A Note on Flips in Diagonal Rectangulations

Rectangulations are partitions of a square into axis-aligned rectangles. A number of results provide bijections between combinatorial equivalence classes of rectangulations and families of pattern-avoiding permutations. Other results deal with local changes involving a single edge of a rectangulation, referred to as flips, edge rotations, or edge pivoting. Such operations induce a graph on equivalence classes of rectangulations, related to so-called flip graphs on triangulations and other families of geometric partitions. In this note, we consider a family of flip operations on the equivalence classes of diagonal rectangulations, and their interpretation as transpositions in the associated Baxter permutations, avoiding the vincular patterns { 3{14}2, 2{41}3 }. This complements results from Law and Reading (JCTA, 2012) and provides a complete characterization of flip operations on diagonal rectangulations, in both geometric and combinatorial terms

Computing Optimal Shortcuts for Networks

We study augmenting a plane Euclidean network with a segment, called shortcut, to minimize the largest distance between any two points along the edges of the resulting network. Questions of this type have received considerable attention recently, mostly for discrete variants of the problem. We study a fully continuous setting, where all points on the network and the inserted segment must be taken into account. We present the first results on the computation of optimal shortcuts for general networks in this model, together with several results for networks that are paths, restricted to two types of shortcuts: shortcuts with a fixed orientation and simple shortcuts

Oral Health Intervention: A Multifaceted Approach to Improve Oral Health Care during Pregnancy

Introduction: Early Childhood Caries (ECC) is the most common chronic disease of childhood Mothers’ oral health status is a strong predictor of the oral health status of their children 2009: Vermont spends $2.7 million treating children ages 0-5 with Early Childhood Caries 2012: Vermont lifts the$495 Medicaid cap on reimbursement for a woman’s dental care during pregnancy and up to 60 days after delivery American College of Obstetrics and Gynecology (ACOG) Guidelines on prenatal dental care are published 2013: 74% of surveyed Vermont providers treating pregnant women are unaware of the Medicaid change 82% of these providers are not using guidelines to assess oral health during pregnancy Objective: To improve prenatal dental referral rates from obstetric providers by facilitating Vermont-specific implementation of ACOG guidelineshttps://scholarworks.uvm.edu/comphp_gallery/1212/thumbnail.jp

Pesquisas em reprodução fomentam mudanças tecnológicas na suinocultura.

Projeto: 11.11.11.111

Health impact pathways related to air quality changes: testing two health risk methodologies over a local traffic case study

Air pollution causes damage and imposes risks on human health, especially in cities, where the pollutant load is a major concern, although the extent of these effects is still largely unknown. Thus, taking the busiest road traffic area in Portugal as a local case study (600 m × 600 m domain, 4 m2 spatial resolution), the objective of this work was to investigate two health risk methodologies (linear and nonlinear), which were applied for estimating short-term health impacts related to daily variations of high-resolution ambient nitrogen dioxide ( NO2) concentrations modelled for winter and summer periods. Both approaches are based on the same general equation and health input metrics, differing only in the relative risk calculation. Health outcomes, translated into the total number of cases and subsequent damage costs, were compared, and their associated uncertainties and challenges for health impact modelling were addressed. Overall, for the winter and summer periods, health outcomes considering the whole simulation domain were lower using the nonlinear methodology (less 27% and 28%, respectively). Spatially, these differences are more noticeable in locations with higher NO2 and population values, where the highest health estimates were obtained. When the daily NO2 exposure was less than 6 μg.m−3, a fact that occurred in 95% of the domain cells and in both periods, relatively small differences between approaches were found. Analysing the seasonality effect, total health impacts derived from the linear and nonlinear applications were greater in summer (around 18% in both approaches). This happens due to the magnitude and spatial variability of NO2, as the other health input metrics remained constant. This exploratory research in local scale health impact assessment (HIA) demonstrated that the use of refined input data could contribute to more accurate health estimates and that the nonlinear approach is probably the most suitable for characterising air pollution episodes, thus providing important support in HIA.The authors are grateful to the Foundation for Science and Technology (FCT, Portugal) for financial support through national funds FCT/MCTES (PIDDAC) to CIMO (UIDB/00690/2020 and UIDP/00690/2020), SusTEC (LA/P/0007/2020) and CESAM (UID P/50017/2020 + UIDB/50017/2020 + LA/P/0094/2020), and for the contract granted to Joana Ferreira (2020.00622.CEECIND). Thanks are also due to the Project “OleaChain: Competências para a sustentabilidade e inovação da cadeia de valor do olival tradicional no Norte Interior de Portugal” (NORTE-06–3559-FSE-000188), an operation to hire highly qualified human resources, funded by NORTE 2020 through the European Social Fund (ESF).info:eu-repo/semantics/publishedVersio

Shortest Paths in Portalgons

Any surface that is intrinsically polyhedral can be represented by a collection of simple polygons (fragments), glued along pairs of equally long oriented edges, where each fragment is endowed with the geodesic metric arising from its Euclidean metric. We refer to such a representation as a portalgon, and we call two portalgons equivalent if the surfaces they represent are isometric. We analyze the complexity of shortest paths. We call a fragment happy if any shortest path on the portalgon visits it at most a constant number of times. A portalgon is happy if all of its fragments are happy. We present an efficient algorithm to compute shortest paths on happy portalgons. The number of times that a shortest path visits a fragment is unbounded in general. We contrast this by showing that the intrinsic Delaunay triangulation of any polyhedral surface corresponds to a happy portalgon. Since computing the intrinsic Delaunay triangulation may be inefficient, we provide an efficient algorithm to compute happy portalgons for a restricted class of portalgons

Continuous mean distance of a weighted graph

We study the concept of the continuous mean distance of a weighted graph. For connected unweighted graphs, the mean distance can be defined as the arithmetic mean of the distances between all pairs of vertices. This parameter provides a natural measure of the compactness of the graph, and has been intensively studied, together with several variants, including its version for weighted graphs. The continuous analog of the (discrete) mean distance is the mean of the distances between all pairs of points on the edges of the graph. Despite being a very natural generalization, to the best of our knowledge this concept has been barely studied, since the jump from discrete to continuous implies having to deal with an infinite number of distances, something that increases the difficulty of the parameter. In this paper we show that the continuous mean distance of a weighted graph can be computed in time quadratic in the number of edges, by two different methods that apply fundamental concepts in discrete algorithms and computational geometry. We also present structural results that allow a faster computation of this continuous parameter for several classes of weighted graphs. Finally, we study the relation between the (discrete) mean distance and its continuous counterpart, mainly focusing on the relevant question of the convergence when iteratively subdividing the edges of the weighted graph