No abstract

One can point to a variety of historical milestones for gender equality in STEM (science, technology, engineering, and mathematics), however, the practical effects are gradual and ongoing. It is important to quantify gender differences in subdomains of scientific work in order to detect potential biases and to monitor progress. In this work, we studied the relevance of gender in scientific collaboration patterns in the Institute for Operations Research and the Management Sciences (INFORMS), a professional organization with sixteen peer-reviewed journals. We constructed a large temporal bipartite network between authors and publications, using the organization's publication data from 1952 to 2016, and augmented the author nodes with gender labels. We characterized differences in several basic statistics of this network over time, highlighting how they change with respect to relevant historical events. We found a steady increase in participation by women (e.g., fraction of authorships by women and of new women authors) starting ∼1980. However, women still comprise less than 25% of the INFORMS society, and are additionally underrepresented among authors with many publications. Finally, we describe a methodology for quantifying differences in the role that authorships by women and men play in the overall connectivity of the network. Specifically, we propose a degree-preserving temporal and geometric null model with emergent communities. We use two measures of edge importance related to diffusion throughout the network, namely effective resistance and edge contraction importance to quantify gender differences in collaboration patterns that go beyond differences in local statistics.

The problem of finding an optimal curve for the target magnetic axis of a stellarator is addressed. Euler-Lagrange equations are derived for finite length three-dimensional curves that extremise their bending energy while yielding fixed integrated torsion. The obvious translational and rotational symmetry is exploited to express solutions in a preferred cylindrical coordinate system in terms of elliptic Jacobi functions. These solution curves, which, up to similarity transformations, depend on three dimensionless parameters, do not necessarily close. Two closure conditions are obtained for the vertical and toroidal displacement (the radial coordinate being trivially periodic) to yield a countably infinite set of one-parameter families of closed non-planar curves. The behaviour of the integrated torsion (Twist of the Frenet frame), the Linking of the Frenet frame and the Writhe of the solution curves is studied in light of the Cȃlugȃreanu theorem. A refreshed interpretation of Mercier's formula for the on-axis rotational transform of stellarator magnetic field-lines is proposed.

How might one test the hypothesis that graphs were sampled from the same distribution? Here, we compare two statistical tests that address this question. The first uses the observed subgraph densities themselves as estimates of those of the underlying distribution. The second test uses a new approach that converts these subgraph densities into estimates of the graph cumulants of the distribution. We demonstrate -via theory, simulation, and application to real data -the superior statistical power of using graph cumulants.