Arithmetic problems share many surface-level features with typical sentences. They assert information about the world, and readers can evaluate this information for sensibility by consulting their memories as the statement unfolds. When people encounter the solution to the problem 3 × 4, the brain elicits a robust ERP effect as a function of answer expectancy (12 being the expected completion; 15 being unexpected). Initially, this was labeled an N400 effect, implying that semantic memory had been accessed. Subsequent work suggested instead that the effect was driven by a target P300 to the correct solutions. The current study manipulates operand format to differentially promote access to language-based semantic representations of arithmetic. Operands were presented either as spoken number words or as sequential Arabic numerals. The critical solution was always an Arabic numeral. In Experiment 1, the correctness of solutions preceded by spoken operands modulated N400 amplitude, whereas solutions preceded by Arabic numerals elicited a P300 for correct problems. In Experiment 2, using only spoken operands, the delay between the second operand and the Arabic numeral solution was manipulated to determine if additional processing time would result in a P300. With a longer delay, an earlier N400 and no distinct P300 were observed. In brief, highly familiar digit operands promoted target detection, whereas spoken numbers promoted semantic level processing-even when solution format itself was held constant. This provides evidence that the brain can process arithmetic fact information at different levels of representational meaningfulness as a function of symbolic format.

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Many studies of bilingual arithmetic report better performance when verifying arithmetic facts in the language of learning (LA+) over the other language (LA−). This could be due to language-specific memory representations, processes established during learning, or to language and task factors not related to math. The current study builds on a small number of event-related potential (ERP) studies to test this question while controlling language proficiency and eliminating potential task confounds. Adults proficient in two languages verified single-digit multiplications presented as spoken number words in LA+ and LA−, separately. ERPs and correctness judgments were measured from solution onset. Equivalent P300 effects, with larger positive amplitude for correct than incorrect solutions, were observed in both languages (Experiment 1A), even when stimuli presentation rate was shortened to increase difficulty (Experiment 1B). This effect paralleled the arithmetic correctness effect for trials presented as all digits (e.g., 2 4 8 versus 2 4 10), reflecting efficient categorization of the solutions, and was distinct from an N400 generated in a word–picture matching task, reflecting meaning processing (Experiment 2). The findings reveal that the language effects on arithmetic are likely driven by language and task factors rather than differences in memory representation in each language.

Highlights d Sleep deprivation improves memory in old mice but worsens it in young ones d Sleep deprivation decreases hippocampal flexibility and spindle counts in young mice d Increased spindle counts are associated with improved memory in old mice d Sleep deprivation improves the quality of hippocampal representations in old mice

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