A new Jacobian matrix for optimal learning of single-layer neural networks

This paper investigates the learning of a wide class of single-hidden-layer feedforward neural networks (SLFNs) with two sets of adjustable parameters, i.e., the nonlinear parameters in the hidden nodes and the linear output weights. The main objective is to both speed up the convergence of second-order learning algorithms such as Levenberg-Marquardt (LM), as well as to improve the network performance. This is achieved here by reducing the dimension of the solution space and by introducing a new Jacobian matrix. Unlike conventional supervised learning methods which optimize these two sets of parameters simultaneously, the linear output weights are first converted into dependent parameters, thereby removing the need for their explicit computation. Consequently, the neural network (NN) learning is performed over a solution space of reduced dimension. A new Jacobian matrix is then proposed for use with the popular second-order learning methods in order to achieve a more accurate approximation of the cost function. The efficacy of the proposed method is shown through an analysis of the computational complexity and by presenting simulation results from four different examples.

Learning soft computing control strategies in a modular neural network architecture

Modelling and control of nonlinear dynamical systems is a challenging problem since the dynamics of such systems change over their parameter space. Conventional methodologies for designing nonlinear control laws, such as gain scheduling, are effective because the designer partitions the overall complex control into a number of simpler sub-tasks. This paper describes a new genetic algorithm based method for the design of a modular neural network (MNN) control architecture that learns such partitions of an overall complex control task. Here a chromosome represents both the structure and parameters of an individual neural network in the MNN controller and a hierarchical fuzzy approach is used to select the chromosomes required to accomplish a given control task. This new strategy is applied to the end-point tracking of a single-link flexible manipulator modelled from experimental data. Results show that the MNN controller is simple to design and produces superior performance compared to a single neural network (SNN) controller which is theoretically capable of achieving the desired trajectory. (C) 2003 Elsevier Ltd. All rights reserved.

Comment on "Electron collisional excitation of argon-like Ni XI using the Breit-Pauli R-matrix method" [Eur. Phys. J. D 42, 235-241 (2007)] - Electron impact excitation of Ni XI

In a recent paper, Verma et al. [Eur. Phys. J. D 42, 235 (2007)] have reported results for energy levels, radiative rates, collision strengths, and effective collision strengths for transitions among the lowest 17 levels of the (1s(2)2s(2)2p(6))3s(2)3p(6), 3s(2)3p(5)3d and 3s3p(6)3d configurations of Ni XI. They adopted the CIV3 and R-matrix codes for the generation of wavefunctions and the scattering process, respectively. In this paper, through two independent calculations performed with the fully relativistic DARC (along with GRASP) and FAC codes, we demonstrate that their results are unreliable. New data are presented and their accuracy is assessed.

2-D R-matrix propagation: A large scale electron scattering simulation dominated by the multiplication of dynamically changing matrices

We examine the computational aspects of propagating a global R-matrix, R, across sub-regions in a 2-D plane. This problem originates in the large scale simulation of electron collisions with atoms and ions at intermediate energies. The propagation is dominated by matrix multiplications which are complicated because of the dynamic nature of R, which changes the designations of its rows and columns and grows in size as the propagation proceeds. The use of PBLAS to solve this problem on distributed memory HPC machines is the main focus of the paper.

A modular approach to luminescent dinuclear ruthenium(II) and rhenium(I) complexes

A series of dinuclear (bipyridine)tricarbonylrhenium(I) and tris(bipyridine)ruthenium(II) complexes have been isolated and characterised, bridged by a flexible diamido ethylene glycol chain. A new stepwise synthetic pathway has been investigated to heterometallic complexes, with the rhenium(I) complexes exhibiting an unusual configuration and inequivalence of the metal centres potentially arising from a surprising hydrogen-bonding interaction between an Re–CO group and an amide proton in low-polarity solvents. This interaction appears to be broken by competing hydrogen-bonding species such as dihydrogen phosphate. This effect was not observed in the corresponding ruthenium(II) complexes, which showed very little interaction with anions. The photophysical characterisation shows that the inclusion of two ester/amide groups to the rhenium centre effectively quenches the fluorescence at room temperature. The ruthenium(II) complexes have considerably stronger fluorescence than the rhenium species, and are less affected by theinclusion of ester and amide groups to the 2,2'-bipyridine chelating group.

Ultrafast Laser-Driven Excitation Dynamics in Ne: An Ab Initio Time-Dependent R-Matrix Approach

An attosecond pump-probe scheme that combines the use of a free-electron laser pulse with an ultrashort pulse is applied in order to explore the ultrafast excitation dynamics in Ne. We describe the multielectron dynamics using a new nonperturbative time-dependent R-matrix theory. This theory enables the interaction of ultrashort light fields with multielectron atoms and atomic ions to be determined from first principles. By probing the emission of an inner 2s electron from Ne we are also able to study the bound state population dynamics during the free-electron laser pulse.

Electron impact excitation collision strengths for neon-like Ni XIX calculated using the relativistic R-matrix method

In a recent paper [Pramana - J. Phys. 64, 129 (2005)] results have been presented for electron impact excitation collision strengths for transitions among the fine-structure levels of the 2s(2)2p(6) and 2s(2)2p(5)3s configurations of Ni XIX. In this paper we demonstrate through an independent calculation with the relativistic R-matrix code that those results are unreliable and the conclusions drawn are invalid.

Time-dependent R -matrix theory for ultrafast atomic processes

We describe an ab initio nonperturbative time-dependent R-matrix theory for ultrafast atomic processes. This theory enables investigations of the interaction of few-femtosecond and -attosecond pulse lasers with complex multielectron atoms and atomic ions. A derivation and analysis of the basic equations are given, which propagate the atomic wave function in the presence of the laser field forward in time in the internal and external R-matrix regions. To verify the accuracy of the approach, we investigate two-photon ionization of Ne irradiated by an intense laser pulse and compare current results with those obtained using the R-matrix Floquet method and an alternative time-dependent method. We also verify the capability of the current approach by applying it to the study of two-dimensional momentum distributions of electrons ejected from Ne due to irradiation by a sequence of 2 as light pulses in the presence of a 780 nm laser field.