Standardized maximim D-optimal designs for enzyme kineticinhibition models

Locally optimal designs for nonlinear models require a single set of nominal values for the unknown parameters.An alternative is the maximin approach that allows the user to specify a range of values for each parameter ofinterest. However, the maximin approach is difficult because we first have to determine the locally optimal designfor each set of nominal values before maximin types of optimal designs can be found via a nested optimizationprocess. We show that particle swarm optimization (PSO) techniques can solve such complex optimizationproblems effectively. We demonstrate numerical results from PSO can help find, for the first time, formulae forstandardized maximin D-optimal designs for nonlinear model with 3 or 4 parameters on the compact andnonnegative design space. Additionally, we show locally and standardized maximin D-optimal designs for inhibitionmodels are not necessarily supported at a minimum number of points. To facilitate use of such designs, wecreate a web-based tool for practitioners to find tailor-made locally and standardized maximin optimal designs

Generalised cellular neural networks (GCNNs) constructed using particle swarm optimisation for spatio-temporal evolutionary pattern identification

Particle swarm optimization (PSO) is introduced to implement a new constructive learning algorithm for training generalized cellular neural networks (GCNNs) for the identification of spatio-temporal evolutionary (STE) systems. The basic idea of the new PSO-based learning algorithm is to successively approximate the desired signal by progressively pursuing relevant orthogonal projections. This new algorithm will thus be referred to as the orthogonal projection pursuit (OPP) algorithm, which is in mechanism similar to the conventional projection pursuit approach. A novel two-stage hybrid training scheme is proposed for constructing a parsimonious GCNN model. In the first stage, the orthogonal projection pursuit algorithm is applied to adaptively and successively augment the network, where adjustable parameters of the associated units are optimized using a particle swarm optimizer. The resultant network model produced at the first stage may be redundant. In the second stage, a forward orthogonal regression (FOR) algorithm, aided by mutual information estimation, is applied to re. ne and improve the initially trained network. The effectiveness and performance of the proposed method is validated by applying the new modeling framework to a spatio-temporal evolutionary system identification problem

Generalised additive multiscale wavelet models constructed using particle swarm optimisation and mutual information for spatio-temporal evolutionary system representation

A new class of generalised additive multiscale wavelet models (GAMWMs) is introduced for high dimensional spatio-temporal evolutionary (STE) system identification. A novel two-stage hybrid learning scheme is developed for constructing such an additive wavelet model. In the first stage, a new orthogonal projection pursuit (OPP) method, implemented using a particle swarm optimisation(PSO) algorithm, is proposed for successively augmenting an initial coarse wavelet model, where relevant parameters of the associated wavelets are optimised using a particle swarm optimiser. The resultant network model, obtained in the first stage, may however be a redundant model. In the second stage, a forward orthogonal regression (FOR) algorithm, implemented using a mutual information method, is then applied to refine and improve the initially constructed wavelet model. The proposed two-stage hybrid method can generally produce a parsimonious wavelet model, where a ranked list of wavelet functions, according to the capability of each wavelet to represent the total variance in the desired system output signal is produced. The proposed new modelling framework is applied to real observed images, relative to a chemical reaction exhibiting a spatio-temporal evolutionary behaviour, and the associated identification results show that the new modelling framework is applicable and effective for handling high dimensional identification problems of spatio-temporal evolution sytems

An Efficient Algorithm for Optimizing Adaptive Quantum Metrology Processes

Quantum-enhanced metrology infers an unknown quantity with accuracy beyond the standard quantum limit (SQL). Feedback-based metrological techniques are promising for beating the SQL but devising the feedback procedures is difficult and inefficient. Here we introduce an efficient self-learning swarm-intelligence algorithm for devising feedback-based quantum metrological procedures. Our algorithm can be trained with simulated or real-world trials and accommodates experimental imperfections, losses, and decoherence

Lattice dynamical wavelet neural networks implemented using particle swarm optimisation for spatio-temporal system identification

Starting from the basic concept of coupled map lattices, a new family of adaptive wavelet neural networks, called lattice dynamical wavelet neural networks (LDWNN), is introduced for spatiotemporal system identification, by combining an efficient wavelet representation with a coupled map lattice model. A new orthogonal projection pursuit (OPP) method, coupled with a particle swarm optimisation (PSO) algorithm, is proposed for augmenting the proposed network. A novel two-stage hybrid training scheme is developed for constructing a parsimonious network model. In the first stage, by applying the orthogonal projection pursuit algorithm, significant wavelet-neurons are adaptively and successively recruited into the network, where adjustable parameters of the associated waveletneurons are optimised using a particle swarm optimiser. The resultant network model, obtained in the first stage, may however be redundant. In the second stage, an orthogonal least squares (OLS) algorithm is then applied to refine and improve the initially trained network by removing redundant wavelet-neurons from the network. The proposed two-stage hybrid training procedure can generally produce a parsimonious network model, where a ranked list of wavelet-neurons, according to the capability of each neuron to represent the total variance in the system output signal is produced. Two spatio-temporal system identification examples are presented to demonstrate the performance of the proposed new modelling framework