The chemical master equation, formulated on the Markov assumption of underlying chemical kinetics, offers an accurate stochastic description of general chemical reaction systems on the mesoscopic scale. The chemical master equation is especially useful when formulating mathematical models of gene regulatory networks and protein-protein interaction networks, where the numbers of molecules of most species are around tens or hundreds. However, solving the master equation directly suffers from the so called "curse of dimensionality" issue. This thesis first tries to study the numerical properties of the master equation using existing numerical methods and parallel machines. Next, approximation algorithms, namely the adaptive aggregation method and the radial basis function collocation method, are proposed as new paths to resolve the "curse of dimensionality". Several numerical results are presented to illustrate the promises and potential problems of these new algorithms. Comparisons with other numerical methods like Monte Carlo methods are also included. Development and analysis of the linear Shepard algorithm and its variants, all of which could be used for high dimensional scattered data interpolation problems, are also included here, as a candidate to help solve the master equation by building surrogate models in high dimensions. / Ph. D.

A solar and diesel-wind hybrid power control systems is proposed in the thesis. The system consists of solar power, wind power, diesel-engine, a static synchronous compensator and an intelligent power controller. MATLAB/Simulink was used to build the dynamic model and simulate the solar and diesel-wind hybrid power system. A static synchronous compensator was used to supply reactive power and regulate the voltage of the hybrid system. To achieve a fast and stable response for the real power control, an intelligent controller was proposed, which consists of the Radial Basis Function Network (RBFN) and the Elman Neural Network (ENN) for maximum power point tracking (MPPT). The pitch angle control of wind power uses ENN controller, and the output is fed to the wind turbine to achieve the MPPT. The solar system uses RBFN, and the output signal is used to control the DC / DC boost converters to achieve the MPPT.

Thesis (MSc (Applied Mathematics))--Stellenbosch University, 2008. / A popular method for interpolating multidimensional scattered data is using radial basis functions. In this thesis we present the basic theory of radial basis function interpolation and also regard the solvability and stability of the method. Solving the interpolant directly has a high computational cost for large datasets, hence using numerical methods to approximate the interpolant is necessary. We consider some recent numerical algorithms. Software to implement radial basis function interpolation and to display the 3D interpolants obtained, is developed. We present results obtained from using our implementation for radial basis functions on GIS and 3D face data as well as an image warping application.

Made available in DSpace on 2014-06-11T19:30:50Z (GMT). No. of bitstreams: 0 Previous issue date: 2010-11-27Bitstream added on 2014-06-13T19:47:13Z : No. of bitstreams: 1 altran_ab_dr_ilha.pdf: 733564 bytes, checksum: 382a61569b0f5da4ceb6a2f45c0815a4 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / A previsão de carga, em sistemas de energia elétrica, constitui-se numa atividade de grande importância, tendo em vista que a maioria dos estudos realizados (fluxo de potência, despacho econômico, planejamento da expansão, compra e venda de energia, etc.) somente poderá ser efetivada se houver a disponibilidade de uma boa estimativa da carga a ser atendida. Deste modo, visando contribuir para que o planejamento e operação dos sistemas de energia elétrica ocorram de forma segura, confiável e econômica, foi desenvolvida uma metodologia para previsão de carga, a previsão multinodal, que pode ser entendida como um sistema inteligente que considera vários pontos da rede elétrica durante a realização da previsão. O sistema desenvolvido conta com o uso de uma rede neural artificial composta por vários módulos, sendo esta do tipo perceptron multicamadas, cujo treinamento é baseado no algoritmo retropropagação. Porém, foi realizada uma modificação na função de ativação da rede, em substituição à função usual, a função sigmoide, foram utilizadas as funções de base radial. Tal metodologia foi aplicada ao problema de previsão de cargas elétricas a curto-prazo (24 horas à frente) / Load forecasting in electric power systems is a very important activity due to several studies, e.g. power flow, economic dispatch, expansion planning, purchase and sale of energy that are extremely dependent on a good estimate of the load. Thus, contributing to a safe, reliable, economic and secure operation and planning this work is developed, which is an intelligent system for multinodal electric load forecasting considering several points of the network. The multinodal system is based on an artificial neural network composed of several modules. The neural network is a multilayer perceptron trained by backpropagation where the traditional sigmoide is substituted by radial basis functions. The methodology is applied to forecast loads 24 hours in advance

Orientadores: Anamaria Gomide, Jorge Stolfi / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Computação / Made available in DSpace on 2018-08-13T10:58:35Z (GMT). No. of bitstreams: 1 Pereira_DanilloRoberto_M.pdf: 891270 bytes, checksum: 71a9debc6a10f8de7083dd3e33c649a6 (MD5) Previous issue date: 2009 / Resumo: A geração de imagens fotorrealisticas e um desafio importante em computação gráfica. Um ingrediente critico para a obtenção do realismo esta o modelo de iluminação. Em 1986, Jim Kajiya apresentou uma equação integral que define o fluxo de luz (radiosidade) num ambiente de maneira precisa; contudo, ate recentemente, os métodos conhecidos para a resolução dessa equação tinham custo computacional e complexidade de implementação elevados. Em 2008, Jaako Lehtinen desenvolveu uma técnica relativamente simples e eficiente para o calculo da iluminação global em cenas virtuais, usando elementos finitos definidos por pontos de amostragem. Neste projeto de Mestrado, implementamos esse método, e comparamos o resultado usando três tipos diferentes de bases: uma base radial, uma base radial normalizada e uma base de Shepard. Alem da comparação visual, calculamos a radiosidade "exata" para uma cena simples e comparamos quantitativamente esse resultado com os resultados do método de Lehtinen com cada uma das três bases. / Abstract: The generation of realistic images is a major challenge in computer graphics. A critical ingredient for realistic rendering is the lighting model. In 1986, Jim Kajiya presented an integral equation that precisely defines the light flow (radiosity) in a virtual environment; however, until recently, the known methods for solving that equation had high computational cost and implementation complexity. In 2008, Jaako Lehtinen developed a relatively simple and efficient technique for the computation of global illumination in virtual scenes, using finite elements defined by sampling points. In this Masters project, we implemented that method, and compared the results using three different types of bases: a radial basis, a normalized radial basis, and a Shepard basis. Besides visual comparison, we computed the "exact" radiosity for a simple scene and compared quantitatively that result with the results obtained by Lehtinen's method with each of the three bases. / Mestrado / Computação Grafica / Mestre em Ciência da Computação

In this thesis, the method of Proper Orthogonal Decomposition (POD) is implemented to construct approximate, reduced order models (ROM) of mesh movement methods. Three mesh movement algorithms are implemented and comparatively evaluated, namely radial basis function interpolation, mesh optimization and elastic deformation. POD models of the mesh movement algorithms are constructed using a series of system observations, or snapshots of a given mesh for a set of boundary deformations. The scalar expansion coefficients for the POD basis modes are computed in three different ways, through coefficient optimization, Galerkin projection of the governing set of equations and coefficient interpolation. It is found that using only coefficient interpolation yields mesh movement models that accurately approximates the full order mesh movement, with CPU cost savings in excess of 99%. We further introduce a novel training procedure whereby the POD models are generated in a fully automated fashion. The technology is applicable to any mesh movement method and enables potential reductions of up to four orders of magnitude in mesh movement related costs. The proposed model can be implemented without having to pre-train the POD model, to any fluid-structure interaction code with an existing mesh movement scheme. Copyright / Dissertation (MEng)--University of Pretoria, 2010. / Mechanical and Aeronautical Engineering / unrestricted

Karst rocky desertification is a progressive process of land degradation in karst regions in which soil is severely, or completely, eroded. This process may be caused by natural factors, such as geological structure, and population pressure leading to poor ecosystem health and lagging economic development. Karst rocky desertification is therefore a significant obstacle to sustainable development in southwest China. We applied a radial basis function network model to assess the risk of karst rocky desertification in northwest Guangxi, a typical karst region located in southwest China. Factors known to influence karst rocky desertification were evaluated using remote sensing and geographic information systems techniques to classify the 23 counties in the study area from low to extreme risk of karst rocky desertification. Counties with extreme or strong karst rocky desertification risk (43.48%, nearly half of the study area) were clustered in the north, central and southeast portions of the study area. Counties with low karst rocky desertification (30.43%) were located in the west, northeast and southwest of the study area. The spatial distribution of karst rocky desertification was moderately correlated to population density.

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In this thesis, we introduce a radial basis function network approach to solve a color image classification problem in a real time industrial application. Radial basis function networks are employed to classify the images of finished wooden parts in terms of their color and species. Other classification methods are also examined in this work. The minimum distance classifiers are presented since they have been employed by the previous research. We give brief definitions about color space, color texture, color quantization, color classification methods. We also give an intensive review of radial basis functions, regularization theory, regularized radial basis function networks, and generalized radial basis function networks. The centers of the radial basis functions are calculated by the k-means clustering algorithm. We examine the k-means algorithm in terms of starting criteria, the movement rule, and the updating rule. The dilations of the radial basis functions are calculated using a statistical method. Learning classifier systems are also employed to solve the same classification problem. Learning classifier systems learn the training samples completely whereas they are not successful to classify the test samples. Finally, we present some simulation results for both radial basis function network method and learning classifier systems method. A comparison is given between the results of each method. The results show that the best classification method examined in this work is the radial basis function network method. / Master of Science

Weather radar imagery is important for several remote sensing applications including tracking of storm fronts and radar echo classification. In particular, tracking of precipitation events is useful for both forecasting and classification of rain/non-rain events since non-rain events usually appear to be static compared to rain events. Recent weather radar imaging-based forecasting approaches [3] consider that precipitation events can be modeled as a combination of localized functions using Radial Basis Function Neural Networks (RBFNNs). Tracking of rain events can be performed by tracking the parameters of these localized functions. The RBFNN-based techniques used in forecasting are not only computationally expensive, but also moderately effective in modeling small size precipitation events. In this thesis, an existing RBFNN technique [3] was implemented to verify its computational efficiency and forecasting effectiveness. The feasibility of modeling precipitation events using RBFNN effectively was evaluated, and several modifications to the existing technique have been proposed.