Comunicação Matemática: O reconhecimento, pelos professores, da singularidade dos conhecimentos matemáticos dos alunos

Este artigo discute o papel da valorização das interações sociais entre os alunos e o professor no desenvolvimento de modos de comunicação e de padrões de interação centrados nos conhecimentos matemáticos individuais dos alunos. Os dados foram recolhidos por mim, em contexto de trabalho colaborativo, com três professoras do 1.º ciclo do ensino básico, assumindo uma perspetiva interpretativa da ação e significação das professoras das conceções e práticas de comunicação matemática na sala de aula. O desenvolvimento das interações entre os próprios alunos e entre estes e as professoras, juntamente com o reconhecimento da singularidade dos conhecimentos matemáticos dos alunos, favoreceram a existência dos modos de comunicação reflexiva e instrutiva e dos padrões de extração e de discussão na comunicação matemática na sala de aula, gerando um sentido de responsabilidade coletiva sobre a aprendizagem da matemática e no reconhecimento do conhecimento do outro (aluno e professor).

Spatial dynamics of team sports exposed by Voronoi diagrams

Team sports represent complex systems: players interact continuously during a game, and exhibit intricate patterns of interaction, which can be identified and investigated at both individual and collective levels. We used Voronoi diagrams to identify and investigate the spatial dynamics of players' behavior in Futsal. Using this tool, we examined 19 plays of a sub-phase of a Futsal game played in a reduced area (20 m(2)) from which we extracted the trajectories of all players. Results obtained from a comparative analysis of player's Voronoi area (dominant region) and nearest teammate distance revealed different patterns of interaction between attackers and defenders, both at the level of individual players and teams. We found that, compared to defenders, larger dominant regions were associated with attackers. Furthermore, these regions were more variable in size among players from the same team but, at the player level, the attackers' dominant regions were more regular than those associated with each of the defenders. These findings support a formal description of the dynamic spatial interaction of the players, at least during the particular sub-phase of Futsal investigated. The adopted approach may be extended to other team behaviors where the actions taken at any instant in time by each of the involved agents are associated with the space they occupy at that particular time.

Developmental and evolutionary assumptions in a study about the impact of premature birth and low income on mother–infant interaction

In order to study the impact of premature birth and low income on mother–infant interaction, four Portuguese samples were gathered: full-term, middle-class (n=99); premature, middle-class (n=63); full-term, low income (n=22); and premature, low income (n=21). Infants were filmed in a free play situation with their mothers, and the results were scored using the CARE Index. By means of multinomial regression analysis, social economic status (SES) was found to be the best predictor of maternal sensitivity and infant cooperative behavior within a set of medical and social factors. Contrary to the expectations of the cumulative risk perspective, two factors of risk (premature birth together with low SES) were as negative for mother–infant interaction as low SES solely. In this study, as previous studies have shown, maternal sensitivity and infant cooperative behavior were highly correlated, as was maternal control with infant compliance. Our results further indicate that, when maternal lack of responsiveness is high, the infant displays passive behavior, whereas when the maternal lack of responsiveness is medium, the infant displays difficult behavior. Indeed, our findings suggest that, in these cases, the link between types of maternal and infant interactive behavior is more dependent on the degree of maternal lack of responsiveness than it is on birth status or SES. The results will be discussed under a developmental and evolutionary reasoning

Measuring spatial interaction behavior in team sports using superimposed Voronoi diagrams

In team sports, the spatial distribution of players on the field is determined by the interaction behavior established at both player and team levels. The distribution patterns observed during a game emerge from specific technical and tactical methods adopted by the teams, and from individual, environmental and task constraints that influence players' behaviour. By understanding how specific patterns of spatial interaction are formed, one can characterize the behavior of the respective teams and players. Thus, in the present work we suggest a novel spatial method for describing teams' spatial interaction behaviour, which results from superimposing the Voronoi diagrams of two competing teams. We considered theoretical patterns of spatial distribution in a well-defined scenario (5 vs 4+ GK played in a field of 20x20m) in order to generate reference values of the variables derived from the superimposed Voronoi diagrams (SVD). These variables were tested in a formal application to empirical data collected from 19 Futsal trials with identical playing settings. Results suggest that it is possible to identify a number of characteristics that can be used to describe players' spatial behavior at different levels, namely the defensive methods adopted by the players.

Equilibrium self-assembly of colloids with distinct interaction sites: Thermodynamics, percolation, and cluster distribution functions

We calculate the equilibrium thermodynamic properties, percolation threshold, and cluster distribution functions for a model of associating colloids, which consists of hard spherical particles having on their surfaces three short-ranged attractive sites (sticky spots) of two different types, A and B. The thermodynamic properties are calculated using Wertheim's perturbation theory of associating fluids. This also allows us to find the onset of self-assembly, which can be quantified by the maxima of the specific heat at constant volume. The percolation threshold is derived, under the no-loop assumption, for the correlated bond model: In all cases it is two percolated phases that become identical at a critical point, when one exists. Finally, the cluster size distributions are calculated by mapping the model onto an effective model, characterized by a-state-dependent-functionality (f) over bar and unique bonding probability (p) over bar. The mapping is based on the asymptotic limit of the cluster distributions functions of the generic model and the effective parameters are defined through the requirement that the equilibrium cluster distributions of the true and effective models have the same number-averaged and weight-averaged sizes at all densities and temperatures. We also study the model numerically in the case where BB interactions are missing. In this limit, AB bonds either provide branching between A-chains (Y-junctions) if epsilon(AB)/epsilon(AA) is small, or drive the formation of a hyperbranched polymer if epsilon(AB)/epsilon(AA) is large. We find that the theoretical predictions describe quite accurately the numerical data, especially in the region where Y-junctions are present. There is fairly good agreement between theoretical and numerical results both for the thermodynamic (number of bonds and phase coexistence) and the connectivity properties of the model (cluster size distributions and percolation locus).

Interaction of formaldehyde and tobacco smoking in the frequency of micronucleus and the XRCC3 Thr241Met polymorphism

Formaldehyde is classified by IARC as carcinogenic to humans (nasopharyngeal cancer). Tobacco smoke has been epidemiologically associated to a higher risk of development of cancer, especially in the oral cavity, larynx and lungs, as these are places of direct contact with many carcinogenic tobacco’s compounds. XRCC3 is involved in homologous recombination repair of cross-links and chromosomal double-strand breaks (Thr241Met polymorphism). The aim of the study is to determine whether there is an in vivo association between genetic polymorphism of the gene XRCC3 and the frequency of genotoxicity biomarkers in subjects exposed or not to formaldehyde and with or without tobacco consumption.

Percolation of colloids with distinct interaction sites

We generalize the Flory-Stockmayer theory of percolation to a model of associating (patchy) colloids, which consists of hard spherical particles, having on their surfaces f short-ranged-attractive sites of m different types. These sites can form bonds between particles and thus promote self-assembly. It is shown that the percolation threshold is given in terms of the eigenvalues of a m x m matrix, which describes the recursive relations for the number of bonded particles on the ith level of a cluster with no loops; percolation occurs when the largest of these eigenvalues equals unity. Expressions for the probability that a particle is not bonded to the giant cluster, for the average cluster size and the average size of a cluster to which a randomly chosen particle belongs, are also derived. Explicit results for these quantities are computed for the case f = 3 and m = 2. We show how these structural properties are related to the thermodynamics of the associating system by regarding bond formation as a (equilibrium) chemical reaction. This solution of the percolation problem, combined with Wertheim's thermodynamic first-order perturbation theory, allows the investigation of the interplay between phase behavior and cluster formation for general models of patchy colloids.

Effects of the interaction of tobacco smoke and alcohol consumption on buccal micronucleus in workers exposed occupationally to formaldehyde

Occupational exposure to formaldehyde (FA) has been shown to induce nasopharyngeal cancer and has been classified as carcinogenic to humans (group 1) on the basis of sufficient evidence in humans. Tobacco smoke has been associated to a higher risk of development of cancer, especially in the oral cavity, larynx and lungs, as these are places of direct contact with many carcinogenic tobacco’s compounds. Alcohol is a recognized agent that influence cells in a genotoxic form, been citied as a strong agent with potential in the development of carcinogenic lesions. Epidemiological evidence points to a strong synergistic effect between cigarette smoking and alcohol consumption in the induction of cancers in the oral cavity. Approximately 90% of human cancers originate from epithelial cells. Therefore, it could be argued that oral epithelial cells represent a preferred target site for early genotoxic events induced by carcinogenic agents entering the body via inhalation and ingestion. The MN assay in buccal cells was also used to study cancerous and precancerous lesions and to monitor the effects of a number of chemopreventive agents.

Substrate interaction with recombinant amidase from Pseudomonas aeruginosa during biocatalysis

The interaction of a variety of substrates with Pseudomonas aeruginosa native amidase (E.C. 3.5.1.4), overproduced in an Escherichia coli strain, was investigated using difference FTIR spectroscopy. The amides used as substrates showed an increase in hydrogen bonding upon association in multimers, which was not seen with esters. Evidence for an overall reduction or weakening of hydrogen bonding while amide and ester substrates are interacting with the enzyme is presented. The results describe a spectroscopic approach for analysis of substrate-amidase interaction and in situ monitoring of the hydrolysis and transferase reaction when amides or esters are used as substrates.

DNA interaction and cytotoxicity studies of new ruthenium(II) cyclopentadienyl derivative complexescontaining heteroaromatic ligands

Four ruthenium(II) complexes with the formula [Ru(eta(5)-C(5)H(5))(PP)L][CF(3)SO(3)], being (PP = two triphenylphosphine molecules), L = 1-benzylimidazole, 1; (PP = two triphenylphosphine molecules), L = 2,2'bipyridine, 2; (PP = two triphenylphosphine molecules), L = 4-Methylpyridine, 3; (PP = 1,2-bis(diphenylphosphine) ethane), L = 4-Methylpyridine, 4, were prepared, in view to evaluate their potentialities as antitumor agents. The compounds were completely characterized by NMR spectroscopy and their crystal and molecular structures were determined by X-ray diffraction. Electrochemical studies were carried out giving for all the compounds quasi-reversible processes. The images obtained by atomic force microscopy (AFM) suggest interaction with pBR322 plasmid DNA. Measurements of the viscosity of solutions of free DNA and DNA incubated with different concentrations of the compounds confirmed this interaction. The cytotoxicity of compounds 1234 was much higher than that of cisplatin against human leukemia cancer cells (HL-60 cells). IC(50) values for all the compounds are in the range of submicromolar amounts. Apoptotic death percentage was also studied resulting similar than that of cisplatin. (C) 2010 Elsevier Inc. All rights reserved.

Evaluation of intermolecular interactions in thioxanthone derivatives: substituent effect on crystal diversity

A family of 9H-thioxanthen-9-one derivatives and two precursors, 2-[(4-bromophenyl) sulfanyl]-5-nitrobenzoic acid and 2-[(4-aminophenyl) sulfanyl]-5-nitrobenzoic acid, were synthesized and studied in order to assess the role of the different substituent groups in determining the supramolecular motifs. From our results we can conclude that Etter's rules are obeyed: whenever present the -COOH head to head strong hydrogen bonding dimer, R-2(2)(8) synthon, prevails as the dominant interaction. As for -NH2, the best donor when present also follows the expected hierarchy, an NH center dot center dot center dot O(COOH) was formed in the acid precursor (2) and an NH center dot center dot center dot O(C=O) in the thioxanthone (4). The main role played by weaker hydrogen bonds such as CH center dot center dot center dot O, and other intermolecular interactions, pi-pi and Br center dot center dot center dot O, as well as the geometric restraints of packing patterns shows the energetic interplay governing crystal packing. A common feature is the relation between the p-p stacking and the unit cell dimensions. A new synthon notation, R`, introduced in this paper, refers to the possibility of accounting for intra- and intermolecular interactions into recognizable and recurring aggregate patterns.

Wrinkling Labyrinth Patterns on Elastomeric Janus Particles

We describe a novel, low-cost and low-tech method for the fabrication of elastomeric Janus particles with diameters ranging from micrometers to millimeters. This consists of UV-irradiating soft urethane/urea elastomer spheres, which are then extracted in toluene and dried. The spheres are thus composed of a single material: no coating or film deposition steps are required. Furthermore, the whole procedure is carried out at ambient temperature and pressure. Long, labyrinthine corrugations ("wrinkles") appear on the irradiated portions of the particles' surfaces, the spatial periodicity of which can be controlled by varying the sizes of particles. The asymmetric morphology of the resulting Janus particles has been confirmed by scanning electron microscopy, atomic force microscopy, and optical microscopy. We have also established that the spheres behave elastically by performing bouncing tests with dried and swollen spheres. Results can be interpreted by assuming that each sphere consists of a thin, stiff surface layer ("skin") lying atop a thicker, softer substrate ("bulk"). The skin's higher stiffness is hypothesized to result from the more extensive cross-linking of the polymer chains located near the surface by the UV radiation. Textures then arise from competition between the effects of bending the skin and compressing the bulk, as the solvent evaporates and the sphere shrinks.

Temporal patterns of TV watching for Portuguese viewers

Audiometer systems provide enormous amounts of detailed TV watching data. Several relevant and interdependent factors may influence TV viewers' behavior. In this work we focus on the time factor and derive Temporal Patterns of TV watching, based on panel data. Clustering base attributes are originated from 1440 binary minute-related attributes, capturing the TV watching status (watch/not watch). Since there are around 2500 panel viewers a data reduction procedure is first performed. K-Means algorithm is used to obtain daily clusters of viewers. Weekly patterns are then derived which rely on daily patterns. The obtained solutions are tested for consistency and stability. Temporal TV watching patterns provide new insights concerning Portuguese TV viewers' behavior.

Environmental and track perturbations on multiple pantograph interaction with catenaries in high-speed trains

The top velocity of high-speed trains is generally limited by the ability to supply the proper amount of energy through the pantograph-catenary interface. The deterioration of this interaction can lead to the loss of contact, which interrupts the energy supply and originates arcing between the pantograph and the catenary, or to excessive contact forces that promote wear between the contacting elements. Another important issue is assessing on how the front pantograph influences the dynamic performance of the rear one in trainsets with two pantographs. In this work, the track and environmental conditions influence on the pantograph-catenary is addressed, with particular emphasis in the multiple pantograph operations. These studies are performed for high speed trains running at 300 km/h with relation to the separation between pantographs. Such studies contribute to identify the service conditions and the external factors influencing the contact quality on the overhead system. (C) 2013 Elsevier Ltd. All rights reserved.

Convective patterns under the Indo-Atlantic << box >>

Using fluid mechanics, we reinterpret the mantle images obtained from global and regional tomography together with geochemical, geological and paleomagnetic observations, and attempt to unravel the pattern of convection in the Indo-Atlantic "box" and its temporal evolution over the last 260 Myr. The << box >> presently contains a) a broad slow seismic anomaly at the CMB which has a shape similar to Pangea 250 Myr ago, and which divides into several branches higher in the lower mantle, b) a "superswell, centered on the western edge of South Africa, c) at least 6 "primary hotspots" with long tracks related to traps, and d) numerous smaller hotspots. In the last 260 Myr, this mantle box has undergone 10 trap events, 7 of them related to continental breakup. Several of these past events are spatially correlated with present-day seismic anomalies and/or upwellings. Laboratory experiments show that superswells, long-lived hotspot tracks and traps may represent three evolutionary stages of the same phenomenon, i.e. episodic destabilization of a hot, chemically heterogeneous thermal boundary layer, close to the bottom of the mantle. When scaled to the Earth's mantle, its recurrence time is on the order of 100-200 Myr. At any given time, the Indo-Atlantic box should contain 3 to 9 of these instabilities at different stages of their development, in agreement with observations. The return flow of the downwelling slabs, although confined to two main << boxes >> (Indo-Atlantic and Pacific) by subduction zone geometry, may therefore not be passive, but rather take the form of active thermochemical instabilities. (c) 2005 Elsevier B.V. All rights reserved.