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Neural markers of attention, including those frequently linked to the event-related potential P3 (P300) or P3b component, vary widely within and across participants. Understanding the neural mechanisms of attention that contribute to the P3 is crucial for better understanding attention-related brain disorders. All ten participants were scanned twice with a resting-state PCASL perfusion MRI and an ERP with a visual oddball task to measure brain resting-state functional connectivity (rsFC) and P3 parameters (P3 amplitudes and P3 latencies). Global rsFC (average rsFC across the entire brain) was associated with both P3 amplitudes (r = 0.57, p = 0.011) and P3 onset latencies (r = −0.56, p = 0.012). The observed P3 parameters were correlated with predicted P3 amplitude from the global rsFC (amplitude: r = +0.48, p = 0.037; latency: r = +0.40, p = 0.088) but not correlated with the rsFC over the most significant individual edge. P3 onset latency was primarily related to long-range connections between the prefrontal and parietal/limbic regions, while P3 amplitudes were related to connections between prefrontal and parietal/occipital, between sensorimotor and subcortical, and between limbic/subcortical and parietal/occipital regions. These results demonstrated the power of resting-state PCASL and P3 correlation with brain global functional connectivity. 

Many compilers, synthesizers, and theorem provers rely on rewrite rules to simplify expressions or prove equivalences. Developing rewrite rules can be difficult: rules may be subtly incorrect, profitable rules are easy to miss, and rulesets must be rechecked or extended whenever semantics are tweaked. Large rulesets can also be challenging to apply: redundant rules slow down rule-based search and frustrate debugging. This paper explores how equality saturation, a promising technique that uses e-graphs to apply rewrite rules, can also be used to infer rewrite rules. E-graphs can compactly represent the exponentially large sets of enumerated terms and potential rewrite rules. We show that equality saturation efficiently shrinks both sets, leading to faster synthesis of smaller, more general rulesets. We prototyped these strategies in a tool dubbed Ruler. Compared to a similar tool built on CVC4, Ruler synthesizes 5.8× smaller rulesets 25× faster without compromising on proving power. In an end-to-end case study, we show Ruler-synthesized rules which perform as well as those crafted by domain experts, and addressed a longstanding issue in a popular open source tool.