Materiais estruturados: qual o seu papel na aprendizágem dos primeiros números?

Dissertação apresentada para obtenção do grau de Mestre em Educação Matemática na Educação Pré-Escolar e no 1.º e 2.º Ciclos do Ensino Básico

Additive adaptive thinking in 1st and 2nd grades pupils

This paper is part of the Project “Adaptive thinking and flexible computation: Critical issues”. It discusses what is meant by adaptive thinking and presents the results of individual interviews with four pupils. The main goal of the study is to understand pupils’ reasoning when solving numerical tasks involving additive situations, and identify features associated with adaptive thinking. The results show that, in the case of first grade pupils, the semantic aspects of the problem are involved in its resolution and the pupils’ performance appears to be related to the development of number sense. The 2nd grade pupils seem to see the quantitative difference as an invariant numerical relationship.

The differentiation of character state relationships by binary coding and the monothetic subset method / Hymen Marx, George B. Rabb and Harold K. Voris.

v.72:no.1(1977)

Using numerical classification of profiles based on Vis-NIR spectra to distinguish soils from the Piracicaba Region, Brazil

Considering that information from soil reflectance spectra is underutilized in soil classification, this paper aimed to evaluate the relationship of soil physical, chemical properties and their spectra, to identify spectral patterns for soil classes, evaluate the use of numerical classification of profiles combined with spectral data for soil classification. We studied 20 soil profiles from the municipality of Piracicaba, State of São Paulo, Brazil, which were morphologically described and classified up to the 3rd category level of the Brazilian Soil Classification System (SiBCS). Subsequently, soil samples were collected from pedogenetic horizons and subjected to soil particle size and chemical analyses. Their Vis-NIR spectra were measured, followed by principal component analysis. Pearson's linear correlation coefficients were determined among the four principal components and the following soil properties: pH, organic matter, P, K, Ca, Mg, Al, CEC, base saturation, and Al saturation. We also carried out interpretation of the first three principal components and their relationships with soil classes defined by SiBCS. In addition, numerical classification of the profiles based on the OSACA algorithm was performed using spectral data as a basis. We determined the Normalized Mutual Information (NMI) and Uncertainty Coefficient (U). These coefficients represent the similarity between the numerical classification and the soil classes from SiBCS. Pearson's correlation coefficients were significant for the principal components when compared to sand, clay, Al content and soil color. Visual analysis of the principal component scores showed differences in the spectral behavior of the soil classes, mainly among Argissolos and the others soils. The NMI and U similarity coefficients showed values of 0.74 and 0.64, respectively, suggesting good similarity between the numerical and SiBCS classes. For example, numerical classification correctly distinguished Argissolos from Latossolos and Nitossolos. However, this mathematical technique was not able to distinguish Latossolos from Nitossolos Vermelho férricos, but the Cambissolos were well differentiated from other soil classes. The numerical technique proved to be effective and applicable to the soil classification process.

Syntrophic relationships between algae and bacteria in a fresh-water stream and in culture /

Interactions between freshwater algae and bacteria were examined in a natural stream habitat and a laboratory model. Field observations provided circumstantial evidence, in statistical correlation for syntrophy between the microbial populations. This relation is probably subject to control by the temperature and pH of the aquatic environment. Several species of a pond community were isolated in axenic culture and tests were performed to determine the nature of mixed species interactions. Isolation procedures and field studies indicated that selected strains of Chlorella and Azotobacter were closely associated in their natural habitat. With the suspected controlling parameters, pH and temperature, held constant, mixed cultures of algae and bacteria were compared to axenic cultures of the same organisms, and a mutual stimulation of growth was observed. A mixed pure culture apparatus was designed in this laboratory to study the algal-bacterial interaction and to test the hypothesis that such an interaction may take place through a diffusable substance or through certain medium-borne conditions, Azotobacter was found to take up a Chlorella-produced exudate, to stimulate protein synthesis, to enhance chlorophyll production and to cause a numerical increase in the interacting Chlorella population. It is not clear whether control is at the environmental, cellular or genetic level in these mixed population interactions. Experimental observations in the model system, taken with field correlations allow one to state that there may be a direct relationship governing the population fluctuations of these two organisms in their natural stream surroundings.

KAM: Automatic Planning and Interpretation of Numerical Experiments Using Geometrical Methods

KAM is a computer program that can automatically plan, monitor, and interpret numerical experiments with Hamiltonian systems with two degrees of freedom. The program has recently helped solve an open problem in hydrodynamics. Unlike other approaches to qualitative reasoning about physical system dynamics, KAM embodies a significant amount of knowledge about nonlinear dynamics. KAM's ability to control numerical experiments arises from the fact that it not only produces pictures for us to see, but also looks at (sic---in its mind's eye) the pictures it draws to guide its own actions. KAM is organized in three semantic levels: orbit recognition, phase space searching, and parameter space searching. Within each level spatial properties and relationships that are not explicitly represented in the initial representation are extracted by applying three operations ---(1) aggregation, (2) partition, and (3) classification--- iteratively.

PHYLOGENETIC STUDIES OF SOME SPECIES OF THE GENUS COFFEA .2. NUMERICAL-ANALYSIS OF ISOENZYMATIC DATA

Thirteen species of Coffea were studied for five enzymes systems, including alpha and beta esterase, alkaline phosphatase, acid phosphatase, malate dehydrogenase and acid dehydrogenase. Three coefficients of similarity: Simple Matching, Jaccard and Ochiai and three different clustering methods: Single Linkage, Complete Linkage and Unweighted Pair Group, using Arithmetic Averages (UPGMA) were used to analyse the data.The phylogenetic relationships among the twelve diploid species and between them and the tetraploid species C. arabica showed that similarity among species of the same subsection is not always greater than among species of different subsections. In addition, although there are several similarity groups in common, established by isoenzymatic polymorphism, morphological characteristics, chemical data, crossability and geographic distribution, there is no common trend among the phylogenetic relationships as indicated by all these different evaluating procedures.

Delineation of specific management areas for coffee cultivation based on the soil-relief relationship and numerical classification

Predicting and mapping productivity areas allows crop producers to improve their planning of agricultural activities. The primary aims of this work were the identification and mapping of specific management areas allowing coffee bean quality to be predicted from soil attributes and their relationships to relief. The study area was located in the Southeast of the Minas Gerais state, Brazil. A grid containing a total of 145 uniformly spaced nodes 50 m apart was established over an area of 31. 7 ha from which samples were collected at depths of 0. 00-0. 20 m in order to determine physical and chemical attributes of the soil. These data were analysed in conjunction with plant attributes including production, proportion of beans retained by different sieves and drink quality. The results of principal component analysis (PCA) in combination with geostatistical data showed the attributes clay content and available iron to be the best choices for identifying four crop production environments. Environment A, which exhibited high clay and available iron contents, and low pH and base saturation, was that providing the highest yield (30. 4l ha-1) and best coffee beverage quality (61 sacks ha-1). Based on the results, we believe that multivariate analysis, geostatistics and the soil-relief relationships contained in the digital elevation model (DEM) can be effectively used in combination for the hybrid mapping of areas of varying suitability for coffee production. © 2012 Springer Science+Business Media New York.

Variance Reduction in Analytical Chemistry : New Numerical Methods in Chemometrics and Molecular Simulation

This thesis is based on five papers addressing variance reduction in different ways. The papers have in common that they all present new numerical methods. Paper I investigates quantitative structure-retention relationships from an image processing perspective, using an artificial neural network to preprocess three-dimensional structural descriptions of the studied steroid molecules. Paper II presents a new method for computing free energies. Free energy is the quantity that determines chemical equilibria and partition coefficients. The proposed method may be used for estimating, e.g., chromatographic retention without performing experiments. Two papers (III and IV) deal with correcting deviations from bilinearity by so-called peak alignment. Bilinearity is a theoretical assumption about the distribution of instrumental data that is often violated by measured data. Deviations from bilinearity lead to increased variance, both in the data and in inferences from the data, unless invariance to the deviations is built into the model, e.g., by the use of the method proposed in paper III and extended in paper IV. Paper V addresses a generic problem in classification; namely, how to measure the goodness of different data representations, so that the best classifier may be constructed. Variance reduction is one of the pillars on which analytical chemistry rests. This thesis considers two aspects on variance reduction: before and after experiments are performed. Before experimenting, theoretical predictions of experimental outcomes may be used to direct which experiments to perform, and how to perform them (papers I and II). After experiments are performed, the variance of inferences from the measured data are affected by the method of data analysis (papers III-V).

Numerical simulations of magma chamber dynamics at Campi Flegrei, and associated seismicity, deformation and gravity changes

Understanding the complex relationships between quantities measured by volcanic monitoring network and shallow magma processes is a crucial headway for the comprehension of volcanic processes and a more realistic evaluation of the associated hazard. This question is very relevant at Campi Flegrei, a volcanic quiescent caldera immediately north-west of Napoli (Italy). The system activity shows a high fumarole release and periodic ground slow movement (bradyseism) with high seismicity. This activity, with the high people density and the presence of military and industrial buildings, makes Campi Flegrei one of the areas with higher volcanic hazard in the world. In such a context my thesis has been focused on magma dynamics due to the refilling of shallow magma chambers, and on the geophysical signals detectable by seismic, deformative and gravimetric monitoring networks that are associated with this phenomenologies. Indeed, the refilling of magma chambers is a process frequently occurring just before a volcanic eruption; therefore, the faculty of identifying this dynamics by means of recorded signal analysis is important to evaluate the short term volcanic hazard. The space-time evolution of dynamics due to injection of new magma in the magma chamber has been studied performing numerical simulations with, and implementing additional features in, the code GALES (Longo et al., 2006), recently developed and still on the upgrade at the Istituto Nazionale di Geofisica e Vulcanologia in Pisa (Italy). GALES is a finite element code based on a physico-mathematical two dimensional, transient model able to treat fluids as multiphase homogeneous mixtures, compressible to incompressible. The fundamental equations of mass, momentum and energy balance are discretised both in time and space using the Galerkin Least-Squares and discontinuity-capturing stabilisation technique. The physical properties of the mixture are computed as a function of local conditions of magma composition, pressure and temperature.The model features enable to study a broad range of phenomenologies characterizing pre and sin-eruptive magma dynamics in a wide domain from the volcanic crater to deep magma feeding zones. The study of displacement field associated with the simulated fluid dynamics has been carried out with a numerical code developed by the Geophysical group at the University College Dublin (O’Brien and Bean, 2004b), with whom we started a very profitable collaboration. In this code, the seismic wave propagation in heterogeneous media with free surface (e.g. the Earth’s surface) is simulated using a discrete elastic lattice where particle interactions are controlled by the Hooke’s law. This method allows to consider medium heterogeneities and complex topography. The initial and boundary conditions for the simulations have been defined within a coordinate project (INGV-DPC 2004-06 V3_2 “Research on active volcanoes, precursors, scenarios, hazard and risk - Campi Flegrei”), to which this thesis contributes, and many researchers experienced on Campi Flegrei in volcanological, seismic, petrological, geochemical fields, etc. collaborate. Numerical simulations of magma and rock dynamis have been coupled as described in the thesis. The first part of the thesis consists of a parametric study aimed at understanding the eect of the presence in magma of carbon dioxide in magma in the convection dynamics. Indeed, the presence of this volatile was relevant in many Campi Flegrei eruptions, including some eruptions commonly considered as reference for a future activity of this volcano. A set of simulations considering an elliptical magma chamber, compositionally uniform, refilled from below by a magma with volatile content equal or dierent from that of the resident magma has been performed. To do this, a multicomponent non-ideal magma saturation model (Papale et al., 2006) that considers the simultaneous presence of CO2 and H2O, has been implemented in GALES. Results show that the presence of CO2 in the incoming magma increases its buoyancy force promoting convection ad mixing. The simulated dynamics produce pressure transients with frequency and amplitude in the sensitivity range of modern geophysical monitoring networks such as the one installed at Campi Flegrei . In the second part, simulations more related with the Campi Flegrei volcanic system have been performed. The simulated system has been defined on the basis of conditions consistent with the bulk of knowledge of Campi Flegrei and in particular of the Agnano-Monte Spina eruption (4100 B.P.), commonly considered as reference for a future high intensity eruption in this area. The magmatic system has been modelled as a long dyke refilling a small shallow magma chamber; magmas with trachytic and phonolitic composition and variable volatile content of H2O and CO2 have been considered. The simulations have been carried out changing the condition of magma injection, the system configuration (magma chamber geometry, dyke size) and the resident and refilling magma composition and volatile content, in order to study the influence of these factors on the simulated dynamics. Simulation results allow to follow each step of the gas-rich magma ascent in the denser magma, highlighting the details of magma convection and mixing. In particular, the presence of more CO2 in the deep magma results in more ecient and faster dynamics. Through this simulations the variation of the gravimetric field has been determined. Afterward, the space-time distribution of stress resulting from numerical simulations have been used as boundary conditions for the simulations of the displacement field imposed by the magmatic dynamics on rocks. The properties of the simulated domain (rock density, P and S wave velocities) have been based on data from literature on active and passive tomographic experiments, obtained through a collaboration with A. Zollo at the Dept. of Physics of the Federici II Univeristy in Napoli. The elasto-dynamics simulations allow to determine the variations of the space-time distribution of deformation and the seismic signal associated with the studied magmatic dynamics. In particular, results show that these dynamics induce deformations similar to those measured at Campi Flegrei and seismic signals with energies concentrated on the typical frequency bands observed in volcanic areas. The present work shows that an approach based on the solution of equations describing the physics of processes within a magmatic fluid and the surrounding rock system is able to recognise and describe the relationships between geophysical signals detectable on the surface and deep magma dynamics. Therefore, the results suggest that the combined study of geophysical data and informations from numerical simulations can allow in a near future a more ecient evaluation of the short term volcanic hazard.

Numerical Magnitude Skills in 6-Years-Old Children: Exploring Specific Associations with Components of Executive Function

Little is known about how children learn to associate numbers with their corresponding magnitude and about individual characteristics contributing to performance differences on the numerical magnitude tasks within a relatively homogenous sample of 6-year-olds. The present study investigated the relationships between components of executive function and two different numerical magnitude skills in a sample of 162 kindergartners. The Symbolic Number Line was predicted by verbal updating and switching, whereas the Symbolic Magnitude Comparison was predicted by inhibition. Both symbolic tasks were predicted by visuo-spatial updating. Current findings suggest that visuo-spatial updating underlies young children’s retrieval and processing of numbers’ magnitude.

A Finite Element Numerical Algorithm for Modelling and Data Fitting in Complex Systems

Numerical modelling methodologies are important by their application to engineering and scientific problems, because there are processes where analytical mathematical expressions cannot be obtained to model them. When the only available information is a set of experimental values for the variables that determine the state of the system, the modelling problem is equivalent to determining the hyper-surface that best fits the data. This paper presents a methodology based on the Galerkin formulation of the finite elements method to obtain representations of relationships that are defined a priori, between a set of variables: y = z(x1, x2,...., xd). These representations are generated from the values of the variables in the experimental data. The approximation, piecewise, is an element of a Sobolev space and has derivatives defined in a general sense into this space. The using of this approach results in the need of inverting a linear system with a structure that allows a fast solver algorithm. The algorithm can be used in a variety of fields, being a multidisciplinary tool. The validity of the methodology is studied considering two real applications: a problem in hydrodynamics and a problem of engineering related to fluids, heat and transport in an energy generation plant. Also a test of the predictive capacity of the methodology is performed using a cross-validation method.

Numerical modelling of agglomerate degradation

In the processing industries particulate materials are often in the form of powders which themselves are agglomerations of much smaller sized particles. During powder processing operations agglomerate degradation occurs primarily as a result of collisions between agglomerates and between agglomerates and the process equipment. Due to the small size of the agglomerates and the very short duration of the collisions it is currently not possible to obtain sufficiently detailed quantitative information from real experiments to provide a sound theoretically based strategy for designing particles to prevent or guarantee breakage. However, with the aid of computer simulated experiments, the micro-examination of these short duration dynamic events is made possible. This thesis presents the results of computer simulated experiments on a 2D monodisperse agglomerate in which the algorithms used to model the particle-particle interactions have been derived from contact mechanics theories and, necessarily, incorporate contact adhesion. A detailed description of the theoretical background is included in the thesis. The results of the agglomerate impact simulations show three types of behaviour depending on whether the initial impact velocity is high, moderate or low. It is demonstrated that high velocity impacts produce extensive plastic deformation which leads to subsequent shattering of the agglomerate. At moderate impact velocities semi-brittle fracture is observed and there is a threshold velocity below which the agglomerate bounces off the wall with little or no visible damage. The micromechanical processes controlling these different types of behaviour are discussed and illustrated by computer graphics. Further work is reported to demonstrate the effect of impact velocity and bond strength on the damage produced. Empirical relationships between impact velocity, bond strength and damage are presented and their relevance to attrition and comminution is discussed. The particle size distribution curves resulting from the agglomerate impacts are also provided. Computer simulated diametrical compression tests on the same agglomerate have also been carried out. Simulations were performed for different platen velocities and different bond strengths. The results show that high platen velocities produce extensive plastic deformation and crushing. Low platen velocities produce semi-brittle failure in which cracks propagate from the platens inwards towards the centre of the agglomerate. The results are compared with the results of the agglomerate impact tests in terms of work input, applied velocity and damage produced.

Reference list of 265 sources used for the discovery of relationships between data clusters and metadata properties

Visual cluster analysis provides valuable tools that help analysts to understand large data sets in terms of representative clusters and relationships thereof. Often, the found clusters are to be understood in context of belonging categorical, numerical or textual metadata which are given for the data elements. While often not part of the clustering process, such metadata play an important role and need to be considered during the interactive cluster exploration process. Traditionally, linked-views allow to relate (or loosely speaking: correlate) clusters with metadata or other properties of the underlying cluster data. Manually inspecting the distribution of metadata for each cluster in a linked-view approach is tedious, specially for large data sets, where a large search problem arises. Fully interactive search for potentially useful or interesting cluster to metadata relationships may constitute a cumbersome and long process. To remedy this problem, we propose a novel approach for guiding users in discovering interesting relationships between clusters and associated metadata. Its goal is to guide the analyst through the potentially huge search space. We focus in our work on metadata of categorical type, which can be summarized for a cluster in form of a histogram. We start from a given visual cluster representation, and compute certain measures of interestingness defined on the distribution of metadata categories for the clusters. These measures are used to automatically score and rank the clusters for potential interestingness regarding the distribution of categorical metadata. Identified interesting relationships are highlighted in the visual cluster representation for easy inspection by the user. We present a system implementing an encompassing, yet extensible, set of interestingness scores for categorical metadata, which can also be extended to numerical metadata. Appropriate visual representations are provided for showing the visual correlations, as well as the calculated ranking scores. Focusing on clusters of time series data, we test our approach on a large real-world data set of time-oriented scientific research data, demonstrating how specific interesting views are automatically identified, supporting the analyst discovering interesting and visually understandable relationships.