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RBFs are useful in scientific computing. In this thesis, we are interested in the positions of collocation points and RBF centers which causes the matrix for RBF interpolation singular and ill-conditioned. We explore the best bases by minimizing error function in supremum norm and root mean squares. We also use radial basis function to interpolate shifted data and find the best basis in certain sense. In the second part, we solve ill-posed problems by radial basis collocation method with different radial basis functions and various number of bases. If the solution is not unique, then the numerical solutions are different for different bases. To construct all the solutions, we can choose one approximation solution and add the linear combinations of the difference functions for various bases. If the solution does not exist, we show the numerical solution always fail to satisfy the origin equation.

In this thesis, we propose a new class of learning models, namely the additive generalized radial basis function networks (AGRBFNs), for general nonlinear regression problems. This class of learning machines combines the generalized radial basis function networks (GRBFNs) commonly used in general machine learning problems and the additive models (AMs) frequently encountered in semiparametric regression problems. In statistical regression theory, AM is a good compromise between the linear model and the nonparametric model. In order for more general network structure hoping to address more general data sets, the AMs are embedded in the output layer of the GRBFNs to form the AGRBFNs. Simple weights updating rules based on incremental gradient descent will be derived. Several illustrative examples are provided to compare the performances for the classical GRBFNs and the proposed AGRBFNs. Simulation results show that upon proper selection of the hidden nodes and the bandwidth of the kernel smoother used in additive output layer, AGRBFNs can give better fits than the classical GRBFNs. Furthermore, for the given learning problem, AGRBFNs usually need fewer hidden nodes than those of GRBFNs for the same level of accuracy.

Accurate rainfall forecasting using weather radar imagery has always been a crucial and predominant task in the field of meteorology [1], [2], [3] and [4]. Competitive Radial Basis Function Neural Networks (CRBFNN) [5] is one of the methods used for weather radar image based forecasting. Recently, an alternative CRBFNN based approach [6] was introduced to model the precipitation events. The difference between the techniques presented in [5] and [6] is in the approach used to model the rainfall image. Overall, it was shown that the modified CRBFNN approach [6] is more computationally efficient compared to the CRBFNN approach [5]. However, both techniques [5] and [6] share the same prediction stage. In this thesis, a different GRBFNN approach is presented for forecasting Gaussian envelope parameters. The proposed method investigates the concept of parameter dependency among Gaussian envelopes. Experimental results are also presented to illustrate the advantage of parameters prediction over the independent series prediction.

Submitted by Amanda Silva (amanda.osilva2@ufpe.br) on 2015-03-03T14:16:54Z No. of bitstreams: 2 Dissertação Mariel Cadena da Matta.pdf: 2355898 bytes, checksum: 9c0530af680cf965137a2385d949b799 (MD5) license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) / Made available in DSpace on 2015-03-03T14:16:54Z (GMT). No. of bitstreams: 2 Dissertação Mariel Cadena da Matta.pdf: 2355898 bytes, checksum: 9c0530af680cf965137a2385d949b799 (MD5) license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Previous issue date: 2013 / FACEPE / A Dosimetria citogenética empregando análise de cromossomos dicêntricos é o “padrão ouro” para estimativas da dose absorvida após exposições acidentais às radiações ionizantes. Todavia, este método é laborioso e dispendioso, o que torna necessária a introdução de ferramentas computacionais que dinamizem a contagem dessas aberrações cromossômicas radioinduzidas. Os atuais softwares comerciais, utilizados no processamento de imagens em Biodosimetria, são em sua maioria onerosos e desenvolvidos em sistemas dedicados, não podendo ser adaptados para microscópios de rotina laboratorial. Neste contexto, o objetivo da pesquisa foi o desenvolvimento do software ChromoSomeClassification para processamento de imagens de metáfases de linfócitos (não irradiados e irradiados) coradas com Giemsa a 5%. A principal etapa da análise citogenética automática é a separação correta dos cromossomos do fundo, pois a execução incorreta desta fase compromete o desenvolvimento da classificação automática. Desta maneira, apresentamos uma proposta para a sua resolução baseada no aprimoramento da imagem através das técnicas de mudança do sistema de cores, subtração do background e aumento do contraste pela modificação do histograma. Assim, a segmentação por limiar global simples, seguida por operadores morfológicos e pela técnica de separação de objetos obteve uma taxa de acerto de 88,57%. Deste modo, os cromossomos foram enfileirados e contabilizados, e assim, a etapa mais laboriosa da Dosimetria citogenética foi realizada. As características extraídas dos cromossomos isolados foram armazenadas num banco de dados para que a classificação automática fosse realizada através da Rede Neural com Funções de Ativação de Base Radial (RBF). O software proposto alcançou uma taxa de sensibilidade de 76% e especificidade de 91% que podem ser aprimoradas através do acréscimo do número de objetos ao banco de dados e da extração de mais características dos cromossomos.

Some metals, such as Ti-6Al-4V, have a high elongation to failure when strained at certain rates and temperatures. Superplastic forming is the utilisation of this property, and it can be used to form thin, geometrically complex components. Superplastic forming is a slow process, and this is one of the reasons why it is an expensive manufacturing process. Localised thinning occurs if the specimen is strained too quickly, and components with locally thin wall thickness fail prematurely. The goal of this study is to find a technique that can be used to minimise the forming time while limiting the minimum final thickness. The superplastic forming process is investigated with the finite element method. The finite element method requires a material model which describes the superplastic behaviour of the metal. Several material models are investigated in order to select a material model that can show localised thinning at higher strain rates. The material models are calibrated with stress-strain data, grain size-time data and strain rate sensitivity-strain data. The digitised data from literature is for Ti-6Al-4V with three different initial grain sizes strained at different strain rates at 927 C. The optimisation of the forming time is done with an approximate optimisation algorithm. This algorithm involves fitting a metamodel to simulated data, and using the metamodels to find the optimum instead of using the finite element model directly. One metamodel is fitted to the final forming time results, and another metamodel is fitted to the final minimum thickness results. A regressive radial basis function method is used to construct the metamodels. The interpolating radial basis function method proved to be unreliable at the design space boundaries due to non-smooth finite element results. The non-smooth results are due to the problem being path dependent. The final forming time of the superplastic forming of a rectangular box was successfully minimised while limiting the final minimum thickness. The metamodels predicted that allowing a 4% decrease in the minimum allowable thickness (1.0 mm to 0.96 mm) and a 1 mm gap between the sheet and the die corner the forming time is decreased by 28.84%. The finite element verification indicates that the final minimum thickness reduced by 3.8% and that the gap between the sheet and the die corner is less than 1 mm, resulting in the forming time being reduced by 28.81%. / Dissertation (MEng)--University of Pretoria, 2017. / Mechanical and Aeronautical Engineering / MEng / Unrestricted

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Cardiovascular diseases (CVD) are the number one causes of death in the world. According to the world Health Organization (WHO) 17.5 million people died from cardiovascular disease in 2005, representing 30 % of all global deaths . Of these deaths, 7.6 million were due to heart attacks and 5.7 million due to stroke. If current trends are allowed to continue, by 2015 an estimated 20 million people will die annually from cardiovascular disease. The trends are similar in the United States where on an average 1 person dies every 37 seconds due to CVD. In 2008 an estimated 770,000 Americans will experience a new heart attack (coronary stenosis) and 600,000 will experience a first stroke. Although the exact causes of cardiovascular disease are not well understood, hemodynamics has been long thought to play a primary role in the progression of cardiovascular disease and stroke. There is strong evidence linking the fluid mechanical forces to the transduction mechanisms that trigger biochemical response leading to atherosclerosis or plaque formation. It is hypothesized that the emergence of abnormal fluid mechanical stresses which dictate the cell mechanotransduction mechanisms and lead to disease progression is dependent on the geometry and compliance of arteries, and pulsatility of blood flow. Understanding of such hemodynamic regulation in relation to atherosclerosis is of significant clinical importance in the prediction and progression of heart disease as well as design of prosthetic devices such as stents. The current work will systematically study the effects of compliance and complex geometry and the resulting fluid mechanical forces. The objective of this work is to understand the relationship of fluid mechanics and disease conditions using both experimental and computational methods where (a) Compliance effects are studied in idealized stenosed coronary and peripheral arteries using Digital Particle Image Velocimetry (DPIV), (b) Complex geometric effects of stented arteries with emphasis on its design parameters is investigated using CFD, Also (c) a novel method to improve the accuracy of velocity gradient estimation in the presence of noisy flow fields such as in DPIV where noise is inherently present is introduced with the objective to improve accuracy in the estimation of WSS, which are of paramount hemodynamic importance. The broad impact of the current work extends to the understanding of fundamental physics associated with arterial disease progression which can lead to better design of prosthetic devices, and also to better disease diagnostics. / Ph. D.

This dissertation considers certain issues in support vector machines (SVMs), including a description of their construction, aspects of certain exponential kernels used in some SVMs, and a presentation of an algorithm that computes the necessary elements of their operation with proof of convergence. In its first section, this dissertation provides a reasonably complete description of SVMs and their theoretical basis, along with a few motivating examples and counterexamples. This section may be used as an accessible, stand-alone introduction to the subject of SVMs for the advanced undergraduate. Its second section provides a proof of the positive-definiteness of a certain useful function here called E and dened as follows: Let V be a complex inner product space. Let N be a function that maps a vector from V to its norm. Let p be a real number between 0 and 2 inclusive and for any in V , let ( be N() raised to the p-th power. Finally, let a be a positive real number. Then E() is exp(()). Although the result is not new (other proofs are known but involve deep properties of stochastic processes) this proof is accessible to advanced undergraduates with a decent grasp of linear algebra. Its final section presents an algorithm by Dr. Kallman (preprint), based on earlier Russian work by B.F. Mitchell, V.F Demyanov, and V.N. Malozemov, and proves its convergence. The section also discusses briefly architectural features of the algorithm expected to result in practical speed increases.