Desenvolvendo o pensamento algébrico no 2.º ciclo do ensino básico: o sentido dos símbolos e da generalização

Dissertação apresentada à Escola Superior de Educação de Lisboa para obtenção do grau de mestre em Educação Matemática na Educação Pré-escolar e nos 1.º e 2.º Ciclos do Ensino Básico

Nonmonotone hybrid tabu search for inequalities and equalities: an experimental study

The main goal of this paper is to analyze the behavior of nonmono- tone hybrid tabu search approaches when solving systems of nonlinear inequalities and equalities through the global optimization of an appro- priate merit function. The algorithm combines global and local searches and uses a nonmonotone reduction of the merit function to choose the local search. Relaxing the condition aims to call the local search more often and reduces the overall computational e ort. Two variants of a perturbed pattern search method are implemented as local search. An experimental study involving a variety of problems available in the lit- erature is presented.

Uncertainty assessment approach for composite structures based on global sensitivity indices

The problem of uncertainty propagation in composite laminate structures is studied. An approach based on the optimal design of composite structures to achieve a target reliability level is proposed. Using the Uniform Design Method (UDM), a set of design points is generated over a design domain centred at mean values of random variables, aimed at studying the space variability. The most critical Tsai number, the structural reliability index and the sensitivities are obtained for each UDM design point, using the maximum load obtained from optimal design search. Using the UDM design points as input/output patterns, an Artificial Neural Network (ANN) is developed based on supervised evolutionary learning. Finally, using the developed ANN a Monte Carlo simulation procedure is implemented and the variability of the structural response based on global sensitivity analysis (GSA) is studied. The GSA is based on the first order Sobol indices and relative sensitivities. An appropriate GSA algorithm aiming to obtain Sobol indices is proposed. The most important sources of uncertainty are identified.

Prevalence of alcohol and tobacco use among Brazilian adolescents: a systematic review

OBJECTIVE: To analyze alcohol and tobacco use among Brazilian adolescents and identify higher-risk subgroups. METHODS: A systematic review of the literature was conducted. Searches were performed using four databases (LILACS, MEDLINE /PubMed, Web of Science, and Google Scholar), specialized websites and the references cited in retrieved articles. The search was done in English and Portuguese and there was no limit on the year of publication (up to June 2011). From the search, 59 studies met all the inclusion criteria: to involve Brazilian adolescents aged 10-19 years; to assess the prevalence of alcohol and/or tobacco use; to use questionnaires or structured interviews to measure the variables of interest; and to be a school or population-based study that used methodological procedures to ensure representativeness of the target population (i.e. random sampling). RESULTS: The prevalence of current alcohol use (at the time of the investigation or in the previous month) ranged from 23.0% to 67.7%. The mean prevalence was 34.9% (reflecting the central trend of the estimates found in the studies). The prevalence of current tobacco use ranged from 2.4% to 22.0%, and the mean prevalence was 9.3%. A large proportion of the studies estimated prevalences of frequent alcohol use (66.7%) and heavy alcohol use (36.8%) of more than 10%. However, most studies found prevalences of frequent and heavy tobacco use of less than 10%. The Brazilian literature has highlighted that environmental factors (religiosity, working conditions, and substance use among family and friends) and psychosocial factors (such as conflicts with parents and feelings of negativeness and loneliness) are associated with the tobacco and alcohol use among adolescents. CONCLUSIONS: The results suggest that consumption of alcohol and tobacco among adolescents has reached alarming prevalences in various localities in Brazil. Since unhealthy behavior tends to continue from adolescence into adulthood, public policies aimed towards reducing alcohol and tobacco use among Brazilians over the medium and long terms may direct young people and the subgroups at higher risk towards such behavior.

Constraint reasoning for differential models

The basic motivation of this work was the integration of biophysical models within the interval constraints framework for decision support. Comparing the major features of biophysical models with the expressive power of the existing interval constraints framework, it was clear that the most important inadequacy was related with the representation of differential equations. System dynamics is often modelled through differential equations but there was no way of expressing a differential equation as a constraint and integrate it within the constraints framework. Consequently, the goal of this work is focussed on the integration of ordinary differential equations within the interval constraints framework, which for this purpose is extended with the new formalism of Constraint Satisfaction Differential Problems. Such framework allows the specification of ordinary differential equations, together with related information, by means of constraints, and provides efficient propagation techniques for pruning the domains of their variables. This enabled the integration of all such information in a single constraint whose variables may subsequently be used in other constraints of the model. The specific method used for pruning its variable domains can then be combined with the pruning methods associated with the other constraints in an overall propagation algorithm for reducing the bounds of all model variables. The application of the constraint propagation algorithm for pruning the variable domains, that is, the enforcement of local-consistency, turned out to be insufficient to support decision in practical problems that include differential equations. The domain pruning achieved is not, in general, sufficient to allow safe decisions and the main reason derives from the non-linearity of the differential equations. Consequently, a complementary goal of this work proposes a new strong consistency criterion, Global Hull-consistency, particularly suited to decision support with differential models, by presenting an adequate trade-of between domain pruning and computational effort. Several alternative algorithms are proposed for enforcing Global Hull-consistency and, due to their complexity, an effort was made to provide implementations able to supply any-time pruning results. Since the consistency criterion is dependent on the existence of canonical solutions, it is proposed a local search approach that can be integrated with constraint propagation in continuous domains and, in particular, with the enforcing algorithms for anticipating the finding of canonical solutions. The last goal of this work is the validation of the approach as an important contribution for the integration of biophysical models within decision support. Consequently, a prototype application that integrated all the proposed extensions to the interval constraints framework is developed and used for solving problems in different biophysical domains.

Engineering a search and rescue application with a wireless sensor network - based localization mechanism

The advent of Wireless Sensor Network (WSN) technologies is paving the way for a panoply of new ubiquitous computing applications, some of them with critical requirements. In the ART-WiSe framework, we are designing a two-tiered communication architecture for supporting real-time and reliable communications in WSNs. Within this context, we have been developing a test-bed application, for testing, validating and demonstrating our theoretical findings - a search&rescue/pursuit-evasion application. Basically, a WSN deployment is used to detect, localize and track a target robot and a station controls a rescuer/pursuer robot until it gets close enough to the target robot. This paper describes how this application was engineered, particularly focusing on the implementation of the localization mechanism.

Screening for depressive symptoms in older adults in the Family Health Strategy, Porto Alegre, Brazil

OBJECTIVE To analyze the prevalence of depression in older adults and associated factors. METHODS Cross-sectional study using a stratified random sample of 621 individuals aged ≥ 60 from 27 family health teams in Porto Alegre, RS, Southern Brazil, between 2010 and 2012. Community health agents measured depression using the 15-item Geriatric Depression Scale. Scores of ≥ 6 were considered as depression and between 11 and 15 as severe depression. Poisson regression was used to search for independent associations of sociodemographic and self-perceived health with both depression and its severity. RESULTS The prevalence of depression was 30.6% and was significantly higher in women (35.9% women versus 20.9% men, p < 0.001). The variables independently associated with depression were: female gender (PR = 1.4, 95%CI 1.1;1.8); low education, especially illiteracy (PR = 1.8, 95%CI 1.2;2 6); regular self-rated health (OR = 2.2, 95%CI 1.6;3.0); and poor/very poor self-rated health (PR = 4.0, 95%CI 2.9;5.5). Except for education, the strength of association of these factors increases significantly in severe depression. CONCLUSIONS A high prevalence of depression was observed in the evaluations conducted by community health agents, professionals who are not highly specialized. The findings identified using the 15-item Geriatric Depression Scale in this way are similar to those in the literature, with depression more associated with low education, female gender and worse self-rated health. From a primary health care strategic point of view, the findings become still more relevant, indicating that community health agents could play an important role in identifying depression in older adults.

Direct search optimization application programming interface with remote access

Search Optimization methods are needed to solve optimization problems where the objective function and/or constraints functions might be non differentiable, non convex or might not be possible to determine its analytical expressions either due to its complexity or its cost (monetary, computational, time,...). Many optimization problems in engineering and other fields have these characteristics, because functions values can result from experimental or simulation processes, can be modelled by functions with complex expressions or by noise functions and it is impossible or very difficult to calculate their derivatives. Direct Search Optimization methods only use function values and do not need any derivatives or approximations of them. In this work we present a Java API that including several methods and algorithms, that do not use derivatives, to solve constrained and unconstrained optimization problems. Traditional API access, by installing it on the developer and/or user computer, and remote API access to it, using Web Services, are also presented. Remote access to the API has the advantage of always allow the access to the latest version of the API. For users that simply want to have a tool to solve Nonlinear Optimization Problems and do not want to integrate these methods in applications, also two applications were developed. One is a standalone Java application and the other a Web-based application, both using the developed API.

Filters method in direct search optimization, new measures to admissibility

Constrained nonlinear optimization problems are usually solved using penalty or barrier methods combined with unconstrained optimization methods. Another alternative used to solve constrained nonlinear optimization problems is the lters method. Filters method, introduced by Fletcher and Ley er in 2002, have been widely used in several areas of constrained nonlinear optimization. These methods treat optimization problem as bi-objective attempts to minimize the objective function and a continuous function that aggregates the constraint violation functions. Audet and Dennis have presented the rst lters method for derivative-free nonlinear programming, based on pattern search methods. Motivated by this work we have de- veloped a new direct search method, based on simplex methods, for general constrained optimization, that combines the features of the simplex method and lters method. This work presents a new variant of these methods which combines the lters method with other direct search methods and are proposed some alternatives to aggregate the constraint violation functions.

A web-based tool to evaluate the iterative processes of direct search methods

Constrained and unconstrained Nonlinear Optimization Problems often appear in many engineering areas. In some of these cases it is not possible to use derivative based optimization methods because the objective function is not known or it is too complex or the objective function is non-smooth. In these cases derivative based methods cannot be used and Direct Search Methods might be the most suitable optimization methods. An Application Programming Interface (API) including some of these methods was implemented using Java Technology. This API can be accessed either by applications running in the same computer where it is installed or, it can be remotely accessed through a LAN or the Internet, using webservices. From the engineering point of view, the information needed from the API is the solution for the provided problem. On the other hand, from the optimization methods researchers’ point of view, not only the solution for the problem is needed. Also additional information about the iterative process is useful, such as: the number of iterations; the value of the solution at each iteration; the stopping criteria, etc. In this paper are presented the features added to the API to allow users to access to the iterative process data.

Self-adaptive combination of global tabu search and local search for nonlinear equations

Solving systems of nonlinear equations is a very important task since the problems emerge mostly through the mathematical modelling of real problems that arise naturally in many branches of engineering and in the physical sciences. The problem can be naturally reformulated as a global optimization problem. In this paper, we show that a self-adaptive combination of a metaheuristic with a classical local search method is able to converge to some difficult problems that are not solved by Newton-type methods.

Direct-search penalty/barrier methods

In Nonlinear Optimization Penalty and Barrier Methods are normally used to solve Constrained Problems. There are several Penalty/Barrier Methods and they are used in several areas from Engineering to Economy, through Biology, Chemistry, Physics among others. In these areas it often appears Optimization Problems in which the involved functions (objective and constraints) are non-smooth and/or their derivatives are not know. In this work some Penalty/Barrier functions are tested and compared, using in the internal process, Derivative-free, namely Direct Search, methods. This work is a part of a bigger project involving the development of an Application Programming Interface, that implements several Optimization Methods, to be used in applications that need to solve constrained and/or unconstrained Nonlinear Optimization Problems. Besides the use of it in applied mathematics research it is also to be used in engineering software packages.

Multi-criteria optimization manipulator trajectory planning

In the last twenty years genetic algorithms (GAs) were applied in a plethora of fields such as: control, system identification, robotics, planning and scheduling, image processing, and pattern and speech recognition (Bäck et al., 1997). In robotics the problems of trajectory planning, collision avoidance and manipulator structure design considering a single criteria has been solved using several techniques (Alander, 2003). Most engineering applications require the optimization of several criteria simultaneously. Often the problems are complex, include discrete and continuous variables and there is no prior knowledge about the search space. These kind of problems are very more complex, since they consider multiple design criteria simultaneously within the optimization procedure. This is known as a multi-criteria (or multiobjective) optimization, that has been addressed successfully through GAs (Deb, 2001). The overall aim of multi-criteria evolutionary algorithms is to achieve a set of non-dominated optimal solutions known as Pareto front. At the end of the optimization procedure, instead of a single optimal (or near optimal) solution, the decision maker can select a solution from the Pareto front. Some of the key issues in multi-criteria GAs are: i) the number of objectives, ii) to obtain a Pareto front as wide as possible and iii) to achieve a Pareto front uniformly spread. Indeed, multi-objective techniques using GAs have been increasing in relevance as a research area. In 1989, Goldberg suggested the use of a GA to solve multi-objective problems and since then other researchers have been developing new methods, such as the multi-objective genetic algorithm (MOGA) (Fonseca & Fleming, 1995), the non-dominated sorted genetic algorithm (NSGA) (Deb, 2001), and the niched Pareto genetic algorithm (NPGA) (Horn et al., 1994), among several other variants (Coello, 1998). In this work the trajectory planning problem considers: i) robots with 2 and 3 degrees of freedom (dof ), ii) the inclusion of obstacles in the workspace and iii) up to five criteria that are used to qualify the evolving trajectory, namely the: joint traveling distance, joint velocity, end effector / Cartesian distance, end effector / Cartesian velocity and energy involved. These criteria are used to minimize the joint and end effector traveled distance, trajectory ripple and energy required by the manipulator to reach at destination point. Bearing this ideas in mind, the paper addresses the planning of robot trajectories, meaning the development of an algorithm to find a continuous motion that takes the manipulator from a given starting configuration up to a desired end position without colliding with any obstacle in the workspace. The chapter is organized as follows. Section 2 describes the trajectory planning and several approaches proposed in the literature. Section 3 formulates the problem, namely the representation adopted to solve the trajectory planning and the objectives considered in the optimization. Section 4 studies the algorithm convergence. Section 5 studies a 2R manipulator (i.e., a robot with two rotational joints/links) when the optimization trajectory considers two and five objectives. Sections 6 and 7 show the results for the 3R redundant manipulator with five goals and for other complementary experiments are described, respectively. Finally, section 8 draws the main conclusions.

Dentistry and HIV/AIDS related stigma

OBJECTIVE To analyze HIV/AIDS positive individual’s perception and attitudes regarding dental services.METHODS One hundred and thirty-four subjects (30.0% of women and 70.0% of men) from Nuevo León, Mexico, took part in the study (2014). They filled out structured, analytical, self-administered, anonymous questionnaires. Besides the sociodemographic variables, the perception regarding public and private dental services and related professionals was evaluated, as well as the perceived stigma associated with HIV/AIDS, through a Likert-type scale. The statistical evaluation included a factorial and a non-hierarchical cluster analysis.RESULTS Social inequalities were found regarding the search for public and private dental professionals and services. Most subjects reported omitting their HIV serodiagnosis and agreed that dentists must be trained and qualified to treat patients with HIV/AIDS. The factorial analysis revealed two elements: experiences of stigma and discrimination in dental appointments and feelings of concern regarding the attitudes of professionals or their teams concerning patients’ HIV serodiagnosis. The cluster analysis identified three groups: users who have not experienced stigma or discrimination (85.0%); the ones who have not had those experiences, but feel somewhat concerned (12.7%); and the ones who underwent stigma and discrimination and feel concerned (2.3%).CONCLUSIONS We observed a low percentage of stigma and discrimination in dental appointments; however, most HIV/AIDS patients do not reveal their serodiagnosis to dentists out of fear of being rejected. Such fact implies a workplace hazard to dental professionals, but especially to the very own health of HIV/AIDS patients, as dentists will not be able to provide them a proper clinical and pharmaceutical treatment.

A genetic algorithm for the job shop scheduling with a new local search using Monte Carlo method

This paper presents a methodology for applying scheduling algorithms using Monte Carlo simulation. The methodology is based on a decision support system (DSS). The proposed methodology combines a genetic algorithm with a new local search using Monte Carlo Method. The methodology is applied to the job shop scheduling problem (JSSP). The JSSP is a difficult problem in combinatorial optimization for which extensive investigation has been devoted to the development of efficient algorithms. The methodology is tested on a set of standard instances taken from the literature and compared with others. The computation results validate the effectiveness of the proposed methodology. The DSS developed can be utilized in a common industrial or construction environment.