Ciências e Tecnologia | Artigos em revistas internacionais / Papers in international journals
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- Acquisition of competencies in mathematics through gamesPublication . Ferreira, Maria Cristina; Pereira, José António; Oliveira, AmilcarThe objective of this paper is to present the fundamentals of game theory and illustrate how the theory can be applied in education of Mathematics.Literature specific applications of game theory across all levels of instructor-led education. With a game theory model, we provide a mathematical description of a social situation in which two or more individuals or players interact. We strongly suggestthat traditional teaching techniques of mathematics should be complemented with games.
- Alterações climáticas, perceções e racionalidadesPublication . Viegas, Vanda; Azeiteiro, Ulisses; Dias, João Alveirinho; Alves, FátimaConsiderando que as Alterações Climáticas (AC) – uma das cinco áreas-guia da Estratégia 2020 da Comissão Europeia – são um problema global que requer respostas locais articuladas aos níveis macro, meso e micro; e que a sua compreensão implica a identificação das relações reciprocamente influentes entre a Natureza, a Sociedade e a Cultura; qualquer intervenção – seja no sentido da mitigação das AC, seja no sentido da adaptação às AC – envolve necessariamente essa mesma sociedade, em toda a complexidade das suas dimensões socioculturais e ambientais. Neste artigo, enquadrado pelas teorias compreensivas, refletimos brevemente sobre algumas das inter-relações entre os sistemas climáticos, ambientais e socioculturais e defendemos que as racionalidades leigas, por se enraizarem em tipos e fontes de saber plurais, são um dos pilares para melhor se compreender e lidar com o fenómeno das AC. Whereas Climate Change (CC) – one of the five prioritary areas of the Strategy 2020 of the European Commission – is a global challenge needing local responses, articulated at the macro, meso and micro levels; and while its understanding entails identifying mutually influential relationships between Nature, Society and Culture, any intervention – either to mitigate or adapt to CC – necessarily involves society itself, in the full complexity of its sociocultural and environmental dimensions. In a world in the midst of a major demographic transition, with a population expected to reach 9 billion by 2050, issues like sustainability, resource use, scarcity and sharing, have been interwoven in the international, regional and local arenas. This paper develops in the light of comprehensive theories. The methodological procedures are based upon desk research and all the work relies on the reflexive notion and today´s ubiquitous complexity. The spirit of this pivotal approach is the interest in knowledge, curiosity for different dimensions of knowledge and how it is (re)produced, articulated and reflected in the relationships of the individual human being, with itself, with other human beings, with other living creatures and with the environment. This papers argues that the lay rationalities, because they take root in various types and sources of knowledge, are one of the pillars to better understand and deal with the phenomenon of CC. Part one of this paper makes a brief reference to ethical implications, preceded by a succinct analysis of the key dynamics and processes, which are considered responsible for the variability and climate change in a diachronic perspective. Part two discusses some of the sustainability issues, with a brief introduction to the pathways and strategies for mitigating and adapting to CC, which have been outlined and lie ahead, linking the global dimension to the local dimension, governments to markets and to civil society. Finally, focusing on lay rationalities, a brief approach is sought regarding the issues of reflexivity, social capital and the ‘knowledge-power’ concept, keeping in mind that the study of the social reality, which is complex in nature, is always a (de)constructed exercise of dialectics between generalization and specialization.
- An algorithm to discover the k-clique cover in networksPublication . Cavique, Luís; Mendes, Armando B.; Santos, Jorge M. A.In social network analysis, a k-clique is a relaxed clique, i.e., a k-clique is a quasi-complete sub-graph. A k-clique in a graph is a sub-graph where the distance between any two vertices is no greater than k. The visualization of a small number of vertices can be easily performed in a graph. However, when the number of vertices and edges increases the visualization becomes incomprehensible. In this paper, we propose a new graph mining approach based on k-cliques. The concept of relaxed clique is extended to the whole graph, to achieve a general view, by covering the network with k-cliques. The sequence of k-clique covers is presented, combining small world concepts with community structure components. Computational results and examples are presented.
- An analysis of network and resource indicators for resource-constrained project scheduling problem instancesPublication . Vanhoucke, Mario; Coelho, JoséIn the past decades, the resource on the resource-constrained project scheduling problem (RCPSP) has grown rapidly, resulting in an overwhelming amount of solution procedures that provide (near)-optimal solutions in a reasonable time. Despite the rapid progress, little is still known what makes a project instance hard to solve. Inspired by a previous research study that has shown that even small instances with only up to 30 activities is sometimes hard to solve, the current study provides an analysis of the project data used in the academic literature. More precisely, it investigates the ability of four well-known resource indicators to predict the hardness of an RCPSP instance. The study introduces a new instance equivalence concept to show that instances might have very different values for their resource indicators without changing any possible solution for this instance. The concept is based on four theorems and a search algorithm that transforms existing instances into new equivalent instances with more compact resources. This algorithm illustrates that the use of resource indicators to predict the hardness of an instance is sometimes misleading. In a set of computational experiment on more than 10,000 instances, it is shown that the newly constructed equivalent instances have values for the resource indicators that are not only different than the values of the original instances, but also often are better in predicting the hardness the project instances. It is suggested that the new equivalent instances are used for further research to compare results on the new instances with results obtained from the original dataset.
- An approach to distribution of the product of two normal variablesPublication . Oliveira, Amilcar; Seijas-Macias, J. AntonioThe distribution of product of two normally distributed variables come from the first part of the XX Century. First works about this issue were [1] and [2] showed that under certain conditions the product could be considered as a normally distributed. A more recent approach is [3] that studied approximation to density function of the product using three methods: numerical integration, Monte Carlo simulation and analytical approximation to the result using the normal distribution. They showed as the inverse variation coefficient µ/σ increases, the distribution of the product of two independent normal variables tends towards a normal distribution. Our study is focused in Ware and Lad approaches. The objective was studying which factors have more influence in the presence of normality for the product of two independent normal variables. We have considered two factors: the inverse of the variation coefficient value µ/σ and the combined ratio (product of the two means divided by standard deviation): (µ1µ2(/σ for two normal variables with the same variance. Our results showed that for low values of the inverse of the variation coefficient (less than 1) normal distribution is not a good approximation for the product. Another one, influence of the combined ratio value is less than influence of the inverse of coefficients of variation value.
- An approach using SAT solvers for the RCPSP with logical constraintsPublication . Vanhoucke, Mario; Coelho, JoséThis paper presents a new solution approach to solve the resource-constrained project scheduling problem in the presence of three types of logical constraints. Apart from the traditional AND constraints with minimal time-lags, these precedences are extended to OR constraints and bidirectional (BI) relations. These logical constraints extend the set of relations between pairs of activities and make the RCPSP definition somewhat different from the traditional RCPSP research topics in literature. It is known that the RCPSP with AND constraints, and hence its extension to OR and BI constraints, is NP-hard. The new algorithm consists of a set of network transformation rules that removes the OR and BI logical constraints to transform them into AND constraints and hereby extends the set of activities to maintain the original logic. A satisfiability (SAT) solver is used to guarantee the original precedence logic and is embedded in a metaheuristic search to resource feasible schedules that respect both the limited renewable resource availability as well as the precedence logic. Computational results on two well-known datasets from literature show that the algorithm can compete with the multi-mode algorithms from literature when no logical constraints are taken into account. When the logical constraints are taken into account, the algorithm can report major reductions in the project makespan for most of the instances within a reasonable time.
- An efficient genetic programming approach to design priority rules for resource-constrained project scheduling problemPublication . Luo, Jingyu; Vanhoucke, Mario; Coelho, José; Guo, WeikangIn recent years, machine learning techniques, especially genetic programming (GP), have been a powerful approach for automated design of the priority rule-heuristics for the resource-constrained project scheduling problem (RCPSP). However, it requires intensive computing effort, carefully selected training data and appropriate assessment criteria. This research proposes a GP hyper-heuristic method with a duplicate removal technique to create new priority rules that outperform the traditional rules. The experiments have verified the efficiency of the proposed algorithm as compared to the standard GP approach. Furthermore, the impact of the training data selection and fitness evaluation have also been investigated. The results show that a compact training set can provide good output and existing evaluation methods are all usable for evolving efficient priority rules. The priority rules designed by the proposed approach are tested on extensive existing datasets and newly generated large projects with more than 1,000 activities. In order to achieve better performance on small-sized projects, we also develop a method to combine rules as efficient ensembles. Computational comparisons between GP-designed rules and traditional priority rules indicate the superiority and generalization capability of the proposed GP algorithm in solving the RCPSP.
- An evaluation of the adequacy of project network generators with systematically sampled networksPublication . Vanhoucke, Mario; Coelho, José; Debels, Dieter; Maenhout, Broos; Tavares, Luís ValadaresThis paper evaluates and compares different network generators to generate project scheduling problem instances based on indicators measuring the topological network structure. We review six topological network indicators in order to describe the detailed structure of a project network. These indicators were originally developed by [L.V. Tavares, J.A. Ferreira and J.S. Coelho, The risk of delay of a project in terms of the morphology of its network, European Journal of Operational Research 119 (1999), 510–537] and have been modified, or sometimes completely replaced, by alternative indicators to describe the network topology. The contribution of this paper is twofold. Firstly, we generate a large amount of different networks with four project network generators. Our general conclusions are that none of the network generators are able to capture the complete feasible domain of all networks. Additionally, each network generator covers its own network-specific domain and, consequently, contributes to the generation of data sets. Secondly, we perform computational results on the well-known resource-constrained project scheduling problem to prove that our indicators are reliable and have significant, predictive power to serve as complexity indicators.
- An exact composite lower bound strategy for the resource-constrained project scheduling problemPublication . Coelho, José; Vanhoucke, MarioThis paper reports on results for the well-known resource-constrained project scheduling problem. A branch-and-bound procedure is developed that takes into account all best performing components from literature, varying branching schemes and search strategies, using the best performing dominance rules and assembling these components into a unified search algorithm. A composite lower bound strategy that statically and dynamically selects the best performing bounds from literature is used to find optimal solutions within reasonable times. An extensive computational experiment is set up to determine the best combination of the various components used in the procedure, in order to benchmark the current existing knowledge on four different datasets from the literature. By varying the network topology, resource scarceness and the size of the projects, the computational experiments are carried out on a diverse set of projects. The procedure was able to find some new lower bounds and optimal solutions for the PSPLIB instances. Moreover, new best known results are reported for other, more diverse datasets that can be used in future research studies. The experiments revealed that even project instances with 30 activities cannot be solved to optimality when the topological structure is varied.
- An immersive musical instrument prototypePublication . Valbom, Leonel; Marcos, AdéritoThis article describes a prototype immersive musical instrument that expands the concepts of traditional musical elements and allows the integration of a spatial dimension using 3D music and sound objects into the musical environment by employing physical, visual, and sound immersion. From the prototype's evaluation results, the authors conclude that immersive musical instruments naturally give users a way to perform, compose, or improvise music (in real time) with a high degree of control.