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Sequential learning models situations where agents predict a ground truth in sequence, by using their private, noisy measurements, and the predictions of agents who came earlier in the sequence. We study sequential learning in a social network, where agents only see the actions of the previous agents in their own neighborhood. The fraction of agents who predict the ground truth correctly depends heavily on both the network topology and the ordering in which the predictions are made. A natural question is to find an ordering, with a given network, to maximize the (expected) number of agents who predict the ground truth correctly. In this paper, we show that it is in fact NP-hard to answer this question for a general network, with both the Bayesian learning model and a simple majority rule model. Finally, we show that even approximating the answer is hard. 

Abstract BackgroundFolate is an essential B-group vitamin and a key methyl donor with important biological functions including DNA methylation regulation. Normal neurodevelopment and physiology are sensitive to the cellular folate levels. Either deficiency or excess of folate may lead to neurological disorders. Recently, folate has been linked to tRNA cytosine-5 methylation (m⁵C) and translation in mammalian mitochondria. However, the influence of folate intake on neuronal mRNA m⁵C modification and translation remains largely unknown. Here, we provide transcriptome-wide landscapes of m⁵C modification in poly(A)-enriched RNAs together with mRNA transcription and translation profiles for mouse neural stem cells (NSCs) cultured in three different concentrations of folate. ResultsNSCs cultured in three different concentrations of folate showed distinct mRNA methylation profiles. Despite uncovering only a few differentially expressed genes, hundreds of differentially translated genes were identified in NSCs with folate deficiency or supplementation. The differentially translated genes induced by low folate are associated with cytoplasmic translation and mitochondrial function, while the differentially translated genes induced by high folate are associated with increased neural stem cell proliferation. Interestingly, compared to total mRNAs, polysome mRNAs contained high levels of m⁵C. Furthermore, an integrative analysis indicated a transcript-specific relationship between RNA m⁵C methylation and mRNA translation efficiency. ConclusionsAltogether, our study reports a transcriptome-wide influence of folate on mRNA m⁵C methylation and translation in NSCs and reveals a potential link between mRNA m⁵C methylation and mRNA translation.