mathbf{k} Q)$ and $w$-simple-minded systems in $\mathsf{C}_{-w} (\mathbf{k}
Q)$. This generalises the same result of Iyama-Jin in the case that $Q$ is
Dynkin. A key step in our proof is the observation that the heart $\mathsf{H}$
of a bounded t-structure in a Hom-finite, Krull-Schmidt, $\mathbf{k}$-linear
saturated triangulated category $\mathsf{D}$ is functorially finite in
$\mathsf{D}$ if and only if $\mathsf{H}$ has enough injectives and enough
projectives. We then establish a bijection between $w$-simple-minded systems in
$\mathsf{C}_{-w} (\mathbf{k} Q)$ and positive $w$-noncrossing partitions of the
corresponding Weyl group $W_Q$.
