Gaussian process approximations of stochastic differential equations

Stochastic differential equations arise naturally in a range of contexts, from financial to environmental modeling. Current solution methods are limited in their representation of the posterior process in the presence of data. In this work, we present a novel Gaussian process approximation to the posterior measure over paths for a general class of stochastic differential equations in the presence of observations. The method is applied to two simple problems: the Ornstein-Uhlenbeck process, of which the exact solution is known and can be compared to, and the double-well system, for which standard approaches such as the ensemble Kalman smoother fail to provide a satisfactory result. Experiments show that our variational approximation is viable and that the results are very promising as the variational approximate solution outperforms standard Gaussian process regression for non-Gaussian Markov processes.

A verifiable solution to the MEG inverse problem

Magnetoencephalography (MEG) is a non-invasive brain imaging technique with the potential for very high temporal and spatial resolution of neuronal activity. The main stumbling block for the technique has been that the estimation of a neuronal current distribution, based on sensor data outside the head, is an inverse problem with an infinity of possible solutions. Many inversion techniques exist, all using different a-priori assumptions in order to reduce the number of possible solutions. Although all techniques can be thoroughly tested in simulation, implicit in the simulations are the experimenter's own assumptions about realistic brain function. To date, the only way to test the validity of inversions based on real MEG data has been through direct surgical validation, or through comparison with invasive primate data. In this work, we constructed a null hypothesis that the reconstruction of neuronal activity contains no information on the distribution of the cortical grey matter. To test this, we repeatedly compared rotated sections of grey matter with a beamformer estimate of neuronal activity to generate a distribution of mutual information values. The significance of the comparison between the un-rotated anatomical information and the electrical estimate was subsequently assessed against this distribution. We found that there was significant (P < 0.05) anatomical information contained in the beamformer images across a number of frequency bands. Based on the limited data presented here, we can say that the assumptions behind the beamformer algorithm are not unreasonable for the visual-motor task investigated.

Combined bioreaction and separation in a simulated counter-current chromatographic bioreactor-separator system

The objective of this work has been to investigate the principle of combined bioreaction and separation in a simulated counter-current chromatographic bioreactor-separator system (SCCR-S). The SCCR-S system consisted of twelve 5.4cm i.d x 75cm long columns packed with calcium charged cross-linked polystyrene resin. Three bioreactions, namely the saccharification of modified starch to maltose and dextrin using the enzyme maltogenase, the hydrolysis of lactose to galactose and glucose in the presence of the enzyme lactase and the biosynthesis of dextran from sucrose using the enzyme dextransucrase. Combined bioreaction and separation has been successfully carried out in the SCCR-S system for the saccharification of modified starch to maltose and dextrin. The effects of the operating parameters (switch time, eluent flowrate, feed concentration and enzyme activity) on the performance of the SCCR-S system were investigated. By using an eluent of dilute enzyme solution, starch conversions of up to 60% were achieved using lower amounts of enzyme than the theoretical amount required by a conventional bioreactor to produce the same amount of maltose over the same time period. Comparing the SCCR-S system to a continuous annular chromatograph (CRAC) for the saccharification of modified starch showed that the SCCR-S system required only 34.6-47.3% of the amount of enzyme required by the CRAC. The SCCR-S system was operated in the batch and continuous modes as a bioreactor-separator for the hydrolysis of lactose to galactose and glucose. By operating the system in the continuous mode, the operating parameters were further investigated. During these experiments the eluent was deionised water and the enzyme was introduced into the system through the same port as the feed. The galactose produced was retarded and moved with the stationary phase to be purge as the galactose rich product (GalRP) while the glucose moved with the mobile phase and was collected as the glucose rich product (GRP). By operating at up to 30%w/v lactose feed concentrations, complete conversions were achieved using only 48% of the theoretical amount of enzyme required by a conventional bioreactor to hydrolyse the same amount of glucose over the same time period. The main operating parameters affecting the performance of the SCCR-S system operating in the batch mode were investigated and the results compared to those of the continuous operation of the SCCR-S system. . During the biosynthesis of dextran in the SCCR-S system, a method of on-line regeneration of the resin was required to operate the system continuously. Complete conversion was achieved at sucrose feed concentrations of 5%w/v with fructose rich. products (FRP) of up to 100% obtained. The dextran rich products were contaninated by small amounts of glucose and levan formed during the bioreaction. Mathematical modelling and computer simulation of the SCCR-S. system operating in the continuous mode for the hydrolysis of lactose has been carried out. .

Developments and extensions of Roth's method of double Fourier series with applications to the solution of electromagnetic field problems

The first part of the thesis compares Roth's method with other methods, in particular the method of separation of variables and the finite cosine transform method, for solving certain elliptic partial differential equations arising in practice. In particular we consider the solution of steady state problems associated with insulated conductors in rectangular slots. Roth's method has two main disadvantages namely the slow rate of con­vergence of the double Fourier series and the restrictive form of the allowable boundary conditions. A combined Roth-separation of variables method is derived to remove the restrictions on the form of the boundary conditions and various Chebyshev approximations are used to try to improve the rate of convergence of the series. All the techniques are then applied to the Neumann problem arising from balanced rectangular windings in a transformer window. Roth's method is then extended to deal with problems other than those resulting from static fields. First we consider a rectangular insulated conductor in a rectangular slot when the current is varying sinusoidally with time. An approximate method is also developed and compared with the exact method.The approximation is then used to consider the problem of an insulated conductor in a slot facing an air gap. We also consider the exact method applied to the determination of the eddy-current loss produced in an isolated rectangular conductor by a transverse magnetic field varying sinusoidally with time. The results obtained using Roth's method are critically compared with those obtained by other authors using different methods. The final part of the thesis investigates further the application of Chebyshdev methods to the solution of elliptic partial differential equations; an area where Chebyshev approximations have rarely been used. A poisson equation with a polynomial term is treated first followed by a slot problem in cylindrical geometry.

Aircraft rotable inventory optimisation: development of a new solution

Analysis of the use of ICT in the aerospace industry has prompted the detailed investigation of an inventory-planning problem. There is a special class of inventory, consisting of expensive repairable spares for use in support of aircraft operations. These items, called rotables, are not well served by conventional theory and systems for inventory management. The context of the problem, the aircraft maintenance industry sector, is described in order to convey some of its special characteristics in the context of operations management. A literature review is carried out to seek existing theory that can be applied to rotable inventory and to identify a potential gap into which newly developed theory could contribute. Current techniques for rotable planning are identified in industry and the literature: these methods are modelled and tested using inventory and operational data obtained in the field. In the expectation that current practice leaves much scope for improvement, several new models are proposed. These are developed and tested on the field data for comparison with current practice. The new models are revised following testing to give improved versions. The best model developed and tested here comprises a linear programming optimisation, which finds an optimal level of inventory for multiple test cases, reflecting changing operating conditions. The new model offers an inventory plan that is up to 40% less expensive than that determined by current practice, while maintaining required performance.

A learning feed-forward current controller for linear reciprocating vapor compressors

Direct-drive linear reciprocating compressors offer numerous advantages over conventional counterparts which are usually driven by a rotary induction motor via a crank shaft. However, to ensure efficient and reliable operation under all conditions, it is essential that motor current of a linear compressor follows a sinusoidal current command with a frequency which matches the system resonant frequency. The design of a high-performance current controller for linear compressor drive presents a challenge since the system is highly nonlinear, and an effective solution must be low cost. In this paper, a learning feed-forward current controller for the linear compressors is proposed. It comprises a conventional feedback proportional-integral controller and a feed-forward B-spline neural network (BSNN). The feed-forward BSNN is trained online and in real time in order to minimize the current tracking error. Extensive simulation and experiment results with a prototype linear compressor show that the proposed current controller exhibits high steady state and transient performance. © 2009 IEEE.

DISCUS : an end-to-end solution for ubiquitous broadband optical access

Fiber to the premises has promised to increase the capacity in telecommunications access networks for well over 30 years. While it is widely recognized that optical-fiber-based access networks will be a necessity in the shortto medium-term future, its large upfront cost and regulatory issues are pushing many operators to further postpone its deployment, while installing intermediate unambitious solutions such as fiber to the cabinet. Such high investment cost of both network access and core capacity upgrade often derives from poor planning strategies that do not consider the necessity to adequately modify the network architecture to fully exploit the cost benefit that a fiber-centric solution can bring. DISCUS is a European Framework 7 Integrated Project that, building on optical-centric solutions such as long-reach passive optical access and flat optical core, aims to deliver a cost-effective architecture for ubiquitous broadband services. DISCUS analyzes, designs, and demonstrates end-to-end architectures and technologies capable of saving cost and energy by reducing the number of electronic terminations in the network and sharing the deployment costs among a larger number of users compared to current fiber access systems. This article describes the network architecture and the supporting technologies behind DISCUS, giving an overview of the concepts and methodologies that will be used to deliver our end-to-end network solution. © 2013 IEEE.