Wave chaotic behaviour generated by linear systems

It is shown that regimes with dynamical chaos are inherent not only to nonlinear system but they can be generated by initially linear systems and the requirements for chaotic dynamics and characteristics need further elaboration. Three simplest physical models are considered as examples. In the first, dynamic chaos in the interaction of three linear oscillators is investigated. Analogous process is shown in the second model of electromagnetic wave scattering in a double periodical inhomogeneous medium occupying half-space. The third model is a linear parametric problem for the electromagnetic field in homogeneous dielectric medium which permittivity is modulated in time. © 2008 Springer Science+Business Media, LLC.

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.

Neural network control of a gas turbine

In this paper we explore the practical use of neural networks for controlling complex non-linear systems. The system used to demonstrate this approach is a simulation of a gas turbine engine typical of those used to power commercial aircraft. The novelty of the work lies in the requirement for multiple controllers which are used to maintain system variables in safe operating regions as well as governing the engine thrust.

Rapid heuristic projection on simplicial cones

A very fast heuristic iterative method of projection on simplicial cones is presented. It consists in solving two linear systems at each step of the iteration. The extensive experiments indicate that the method furnishes the exact solution in more then 99.7 percent of the cases. The average number of steps is 5.67 (we have not found any examples which required more than 13 steps) and the relative number of steps with respect to the dimension decreases dramatically. Roughly speaking, for high enough dimensions the absolute number of steps is independent of the dimension.

Temporal finite elements in the dynamic analysis of structures

This thesis demonstrates that the use of finite elements need not be confined to space alone, but that they may also be used in the time domain, It is shown that finite element methods may be used successfully to obtain the response of systems to applied forces, including, for example, the accelerations in a tall structure subjected to an earthquake shock. It is further demonstrated that at least one of these methods may be considered to be a practical alternative to more usual methods of solution. A detailed investigation of the accuracy and stability of finite element solutions is included, and methods of applications to both single- and multi-degree of freedom systems are described. Solutions using two different temporal finite elements are compared with those obtained by conventional methods, and a comparison of computation times for the different methods is given. The application of finite element methods to distributed systems is described, using both separate discretizations in space and time, and a combined space-time discretization. The inclusion of both viscous and hysteretic damping is shown to add little to the difficulty of the solution. Temporal finite elements are also seen to be of considerable interest when applied to non-linear systems, both when the system parameters are time-dependent and also when they are functions of displacement. Solutions are given for many different examples, and the computer programs used for the finite element methods are included in an Appendix.

Quantifying short-term dynamics of Parkinson's disease using self-reported symptom data from an internet social network

Background: Parkinson’s disease (PD) is an incurable neurological disease with approximately 0.3% prevalence. The hallmark symptom is gradual movement deterioration. Current scientific consensus about disease progression holds that symptoms will worsen smoothly over time unless treated. Accurate information about symptom dynamics is of critical importance to patients, caregivers, and the scientific community for the design of new treatments, clinical decision making, and individual disease management. Long-term studies characterize the typical time course of the disease as an early linear progression gradually reaching a plateau in later stages. However, symptom dynamics over durations of days to weeks remains unquantified. Currently, there is a scarcity of objective clinical information about symptom dynamics at intervals shorter than 3 months stretching over several years, but Internet-based patient self-report platforms may change this. Objective: To assess the clinical value of online self-reported PD symptom data recorded by users of the health-focused Internet social research platform PatientsLikeMe (PLM), in which patients quantify their symptoms on a regular basis on a subset of the Unified Parkinson’s Disease Ratings Scale (UPDRS). By analyzing this data, we aim for a scientific window on the nature of symptom dynamics for assessment intervals shorter than 3 months over durations of several years. Methods: Online self-reported data was validated against the gold standard Parkinson’s Disease Data and Organizing Center (PD-DOC) database, containing clinical symptom data at intervals greater than 3 months. The data were compared visually using quantile-quantile plots, and numerically using the Kolmogorov-Smirnov test. By using a simple piecewise linear trend estimation algorithm, the PLM data was smoothed to separate random fluctuations from continuous symptom dynamics. Subtracting the trends from the original data revealed random fluctuations in symptom severity. The average magnitude of fluctuations versus time since diagnosis was modeled by using a gamma generalized linear model. Results: Distributions of ages at diagnosis and UPDRS in the PLM and PD-DOC databases were broadly consistent. The PLM patients were systematically younger than the PD-DOC patients and showed increased symptom severity in the PD off state. The average fluctuation in symptoms (UPDRS Parts I and II) was 2.6 points at the time of diagnosis, rising to 5.9 points 16 years after diagnosis. This fluctuation exceeds the estimated minimal and moderate clinically important differences, respectively. Not all patients conformed to the current clinical picture of gradual, smooth changes: many patients had regimes where symptom severity varied in an unpredictable manner, or underwent large rapid changes in an otherwise more stable progression. Conclusions: This information about short-term PD symptom dynamics contributes new scientific understanding about the disease progression, currently very costly to obtain without self-administered Internet-based reporting. This understanding should have implications for the optimization of clinical trials into new treatments and for the choice of treatment decision timescales.

Regeneration limit of classical Shannon capacity

Since Shannon derived the seminal formula for the capacity of the additive linear white Gaussian noise channel, it has commonly been interpreted as the ultimate limit of error-free information transmission rate. However, the capacity above the corresponding linear channel limit can be achieved when noise is suppressed using nonlinear elements; that is, the regenerative function not available in linear systems. Regeneration is a fundamental concept that extends from biology to optical communications. All-optical regeneration of coherent signal has attracted particular attention. Surprisingly, the quantitative impact of regeneration on the Shannon capacity has remained unstudied. Here we propose a new method of designing regenerative transmission systems with capacity that is higher than the corresponding linear channel, and illustrate it by proposing application of the Fourier transform for efficient regeneration of multilevel multidimensional signals. The regenerative Shannon limit -the upper bound of regeneration efficiency -is derived. © 2014 Macmillan Publishers Limited. All rights reserved.

Q parameter estimation using numerical simulations for linear and nonlinear transmission systems

We compare the Q parameter obtained from scalar, semi-analytical and full vector models for realistic transmission systems. One set of systems is operated in the linear regime, while another is using solitons at high peak power. We report in detail on the different results obtained for the same system using different models. Polarisation mode dispersion is also taken into account and a novel method to average Q parameters over several independent simulation runs is described. © 2006 Elsevier B.V. All rights reserved.

Semi-analytical Q parameter estimate in linear and nonlinear transmission systems

We compare the Q parameter obtained from the semi-analytical model with scalar and vector models for two realistic transmission systems. First a linear system with a compensated dispersion map and second a soliton transmission system.

Pole tip recession in linear tape systems

The tribology of linear tape storage system including Linear Tape Open (LTO) and Travan5 was investigated by combining X-ray Photoelectron Spectroscopy (XPS), Auger Electron Spectroscopy (AES), Optical Microscopy and Atomic Force Microscopy (AFM) technologies. The purpose of this study was to understand the tribology mechanism of linear tape systems then projected recording densities may be achieved in future systems. Water vapour pressure or Normalized Water Content (NWC) rather than the Relative Humidity (RH) values (as are used almost universally in this field) determined the extent of PTR and stain (if produced) in linear heads. Approximately linear dependencies were found for saturated PTR increasing with normalized water content increasing over the range studied using the same tape. Fe Stain (if produced) preferentially formed on the head surfaces at the lower water contents. The stain formation mechanism had been identified. Adhesive bond formation is a chemical process that is governed by temperature. Thus the higher the contact pressure, the higher the contact temperature in the interface of head and tape, was produced higher the probability of adhesive bond formation and the greater the amount of transferred material (stain). Water molecules at the interface saturate the surface bonds and makes adhesive junctions less likely. Tape polymeric binder formulation also has a significant role in stain formation, with the latest generation binders producing less transfer of material. This is almost certainly due to higher cohesive bonds within the body of the magnetic layer. TiC in the two-phase ceramic tape-bearing surface (AlTiC) was found to oxidise to form TiO2.The oxidation rate of TiC increased with water content increasing. The oxide was less dense than the underlying carbide; hence the interface between TiO2 oxide and TiC was stressed. Removals of the oxide phase results in the formation of three-body abrasive particles that were swept across the tape head, and gave rise to three-body abrasive wear, particularly in the pole regions. Hence, PTR and subsequent which signal loss and error growth. The lower contact pressure of the LTO system comparing with the Travan5 system ensures that fewer and smaller three-body abrasive particles were swept across the poles and insulator regions. Hence, lower contact pressure, as well as reducing stain in the same time significantly reduces PTR in the LTO system.

The tribology of linear tape recording systems

This thesis is devoted to the tribology at the head~to~tape interface of linear tape recording systems, OnStream ADRTM system being used as an experimental platform, Combining experimental characterisation with computer modelling, a comprehensive picture of the mechanisms involved in a tape recording system is drawn. The work is designed to isolate the mechanisms responsible for the physical spacing between head and tape with the aim of minimising spacing losses and errors and optimising signal output. Standard heads-used in ADR current products-and prototype heads- DLC and SPL coated and dummy heads built from a AI203-TiC and alternative single-phase ceramics intended to constitute the head tape-bearing surface-are tested in controlled environment for up to 500 hours (exceptionally 1000 hours), Evidences of wear on the standard head are mainly observable as a preferential wear of the TiC phase of the AI203-TiC ceramic, The TiC grains are believed to delaminate due to a fatigue wear mechanism, a hypothesis further confirmed via modelling, locating the maximum von Mises equivalent stress at a depth equivalent to the TiC recession (20 to 30 nm). Debris of TiC delaminated residues is moreover found trapped within the pole-tip recession, assumed therefore to provide three~body abrasive particles, thus increasing the pole-tip recession. Iron rich stain is found over the cycled standard head surface (preferentially over the pole-tip and to a lesser extent over the TiC grains) at any environment condition except high temperature/humidity, where mainly organic stain was apparent, Temperature (locally or globally) affects staining rate and aspect; stain transfer is generally promoted at high temperature. Humidity affects transfer rate and quantity; low humidity produces, thinner stains at higher rate. Stain generally targets preferentially head materials with high electrical conductivity, i.e. Permalloy and TiC. Stains are found to decrease the friction at the head-to-tape interface, delay the TiC recession hollow-out and act as a protective soft coating reducing the pole-tip recession. This is obviously at the expense of an additional spacing at the head-to-tape interface of the order of 20 nm. Two kinds of wear resistant coating are tested: diamond like carbon (DLC) and superprotective layer (SPL), 10 nm and 20 to 40 nm thick, respectively. DLC coating disappears within 100 hours due possibly to abrasive and fatigue wear. SPL coatings are generally more resistant, particularly at high temperature and low humidity, possibly in relation with stain transfer. 20 nm coatings are found to rely on the substrate wear behaviour whereas 40 nm coatings are found to rely on the adhesive strength at the coating/substrate interface. These observations seem to locate the wear-driving forces 40 nm below the surface, hence indicate that for coatings in the 10 nm thickness range-· i,e. compatible with high-density recording-the substrate resistance must be taken into account. Single-phase ceramic as candidate for wear-resistant tape-bearing surface are tested in form of full-contour dummy-heads. The absence of a second phase eliminates the preferential wear observed at the AI203-TiC surface; very low wear rates and no evidence of brittle fracture are observed.

A principled approach to interactive hierarchical non-linear visualization of high-dimensional data

Hierarchical visualization systems are desirable because a single two-dimensional visualization plot may not be sufficient to capture all of the interesting aspects of complex high-dimensional data sets. We extend an existing locally linear hierarchical visualization system PhiVis [1] in several directions: bf(1) we allow for em non-linear projection manifolds (the basic building block is the Generative Topographic Mapping -- GTM), bf(2) we introduce a general formulation of hierarchical probabilistic models consisting of local probabilistic models organized in a hierarchical tree, bf(3) we describe folding patterns of low-dimensional projection manifold in high-dimensional data space by computing and visualizing the manifold's local directional curvatures. Quantities such as magnification factors [3] and directional curvatures are helpful for understanding the layout of the nonlinear projection manifold in the data space and for further refinement of the hierarchical visualization plot. Like PhiVis, our system is statistically principled and is built interactively in a top-down fashion using the EM algorithm. We demonstrate the visualization system principle of the approach on a complex 12-dimensional data set and mention possible applications in the pharmaceutical industry.

Efficient Bayesian inference for learning in the Ising linear perceptron and signal detection in CDMA

Efficient new Bayesian inference technique is employed for studying critical properties of the Ising linear perceptron and for signal detection in code division multiple access (CDMA). The approach is based on a recently introduced message passing technique for densely connected systems. Here we study both critical and non-critical regimes. Results obtained in the non-critical regime give rise to a highly efficient signal detection algorithm in the context of CDMA; while in the critical regime one observes a first-order transition line that ends in a continuous phase transition point. Finite size effects are also studied. © 2006 Elsevier B.V. All rights reserved.

Technical efficiency:efficiency, change, technical progress and productivity growth in the national health systems of continental African countries

In May 2006, the Ministers of Health of all the countries on the African continent, at a special session of the African Union, undertook to institutionalise efficiency monitoring within their respective national health information management systems. The specific objectives of this study were: (i) to assess the technical efficiency of National Health Systems (NHSs) of African countries for measuring male and female life expectancies, and (ii) to assess changes in health productivity over time with a view to analysing changes in efficiency and changes in technology. The analysis was based on a five-year panel data (1999-2003) from all the 53 countries of continental Africa. Data Envelopment Analysis (DEA) - a non-parametric linear programming approach - was employed to assess the technical efficiency. Malmquist Total Factor Productivity (MTFP) was used to analyse efficiency and productivity change over time among the 53 countries' national health systems. The data consisted of two outputs (male and female life expectancies) and two inputs (per capital total health expenditure and adult literacy). The DEA revealed that 49 (92.5%) countries' NHSs were run inefficiently in 1999 and 2000; 50 (94.3%), 48 (90.6%) and 47 (88.7%) operated inefficiently in 2001, 2002, and 2003 respectively. All the 53 countries' national health systems registered improvements in total factor productivity attributable mainly to technical progress. Fifty-two countries did not experience any change in scale efficiency, while thirty (56.6%) countries' national health systems had a Pure Efficiency Change (PEFFCH) index of less than one, signifying that those countries' NHSs pure efficiency contributed negatively to productivity change. All the 53 countries' national health systems registered improvements in total factor productivity, attributable mainly to technical progress. Over half of the countries' national health systems had a pure efficiency index of less than one, signifying that those countries' NHSs pure efficiency contributed negatively to productivity change. African countries may need to critically evaluate the utility of institutionalising Malmquist TFP type of analyses to monitor changes in health systems economic efficiency and productivity over time. African national health systems, per capita total health expenditure, technical efficiency, scale efficiency, Malmquist indices of productivity change, DEA

Approximate Bayesian techniques for inference in stochastic dynamical systems

This thesis is concerned with approximate inference in dynamical systems, from a variational Bayesian perspective. When modelling real world dynamical systems, stochastic differential equations appear as a natural choice, mainly because of their ability to model the noise of the system by adding a variant of some stochastic process to the deterministic dynamics. Hence, inference in such processes has drawn much attention. Here two new extended frameworks are derived and presented that are based on basis function expansions and local polynomial approximations of a recently proposed variational Bayesian algorithm. It is shown that the new extensions converge to the original variational algorithm and can be used for state estimation (smoothing). However, the main focus is on estimating the (hyper-) parameters of these systems (i.e. drift parameters and diffusion coefficients). The new methods are numerically validated on a range of different systems which vary in dimensionality and non-linearity. These are the Ornstein-Uhlenbeck process, for which the exact likelihood can be computed analytically, the univariate and highly non-linear, stochastic double well and the multivariate chaotic stochastic Lorenz '63 (3-dimensional model). The algorithms are also applied to the 40 dimensional stochastic Lorenz '96 system. In this investigation these new approaches are compared with a variety of other well known methods such as the ensemble Kalman filter / smoother, a hybrid Monte Carlo sampler, the dual unscented Kalman filter (for jointly estimating the systems states and model parameters) and full weak-constraint 4D-Var. Empirical analysis of their asymptotic behaviour as a function of observation density or length of time window increases is provided.