Yefei Wang

Using the corpus of JSTOR articles, we investigate the role of gender in collaboration patterns across the scholarly landscape by analyzing gender-based homophily--the tendency for researchers to co-author with individuals of the same gender. For a nuanced analysis of gender homophily, we develop methodology necessitated by the fact that the data comprises heterogeneous sub-disciplines and that not all authorships are exchangeable. In particular, we distinguish three components of gender homophily in collaborations: a structural component that is due to demographics and non-gendered authorship norms of a scholarly community, a compositional component which is driven by varying gender representation across sub-disciplines, and a behavioral component which we define as the remainder of observed homophily after its structural and compositional components have been taken into account. Using minimal modeling assumptions, we measure and test for behavioral homophily. We find that significant behavioral homophily can be detected across the JSTOR corpus and show that this finding is robust to missing gender indicators in our data. In a secondary analysis, we show that the proportion of female representation in a field is positively associated with significant behavioral homophily.

Let ≤r and ≤sbe two binary relations on 2ℕ which are meant as reducibilities. Let both relations be closed under finite variation and consider the uniform distribution on 2ℕ, which is obtained by choosing elements of 2ℕ by independent tosses of a fair coin.Then we might ask for the probability that the lower ≤r-cone of a randomly chosen set X, that is, the class of all sets A with A ≤rX, differs from the lower ≤s-cone of X. By c osure under finite variation, the Kolmogorov 0-1 aw yields immediately that this probability is either 0 or 1; in case it is 1, the relations are said to be separable by random oracles.Again by closure under finite variation, for every given set A, the probability that a randomly chosen set X is in the upper ≤r-cone of A is either 0 or 1; let Almostr be the class of sets for which the upper ≤r-cone has measure 1. In the following, results about separations by random oracles and about Almost classes are obtained in the context of generalized reducibilities, that is, for binary relations on 2ℕ which can be defined by a countable set of total continuous functionals on 2ℕ in the same way as the usual resource-bounded reducibilities are defined by an enumeration of appropriate oracle Turing machines. The concept of generalized reducibility comprises a natura resource-bounded reducibilities, but is more general; in particular, it does not involve any kind of specific machine model or even effectivity. The results on generalized reducibilities yield corollaries about specific resource-bounded reducibilities, including several results which have been shown previously in the setting of time or space bounded Turing machine computations