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Relational integration is required when multiple explicit representations of relations between entities must be jointly considered to make inferences. We provide an overview of the neural substrate of relational integration in humans and the processes that support it, focusing on work on analogical and deductive reasoning. In addition to neural evidence, we consider behavioral and computational work that has informed neural investigations of the representations of individual relations and of relational integration. In very general terms, evidence from neuroimaging, neuropsychological, and neuromodulatory studies points to a small set of regions (generally left lateralized) that appear to constitute key substrates for component processes of relational integration. These include posterior parietal cortex, implicated in the representation of first-order relations (e.g., A:B); rostrolateral pFC, apparently central in integrating first-order relations so as to generate and/or evaluate higher-order relations (e.g., A:B::C:D); dorsolateral pFC, involved in maintaining relations in working memory; and ventrolateral pFC, implicated in interference control (e.g., inhibiting salient information that competes with relevant relations). Recent work has begun to link computational models of relational representation and reasoning with patterns of neural activity within these brain areas. 

The ability to generate and process semantic relations is central to many aspects of human cognition. Theorists have long debated whether such relations are coarsely coded as links in a semantic network or finely coded as distributed patterns over some core set of abstract relations. The form and content of the conceptual and neural representations of semantic relations are yet to be empirically established. Using sequential presentation of verbal analogies, we compared neural activities in making analogy judgments with predictions derived from alternative computational models of relational dissimilarity to adjudicate among rival accounts of how semantic relations are coded and compared in the brain. We found that a frontoparietal network encodes the three relation types included in the design. A computational model based on semantic relations coded as distributed representations over a pool of abstract relations predicted neural activities for individual relations within the left superior parietal cortex and for second-order comparisons of relations within a broader left-lateralized network. 

Abstract The performance of the ATLAS Inner Detector alignment has been studied using pp collision data at $$\sqrt{s} = 13\,\hbox {TeV}$$ s = 13 TeV collected by the ATLAS experiment during Run 2 (2015–2018) of the Large Hadron Collider (LHC). The goal of the detector alignment is to determine the detector geometry as accurately as possible and correct for time-dependent movements. The Inner Detector alignment is based on the minimization of track-hit residuals in a sequence of hierarchical levels, from global mechanical assembly structures to local sensors. Subsequent levels have increasing numbers of degrees of freedom; in total there are almost 750,000. The alignment determines detector geometry on both short and long timescales, where short timescales describe movements within an LHC fill. The performance and possible track parameter biases originating from systematic detector deformations are evaluated. Momentum biases are studied using resonances decaying to muons or to electrons. The residual sagitta bias and momentum scale bias after alignment are reduced to less than $$\sim 0.1\hbox { TeV}^{-1}$$ ∼ 0.1 TeV - 1 and $$0.9\times 10^{-3}$$ 0.9 × 10 - 3 , respectively. Impact parameter biases are also evaluated using tracks within jets.