Theoretical Interpretations and Applications of Radial Basis Function Networks

Medical applications usually used Radial Basis Function Networks just as Artificial Neural Networks. However, RBFNs are Knowledge-Based Networks that can be interpreted in several way: Artificial Neural Networks, Regularization Networks, Support Vector Machines, Wavelet Networks, Fuzzy Controllers, Kernel Estimators, Instanced-Based Learners. A survey of their interpretations and of their corresponding learning algorithms is provided as well as a brief survey on dynamic learning algorithms. RBFNs' interpretations can suggest applications that are particularly interesting in medical domains

Registration-based model reduction of parameterized two-dimensional conservation laws

We propose a nonlinear registration-based model reduction procedure for rapid and reliable solution of parameterized two-dimensional steady conservation laws. This class of problems is challenging for model reduction techniques due to the presence of nonlinear terms in the equations and also due to the presence of parameter-dependent discontinuities that cannot be adequately represented through linear approximation spaces. Our approach builds on a general (i.e., independent of the underlying equation) registration procedure for the computation of a mapping Φ that tracks moving features of the solution field and on an hyper-reduced least-squares Petrov-Galerkin reduced-order model for the rapid and reliable computation of the solution coefficients. The contributions of this work are twofold. First, we investigate the application of registration-based methods to two-dimensional hyperbolic systems. Second, we propose a multi-fidelity approach to reduce the offline costs associated with the construction of the parameterized mapping and the reduced-order model. We discuss the application to an inviscid supersonic flow past a parameterized bump, to illustrate the many features of our method and to demonstrate its effectiveness

Similarity-based methods: a general framework for classification, approximation and association

Similarity-based methods (SBM) are a generalization of the minimal distance (MD) methods which form a basis of several machine learning and pattern recognition methods. Investigation of similarity leads to a fruitful framework in which many classification, approximation and association methods are accommodated. Probability p(C|X;M) of assigning class C to a vector X, given a classification modelM, depends on adaptive parameters and procedures used in construction of the model. Systematic overview of choices available for model building is described and numerous improvements suggested. Similarity-Based Methods have natural neural-network type realizations. Such neural network models as the Radial Basis Functions (RBF) and the Multilayer Perceptrons (MLPs) are included in this framework as special cases. SBM may also include several different submodels and a procedure to combine their results. Many new versions of similarity-based methods are derived from this framework. A search in the space of all methods belonging to the SBM framework finds a particular combination of parameterizations and procedures that is most appropriate for a given data. No single classification method can beat this approach. Preliminary implementation of SBM elements tested on a realworld datasets gave very good results

Computational physics of the mind

In the XIX century and earlier such physicists as Newton, Mayer, Hooke, Helmholtz and Mach were actively engaged in the research on psychophysics, trying to relate psychological sensations to intensities of physical stimuli. Computational physics allows to simulate complex neural processes giving a chance to answer not only the original psychophysical questions but also to create models of mind. In this paper several approaches relevant to modeling of mind are outlined. Since direct modeling of the brain functions is rather limited due to the complexity of such models a number of approximations is introduced. The path from the brain, or computational neurosciences, to the mind, or cognitive sciences, is sketched, with emphasis on higher cognitive functions such as memory and consciousness. No fundamental problems in understanding of the mind seem to arise. From computational point of view realistic models require massively parallel architectures

Applied Mathematics and Computational Physics

As faster and more efficient numerical algorithms become available, the understanding of the physics and the mathematical foundation behind these new methods will play an increasingly important role. This Special Issue provides a platform for researchers from both academia and industry to present their novel computational methods that have engineering and physics applications

Signal processing and image restoration techniques for two-dimensional eddy current nondestructive evaluation

This dissertation presents a comprehensive study on the forward modeling methods, signal processing techniques, and image restoration techniques for two-dimensional eddy current nondestructive evaluation. The basic physical forward method adopted in this study is the volume integral method. We have applied this model to the eddy current modeling problem for half space geometry and thin plate geometry. To reduce the computational complexity of the volume integral method, we have developed a wavelet expansion method which utilizes the multiresolution compression capability of the wavelet basis to greatly reduce the amount of computation with small loss in accuracy. To further improve the speed of forward modeling, we have developed a fast eddy current model based on a radial basis function neural network. This dissertation also contains investigations on signal processing techniques to enhance flaw signals in two-dimensional eddy current inspection data. The processing procedures developed in this study include a set of preprocessing techniques, a background removal technique based on principal component analysis, and grayscale morphological operations to detect flaw signals. Another important part of the dissertation concerns image restoration techniques which can remove the blurring in impedance change images due to the diffusive nature of the eddy current testing. We have developed two approximate linear image restoration methods--the Wiener filtering method and the maximum entropy method. Both linear restoration methods are based on an approximate linear forward model formulated by using the Born approximation. To improve the quality of restoration, we have also developed nonlinear image restoration methods based on simulated annealing and a genetic algorithm. Those nonlinear methods are based on the neural network forward model which is more accurate than the approximate linear forward model