Drawing Shortest Paths in Geodetic Graphs

Motivated by the fact that in a space where shortest paths are unique, no two shortest paths meet twice, we study a question posed by Greg Bodwin: Given a geodetic graph $G$, i.e., an unweighted graph in which the shortest path between any pair of vertices is unique, is there a philogeodetic drawing of $G$, i.e., a drawing of $G$ in which the curves of any two shortest paths meet at most once? We answer this question in the negative by showing the existence of geodetic graphs that require some pair of shortest paths to cross at least four times. The bound on the number of crossings is tight for the class of graphs we construct. Furthermore, we exhibit geodetic graphs of diameter two that do not admit a philogeodetic drawing.Comment: Appears in the Proceedings of the 28th International Symposium on Graph Drawing and Network Visualization (GD 2020

Fatores que influenciam na hidratação de atletas de futebol

A hidratação é um fator de extrema importância para um melhor rendimento de atletas de futebol. Essa revisão procurou focar-se nos principais fatores que influenciam a hidratação de atletas de futebol. Durante uma partida não existem paradas regulares, apesar de algumas tentativas já estarem sendo feitas por algumas federações, ainda que em caráter experimental. O desempenho dos atletas é influenciado por fatores como aclimatização, nível de hidratação, esvaziamento gástrico e condição climática. A depleção de glicogênio muscular é a principal causa da perda do desempenho durante as partidas de futebol, principalmente no segundo tempo, onde há maior incidência de gols marcados e sofridos. Mediante a isso, é importante que antes, durante e após os jogos e treinamentos os atletas façam a ingestão de carboidrato para manter os níveis glicêmicos altos,  evitando o surgimento prematuro da fadiga. Também é importante a reposição de eletrólitos como sódio e potássio. Normalmente a reposição dos eletrólitos é mais eficiente quando feita através da alimentação. Existe a necessidade da conscientização dos atletas para que criem o hábito de ingerir líquidos regularmente, ou seja, antes, durante e após treinamentos e competições, de acordo com suas respostas individuais ao calor.  Palavras-chave: Reposição Hídrica. Esvaziamento gástrico. Futebol. Carboidrato

Reducing the environmental impact of surgery on a global scale: systematic review and co-prioritization with healthcare workers in 132 countries

Abstract Background Healthcare cannot achieve net-zero carbon without addressing operating theatres. The aim of this study was to prioritize feasible interventions to reduce the environmental impact of operating theatres. Methods This study adopted a four-phase Delphi consensus co-prioritization methodology. In phase 1, a systematic review of published interventions and global consultation of perioperative healthcare professionals were used to longlist interventions. In phase 2, iterative thematic analysis consolidated comparable interventions into a shortlist. In phase 3, the shortlist was co-prioritized based on patient and clinician views on acceptability, feasibility, and safety. In phase 4, ranked lists of interventions were presented by their relevance to high-income countries and low–middle-income countries. Results In phase 1, 43 interventions were identified, which had low uptake in practice according to 3042 professionals globally. In phase 2, a shortlist of 15 intervention domains was generated. In phase 3, interventions were deemed acceptable for more than 90 per cent of patients except for reducing general anaesthesia (84 per cent) and re-sterilization of ‘single-use’ consumables (86 per cent). In phase 4, the top three shortlisted interventions for high-income countries were: introducing recycling; reducing use of anaesthetic gases; and appropriate clinical waste processing. In phase 4, the top three shortlisted interventions for low–middle-income countries were: introducing reusable surgical devices; reducing use of consumables; and reducing the use of general anaesthesia. Conclusion This is a step toward environmentally sustainable operating environments with actionable interventions applicable to both high– and low–middle–income countries

2-Layer k-Planar Graphs: Density, Crossing Lemma, Relationships, and Pathwidth

The 2-layer drawing model is a well-established paradigm to visualize bipartite graphs. Several beyond-planar graph classes have been studied under this model. Surprisingly, however, the fundamental class of k-planar graphs has been considered only for k= 1 in this context. We provide several contributions that address this gap in the literature. First, we show tight density bounds for the classes of 2-layer k-planar graphs with k∈ { 2, 3, 4, 5 }. Based on these results, we provide a Crossing Lemma for 2-layer k-planar graphs, which then implies a general density bound for 2-layer k-planar graphs. We prove this bound to be almost optimal with a corresponding lower bound construction. Finally, we study relationships between k-planarity and h-quasiplanarity in the 2-layer model and show that 2-layer k-planar graphs have pathwidth at most k+ 1

<b> Performance in all-out intermittent short-duration exercise bouts: active vs passive recovery </b>

The purpose of this study was to verify the influence of recovery type on intermittent exercise performance. Fifteen physically active male subjects performed two intermittent exercises on two occasions. The intermittent exercises involved ten all-out 10-s cycling sprints interspersed with 30 seconds of active or passive recovery. The sprint bouts were carried out on an cycle ergometer, loaded to 0.075 kp.kg-1 of body mass and were separated either by 30 seconds of active recovery at a work rate of 1 kp and at a frequency of 60 rpm or by 30 seconds of rest on the cycle saddle. Peak and Mean power output were recorded for each of the ten bouts. An exponential regression curve was fi tted to the ten Peak Powerand the ten Mean Power points and a Fatigue Index was determined. Two-way ANOVA for repeated measures was used to compare bouts and recoveries. Statistical signifi cance was set at p RESUMO O objetivo do presente estudo foi verifi car a infl uência do tipo de recuperação sobre o desempenho em exercício intermitente. Quinze sujeitos do gênero masculino realizaram exercícios intermitentes em duas ocasiões. O exercício intermitente consistiu na repetição de dez blocos de 10 s de esforço máximo, intercalados com 30 s de pausa ativa ou passiva. Os blocos de esforço foram realizados na carga correspondente a 7,5% da massa corporal e separados por 30 s de recuperação ativa, na carga de 1 kp e na freqüência de pedal de 60 rpm ou por 30 s de repouso sentado no banco do cicloergômetro na recuperação passiva. A Potência de Pico e a Potência Média de cada bloco de esforço foram obtidas. Foi realizado ajuste exponencial sobre os dez valores de Potência de pico e de Potência Média, e também foi determinadoo Índice de Fadiga. Para a comparação entre os tipos de recuperação e entre os blocos de esforço foi realizada a Anova a dois fatores para medidas repetidas. Foi adotado o nível de signifi cância de 0,05. Não houve diferença signifi cativa entre a recuperação ativa e passiva para a Potência de Pico (9,0±1,3 vs 9,2±1,3 W.kg-1, p=0,11), Potência Média (7,3±1,3 vs 7,1±1,2 W.kg-1, p=0,08), Índice de Fadiga da Potência de Pico (29±9 vs 27±8 %, p=0,13) e Índice de Fadiga da Potência Média (34±11 vs 34±10 %, p=0,43). Conclui-se que o tipo de recuperação não influencia o desempenho intermitente em blocos de esforço de curta duração e alta intensidade

Drawing Shortest Paths in Geodetic Graphs

Motivated by the fact that in a space where shortest paths are unique, no two shortest paths meet twice, we study a question posed by Greg Bodwin: Given a geodetic graph G, i.e., an unweighted graph in which the shortest path between any pair of vertices is unique, is there a philogeodetic drawing of G, i.e., a drawing of G in which the curves of any two shortest paths meet at most once? We answer this question in the negative by showing the existence of geodetic graphs that require some pair of shortest paths to cross at least four times. The bound on the number of crossings is tight for the class of graphs we construct. Furthermore, we exhibit geodetic graphs of diameter two that do not admit a philogeodetic drawing. © 2020, Springer Nature Switzerland AG.12 month embargo; first published online 14 February 2021This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]