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1. Irritability and Social Media Use in US Adults

   https://doi.org/10.1001/jamanetworkopen.2024.52807  

   Perlis, Roy H; Uslu, Ata; Schulman, Jonathan; Gunning, Faith M; Santillana, Mauricio; Baum, Matthew A; Druckman, James N; Ognyanova, Katherine; Lazer, David (January 2025, JAMA Network Open)

   ImportanceEfforts to understand the complex association between social media use and mental health have focused on depression, with little investigation of other forms of negative affect, such as irritability and anxiety. ObjectiveTo characterize the association between self-reported use of individual social media platforms and irritability among US adults. Design, Setting, and ParticipantsThis survey study analyzed data from 2 waves of the COVID States Project, a nonprobability web-based survey conducted between November 2, 2023, and January 8, 2024, and applied multiple linear regression models to estimate associations with irritability. Survey respondents were aged 18 years and older. ExposureSelf-reported social media use. Main Outcomes and MeasuresThe primary outcome was score on the Brief Irritability Test (range, 5-30), with higher scores indicating greater irritability. ResultsAcross the 2 survey waves, there were 42 597 unique participants, with mean (SD) age 46.0 (17.0) years; 24 919 (58.5%) identified as women, 17 222 (40.4%) as men, and 456 (1.1%) as nonbinary. In the full sample, 1216 (2.9%) identified as Asian American, 5939 (13.9%) as Black, 5322 (12.5%) as Hispanic, 624 (1.5%) as Native American, 515 (1.2%) as Pacific Islander, 28 354 (66.6%) as White, and 627 (1.5%) as other (ie, selecting the other option prompted the opportunity to provide a free-text self-description). In total, 33 325 (78.2%) of the survey respondents reported daily use of at least 1 social media platform, including 6037 (14.2%) using once a day, 16 678 (39.2%) using multiple times a day, and 10 610 (24.9%) using most of the day. Frequent use of social media was associated with significantly greater irritability in univariate regression models (for more than once a day vs never, 1.43 points [95% CI, 1.22-1.63 points]; for most of the day vs never, 3.37 points [95% CI, 3.15-3.60 points]) and adjusted models (for more than once a day, 0.38 points [95% CI, 0.18-0.58 points]; for most of the day, 1.55 points [95% CI, 1.32-1.78 points]). These associations persisted after incorporating measures of political engagement. Conclusions and RelevanceIn this survey study of 42 597 US adults, irritability represented another correlate of social media use that merits further characterization, in light of known associations with depression and suicidality. 

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2. Rationality of forms of M¯0,n$$\overline{{\mathcal {M}}}_{0,n}$$

   https://doi.org/10.1112/jlms.70097  

   Hassett, Brendan; Tschinkel, Yuri; Zhang, Zhijia (February 2025, Journal of the London Mathematical Society)

   Abstract We study equivariant geometry and rationality of moduli spaces of points on the projective line, for twists associated with permutations of the points. 

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3. Optimal Small Scale Equidistribution of Lattice Points on the Sphere, Heegner Points, and Closed Geodesics

   https://doi.org/10.1002/cpa.22076  

   Humphries, Peter; Radziwiłł, Maksym (September 2022, Communications on Pure and Applied Mathematics)

   Abstract We asymptotically estimate the variance of the number of lattice points in a thin, randomly rotated annulus lying on the surface of the sphere. This partially resolves a conjecture of Bourgain, Rudnick, and Sarnak. We also obtain estimates that are valid for all balls and annuli that are not too small. Our results have several consequences: for a conjecture of Linnik on sums of two squares and a “microsquare”, a conjecture of Bourgain and Rudnick on the number of lattice points lying in small balls on the surface of the sphere, the covering radius of the sphere, and the distribution of lattice points in almost all thin regions lying on the surface of the sphere. Finally, we show that for a density 1. subsequence of squarefree integers, the variance exhibits a different asymptotic behaviour for balls of volume with . We also obtain analogous results for Heegner points and closed geodesics. Interestingly, we are able to prove some slightly stronger results for closed geodesics than for Heegner points or lattice points on the surface of the sphere. A crucial observation that underpins our proof is the different behaviour of weighting functions for annuli and for balls. © 2022 Courant Institute of Mathematics and Wiley Periodicals LLC. 

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4. Youden's demon is Sylvester's problem

   https://doi.org/10.1112/mtk.70015  

   Frick, Florian; Newman, Andrew; Pegden, Wesley (February 2025, Mathematika)

   Abstract If four people with Gaussian‐distributed heights stand at Gaussian positions on the plane, the probability that there are exactly two people whose height is above the average of the four is exactly the same as the probability that they stand in convex position; both probabilities are . We show that this is a special case of a more general phenomenon: The problem of determining the position of the mean among the order statistics of Gaussian random points on the real line (Youden's demon problem) is the same as a natural generalization of Sylvester's four point problem to Gaussian points in . Our main tool is the observation that the Gale dual of independent samples in itself can be taken to be a set of independent points (translated to have barycenter at the origin) when the distribution of the points is Gaussian. 

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5. Maximal Polarization for Periodic Configurations on the Real Line

   https://doi.org/10.1093/imrn/rnae003  

   Faulhuber, Markus; Steinerberger, Stefan (February 2024, International Mathematics Research Notices)

   Abstract We prove that among all 1-periodic configurations $$\Gamma $$ of points on the real line $$\mathbb{R}$$ the quantities $$\min _{x \in \mathbb{R}} \sum _{\gamma \in \Gamma } e^{- \pi \alpha (x - \gamma )^{2}}$$ and $$\max _{x \in \mathbb{R}} \sum _{\gamma \in \Gamma } e^{- \pi \alpha (x - \gamma )^{2}}$$ are maximized and minimized, respectively, if and only if the points are equispaced and whenever the number of points $$n$$ per period is sufficiently large (depending on $$\alpha $$). This solves the polarization problem for periodic configurations with a Gaussian weight on $$\mathbb{R}$$ for large $$n$$. The first result is shown using Fourier series. The second result follows from the work of Cohn and Kumar on universal optimality and holds for all $$n$$ (independent of $$\alpha $$). 

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