The Queue-Number of Posets of Bounded Width or Height

Heath and Pemmaraju conjectured that the queue-number of a poset is bounded by its width and if the poset is planar then also by its height. We show that there are planar posets whose queue-number is larger than their height, refuting the second conjecture. On the other hand, we show that any poset of width $2$ has queue-number at most $2$, thus confirming the first conjecture in the first non-trivial case. Moreover, we improve the previously best known bounds and show that planar posets of width $w$ have queue-number at most $3w-2$ while any planar poset with $0$ and $1$ has queue-number at most its width.Comment: 14 pages, 10 figures, Appears in the Proceedings of the 26th International Symposium on Graph Drawing and Network Visualization (GD 2018

Pure strategy dominance with quasiconcave utility functions

By a result of Pearce (1984), in a finite strategic form game, the set of a player's serially undominated strategies coincides with her set of rationalizable strategies. In this note we consider an extension of this result that applies to games with continuous utility functions that are quasiconcave in own action. We prove that in such games, when the players are endowed with compact, metrizable, and convex action spaces, a strategy of some player is dominated by some other pure strategy if and only if it is not a best reply to any belief over the strategies adopted by her opponents. For own-quasiconcave games, this can be used to give a characterization of the set of rationalizable strategies, different from the one given by Pearce. Moreover, expected utility functions defined on the mixed extension of a game are always own-quasiconcave, and therefore the result in this note generalizes Pearce''s characterization to infinite games, by a simple shift of perspective.

Risk of cardiovascular disease in first and second generation Mexican-Americans.

This study examines the cardiovascular disease (CVD) risk profiles of first generation (FG) and second generation (SG) Mexican-Americans (MA) in two large national studies--the Hispanic Health and Nutrition Examination Study (HHANES) (1982-1984) and the National Health and Examination Study (NHANES) (1999-2004). The main outcome measures were five individual risk indicators of CVD (total cholesterol, HDL cholesterol, hypertension, diabetes, and smoking) and a composite measure (the Framingham Risk Score [FRS]). The analyses included cross-survey (pseudocohort) and within-survey (cross-sectional) comparisons. In multivariate analyses, SG men had higher rates of hypertension and lower rates of smoking than FG men; and SG women had lower total cholesterol levels, higher rates of hypertension, and lower rates of smoking than FG women. There was no generational difference in the FRS in men or women. The cross-survey comparisons detected generational differences in CVD risk factors not detected in within-survey comparisons, particularly among MA women. Future studies of generational differences in risk should consider using pseudocohort comparisons when possible

Boxicity and separation dimension

A family $\mathcal{F}$ of permutations of the vertices of a hypergraph $H$ is called 'pairwise suitable' for $H$ if, for every pair of disjoint edges in $H$, there exists a permutation in $\mathcal{F}$ in which all the vertices in one edge precede those in the other. The cardinality of a smallest such family of permutations for $H$ is called the 'separation dimension' of $H$ and is denoted by $\pi(H)$. Equivalently, $\pi(H)$ is the smallest natural number $k$ so that the vertices of $H$ can be embedded in $\mathbb{R}^k$ such that any two disjoint edges of $H$ can be separated by a hyperplane normal to one of the axes. We show that the separation dimension of a hypergraph $H$ is equal to the 'boxicity' of the line graph of $H$. This connection helps us in borrowing results and techniques from the extensive literature on boxicity to study the concept of separation dimension.Comment: This is the full version of a paper by the same name submitted to WG-2014. Some results proved in this paper are also present in arXiv:1212.6756. arXiv admin note: substantial text overlap with arXiv:1212.675