Fast unsupervised technique for extraction of endmembers spectra from hyperspectral data

One of the most challenging task underlying many hyperspectral imagery applications is the linear unmixing. The key to linear unmixing is to find the set of reference substances, also called endmembers, that are representative of a given scene. This paper presents the vertex component analysis (VCA) a new method to unmix linear mixtures of hyperspectral sources. The algorithm is unsupervised and exploits a simple geometric fact: endmembers are vertices of a simplex. The algorithm complexity, measured in floating points operations, is O (n), where n is the sample size. The effectiveness of the proposed scheme is illustrated using simulated data.

On the requirements of interpolating polynomials for path motion constraints

In the framework of multibody dynamics, the path motion constraint enforces that a body follows a predefined curve being its rotations with respect to the curve moving frame also prescribed. The kinematic constraint formulation requires the evaluation of the fourth derivative of the curve with respect to its arc length. Regardless of the fact that higher order polynomials lead to unwanted curve oscillations, at least a fifth order polynomials is required to formulate this constraint. From the point of view of geometric control lower order polynomials are preferred. This work shows that for multibody dynamic formulations with dependent coordinates the use of cubic polynomials is possible, being the dynamic response similar to that obtained with higher order polynomials. The stabilization of the equations of motion, always required to control the constraint violations during long analysis periods due to the inherent numerical errors of the integration process, is enough to correct the error introduced by using a lower order polynomial interpolation and thus forfeiting the analytical requirement for higher order polynomials.

Seasonal variation of anti-resa/Pf155 Plasmodium falciparum antibodies in three localities from the state of Amapá, Brazil

Anti-RESA/Pf155 antibodies were assayed in sera of individuals from three localities (Laranjal do Jari, Vila Padaria and Vila Paraíso) in the State of Amapá, Brazil, during the long-rains and short-rains seasons. All of these had negative blood smears for malaria. Most of the sera collected were positive in Indirect Fluorescent Antibody (IFA) with P. falciparum parasites, with no seasonal variation. A high percentage of these sera (62% to 100%) was RESA positive by Modified Indirect Fluorescent Antibody (MIFA), with a significant (p < 0.05) increase of geometric mean titers during the short-rains season, when the transmission of the disease is highest. ELISA with three repetitive RESA peptides (EENV)3 (4x3), (EENVEHDA)2 (8x2) and (DDEHVEEPTVA)2(11x2) did not reveal statistically significant seasonal variations, although a small enhancement of positivity was observed in V. Padaria (15.3 to 38.8%) in the short-rains season with the 8x2 peptides, and with 4x3 and 8x2 peptides in V. Paraíso, with a decrease in 11x2. MIFA titers appeared to be correlated mainly to the peptide 4x3 and it was the immunodominant in the three localities.

Identification of factors and groups at risk of infection with Schistosoma mansoni: a strategy for the implementation of control measures?

A fourteen year schistosomiasis control program in Peri-Peri (Capim Branco, MG) reduced prevalence from 43.5 to 4.4%; incidence from 19.0 to 2.9%, the geometric mean of the number of eggs from 281 to 87 and the level of the hepatoesplenic form cases from 5.9 to 0.0%. In 1991, three years after the interruption of the program, the prevalence had risen to 19.6%. The district consists of Barbosa (a rural area) and Peri-Peri itself (an urban area). In 1991, the prevalence in the two areas was 28.4% and 16.0% respectively. A multivariate analysis of risk factors for schistosomiasis indicated the domestic agricultural activity with population attributive risk (PAR) of 29.82%, the distance (< 10 m) from home to water source (PAR = 25.93%) and weekly fishing (PAR = 17.21%) as being responsible for infections in the rural area. The recommended control measures for this area are non-manual irrigation and removal of homes to more than ten meters from irrigation ditches. In the urban area, it was observed that swimming at weekly intervals (PAR = 20.71%), daily domestic agricultural activity (PAR = 4.07%) and the absence of drinking water in the home (PAR=4.29%) were responsible for infections. Thus, in the urban area the recommended control measures are the substitution of manual irrigation with an irrigation method that avoids contact with water, the creation of leisure options of the population and the provision of a domestic water supply. The authors call attention to the need for the efficacy of multivariate analysis of risk factors to be evaluated for schistosomiasis prior to its large scale use as a indicator of the control measures to be implemented.

Unmixing hyperspectral data: independent and dependent component analysis

The development of high spatial resolution airborne and spaceborne sensors has improved the capability of ground-based data collection in the fields of agriculture, geography, geology, mineral identification, detection [2, 3], and classification [4–8]. The signal read by the sensor from a given spatial element of resolution and at a given spectral band is a mixing of components originated by the constituent substances, termed endmembers, located at that element of resolution. This chapter addresses hyperspectral unmixing, which is the decomposition of the pixel spectra into a collection of constituent spectra, or spectral signatures, and their corresponding fractional abundances indicating the proportion of each endmember present in the pixel [9, 10]. Depending on the mixing scales at each pixel, the observed mixture is either linear or nonlinear [11, 12]. The linear mixing model holds when the mixing scale is macroscopic [13]. The nonlinear model holds when the mixing scale is microscopic (i.e., intimate mixtures) [14, 15]. The linear model assumes negligible interaction among distinct endmembers [16, 17]. The nonlinear model assumes that incident solar radiation is scattered by the scene through multiple bounces involving several endmembers [18]. Under the linear mixing model and assuming that the number of endmembers and their spectral signatures are known, hyperspectral unmixing is a linear problem, which can be addressed, for example, under the maximum likelihood setup [19], the constrained least-squares approach [20], the spectral signature matching [21], the spectral angle mapper [22], and the subspace projection methods [20, 23, 24]. Orthogonal subspace projection [23] reduces the data dimensionality, suppresses undesired spectral signatures, and detects the presence of a spectral signature of interest. The basic concept is to project each pixel onto a subspace that is orthogonal to the undesired signatures. As shown in Settle [19], the orthogonal subspace projection technique is equivalent to the maximum likelihood estimator. This projection technique was extended by three unconstrained least-squares approaches [24] (signature space orthogonal projection, oblique subspace projection, target signature space orthogonal projection). Other works using maximum a posteriori probability (MAP) framework [25] and projection pursuit [26, 27] have also been applied to hyperspectral data. In most cases the number of endmembers and their signatures are not known. Independent component analysis (ICA) is an unsupervised source separation process that has been applied with success to blind source separation, to feature extraction, and to unsupervised recognition [28, 29]. ICA consists in finding a linear decomposition of observed data yielding statistically independent components. Given that hyperspectral data are, in given circumstances, linear mixtures, ICA comes to mind as a possible tool to unmix this class of data. In fact, the application of ICA to hyperspectral data has been proposed in reference 30, where endmember signatures are treated as sources and the mixing matrix is composed by the abundance fractions, and in references 9, 25, and 31–38, where sources are the abundance fractions of each endmember. In the first approach, we face two problems: (1) The number of samples are limited to the number of channels and (2) the process of pixel selection, playing the role of mixed sources, is not straightforward. In the second approach, ICA is based on the assumption of mutually independent sources, which is not the case of hyperspectral data, since the sum of the abundance fractions is constant, implying dependence among abundances. This dependence compromises ICA applicability to hyperspectral images. In addition, hyperspectral data are immersed in noise, which degrades the ICA performance. IFA [39] was introduced as a method for recovering independent hidden sources from their observed noisy mixtures. IFA implements two steps. First, source densities and noise covariance are estimated from the observed data by maximum likelihood. Second, sources are reconstructed by an optimal nonlinear estimator. Although IFA is a well-suited technique to unmix independent sources under noisy observations, the dependence among abundance fractions in hyperspectral imagery compromises, as in the ICA case, the IFA performance. Considering the linear mixing model, hyperspectral observations are in a simplex whose vertices correspond to the endmembers. Several approaches [40–43] have exploited this geometric feature of hyperspectral mixtures [42]. Minimum volume transform (MVT) algorithm [43] determines the simplex of minimum volume containing the data. The MVT-type approaches are complex from the computational point of view. Usually, these algorithms first find the convex hull defined by the observed data and then fit a minimum volume simplex to it. Aiming at a lower computational complexity, some algorithms such as the vertex component analysis (VCA) [44], the pixel purity index (PPI) [42], and the N-FINDR [45] still find the minimum volume simplex containing the data cloud, but they assume the presence in the data of at least one pure pixel of each endmember. This is a strong requisite that may not hold in some data sets. In any case, these algorithms find the set of most pure pixels in the data. Hyperspectral sensors collects spatial images over many narrow contiguous bands, yielding large amounts of data. For this reason, very often, the processing of hyperspectral data, included unmixing, is preceded by a dimensionality reduction step to reduce computational complexity and to improve the signal-to-noise ratio (SNR). Principal component analysis (PCA) [46], maximum noise fraction (MNF) [47], and singular value decomposition (SVD) [48] are three well-known projection techniques widely used in remote sensing in general and in unmixing in particular. The newly introduced method [49] exploits the structure of hyperspectral mixtures, namely the fact that spectral vectors are nonnegative. The computational complexity associated with these techniques is an obstacle to real-time implementations. To overcome this problem, band selection [50] and non-statistical [51] algorithms have been introduced. This chapter addresses hyperspectral data source dependence and its impact on ICA and IFA performances. The study consider simulated and real data and is based on mutual information minimization. Hyperspectral observations are described by a generative model. This model takes into account the degradation mechanisms normally found in hyperspectral applications—namely, signature variability [52–54], abundance constraints, topography modulation, and system noise. The computation of mutual information is based on fitting mixtures of Gaussians (MOG) to data. The MOG parameters (number of components, means, covariances, and weights) are inferred using the minimum description length (MDL) based algorithm [55]. We study the behavior of the mutual information as a function of the unmixing matrix. The conclusion is that the unmixing matrix minimizing the mutual information might be very far from the true one. Nevertheless, some abundance fractions might be well separated, mainly in the presence of strong signature variability, a large number of endmembers, and high SNR. We end this chapter by sketching a new methodology to blindly unmix hyperspectral data, where abundance fractions are modeled as a mixture of Dirichlet sources. This model enforces positivity and constant sum sources (full additivity) constraints. The mixing matrix is inferred by an expectation-maximization (EM)-type algorithm. This approach is in the vein of references 39 and 56, replacing independent sources represented by MOG with mixture of Dirichlet sources. Compared with the geometric-based approaches, the advantage of this model is that there is no need to have pure pixels in the observations. The chapter is organized as follows. Section 6.2 presents a spectral radiance model and formulates the spectral unmixing as a linear problem accounting for abundance constraints, signature variability, topography modulation, and system noise. Section 6.3 presents a brief resume of ICA and IFA algorithms. Section 6.4 illustrates the performance of IFA and of some well-known ICA algorithms with experimental data. Section 6.5 studies the ICA and IFA limitations in unmixing hyperspectral data. Section 6.6 presents results of ICA based on real data. Section 6.7 describes the new blind unmixing scheme and some illustrative examples. Section 6.8 concludes with some remarks.

Projeto de uma ponte atirantada rodoferroviária sobre o rio Lima, Viana do Castelo

Trabalho académico com o objetivo do autor desenvolver um estudo prévio e um projeto de uma travessia sobre o rio Lima, na cidade de Viana do Castelo constituída por uma ponte de tirantes rodoferroviária. O projeto académico visa, também, desenvolver e compreender: os conceitos básicos, as metodologias de conceção, e o funcionamento de estruturas desse género. O motivo principal da escolha do tema é a necessidade de uma alternativa à ponte Eiffel em Viana do Castelo, e juntando o facto de em Portugal não existir nenhuma obra de arte de tirantes rodoferroviária até ao presente, seria interessante estudar e projetar uma estrutura rodoferroviária de tirantes. Das diversas possibilidades de sistemas estruturais estudados, adotou-se uma ponte que acomodará 4 vias rodoviárias e 2 vias ferroviárias, com um desenvolvimento total de 660 metros, constituída por dois vãos laterais com 165 metros cada um, e com um vão central de 330 metros. A obra de arte será em semi-leque com dois planos de tirantes, ancorados a duas torres de betão em Y invertido de altura aproximadamente de 110 metros. O tabuleiro será duplo misto aço-betão, constituído por duas vigas trianguladas do tipo Warren, e por carlingas, afastadas entre si de 15 metros com secções tubulares metálicas de espessura variável. As carlingas ao nível superior suportam a laje de betão, que constitui a rodovia, e inferiormente, suportam outra laje de betão para a parte ferroviária. O trabalho inicia-se com o enquadramento conceptual geral da envolvente da obra de arte, seguidamente com apresentação da evolução histórica ao longo do tempo das pontes de tirantes, e à apresentação de algumas pontes rodoferroviárias de tirantes. É realizada uma análise preliminar, onde se estudam as restrições, as condicionantes, o local de implantação, e o sistema da configuração geométrica a adotar na conceção estrutural. São descritos todos os tipos de materiais, equipamentos a utilizar, bem como as suas características mecânicas necessárias para o cálculo estrutural. A quantificação das ações e das combinações de cálculo efetuaram-se de acordo com as normas em vigor nacionais e europeias, designadamente os Eurocódigos das várias especialidades e o Regulamento de Segurança e Ações para Estruturas de Edifícios e Pontes. Efetuou-se um pré-dimensionamento e uma otimização de vários sistemas estruturais possíveis de todos os elementos estruturais, tendo em conta variáveis de estudo como a economia e a resistência estrutural das secções, por forma a chegar à solução final. A estrutura foi discretizada e analisada num modelo estático tridimensional num programa de cálculo automático. A análise de resultados foi efetuada longitudinalmente para a verificação dos Estados Limites Últimos e Estados Limites de Utilização dos elementos estruturais que constituem a ponte. Foi ainda efetuada uma estimativa orçamental da ponte no rio Lima na cidade de Viana do Castelo.

Tectónica da cadeia da Arrábida

Geociências, Museu Nac. Hist. Nat. Univ. Lisboa, nº 2, 35-84

Metodologia das opções reais na avaliação de investimentos produtivos: aplicação de um modelo de uma variável estocástica

Os critérios neoclássicos de investimento ignoram três características fundamentais, presentes na grande maioria dos projetos de investimento produtivos, sendo elas a Flexibilidade, a Incerteza e a Irreversibilidade. Face a essas características, a abordagem das Opções Reais parece ser a única abordagem competente quando comparada com critérios como Payback, Taxa Interna de Rendibilidade ou Valor Atual Líquido. Com vista a confirmar estas afirmações, aplica-se a uma situação simulada o modelo de uma variável estocástica, que segue um processo estocástico, mais concretamente um Geometric Brownian Motion com drift, apresentado por Dixit e Pindyck (1994), modelo este que a par dos modelos de duas variáveis estocásticas, como são exemplos os desenvolvidos por McDonald e Siegel (1986) e Adkins e Paxson (2011), constituem aquele que é, tanto quanto sabemos, o “estado da arte” da temática. Com base nesta aplicação recolhemos evidências de que, de facto, através da consideração de oportunidades de investimento perspetivadas em Opções Reais diminuímos a probabilidade de incorrer em decisões de investimento que não são, de acordo com este critério, ótimas para maximizar o valor do projeto em questão.

Secondary dengue infection in schoolchildren in a dengue endemic area in the State of Rio de Janeiro, Brazil

A seroepidemiologic survey was carried out in schoolchildren from public schools of the Niterói municipality, state of Rio de Janeiro, Brazil, after a period of sequential epidemics by dengue virus type 1 and 2 (DEN-1 and DEN-2). 450 blood samples were obtained by fingertip puncture and collected on filter paper discs. The hemagglutination inhibition (HAI) test was carried out using DEN-1 and DEN-2 antigens. HAI titres were demonstrated in 66% (297/450) of the sera and the geometric means of the titres were 1/182 and 1/71 for DEN-1 and DEN-2, respectively. Secondary infections were observed in 61% (181/297) of positive cases. Among these, 75% (135/181) were under fifteen years old. No dengue haemorrhagic fever (DHF) was reported in these children. Asymptomatic or oligosymptomatic infections were detected in 56% of the studied population. The absolute and relative frequencies of positive tests by age group and sex did not evidence statistically significant difference. The number of individuals infected probably produced a immunologic barrier responsible for the non occurrence of dengue epidemic in the latter years.

IMMUNOGENICITY OF LOW-DOSE INTRAMUSCULAR AND INTRADERMAL VACCINATION WITH RECOMBINANT HEPATITIS B VACCINE

The study is a randomized trial using recombinant DNA vaccine to determine whether an intramuscular 10 µg dose or intradermal 2 µg induces satisfactory anti-HBs levels compared to the standard dose of intramuscular 20 µg. participants were 359 healthy medical and nurse students randomly allocated to one of the three groups: Group I - IM 20 µg; Group II - IM 10 µg; Group III - ID 2 µg at 0, 1 and 6 months. Anti-HBs titres were measured after complete vaccine schedule by ELISA/Pasteur. Baseline variables were similar among groups and side effects were mild after any dose. Vaccinees in the IM-10 µg group had seroconversion rate and geometric mean titre (GMT 2344 IU L-1), not significant different from the IM-20 µg group (GMT 4570 IU L-1). On the contrary, 21.4% of the ID - 2 µg recipients mount antibody concentration below 10 IU L1 and GMT of 91 IU L-1, a statiscally significant difference compared with the standard schedule IM-20 µg (p < 0.001). A three dose regimen of half dosse IM could be considered an appropriate schedule to prevent hepatitis B in young health adults which is of relevance to the expansion of hepatitis B vaccine programme

DETECTION OF IgM ANTIBODIES TO Schistosoma mansoni GUT-ASSOCIATED ANTIGENS FOR THE STUDY OF THE DYNAMICS OF SCHISTOSOMIASIS TRANSMISSION IN AN ENDEMIC AREA WITH LOW WORM BURDEN

For a period of 2 years, five follow-up measures of prevalence and incidence rates were estimated in a prospective study of S. mansoni infection in a group of schoolchildren who were living in a rural area of the Municipality of Itariri (São Paulo, Brazil), where schistosomiasis is transmitted by Biomphalaria tenagophila. Infection was determined by the examination of three Kato-Katz stool slides, and the parasitological findings were analyzed in comparison to serological data. In the five surveys, carried out at 6-month intervals (March-April and September-October), the prevalences were, respectively, 8.6, 6.8, 9.9, 5.8 and 17.2% by the Kato-Katz, and 56.5, 52.6, 60.8, 53.5 and 70.1% by the immunofluorescence test (IFT). Geometric mean egg counts were low: 57.8, 33.0, 35.6, 47.3 and 40.9 eggs per gram of feces, respectively. Of the total of 299 schoolchildren, who submitted five blood samples at 6-month intervals, one for each survey, 40% were IFT-positive throughout the study, and 22% were IFT-negative in all five surveys. Seroconversion from IFT negative to positive, indicating newly acquired S. mansoni infection, was observed more frequently in surveys carried out during March-April (after Summer holidays), than during September-October. Seasonal trends were not statistically significant for detection of S. mansoni eggs in stool. The results indicate that the use of IgM-IFT is superior to parasitological methods for detection of incidence of S. mansoni infection in areas with low worm burden.

Projeto Alternativo ao Nó de Ligação do Pópulo

O presente trabalho visa, o estudo e a elaboração de um projeto de execução de um Nó de Ligação em trevo completo. O projeto requer um estudo cuidado da geometria das estradas principais existentes, das características do terreno e de todas as restantes condicionantes que se impõe à realização do mesmo. Esta fase do projeto é decisiva para o desenvolvimento e o sucesso do projeto, nos diversos aspetos técnicos, económicos e ambientais relacionados. Após o enquadramento do nó de ligação em trevo no terreno, procedeu-se à localização dos quatro ramos de ligação direta, ao seu traçado geométrico e as ligações às estradas principais. Seguidamente, realizou-se o traçado de todos os restabelecimentos necessários para a circulação nas vias pré-existentes e o seu acesso ao nó. Este trabalho foi realizado aplicando todos os conhecimentos adquiridos na Licenciatura em Engenharia Civil e no Mestrado em Engenharia Civil no Ramo das Infraestruturas e Ambiente no ISEP, com especial importância em Vias de Comunicação e Infraestruturas de Transportes. Todos os procedimentos de definição geométrica e analítica do nó de ligação em trevo foram realizados recorrendo ao programa para computador “AutoCAD Civil 2013”.

Estudo de delaminação em compósitos de matriz polimérica

A aplicação do material compósito é neste momento bastante vasta, graças à combinação das suas características específicas, tais como, maior resistência específica e módulos específicos e melhor resistência à fadiga, quando comparados com os metais convencionais. Tais características, quando requeridas, tornam este material ideal para aplicações estruturais. Esta caminhada de sucesso iniciou desde muito cedo, quando o material compósito já era utilizado para fabrico de armas pelos mongóis e na construção civil pelos hebreus e egípcios, contudo, só a partir dos meados do século XX é que despertou interesses para aplicações mais modernas. Atualmente os materiais compósitos são utilizados em equipamentos domésticos, componentes elétricos e eletrónicos, passando por materiais desportivos, pela indústria automóvel e construção civil, até indústrias de grande exigência e visibilidade tecnológica como a aeronáutica, espacial e de defesa. Apesar das boas características apresentadas pelos materiais compósitos, no entanto, estes materiais têm tendência a perderem as suas propriedades quando submetidas a algumas operações de acabamento como a furação. A furação surge da necessidade de ligação de peças de um mesmo mecanismo. Os furos obtidos por este processo devem ser precisos e sem danos para garantir ligações de alta resistência e também precisas. A furação nos materiais compósitos é bastante complexa devido à sua heterogeneidade, anisotropia, sensibilidade ao calor e pelo facto de os reforços serem extremamente abrasivos. A operação de furação pode causar grandes danos na peça, como a delaminação a entrada, defeitos de circularidade do furo, danos de origem térmica e a delaminação à saída que se apresenta como o mais frequente e indesejável. Com base nesses pressupostos é que este trabalho foi desenvolvido de forma a tentar obter processos simples para determinação e previsão de danos em polímeros reforçados com fibras (de carbono neste caso) de forma a precavê-los. De forma a conseguir estes objetivos, foram realizados ensaios de início de delaminação segundo a proposta de Lachaud et al. e ensaios de pin-bearing segundo a proposta de Khashaba et al. Foram também examinadas extensões de danos de acordo com o modelo de Fator de delaminação ajustado apresentado por Davim et al. A partir dos ensaios, de pin-bearing, realizados foram analisadas influências do material e geometria da broca, do avanço utilizado na furação e de diferentes orientações de empilhamentos de placas na delaminação de laminados compósitos e ainda a influências dessas variáveis na força de rutura por pin-bearing. As principais conclusões tiradas daqui são que a delaminação aumenta com o aumento do avanço, o que já era esperado, as brocas em carboneto de tungsténio são as mais recomendas para a furação do material em causa e que a delaminação é superior para a placa cross-ply quando comparada com placas unidirecionais. Para a situação de ensaios de início de delaminação foram analisadas as influências da variação da espessura não cortada por baixo da broca/punção, de diferentes geometrias de brocas, da alteração de velocidade de ensaio e diferentes orientações de empilhamentos de placas na força de início de delaminação. Deste ensaio as principais conclusões são que a força de início de delaminação aumenta com o aumenta da espessura não cortada e a influência da velocidade de ensaio altera com a variação das orientações de empilhamento.

Evolutive behavior towards cardiomyopathy of treated (nifurtimox or benznidazole) and untreated chronic chagasic patients

The aim of this work was to compare the evolution of chronic chagasic untreated patients (UTPs) with that of benznidazole or nifurtimox-treated patients (TPs). A longitudinal study from a low endemic area (Santa Fe city, Argentina) was performed during an average period of 14 years. Serological and parasitological analyses with clinical exams, ECG and X-chest ray were carried out. At the onset, 19/198 infected patients showed chagasic cardiomyopathy (CrChM) while 179 were asymptomatic. In this latter group the frequency of CrChM during the follow-up was lower in TPs compared with UTPs (3.2% vs 7%). Within the CrChM group, 2/5 TPs showed aggravated myopathy whereas this happened in 9/14 UTPs. Comparing the clinical evolution of all patients, 5.9% of TPs and 13% of UTPs had unfavourable evolution, but the difference is not statistically relevant. Serological titers were assessed by IIF. Titers equal to or lower than 1/64 were obtained in 86% of the TPs, but only in 38% of UTPs. The differences were statistically significant (geometric mean: 49.36 vs. 98.2). Antiparasitic assessment of the drugs (xenodiagnosis) proved to be effective. The low sensitivity in chronic chagasic patients must be born in mind. Despite treated patients showed a better clinical evolution and lower antibody levels than untreated ones, it is necessary to carry on doing research in order to improve therapeutic guidelines, according to the risk/benefit equation and based on scientific and ethical principles.

Brincando com formas geométricas e cores: Um pé no Triângulo… Uma mão no Pentágono...

Neste artigo é analisada a construção do conhecimento matemático num jardim de infância do Porto, através do jogo; em particular, tratamos as formas geométricas e os diagramas de Carroll. Estes temas foram abordados, de uma forma integrada, numa atividade que também envolveu a expressão motora. Esta estratégia revelou-se uma boa forma de motivar as crianças do grupo para conteúdos complexos. Debruçamo-nos neste artigo sobre as fases de observação, planificação, ação e avaliação da atividade. Concluímos que os objetivos traçados foram ao encontro das necessidades e interesses das crianças e que a atividade contribuiu para o seu desenvolvimento integral e integrado.