Symbolic number knowledge is strongly related to mathematical performance for both children and adults. We present a model of symbolic number relations in which increasing skill is a function of hierarchical integration of symbolic associations. We tested the model by contrasting the performance of two groups of adults. One group was educated in China (n = 71) and had substantially higher levels of mathematical skill compared to the other group who was educated in Canada (n = 68). Both groups completed a variety of symbolic number tasks, including measures of cardinal number knowledge (number comparisons), ordinal number knowledge (ordinal judgments) and arithmetic fluency, as well as other mathematical measures, including number line estimation, fraction/algebra arithmetic and word problem solving. We hypothesized that Chinese-educated individuals, whose mathematical experiences include a strong emphasis on acquiring fluent access to symbolic associations among numbers, would show more integrated number symbol knowledge compared to Canadian-educated individuals. Multi-group path analysis supported the hierarchical symbol integration hypothesis. We discuss the implications of these results for understanding why performance on simple number processing tasks is persistently related to measures of mathematical performance that also involve more complex and varied numerical skills.

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Metabolic engineering aims to achieve high yields of desired products. The most common strategies focus on optimization of metabolic flux distributions. The dynamic activation or inhibition of gene expression through quorum sensing (QS) has been applied to metabolic engineering. In this study, we designed and constructed a series of QS-based bifunctional dynamic switches (QS switches) capable of synchronizing the up-regulation and down-regulation of genes at different times and intervals. The bifunctional QS switches were based on the Esa QS system, because EsaR regulatory proteins can act as transcriptional activator and repressor. The QS switches’ effectiveness and feasibility were verified through fluorescence characterization. Finally, the QS switches were applied to the production of 5-aminolevulinic acid (ALA) and poly-β-hydroxybutyrate (PHB) to solve two key metabolic engineering problems: necessary gene knockout and redirection of metabolic flux. The production of PHB and ALA was increased 6- and 12-fold in Escherichia coli, respectively.

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Transcranial direct current stimulation (tDCS) is a non-invasive brain stimulation technique that can modulate cortical excitability. Although the clinical value of tDCS has been advocated, the potential of tDCS in cognitive rehabilitation of face processing deficits is less understood. Face processing has been associated with the occipito-temporal cortex (OT). The present study investigated whether face processing in healthy adults can be modulated by applying tDCS over the OT. Experiment 1 investigated whether tDCS can affect N170, a face-sensitive ERP component, with a face orientation judgment task. The N170 in the right hemisphere was reduced in active stimulation conditions compared with the sham stimulation condition for both upright faces and inverted faces. Experiment 2 further demonstrated that tDCS can modulate the composite face effect, a type of holistic processing that reflects the obligatory attention to all parts of a face. The composite face effect was reduced in active stimulation conditions compared with the sham stimulation condition. Additionally, the current polarity did not modulate the effect of tDCS in the two experiments. The present study demonstrates that N170 can be causally manipulated by stimulating the OT with weak currents. Furthermore, our study provides evidence that obligatory attention to all parts of a face can be affected by the commonly used tDCS parameter setting.