Properties of Higher Order Correlation Function Tests for Nonlinear Model Validation.

Problems related to nonlinear model validation are addressed and properties associated with nonlinear detection, diagnostic power and asymptotic correction are analysed

Nonlinear Model Validation Using Correlation Tests

New higher order correlation tests which use model residuals combined with system inputs and outputs are presented to check the validity of a general class of nonlinear models. The new method is illustrated by testing both simple and complex nonlinear system models

Fast Orthogonal Identification of Nonlinear Stochastic Models and Radial Basis Function Neural Networks

A new fast orthogonal estimation algorithm is derived for a wide class of nonlinear stochastic models including training radial basis function neural networks. The selection of significant regressors and the estimation of unknown parameters in the presence of nonlinear noise sources are considered and simulated examples are included to demonstrate the efficiency of the new procedure

Techniques of replica symmetry breaking and the storage problem of the McCulloch-Pitts neuron

In this article the framework for Parisi's spontaneous replica symmetry breaking is reviewed, and subsequently applied to the example of the statistical mechanical description of the storage properties of a McCulloch-Pitts neuron. The technical details are reviewed extensively, with regard to the wide range of systems where the method may be applied. Parisi's partial differential equation and related differential equations are discussed, and a Green function technique introduced for the calculation of replica averages, the key to determining the averages of physical quantities. The ensuing graph rules involve only tree graphs, as appropriate for a mean-field-like model. The lowest order Ward-Takahashi identity is recovered analytically and is shown to lead to the Goldstone modes in continuous replica symmetry breaking phases. The need for a replica symmetry breaking theory in the storage problem of the neuron has arisen due to the thermodynamical instability of formerly given solutions. Variational forms for the neuron's free energy are derived in terms of the order parameter function x(q), for different prior distribution of synapses. Analytically in the high temperature limit and numerically in generic cases various phases are identified, among them one similar to the Parisi phase in the Sherrington-Kirkpatrick model. Extensive quantities like the error per pattern change slightly with respect to the known unstable solutions, but there is a significant difference in the distribution of non-extensive quantities like the synaptic overlaps and the pattern storage stability parameter. A simulation result is also reviewed and compared to the prediction of the theory.Comment: 103 Latex pages (with REVTeX 3.0), including 15 figures (ps, epsi, eepic), accepted for Physics Report

Rational Model Identification Using an Extended Least Squares Algorithm.

A new least squares based parameter estimation algorithm s derived for non-linear systems which can be represented by a rational model defined as the ratio of two polynomial expansions of past system inputs, outputs and noise. Simulation results are included to illustrate the performance of the new algorithm

Frequency Response Functions for Nonlinear Rational Models.

A recursive algorithm which maps a general class of nonlinear rational model, defined as the ratio of two polynomial functions, into the frequency domain is derived using the harmonic expansion method. The new algorithm provides, for the first time, a direct analytic map from the time domain rational model parameters to the higher order frequency response functions. Complex nonlinear time domain behaviours can be analysed and interpreted in the frequency domain and simulated examples are included to illustrate the concepts involved

A Regularised Least Squares Algorithm for Nonlinear Rational Model Identification

A new regularised least squares estimation algorithm is derived for the estimation of nonlinear dynamic rational models. Theoretical analysis and numerical simulations demonstrate that the new algorithm provides improved estimates compared with previously developed rational model estimators

Bimetallic copper palladium nanorods: plasmonic properties and palladium content effects

Cu is an inexpensive alternative plasmonic metal with optical behaviour comparable to Au but with much poorer environmental stability. Alloying with a more stable metal can improve stability and add functionality, with potential effects on the plasmonic properties. Here we investigate the plasmonic behaviour of Cu nanorods and Cu–CuPd nanorods containing up to 46 mass percent Pd. Monochromated scanning transmission electron microscopy electron energy-loss spectroscopy first reveals the strong length dependence of multiple plasmonic modes in Cu nanorods, where the plasmon peaks redshift and narrow with increasing length. Next, we observe an increased damping (and increased linewidth) with increasing Pd content, accompanied by minimal frequency shift. These results are corroborated by and expanded upon with numerical simulations using the electron-driven discrete dipole approximation. This study indicates that adding Pd to nanostructures of Cu is a promising method to expand the scope of their plasmonic applications

Partial wave analysis of J/\psi \to \gamma \phi \phi

Using $5.8 \times 10^7 J/\psi$ events collected in the BESII detector, the radiative decay $J/\psi \to \gamma \phi \phi \to \gamma K^+ K^- K^0_S K^0_L$ is studied. The $\phi\phi$ invariant mass distribution exhibits a near-threshold enhancement that peaks around 2.24 GeV/$c^{2}$. A partial wave analysis shows that the structure is dominated by a $0^{-+}$ state ($\eta(2225)$) with a mass of $2.24^{+0.03}_{-0.02}{}^{+0.03}_{-0.02}$ GeV/$c^{2}$ and a width of $0.19 \pm 0.03^{+0.06}_{-0.04}$ GeV/$c^{2}$. The product branching fraction is: $Br(J/\psi \to \gamma \eta(2225))\cdot Br(\eta(2225)\to \phi\phi) = (4.4 \pm 0.4 \pm 0.8)\times 10^{-4}$.Comment: 11 pages, 4 figures. corrected proof for journa

Measurements of the observed cross sections for e+e−→e^+e^-\to exclusive light hadrons containing π0π0\pi^0\pi^0 at s=3.773\sqrt s= 3.773, 3.650 and 3.6648 GeV

By analyzing the data sets of 17.3, 6.5 and 1.0 pb$^{-1}$ taken, respectively, at $\sqrt s= 3.773$, 3.650 and 3.6648 GeV with the BES-II detector at the BEPC collider, we measure the observed cross sections for $e^+e^-\to \pi^+\pi^-\pi^0\pi^0$, $K^+K^-\pi^0\pi^0$, $2(\pi^+\pi^-\pi^0)$, $K^+K^-\pi^+\pi^-\pi^0\pi^0$ and $3(\pi^+\pi^-)\pi^0\pi^0$ at the three energy points. Based on these cross sections we set the upper limits on the observed cross sections and the branching fractions for $\psi(3770)$ decay into these final states at 90% C.L..Comment: 7 pages, 2 figure