Chip-firing groups of iterated cones

Let $\Gamma$ be a finite graph and let $\Gamma_n$ be the "$n$th cone over $\Gamma$" (i.e., the join of $\Gamma$ and the complete graph $K_n$). We study the asymptotic structure of the chip-firing group $\text{Pic}^0(\Gamma_n)$.Comment: 8 pages. v4: added Remark 1.

Heights on stacks and a generalized Batyrev-Manin-Malle conjecture

We define a notion of height for rational points with respect to a vector bundle on a proper algebraic stack with finite diagonal over a global field, which generalizes the usual notion for rational points on projective varieties. We explain how to compute this height for various stacks of interest (for instance: classifying stacks of finite groups, symmetric products of varieties, moduli stacks of abelian varieties, weighted projective spaces). In many cases our uniform definition reproduces ways already in use for measuring the complexity of rational points, while in others it is something new. Finally, we formulate a conjecture about the number of rational points of bounded height (in our sense) on a stack X, which specializes to the Baytev-Manin conjecture when X is a scheme and to Malle's conjecture when X is the classifying stack of a finite group.Comment: 61 pages; comments very welcom

A heuristic for the distribution of point counts for random curves over a finite field

How many rational points are there on a random algebraic curve of large genus $g$ over a given finite field $\mathbb{F}_q$? We propose a heuristic for this question motivated by a (now proven) conjecture of Mumford on the cohomology of moduli spaces of curves; this heuristic suggests a Poisson distribution with mean $q+1+1/(q-1)$. We prove a weaker version of this statement in which $g$ and $q$ tend to infinity, with $q$ much larger than $g$.Comment: 16 pages; v2: refereed version, Philosophical Transactions of the Royal Society A 201

Measuring Attitudes about Intimate Partner Violence against Women: The ATT-IPV Scale

In lower-income settings, women more often than men justify intimate partner violence (IPV). Yet, the role of measurement invariance across gender is unstudied. We developed the ATT-IPV scale to measure attitudes about physical violence against wives in 1,055 married men and women ages 18-50 in My Hao district, Vietnam. Across 10 items about transgressions of the wife, women more often than men agreed that a man had good reason to hit his wife (3 % to 92 %; 0 % to 67 %). In random split-half samples, one-factor exploratory factor analysis (EFA) (N 1 = 527) and confirmatory factor analysis (CFA) (N 2 = 528) models for nine items with sufficient variability had significant loadings (0.575-0.883; 0.502-0.897) and good fit (RMSEA = 0.068, 0.048; CFI = 0.951, 0.978, TLI = 0.935, 0.970). Three items had significant uniform differential item functioning (DIF) by gender, and adjustment for DIF revealed that measurement noninvariance was partially masking men’s lower propensity than women to justify IPV. A CFA model for the six items without DIF had excellent fit (RMSEA = 0.019, CFI = 0.994, TLI = 0.991) and an attitudinal gender gap similar to the DIF-adjusted nine-item model, suggesting that the six-item scale reliably measures attitudes about IPV across gender. Researchers should validate the scale in urban Vietnam and elsewhere and decompose DIF-adjusted gender attitudinal gaps

Measuring Attitudes about Women’s Recourse after Exposure to Intimate Partner Violence: The ATT-RECOURSE Scale

Attitudes about intimate partner violence (IPV) against women are widely surveyed, but attitudes about women’s recourse after exposure to IPV are understudied, despite their importance for intervention. Designed through qualitative research and administered in a probability sample of 1,054 married men and women 18 to 50 years in My Hao District, Vietnam, the ATT-RECOURSE scale measures men’s and women’s attitudes about a wife’s recourse after exposure to physical IPV. Data were initially collected for nine items. Exploratory factor analysis (EFA) with one random split-half sample (N 1 = 526) revealed a one-factor model with significant loadings (0.316-0.686) for six items capturing a wife’s silence, informal recourse, and formal recourse. A confirmatory factor analysis (CFA) with the other random split-half sample (N 2 = 528) showed adequate fit for the six-item model and significant factor loadings of similar magnitude to the EFA results (0.412-0.669). For the six items retained, men consistently favored recourse more often than did women (52.4%-66.0% of men vs. 41.9%-55.2% of women). Tests for uniform differential item functioning (DIF) by gender revealed one item with significant uniform DIF, and adjusting for this revealed an even larger gap in men’s and women’s attitudes, with men favoring recourse, on average, more than women. The six-item ATT-RECOURSE scale is reliable across independent samples and exhibits little uniform DIF by gender, supporting its use in surveys of men and women. Further methodological research is discussed. Research is needed in Vietnam about why women report less favorable attitudes than men regarding women’s recourse after physical IPV