SummaryPrimates are remarkably adept at ranking each other within social hierarchies, a capacity that is critical to successful group living. Surprisingly little, however, is understood about the neurobiology underlying this quintessential aspect of primate cognition. In our experiment, participants first acquired knowledge about a social and a nonsocial hierarchy and then used this information to guide investment decisions. We found that neural activity in the amygdala tracked the development of knowledge about a social, but not a nonsocial, hierarchy. Further, structural variations in amygdala gray matter volume accounted for interindividual differences in social transitivity performance. Finally, the amygdala expressed a neural signal selectively coding for social rank, whose robustness predicted the influence of rank on participants’ investment decisions. In contrast, we observed that the linear structure of both social and nonsocial hierarchies was represented at a neural level in the hippocampus. Our study implicates the amygdala in the emergence and representation of knowledge about social hierarchies and distinguishes the domain-general contribution of the hippocampus.

Complex emotional experience is simplified and broken down into more elemental components for the service of scientific study. With this simplification, it is unclear which theoretical approach is most useful, and whether these more elemental components have a basis in underlying psychological computation or neural circuitry. Brain systems related to positive and negative processing have been studied across levels of analysis, from large-scale brain networks (macro-level), to specific circuits between brain regions (meso-level), to distributions of neurons within regions (micro-level). Although valence and arousal have been thought to comprise a "core" affect, our emotional lives are often filled with mixed emotions where positivity and negativity appear to co-occur, and psychological models need to account for these states. Indeed, a burgeoning line of research focuses on these states of ambivalence, and neuroeconomic theory is increasingly considering how decision-making unfolds in uncertain situations. Here we review the neuroscience literature on systems that support the processing of positive and negative information across levels of analysis, and illustrate how the spectrum of valenced information is supported by both separable and overlapping brain systems. We argue that this brain organization allows for the simultaneous and parallel processing of multiple types of valenced information, and discuss how this might give rise to mixed evaluative processes. We clarify and continue a distinction made in this issue between "perceptions of affective quality" and the "experience of emotions," drawing from our operationalization of these psychological terms in previous theoretical frameworks (Cunningham & Zelazo, 2007; Cunningham, Zelazo, Packer, & van Bavel, 2007). Our affective responses to internally and externally generated stimuli are shaped by previous experience, our current states, and our expectations for the future (Cunningham, Dunfield, & Stillman, 2013; Cunningham et al., 2007). Thus, the interactions among multiple systems and the current representations active at a particular time contribute to

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The quantum approximate optimization algorithm (QAOA) promises to solve classically intractable computational problems in the area of combinatorial optimization. A growing amount of evidence suggests that the originally proposed form of the QAOA ansatz is not optimal, however. To address this problem, we propose an alternative ansatz, which we call QAOA+, that augments the traditional p = 1 QAOA ansatz with an additional multiparameter problem-independent layer. The QAOA+ ansatz allows obtaining higher approximation ratios than p = 1 QAOA while keeping the circuit depth below that of p = 2 QAOA, as benchmarked on the MaxCut problem for random regular graphs. We additionally show that the proposed QAOA+ ansatz, while using a larger number of trainable classical parameters than with the standard QAOA, in most cases outperforms alternative multiangle QAOA ansätze.