In (Semigroup Forum 77: 325-338, 2008) Mahmoudi M. and Renshaw J. solved a study that covers of cyclic $S$-acts over monoids. This article is an attempt to initiate the covers of finitely generated $S$-acts. We give a necessary and sufficient condition for a monoid to have the properties that $n$-generated $S$-acts have strongly flat covers, Condition $(P)$ covers and projective covers. The main conclusions extend some known results. We show also that Condition $(P)$ covers of finitely generated $S$-acts are not unique, unlike the situation for strongly flat covers. Additionally, we demonstrate that the property of Enochs' $\mathcal{X}$-precover of $S$-act $A$, where $\mathcal{X}$ denotes a class of $S$-acts that are closed under isomorphisms.

Mitochondrial DNA copy number (mtDNAcn) is associated with mitochondrial function contributing various diseases. Understanding of the association between mtDNAcn and infant neurodevelopment, as well as the role of racial disparities, remains unknown. A cohort study was conducted with 55 preterm infants and a single blood sample was collected from each infant during their NICU stay to measure mtDNAcn. NICU Network Neurobehavioral Scale (NNNS) and Bayley Scale of Infant Developmental testing Edition III was assessed during NICU until 2 years of corrected age (CA). Linear regression models were performed to investigate the relationship between the clinical characteristics, neurobehavioral outcomes and mtDNAcn. Majority of our subjects were male, White, non-Hispanic, had C-section, and without preterm premature rupture of membrane (PPROM). Increased mtDNAcn was found associated with younger birth gestational age (GA), nonoptimal neurodevelopment. However, the opposite associations between mtDNAcn and neurodevelopmental outcomes were observed between Black and White infants up to 1 year of CA. Adverse early life experience, together with increased mtDNAcn in White infants, and decreased mtDNAcn in Black infants may be considered as significant positive predictors of poor early life neurodevelopmental outcomes in infants.