Detecting Weakly Simple Polygons

A closed curve in the plane is weakly simple if it is the limit (in the Fr\'echet metric) of a sequence of simple closed curves. We describe an algorithm to determine whether a closed walk of length n in a simple plane graph is weakly simple in O(n log n) time, improving an earlier O(n^3)-time algorithm of Cortese et al. [Discrete Math. 2009]. As an immediate corollary, we obtain the first efficient algorithm to determine whether an arbitrary n-vertex polygon is weakly simple; our algorithm runs in O(n^2 log n) time. We also describe algorithms that detect weak simplicity in O(n log n) time for two interesting classes of polygons. Finally, we discuss subtle errors in several previously published definitions of weak simplicity.Comment: 25 pages and 13 figures, submitted to SODA 201

Profile 7: Dancing on the Through-Line: Rennie Harris and the Past and Future of Hip-Hop Dance

The career of hip-hop artist and visionary choreographer Rennie Harris, and his profound influence on street dancinghttps://digitalcommons.colum.edu/cap_vistas/1006/thumbnail.jp

Untangling Planar Curves

Any generic closed curve in the plane can be transformed into a simple closed curve by a finite sequence of local transformations called homotopy moves. We prove that simplifying a planar closed curve with n self-crossings requires Theta(n^{3/2}) homotopy moves in the worst case. Our algorithm improves the best previous upper bound O(n^2), which is already implicit in the classical work of Steinitz; the matching lower bound follows from the construction of closed curves with large defect, a topological invariant of generic closed curves introduced by Aicardi and Arnold. This lower bound also implies that Omega(n^{3/2}) degree-1 reductions, series-parallel reductions, and Delta-Y transformations are required to reduce any planar graph with treewidth Omega(sqrt{n}) to a single edge, matching known upper bounds for rectangular and cylindrical grid graphs. Finally, we prove that Omega(n^2) homotopy moves are required in the worst case to transform one non-contractible closed curve on the torus to another; this lower bound is tight if the curve is homotopic to a simple closed curve

Work Related Paternal Absence among Petroleum Workers in Canada

Work-Related Parental Absence (WRPA) is common in contemporary family life. Industries such as aviation, fishing, logging, mining, and petroleum extraction all require the employee to work away from family from short to significant periods of time. In Canada’s petroleum industry, work schedules that involve parental absence are especially common. There has been ample research conducted on the impact of military deployment on families, some research on how mining families are impacted by WRPA, and a small amount of research on the effects of WRPA among offshore European petroleum workers and their families. However, there is no research currently available that investigates the impact of WRPA on Canadian oil and gas petroleum workers and their families. In this article, we share the results of a qualitative study that examined the experience of WRPA through interviewing 10 heterosexual couples. Use of Interpretive Phenomenological Analysis identified a tripartite thematic structure consisting of positive, negative, and neutral aspects of the WRPA experience, which in turn were shaped by specific adaptive strategies undertaken by families. The results of this research provide important insights into a common, yet poorly understood, lifestyle within the Canadian employment landscape

Lower Bounds for Electrical Reduction on Surfaces

We strengthen the connections between electrical transformations and homotopy from the planar setting - observed and studied since Steinitz - to arbitrary surfaces with punctures. As a result, we improve our earlier lower bound on the number of electrical transformations required to reduce an n-vertex graph on surface in the worst case [SOCG 2016] in two different directions. Our previous Omega(n^{3/2}) lower bound applies only to facial electrical transformations on plane graphs with no terminals. First we provide a stronger Omega(n^2) lower bound when the planar graph has two or more terminals, which follows from a quadratic lower bound on the number of homotopy moves in the annulus. Our second result extends our earlier Omega(n^{3/2}) lower bound to the wider class of planar electrical transformations, which preserve the planarity of the graph but may delete cycles that are not faces of the given embedding. This new lower bound follow from the observation that the defect of the medial graph of a planar graph is the same for all its planar embeddings

Variations in Public Health Governance

Background: Studies of public health departments have found mixed results regarding the relevance of governance through local boards of health (LBOHs). Some studies find that LBOHs can be an important component in higher performance by local health departments. Other analyses, however, find no advantage for local health departments having or not having a LBOH. The hypothesis was that a typology of LBOHs nationwide can define different types of LBOHs based on their powers and responsibilities. Methods: Using national profile sample data from the National Association of Local Boards of Health, LBOHs were categorized using 34 variables based on four domains of responsibilities and duties: enforcement powers, regulatory powers, human resource powers, and budgetary powers. Correlations between types of LBOHs defined by this typology were then computed, and whether they shared significant characteristics in terms of the race, ethnicity, sex, and educational demographics of their board members was determined. ArcGIS was used to analyze the data spatially for regional and national patterns. Results: LBOHs vary considerably across the country - from LBOHs with no budgetary, enforcement, regulatory, or human resources authorities to those that have all four. Conclusions: Different types of LBOHs may have different influences on their associated local boards of health. This study provides a typology for future research to allow analysts to distinguish different types of LBOHs nationally

Deformation of Axion Potentials: Implications for Spontaneous Baryogenesis, Dark Matter, and Isocurvature Perturbations

We show that both the baryon asymmetry of the universe and dark matter (DM) can be accounted for by the dynamics of a single axion-like field. In this scenario, the observed baryon asymmetry is produced through spontaneous baryogenesis---driven by the early evolution of the axion---while its late-time coherent oscillations explain the observed DM abundance. Typically, spontaneous baryogenesis via axions is only successful in regions of parameter space where the axion is relatively heavy, rendering it highly unstable and unfit as a dark matter candidate. However, we show that a field-dependent wavefunction renormalization can arise which effectively "deforms" the axion potential, allowing for efficient generation of baryon asymmetry while maintaining a light and stable axion. Meanwhile, such deformations of the potential induce non-trivial axion dynamics, including a tracking behavior during its intermediate phase of evolution. This attractor-like dynamics dramatically reduces the sensitivity of the axion relic abundance to initial conditions and naturally suppresses DM isocurvature perturbations. Finally, we construct an explicit model realization, using a continuum-clockwork axion, and survey the details of its phenomenological viability