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.

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Mesh free modeling techniques are a promising alternative to traditional meshed methods for solving computational fluid dynamics problems. These techniques aim to solve for the field variable using solely the values of nodes and therefore do not require the generation of a mesh. This results in a process that can be much more reliably automated and is therefore attractive. Radial basis functions (RBFs) are one type of "meshless" method that has shown considerable growth in the past 50 years. Using these RBFs to directly solve a partial differential equation is known as Kansa's method and has been used to successfully solve many flow problems. The problem with Kansa's method is that there is no formal guarantee that its solution matrix will be non-singular. More recently, an expansion on Kansa's method was proposed that incorporates the boundary and PDE operators into the solution of the field variable. This method, known as Hermitian method, has been shown to be non-singular provided certain nodal criteria are met. This work aims to perform a comparison between Kansa and Hermitian methods to aid in future selection of a method. These two methods were used to solve steady and transient one-dimensional convection-diffusion problems. The methods are compared in terms of accuracy (error) and computational complexity (conditioning number) in order to evaluate overall performance. Results suggest that the Hermitian method does slightly outperform Kansa method at the cost of a more ill-conditioned collocation matrix.

The rapid increase in computational power over the last decade has unlocked the possibility of providing patient-specific healthcare via simulation and data assimilation. In the past 2 decades, computational approaches to simulating cardiovascular flows have advanced significantly due to intense research and adoption of methods in medical device companies. A significant source of friction in porting these tools to the hospital and getting in the hands of surgeons is due to the expertise required to handle the geometry pre-processing and meshing of models. Meshless meth- ods reduce the amount of corner cases which makes it easier to develop robust tools surgeons need. To accurately simulate modifications to a region of vasculature as in surgical planning, the entire system must be modeled. Unfortunately, this is computationally prohibitive even on to- day’s machines. To circumvent this issue, the Radial-Basis Function Finite Difference (RBF-FD) method for solution of the higher-dimensional (2D/3D) region of interest is tightly-coupled to a 0D Lumped-Parameter Model (LPM) for solution of the peripheral circulation. The incompress- ible flow equations are updated by an explicit time-marching scheme based on a pressure-velocity correction algorithm. The inlets and outlets of the domain are tightly coupled with the LPM which contains elements that draw from a fluid-electrical analogy such as resistors, capacitors, and in- ductors that represent the viscous resistance, vessel compliance, and flow inertia, respectively. The localized RBF meshless approach is well-suited for modeling complicated non-Newtonian hemo- dynamics due to ease of spatial discretization, ease of addition of multi-physics interactions such as fluid-structure interaction of the vessel wall, and ease of parallelization for fast computations. This work introduces the tight coupling of meshless methods and LPMs for fast and accurate hemody- namic simulations. The results show the efficacy of the method to be used in building robust tools to inform surgical decisions and further development is motivated.

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

We present a unifying framework for the global optimization of functions which are expensive to evaluate. The framework is based on a Bayesian interpretation of radial basis function interpolation which incorporates existing methods such as Kriging, Gaussian process regression and neural networks. This viewpoint enables the application of Bayesian decision theory to derive a sequential global optimization algorithm which can be extended to include existing algorithms of this type in the literature. By posing the optimization problem as a sequence of sampling decisions, we optimize a general cost function at each stage of the algorithm. An extension to multi-stage decision processes is also discussed. The key idea of the framework is to replace the underlying expensive function by a cheap surrogate approximation. This enables the use of existing branch and bound techniques to globally optimize the cost function. We present a rigorous analysis of the canonical branch and bound algorithm in this setting as well as newly developed algorithms for other domains including convex sets. In particular, by making use of Lipschitz continuity of the surrogate approximation, we develop an entirely new algorithm based on overlapping balls. An application of the framework to the integration of expensive functions over rectangular domains and spherical surfaces in low dimensions is also considered. To assess performance of the framework, we apply it to canonical examples from the literature as well as an industrial model problem from oil reservoir simulation.

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.

Resumo: 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) / Abstract: 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 / Orientador: Carlos Roberto. Minussi / Coorientador: Francisco Villarreal Alvarado / Banca: Anna Diva Plasencia Lotufo / Banca: Maria do Carmo Gomes da Silveira / Banca: Gelson da Cruz Junior / Banca: Edmárcio Antonio Belati / Doutor

This thesis describes the implementation of a Radial Basis Function (RBF) network to be used in predicting the effectiveness of various strategies for reducing the Vehicle Trip Rate (VTR) of a worksite. Three methods of learning were utilized in training the Gaussian hidden units of the network, those being a) output weight adjustment using the Delta rule b) adjustable reference vectors in conjunction with weight adjustment, and c) a combination of adjustable centers and adjustable sigma values for each RBF neuron with the Delta rule. The justification for utilizing each of the more advanced levels of training is provided using a series of tests and performance comparisons. The network architecture is then selected based upon a series of initial trials for an optimum number of hidden Radial Basis neurons. In a similar manner, the training time is determined after finding a maximum number of epochs during which there is a significant change in the SSE. The network was compared for effectiveness against each of the following methods of data analysis: force-entered regression, backward regression, forward regression, stepwise regression, and two types of back-propagation networks based upon the attributes discovered to be most predictive by these regression techniques. A comparison of the learning methods used on the Radial Basis network shows the third learning strategy to be the most efficient for training, yielding the lowest sum of squared errors (SSE) in the shortest number of training epochs. The result of comparing the RBF implementation against the other methods mentions shows the superiority of the Radial Basis method for predictive ability.

Nonlinear multivariate statistical techniques on fast computers offer the potential to capture more of the dynamics of the high dimensional, noisy systems underlying financial markets than traditional models, while making fewer restrictive assumptions. This thesis presents a collection of practical techniques to address important estimation and confidence issues for Radial Basis Function networks arising from such a data driven approach, including efficient methods for parameter estimation and pruning, a pointwise prediction error estimator, and a methodology for controlling the "data mining'' problem. Novel applications in the finance area are described, including customized, adaptive option pricing and stock price prediction.