Pattern recognition theory in nonlinear signal processing

A body of research has developed within the context of nonlinear signal and image processing that deals with the automatic, statistical design of digital window-based filters. Based on pairs of ideal and observed signals, a filter is designed in an effort to minimize the error between the ideal and filtered signals. The goodness of an optimal filter depends on the relation between the ideal and observed signals, but the goodness of a designed filter also depends on the amount of sample data from which it is designed. In order to lessen the design cost, a filter is often chosen from a given class of filters, thereby constraining the optimization and increasing the error of the optimal filter. To a great extent, the problem of filter design concerns striking the correct balance between the degree of constraint and the design cost. From a different perspective and in a different context, the problem of constraint versus sample size has been a major focus of study within the theory of pattern recognition. This paper discusses the design problem for nonlinear signal processing, shows how the issue naturally transitions into pattern recognition, and then provides a review of salient related pattern-recognition theory. In particular, it discusses classification rules, constrained classification, the Vapnik-Chervonenkis theory, and implications of that theory for morphological classifiers and neural networks. The paper closes by discussing some design approaches developed for nonlinear signal processing, and how the nature of these naturally lead to a decomposition of the error of a designed filter into a sum of the following components: the Bayes error of the unconstrained optimal filter, the cost of constraint, the cost of reducing complexity by compressing the original signal distribution, the design cost, and the contribution of prior knowledge to a decrease in the error. The main purpose of the paper is to present fundamental principles of pattern recognition theory within the framework of active research in nonlinear signal processing.

Nonlinear optical properties of tungstate fluorophosphate glasses

The optical nonlinearity of tungstate fluorophosphate glasses, synthesized in the NaPO3-BaF2-WO3 system, was investigated through experiments based on the third-order susceptibility, chi((3)). Nonlinear (NL) refraction and NL absorption measurements in the picosecond regime were performed using the Z-scan technique at 532 nm. NL refractive index, n(2)proportional toRe chi((3)), ranging from 0.4x10(-14) cm(2)/W to 0.6x10(-14) cm(2)/W were determined. The two-photon absorption coefficient, alpha(2)proportional toIm chi((3)), for excitation at 532 nm, vary from 0.3 to 0.5 cm/GW. Light induced birefringence experiments performed in the femtosecond regime indicate that the response time of the nonlinearity at 800 nm is faster than 100 fs. The experiments show that chi((3)) is enhanced when the WO3 concentration increases and this behavior is attributed to the hyperpolarizabilities associated to W-O bonds. (C) 2004 American Institute of Physics.

Energy localization in the Peyrard-Bishop DNA model

We study energy localization on the oscillator chain proposed by Peyrard and Bishop to model DNA. We search numerically for conditions with initial energy in a small subgroup of consecutive oscillators of a finite chain and such that the oscillation amplitude is small outside this subgroup on a long time scale. We use a localization criterion based on the information entropy and verify numerically that such localized excitations exist when the nonlinear dynamics of the subgroup oscillates with a frequency inside the reactive band of the linear chain. We predict a mimium value for the Morse parameter (mu>2.25) (the only parameter of our normalized model), in agreement with the numerical calculations (an estimate for the biological value is mu=6.3). For supercritical masses, we use canonical perturbation theory to expand the frequencies of the subgroup and we calculate an energy threshold in agreement with the numerical calculations.

Approximate expression for the energy of a D-dimensional anharmonic oscillator

An approximate expression is constructed for the energy of an anharmonic potential with centrifugal barrier. In order to obtain such an analytical expression, the quasi-exact solvability is used and then a fitting of these exact solutions is done.

Nonlinear characteristics of Cr2O3, WO3, ZnO and CoO doped SnO2 varistors

SnO2 based ceramics doped with 1.0 mol% ZnO, 1.0 mol% CoO, 0.1 mol% WO3 and 0.05 mol% Cr2O3 show varistor behavior with nonlinear coefficient alpha = 33, breakdown electric field E-B = 12.5 kV/cm, leakage current I = 0.63 mA/cm(2) and average grain size of 1.52 mu m. Experimental evidence shows that the addition of Cr2O3 improves the nonlinear properties of the samples significantly, the impedance data, represented by means of Nyquist diagrams, show a dramatic increase in the resistivity for the samples doped with Cr2O3. (C) 2005 Elsevier B.V. All rights reserved.

VARIATIONAL SPIKED OSCILLATOR

A variational analysis of the spiked harmonic oscillator Hamiltonian -d2/dr2 + r2 + lambda/r5/2, lambda > 0, is reported. A trial function automatically satisfying both the Dirichlet boundary condition at the origin and the boundary condition at infinity is introduced. The results are excellent for a very large range of values of the coupling parameter lambda, suggesting that the present variational function is appropriate for the treatment of the spiked oscillator in all its regimes (strong, moderate, and weak interactions).

Influence of La2O3, Pr2O3 and CeO2 on the nonlinear properties of SnO2 multicomponent varistors

The influence of La2O3, Pr2O3 and CeO2 on a new class of polycrystalline ceramics with nonlinear properties based on SnO2, was investigated. La2O3 and Pr2O3 were found to precipitate at the grain boundary region, causing a considerable increase in the nonlinear behavior. It was found that CeO2 forms a solid solution in the bulk but. unlike La2O3 and Pr2O3, it does not increase the nonlinear behavior. A higher nonlinear coefficient of similar to80 was obtained for La2O3-doped SnO2-based systems. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Negative nonlinear absorption in Er3+-doped fluoroindate glass

We report the observation of negative nonlinear absorption in fluoroindate glasses doped with erbium ions. The pumping wavelength is 800 nm which is doubly resonant with Er3+ ions transitions. A large nonlinear intensity dependence of the optical transmittance and strong upconverted fluorescence are obtained. The dependence of the upconverted fluorescence intensity with the laser power is described by a system of coupled-rate equations for the energy levels' populations. (C) 1998 American Institute of Physics. [S0021-8979(98)07816-5].

Femtosecond nonlinear optical properties of tellurite glasses

The third-order nonlinear optical properties of tellurite glasses with different compositions were investigated in the femtosecond regime at 810 nm. Using the I-scan technique, positive nonlinear refractive indices of similar to 10(-15) cm(2)/W were measured. The authors also determined that nonlinear absorption was negligible for all studied samples. This result, added to their good chemical stability, indicates that tellurite glasses are promising materials for ultrafast photonic applications. (c) 2006 American Institute of Physics.

Nonlinear parameter estimation in laminar forced convection within a circular sector tube

In this article we examine an inverse heat convection problem of estimating unknown parameters of a parameterized variable boundary heat flux. The physical problem is a hydrodynamically developed, thermally developing, three-dimensional steady state laminar flow of a Newtonian fluid inside a circular sector duct, insulated in the flat walls and subject to unknown wall heat flux at the curved wall. Results are presented for polynomial and sinusoidal trial functions, and the unknown parameters as well as surface heat fluxes are determined. Depending on the nature of the flow, on the position of experimental points the inverse problem sometimes could not be solved. Therefore, an identification condition is defined to specify a condition under which the inverse problem can be solved. Once the parameters have been computed it is possible to obtain the statistical significance of the inverse problem solution. Therefore, approximate confidence bounds based on standard statistical linear procedure, for the estimated parameters, are analyzed and presented.

NONLINEAR SURFACE-WAVE EXCITATIONS IN THE BENARD-MARANGONI SYSTEM

We examine the appearance of surface waves governed by Burgers and Korteweg-de Vries equations in a shallow viscous heated fluid. We consider waves triggered by a surface-tension variation induced by both temperature and concentration gradients. We also establish the range of parameters for which the above-mentioned equations appear.

Nonadiabatic calculations of the oscillator strengths for the helium atom in the hyperspherical adiabatic approach

Energies and wavefunctions are calculated for the bound states of the helium atom in the hyperspherical adiabatic approach by the full inclusion of nonadiabatic couplings. We show that the use of appropriate asymptotic radial boundary conditions not only allows the efficient calculation of energies accurate up to a few ppm for the ground state but also gives increasingly precise results for high-lying excited states with a unique set of equations. The accuracy of the wavefunctions is demonstrated by the calculation of oscillator strengths in the length form for transitions between stares ii S-1(e) and (n + 1) P-1(0) up to n = 29, in agreement with variational calculations.

Nonlinear behavior of TiO2 center dot Ta2O5 center dot MnO2 material doped with BaO and Bi2O3

A study was made on the effect of the addition of BaO (0.025-0.05 mol%) and Bi2O3 (0.025-0.05 mol%) to the TiO2.Ta2O5.MnO2 material. The samples were characterized by X-ray diffraction, and current-voltage measurements were accomplished for determination of the nonlinear coefficient. An analysis was made to evaluate the microstructural characteristics of the materials. The most appropriate sintering conditions for the materials were analyzed with the purpose of obtaining the best nonlinear coefficient associated with the smallest breakdown electric field. After sintering at 1400 degreesC for 2 h, a low-voltage (30 V cm(-1)) varistor was obtained, which, however, presented a low nonlinear coefficient (6). It was found that the sintering conditions must be controlled in order to improve the electrical properties of these materials. (C) 2004 Elsevier B.V. All rights reserved.