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Let 
$Q$ be an acyclic quiver and 
$w \geqslant 1$ 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 
$W_Q$.
