Strabismus, visual acuity, and uncorrected refractive error in Portuguese children aged 6 to 11 years

Introduction: Visual anomalies that affect school-age children represent an important public health problem. Data on the prevalence are lacking in Portugal but is needed for planning vision services. This study was conducted to determine the prevalence of strabismus, decreased visual acuity, and uncorrected refractive error in Portuguese children aged 6 to 11 years. Methods and materials: A cross-sectional study was carried out on a sample of 672 school-age children (7.69 ± 1.19 years). Children received an orthoptic assessment (visual acuity, ocular alignment, and ocular movements) and non-cycloplegic autorefraction. Results: After orthoptic assessment, 13.8% of children were considered abnormal (n = 93). Manifest strabismus was found in 4% of the children. Rates of esotropia (2.1%) were slightly higher than exotropia (1.8%). Strabismus rates were not statistically significant different per sex (p = 0.681) and grade (p = 0.228). Decreased visual acuity at distance was present in 11.3% of children. Visual acuity ≤20/66 (0.5 logMAR) was found in 1.3% of the children. We also found that 10.3% of children had an uncorrected refractive error. Conclusions: Strabismus affects a small proportion of the Portuguese school-age children. Decreased visual acuity and uncorrected refractive error affected a significant proportion of school-age children. New policies need to be developed to address this public health problem.

Power law analysis of financial index dynamics

Power law PL and fractional calculus are two faces of phenomena with long memory behavior. This paper applies PL description to analyze different periods of the business cycle. With such purpose the evolution of ten important stock market indices DAX, Dow Jones, NASDAQ, Nikkei, NYSE, S&P500, SSEC, HSI, TWII, and BSE over time is studied. An evolutionary algorithm is used for the fitting of the PL parameters. It is observed that the PL curve fitting constitutes a good tool for revealing the signal main characteristics leading to the emergence of the global financial dynamic evolution.

Evaluation of maternal and neonatal hospital care: quality index of completeness

OBJECTIVE Develop an index to evaluate the maternal and neonatal hospital care of the Brazilian Unified Health System.METHODS This descriptive cross-sectional study of national scope was based on the structure-process-outcome framework proposed by Donabedian and on comprehensive health care. Data from the Hospital Information System and the National Registry of Health Establishments were used. The maternal and neonatal network of Brazilian Unified Health System consisted of 3,400 hospitals that performed at least 12 deliveries in 2009 or whose number of deliveries represented 10.0% or more of the total admissions in 2009. Relevance and reliability were defined as criteria for the selection of variables. Simple and composite indicators and the index of completeness were constructed and evaluated, and the distribution of maternal and neonatal hospital care was assessed in different regions of the country.RESULTS A total of 40 variables were selected, from which 27 single indicators, five composite indicators, and the index of completeness of care were built. Composite indicators were constructed by grouping simple indicators and included the following variables: hospital size, level of complexity, delivery care practice, recommended hospital practice, and epidemiological practice. The index of completeness of care grouped the five variables and classified them in ascending order, thereby yielding five levels of completeness of maternal and neonatal hospital care: very low, low, intermediate, high, and very high. The hospital network was predominantly of small size and low complexity, with inadequate child delivery care and poor development of recommended and epidemiological practices. The index showed that more than 80.0% hospitals had a low index of completeness of care and that most qualified heath care services were concentrated in the more developed regions of the country.CONCLUSIONS The index of completeness proved to be of great value for monitoring the maternal and neonatal hospital care of Brazilian Unified Health System and indicated that the quality of health care was unsatisfactory. However, its application does not replace specific evaluations.

Matching CO2 large point sources and potential geological storage sites in mainland Portugal

Dissertação apresentada na Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa para obtenção do grau de Mestre em Engenharia do Ambiente, Perfil Gestão e Sistemas Ambientais

Effect of the exposure to maternal smoking during pregnancy and childhood on the body mass index until adolescence

OBJECTIVE Investigate the effect of exposure to smoking during pregnancy and early childhood on changes in the body mass index (BMI) from birth to adolescence.METHODS A population-based cohort of children (0-5 years old) from Cuiabá, Midwest Brazil, was assessed in 1999-2000 (n = 2,405). Between 2009 and 2011, the cohort was re-evaluated. Information about birth weight was obtained from medical records, and exposure to smoking during pregnancy and childhood was assessed at the first interview. Linear mixed effects models were used to estimate the association between exposure to maternal smoking during pregnancy and preschool age, and the body mass index of children at birth, childhood and adolescence.RESULTS Only 11.3% of the mothers reported smoking during pregnancy, but most of them (78.2%) also smoked during early childhood. Among mothers who smoked only during pregnancy (n = 59), 97.7% had smoked only in the first trimester. The changes in body mass index at birth and in childhood were similar for children exposed and those not exposed to maternal smoking. However, from childhood to adolescence the rate of change in the body mass index was higher among those exposed only during pregnancy than among those who were not exposed.CONCLUSIONS Exposure to smoking only during pregnancy, especially in the first trimester, seems to affect changes in the body mass index until adolescence, supporting guidelines that recommend women of childbearing age to stop smoking.

Evaluation of the influence of testing parameters on the melt flow index of thermoplastics

The main goals of the present work are the evaluation of the influence of several variables and test parameters on the melt flow index (MFI) of thermoplastics, and the determination of the uncertainty associated with the measurements. To evaluate the influence of test parameters on the measurement of MFI the design of experiments (DOE) approach has been used. The uncertainty has been calculated using a "bottom-up" approach given in the "Guide to the Expression of the Uncertainty of Measurement" (GUM). Since an analytical expression relating the output response (MFI) with input parameters does not exist, it has been necessary to build mathematical models by adjusting the experimental observations of the response variable in accordance with each input parameter. Subsequently, the determination of the uncertainty associated with the measurement of MFI has been performed by applying the law of propagation of uncertainty to the values of uncertainty of the input parameters. Finally, the activation energy (Ea) of the melt flow at around 200 degrees C and the respective uncertainty have also been determined.

Behavioural development in a matching-to-sample task and token use by an infant chimpanzee reared by his mother

Animal Cognition, V.6, pp. 259–267

Evaluating the combination of relaxation and argumentation in ontology matching negotiation

No decorrer dos últimos anos, os agentes (inteligentes) de software foram empregues como um método para colmatar as dificuldades associadas com a gestão, partilha e reutilização de um crescente volume de informação, enquanto as ontologias foram utilizadas para modelar essa mesma informação num formato semanticamente explícito e rico. À medida que a popularidade da Web Semântica aumenta e cada vez informação é partilhada sob a forma de ontologias, o problema de integração desta informação amplifica-se. Em semelhante contexto, não é expectável que dois agentes que pretendam cooperar utilizem a mesma ontologia para descrever a sua conceptualização do mundo. Inclusive pode revelar-se necessário que agentes interajam sem terem conhecimento prévio das ontologias utilizadas pelos restantes, sendo necessário que as conciliem em tempo de execução num processo comummente designado por Mapeamento de Ontologias [1]. O processo de mapeamento de ontologias é normalmente oferecido como um serviço aos agentes de negócio, podendo ser requisitado sempre que seja necessário produzir um alinhamento. No entanto, tendo em conta que cada agente tem as suas próprias necessidades e objetivos, assim como a própria natureza subjetiva das ontologias que utilizam, é possível que tenham diferentes interesses relativamente ao processo de alinhamento e que, inclusive, recorram aos serviços de mapeamento que considerem mais convenientes [1]. Diferentes matchers podem produzir resultados distintos e até mesmo contraditórios, criando-se assim conflitos entre os agentes. É necessário que se proceda então a uma tentativa de resolução dos conflitos existentes através de um processo de negociação, de tal forma que os agentes possam chegar a um consenso relativamente às correspondências que devem ser utilizadas na tradução de mensagens a trocar. A resolução de conflitos é considerada uma métrica de grande importância no que diz respeito ao processo de negociação [2]: considera-se que existe uma maior confiança associada a um alinhamento quanto menor o número de conflitos por resolver no processo de negociação que o gerou. Desta forma, um alinhamento com um número elevado de conflitos por resolver apresenta uma confiança menor que o mesmo alinhamento associado a um número elevado de conflitos resolvidos. O processo de negociação para que dois ou mais agentes gerem e concordem com um alinhamento é denominado de Negociação de Mapeamentos de Ontologias. À data existem duas abordagens propostas na literatura: (i) baseadas em Argumentação (e.g. [3] [4]) e (ii) baseadas em Relaxamento [5] [6]. Cada uma das propostas expostas apresenta um número de vantagens e limitações. Foram propostas várias formas de combinação das duas técnicas [2], com o objetivo de beneficiar das vantagens oferecidas e colmatar as suas limitações. No entanto, à data, não são conhecidas experiências documentadas que possam provar tal afirmação e, como tal, não é possível atestar que tais combinações tragam, de facto, o benefício que pretendem. O trabalho aqui apresentado pretende providenciar tais experiências e verificar se a afirmação de melhorias em relação aos resultados das técnicas individuais se mantém. Com o objetivo de permitir a combinação e de colmatar as falhas identificadas, foi proposta uma nova abordagem baseada em Relaxamento, que é posteriormente combinada com as abordagens baseadas em Argumentação. Os seus resultados, juntamente com os da combinação, são aqui apresentados e discutidos, sendo possível identificar diferenças nos resultados gerados por combinações diferentes e possíveis contextos de utilização.

Análise da acuidade visual no implante de LIO fáquica em miopias elevadas

Introdução – Na correção de miopias elevadas, a cirurgia por implante de lente intraocular fáquica tem tido progressivamente uma maior adesão em relação à cirurgia por laser. Compara-se a acuidade visual (AV) antes e após a cirurgia implanto-refrativa, verificando-se a efetividade deste método no incremento da visão em miopias elevadas. Metodologia – Foram analisados, retrospetivamente, 70 olhos de 41 pacientes, com miopia elevada, entre os 20 e 50 anos, submetidos a cirurgia implanto-refrativa entre 2009 e 2012. Resultados – Um dia após cirurgia, 42,86% da amostra melhorou a AV, 34,29% manteve e 22,85% diminuiu. Após 30 dias observou-se um aumento generalizado da quantidade de visão, sendo que: 64,29% atingiu os 10/10 de AV, 24,29% alcançou entre 9/10-7/10 e 11,42% entre 6/10-4/10. Conclusão – Comprovou-se a efetividade desta técnica cirúrgica, verificando-se o aumento da AV em 52,86% da amostra.

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.

Vertex component analysis: a geometric-based approach to unmix hyperspectral data

Hyperspectral remote sensing exploits the electromagnetic scattering patterns of the different materials at specific wavelengths [2, 3]. Hyperspectral sensors have been developed to sample the scattered portion of the electromagnetic spectrum extending from the visible region through the near-infrared and mid-infrared, in hundreds of narrow contiguous bands [4, 5]. The number and variety of potential civilian and military applications of hyperspectral remote sensing is enormous [6, 7]. Very often, the resolution cell corresponding to a single pixel in an image contains several substances (endmembers) [4]. In this situation, the scattered energy is a mixing of the endmember spectra. A challenging task underlying many hyperspectral imagery applications is then decomposing a mixed pixel into a collection of reflectance spectra, called endmember signatures, and the corresponding abundance fractions [8–10]. Depending on the mixing scales at each pixel, the observed mixture is either linear or nonlinear [11, 12]. Linear mixing model holds approximately when the mixing scale is macroscopic [13] and there is negligible interaction among distinct endmembers [3, 14]. If, however, the mixing scale is microscopic (or intimate mixtures) [15, 16] and the incident solar radiation is scattered by the scene through multiple bounces involving several endmembers [17], the linear model is no longer accurate. Linear spectral unmixing has been intensively researched in the last years [9, 10, 12, 18–21]. It considers that a mixed pixel is a linear combination of endmember signatures weighted by the correspondent abundance fractions. Under this model, and assuming that the number of substances and their reflectance spectra are known, hyperspectral unmixing is a linear problem for which many solutions have been proposed (e.g., maximum likelihood estimation [8], spectral signature matching [22], spectral angle mapper [23], subspace projection methods [24,25], and constrained least squares [26]). In most cases, the number of substances and their reflectances are not known and, then, hyperspectral unmixing falls into the class of blind source separation problems [27]. Independent component analysis (ICA) has recently been proposed as a tool to blindly unmix hyperspectral data [28–31]. ICA is based on the assumption of mutually independent sources (abundance fractions), which is not the case of hyperspectral data, since the sum of abundance fractions is constant, implying statistical dependence among them. This dependence compromises ICA applicability to hyperspectral images as shown in Refs. [21, 32]. In fact, ICA finds the endmember signatures by multiplying the spectral vectors with an unmixing matrix, which minimizes the mutual information among sources. If sources are independent, ICA provides the correct unmixing, since the minimum of the mutual information is obtained only when sources are independent. This is no longer true for dependent abundance fractions. Nevertheless, some endmembers may be approximately unmixed. These aspects are addressed in Ref. [33]. Under the linear mixing model, the observations from a scene are in a simplex whose vertices correspond to the endmembers. Several approaches [34–36] have exploited this geometric feature of hyperspectral mixtures [35]. Minimum volume transform (MVT) algorithm [36] determines the simplex of minimum volume containing the data. The method presented in Ref. [37] is also of MVT type but, by introducing the notion of bundles, it takes into account the endmember variability usually present in hyperspectral mixtures. The MVT type approaches are complex from the computational point of view. Usually, these algorithms find in the first place the convex hull defined by the observed data and then fit a minimum volume simplex to it. For example, the gift wrapping algorithm [38] computes the convex hull of n data points in a d-dimensional space with a computational complexity of O(nbd=2cþ1), where bxc is the highest integer lower or equal than x and n is the number of samples. The complexity of the method presented in Ref. [37] is even higher, since the temperature of the simulated annealing algorithm used shall follow a log( ) law [39] to assure convergence (in probability) to the desired solution. Aiming at a lower computational complexity, some algorithms such as the pixel purity index (PPI) [35] and the N-FINDR [40] still find the minimum volume simplex containing the data cloud, but they assume the presence of at least one pure pixel of each endmember in the data. 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. PPI algorithm uses the minimum noise fraction (MNF) [41] as a preprocessing step to reduce dimensionality and to improve the signal-to-noise ratio (SNR). The algorithm then projects every spectral vector onto skewers (large number of random vectors) [35, 42,43]. The points corresponding to extremes, for each skewer direction, are stored. A cumulative account records the number of times each pixel (i.e., a given spectral vector) is found to be an extreme. The pixels with the highest scores are the purest ones. N-FINDR algorithm [40] is based on the fact that in p spectral dimensions, the p-volume defined by a simplex formed by the purest pixels is larger than any other volume defined by any other combination of pixels. This algorithm finds the set of pixels defining the largest volume by inflating a simplex inside the data. ORA SIS [44, 45] is a hyperspectral framework developed by the U.S. Naval Research Laboratory consisting of several algorithms organized in six modules: exemplar selector, adaptative learner, demixer, knowledge base or spectral library, and spatial postrocessor. The first step consists in flat-fielding the spectra. Next, the exemplar selection module is used to select spectral vectors that best represent the smaller convex cone containing the data. The other pixels are rejected when the spectral angle distance (SAD) is less than a given thresh old. The procedure finds the basis for a subspace of a lower dimension using a modified Gram–Schmidt orthogonalizati on. The selected vectors are then projected onto this subspace and a simplex is found by an MV T pro cess. ORA SIS is oriented to real-time target detection from uncrewed air vehicles using hyperspectral data [46]. In this chapter we develop a new algorithm to unmix linear mixtures of endmember spectra. First, the algorithm determines the number of endmembers and the signal subspace using a newly developed concept [47, 48]. Second, the algorithm extracts the most pure pixels present in the data. Unlike other methods, this algorithm is completely automatic and unsupervised. To estimate the number of endmembers and the signal subspace in hyperspectral linear mixtures, the proposed scheme begins by estimating sign al and noise correlation matrices. The latter is based on multiple regression theory. The signal subspace is then identified by selectin g the set of signal eigenvalue s that best represents the data, in the least-square sense [48,49 ], we note, however, that VCA works with projected and with unprojected data. The extraction of the end members exploits two facts: (1) the endmembers are the vertices of a simplex and (2) the affine transformation of a simplex is also a simplex. As PPI and N-FIND R algorithms, VCA also assumes the presence of pure pixels in the data. The algorithm iteratively projects data on to a direction orthogonal to the subspace spanned by the endmembers already determined. The new end member signature corresponds to the extreme of the projection. The algorithm iterates until all end members are exhausted. VCA performs much better than PPI and better than or comparable to N-FI NDR; yet it has a computational complexity between on e and two orders of magnitude lower than N-FINDR. The chapter is structure d as follows. Section 19.2 describes the fundamentals of the proposed method. Section 19.3 and Section 19.4 evaluate the proposed algorithm using simulated and real data, respectively. Section 19.5 presents some concluding remarks.

Burrows-wheeler transform in secondary memory

Master’s Thesis in Computer Engineering

Developing and implementing an environmental performance index for the Portuguese military

Business Strategy and the Environment nº 15, p. 71–86

Milk intake is inversely related to body mass index and body fat in girls

Dairy foods comprise a range of products with varying nutritional content. The intake of dairy products (DPs) has been shown to have beneficial effects on body weight and body fat. This study aimed to examine the independent association between DP intake, body mass index (BMI), and percentage body fat (%BF) in adolescents. A cross-sectional, school-based study was conducted with 1,001 adolescents (418 boys), ages 15–18 years, from the Azorean Archipelago, Portugal. Anthropometric measurements were recorded (weight and height), and %BF was assessed using bioelectric impedance analysis. Adolescent food intake was measured using a self-administered, semiquantitative food frequency questionnaire. Data were analyzed separately for girls and boys, and separate multiple linear regression analysis was used to estimate the association between total DP, milk, yogurt, and cheese intake, BMI, and %BF, adjusting for potential confounders. For boys and girls, respectively, total DP consumption was 2.6 ± 1.9 and 2.9 ± 2.5 servings/day (P = 0.004), while milk consumption was 1.7 ± 1.4 and 2.0 ± 1.7 servings/day (P = 0.001), yogurt consumption was 0.5 ± 0.6 and 0.4 ± 0.7 servings/day (P = 0.247), and cheese consumption was 0.4 ± 0.6 and 0.5 ± 0.8 servings/day (P = 0.081). After adjusting for age, birth weight, energy intake, protein, total fat, sugar, dietary fiber, total calcium intake, low-energy reporters, parental education, pubertal stage, and physical activity, only milk intake was negatively associated with BMI and %BF in girls (respectively, girls: β = −0.167, P = 0.013; boys: β = −0.019, P = 0.824 and girls: β = −0.143, P = 0.030; boys: β = −0.051, P = 0.548). Conclusion: We found an inverse association between milk intake and both BMI and %BF only in girls.

An efficient numerical scheme for solving multi-dimensional fractional optimal control problems with a quadratic performance index

The shifted Legendre orthogonal polynomials are used for the numerical solution of a new formulation for the multi-dimensional fractional optimal control problem (M-DFOCP) with a quadratic performance index. The fractional derivatives are described in the Caputo sense. The Lagrange multiplier method for the constrained extremum and the operational matrix of fractional integrals are used together with the help of the properties of the shifted Legendre orthonormal polynomials. The method reduces the M-DFOCP to a simpler problem that consists of solving a system of algebraic equations. For confirming the efficiency and accuracy of the proposed scheme, some test problems are implemented with their approximate solutions.