Dynamical analysis in growth models: Blumberg’s equation

We present a new dynamical approach to the Blumberg's equation, a family of unimodal maps. These maps are proportional to Beta(p, q) probability densities functions. Using the symmetry of the Beta(p, q) distribution and symbolic dynamics techniques, a new concept of mirror symmetry is defined for this family of maps. The kneading theory is used to analyze the effect of such symmetry in the presented models. The main result proves that two mirror symmetric unimodal maps have the same topological entropy. Different population dynamics regimes are identified, when the intrinsic growth rate is modified: extinctions, stabilities, bifurcations, chaos and Allee effect. To illustrate our results, we present a numerical analysis, where are demonstrated: monotonicity of the topological entropy with the variation of the intrinsic growth rate, existence of isentropic sets in the parameters space and mirror symmetry.

Lack of association between iron status at birth and growth of preterm infants

OBJECTIVE: To assess the association between iron status at birth and growth of preterm infants. METHODS: Ninety-five premature babies (26 to 36 weeks of gestational age) born from July 2000 to May 2001 in a public hospital in Rio de Janeiro, Southeastern Brazil, were followed up for six months, corrected by gestational age. Iron measurements at birth were available for 82 mothers and 78 children: hemoglobin, hematocrit, mean corpuscular volume and plasma iron. All children received free doses of iron supplement (2 mg/kg/day) during the follow-up period and up to two years of age. Multivariate linear regression analyses with repeated measurements were performed to assess factors associated to linear growth. RESULTS: Growth was more pronounced up to 40 weeks of gestational age, increasing about 1.0 cm/week and then slowing down to 0.75 cm/week. The multivariate analysis showed growth was positively associated with birth weight (0.4 cm/100 g; p<0.001) and negatively associated with gestational age at birth (-0.5 cm/week; p<0.001). There was no association between cord iron and mother iron measurements and growth (p>0.60 for all measures). Only two children had anemia at birth, whereas 43.9% of mothers were anemic (hemoglobin <11 g/dl). Also, there was no correlation between anemia indicators of mothers and children at birth (r<0.15; p>0.20). CONCLUSIONS: Maternal anemia was not associated with anemia in preterm infants and iron status of mothers and children at birth was not associated with short-term growth of preterm infants.

An Extension of Gompertzian Growth Dynamics Weibull and Frechet Models

In this work a new probabilistic and dynamical approach to an extension of the Gompertz law is proposed. A generalized family of probability density functions, designated by Beta* (p, q), which is proportional to the right hand side of the Tsoularis-Wallace model, is studied. In particular, for p = 2, the investigation is extended to the extreme value models of Weibull and Frechet type. These models, described by differential equations, are proportional to the hyper-Gompertz growth model. It is proved that the Beta* (2, q) densities are a power of betas mixture, and that its dynamics are determined by a non-linear coupling of probabilities. The dynamical analysis is performed using techniques of symbolic dynamics and the system complexity is measured using topological entropy. Generally, the natural history of a malignant tumour is reflected through bifurcation diagrams, in which are identified regions of regression, stability, bifurcation, chaos and terminus.

Topological Complexity and Predictability in the Dynamics of a Tumor Growth Model with Shilnikov's Chaos

Dynamical systems modeling tumor growth have been investigated to determine the dynamics between tumor and healthy cells. Recent theoretical investigations indicate that these interactions may lead to different dynamical outcomes, in particular to homoclinic chaos. In the present study, we analyze both topological and dynamical properties of a recently characterized chaotic attractor governing the dynamics of tumor cells interacting with healthy tissue cells and effector cells of the immune system. By using the theory of symbolic dynamics, we first characterize the topological entropy and the parameter space ordering of kneading sequences from one-dimensional iterated maps identified in the dynamics, focusing on the effects of inactivation interactions between both effector and tumor cells. The previous analyses are complemented with the computation of the spectrum of Lyapunov exponents, the fractal dimension and the predictability of the chaotic attractors. Our results show that the inactivation rate of effector cells by the tumor cells has an important effect on the dynamics of the system. The increase of effector cells inactivation involves an inverse Feigenbaum (i.e. period-halving bifurcation) scenario, which results in the stabilization of the dynamics and in an increase of dynamics predictability. Our analyses also reveal that, at low inactivation rates of effector cells, tumor cells undergo strong, chaotic fluctuations, with the dynamics being highly unpredictable. Our findings are discussed in the context of tumor cells potential viability.

Empreendedorismo Social, o papel das IPSS: estudo de caso

O empreendedorismo social tem vindo, nas últimas décadas, a ser denominado como um novo paradigma determinante para o funcionamento da economia, em grande parte, porque a economia social tornou-se basilar na sociedade, por um lado, pelo crescimento exponencial da exclusão social, elevado desemprego e envelhecimento da população e, por outro, devido às dificuldades orçamentais dos governos. O empreendedorismo social, utilizado por Instituições Particulares de Solidariedade Social sem fins lucrativos, procura resolver problemas sociais de forma inovadora e sustentável, com a finalidade de dar resposta aos grandes desafios sociais da atualidade, através da ação social na prevenção e no apoio nas diversas situações de fragilidade, exclusão ou carência humana, promovendo a inclusão, a integração social e o desenvolvimento local. O objetivo fundamental do presente trabalho, pretende verificar até que ponto as IPSS podem ser definidas como empreendedores sociais, através da prestação de serviços, nas variadas áreas à população local, de forma a alcançar o valor social. Neste estudo enveredou-se pela metodologia qualitativa, utilizando o método do estudo de caso único, recorrendo ao questionário como instrumento de recolha de dados numa instituição particular de solidariedade social do concelho da Maia. Deste estudo foi possível concluir a IPSS tem uma proximidade às populações, através das diversas valências vocacionadas para a resolução de problemas sociais emergentes, promovendo a inclusão a integração social, e alcançar o valor social. Assim, consideramos a IPSS estudada como sendo parte integrante e promotora do empreendedorismo social.

Phase growth control in low temperature PLD Co: TiO2 films by pressure

This paper reports on the structural and optical properties of Co-doped TiO2 thin films grown onto (0001)Al2O3 substrates by non-reactive pulsed laser deposition (PLD) using argon as buffer gas. It is shown that by keeping constant the substrate temperature at as low as 310 degrees C and varying only the background gas pressure between 7 Pa and 70 Pa, it is possible to grow either epitaxial rutile or pure anatase thin films, as well as films with a mixture of both polymorphs. The optical band gaps of the films are red shifted in comparison with the values usually reported for undoped TiO2, which is consistent with n-type doping of the TiO2 matrix. Such band gap red shift brings the absorption edge of the Co-doped TiO2 films into the visible region, which might favour their photocatalytic activity. Furthermore, the band gap red shift depends on the films' phase composition, increasing with the increase of the Urbach energy for increasing rutile content. (C) 2012 Elsevier B.V. All rights reserved.

Da escrita do nome à escrita de textos: estratégias de abordagem à escrita na educação Pré-Escolar e 1º ciclo do Ensino Básico

Mestrado (PES II), Educação Pré-Escolar e Ensino do 1º Ciclo do Ensino Básico, 27 de Junho de 2014, Universidade dos Açores.

Growth responses of Macrocystis pyrifera (Laminariales), Southern Chile, juvenile sporophytes to nutrient limitation

1st Mares Conference on Marine Ecosystems Health and Conservation. Olhão, Portugal 17-21 November 2014.

Mathematical education and interdisciplinarity : promoting public awareness of mathematics in the Azores

Mathematical literacy in Portugal is very unsatisfactory in what concerns international standards. Even more disturbingly, the Azores archipelago ranks as one of the worst regions of Portugal in this respect. We reason that the popularisation of Mathematics through interactive exhibitions and activities can contribute actively to disseminate mathematical knowledge, increase awareness of the importance of Mathematics in today’s world and change its negative perception by the majority of the citizens. Although a significant investment has been undertaken by the local regional government in creating several science centres for the popularisation of Science, there is no centre for the popularisation of Mathematics. We present our first steps towards bringing Mathematics to unconventional settings by means of hands-on activities. We describe in some detail three activities. One activity has to do with applying trigonometry to measure distances in Astronomy, which can also be applied to Earth objects. Another activity concerns the presence of numerical patterns in the Azorean flora. The third activity explores geometrical patterns in the Azorean cultural heritage. It is our understanding that the implementation of these and other easy-to-follow and challenging activities will contribute to the awareness of the importance and beauty of Mathematics.

Caracterização da matéria orgânica natural em águas para consumo humano

O tratamento de água para consumo humano tem por objectivos não só a sua qualidade em termos de parâmetros químicos e físicos, como também microbiológicos. Considerando que a MON pode afectar os sistemas de tratamento, a sua redução minimiza a formação de subprodutos de desinfecção, como por exemplo os trihalometanos e diminui o crescimento de microrganismos ao longo do sistema de distribuição. Nesse sentido tem havido recentemente uma grande evolução na investigação relativamente à remoção de matéria orgânica natural. O principal objectivo deste trabalho foi o de caracterizar a matéria orgânica presente na água bruta e ao longo do processo de tratamento, assim como a sua evolução sazonal. Os dados obtidos a partir desta caracterização poderão contribuir para uma futura optimização no processo de tratamento de águas de consumo. O processo utilizado baseou-se na sorção da matéria orgânica dissolvida em diferentes tipos de resinas de permuta iónica, DAX-8, DAX-4 e IRA-958, permitindo a sua separação em várias fracções: ácidos muito hidrofóbicos (VHA), ácidos ligeiramente hidrofóbicos (SHA), compostos hidrofílicos carregados (CHA) e hidrofílicos neutros (NEU). De acordo com os resultados obtidos apenas a fracção NEU demonstrou ter uma tendência sazonal, apresentando valores máximos no Verão, nos pontos de amostragem referentes à água bruta superficial (PA802) e água bruta superficial após pré-tratamento por filtração (PA800). Os valores de COD não mostraram uma variação sazonal para as amostras de água bruta superficial que rondaram os 2 mg C/L ao longo do período de amostragem (Julho a Outubro), durante o qual se verificou uma baixa pluviosidade e temperaturas médias muito semelhantes. Os compostos NEU predominam em todos os pontos de amostragem não apresentando uma tendência definida ao longo do tratamento. Observou-se uma diminuição das fracções SHA e CHA ao longo do tratamento. Não se pode indicar uma tendência definida relativamente à fracção VHA. Verifica-se globalmente uma diminuição do teor de MON ao longo do tratamento. Este trabalho demonstrou que na água bruta superficial existe uma predominância dos compostos NEU, seguidos dos SHA, dos VHA e finalmente dos compostos CHA. Na água bruta captada no sub-leito do rio, verifica-se apenas a existência dos compostos NEU, sendo as restantes fracções praticamente nulas. Os valores mais elevados de TSUVA254nm foram obtidos para as amostras que não sofreram qualquer tratamento, água bruta do sub-leito (PA903) e superficial (PA802), e água bruta após pré-filtração (PA800). Nos restantes pontos de amostragem, apesar de se verificarem valores inferiores, não se observa uma diminuição deste parâmetro ao longo do tratamento, nem uma variação sazonal. Os valores de TSUVA254nm obtidos são geralmente inferiores a 3 L.mgC-1.m-1, correspondendo a materiais não húmicos, que são considerados biodegradáveis. Para as amostras de água tratada os valores oscilam entre os 1,23 e 1,58 L.mgC-1.m-1, valores inferiores a 2 L.mgC-1.m-1, o que é considerado um valor de referência ao nível do tratamento, segundo a USEPA.

Growth patterns in early childhood and the onset of menarche before age twelve

OBJECTIVE: To examine the relationship between growth patterns in early childhood and the onset of menarche before age 12. METHODS: The study included 2,083 women from a birth cohort study conducted in the city of Pelotas, Southern Brazil, starting in 1982. Anthropometric, behavioral, and pregnancy-related variables were collected through home interviews. Statistical analyses were performed using Pearson's chi-square and chi-square test for linear trends. A multivariable analysis was carried out using Poisson regression based on a hierarchical model. RESULTS: Mean age of menarche was 12.4 years old and the prevalence of menarche before age 12 was 24.3%. Higher weight-for-age, height-for-age, and weight-for-height z-scores at 19.4 and 43.1 months of age were associated with linear tendencies of increased prevalence and relative risks of the onset of menarche before age 12. Girls who experienced rapid growth in weight-for-age z-score from birth to 19.4 months of age and in weight-for-age or height-for-age z-scores from 19.4 to 43.1 months of age also showed higher risk of menarche before age 12. Higher risk was seen when rapid growth in weight-for-age z-score was seen during these age intervals and the highest risk was found among those in the first tertile of Williams' curve at birth. Rapid growth in weight-for-height z-score was not associated with menarche before age 12. CONCLUSIONS: Menarche is affected by nutritional status and growth patterns during early childhood. Preventing overweight and obesity during early childhood and keeping a "normal" growth pattern seem crucial for the prevention of health conditions during adulthood.

Symphysis-fundal height curve in the diagnosis of fetal growth deviations

OBJECTIVE: To validate a new symphysis-fundal curve for screening fetal growth deviations and to compare its performance with the standard curve adopted by the Brazilian Ministry of Health. METHODS: Observational study including a total of 753 low-risk pregnant women with gestational age above 27 weeks between March to October 2006 in the city of João Pessoa, Northeastern Brazil. Symphisys-fundal was measured using a standard technique recommended by the Brazilian Ministry of Health. Estimated fetal weight assessed through ultrasound using the Brazilian fetal weight chart for gestational age was the gold standard. A subsample of 122 women with neonatal weight measurements was taken up to seven days after estimated fetal weight measurements and symphisys-fundal classification was compared with Lubchenco growth reference curve as gold standard. Sensitivity, specificity, positive and negative predictive values were calculated. The McNemar χ2 test was used for comparing sensitivity of both symphisys-fundal curves studied. RESULTS: The sensitivity of the new curve for detecting small for gestational age fetuses was 51.6% while that of the Brazilian Ministry of Health reference curve was significantly lower (12.5%). In the subsample using neonatal weight as gold standard, the sensitivity of the new reference curve was 85.7% while that of the Brazilian Ministry of Health was 42.9% for detecting small for gestational age. CONCLUSIONS: The diagnostic performance of the new curve for detecting small for gestational age fetuses was significantly higher than that of the Brazilian Ministry of Health reference curve.

Growth and Raman scattering characterization of Cu2ZnSnS4 thin films

In the present work we report the results of the growth, morphological and structural characterization of Cu2ZnSnS4 (CZTS) thin films prepared by sulfurization of DC magnetron sputtered Cu/Zn/Sn precursor layers. The adjustment of the thicknesses and the properties of the precursors were used to control the final composition of the films. Its properties were studied by SEM/EDS, XRD and Raman scattering. The influence of the sulfurization temperature on the morphology, composition and structure of the films has been studied. With the presented method we have been able to prepare CZTS thin films with the kesterite structure.

Growth pressure dependence of Cu2ZnSnSe4 properties

In this work, we show a set of growth conditions, for the two step process, with which the growth of CZTSe is successful and reproducible. The properties of the best CTZSe thin films grown by this method were examined by SEM/EDS, XRD, Raman scattering, AFM/EFM, transmittance and reflectance measurements, photoluminescence (PL) measurements and hot point probe. A broad emission band was observed in the photoluminescence spectrum of the CZTSe thin film. The band gap energy was estimated to be around 1.05 eV at room temperature, using the transmittance and reflectance data, and CZTSe samples show p-type conductivity with the hot point probe. The different characterization techniques show that we could grow single phase CZTSe thin films with our optimized process conditions.

Influence of selenization pressure on the growth of Cu2ZnSnSe4 films from stacked metallic layers

Cu2ZnSnSe4 (CZTSe) is a p-type semiconductor with a high absorption coefficient, 104 to 105 cm-1, and is being seen as a possible replacement for Cu(In,Ga)Se2 in thin film solar cells. Yet, there are some fundamental properties of CZTSe that are not well known, one of them is its band gap. In order to resolve its correct value it is necessary to improve the growth conditions to ensure that single phase crystalline thin films are obtained. One of the problems encountered when growing CZTSe is the loss of Sn through evaporation of SnSe. Stoichiometric films are then difficult to obtain and usually there are other phases present. One possible way to overcome this problem is to increase the pressure of growth of CZTSe. This can be done by introducing an atmosphere of an inert gas like Ar or N2. In this work we report the results of morphological, structural and optical studies of the properties of CZTSe thin films grown by selenization of DC magnetron sputtered metallic layers under different Ar pressures. The films are analysed by SEM/EDS, Raman scattering and XRD.