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An alternating method for Cauchy problems for Helmholtz-type operators in non-homogeneous medium

Kozlov & Maz'ya (1989, Algebra Anal., 1, 144–170) proposed an alternating iterative method for solving Cauchy problems for general strongly elliptic and formally self-adjoint systems. However, in many applied problems, operators appear that do not satisfy these requirements, e.g. Helmholtz-type operators. Therefore, in this study, an alternating procedure for solving Cauchy problems for self-adjoint non-coercive elliptic operators of second order is presented. A convergence proof of this procedure is given.

A mixture density network approach to modelling and exploiting uncertainty in nonlinear control problems

In nonlinear and stochastic control problems, learning an efficient feed-forward controller is not amenable to conventional neurocontrol methods. For these approaches, estimating and then incorporating uncertainty in the controller and feed-forward models can produce more robust control results. Here, we introduce a novel inversion-based neurocontroller for solving control problems involving uncertain nonlinear systems which could also compensate for multi-valued systems. The approach uses recent developments in neural networks, especially in the context of modelling statistical distributions, which are applied to forward and inverse plant models. Provided that certain conditions are met, an estimate of the intrinsic uncertainty for the outputs of neural networks can be obtained using the statistical properties of networks. More generally, multicomponent distributions can be modelled by the mixture density network. Based on importance sampling from these distributions a novel robust inverse control approach is obtained. This importance sampling provides a structured and principled approach to constrain the complexity of the search space for the ideal control law. The developed methodology circumvents the dynamic programming problem by using the predicted neural network uncertainty to localise the possible control solutions to consider. A nonlinear multi-variable system with different delays between the input-output pairs is used to demonstrate the successful application of the developed control algorithm. The proposed method is suitable for redundant control systems and allows us to model strongly non-Gaussian distributions of control signal as well as processes with hysteresis. © 2004 Elsevier Ltd. All rights reserved.

Direct and Inverse Spectral Problems for (2N + 1)-Diagonal, Complex, Symmetric, Non-Hermitian Matrices

2000 Mathematics Subject Classification: 42C05.

A domain decomposition based algorithm for non-linear 2D inverse heat conduction problems

Inverse heat conduction problems (IHCPs) appear in many important scientific and technological fields. Hence analysis, design, implementation and testing of inverse algorithms are also of great scientific and technological interest. The numerical simulation of 2-D and –D inverse (or even direct) problems involves a considerable amount of computation. Therefore, the investigation and exploitation of parallel properties of such algorithms are equally becoming very important. Domain decomposition (DD) methods are widely used to solve large scale engineering problems and to exploit their inherent ability for the solution of such problems.

Variational ensemble Kalman filtering applied to data assimilation problems in computational fluid dynamics

One challenge on data assimilation (DA) methods is how the error covariance for the model state is computed. Ensemble methods have been proposed for producing error covariance estimates, as error is propagated in time using the non-linear model. Variational methods, on the other hand, use the concepts of control theory, whereby the state estimate is optimized from both the background and the measurements. Numerical optimization schemes are applied which solve the problem of memory storage and huge matrix inversion needed by classical Kalman filter methods. Variational Ensemble Kalman filter (VEnKF), as a method inspired the Variational Kalman Filter (VKF), enjoys the benefits from both ensemble methods and variational methods. It avoids filter inbreeding problems which emerge when the ensemble spread underestimates the true error covariance. In VEnKF this is tackled by resampling the ensemble every time measurements are available. One advantage of VEnKF over VKF is that it needs neither tangent linear code nor adjoint code. In this thesis, VEnKF has been applied to a two-dimensional shallow water model simulating a dam-break experiment. The model is a public code with water height measurements recorded in seven stations along the 21:2 m long 1:4 m wide flume’s mid-line. Because the data were too sparse to assimilate the 30 171 model state vector, we chose to interpolate the data both in time and in space. The results of the assimilation were compared with that of a pure simulation. We have found that the results revealed by the VEnKF were more realistic, without numerical artifacts present in the pure simulation. Creating a wrapper code for a model and DA scheme might be challenging, especially when the two were designed independently or are poorly documented. In this thesis we have presented a non-intrusive approach of coupling the model and a DA scheme. An external program is used to send and receive information between the model and DA procedure using files. The advantage of this method is that the model code changes needed are minimal, only a few lines which facilitate input and output. Apart from being simple to coupling, the approach can be employed even if the two were written in different programming languages, because the communication is not through code. The non-intrusive approach is made to accommodate parallel computing by just telling the control program to wait until all the processes have ended before the DA procedure is invoked. It is worth mentioning the overhead increase caused by the approach, as at every assimilation cycle both the model and the DA procedure have to be initialized. Nonetheless, the method can be an ideal approach for a benchmark platform in testing DA methods. The non-intrusive VEnKF has been applied to a multi-purpose hydrodynamic model COHERENS to assimilate Total Suspended Matter (TSM) in lake Säkylän Pyhäjärvi. The lake has an area of 154 km2 with an average depth of 5:4 m. Turbidity and chlorophyll-a concentrations from MERIS satellite images for 7 days between May 16 and July 6 2009 were available. The effect of the organic matter has been computationally eliminated to obtain TSM data. Because of computational demands from both COHERENS and VEnKF, we have chosen to use 1 km grid resolution. The results of the VEnKF have been compared with the measurements recorded at an automatic station located at the North-Western part of the lake. However, due to TSM data sparsity in both time and space, it could not be well matched. The use of multiple automatic stations with real time data is important to elude the time sparsity problem. With DA, this will help in better understanding the environmental hazard variables for instance. We have found that using a very high ensemble size does not necessarily improve the results, because there is a limit whereby additional ensemble members add very little to the performance. Successful implementation of the non-intrusive VEnKF and the ensemble size limit for performance leads to an emerging area of Reduced Order Modeling (ROM). To save computational resources, running full-blown model in ROM is avoided. When the ROM is applied with the non-intrusive DA approach, it might result in a cheaper algorithm that will relax computation challenges existing in the field of modelling and DA.

Linear non-local diffusion problems in metric measure spaces

The aim of this paper is to provide a comprehensive study of some linear non-local diffusion problems in metric measure spaces. These include, for example, open subsets in ℝN, graphs, manifolds, multi-structures and some fractal sets. For this, we study regularity, compactness, positivity and the spectrum of the stationary non-local operator. We then study the solutions of linear evolution non-local diffusion problems, with emphasis on similarities and differences with the standard heat equation in smooth domains. In particular, we prove weak and strong maximum principles and describe the asymptotic behaviour using spectral methods.

Holomorphic functions on non-Runge domains and related problems.

Let U be a domain in CN that is not a Runge domain. We study the topological and algebraic properties of the family of holomorphic functions on U which cannot be approximated by polynomials.

numerical problems in the calculation of electric field and charge density profiles for mass impregnated non-draining hvdc cables subjected to fast polarity reversals

The goal of this simulation thesis is to present a tool for studying and eliminating various numerical problems observed while analyzing the behavior of the MIND cable during fast voltage polarity reversal. The tool is built on the MATLAB environment, where several simulations were run to achieve oscillation-free results. This thesis will add to earlier research on HVDC cables subjected to polarity reversals. Initially, the code does numerical simulations to analyze the electric field and charge density behavior of a MIND cable for certain scenarios such as before, during, and after polarity reversal. However, the primary goal is to reduce numerical oscillations from the charge density profile. The generated code is notable for its usage of the Arithmetic Mean Approach and the Non-Uniform Field Approach for filtering and minimizing oscillations even under time and temperature variations.

Data driven regularization models of non-linear ill-posed inverse problems in imaging

Imaging technologies are widely used in application fields such as natural sciences, engineering, medicine, and life sciences. A broad class of imaging problems reduces to solve ill-posed inverse problems (IPs). Traditional strategies to solve these ill-posed IPs rely on variational regularization methods, which are based on minimization of suitable energies, and make use of knowledge about the image formation model (forward operator) and prior knowledge on the solution, but lack in incorporating knowledge directly from data. On the other hand, the more recent learned approaches can easily learn the intricate statistics of images depending on a large set of data, but do not have a systematic method for incorporating prior knowledge about the image formation model. The main purpose of this thesis is to discuss data-driven image reconstruction methods which combine the benefits of these two different reconstruction strategies for the solution of highly nonlinear ill-posed inverse problems. Mathematical formulation and numerical approaches for image IPs, including linear as well as strongly nonlinear problems are described. More specifically we address the Electrical impedance Tomography (EIT) reconstruction problem by unrolling the regularized Gauss-Newton method and integrating the regularization learned by a data-adaptive neural network. Furthermore we investigate the solution of non-linear ill-posed IPs introducing a deep-PnP framework that integrates the graph convolutional denoiser into the proximal Gauss-Newton method with a practical application to the EIT, a recently introduced promising imaging technique. Efficient algorithms are then applied to the solution of the limited electrods problem in EIT, combining compressive sensing techniques and deep learning strategies. Finally, a transformer-based neural network architecture is adapted to restore the noisy solution of the Computed Tomography problem recovered using the filtered back-projection method.

Pedagogia do esporte : organização, sistematização, aplicação e avaliação de conteúdos esportivos na educação não formal = Sport pedagogy : organization, systematization and application of sports content in non-formal education

Universidade Estadual de Campinas . Faculdade de Educação Física

Weekend/weekday differences in concentrations of ozone, nox, and non-methane hydrocarbon in the metropolitan area of São Paulo

Ozone and inhalable particulate matter are the major air pollutants in the Metropolitan Area of São Paulo, Brazil, a region that has more than 19 million inhabitants and approximately 7 million registered vehicles. Proximity of roadways, adjacent land use, and local circulation are just some of the factors that can affect the results of monitoring of pollutant concentrations. The so-called weekend effect (higher ozone concentrations on weekends than on weekdays) might be related to the fact that concentrations of ozone precursors, such as nitrogen oxides (NOx) and Non Methane-Hydrocarbon (NMHC), are relatively lower on weekends. This phenomenon has been reported in some areas of the United States since the 1970s. The differences between the concentrations of ozone in period of weekend and weekday, were obtained from analysis of data hourly average of CETESB for 2004, studied the precursors to the formation of troposphere ozone, the meteorological variables and traffic profile for RMSP. Because of the proximity to sources of emissions from the station Pinheiros showed higher concentrations of NO and NO² and greater variations to the periods weekend and weekday. With fewer vehicles circulating during the weekend, and consequently less emission of pollutants, it has cleaner air and less concentration of NO and NO², there is the ideal setting to the formation of troposphere ozone, despite the lower concentration of NO². The proximity with the source emissions, aided by the increased availability of solar radiation and the presence of ozone precursors, were factors conditions for the occurrence of weekend effect.

Prevalence of non-communicable diseases in Brazilian children: follow-up at school age of two Brazilian birth cohorts of the 1990's

Background: Few cohort studies have been conducted in low and middle-income countries to investigate non-communicable diseases among school-aged children. This article aims to describe the methodology of two birth cohorts, started in 1994 in Ribeirao Preto (RP), a more developed city, and in 1997/98 in Sao Luis (SL), a less developed town. Methods: Prevalences of some non-communicable diseases during the first follow-up of these cohorts were estimated and compared. Data on singleton live births were obtained at birth (2858 in RP and 2443 in SL). The follow-up at school age was conducted in RP in 2004/05, when the children were 9-11 years old and in SL in 2005/06, when the children were 7-9 years old. Follow-up rates were 68.7% in RP (790 included) and 72.7% in SL (673 participants). The groups of low (<2500 g) and high (>= 4250 g) birthweight were oversampled and estimates were corrected by weighting. Results: In the more developed city there was a higher percentage of non-nutritive sucking habits (69.1% vs 47.9%), lifetime bottle use (89.6% vs 68.3%), higher prevalence of primary headache in the last 15 days (27.9% vs 13.0%), higher positive skin tests for allergens (44.3% vs 25.3%) and higher prevalence of overweight (18.2% vs 3.6%), obesity (9.5% vs 1.8%) and hypertension (10.9% vs 4.6%). In the less developed city there was a larger percentage of children with below average cognitive function (28.9% vs 12.2%), mental health problems (47.4% vs 38.4%), depression (21.6% vs 6.0%) and underweight (5.8% vs 3.6%). There was no difference in the prevalence of bruxism, recurrent abdominal pain, asthma and bronchial hyperresponsiveness between cities. Conclusions: Some non-communicable diseases were highly prevalent, especially in the more developed city. Some high rates suggest that the burden of non-communicable diseases will be high in the future, especially mental health problems.

Non-linear boundary element formulation applied to contact analysis using tangent operator

This work presents a non-linear boundary element formulation applied to analysis of contact problems. The boundary element method (BEM) is known as a robust and accurate numerical technique to handle this type of problem, because the contact among the solids occurs along their boundaries. The proposed non-linear formulation is based on the use of singular or hyper-singular integral equations by BEM, for multi-region contact. When the contact occurs between crack surfaces, the formulation adopted is the dual version of BEM, in which singular and hyper-singular integral equations are defined along the opposite sides of the contact boundaries. The structural non-linear behaviour on the contact is considered using Coulomb`s friction law. The non-linear formulation is based on the tangent operator in which one uses the derivate of the set of algebraic equations to construct the corrections for the non-linear process. This implicit formulation has shown accurate as the classical approach, however, it is faster to compute the solution. Examples of simple and multi-region contact problems are shown to illustrate the applicability of the proposed scheme. (C) 2011 Elsevier Ltd. All rights reserved.