O problema da árvore de suporte de custo mínimo com restrições de peso

Doutoramento em MatemáticaNesta tese abordam-se várias formulações e diferentes métodos para resolver o Problema da Árvore de Suporte de Custo Mínimo com Restrições de Peso (WMST – Weight-constrained Minimum Spanning Tree Problem). Este problema, com aplicações no desenho de redes de comunicações e telecomunicações, é um problema de Otimização Combinatória NP-difícil. O Problema WMST consiste em determinar, numa rede com custos e pesos associados às arestas, uma árvore de suporte de custo mínimo de tal forma que o seu peso total não exceda um dado limite especificado. Apresentam-se e comparam-se várias formulações para o problema. Uma delas é usada para desenvolver um procedimento com introdução de cortes baseado em separação e que se tornou bastante útil na obtenção de soluções para o problema. Tendo como propósito fortalecer as formulações apresentadas, introduzem-se novas classes de desigualdades válidas que foram adaptadas das conhecidas desigualdades de cobertura, desigualdades de cobertura estendida e desigualdades de cobertura levantada. As novas desigualdades incorporam a informação de dois conjuntos de soluções: o conjunto das árvores de suporte e o conjunto saco-mochila. Apresentam-se diversos algoritmos heurísticos de separação que nos permitem usar as desigualdades válidas propostas de forma eficiente. Com base na decomposição Lagrangeana, apresentam-se e comparam-se algoritmos simples, mas eficientes, que podem ser usados para calcular limites inferiores e superiores para o valor ótimo do WMST. Entre eles encontram-se dois novos algoritmos: um baseado na convexidade da função Lagrangeana e outro que faz uso da inclusão de desigualdades válidas. Com o objetivo de obter soluções aproximadas para o Problema WMST usam-se métodos heurísticos para encontrar uma solução inteira admissível. Os métodos heurísticos apresentados são baseados nas estratégias Feasibility Pump e Local Branching. Apresentam-se resultados computacionais usando todos os métodos apresentados. Os resultados mostram que os diferentes métodos apresentados são bastante eficientes para encontrar soluções para o Problema WMST.In this thesis we discuss several formulations and different methods to solve the Weight-constrained Minimum Spanning Tree Problem (WMST). This problem, with applications in the design of communication networks and telecommunications, is a NP-hard combinatorial optimization problem. The WMST problem aims at obtaining, in a network with costs and weights associated to its edges, a minimum cost spanning tree such that its total weight does not exceed a given specified parameter. Various formulations to the problem are presented and compared. One is used to develop a procedure to introduce cuts based on separation and that became quite useful in obtaining solutions to the problem. To strengthen the formulations, new classes of valid inequalities, adapted from the well-known cover inequalities, extended cover inequalities and lifted cover inequalities, are introduced. These new inequalities incorporate information from two sets of solutions: the spanning trees set and the knapsack set. We present several separation heuristic algorithms that allow us to efficiently use the proposed valid inequalities. Based on Lagrangean decomposition, simple and efficient algorithms are presented and compared. The algorithms can be used to obtain upper and lower bounds to the optimal value of the WMST problem. Among them are two new algorithms: one based on the convexity of the Lagrangean function and another making use of the inclusion of valid inequalities. In order to obtain approximate solutions to the WMST problem, heuristic methods are used to find feasible solutions. The heuristic methods presented are based on the Feasibility Pump and Local Branching strategies. We present computational results using all these methods. Results show that the different methods presented are very efficient for finding solutions to the WMST problem

Problema da árvore de suporte de custo mínimo com restrições de diâmetro

Mestrado em MatemáticaNesta tese desenvolvem-se alguns métodos heurísticos para o Problema da Árvore de Suporte de Custo Mínimo com Restrições de Diâmetro que é um problema de Optimização Combinatória. Este problema tem aplicação na área das telecomunicações e insere-se no âmbito de problemas do Desenho Topológico de Redes de Telecomunicações. O Problema do Desenho de Redes de Terminais consiste em encontrar a melhor maneira de ligar n terminais em diferentes localizações a um nodo central. A topologia óptima deste problema corresponde a uma árvore de suporte de custo mínimo. No Problema da Árvore de Suporte de Custo Mínimo com Restrições de Diâmetro pretende-se determinar uma árvore de suporte de custo mínimo cujo diâmetro não ultrapasse um determinado valor máximo (D). Esta imposição melhora o desempenho da rede. Apresentam-se três heurísticas greedy que seleccionam iterativamente uma aresta a ser incluída na árvore e que se distinguem apenas na forma como são escolhidos os elementos iniciais (nodo/aresta). Descreve-se uma heurística de trocas locais (ou melhoramento) que efectua algumas trocas de arestas de acordo com uma regra estabelecida. Descrevem-se quatro heurísticas de aproximação que adaptam soluções de outro problema ao problema em questão. Na primeira destas heurísticas eliminam-se arestas da árvore de suporte de custo mínimo e, depois, constrói-se a árvore a partir da subárvore obtida. Na segunda proíbe-se a presença na solução de cada uma das arestas de um dado conjunto. Na terceira heurística exige-se que cada aresta de um dado conjunto esteja na solução e, na última exige-se que cada uma das arestas de um dado conjunto esteja na solução e que um conjunto de arestas não esteja na solução. Apresentam-se resultados computacionais que mostram que as Heurísticas de Aproximação são as que obtêm melhores resultados.In this thesis we present some heuristics methods developed to the Diameter constrained Minimum Spanning Tree problem (DMST), which is a Combinatorial Optimization Problem. This is a telecommunication network design problem and the terminal layout problem consists of finding the best way to link n terminals, at different locations, to a central node. The optimal topology for these problems corresponds to a minimum spanning tree. In the DMST we want to obtain a minimum spanning tree which diameter does not surpass a maximum value (D). The diameter constraint improves the performance of the network. We present three greedy heuristics that iteratively select an edge to be added to the tree and are distinguished in the form how initial elements (a node or an edge) are selected. We describe a local exchanges heuristic where improvements are accomplished with some edges exchanges according to an established rule. We also describe four approximation heuristics that adapt solutions from another problem to this problem. On the first heuristic we start it by eliminating edges from the minimal spanning tree and then we build the new tree from the obtained subtree. On the second heuristic, the presence of each edge of a certain set is forbidden in the solution. On the third heuristic, it is demanded that each edge of a certain set is present in the solution, and on the last heuristic it is demanded that each one of the edges of a certain set is present in the solution and that a set of edges is not in the solution. Our computational experience shows that the best results are achieved with the approximation heuristics

Prevalence, associated factors and outcomes of pressure injuries in adult intensive care unit patients: the DecubICUs study

Funder: European Society of Intensive Care Medicine; doi: http://dx.doi.org/10.13039/501100013347Funder: Flemish Society for Critical Care NursesAbstract: Purpose: Intensive care unit (ICU) patients are particularly susceptible to developing pressure injuries. Epidemiologic data is however unavailable. We aimed to provide an international picture of the extent of pressure injuries and factors associated with ICU-acquired pressure injuries in adult ICU patients. Methods: International 1-day point-prevalence study; follow-up for outcome assessment until hospital discharge (maximum 12 weeks). Factors associated with ICU-acquired pressure injury and hospital mortality were assessed by generalised linear mixed-effects regression analysis. Results: Data from 13,254 patients in 1117 ICUs (90 countries) revealed 6747 pressure injuries; 3997 (59.2%) were ICU-acquired. Overall prevalence was 26.6% (95% confidence interval [CI] 25.9–27.3). ICU-acquired prevalence was 16.2% (95% CI 15.6–16.8). Sacrum (37%) and heels (19.5%) were most affected. Factors independently associated with ICU-acquired pressure injuries were older age, male sex, being underweight, emergency surgery, higher Simplified Acute Physiology Score II, Braden score 3 days, comorbidities (chronic obstructive pulmonary disease, immunodeficiency), organ support (renal replacement, mechanical ventilation on ICU admission), and being in a low or lower-middle income-economy. Gradually increasing associations with mortality were identified for increasing severity of pressure injury: stage I (odds ratio [OR] 1.5; 95% CI 1.2–1.8), stage II (OR 1.6; 95% CI 1.4–1.9), and stage III or worse (OR 2.8; 95% CI 2.3–3.3). Conclusion: Pressure injuries are common in adult ICU patients. ICU-acquired pressure injuries are associated with mainly intrinsic factors and mortality. Optimal care standards, increased awareness, appropriate resource allocation, and further research into optimal prevention are pivotal to tackle this important patient safety threat

Prevalence, associated factors and outcomes of pressure injuries in adult intensive care unit patients: the DecubICUs study

Funder: European Society of Intensive Care Medicine; doi: http://dx.doi.org/10.13039/501100013347Funder: Flemish Society for Critical Care NursesAbstract: Purpose: Intensive care unit (ICU) patients are particularly susceptible to developing pressure injuries. Epidemiologic data is however unavailable. We aimed to provide an international picture of the extent of pressure injuries and factors associated with ICU-acquired pressure injuries in adult ICU patients. Methods: International 1-day point-prevalence study; follow-up for outcome assessment until hospital discharge (maximum 12 weeks). Factors associated with ICU-acquired pressure injury and hospital mortality were assessed by generalised linear mixed-effects regression analysis. Results: Data from 13,254 patients in 1117 ICUs (90 countries) revealed 6747 pressure injuries; 3997 (59.2%) were ICU-acquired. Overall prevalence was 26.6% (95% confidence interval [CI] 25.9–27.3). ICU-acquired prevalence was 16.2% (95% CI 15.6–16.8). Sacrum (37%) and heels (19.5%) were most affected. Factors independently associated with ICU-acquired pressure injuries were older age, male sex, being underweight, emergency surgery, higher Simplified Acute Physiology Score II, Braden score 3 days, comorbidities (chronic obstructive pulmonary disease, immunodeficiency), organ support (renal replacement, mechanical ventilation on ICU admission), and being in a low or lower-middle income-economy. Gradually increasing associations with mortality were identified for increasing severity of pressure injury: stage I (odds ratio [OR] 1.5; 95% CI 1.2–1.8), stage II (OR 1.6; 95% CI 1.4–1.9), and stage III or worse (OR 2.8; 95% CI 2.3–3.3). Conclusion: Pressure injuries are common in adult ICU patients. ICU-acquired pressure injuries are associated with mainly intrinsic factors and mortality. Optimal care standards, increased awareness, appropriate resource allocation, and further research into optimal prevention are pivotal to tackle this important patient safety threat

Correction to: Prevalence, associated factors and outcomes of pressure injuries in adult intensive care unit patients: the DecubICUs study

The original version of this article unfortunately contained a mistake

Characterisation of microbial attack on archaeological bone

As part of an EU funded project to investigate the factors influencing bone preservation in the archaeological record, more than 250 bones from 41 archaeological sites in five countries spanning four climatic regions were studied for diagenetic alteration. Sites were selected to cover a range of environmental conditions and archaeological contexts. Microscopic and physical (mercury intrusion porosimetry) analyses of these bones revealed that the majority (68%) had suffered microbial attack. Furthermore, significant differences were found between animal and human bone in both the state of preservation and the type of microbial attack present. These differences in preservation might result from differences in early taphonomy of the bones. © 2003 Elsevier Science Ltd. All rights reserved

Prevalence, associated factors and outcomes of pressure injuries in adult intensive care unit patients: the DecubICUs study

Funder: European Society of Intensive Care Medicine; doi: http://dx.doi.org/10.13039/501100013347Funder: Flemish Society for Critical Care NursesAbstract: Purpose: Intensive care unit (ICU) patients are particularly susceptible to developing pressure injuries. Epidemiologic data is however unavailable. We aimed to provide an international picture of the extent of pressure injuries and factors associated with ICU-acquired pressure injuries in adult ICU patients. Methods: International 1-day point-prevalence study; follow-up for outcome assessment until hospital discharge (maximum 12 weeks). Factors associated with ICU-acquired pressure injury and hospital mortality were assessed by generalised linear mixed-effects regression analysis. Results: Data from 13,254 patients in 1117 ICUs (90 countries) revealed 6747 pressure injuries; 3997 (59.2%) were ICU-acquired. Overall prevalence was 26.6% (95% confidence interval [CI] 25.9–27.3). ICU-acquired prevalence was 16.2% (95% CI 15.6–16.8). Sacrum (37%) and heels (19.5%) were most affected. Factors independently associated with ICU-acquired pressure injuries were older age, male sex, being underweight, emergency surgery, higher Simplified Acute Physiology Score II, Braden score 3 days, comorbidities (chronic obstructive pulmonary disease, immunodeficiency), organ support (renal replacement, mechanical ventilation on ICU admission), and being in a low or lower-middle income-economy. Gradually increasing associations with mortality were identified for increasing severity of pressure injury: stage I (odds ratio [OR] 1.5; 95% CI 1.2–1.8), stage II (OR 1.6; 95% CI 1.4–1.9), and stage III or worse (OR 2.8; 95% CI 2.3–3.3). Conclusion: Pressure injuries are common in adult ICU patients. ICU-acquired pressure injuries are associated with mainly intrinsic factors and mortality. Optimal care standards, increased awareness, appropriate resource allocation, and further research into optimal prevention are pivotal to tackle this important patient safety threat

Correction to: Prevalence, associated factors and outcomes of pressure injuries in adult intensive care unit patients: the DecubICUs study (Intensive Care Medicine, (2021), 47, 2, (160-169), 10.1007/s00134-020-06234-9)

The original version of this article unfortunately contained a mistake. The members of the ESICM Trials Group Collaborators were not shown in the article but only in the ESM. The full list of collaborators is shown below. The original article has been corrected

Prevalence, associated factors and outcomes of pressure injuries in adult intensive care unit patients: the DecubICUs study

Funder: European Society of Intensive Care Medicine; doi: http://dx.doi.org/10.13039/501100013347Funder: Flemish Society for Critical Care NursesAbstract: Purpose: Intensive care unit (ICU) patients are particularly susceptible to developing pressure injuries. Epidemiologic data is however unavailable. We aimed to provide an international picture of the extent of pressure injuries and factors associated with ICU-acquired pressure injuries in adult ICU patients. Methods: International 1-day point-prevalence study; follow-up for outcome assessment until hospital discharge (maximum 12 weeks). Factors associated with ICU-acquired pressure injury and hospital mortality were assessed by generalised linear mixed-effects regression analysis. Results: Data from 13,254 patients in 1117 ICUs (90 countries) revealed 6747 pressure injuries; 3997 (59.2%) were ICU-acquired. Overall prevalence was 26.6% (95% confidence interval [CI] 25.9–27.3). ICU-acquired prevalence was 16.2% (95% CI 15.6–16.8). Sacrum (37%) and heels (19.5%) were most affected. Factors independently associated with ICU-acquired pressure injuries were older age, male sex, being underweight, emergency surgery, higher Simplified Acute Physiology Score II, Braden score 3 days, comorbidities (chronic obstructive pulmonary disease, immunodeficiency), organ support (renal replacement, mechanical ventilation on ICU admission), and being in a low or lower-middle income-economy. Gradually increasing associations with mortality were identified for increasing severity of pressure injury: stage I (odds ratio [OR] 1.5; 95% CI 1.2–1.8), stage II (OR 1.6; 95% CI 1.4–1.9), and stage III or worse (OR 2.8; 95% CI 2.3–3.3). Conclusion: Pressure injuries are common in adult ICU patients. ICU-acquired pressure injuries are associated with mainly intrinsic factors and mortality. Optimal care standards, increased awareness, appropriate resource allocation, and further research into optimal prevention are pivotal to tackle this important patient safety threat