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  1. Free, publicly-accessible full text available July 3, 2024
  2. Free, publicly-accessible full text available May 1, 2024
  3. In 1946, Erd\H{o}s posed the distinct distance problem, which seeks to findthe minimum number of distinct distances between pairs of points selected fromany configuration of $n$ points in the plane. The problem has since beenexplored along with many variants, including ones that extend it into higherdimensions. Less studied but no less intriguing is Erd\H{o}s' distinct angleproblem, which seeks to find point configurations in the plane that minimizethe number of distinct angles. In their recent paper "Distinct Angles inGeneral Position," Fleischmann, Konyagin, Miller, Palsson, Pesikoff, and Wolfuse a logarithmic spiral to establish an upper bound of $O(n^2)$ on the minimumnumber of distinct angles in the plane in general position, which prohibitsthree points on any line or four on any circle. We consider the question of distinct angles in three dimensions and providebounds on the minimum number of distinct angles in general position in thissetting. We focus on pinned variants of the question, and we examine explicitconstructions of point configurations in $\mathbb{R}^3$ which useself-similarity to minimize the number of distinct angles. Furthermore, westudy a variant of the distinct angles question regarding distinct angle chainsand provide bounds on the minimum number of distinct chains in $\mathbb{R}^2$and $\mathbb{R}^3$. 
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  4. Abstract

    Project Mars released what it claims to be a completely new dataset of 250 wars fought since 1800 and claims these data do not suffer from Western biases of other data projects (e.g., the Correlates of War [CoW]) that apparently overlook non-Western conflicts. These data featured prominently in a recent argument in Divided Armies (2020) about the negative relationship between military inequality and battlefield performance. Our appraisal of both the data and the argument advanced in Divided Armies suggests some caution with these claims. Project Mars does not amount to a completely new dataset on conventional wars. Instead, Project Mars only evaluated CoW's interstate war data, missed that the bulk of its wars are available elsewhere in CoW's data repository (i.e., as intrastate or extrastate wars), and may have missed important observations in CoW's typology (prominently intrastate wars) that could double the size of Project Mars. Combined with additional misgivings about the quality of Project Mars’ coding and how the military inequality data were not constructed as Project Mars implies, these have important implications for the core argument advanced in Divided Armies. Scholars of war should not pool wars in their statistical models as Project Mars does.

     
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  5. null (Ed.)