On Minimizing Crossings in Storyline Visualizations

In a storyline visualization, we visualize a collection of interacting characters (e.g., in a movie, play, etc.) by $x$-monotone curves that converge for each interaction, and diverge otherwise. Given a storyline with $n$ characters, we show tight lower and upper bounds on the number of crossings required in any storyline visualization for a restricted case. In particular, we show that if (1) each meeting consists of exactly two characters and (2) the meetings can be modeled as a tree, then we can always find a storyline visualization with $O(n\log n)$ crossings. Furthermore, we show that there exist storylines in this restricted case that require $\Omega(n\log n)$ crossings. Lastly, we show that, in the general case, minimizing the number of crossings in a storyline visualization is fixed-parameter tractable, when parameterized on the number of characters $k$. Our algorithm runs in time $O(k!^2k\log k + k!^2m)$, where $m$ is the number of meetings.Comment: 6 pages, 4 figures. To appear at the 23rd International Symposium on Graph Drawing and Network Visualization (GD 2015

Mixed Braid Group Actions From Deformations of Surface Singularities

We consider a set of toric Calabi-Yau varieties which arise as deformations of the small resolutions of type A surface singularities. By careful analysis of the heuristics of B-brane transport in the associated GLSMs, we predict the existence of a mixed braid group action on the derived category of each variety, and then prove that this action does indeed exist. This generalizes the braid group action found by Seidel and Thomas for the undeformed resolutions. We also show that the actions for different deformations are related, in a way that is predicted by the physical heuristics.Comment: 37 pages, including many figures and example

The Ising model and Special Geometries

We show that the globally nilpotent G-operators corresponding to the factors of the linear differential operators annihilating the multifold integrals $\chi^{(n)}$ of the magnetic susceptibility of the Ising model ($n \le 6$) are homomorphic to their adjoint. This property of being self-adjoint up to operator homomorphisms, is equivalent to the fact that their symmetric square, or their exterior square, have rational solutions. The differential Galois groups are in the special orthogonal, or symplectic, groups. This self-adjoint (up to operator equivalence) property means that the factor operators we already know to be Derived from Geometry, are special globally nilpotent operators: they correspond to "Special Geometries". Beyond the small order factor operators (occurring in the linear differential operators associated with $\chi^{(5)}$ and $\chi^{(6)}$), and, in particular, those associated with modular forms, we focus on the quite large order-twelve and order-23 operators. We show that the order-twelve operator has an exterior square which annihilates a rational solution. Then, its differential Galois group is in the symplectic group $Sp(12, \mathbb{C})$. The order-23 operator is shown to factorize in an order-two operator and an order-21 operator. The symmetric square of this order-21 operator has a rational solution. Its differential Galois group is, thus, in the orthogonal group $SO(21, \mathbb{C})$.Comment: 33 page

Differences in hip bone mineral density may explain the hip fracture pattern in osteoarthritic hips

Introduction In patients with osteoarthritis of the hip (OAH), trochanteric fractures are much more common than femoral neck fractures. One reason may be altered bone composition in the proximal femurs. OAH often leads to a fixed external rotation of the hip, leading to difficulties in positioning during DXA measurements. We compared BMD in OAH-affected legs and healthy legs

Are health systems interventions gender blind? examining health system reconstruction in conflict affected states

Background Global health policy prioritizes improving the health of women and girls, as evident in the Sustainable Development Goals (SDGs), multiple women’s health initiatives, and the billions of dollars spent by international donors and national governments to improve health service delivery in low-income countries. Countries recovering from fragility and conflict often engage in wide-ranging institutional reforms, including within the health system, to address inequities. Research and policy do not sufficiently explore how health system interventions contribute to the broader goal of gender equity. Methods This paper utilizes a framework synthesis approach to examine if and how rebuilding health systems affected gender equity in the post-conflict contexts of Mozambique, Timor Leste, Sierra Leone, and Northern Uganda. To undertake this analysis, we utilized the WHO health systems building blocks to establish benchmarks of gender equity. We then identified and evaluated a broad range of available evidence on these building blocks within these four contexts. We reviewed the evidence to assess if and how health interventions during the post-conflict reconstruction period met these gender equity benchmarks. Findings Our analysis shows that the four countries did not meet gender equitable benchmarks in their health systems. Across all four contexts, health interventions did not adequately reflect on how gender norms are replicated by the health system, and conversely, how the health system can transform these gender norms and promote gender equity. Gender inequity undermined the ability of health systems to effectively improve health outcomes for women and girls. From our findings, we suggest the key attributes of gender equitable health systems to guide further research and policy. Conclusion The use of gender equitable benchmarks provides important insights into how health system interventions in the post-conflict period neglected the role of the health system in addressing or perpetuating gender inequities. Given the frequent contact made by individuals with health services, and the important role of the health system within societies, this gender blind nature of health system engagement missed an important opportunity to contribute to more equitable and peaceful societies

Water-Resources Investigations Report 83-4030

From introduction: The objectives of the study were to (1) determine the areal extent, thickness, and water-yielding capability of aquifers in the surficial deposits, (2) estimate the amount of water in storage in the aquifers, (3) determine the chemical quality of water in the aquifers and, (4) establish observation wells to monitor the effects of ground-water development on water levels and storage in the aquifers

Water Resources Investigations Report 115-76

Report providing information about the water resources of the Munabo Valley in southeastern Puerto Rico, including the principal source of water, chemical composition, hydraulic conductivities, average transmissivity, and suggestions for water supplementation