Complexity of Monte Carlo algorithms for a class of integral equations

In this work we study the computational complexity of a class of grid Monte Carlo algorithms for integral equations. The idea of the algorithms consists in an approximation of the integral equation by a system of algebraic equations. Then the Markov chain iterative Monte Carlo is used to solve the system. The assumption here is that the corresponding Neumann series for the iterative matrix does not necessarily converge or converges slowly. We use a special technique to accelerate the convergence. An estimate of the computational complexity of Monte Carlo algorithm using the considered approach is obtained. The estimate of the complexity is compared with the corresponding quantity for the complexity of the grid-free Monte Carlo algorithm. The conditions under which the class of grid Monte Carlo algorithms is more efficient are given.

Femtosecond evolution of spatially inhomogeneous carrier excitations: part 2: stochastic approach and GRID implementation

We present a stochastic approach for solving the quantum-kinetic equation introduced in Part I. A Monte Carlo method based on backward time evolution of the numerical trajectories is developed. The computational complexity and the stochastic error are investigated numerically. Variance reduction techniques are applied, which demonstrate a clear advantage with respect to the approaches based on symmetry transformation. Parallel implementation is realized on a GRID infrastructure.

A new RBF neural network with boundary value constraints

We present a novel topology of the radial basis function (RBF) neural network, referred to as the boundary value constraints (BVC)-RBF, which is able to automatically satisfy a set of BVC. Unlike most existing neural networks whereby the model is identified via learning from observational data only, the proposed BVC-RBF offers a generic framework by taking into account both the deterministic prior knowledge and the stochastic data in an intelligent manner. Like a conventional RBF, the proposed BVC-RBF has a linear-in-the-parameter structure, such that it is advantageous that many of the existing algorithms for linear-in-the-parameters models are directly applicable. The BVC satisfaction properties of the proposed BVC-RBF are discussed. Finally, numerical examples based on the combined D-optimality-based orthogonal least squares algorithm are utilized to illustrate the performance of the proposed BVC-RBF for completeness.

Experimental design and model construction algorithms for radial basis function networks

New construction algorithms for radial basis function (RBF) network modelling are introduced based on the A-optimality and D-optimality experimental design criteria respectively. We utilize new cost functions, based on experimental design criteria, for model selection that simultaneously optimizes model approximation, parameter variance (A-optimality) or model robustness (D-optimality). The proposed approaches are based on the forward orthogonal least-squares (OLS) algorithm, such that the new A-optimality- and D-optimality-based cost functions are constructed on the basis of an orthogonalization process that gains computational advantages and hence maintains the inherent computational efficiency associated with the conventional forward OLS approach. The proposed approach enhances the very popular forward OLS-algorithm-based RBF model construction method since the resultant RBF models are constructed in a manner that the system dynamics approximation capability, model adequacy and robustness are optimized simultaneously. The numerical examples provided show significant improvement based on the D-optimality design criterion, demonstrating that there is significant room for improvement in modelling via the popular RBF neural network.

Minimum stable convergence criteria for stochastic diffusion search

An analysis of Stochastic Diffusion Search (SDS), a novel and efficient optimisation and search algorithm, is presented, resulting in a derivation of the minimum acceptable match resulting in a stable convergence within a noisy search space. The applicability of SDS can therefore be assessed for a given problem.

Communicating neurons: a connectionist spiking neuron implementation of stochastic diffusion search

An information processing paradigm in the brain is proposed, instantiated in an artificial neural network using biologically motivated temporal encoding. The network will locate within the external world stimulus, the target memory, defined by a specific pattern of micro-features. The proposed network is robust and efficient. Akin in operation to the swarm intelligence paradigm, stochastic diffusion search, it will find the best-fit to the memory with linear time complexity. information multiplexing enables neurons to process knowledge as 'tokens' rather than 'types'. The network illustrates possible emergence of cognitive processing from low level interactions such as memory retrieval based on partial matching. (C) 2007 Elsevier B.V. All rights reserved.

On improvement of classification accuracy for stochastic discrimination

Stochastic discrimination (SD) depends on a discriminant function for classification. In this paper, an improved SD is introduced to reduce the error rate of the standard SD in the context of a two-class classification problem. The learning procedure of the improved SD consists of two stages. Initially a standard SD, but with shorter learning period is carried out to identify an important space where all the misclassified samples are located. Then the standard SD is modified by 1) restricting sampling in the important space, and 2) introducing a new discriminant function for samples in the important space. It is shown by mathematical derivation that the new discriminant function has the same mean, but with a smaller variance than that of the standard SD for samples in the important space. It is also analyzed that the smaller the variance of the discriminant function, the lower the error rate of the classifier. Consequently, the proposed improved SD improves standard SD by its capability of achieving higher classification accuracy. Illustrative examples are provided to demonstrate the effectiveness of the proposed improved SD.

Modeling entangled dynamics: comparison between stochastic single-chain and multichain models

To test the effectiveness of stochastic single-chain models in describing the dynamics of entangled polymers, we systematically compare one such model; the slip-spring model; to a multichain model solved using stochastic molecular dynamics(MD) simulations (the Kremer-Grest model). The comparison involves investigating if the single-chain model can adequately describe both a microscopic dynamical and a macroscopic rheological quantity for a range of chain lengths. Choosing a particular chain length in the slip-spring model, the parameter values that best reproduce the mean-square displacement of a group of monomers is determined by fitting toMDdata. Using the same set of parameters we then test if the predictions of the mean-square displacements for other chain lengths agree with the MD calculations. We followed this by a comparison of the time dependent stress relaxation moduli obtained from the two models for a range of chain lengths. After identifying a limitation of the original slip-spring model in describing the static structure of the polymer chain as seen in MD, we remedy this by introducing a pairwise repulsive potential between the monomers in the chains. Poor agreement of the mean-square monomer displacements at short times can be rectified by the use of generalized Langevin equations for the dynamics and resulted in significantly improved agreement.

Adaptive deadbeat control of stochastic systems

This paper considers the use of a discrete-time deadbeat control action on systems affected by noise. Variations on the standard controller form are discussed and comparisons are made with controllers in which noise rejection is a higher priority objective. Both load and random disturbances are considered in the system description, although the aim of the deadbeat design remains as a tailoring of reference input variations. Finally, the use of such a deadbeat action within a self-tuning control framework is shown to satisfy, under certain conditions, the self-tuning property, generally though only when an extended form of least-squares estimation is incorporated.

New algorithms for synthesized design of optical filters

Chebyshev optical-filter algorithms for low-cost microcomputers have been improved. An offset ripple is now used for better transmission/matching in low-pass stacks. A prototype for narrowband filters is now more general and nearer practicability.

Application of the entropy technique and genetic algorithms to construction site layout planning of medium-size projects

Genetic algorithms (GAs) have been introduced into site layout planning as reported in a number of studies. In these studies, the objective functions were defined so as to employ the GAs in searching for the optimal site layout. However, few studies have been carried out to investigate the actual closeness of relationships between site facilities; it is these relationships that ultimately govern the site layout. This study has determined that the underlying factors of site layout planning for medium-size projects include work flow, personnel flow, safety and environment, and personal preferences. By finding the weightings on these factors and the corresponding closeness indices between each facility, a closeness relationship has been deduced. Two contemporary mathematical approaches - fuzzy logic theory and an entropy measure - were adopted in finding these results in order to minimize the uncertainty and vagueness of the collected data and improve the quality of the information. GAs were then applied to searching for the optimal site layout in a medium-size government project using the GeneHunter software. The objective function involved minimizing the total travel distance. An optimal layout was obtained within a short time. This reveals that the application of GA to site layout planning is highly promising and efficient.

Evaluation of peak-picking algorithms for protein mass spectrometry

Peak picking is an early key step in MS data analysis. We compare three commonly used approaches to peak picking and discuss their merits by means of statistical analysis. Methods investigated encompass signal-to-noise ratio, continuous wavelet transform, and a correlation-based approach using a Gaussian template. Functionality of the three methods is illustrated and discussed in a practical context using a mass spectral data set created with MALDI-TOF technology. Sensitivity and specificity are investigated using a manually defined reference set of peaks. As an additional criterion, the robustness of the three methods is assessed by a perturbation analysis and illustrated using ROC curves.