Error Estimation

RESUMEN.-El MEC ha demostrado ser una poderosa herramienta para el análisis de pr~ blemas. elásticos y de potencial en dominios bidimensionales y tridimensionales. Al igual que el MEF, es posible desarrollar versiones h-adaptables y p-adapta bles que minimicen el esfuerzo humano en la preparación de los datos y aseguren uña solución suficientemente precisa. Este trabajo se ocupa, justamente, de desarrollar la versión p~adaptable del MEC para problemas de potencial, haciendo hincapié en el establecimiento de criterios apropiados para controlar el proceso automático de refinamiento de la solución, como es el caso de los indicadores locales y estimadores globales. Se presentan algunos ejemplos ilustrativos y se discute la efectividad de la convergencia-p frente a la convergencia-h.

Previously, we have developed a novel spatial discretization error estimator, the "residual source" estimator, in which an error transport problem, analogous to the discretized transport equation, is solved to acquire an estimate of the error, with a residual term acting as a fixed source. Like all error estimators, the residual source estimator suffers inaccuracy and imprecision in the proximity of singular characteristics, lines across which the solution is irregular. Estimator performance worsens as the irregularities become more pronounced, especially so if the true solution itself is discontinuous. This work introduces a modification to the residual approximation procedure that seeks to reduce the adverse effects of the singular characteristics on the error estimate. A partial singular characteristic tracking scheme is implemented to reduce the portion of the error in the numerical solution born by irregularities in the true solution. This treated numerical solution informs the residual approximations. The partial singular characteristic tracking scheme greatly enhances the numerical solution for a problem with prominent singular characteristics. The residual approximation and resultant residual source error estimate are likewise improved by the scheme, which only incurs the computational cost of an extra inner iteration.

Vehicular ad hoc networks (VANETs) are used for improving traffic efficiency and road safety. However, VANETs are vulnerable to various attacks from malicious vehicles. Malicious vehicles can disrupt the normal operation of VANET applications by broadcasting bogus event messages that may cause accidents, threatening people's lives. Therefore, the receiver node needs to evaluate the authenticity and trustworthiness of the sender vehicles and their messages before acting. Although several solutions for trust management in VANETs have been proposed to address these issues of malicious vehicles, existing trust management schemes have two main issues. Firstly, these schemes have no authentication components and assume the nodes are authenticated before communicating. Consequently, these schemes do not meet VANET security and privacy requirements. Secondly, existing trust management schemes are not designed to operate in various contexts of VANETs that occur frequently due to sudden variations in the network dynamics, making existing solutions impractical for VANETs. In this paper, we present a novel blockchain-assisted privacypreserving and context-aware trust management framework that combines a blockchain-assisted privacy-preserving authentication scheme and a context-aware trust management scheme for securing communications in VANETs. The authentication scheme is proposed to enable anonymous and mutual authentication of vehicular nodes and their messages and meet VANET efficiency, security, and privacy requirements. The context-aware trust management scheme is proposed to evaluate the trustworthiness of the sender vehicles and their messages, and successfully detect malicious vehicles and their false/bogus messages and eliminate them from the network, thereby ensuring safe, secure, and efficient communications in VANETs. In contrast to existing trust schemes, the proposed framework can operate and adapt to various contexts/scenarios in VANETs while meeting all VANET security and privacy requirements. According to efficiency analysis and simulation results, the proposed framework outperforms the baseline schemes and demonstrates to be secure, effective, and robust for enhancing vehicular communication security.

Network is very crucial. The vehicles in the road form a network enabling the passengers with infotainment and security. Emergency messages can be disseminated in the VANET scenario for securing the lives of people by avoiding the situations like chain collisions. The main aim of such messages is to provide safety. So these messages should be genuine one and propagated to all the vehicles in the scenario without any delay. In this paper, clustering technique is used along with the trust relationship to disseminate emergency messages in the network to secure the vehicles from hazardous conditions.

Response surface functions are often used as simple and inexpensive replacements for computationally expensive computer models that simulate the behavior of a complex system over some parameter space. "Progressive" response surfaces are built up incrementally as global information is added from new sample points added to the previous points in the parameter space. As the response surfaces are globally upgraded, indications of the convergence of the response surface approximation to the exact (fitted) function can be inferred. Sampling points can be incrementally added in a structured or unstructured fashion. Whatever the approach, it is usually desirable to sample the entire parameter space uniformly (at least in early stages of sampling). At later stages of sampling, depending on the nature of the quantity being resolved it may be desirable to continue sampling uniformly (progressive response surfaces), or to switch to a focusing/economizing strategy of preferentially sampling certain regions of the parameter space based on information gained in previous stages of sampling ("adaptive" response surfaces). Here we consider progressive response surfaces where a balanced representation of global response over the parameter space is desired. We use Kriging and Moving-Least-Squares methods to fit Halton quasi-Monte-Carlo data samples and interpolate over the parameter space. On 2-D test problems we use the response surfaces to compute various response measures and assess the accuracy/applicability of heuristic error estimates based on convergence behavior of the computed response quantities. Where applicable we apply Richardson Extrapolation for estimates of error and asymptotic convergence, and assess the accuracy of these estimates. We seek to develop a robust methodology for constructing progressive response surface approximations with reliable error estimates.

On the approximation of the spectrum of the Stokes operator RAIRO -Modélisation mathématique et analyse numérique, tome 23, n o 1 (1989), p. 129-136. <http © AFCET, 1989, tous droits réservés. L'accès aux archives de la revue « RAIRO -Modélisation mathématique et analyse numérique » implique l'accord avec les conditions générales d'utilisation (). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques am MATHEMATICAL MOOEUJNG AND NUMERICAL ANALYSIS .'UI MODÉLISATION MATHÉMATIQUE ET ANALYSE NUMÉRIQUE

Response surface functions are often used as simple and inexpensive replacements for computationally expensive computer models that simulate the behavior of a complex system over some parameter space. "Progressive" response surfaces are built up incrementally as global information is added from new sample points added to the previous points in the parameter space. As the response surfaces are globally upgraded, indications of the convergence of the response surface approximation to the exact (fitted) function can be inferred. Sampling points can be incrementally added in a structured or unstructured fashion. Whatever the approach, it is usually desirable to sample the entire parameter space uniformly (at least in early stages of sampling). At later stages of sampling, depending on the nature of the quantity being resolved it may be desirable to continue sampling uniformly (progressive response surfaces), or to switch to a focusing/economizing strategy of preferentially sampling certain regions of the parameter space based on information gained in previous stages of sampling ("adaptive" response surfaces). Here we consider progressive response surfaces where a balanced representation of global response over the parameter space is desired. We use Kriging and Moving-Least-Squares methods to fit Halton quasi-Monte-Carlo data samples and interpolate over the parameter space. On 2-D test problems we use the response surfaces to compute various response measures and assess the accuracy/applicability of heuristic error estimates based on convergence behavior of the computed response quantities. Where applicable we apply Richardson Extrapolation for estimates of error and asymptotic convergence, and assess the accuracy of these estimates. We seek to develop a robust methodology for constructing progressive response surface approximations with reliable error estimates.

First, the paper proposes the method for interpolation of any experimentally obtained symmetric hysteresis loop curve (SHLC) with accuracy and computation efficiency at discrete Fourier transformation (DFT) level. Second, the method has been further developed so that, based on the family of the properly chosen and measured SHLCs, it reliably and accurately predicts an arbitrary inner SHLC. Sinusoidal magnetic flux, along with applied zero crossing sampling system, allows for the introduction of the pure linearization approach. The novelty of this approach is a direct transformation of a cosine polynomial (CP) interpolating of one SHLC over the set of equidistant nodes in the electric angle (EA) domain to the algebraic polynomial (AP) interpolating the same SHLC over the set of nonequidistant Chebyshev nodes in the magnetic flux (MF) domain, with the accuracy remaining unchanged. Based on the results of the interpolation error analyses, the SHLC measurement has been proposed for nonequidistant values of magnetic flux at the loop tip, matching the Chebyshev nodes of the second kind. This is the second novelty which enables a successful prediction of an arbitrary inner SHLC.

Na casa das palavras chegavam os poetas. As palavras, guardadas em velhos frascos de cristal, esperavam pelos poetas e se ofereciam, loucas de vontade de ser escolhidas: elas rogavam aos poetas que as olhassem, as cheirassem, as tocassem, as provassem. Os poetas abriam os frascos, provavam palavras com o dedo e então lambiam os lábios ou fechavam a cara. Os poetas andavam em busca de palavras que não conheciam, e também buscavam palavras que conheciam e tinham perdido. Eduardo Galeano. O livro dos abraços, 2002. p.13. Uma única palavra pode provocar em nós inúmeros sentimentos, tais como os de alegria, empolgação, inquietude, desconforto, prazer... As palavras multiplicam ideias e são capazes de nos fazer lamber os lábios ou fechar a cara, como sugere Galeano. O livro de Viviane Maria Alessi, Rodas de conversa: uma análise das vozes infantis na perspectiva do círculo de Bakhtin, fala de palavras descobertas, repetidas, esquecidas, inventadas, silenciadas, misturadas e agitadas nos frascos do pensamento. Palavras que dançam, circulam e cirandam entre crianças e adultos nas rodas de conversas.

Escherichia coli (E.coli) is a widely used indicator of fecal contamination in water bodies. External contact and subsequent ingestion of bacteria coming from fecal contamination can lead to harmful health effects. Since E.coli data are sometimes limited, the objective of this study is to use secondary information in the form of turbidity to improve the assessment of E.coli at un-monitored locations. We obtained all E.coli and turbidity monitoring data available from existing monitoring networks for the 2000 -2006 time period for the Raritan River Basin, New Jersey. Using collocated measurements we developed a predictive model of E.coli from turbidity data. Using this model, soft data are constructed for E.coli given turbidity measurements at 739 space/time locations where only turbidity was measured. Finally, the Bayesian Maximum Entropy (BME) method of modern space/ time geostatistics was used for the data integration of monitored and predicted E.coli data to produce maps showing E.coli concentration estimated daily across the river basin. The addition of soft data in conjunction with the use of river distances reduced estimation error by about 30%. Furthermore, based on these maps, up to 35% of river miles in the Raritan Basin had a probability of E.coli impairment greater than 90% on the most polluted day of the study period.

This paper addresses the issue of measurement errors in visual servoing. The error characteristics of the vision based state estimation and the associated uncertainty of the control are investigated. The major contribution is the analysis of the propagation of image error through pose estimation and visual servoing control law. Using the analysis, two classical visual servoing methods are evaluated: position-based and 2 1/2 D visual servoing. The evaluation offers a tool to build and analyze hybrid control systems such as switching or partitioning control.

Quantification of residual stress gradients can provide great improvements in understanding the complex interactions between microstructure, mechanical state, mode(s) of failure and structural integrity. Highly focused local probe non-destructive techniques such as X-ray Diffraction (XRD), electron diffraction or Raman spectroscopy have an established track record in determining spatial variations of the relative changes in residual stress with respect to a reference state for many structural materials. However, the interpretation of these measurements in terms of absolute stress values requires a strain-free sample often difficult to obtain due to the influence of chemistry, microstructure or processing route. With the increasing availability of Focused Ion Beam (FIB) instruments, a new approach has been developed known as the microscale ring-core Focused Ion Beam-Digital Image Correlation (FIB-DIC). This technique is becoming the principal tool for quantifying absolute in-plane residual stresses. It can be applied to a broad range of materials: crystalline and amorphous metallic alloys and ceramics, polymers, composites and biomaterials. The precise nanoscale positioning and well-defined gauge volume 2 of this experimental technique make it eminently suitable for spatially resolved analysis, i.e. residual stress profiling and mapping. Following a summary of micro-stress evaluation approaches, we focus our attention on FIB-DIC methods, and assess the application of microscale ring-core methods for spatially resolved residual stress profiling. The sequential ring-core milling FIB-DIC method allows micro-to macro-scale mapping at the step of 10-1000 μm, whilst the parallel FIB-DIC approach exploits simultaneous milling operation to quantify stress profiles at the micron scale (1-10 μm). Cross-validation against XRD results confirms that these approaches represent accurate, reliable and effective residual stress mapping methods.

Quantification of residual stress gradients can provide great improvements in understanding the complex interactions between microstructure, mechanical state, mode(s) of failure and structural integrity. Highly focused local probe non-destructive techniques such as X-ray Diffraction (XRD), electron diffraction or Raman spectroscopy have an established track record in determining spatial variations of the relative changes in residual stress with respect to a reference state for many structural materials. However, the interpretation of these measurements in terms of absolute stress values requires a strain-free sample often difficult to obtain due to the influence of chemistry, microstructure or processing route. With the increasing availability of Focused Ion Beam (FIB) instruments, a new approach has been developed known as the microscale ring-core Focused Ion Beam-Digital Image Correlation (FIB-DIC). This technique is becoming the principal tool for quantifying absolute in-plane residual stresses. It can be applied to a broad range of materials: crystalline and amorphous metallic alloys and ceramics, polymers, composites and biomaterials. The precise nanoscale positioning and well-defined gauge volume 2 of this experimental technique make it eminently suitable for spatially resolved analysis, i.e. residual stress profiling and mapping. Following a summary of micro-stress evaluation approaches, we focus our attention on FIB-DIC methods, and assess the application of microscale ring-core methods for spatially resolved residual stress profiling. The sequential ring-core milling FIB-DIC method allows micro-to macro-scale mapping at the step of 10-1000 μm, whilst the parallel FIB-DIC approach exploits simultaneous milling operation to quantify stress profiles at the micron scale (1-10 μm). Cross-validation against XRD results confirms that these approaches represent accurate, reliable and effective residual stress mapping methods.

Recent matrix completion based methods have not been able to properly model the Haplotype Assembly Problem (HAP) for noisy observations. To deal with such cases, we propose a new Minimum Error Correction (MEC) based matrix completion problem over the manifold of rank-one matrices. We then prove the convergence of a specific iterative algorithm to solve this problem. From the simulation results, the proposed method not only outperforms some well-known matrix completion based methods, but also shows a more accurate result compared to a most recent MEC based algorithm for haplotype estimation.

A method for error estimation of isogeometric analysis of plane stress problems which is the based on stress recovery and using the super convergent properties of the Gauss points, has been already introduced. This paper is devoted to the development of the method and study of the effects of these supercovergent points on the solution improvement and error estimation of axisymmetric problems by the isogeometric analysis method. It is concluded that by using these optimal points for stress recovery and error estimation by isogeometric analysis a considerable improvement is attained.

A method for error estimation of isogeometric analysis of plane stress problems, based on stress recovery by using the super convergent properties of the Gauss points, was introduced. In this paper, a different approach for improvement of stresses based on the satisfaction of equilibrium equations by taking into consideration of two elasticity problems is followed and the effect of the number of the Gauss quadrature points is studied. In this approach, the equilibrium equations are satisfied for each patch of the isogeometric analysis model and it has been shown that the recovered stresses are more accurate than the previous method where the super-convergent properties were used. To demonstrate the performance and efficiency of the method a couple of elasticity problems are considered and the obtained results are compared with the previous method and exact solutions. The results indicate that the suggested method can be employed for error estimation and stress recovery in the isogeometrical analysis method.

This article concerns the numerical study of the behaviour of a flexible beam of Euler-Bernoulli to which one adds to its internal composition a damping of the viscous type. This damping naturally exerts a dissipative force (or viscous damping force) on the beam and opposes any deformation, in proportion to the rate of deformation. We are therefore interested in the impact of the damper on the exponential stability of the beam. We develop here a numerical method which faithfully reproduces the theoretical results obtained by several authors. Simulations are provided to illustrate our results.

The aim of this paper is to develop an intrinsic regression model for the analysis of positive-definite matrices as responses in a Riemannian manifold and their association with a set of covariates, such as age and gender, in a Euclidean space. The primary motivation and application of the proposed methodology is in medical imaging. Because the set of positive-definite matrices do not form a vector space, directly applying classical multivariate regression may be inadequate in establishing the relationship between positive-definite matrices and covariates of interest, such as age and gender, in real applications. Our intrinsic regression model, which is a semiparametric model, uses a link function to map from the Euclidean space of covariates to the Riemannian manifold of positivedefinite matrices. We develop an estimation procedure to calculate parameter estimates and establish their limiting distributions. We develop score statistics to test linear hypotheses on unknown parameters and develop a test procedure based on a resampling method to simultaneously assess the statistical significance of linear hypotheses across a large region of interest. Simulation studies are used to demonstrate the methodology and examine the finite sample performance of the test procedure for controlling the family-wise error rate. We apply our methods to the detection of statistical significance of diagnostic effects on the integrity of white matter in a diffusion tensor study of human immunodeficiency virus. Supplemental materials for this article are available online.

Hill reservoirs are rain water‐harvesting structures that have been increasingly adopted in arid and semi‐arid regions, such as North Africa, to capture and conserve runoff water and for use as alternative water resources in agricultural development. Currently, process‐based information on reservoir hydrology is needed to improve reservoir management practices.The study aims to develop an approach to estimate the reservoir–subsurface exchange flux and its associated error at the annual, monthly, and intra‐monthly time scales to better understand the hydrological functioning and dynamics of hill reservoirs. This approach is based on a hydrological water balance of the hill reservoir by considering all water input and output fluxes and their associated errors.The results demonstrate the ability and relevance of the approach in estimating the net reservoir–subsurface exchange flux and its error estimations at various time scales. Its application on the Kamech catchment (Northern Tunisi...

In this paper we consider error estimation for image restoration problems based on generalized Bregman distances. This error estimation technique has been used to derive convergence rates of variational regularization schemes for linear and nonlinear inverse problems by the authors before (cf. [4, 21, 22]), but so far it was not applied to image restoration in a systematic way. Due to the flexibility of the Bregman distances, this approach is particularly attractive for imaging tasks, where often singular energies (nondifferentiable, not strictly convex) are usedto achieve certain tasks such as preservation of edges. Besides the discussion of the variational image restoration schemes, our main goal in this paper is to extend the error estimation approach to iterative regularization schemes (and timecontinuous flows) that have emerged recently as multiscale restoration techniques and could improve some shortcomings of the variational schemes. We derive error estimates between the iterates and the exact image both in the case of clean and noisy data, the latter also giving indications on the choice of termination criteria. The error estimates are applied to various image restoration approaches such as denoising and decomposition by total variation and wavelet methods. We shall see that interesting results for various restoration approaches can be deduced from our general results by just exploring the structure of subgradients.

Deep learning (DL) is a numerical method that approximates functions. Recently, its use has become attractive for the simulation and inversion of multiple problems in computational mechanics, including the inversion of borehole logging measurements for oil and gas applications. In this context, DL methods exhibit two key attractive features: (a) once trained, they enable to solve an inverse problem in a fraction of a second, which is convenient for borehole geosteering operations as well as in other real‐time inversion applications. (b) DL methods exhibit a superior capability for approximating highly complex functions across different areas of knowledge. Nevertheless, as it occurs with most numerical methods, DL also relies on expert design decisions that are problem specific to achieve reliable and robust results. Herein, we investigate two key aspects of deep neural networks (DNNs) when applied to the inversion of borehole resistivity measurements: error control and adequate sele...

This work analyzes the influence of the discretization error associated with the finite element (FE) analyses of each design configuration proposed by the structural shape optimization algorithms over the behavior of the algorithm. The paper clearly shows that if FE analyses are not accurate enough, the final solution provided by the optimization algorithm will neither be optimal nor satisfy the constraints. The need for the use of adaptive FE analysis techniques in shape optimum design will be shown. The paper proposes the combination of two strategies to reduce the computational cost related to the use of mesh adaptivity in evolutionary optimization algorithms: (a) the use of an algorithm for the mesh generation by projection of the discretization error, which reduces the computational cost associated with the adaptive FE analysis of each geometrical configuration and (b) the successive increase of the required accuracy of the FE analyses in order to obtain a considerable reduction of the computational cost in the early stages of the optimization process.

The focus is on a model reduction framework for parameterized elliptic eigenvalue problems by a reduced basis method. In contrast to the standard single output case, one is interested in approximating several outputs simultaneously, namely a certain number of the smallest eigenvalues. For a fast and reliable evaluation of these input-output relations, we analyze a posteriori error estimators for eigenvalues. Moreover, we present different greedy strategies and study systematically their performance. Special attention needs to be paid to multiple eigenvalues whose appearance is parameter-dependent. Our methods are of particular interest for applications in vibro-acoustics.

Actualmente el desarrollo de software para el análisis de sistemas de ingeniería a través del método de los elementos finitos está notablemente influenciado por la solución al problema "EL METODO DE LOS ELEMENTOS FINITOS ADAPTABLE". Una estimación confiable del error es el punto central en el planteamiento de la solución a este problema. A partir de 1987 con la publicación de Zienkiewicz y Zhul, numerosos trabajos han sido publicados tratando de proponer estimadores de error y estrategias de refinamiento que sean computacionalmente aceptables para resolver este problema. En esta publicación se presenta una solución al método de los elementos finitos adaptable, basada en un nuevo tipo de estimador de error, obtenido de los trabajos de Johnson y Hansbo Este nuevo estimador constituye una generalización al propuesto por Zienkiewicz y Zhu y la idea central es comparar ambos estimadores.

In this paper a new error estimator based on tangential derivative Boundary Integral Equation residuals for 2D Laplace and Helmholtz equations is shown. The direct problem for general mixed boundary conditions is solved using standard and hypersingular boundary integral equations. The exact solution is broken down into two parts: the approximated solution and the error function. Based on theoretical considerations, it is shown that tangential derivative Boundary Integral Equation residuals closely correlate to the errors in the tangential derivative of the solution. A similar relationship is shown for nodal sensitivities and tangential derivative errors. Numerical examples show that the tangential Boundary Integral Equation residual is a better error estimator than nodal sensitivity, because of the accuracy of the predictions and the lesser computational effort.

To solve stochastic problems with geometric uncertainties, one can transform the original problem in a domain with stochastic boundaries and interfaces to a problem defined in a deterministic domain with uncertainties in the material behavior. The latter problem is then discretized. There exist infinitely many random mappings that lead to identical results in the continuous domain but not in the discretized domain. In this paper, an a priori error indicator is proposed for electromagnetic problems with scalar and vector potential formulations. This leads to criteria for selecting random mappings that reduce the numerical error. In an illustrative numerical example, the proposed a priori error indicator is compared with an a posteriori estimator for both potential formulations Index Terms-Stochastic problem, random domain, transformation method, random mapping, a priori error indicator, static fields.

O presente texto é parte do resultado de uma pesquisa de doutorado em Educação, concluída em 2022 na Universidade São Francisco . Trata-se um estudo qualitativo de cunho bibliográfico, que se apropriou de conceitos da Filosofia da Libertação de Enrique Dussel, aos quais serviram de base para problematizações e reflexões quanto à prática docente diante das experiências e atitudes cotidianas na educação de crianças na creche. Desenvolveu-se também, uma pesquisa de campo in loco, através de entrevistas com docentes, com a observação participante e análises dos documentos normativos da instituição e do sistema educacional brasileiro, com a permissão do Comitê de Ética e Pesquisa, Registro CAAE n. 37547120.6.0000.5514. Buscou-se identificar as concepções e as especificidades da Educação Infantil na creche, de uma escola do interior do estado de São Paulo e tecer um diálogo com a “pedagógica” dusseliana, para se pensar a “alteridade”, a partir da Filosofia da Libertação, aplicada na práxis da Educação Infantil na creche.

En este artículo, se presenta un proceso h-adaptativo que define una malla óptima para calcular la solución de problemas de contorno parabólicos usando el método de Diferencias Miméticas. La estimación del error, en la variable espacial, se hace a partir de la versión discreta del operador gradiente. La experimentación numérica evidencia el buen comportamiento del procedimiento.

Mountainous watersheds have always been a challenge for modelers due to large variability and insufficient ground observations, which cause forcing data, model structure, and parameter uncertainty. This study employed Differential Evolution Adaptive Metropolis (DREAM) algorithm which utilizes Markov Chain Monte Carlo (MCMC) approach to account for forcing data uncertainty. A conceptual degree day snowmelt model, MIKE 11 NAM (Nedbor Afstromnings Model), was used to simulate snowmelt runoff from Ilgaz basin, with an area of 28.4 km2 area, located in the northern part of Turkey. The mean elevation is around 1700 m and the basin is covered with broadleaf forest and has mainly brown soil with a high water holding capacity. Precipitation and evapotranspiration (ET) values were optimized in combination with model parameters conditioned on observed discharges and corrected values of input data were utilized for calibration and validation. Results showed that the observed precipitation was o...

RESUMO: O presente trabalho tem por objetivo entrelaçar as narrativas de educadoras e fundadoras de uma instituição de educação infantil e suas práticas de educação e cuidado de crianças em uma periferia economicamente empobrecida de Belo Horizonte. Através de uma abordagem etnográfica, reconstruímos algumas lembranças da construção desta creche comunitária e alguns momentos da própria infância das educadoras, consideradas como elementos centrais para a análise de algumas práticas institucionais. A análise das narrativas das educadoras e das suas práticas cotidianas demonstra que a forma de rememorar implica e está implicada na maneira de reconstruir tais práticas, muitas vezes garantindo os direitos sociais das crianças atendidas e, outras vezes, impedindo esses mesmos direitos.

Akademisk avhandling som med tillstånd av Kungl Tekniska högskolan framlägges till offentlig granskning för avläggande av teknologie doktorsexamen i tillämpad matematik och beräkningsmatematik med inriktning mot numerisk analys fredagen den 9 december 2016 klockan 10.00 i sal D2, Lindstedtsvägen 5, KTH, Stockholm.

Aos professores, meus colegas, do Curso de Especialização em Educação Infantil, pela troca sempre tão generosa. À minha querida amiga Gabriela Irigoyen, por sempre me socorrer na hora em que preciso e por fazer parte da minha vida. À amiga Mariana Roncarati, pela leitura atenciosa da tese. À amiga Rosane Monteiro, por ouvir minhas aflições e conquistas ao longo de nossas idas e vindas para a Baixada. À minha querida amiga Leonor Toledo, pela nossa amizade que sobrevive a teses, filhos, desafios do cotidiano. Amizade sólida que permanece independente de qualquer distância. Às queridas Marina Castro e Liana Castro, amizades construídas durante o período do doutorado, que extrapolaram o cenário acadêmico e ganharam vida. Obrigada pela alegria que vocês me trazem. À querida Nazareth Salutto, amiga de todas as horas. Obrigada pela escuta, pelo ombro, pelo colo. Por ler a tese com delicadeza, por me fazer acreditar na minha capacidade. Por dividir comigo as angústias e as alegrias da vida. Com sua amizade, tudo fica muito melhor. À minha querida tia Ângela, por ter despertado em mim, ainda criança, a paixão pela educação. À minha madrinha Mônica, pelo cuidado, pela torcida constante e pelas preces. À Clarissa, minha irmã, companheira desde minhas primeiras histórias. E, por trazer, Rafael e Isabela para minha vida. Ao Tio, por ser uma referência, um pilar. Mãe, se hoje eu conto essa história é porque aprendi com você que escutar e olhar no olho são a única maneira que temos de chegar perto e conhecer de verdade. Essa conquista é sua também. Ao Edauro, por me dizer, há anos, que "já sabia". Sua presença e seu amor me fortalecem todos os dias. Ao Leon, meu filho, que há quinze anos, me ensina que educar é estar presente e comprometido; é saber escutar e dizer; é, antes de tudo, se responsabilizar pelo outro. E amar fazer isso tudo.

Feed forward neural networks receive a growing attention as a data modelling tool in economic classification problems. It is well-known that controlling the design of a neural network can be cumbersome. Inaccuracies may lead to a manifold of problems in the application such as higher errors due to local optima, overfitting and ill-conditioning of the network, especially when the number of observations is small. In this paper we provide a method to overcome these difficulties by regulating the flexibility of the network and by rendering measures for validating the final network. In particular a method is proposed to equilibrate the number of hidden neurons and the value of the weight decay parameter based on 5 and 10-fold cross-validation. In the validation process the performance of the neural network is compared with a linear model with the same input variables. The degree of monotonicity with respect to each explanatory variable is calculated by numerical differentiation. The outcomes of this analysis is compared to what is expected from economic theory. Furthermore we propose a scheme for the application of monotonic neural networks to problems where monotonicity with respect to the explanatory variables is known a priori. The methods are illustrated in two case studies: predicting the price of housing in Boston metropolitan area and the classification of bond ratings.

The present work deals with storm classification, using the Storm Power Index, and beach morphological response to storm events in the Gulf of Cadiz (SW Spain). Over the 1958-2001 period, 377 events divided into five classes ranging from 'weak' to 'extreme' were characterized. Classes I (weak) and II (moderate) accounted for 60% and 23% of events, respectively. Class III (significant), were 9% of the recorded events and Classes IV (severe) and V (extreme) accounted for 5% and 2%, respectively. The probability of storm occurrence per year ranged from 93% for Class I to 15% for Class V. In order to characterize beach response to storm events, 214 beach profiles carried out with a monthly periodicity over the 1996-1998 period along the Chipiona-Rota littoral were analysed, as well as published data. Different beach types were observed: (i) 'Intermediate' beaches underwent important vertical relief changes ranging from 0.3 m to 1.33 m associated with average slope changes from tan b = 0.06 to tan b = 0.03; (ii) the 'dissipative' beaches were characterized by smaller and homogeneous foreshore vertical changes, from c. 0.36 m to 0.65 m, according to the parallel retreat mechanism characterized by small slope variations (from tan b = 0.025 to tan b = 0.035); and (iii) 'intermediate with rock shore platform' experienced small morphological and foreshore slope variations, related to both beach pivoting and parallel retreat mechanisms. The most important morphological changes were due to the impact of usually 'weak' and 'moderate' events during October and November that produced berm erosion and upper foreshore lowering, and the impact of 'severe', 'significant' and 'extreme' events in December and January which produced dune escarpment, overwash and/or damage to coastal structures.

Gupta in [6] introduced a general family of linear positive operators which produce large number of well known linear positive operators as particular cases. As the family of operators proposed by Gupta provides a unified approach this motivated us to extend the studies, and we establish some convergence estimates of these important operators. We estimate an asymptotic formula and the rate of convergence for these operators for the function having derivatives of bounded variation.

The approach introduced recently by Albrecht to derive order conditions for Runge-Kutta formulas based on the theory of A-methods is also very powerful for the general linear methods. In this paper, using Albrecht's approach, we formulate the general theory of order conditions for a class of general linear methods where the components of the propagating vector of approximations to the solution have different orders. Using this theory we derive a class of diagonally implicit multistage integration methods (DIMSIMs) for which the global order is equal to the local order. We also derive a class of general linear methods with two nodal approximations of different orders which facilitate local error estimation. Our theory also applies to the class of two-step Runge-Kutta introduced recently by Jackiewicz and Tracogna .

In the present paper, we study a certain integral modification of the well known Baskakov operators with the weight function of Beta basis function. We establish pointwise convergence, an asymptotic formula an error estimation and an inverse result in simultaneous approximation for these new operators.

In this paper we study the mixed summation-integral type operators having Szasz and Beta basis functions in summation and integration, respectively, we obtain the rate of point-wise convergence, a Voronovskaja type asymptotic formula and an error estimate in simultaneous approximation.

In this paper we study the mixed summation-integral type operators having Szasz and Beta basis functions in summation and integration, respectively, we obtain the rate of point-wise convergence, a Voronovskaja type asymptotic formula and an error estimate in simultaneous approximation.

The purpose of this paper is to propose a new quadrature formula for integrals with nearby singularities. In the boundary element method, the integrands of nearby singular boundary integrals vary drastically with the distance between the field and the source point. Especially, field variables and their derivatives at a field point near a boundary cannot be computed accurately. In the present paper a quadrature formula for l-isolated singularities near the integration interval, based on Lagrange interpolatory polynomials, is obtained. The error estimation of the proposed formula is also given. Quadrature formulas for regular and singular integrals with conjugate poles are derived. Numerical examples are given and the proposed quadrature rules present the expected polynomial accuracy.

Here, we study the flow of energy between coupled simulators in a co-simulation environment using the concept of power bonds. We introduce energy residuals which are a direct expression of the coupling errors and hence the accuracy of co-simulation results. We propose a novel Energy-Conservation-based Co-Simulation method (ECCO) for adaptive macro step size control to improve accuracy and efficiency. In contrast to most other co-simulation algorithms, this method is noniterative and only requires knowledge of the current coupling data. Consequently, it allows for significant speed ups and the protection of sensitive information contained within simulator models. A quarter car model with linear and nonlinear damping serves as a co-simulation benchmark and verifies the capabilities of the energy residual concept: Reductions in the errors of up to 93 % are achieved at no additional computational cost.

Residual impedance correction in impedance analyzers when using an asymmetrical test fixture needs three reference measurements, usually open circuit, short circuit, and load (meaning an impedance close to the impedance under test). This paper provides an error estimate for impedance measurements that apply a simple open/short correction in spite of using an asymmetrical test fixture. Experimental results show that the minimal error is obtained for impedance values close to the geometric mean of the short-circuit and open-circuit impedances, and that the theoretical prediction is indeed an upper limit for the actual error.

Sarmento e Cristina Gouvea. "Os pais podem vir e não precisa estar com a roupa na cor da escola" foi a fala de Melissa 1 , de cinco anos, matriculada no Centro de Referência em Educação Infantil Realengo 2 do Colégio Pedro II, ao solicitar a participação dos pais nas comemorações de aniversário realizadas no Colégio. O diálogo aconteceu durante a reunião do Conselho de Alunos Representantes de Turma (CART). Esclarecimentos a respeito do CART serão abordados mais adiante. O que destacaremos inicialmente tem a ver com o objetivo deste texto: o que nós adultos podemos aprender com as crianças? Quando paramos para ouvi-las e o que elas nos dizem? O pedido expressa um querer e provoca a reflexão sobre o protagonismo infantil, para além das cores da escola, azul e branca. Esta expressão ganha sentido no conhecimento sobre a exigência institucional em torno do uso do uniforme e revela a tentativa da criança de flexibilizar esse uso. Ela traça uma perspectiva de viabilização da presença dos responsáveis nas festas, tentando dar conta, ao mesmo tempo, da regra e da inquietação pela ausência. Para além da compreensão de uma regra institucional, sua fala nos convida a pensar a respeito das cores de uma escola. Que cor uma escola tem ou que cor uma escola pode ter? Este texto não tem o intuito de apresentar uma resposta exata para esta questão, mas discutir a possibilidade de pintar uma escola com as crianças e não para elas. Neste sentido, o desafio posto é de olhar a criança como outro, estabelecer um diálogo com ela. 1 Por uma questão ética, optamos por usar nomes fictícios. 2 Trata-se da única unidade de Educação Infantil no Colégio Pedro II, inaugurada em 2012 e construída com recursos financeiros do PROINFÂNCIA-Programa Nacional de Reestruturação e Aquisição de Equipamentos para a Rede Escolar Pública de Educação Infantil, instituído pela resolução n. 6 de 24 de abril de 2007, como parte das ações do Plano de Desenvolvimento da Educação (PDE) do Ministério da Educação.