Strip Planarity Testing of Embedded Planar Graphs

In this paper we introduce and study the strip planarity testing problem, which takes as an input a planar graph $G(V,E)$ and a function $\gamma:V \rightarrow \{1,2,\dots,k\}$ and asks whether a planar drawing of $G$ exists such that each edge is monotone in the $y$-direction and, for any $u,v\in V$ with $\gamma(u)<\gamma(v)$, it holds $y(u)<y(v)$. The problem has strong relationships with some of the most deeply studied variants of the planarity testing problem, such as clustered planarity, upward planarity, and level planarity. We show that the problem is polynomial-time solvable if $G$ has a fixed planar embedding.Comment: 24 pages, 12 figures, extended version of 'Strip Planarity Testing' (21st International Symposium on Graph Drawing, 2013

Surveillance of paediatric exposures to liquid laundry detergent pods in Italy

Objective To analyse paediatric exposures to pod and traditional laundry detergents in Italy and changes in exposure trends. Methods Analyses of a series of patients aged &lt;5 years and exposed to laundry detergents between September 2010 and June 2015, identified by the National Poison Control in Milan. Results In comparison with patients exposed to traditional laundry detergents (n=1150), a higher proportion of those exposed to pods (n=1649) were managed in hospital (68% vs 42%), had clinical effects (75% vs 22%) and moderate/high severity outcomes (13% vs &lt;1%). Exposure rates were stable over time for traditional detergents (average 0.65 cases/day), but an abrupt decline in major company pods was seen in December 2012, 4 months after the introduction of opaque outer packaging (from 1.03 to 0.36 cases/day and from 1.88 to 0.86 cases/million units sold). The odds of clinical effects was higher for exposure to pods than for traditional detergents (OR=10.8; 95% CI 9.0 to 12.9). Among patients exposed to pods, the odds of moderate/high severity outcomes was four times higher for children aged &lt;1 years than for the other age groups (OR=3.9; 95% CI 2.2 to 7.0). Ten children exposed to laundry detergent pods had high severity outcomes while no children exposed to traditional laundry detergents developed high severity effects. Conclusions The study confirms that exposure to laundry detergent pods is more dangerous than exposure to traditional detergents. In Italy, 4 months after the introduction of opaque outer packaging by a major company, product-specific exposure rates decreased sharply, suggesting that reducing visibility of laundry detergent pods may be an effective preventive measure. Further efforts are needed to improve safety

Optimal Morphs of Convex Drawings

We give an algorithm to compute a morph between any two convex drawings of the same plane graph. The morph preserves the convexity of the drawing at any time instant and moves each vertex along a piecewise linear curve with linear complexity. The linear bound is asymptotically optimal in the worst case.Comment: To appear in SoCG 201

Relaxing the Constraints of Clustered Planarity

In a drawing of a clustered graph vertices and edges are drawn as points and curves, respectively, while clusters are represented by simple closed regions. A drawing of a clustered graph is c-planar if it has no edge-edge, edge-region, or region-region crossings. Determining the complexity of testing whether a clustered graph admits a c-planar drawing is a long-standing open problem in the Graph Drawing research area. An obvious necessary condition for c-planarity is the planarity of the graph underlying the clustered graph. However, such a condition is not sufficient and the consequences on the problem due to the requirement of not having edge-region and region-region crossings are not yet fully understood. In order to shed light on the c-planarity problem, we consider a relaxed version of it, where some kinds of crossings (either edge-edge, edge-region, or region-region) are allowed even if the underlying graph is planar. We investigate the relationships among the minimum number of edge-edge, edge-region, and region-region crossings for drawings of the same clustered graph. Also, we consider drawings in which only crossings of one kind are admitted. In this setting, we prove that drawings with only edge-edge or with only edge-region crossings always exist, while drawings with only region-region crossings may not. Further, we provide upper and lower bounds for the number of such crossings. Finally, we give a polynomial-time algorithm to test whether a drawing with only region-region crossings exist for biconnected graphs, hence identifying a first non-trivial necessary condition for c-planarity that can be tested in polynomial time for a noticeable class of graphs

On Planar Greedy Drawings of 3-Connected Planar Graphs

A graph drawing is greedy if, for every ordered pair of vertices (x,y), there is a path from x to y such that the Euclidean distance to y decreases monotonically at every vertex of the path. Greedy drawings support a simple geometric routing scheme, in which any node that has to send a packet to a destination "greedily" forwards the packet to any neighbor that is closer to the destination than itself, according to the Euclidean distance in the drawing. In a greedy drawing such a neighbor always exists and hence this routing scheme is guaranteed to succeed. In 2004 Papadimitriou and Ratajczak stated two conjectures related to greedy drawings. The greedy embedding conjecture states that every 3-connected planar graph admits a greedy drawing. The convex greedy embedding conjecture asserts that every 3-connected planar graph admits a planar greedy drawing in which the faces are delimited by convex polygons. In 2008 the greedy embedding conjecture was settled in the positive by Leighton and Moitra. In this paper we prove that every 3-connected planar graph admits a planar greedy drawing. Apart from being a strengthening of Leighton and Moitra\u27s result, this theorem constitutes a natural intermediate step towards a proof of the convex greedy embedding conjecture

STATIC AND DYNAMIC BEHAVIOUR ASSESSMENT OF THE TRAJAN ARCH BY MEANS OF NEW MONITORING TECHNOLOGIES

An effective assessment of the static and dynamic structural behavior of historical monuments requires the development and validation of suitable adaptive structural models using high-quality experimental data acquired with an effectively continuous and distributed monitoring. Furthermore, the adaptive strategy allows an efficient evaluation of the health status and of the evolution along the time of a historical monument, providing relevant information to plan appropriate actions for its long-term preservation. The Trajan Arch in Benevento chosen as a case of study to develop and apply this new adaptive strategy in cultural heritage conservation. The paper, after a description of the innovative monitoring system, based on state-of-the-art mechanical sensors, presents and discusses the results of two tests, comparing the measurements with the predictions of an adaptive structural FEM model developed for the dynamical simulation of the Trajan Arch

Prenatal Attachment and Perinatal Depression: A Systematic Review

Pregnancy is a period of complex bio-psychological changes, during which the development of an attachment bond to the fetus takes on a central role. Depressive symptoms are common during this period. Both symptoms of depression and low levels of prenatal attachment are related to negative outcomes in caregivers and infants. Following the Preferred Reporting Items for Systematic Review and Meta-Analysis (PRISMA) statement, this systematic review analyzes and systematizes 41 studies concerning the association between prenatal attachment and perinatal depression. The majority of the studies reported a significant association between the two. Specifically, prenatal depressive symptoms were found to be negatively associated with prenatal attachment. Furthermore, lower levels of prenatal attachment were related to higher postnatal depressive symptoms, although fewer studies assessed this association. While these results were found across different populations, conflicting findings emerged, suggesting they should be interpreted with caution, particularly in male samples and in non-normative pregnancies (e.g., high-risk pregnancies, medically assisted pregnancies, and pregnancies with previous perinatal losses). These results are clinically important for the perinatal screening process and for implementing preventive and treatment programs. However, future studies are needed to further confirm and generalize these results