Approximating differentiable relationships between delay embedded dynamical systems with radical basis functions

This thesis is about the study of relationships between experimental dynamical systems. The basic approach is to fit radial basis function maps between time delay embeddings of manifolds. We have shown that under certain conditions these maps are generically diffeomorphisms, and can be analysed to determine whether or not the manifolds in question are diffeomorphically related to each other. If not, a study of the distribution of errors may provide information about the lack of equivalence between the two. The method has applications wherever two or more sensors are used to measure a single system, or where a single sensor can respond on more than one time scale: their respective time series can be tested to determine whether or not they are coupled, and to what degree. One application which we have explored is the determination of a minimum embedding dimension for dynamical system reconstruction. In this special case the diffeomorphism in question is closely related to the predictor for the time series itself. Linear transformations of delay embedded manifolds can also be shown to have nonlinear inverses under the right conditions, and we have used radial basis functions to approximate these inverse maps in a variety of contexts. This method is particularly useful when the linear transformation corresponds to the delay embedding of a finite impulse response filtered time series. One application of fitting an inverse to this linear map is the detection of periodic orbits in chaotic attractors, using suitably tuned filters. This method has also been used to separate signals with known bandwidths from deterministic noise, by tuning a filter to stop the signal and then recovering the chaos with the nonlinear inverse. The method may have applications to the cancellation of noise generated by mechanical or electrical systems. In the course of this research a sophisticated piece of software has been developed. The program allows the construction of a hierarchy of delay embeddings from scalar and multi-valued time series. The embedded objects can be analysed graphically, and radial basis function maps can be fitted between them asynchronously, in parallel, on a multi-processor machine. In addition to a graphical user interface, the program can be driven by a batch mode command language, incorporating the concept of parallel and sequential instruction groups and enabling complex sequences of experiments to be performed in parallel in a resource-efficient manner.

Neural network enhanced self tuning adaptive control application for non-linear control of dynamic systems

The main theme of research of this project concerns the study of neutral networks to control uncertain and non-linear control systems. This involves the control of continuous time, discrete time, hybrid and stochastic systems with input, state or output constraints by ensuring good performances. A great part of this project is devoted to the opening of frontiers between several mathematical and engineering approaches in order to tackle complex but very common non-linear control problems. The objectives are: 1. Design and develop procedures for neutral network enhanced self-tuning adaptive non-linear control systems; 2. To design, as a general procedure, neural network generalised minimum variance self-tuning controller for non-linear dynamic plants (Integration of neural network mapping with generalised minimum variance self-tuning controller strategies); 3. To develop a software package to evaluate control system performances using Matlab, Simulink and Neural Network toolbox. An adaptive control algorithm utilising a recurrent network as a model of a partial unknown non-linear plant with unmeasurable state is proposed. Appropriately, it appears that structured recurrent neural networks can provide conveniently parameterised dynamic models for many non-linear systems for use in adaptive control. Properties of static neural networks, which enabled successful design of stable adaptive control in the state feedback case, are also identified. A survey of the existing results is presented which puts them in a systematic framework showing their relation to classical self-tuning adaptive control application of neural control to a SISO/MIMO control. Simulation results demonstrate that the self-tuning design methods may be practically applicable to a reasonably large class of unknown linear and non-linear dynamic control systems.

Alginates as therapeutic and drug delivery systems

Alginate is widely used as a viscosity enhancer in many different pharmaceutical formulations. The aim of this thesis is to quantitatively describe the functions of this polyelectrolyte in pharmaceutical systems. To do this the techniques used were Viscometry, Light Scattering, Continuous and Oscillatory Shear Rheometry, Numerical Analysis and Diffusion. Molecular characterization of the Alginate was carried out using Viscometry and Light Scattering to determine the molecular weight, the radius of gyration, the second virial coefficient and the Kuhn statistical segment length. The results showed good agreement with similar parameters obtained in previous studies. By blending Alginate with other polyelectrolytes, Xanthan Gum and 'Carbopol', in various proportions and with various methods of low and high shear preparation, a very wide range of dynamic rheological properties was found. Using oscillatory testing, the parameters often varied over several decades of magnitude. It was shown that the determination of the viscous and elastic components is particularly useful in describing the rheological 'profiles' of suspending agent blends and provides a step towards the non-empirical formulation of pharmaceutical disperse systems. Using numerical analysis of equations describing planar diffusion, it was shown that the analysis of drug release profiles alone does not provide unambiguous information about the mechanism of rate control. These principles were applied to the diffusion of Ibuprofen in Calcium Alginate gels. For diffusion in such non-Newtonian systems, emphasis was placed on the use of the elastic as well as the viscous component of viscoelasticity. It was found that the diffusion coefficients were relatively unaffected by increases in polymer concentration up to 5 per cent, yet the elasticities measured by oscillatory shear rheometry were increased. This was interpreted in the light of several theories of diffusion in gels.

Selective localization of organoclay and effects on the morphology and mechanical properties of LDPE/PA11 blends with distributed and co-continuous morphology

A study was made on the effect of small amounts of organically modified clay on the morphology and mechanical properties of blends of low-density polyethylene and polyamide 11 at different compositions. The influence of the filler on the blend morphology was investigated using wide angle X-ray diffractometry, scanning and transmission electron microscopy and selective extraction experiments. The filler was found to locate predominantly in the more hydrophilic polyamide phase. Although such uneven distribution does not have a significant effect on the onset of phase co-continuity of the polymer components, it brings about a drastic refinement of the microstructure for the blends both with droplets/matrix and co-continuous morphologies. In addition to the expected reinforcing action of the filler, the resulting fine microstructure plays an important role in enhancing the mechanical properties of the blends. This is essentially because of a good quality of stress transfer across the interface between the constituents, which also seems to benefit for a good interfacial adhesion promoted by the filler. Our results provide the experimental evidence for the capabilities of nanoparticles added to multiphase polymer systems to act selectively as a reinforcing agent for specific domains of the material and as a medium able to assist the refinement of the polymer phases during mixing.

Phase shift keyed systems based on a gain switched laser transmitter

Return-to-Zero (RZ) and Non-Return-to-Zero (NRZ) Differential Phase Shift Keyed (DPSK) systems require cheap and optimal transmitters for widespread implementation. The authors report on a gain switched Discrete Mode (DM) laser that can be employed as a cost efficient transmitter in a 10.7 Gb/s RZ DPSK system and compare its performance to that of a gain switched Distributed Feed-Back (DFB) laser. Experimental results show that the gain switched DM laser readily provides error free performance and a receiver sensitivity of -33.1 dBm in the 10.7 Gbit/s RZ DPSK system. The standard DFB laser on the other hand displays an error floor at 10(-1) in the same RZ DPSK system. The difference in performance, between the two types of gain switched transmitters, is analysed by investigating their linewidths. We also demonstrate, for the first time, the generation of a highly coherent gain switched pulse train which displays a spectral comb of approximately 13 sidebands spaced by the 10.7 GHz modulation frequency. The filtered side-bands are then employed as narrow linewidth Continuous Wave (CW) sources in a 10.7 Gb/s NRZ DPSK system.

Changing employment relation systems in Japan:cases of the Mitsubishi Chemical Group and the Federation of Shinkin Banks

Over the past decade or so a number of changes have been observed in traditional Japanese employment relations (ERs) systems such as an increase in non-regular workers, a move towards performance-based systems and a continuous decline in union membership. There is a large body of Anglo-Saxon and Japanese literature providing evidence that national factors such as national institutions, national culture, and the business and economic environment have significantly influenced what were hitherto three ‘sacred’ aspects of Japanese ERs systems (ERSs). However, no research has been undertaken until now at the firm level regarding the extent to which changes in national factors influence ERSs across firms. This article develops a model to examine the impact of national factors on ER systems; and analyses the impact of national factors at the firm level ER systems. Based on information collected from two different groups of companies, namely Mitsubishi Chemical Group (MCG) and Federation of Shinkin Bank (FSB) the research finds that except for a few similarities, the impact of national factors is different on Japanese ER systems at the firm level. This indicates that the impact of national factors varies in the implementation of employment relations factors. In the case of MCG, national culture has less to do with seniority-based system. Study also reveals that the national culture factors have also less influence on an enterprise-based system in the case of FSB. This analysis is useful for domestic and international organizations as it helps to better understand the role of national factors in determining Japanese ERSs.

Complexity of classical dynamics of molecular systems. I. Methodology

Methods for the calculation of complexity have been investigated as a possible alternative for the analysis of the dynamics of molecular systems. “Computational mechanics” is the approach chosen to describe emergent behavior in molecular systems that evolve in time. A novel algorithm has been developed for symbolization of a continuous physical trajectory of a dynamic system. A method for calculating statistical complexity has been implemented and tested on representative systems. It is shown that the computational mechanics approach is suitable for analyzing the dynamic complexity of molecular systems and offers new insight into the process.

Probabilistic control for uncertain systems

In this paper a new framework has been applied to the design of controllers which encompasses nonlinearity, hysteresis and arbitrary density functions of forward models and inverse controllers. Using mixture density networks, the probabilistic models of both the forward and inverse dynamics are estimated such that they are dependent on the state and the control input. The optimal control strategy is then derived which minimizes uncertainty of the closed loop system. In the absence of reliable plant models, the proposed control algorithm incorporates uncertainties in model parameters, observations, and latent processes. The local stability of the closed loop system has been established. The efficacy of the control algorithm is demonstrated on two nonlinear stochastic control examples with additive and multiplicative noise.

Nonlinear inverse synthesis for high spectral efficiency transmission in optical fibers

In linear communication channels, spectral components (modes) defined by the Fourier transform of the signal propagate without interactions with each other. In certain nonlinear channels, such as the one modelled by the classical nonlinear Schrödinger equation, there are nonlinear modes (nonlinear signal spectrum) that also propagate without interacting with each other and without corresponding nonlinear cross talk, effectively, in a linear manner. Here, we describe in a constructive way how to introduce such nonlinear modes for a given input signal. We investigate the performance of the nonlinear inverse synthesis (NIS) method, in which the information is encoded directly onto the continuous part of the nonlinear signal spectrum. This transmission technique, combined with the appropriate distributed Raman amplification, can provide an effective eigenvalue division multiplexing with high spectral efficiency, thanks to highly suppressed channel cross talk. The proposed NIS approach can be integrated with any modulation formats. Here, we demonstrate numerically the feasibility of merging the NIS technique in a burst mode with high spectral efficiency methods, such as orthogonal frequency division multiplexing and Nyquist pulse shaping with advanced modulation formats (e.g., QPSK, 16QAM, and 64QAM), showing a performance improvement up to 4.5 dB, which is comparable to results achievable with multi-step per span digital back propagation.

Nonlinear inverse synthesis technique for optical links with lumped amplification

The nonlinear inverse synthesis (NIS) method, in which information is encoded directly onto the continuous part of the nonlinear signal spectrum, has been proposed recently as a promising digital signal processing technique for combating fiber nonlinearity impairments. However, because the NIS method is based on the integrability property of the lossless nonlinear Schrödinger equation, the original approach can only be applied directly to optical links with ideal distributed Raman amplification. In this paper, we propose and assess a modified scheme of the NIS method, which can be used effectively in standard optical links with lumped amplifiers, such as, erbium-doped fiber amplifiers (EDFAs). The proposed scheme takes into account the average effect of the fiber loss to obtain an integrable model (lossless path-averaged model) to which the NIS technique is applicable. We found that the error between lossless pathaveraged and lossy models increases linearly with transmission distance and input power (measured in dB). We numerically demonstrate the feasibility of the proposed NIS scheme in a burst mode with orthogonal frequency division multiplexing (OFDM) transmission scheme with advanced modulation formats (e.g., QPSK, 16QAM, and 64QAM), showing a performance improvement up to 3.5 dB; these results are comparable to those achievable with multi-step per span digital backpropagation.

Distribution modeling of nonlinear inverse controllers under a Bayesian framework

The inverse controller is traditionally assumed to be a deterministic function. This paper presents a pedagogical methodology for estimating the stochastic model of the inverse controller. The proposed method is based on Bayes' theorem. Using Bayes' rule to obtain the stochastic model of the inverse controller allows the use of knowledge of uncertainty from both the inverse and the forward model in estimating the optimal control signal. The paper presents the methodology for general nonlinear systems and is demonstrated on nonlinear single-input-single-output (SISO) and multiple-input-multiple-output (MIMO) examples. © 2006 IEEE.

A Bayesian approach to modeling the conditional density of the inverse controller

The inverse controller is traditionally assumed to be a deterministic function. This paper presents a pedagogical methodology for estimating the stochastic model of the inverse controller. The proposed method is based on Bayes' theorem. Using Bayes' rule to obtain the stochastic model of the inverse controller allows the use of knowledge of uncertainty from both the inverse and the forward model in estimating the optimal control signal. The paper presents the methodology for general nonlinear systems. For illustration purposes, the proposed methodology is applied to linear Gaussian systems. © 2004 IEEE.

Node centrality for continuous-time quantum walks

The study of complex networks has recently attracted increasing interest because of the large variety of systems that can be modeled using graphs. A fundamental operation in the analysis of complex networks is that of measuring the centrality of a vertex. In this paper, we propose to measure vertex centrality using a continuous-time quantum walk. More specifically, we relate the importance of a vertex to the influence that its initial phase has on the interference patterns that emerge during the quantum walk evolution. To this end, we make use of the quantum Jensen-Shannon divergence between two suitably defined quantum states. We investigate how the importance varies as we change the initial state of the walk and the Hamiltonian of the system. We find that, for a suitable combination of the two, the importance of a vertex is almost linearly correlated with its degree. Finally, we evaluate the proposed measure on two commonly used networks. © 2014 Springer-Verlag Berlin Heidelberg.

A continuous-time quantum walk kernel for unattributed graphs

Kernel methods provide a way to apply a wide range of learning techniques to complex and structured data by shifting the representational problem from one of finding an embedding of the data to that of defining a positive semidefinite kernel. In this paper, we propose a novel kernel on unattributed graphs where the structure is characterized through the evolution of a continuous-time quantum walk. More precisely, given a pair of graphs, we create a derived structure whose degree of symmetry is maximum when the original graphs are isomorphic. With this new graph to hand, we compute the density operators of the quantum systems representing the evolutions of two suitably defined quantum walks. Finally, we define the kernel between the two original graphs as the quantum Jensen-Shannon divergence between these two density operators. The experimental evaluation shows the effectiveness of the proposed approach. © 2013 Springer-Verlag.

Modified nonlinear inverse synthesis for optical links with distributed Raman amplification

We propose a modification of the nonlinear digital signal processing technique based on the nonlinear inverse synthesis for the systems with distributed Raman amplification. The proposed path-average approach offers 3 dB performance gain, regardless of the signal power profile.