Thesis advisor: Henry Braun / Given the call for greater understanding of racial inequality in student achievement in K-12 education, this study contributes a comprehensive, quantitative, longitudinal examination of the achievement gap phenomenon, with particular attention to the organization characteristics of schools and school districts. Employing data from a large number of districts in a single state, it examines the trends in achievement and the growth in achievement after the passage of NCLB. It focuses on mathematics performance from grade 6 to grade 8. Both a traditional descriptive approach and one employing Hierarchical Linear Models were applied and compared. The purpose was not to determine which methodology is superior but to provide complementary perspectives. The comparison between the two approaches revealed similar trends in achievement gaps, but the HLM approach offered a more nuanced description. Nonetheless the results suggest that it is useful to employ both approaches. As to the main question regarding ethnicity, it appears that even if student ethnicity is confounded with other indicators, such as initial score and socio-economic status, it is still an important predictor of both achievement gaps and achievement growth gaps. Moreover, demographic profiles at the school and district levels were also associated with these gaps. / Thesis (PhD) — Boston College, 2009. / Submitted to: Boston College. Lynch School of Education. / Discipline: Educational Research, Measurement, and Evaluation.

[pt] Alguns difeomorfismos de superfícies fechadas possuem apenas medidas invariantes triviais, isto é, medidas cujo suporte está contido no conjunto de pontos fixos. Resultados dessa natureza fazem uso fundamental da classificação dos homeomorfismos de superfície, tornando-os típicos da dimensão 2. Nós atacamos esse problema mostrando que difeomorfismos de superfícies que admitem medidas invariantes não-triviais exibem uma forma de crescimento linear positivo. As técnicas utilizadas são elementares e uma parte significativa dos resultados continua válida em dimensões mais altas. / [en] Some diffeomorphisms of closed surfaces only have trivial invariant probabilities, i.e., those supported on the set of fixed points. Results of this nature make extensive use of the classification of surface homeomorphisms, making them typical of dimension 2. We attack this problem by showing that surface diffeomorphisms admiting non-trivial invariant probabilities exhibit some sort of positive linear growth. The techniques used are elementary and a significant part of the results remains valid in higher dimensions.

Preeclampsia is a placental-related disorder characterized by generalized endothelial activation. Vascular predisposition is associated with the occurrence of preeclampsia and the recurrence risk is substantial. Onset of preeclampsia is preceded by placental hypo-perfusion, and placental over-production of vasoconstrictive agents might explain symptoms such as hypertension and proteinuria. Preeclampsia is associated with the birth of small-for-gestational-age (SGA) infants. The trajectory of postnatal growth in SGA-born children is described as catch-up, but it is unclear whether prenatal preeclampsia is independently associated with postnatal growth. The objectives were: firstly, to study the association between partner change and prior miscarriages on the occurrence of preeclampsia and SGA; secondly, to study postnatal growth in children prenatally exposed to preeclampsia; and thirdly, to address the association between blood pressure (BP) changes during pregnancy and risks of preeclampsia and SGA. Population-based cohort studies were performed with information from the following registers: Swedish Medical Birth Register, Uppsala Mother and Child Database and Stockholm-Gotland Obstetric Database. Associations were estimated with logistic and linear regression analyses, with adjustments for maternal characteristics, including body mass index, pre-gestational diseases and socioeconomic factors. The results were, firstly, that partner change was associated with preeclampsia and SGA birth in the second pregnancy but depended on the outcome of the first pregnancy, and that a history of recurrent miscarriages was associated with increased risks of preeclampsia and SGA. Secondly, prenatal exposure to preeclampsia was associated with increased offspring growth in height during the first five years. This association was also seen in children born with normal birth weight for gestational age. Thirdly, pre-hypertension in late gestation and elevated diastolic BP from early to mid-gestation were both associated with SGA birth. Further, women with pre-hypertension in early gestation without lowered diastolic BP until mid-gestation seemed to represent a risk group for preeclampsia. To conclude, the importance of previous pregnancy outcomes in the antenatal risk evaluation was highlighted. Secondly, the results imply that postnatal growth trajectory is related to maternal preeclampsia, in addition to SGA. Thirdly, the association between BP changes within a normal range and SGA may challenge the clinical cut-off for hypertension in pregnancy.

Introdução: Investigações sobre o crescimento linear e o ganho de peso durante a infância em regiões de baixa e média renda são relevantes ao avanço do conhecimento científico e ao planejamento de ações para promoção da saúde no contexto de transição nutricional que afeta tais áreas. Objetivo: Investigar determinantes do crescimento linear e ganho de peso de crianças residentes no município de Acrelândia, Estado do Acre, Amazônia Ocidental Brasileira. Métodos: O presente estudo longitudinal de base populacional foi constituído a partir de dois inquéritos transversais de base populacional conduzidos em 2003 e 2007, com dois inquéritos de seguimento realizados em 2009 e 2012. Foram realizadas entrevistas domiciliares para levantamento de informações sociodemográficas, características maternas e morbidade recente da criança, além de coleta de amostra de sangue e exame antropométrico. Os desfechos de interesse foram a variação em escores Z de altura e índice de massa corporal (IMC) para idade. Utilizaram-se modelos de regressão linear mistos para a análise dos dados longitudinais. Resultados: Os principais determinantes do crescimento linear mensurado em escores Z de altura para idade durante a infância foram o índice de riqueza domiciliar e a posse de terra, além da altura materna e de peso e comprimento da criança ao nascer. O ganho de peso verificado por escores Z de IMC para idade foi positivamente associado ao índice de riqueza domiciliar e ao IMC materno até os 10 anos de idade. Houve associação positiva entre estado inflamatório de baixo grau na linha de base do estudo (definido por maiores concentrações de proteína C-reativa até 1 mg/L) e incremento em escores Z de IMC para idade durante o seguimento entre crianças a partir de 5 anos de idade. O alelo de risco do gene associado à massa gorda e obesidade (FTO rs9939609) relacionou-se a maior ganho em escores Z de IMC para idade durante a infância, com modificação de efeito pelo estado inicial de vitamina D, com papel genético mais pronunciado entre crianças com concentrações ! insuficientes de vitamina D. O aumento em escores Z de IMC durante a idade escolar foi também associado à resistência à insulina nas crianças estudadas. Conclusão: Em uma área de baixa renda, confirmou-se a influência do contexto socioeconômico e de fatores intergeracionais representados por características maternas sobre o crescimento linear e o ganho de peso na infância. O incremento de peso foi influenciado também por um cenário em que deficiências de micronutrientes, elevada morbidade e interação entre fatores genéticos e nutricionais coexistem com panorama crescente de sobrepeso e obesidade. / Background: Investigations on linear growth and weight gain during childhood in low- to middle-income regions are relevant to scientific knowledge and for the planning of actions focused on health promotion in the context of nutrition transition that affects such areas. Objective: To investigate determinants of linear growth and weight gain among children residing in the town of Acrelândia, Acre State, Western Brazilian Amazon. Methods: This population-based longitudinal study comprised two population-based cross-sectional surveys conducted in 2003 and 2007, and two follow-up assessments conducted in 2009 and 2012. Household interviews collected data on sociodemographic information, maternal characteristics, and childs recent morbidity. Children were also invited for blood sample collection and anthropometric evaluation. Outcomes of interest were change in height for age and body mass index (BMI) for age Z scores. Mixed-effect linear regression models were used in longitudinal data analysis. Results: Main determinants of linear growth in height for age Z scores during childhood were household wealth index and land ownership, as well as maternal height and childs birth weight and length. Weight gain ascertained with BMI for age Z scores was positively associated with household wealth and maternal BMI up to age 10 years. Baseline low-grade inflammatory status (defined as C-reactive protein concentrations up to 1 mg/L) was related to a higher gain in BMI for age Z scores during follow-up among children aged >5 years. Each risk allele of the fat mass and obesity associated gene (FTO rs9939609) was related to a higher increase in BMI for age Z score during childhood, with a significant interaction with baseline vitamin D status, with more pronounced genetic effects among children with vitamin D insufficiency. The increase in BMI for age Z scores during school-aged years was also associated with insulin resistance in children. Conclusion: In a low-income area, we confirmed the influence of the socioeconomic context and intergenerational factors represented by maternal ! characteristics on linear growth and weight gain during childhood. Increases in weight were also influenced by a scenario where micronutrient deficiencies, high morbidity, and interaction between genetic and nutritional factors are coupled with a rising panorama of overweight and obesity.

In this dissertation we will address two types of homogenization problems. The first one is a spectral problem in the realm of lower dimensional theories, whose physical motivation is the study of waves propagation in a domain of very small thickness and where it is introduced a very thin net of heterogeneities. Precisely, we consider an elliptic operator with "ε-periodic coefficients and the corresponding Dirichlet spectral problem in a three-dimensional bounded domain of small thickness δ. We study the asymptotic behavior of the spectrum as ε and δ tend to zero. This asymptotic behavior depends crucially on whether ε and δ are of the same order (δ ≈ ε), or ε is of order smaller than that of δ (δ = ετ , τ < 1), or ε is of order greater than that of δ (δ = ετ , τ > 1). We consider all three cases. The second problem concerns the study of multiscale homogenization problems with linear growth, aimed at the identification of effective energies for composite materials in the presence of fracture or cracks. Precisely, we characterize (n+1)-scale limit pairs (u,U) of sequences {(uεLN⌊Ω,Duε⌊Ω)}ε>0 ⊂ M(Ω;ℝd) × M(Ω;ℝd×N) whenever {uε}ε>0 is a bounded sequence in BV (Ω;ℝd). Using this characterization, we study the asymptotic behavior of periodically oscillating functionals with linear growth, defined in the space BV of functions of bounded variation and described by n ∈ ℕ microscales

Introdução: Investigações sobre o crescimento linear e o ganho de peso durante a infância em regiões de baixa e média renda são relevantes ao avanço do conhecimento científico e ao planejamento de ações para promoção da saúde no contexto de transição nutricional que afeta tais áreas. Objetivo: Investigar determinantes do crescimento linear e ganho de peso de crianças residentes no município de Acrelândia, Estado do Acre, Amazônia Ocidental Brasileira. Métodos: O presente estudo longitudinal de base populacional foi constituído a partir de dois inquéritos transversais de base populacional conduzidos em 2003 e 2007, com dois inquéritos de seguimento realizados em 2009 e 2012. Foram realizadas entrevistas domiciliares para levantamento de informações sociodemográficas, características maternas e morbidade recente da criança, além de coleta de amostra de sangue e exame antropométrico. Os desfechos de interesse foram a variação em escores Z de altura e índice de massa corporal (IMC) para idade. Utilizaram-se modelos de regressão linear mistos para a análise dos dados longitudinais. Resultados: Os principais determinantes do crescimento linear mensurado em escores Z de altura para idade durante a infância foram o índice de riqueza domiciliar e a posse de terra, além da altura materna e de peso e comprimento da criança ao nascer. O ganho de peso verificado por escores Z de IMC para idade foi positivamente associado ao índice de riqueza domiciliar e ao IMC materno até os 10 anos de idade. Houve associação positiva entre estado inflamatório de baixo grau na linha de base do estudo (definido por maiores concentrações de proteína C-reativa até 1 mg/L) e incremento em escores Z de IMC para idade durante o seguimento entre crianças a partir de 5 anos de idade. O alelo de risco do gene associado à massa gorda e obesidade (FTO rs9939609) relacionou-se a maior ganho em escores Z de IMC para idade durante a infância, com modificação de efeito pelo estado inicial de vitamina D, com papel genético mais pronunciado entre crianças com concentrações ! insuficientes de vitamina D. O aumento em escores Z de IMC durante a idade escolar foi também associado à resistência à insulina nas crianças estudadas. Conclusão: Em uma área de baixa renda, confirmou-se a influência do contexto socioeconômico e de fatores intergeracionais representados por características maternas sobre o crescimento linear e o ganho de peso na infância. O incremento de peso foi influenciado também por um cenário em que deficiências de micronutrientes, elevada morbidade e interação entre fatores genéticos e nutricionais coexistem com panorama crescente de sobrepeso e obesidade. / Background: Investigations on linear growth and weight gain during childhood in low- to middle-income regions are relevant to scientific knowledge and for the planning of actions focused on health promotion in the context of nutrition transition that affects such areas. Objective: To investigate determinants of linear growth and weight gain among children residing in the town of Acrelândia, Acre State, Western Brazilian Amazon. Methods: This population-based longitudinal study comprised two population-based cross-sectional surveys conducted in 2003 and 2007, and two follow-up assessments conducted in 2009 and 2012. Household interviews collected data on sociodemographic information, maternal characteristics, and childs recent morbidity. Children were also invited for blood sample collection and anthropometric evaluation. Outcomes of interest were change in height for age and body mass index (BMI) for age Z scores. Mixed-effect linear regression models were used in longitudinal data analysis. Results: Main determinants of linear growth in height for age Z scores during childhood were household wealth index and land ownership, as well as maternal height and childs birth weight and length. Weight gain ascertained with BMI for age Z scores was positively associated with household wealth and maternal BMI up to age 10 years. Baseline low-grade inflammatory status (defined as C-reactive protein concentrations up to 1 mg/L) was related to a higher gain in BMI for age Z scores during follow-up among children aged >5 years. Each risk allele of the fat mass and obesity associated gene (FTO rs9939609) was related to a higher increase in BMI for age Z score during childhood, with a significant interaction with baseline vitamin D status, with more pronounced genetic effects among children with vitamin D insufficiency. The increase in BMI for age Z scores during school-aged years was also associated with insulin resistance in children. Conclusion: In a low-income area, we confirmed the influence of the socioeconomic context and intergenerational factors represented by maternal ! characteristics on linear growth and weight gain during childhood. Increases in weight were also influenced by a scenario where micronutrient deficiencies, high morbidity, and interaction between genetic and nutritional factors are coupled with a rising panorama of overweight and obesity.

This thesis concerns the boundary behavior of solutions to parabolic equations. It consists of a comprehensive summary and four scientific papers. The equations concerned are different generalizations of the heat equation. Paper I concerns the solutions to non-linear parabolic equations with linear growth. For non-negative solutions that vanish continuously on the lateral boundary of an NTA cylinder the following main results are established: a backward Harnack inequality, the doubling property for the Riesz measure associated with such solutions, and the Hölder continuityof the quotient of two such solutions up to the boundary. Paper 2 concerns the solutions to linear degenerate parabolic equations, where the degeneracy is controlled by a Muckenhoupt weight of class 1+2/n. For non-negative solutions that vanish continuously on the lateral boundary of an NTA cylinder the following main results are established: a backward Harnack inequality, the doubling property for the parabolic measure, and the Hölder continuity of the quotient of two such solutions up to the boundary. Paper 3 concerns a fractional heat equation. The first main result is that a solution to the fractional heat equation in Euclidean space of dimension n can be extended as a solution to a certain linear degenerate parabolic equation in the upper half space of dimension n+1. The second main result is the Hölder continuity of quotients of two non-negative solutions that vanish continuously on the latteral boundary of a Lipschitz domain. Paper 4 concerns the solutions to uniformly parabolic linear equations with complex coefficients. The first main result is that under certain assumptions on the opperator the bounds for the single layer potentials associated to the opperator are bounded. The second main result is that these bounds always hold if the opperator is realvalued and symmetric.

This thesis consists of a comprehensive summary and six scientific papers dealing with the boundary behaviour of functions related to parabolic partial differential equations and several complex variables. Paper I concerns solutions to non-linear parabolic equations of linear growth. The main results include a backward Harnack inequality, and the Hölder continuity up to the boundary of quotients of non-negative solutions vanishing on the lateral boundary of an NTA cylinder. It is also shown that the Riesz measure associated with such solutions has the doubling property. Paper II is concerned with solutions to linear degenerate parabolic equations, where the degeneracy is controlled by a weight in the Muckenhoupt class 1+2/n. Two main results are that non-negative solutions which vanish continuously on the lateral boundary of an NTA cylinder satisfy a backward Harnack inequality and that the quotient of two such functions is Hölder continuous up to the boundary. Another result is that the parabolic measure associated to such equations has the doubling property. In Paper III, it is shown that a bounded pseudoconvex domain whose boundary is α-Hölder for each 0&lt;α&lt;1, is hyperconvex. Global estimates of the exhaustion function are given. In Paper IV, it is shown that on the closure of a domain whose boundary locally is the graph of a continuous function, all plurisubharmonic functions with continuous boundary values can be uniformly approximated by smooth plurisubharmonic functions defined in neighbourhoods of the closure of the domain. Paper V studies  Poletsky’s notion of plurisubharmonicity on compact sets. It is shown that a function is plurisubharmonic on a given compact set if, and only if, it can be pointwise approximated by a decreasing sequence of smooth plurisubharmonic functions defined in neighbourhoods of the set. Paper VI introduces the notion of a P-hyperconvex domain. It is shown that in such a domain, both the Dirichlet problem with respect to functions plurisubharmonic on the closure of the domain, and the problem of approximation by smooth plurisubharmoinc functions in neighbourhoods of the closure of the domain have satisfactory answers in terms of plurisubharmonicity on the boundary.