Radial basis function networks with quantized parameters

A RBFN implemented with quantized parameters is proposed and the relative or limited approximation property is presented. Simulation results for sinusoidal function approximation with various quantization levels are shown. The results indicate that the network presents good approximation capability even with severe quantization. The parameter quantization decreases the memory size and circuit complexity required to store the network parameters leading to compact mixed-signal circuits proper for low-power applications. ©2008 IEEE.

Multidimensional polynomial powers of sigmoid (PPS) Wavelet neural networks

Wavelet functions have been used as the activation function in feedforward neural networks. An abundance of R&D has been produced on wavelet neural network area. Some successful algorithms and applications in wavelet neural network have been developed and reported in the literature. However, most of the aforementioned reports impose many restrictions in the classical backpropagation algorithm, such as low dimensionality, tensor product of wavelets, parameters initialization, and, in general, the output is one dimensional, etc. In order to remove some of these restrictions, a family of polynomial wavelets generated from powers of sigmoid functions is presented. We described how a multidimensional wavelet neural networks based on these functions can be constructed, trained and applied in pattern recognition tasks. As an example of application for the method proposed, it is studied the exclusive-or (XOR) problem.

Cubic approximation for the transverse displacement in BEM for elastic plates analysis

This work presents an application for the plate analysis formulation by BEM where 3 boundary equations are used, written for the transverse displacement w and the normal and tangential derivatives partial derivativew/partial derivativen and partial derivativew/partial derivatives. In this extension, the transverse displacement w is approximated by a cubic polynomial and, as a consequence, partial derivativew/partial derivatives has a quadratic approximation. This alternative BEM formulation improves the analysis of thin plates, when compared to the formulation using the linear approximation for the displacements, mainly in the obtaining of the bending moments at the boundary of the plate. The implementation of this proposal to the computational codes is simple. (C) 2004 Published by Elsevier Ltd.

Multiscale Fractal Descriptors and Polynomial Classifier for Partial Pixels Identification in Regions of Interest of Mammographic Images

Computer systems are used to support breast cancer diagnosis, with decisions taken from measurements carried out in regions of interest (ROIs). We show that support decisions obtained from square or rectangular ROIs can to include background regions with different behavior of healthy or diseased tissues. In this study, the background regions were identified as Partial Pixels (PP), obtained with a multilevel method of segmentation based on maximum entropy. The behaviors of healthy, diseased and partial tissues were quantified by fractal dimension and multiscale lacunarity, calculated through signatures of textures. The separability of groups was achieved using a polynomial classifier. The polynomials have powerful approximation properties as classifiers to treat characteristics linearly separable or not. This proposed method allowed quantifying the ROIs investigated and demonstrated that different behaviors are obtained, with distinctions of 90% for images obtained in the Cranio-caudal (CC) and Mediolateral Oblique (MLO) views.

Resonances and subharmonic bifurcations of large amplitude periodic orbits of planar polynomial vector fields

In this work are studied periodic perturbations, depending on two parameters, of planar polynomial vector fields having an annulus of large amplitude periodic orbits, which accumulate on a symmetric infinite heteroclinic cycle. Such periodic orbits and the heteroclinic trajectory can be seen only by the global consideration of the polynomial vector fields on the whole plane, and not by their restriction to any compact set. The global study involving infinity is performed via the Poincare Compactification. It is shown that, for certain types of periodic perturbations, one can seek, in a neighborhood of the origin in the parameter plane, curves C-(m) of subharmonic bifurcations, for which the periodically perturbed system has subharmonics of order m, for any integer m.

Periodic perturbations of quadratic planar polynomial vector fields

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Large amplitude oscillations for a class of symmetric polynomial differential systems in R³

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Mathematical tests about the existence and applications of PPS-wavelets in function approximation problems

Neural networks and wavelet transform have been recently seen as attractive tools for developing eficient solutions for many real world problems in function approximation. Function approximation is a very important task in environments where computation has to be based on extracting information from data samples in real world processes. So, mathematical model is a very important tool to guarantee the development of the neural network area. In this article we will introduce one series of mathematical demonstrations that guarantee the wavelets properties for the PPS functions. As application, we will show the use of PPS-wavelets in pattern recognition problems of handwritten digit through function approximation techniques.

Comparative study between RBF and radial-PPS neural networks

The study of function approximation is motivated by the human limitation and inability to register and manipulate with exact precision the behavior variations of the physical nature of a phenomenon. These variations are referred to as signals or signal functions. Many real world problem can be formulated as function approximation problems and from the viewpoint of artificial neural networks these can be seen as the problem of searching for a mapping that establishes a relationship from an input space to an output space through a process of network learning. Several paradigms of artificial neural networks (ANN) exist. Here we will be investigated a comparative of the ANN study of RBF with radial Polynomial Power of Sigmoids (PPS) in function approximation problems. Radial PPS are functions generated by linear combination of powers of sigmoids functions. The main objective of this paper is to show the advantages of the use of the radial PPS functions in relationship traditional RBF, through adaptive training and ridge regression techniques.

Human face verification based on multidimensional Polynomial Powers of Sigmoid (PPS)

In this paper, we described how a multidimensional wavelet neural networks based on Polynomial Powers of Sigmoid (PPS) can be constructed, trained and applied in image processing tasks. In this sense, a novel and uniform framework for face verification is presented. The framework is based on a family of PPS wavelets,generated from linear combination of the sigmoid functions, and can be considered appearance based in that features are extracted from the face image. The feature vectors are then subjected to subspace projection of PPS-wavelet. The design of PPS-wavelet neural networks is also discussed, which is seldom reported in the literature. The Stirling Universitys face database were used to generate the results. Our method has achieved 92 % of correct detection and 5 % of false detection rate on the database.

Some practical advice on polynomial regression analysis from blocked response surface designs

It is often necessary to run response surface designs in blocks. In this paper the analysis of data from such experiments, using polynomial regression models, is discussed. The definition and estimation of pure error in blocked designs are considered. It is recommended that pure error is estimated by assuming additive block and treatment effects, as this is more consistent with designs without blocking. The recovery of inter-block information using REML analysis is discussed, although it is shown that it has very little impact if thc design is nearly orthogonally blocked. Finally prediction from blocked designs is considered and it is shown that prediction of many quantities of interest is much simpler than prediction of the response itself.

Landau and Kolmogoroff type polynomial inequalities

Let 0polynomials of degree not exceeding n).For the particular case j=1 and m=2, we provide a complete characterisation of the positive constants A and B, for which the corresponding Landau type polynomial inequalities parallel to f'parallel to less than or equal toA parallel to f parallel to + B parallel to f parallel to/ A theta(k) + B mu(k)hold. In each case we determine the corresponding extremal polynomials for which equalities are attained.

Almost strict total positivity and a class of Hurwitz polynomials

We establish sufficient conditions for a matrix to be almost totally positive, thus extending a result of Craven and Csordas who proved that the corresponding conditions guarantee that a matrix is strictly totally positive. Then we apply our main result in order to obtain a new criteria for a real algebraic polynomial to be a Hurwitz one. The properties of the corresponding extremal Hurwitz polynomials are discussed. (C) 2004 Elsevier B.V. All rights reserved.

On the behaviour of zeros of Jacobi polynomials

Denote by x(n,k)(alpha, beta) and x(n,k) (lambda) = x(n,k) (lambda - 1/2, lambda - 1/2) the zeros, in decreasing order, of the Jacobi polynomial P-n((alpha, beta))(x) and of the ultraspherical (Gegenbauer) polynomial C-n(lambda)(x), respectively. The monotonicity of x(n,k)(alpha, beta) as functions of a and beta, alpha, beta > - 1, is investigated. Necessary conditions such that the zeros of P-n((a, b)) (x) are smaller (greater) than the zeros of P-n((alpha, beta))(x) are provided. A. Markov proved that x(n,k) (a, b) < x(n,k)(α, β) (x(n,k)(a, b) > x(n,k)(alpha, beta)) for every n is an element of N and each k, 1 less than or equal to k less than or equal to n if a > alpha and b < β (a < alpha and b > beta). We prove the converse statement of Markov's theorem. The question of how large the function could be such that the products f(n)(lambda) x(n,k)(lambda), k = 1,..., [n/2] are increasing functions of lambda, for lambda > - 1/2, is also discussed. Elbert and Siafarikas proved that f(n)(lambda) = (lambda + (2n(2) + 1)/ (4n + 2))(1/2) obeys this property. We establish the sharpness of their result. (C) 2002 Elsevier B.V. (USA).