Expressividade e Envolvimento em contexto de Jardim de Infância

Relatório apresentado para cumprimento dos requisitos necessários à obtenção do grau de Mestre em Educação Pré Escolar

An Efficient Mixed Integer Programming Algorithm for Minimizing the Training Sample Misclassification Cost in Two-group Classification

In this paper, we introduce the Divide and Conquer (D&C) algorithm, a computationally efficient algorithm for determining classification rules which minimize the training sample misclassification cost in two-group classification. This classification rule can be derived using mixed integer programming (MIP) techniques. However, it is well-documented that the complexity of MIP-based classification problems grows exponentially as a function of the size of the training sample and the number of attributes describing the observations, requiring special-purpose algorithms to solve even small size problems within a reasonable computational time. The D&C algorithm derives its name from the fact that it relies, a.o., on partitioning the problem in smaller, more easily handled subproblems, rendering it substantially faster than previously proposed algorithms. The D&C algorithm solves the problem to the exact optimal solution (i.e., it is not a heuristic that approximates the solution), and allows for the analysis of much larger training samples than previous methods. For instance, our computational experiments indicate that, on average, the D&C algorithm solves problems with 2 attributes and 500 observations more than 3 times faster, and problems with 5 attributes and 100 observations over 50 times faster than Soltysik and Yarnold's software, which may be the fastest existing algorithm. We believe that the D&C algorithm contributes significantly to the field of classification analysis, because it substantially widens the array of data sets that can be analyzed meaningfully using methods which require MIP techniques, in particular methods which seek to minimize the misclassification cost in the training sample. The programs implementing the D&C algorithm are available from the authors upon request

Second Order Mathematical Formulations Programming for Discriminant Analysis

This paper introduces a nonparametric formulation-based mathematical programming (MP) for solving the classification problem in discriminant analysis. This method differs from previously proposed MP-based models in that, even though the final discriminant function is linear in terms of the parameters to be estimated, the formulation is quadratic in terms of the predictor (attribute) variables. By including second order (i.e., quadratic and cross-product) terms of the attribute variables, the model is similar in concept to the usual treatment of multiple predictor variables in statistical methods such as Fisher's linear discriminant analysis, and allows an analysis of how including nonlinear terms and interaction affect the predictive ability of the estimated classification function. Using simulation experiments involving data conditions for which nonlinear classifiers are appropriate, the classificatory performance of this class of second order MP models is compared with that of existing statistical (linear and quadratic) and first order MP-based formulations. The results of these experiments show that the proposed formulation appears to be a very attractive alternative to previously introduced linear and quadratic statistical and linear MP-based classification methods

Nonparametric Two-Group Classification: Concepts and a SAS-Based Software Package

In this paper, we introduce BestClass, a set of SAS macros, available in the mainframe and workstation environment, designed for solving two-group classification problems using a class of recently developed nonparametric classification methods. The criteria used to estimate the classification function are based on either minimizing a function of the absolute deviations from the surface which separates the groups, or directly minimizing a function of the number of misclassified entities in the training sample. The solution techniques used by BestClass to estimate the classification rule utilize the mathematical programming routines of the SAS/OR@ software. Recently, a number of research studies have reported that under certain data conditions this class of classification methods can provide more accurate classification results than existing methods, such as Fisher's linear discriminant function and logistic regression. However, these robust classification methods have not yet been implemented in the major statistical packages, and hence are beyond the reach of those statistical analysts who are unfamiliar with mathematical programming techniques. We use a limited simulation experiment and an example to compare and contrast properties of the methods included in BestClass with existing parametric and nonparametric methods. We believe that BestClass contributes significantly to the field of nonparametric classification analysis, in that it provides the statistical community with convenient access to this recently developed class of methods. BestClass is available from the authors

Stochastic Judgments in the AHP: The Measurement of Rank Reversal Probabilities

Recently, the issue of rank reversal of alternatives in the Analytic Hierarchy Process (AHP) has captured the attention of a number of researchers. Most of the research on rank reversal has addressed the case where the pairwise comparisons of the alternatives are represented by single values, focusing on mathematical properties inherent to the AHP methodology that can lead to rank reversal if a new alternative is added or an existing one is deleted. A second situation, completely unrelated to the mathematical foundations of the AHP, in which rank reversal can occur is the case where the pairwise judgments are stochastic, rather than single values. If the relative preference ratings are uncertain, one has judgment intervals, and as a consequence there is a possibility that the rankings resulting from an AHP analysis are reversed, i.e., incorrect. It is important for modeler and decision maker alike to be aware of the likelihood that this situation of rank reversal will occur. In this paper, we introduce methods for assessing the relative preference of the alternatives in terms of their rankings, if the pairwise comparisons of the alternatives are stochastic. We develop multivariate statistical techniques to obtain point estimates and confidence intervals of the rank reversal probabilities, and show how simulation experiments can be used as an effective and accurate tool for analyzing the stability of the preference rankings under uncertainty. This information about the extent to which the ranking of the alternatives is sensitive to the stochastic nature of the pairwise judgments should be valuable information into the decision making process, much like variability and confidence intervals are crucial tools for statistical inference. Although the focus of our analysis is on stochastic preference judgments, our sampling method for estimating rank reversal probabilities can be extended to the case of non-stochastic imprecise fuzzy judgments. We provide simulation experiments and numerical examples comparing our method with that proposed previously by Saaty and Vargas (1987) for imprecise interval judgments

Scaling of turbulent separating flows

AbstractThe present work investigates the scaling of the turbulent boundary layer in regions of adverse pressure gradient flow. For the first time, direct numerical simulation and experimental data are applied to the theory presented in Cruz and Silva Freire [Cruz, D. O. A., & Silva Freire, A. P. (1998). On single limits and the asymptotic behaviour of separating turbulent boundary layers. International Journal of Heat and Mass Transfer, 41, 2097–2111] to explain how the classical two-layered asymptotic structure reduces to a new structure consistent with the local solutions of Goldstein and of Stratford at a point of zero wall shear stress. The work discusses in detail the behaviour of an adaptable characteristic velocity (uR) that can be used in regions of attached as well as separated flows. In particular, uR is compared to velocity scales based on the local wall shear stress and on the pressure gradient at the wall. This is also made here for the first time. A generalized law of the wall is compared with the numerical and experimental data, showing good agreement. This law is shown to reduce to the classical logarithmic solution and to the solution of Stratford under the relevant limiting conditions

Water Hyacinth (Eichhornia crassipes) As a Possible Alternative Energy Source: A Case Study for INSEE Cement Manufacturing Plant in Puttalam, Sri Lanka

Cement manufacturing is typically energy-intensive process and currently using alternative fuels partially or totally to replace fossil fuels to reduce the energy and environmental costs. Biomass is one of the main alternative fuel utilized by the cement industry with the potential to replace up to 20% of total energy demand. Water hyacinth (WH) is a problematic invasive alien species in aquatic ecosystems of all climatic zones in Sri Lanka. Because of it is non-edible, rapid growth, and freely available in larger quantities, WH has the potential to be used as biomass energy. Several countries have been studied for WH as feedstock for bioenergy production while physical and chemical composition of WH biomass has been tested by many researchers. However, biomass physiochemical properties may be varied by different place and conditions and there is no significant study for industrial application of WH biomass to burn in cement plant kiln as alternative energy source. Thus, this study aimed to elucidate the potential of WH biomass as an alternative energy source for the INSEE cement plant in Puttalam. The study was conducted in three selected reservoirs namely, Tabbowa reservoir (TR), Murukkuwatawana reservoir (MR), and Nawadankulama reservoir (NR) located in Puttalam district Northwestern province of Sri Lanka. The quantity of fresh and dry WH biomass was estimated with the WH covered area and fresh and dry weights of WH in unit area.WH covered area of in each reservoir during 2020 and 2021 was digitized directly in Google earth satellite images using Google Earth Pro software with help of visual interpretation techniques. WH biomass per unit area were measured by the subjective sampling method. WH samples from each reservoir were collected for analyzing biomass, and to determine the fuel characteristics such as net calorific value (NCV), Chlorine and Sulfur content, moisture, volatile matter, fixed carbon, and ash content. According to the results, the fresh WH biomass was recorded as 692.62, 389.85, 23.58 tons in 2020 and 3570.82, 584.53, 33.31 tons in 2021 in the TR, MR, and NR respectively, while the dry WH biomass was recorded as 41.65, 24.65, 1.31 tons in 2020 and 214.74, 36.96, 1.85 tons in 2021 in the TR, MR, and NR respectively. NCV of the WH composite sample was 12.02 MJ/kg. Moisture content, ash content, chlorine and sulfur content were recorded as 13.56%, 10.95%, 1.06%, and 0.14% respectively. Except for chlorine content, other parameters agreed with the acceptable limits for using WH as an alternative energy source for cement industry. To replace 1 ton of coal, 2.2 tons of dry WH were required from 35 tons of fresh WH biomass while to produce 1 ton of clinker, 0.32 tons of dry WH were required from 5.2 tons of fresh WH biomass. Since relatively large quantities are freely available and with high volatile content and calorific value, WH is suitable as an alternative energy source for cement industry. However, economic feasibility should be studied prior to the commercial application. Keywords: Alternative fuel, Biomass, Water hyacinth, Calorific valu

Wind pumping based water supply schemes for remote villages in Sri Lanka

In the remote rural villages in Hambantota district (located in South-East of Sri Lanka) there is no easy access to potable water, and conventional community water supply schemes by pumping water from deep wells is far from the reality. Present study investigates the feasibility of community water supply schemes for sparsely distributed houses in these villages by the installation of a wind rotor coupled to a hand operated deep well pump at a favourable location in the village and storing of water in a tank at a higher elevation. Based on field measurements of wind data, power requirement for hand pump installed in a deep well, the scale model testing of two horizontal axis wind rotors and the performance of a pilot wind pump, potential for introducing wind pumping based community water supply schemes in the district is emphasized