A fast multi-output RBF neural network construction method

This paper investigates the center selection of multi-output radial basis function (RBF) networks, and a multi-output fast recursive algorithm (MFRA) is proposed. This method can not only reveal the significance of each candidate center based on the reduction in the trace of the error covariance matrix, but also can estimate the network weights simultaneously using a back substitution approach. The main contribution is that the center selection procedure and the weight estimation are performed within a well-defined regression context, leading to a significantly reduced computational complexity. The efficiency of the algorithm is confirmed by a computational complexity analysis, and simulation results demonstrate its effectiveness. (C) 2010 Elsevier B.V. All rights reserved.

Modeling Multivariate Interest Rates Using Time-Varying Copulas and Reducible Nonlinear Stochastic Differential Equations

We propose a new approach for modeling nonlinear multivariate interest rate processes based on time-varying copulas and reducible stochastic differential equations (SDEs). In the modeling of the marginal processes, we consider a class of nonlinear SDEs that are reducible to Ornstein--Uhlenbeck (OU) process or Cox, Ingersoll, and Ross (1985) (CIR) process. The reducibility is achieved via a nonlinear transformation function. The main advantage of this approach is that these SDEs can account for nonlinear features, observed in short-term interest rate series, while at the same time leading to exact discretization and closed-form likelihood functions. Although a rich set of specifications may be entertained, our exposition focuses on a couple of nonlinear constant elasticity volatility (CEV) processes, denoted as OU-CEV and CIR-CEV, respectively. These two processes encompass a number of existing models that have closed-form likelihood functions. The transition density, the conditional distribution function, and the steady-state density function are derived in closed form as well as the conditional and unconditional moments for both processes. In order to obtain a more flexible functional form over time, we allow the transformation function to be time varying. Results from our study of U.S. and UK short-term interest rates suggest that the new models outperform existing parametric models with closed-form likelihood functions. We also find the time-varying effects in the transformation functions statistically significant. To examine the joint behavior of interest rate series, we propose flexible nonlinear multivariate models by joining univariate nonlinear processes via appropriate copulas. We study the conditional dependence structure of the two rates using Patton (2006a) time-varying symmetrized Joe--Clayton copula. We find evidence of asymmetric dependence between the two rates, and that the level of dependence is positively related to the level of the two rates. (JEL: C13, C32, G12) Copyright The Author 2010. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org, Oxford University Press.

Spatial evolution of a q-Gaussian laser beam in relativistic plasma

In a recent experimental study, the beam intensity profile of the Vulcan petawatt laser beam was measured; it was found that only 20% of the energy was contained within the full width at half maximum of 6.9 mu m and 50% within 16 mu m, suggesting a long-tailed non-Gaussian transverse beam profile. A q-Gaussian distribution function was suggested therein to reproduce this behavior. The spatial beam profile dynamics of a q-Gaussian laser beam propagating in relativistic plasma is investigated in this article. A non-paraxial theory is employed, taking into account nonlinearity via the relativistic decrease of the plasma frequency. We have studied analytically and numerically the dynamics of a relativistically guided beam and its dependence on the q-parameter. Numerical simulation results are shown to trace the dependence of the focusing length on the q-Gaussian profile.

Fokker-Planck equation for a test-particle weakly coupled to a magnetized plasma

We consider the derivation of a kinetic equation for a charged test particle weakly interacting with an electrostatic plasma in thermal equilibrium, subject to a uniform external magnetic field. The Liouville equation leads to a generalized master equation to second order in the `weak' interaction; a Fokker-Planck-type equation then follows as a `Markovian' approximation. It is shown that such an equation does not preserve the positivity of the distribution function f(x,v;t). By applying techniques developed in the theory of open systems, a correct Fokker-Planck equation is derived. Explicit expressions for the diffusion and drift coefficients, depending on the magnetic field, are obtained.

Locally regularised two-stage learning algorithm for RBF network centre selection

Nonlinear models constructed from radial basis function (RBF) networks can easily be over-fitted due to the noise on the data. While information criteria, such as the final prediction error (FPE), can provide a trade-off between training error and network complexity, the tunable parameters that penalise a large size of network model are hard to determine and are usually network dependent. This article introduces a new locally regularised, two-stage stepwise construction algorithm for RBF networks. The main objective is to produce a parsomous network that generalises well over unseen data. This is achieved by utilising Bayesian learning within a two-stage stepwise construction procedure to penalise centres that are mainly interpreted by the noise.

Application of Nonlinear PCA for Fault Detection in Polymer Extrusion Processes

This paper describes the application of an improved nonlinear principal component analysis (PCA) to the detection of faults in polymer extrusion processes. Since the processes are complex in nature and nonlinear relationships exist between the recorded variables, an improved nonlinear PCA, which incorporates the radial basis function (RBF) networks and principal curves, is proposed. This algorithm comprises two stages. The first stage involves the use of the serial principal curve to obtain the nonlinear scores and approximated data. The second stage is to construct two RBF networks using a fast recursive algorithm to solve the topology problem in traditional nonlinear PCA. The benefits of this improvement are demonstrated in the practical application to a polymer extrusion process.

Two-stage RBF network construction based on particle swarm optimization

The conventional radial basis function (RBF) network optimization methods, such as orthogonal least squares or the two-stage selection, can produce a sparse network with satisfactory generalization capability. However, the RBF width, as a nonlinear parameter in the network, is not easy to determine. In the aforementioned methods, the width is always pre-determined, either by trial-and-error, or generated randomly. Furthermore, all hidden nodes share the same RBF width. This will inevitably reduce the network performance, and more RBF centres may then be needed to meet a desired modelling specification. In this paper we investigate a new two-stage construction algorithm for RBF networks. It utilizes the particle swarm optimization method to search for the optimal RBF centres and their associated widths. Although the new method needs more computation than conventional approaches, it can greatly reduce the model size and improve model generalization performance. The effectiveness of the proposed technique is confirmed by two numerical simulation examples.

Nonrigid Structure-From-Motion From 2-D Images Using Markov Chain Monte Carlo

In this paper we present a new method for simultaneously determining three dimensional (3-D) shape and motion of a non-rigid object from uncalibrated two dimensional (2- D) images without assuming the distribution characteristics. A non-rigid motion can be treated as a combination of a rigid rotation and a non-rigid deformation. To seek accurate recovery of deformable structures, we estimate the probability distribution function of the corresponding features through random sampling, incorporating an established probabilistic model. The fitting between the observation and the projection of the estimated 3-D structure will be evaluated using a Markov chain Monte Carlo based expectation maximisation algorithm. Applications of the proposed method to both synthetic and real image sequences are demonstrated with promising results.

Random neighbor sandpile model with constrained total energy

We propose as energy-constrained sandpile model with random neighbors. The critical behavior of the model is in the same universality class as the mean-field self-organized criticality sandpile. The critical energy E-c depends on the number of neighbors n of each site, but the various exponents do not. For n = 6, we got that E-c = 0.4545; and a self-similar structure of the energy distribution function with five major peaks is also observed. This is a natural result of system dynamics and the way the system is disturbed.

Role of low-energy electrons in Ar emission from low-pressure radio frequency discharge plasma

Optical emission spectra from a low-pressure Ar plasma were studied with high spatial resolution. It has been shown that the intensity ratios of Ar lines excited through metastable levels to those excited directly from the ground state are sensitive to the shape of electron energy distribution function. From these measurements, important information on the spatial variation of plasma parameters can be obtained. (C) 1999 American Institute of Physics. [S0003-6951(99)01629-0].

TEMPORALLY AND SPATIALLY-RESOLVED PLASMA PARAMETERS AND EEDF MEASUREMENTS IN A LOW-FREQUENCY DISCHARGE

A time-resolved Langmuir probe technique is used to measure the dependence of the electron density, electron temperature, plasma potential and electron energy distribution function (EEDF) on the phase of the driving voltage in a RF driven parallel plate discharge. The measurements were made in a low-frequency (100-500 kHz), symmetrically driven, radio frequency discharge operating in H-2, D-2 and Ar at gas pressures of a few hundred millitorr. The EEDFs could not be represented by a single Maxwellian distribution and resembled the time averaged EEDFs reported in 13.56 MHz discharges. The measured parameters showed structure in their spatial and temporal dependence, generally consistent with a simple oscillating sheath model. Electron temperatures of less than 0.1 eV were measured during the phase of the RF cycle when both electrodes are negative with respect to the plasma.

ENHANCED VOLUME PRODUCTION OF NEGATIVE-IONS IN THE POST DISCHARGE OF A MULTICUSP HYDROGEN DISCHARGE

In this paper we demonstrate a new concept in the production of negative hydrogen ions in a low-pressure multicusp discharge. The discharge voltage is modulated to produce a non-Maxwellian, hot-electron plasma during the current pulse, followed by a cool Maxwellian electron plasma in the post discharge. This procedure, of separating in time the required hot and cold electron plasmas required for volume H- production, is called a temporal filter. The time evolution of the electron energy distribution function is measured using the time-resolved second derivative of a Langmuir probe characteristic. Time-resolved measurements of the negative ion density are made using laser photodetachment. The measurements show that the negative ion density in the center of the source, at a gas pressure of 0.07 Pa, increases by a factor of 2 when the discharge is switched off. At this low pressure the average H- beam current extracted from the source, when operated with a discharge current of 1 A in the pulse modulated mode exceeds the H- beam current from a 5 A continuously operated source. The increase in efficiency of the pulsed source is explained in terms of a two-step H- production mechanism.

An efficient particle filter for color-based tracking in complex scenes

In this paper, we introduce an efficient method for particle selection in tracking objects in complex scenes. Firstly, we improve the proposal distribution function of the tracking algorithm, including current observation, reducing the cost of evaluating particles with a very low likelihood. In addition, we use a partitioned sampling approach to decompose the dynamic state in several stages. It enables to deal with high-dimensional states without an excessive computational cost. To represent the color distribution, the appearance of the tracked object is modelled by sampled pixels. Based on this representation, the probability of any observation is estimated using non-parametric techniques in color space. As a result, we obtain a Probability color Density Image (PDI) where each pixel points its membership to the target color model. In this way, the evaluation of all particles is accelerated by computing the likelihood p(z|x) using the Integral Image of the PDI.

Electrostatic shock dynamics in superthermal plasmas

The propagation of ion acoustic shocks in nonthermal plasmas is investigated, both analytically and numerically. An unmagnetized collisionless electron-ion plasma is considered, featuring a superthermal (non-Maxwellian) electron distribution, which is modeled by a ?-(kappa) distribution function. Adopting a multiscale approach, it is shown that the dynamics of low-amplitude shocks is modeled by a hybrid Korteweg-de Vries-Burgers (KdVB) equation, in which the nonlinear and dispersion coefficients are functions of the ? parameter, while the dissipative coefficient is a linear function of the ion viscosity. All relevant shock parameters are shown to depend on ?: higher deviations from a pure Maxwellian behavior induce shocks which are narrower, faster, and of larger amplitude. The stability profile of the kink-shaped solutions of the KdVB equation against external perturbations is investigated. The spatial profile of the shocks is found to depend upon the dispersion and the dissipation term, and the role of the interplay between dispersion and dissipation is elucidated.

Oblique propagation of arbitrary amplitude electron acoustic solitary waves in magnetized kappa-distributed plasmas

The linear and nonlinear properties of large-amplitude electron-acoustic waves are investigated in a magnetized plasma comprising two distinct electron populations (hot and cold) and immobile ions. The hot electrons are assumed to be in a non-Maxwellian state, characterized by an excess of superthermal particles, here modeled by a kappa-type long-tailed distribution function. Waves are assumed to propagate obliquely to the ambient magnetic field. Two types of electrostatic modes are shown to exist in the linear regime, and their properties are briefly analyzed. A nonlinear pseudopotential-type analysis reveals the existence of large-amplitude electrostatic solitary waves and allows for an investigation of their propagation characteristics and existence domain, in terms of the soliton speed (Mach number). The effects of the key plasma configuration parameters, namely the superthermality index and the cold electron density, on the soliton characteristics and existence domain, are studied. The role of obliqueness and magnetic field is discussed.