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The goal of this article is twofold. First, we investigate the linearized Vlasov–Poisson system around a family of spatially homogeneous equilibria in the unconfined setting. Our analysis follows classical strategies from physics (Binney and Tremaine 2008, Galactic Dynamics,(Princeton University Press); Landau 1946, Acad. Sci. USSR. J. Phys.10,25–34; Penrose 1960,Phys. Fluids,3,258–65) and their subsequent mathematical extensions (Bedrossian et al 2022, SIAM J. Math. Anal.,54,4379–406; Degond 1986,Trans. Am. Math. Soc., 294,435–53; Glassey and Schaeffer 1994,Transp. Theory Stat. Phys.,23, 411–53; Grenier et al 2021, Math. Res. Lett., 28,1679–702; Han-Kwan et al, 2021, Commun. Math. Phys. 387, 1405–40; Mouhot and Villani 2011, Acta Math., 207, 29–201). The main novelties are a unified treatment of a broad class of analytic equilibria and the study of a class of generalized Poisson equilibria. For the former, this provides a detailed description of the associated Green’s functions, including in particular precise dissipation rates (which appear to be new), whereas for the latter we exhibit explicit formulas. Second, we review the main result and ideas in our recent work (Ionescu et al, 2022 on the full global nonlinear asymptotic stability of the Poisson equilibrium in R3 

Understanding abstract relations, and reasoning about various instantiations of the same relation, is an important marker in human cognition. Here we focus on development of understanding for the concept of antonymy. We examined whether four- and five-year-olds (N= 67) are able to complete an analogy task involving antonyms, whether language cues facilitate children’s ability to reason about the antonym relation, and how their performance compares with that of two vector-based computational models. We found that explicit relation labels in the form of a relation phrase (“opposites”) improved performance on the task for five-year-olds but not four-year-olds. Five-year-old (but not four-year-old) children were more accurate for adjective and verb antonyms than for noun antonyms. Two computational models showed substantial variability in performance across different lexical classes, and in some cases fell short of children’s accuracy levels. These results suggest that young children acquire a solid understanding of the abstract relation of opposites, and can generalize it to various instantiations across different lexical classes. These developmental results challenge relation models based on vector semantics, and highlight the importance of examining performance across different parts of speech.