Reciprocity—the mutual provisioning of support/goods—is a pervasive feature of social life. Directed networks provide a way to examine the structure of reciprocity in a community. However, measuring social networks involves assumptions about what relationships matter and how to elicit them, which may impact observed reciprocity. In particular, the practice of aggregating multiple sources of data on the same relationship (e.g., “double-sampled” data, where both the “giver” and “receiver” are asked to report on their relationship) may have pronounced impacts on network structure. To investigate these issues, we examine concordance (ties reported by both parties) and reciprocity in a set of directed, double-sampled social support networks. We find low concordance in people’s responses. Taking either the union (including any reported ties) or the intersection (including only concordant ties) of double-sampled relationships results in dramatically higher levels of reciprocity. Using multilevel exponential random graph models of social support networks from 75 villages in India, we show that these changes cannot be fully explained by the increase in the number of ties produced by layer aggregation. Respondents’ tendency to name the same people as both givers and receivers of support plays an important role, but this tendency varies across contexts and relationships type. We argue that no single method should necessarily be seen as the “correct” choice for aggregation of multiple sources of data on a single relationship type. Methods of aggregation should depend on the research question, the context, and the relationship in question.

This paper investigates the issue of stochastic comparison of multi-active redundancies at the component level versus the system level. Based on the assumption that all components are statistically dependent, in the case of complete matching and nonmatching spares, we present some interesting comparison results in the sense of the hazard rate, reversed hazard rate and likelihood ratio orders, respectively. And we also obtain two comparison results between relative agings of resulting systems at the component level and the system level. Several numerical examples are provided to illustrate the theoretical results.

Many problems in combinatorial linear algebra require upper bounds on the number of solutions to an underdetermined system of linear equations $Ax = b$, where the coordinates of the vector x are restricted to take values in some small subset (e.g. $\{\pm 1\}$) of the underlying field. The classical ways of bounding this quantity are to use either a rank bound observation due to Odlyzko or a vector anti-concentration inequality due to Halász. The former gives a stronger conclusion except when the number of equations is significantly smaller than the number of variables; even in such situations, the hypotheses of Halász’s inequality are quite hard to verify in practice. In this paper, using a novel approach to the anti-concentration problem for vector sums, we obtain new Halász-type inequalities that beat the Odlyzko bound even in settings where the number of equations is comparable to the number of variables. In addition to being stronger, our inequalities have hypotheses that are considerably easier to verify. We present two applications of our inequalities to combinatorial (random) matrix theory: (i) we obtain the first non-trivial upper bound on the number of $n\times n$ Hadamard matrices and (ii) we improve a recent bound of Deneanu and Vu on the probability of normality of a random $\{\pm 1\}$ matrix.

Masturbation is a common sexual practice in men, and saliva is often used as a lubricant during masturbation by men who have sex with men. However, the role of saliva use during masturbation in the transmission of chlamydia is still unclear. We developed population-level, susceptible-infected-susceptible compartmental models to explore the role of saliva use during masturbation on the transmission of chlamydia at multiple anatomical sites. In this study, we simulated both solo masturbation and mutual masturbation. Our baseline model did not include masturbation but included transmission routes (anal sex, oral-penile sex, rimming, kissing and sequential sexual practices) we have previously validated (model 1). We added masturbation to model 1 to develop the second model (model 2). We calibrated the model to five clinical datasets separately to assess the effects of masturbation on the prevalence of site-specific infection. The inclusion of masturbation (model 2) significantly worsened the ability of the models to replicate the prevalence of C. trachomatis. Using model 2 and the five data sets, we estimated that saliva use during masturbation was responsible for between 3.9% [95% confidence interval (CI) 2.0–6.8] and 6.2% (95% CI 3.8–10.5) of incident chlamydia cases at all sites. Our models suggest that saliva use during masturbation is unlikely to play a major role in chlamydia transmission between men, and even if it does have a role, about one in seven cases of urethral chlamydia might arise from masturbation.

Lignin is a polyphenolic compound found in plant tissues, especially wood and bark. The lignin content determines the quality of wood biochar in agroecological uses, and is used in the production of synthetic resins and adhesives. Despite its importance in plant physiology and its agricultural and industrial utility, there exists a wide gap of knowledge of lignin contents of tropical hardwood trees of South Asia, except for a few species. We present here the first estimation of lignin content in wood and bark of 48 species from tropical deciduous forests of India. We show that some species are characterized by greater wood lignin (WL) compared with bark lignin (BL) content, contrary to the generalization held for hardwood trees, and suggest a plausible correspondence between the WL to BL ratio and timber quality.