Derivations of variational gaussian process approximation framework

Recently, within the VISDEM project (EPSRC funded EP/C005848/1), a novel variational approximation framework has been developed for inference in partially observed, continuous space-time, diffusion processes. In this technical report all the derivations of the variational framework, from the initial work, are provided in detail to help the reader better understand the framework and its assumptions.

Single uniform FBG for simultaneous measurement of liquid level and temperature

In this paper, we propose and demonstrate a novel scheme for simultaneous measurement of liquid level and temperature based on a simple uniform fiber Bragg grating (FBG) by monitoring both the short-wavelength-loss peaks and its Bragg resonance. The liquid level can be measured from the amplitude changes of the short-wavelength-loss peaks, while temperature can be measured from the wavelength shift of the Bragg resonance. Both theoretical simulation results and experimental results are presented. Such a scheme has some advantages including robustness, simplicity, flexibility in choosing sensitivity and simultaneous temperature measurement capability.

A new variational radial basis function approximation for inference in multivariate diffusions

In this paper we present a radial basis function based extension to a recently proposed variational algorithm for approximate inference for diffusion processes. Inference, for state and in particular (hyper-) parameters, in diffusion processes is a challenging and crucial task. We show that the new radial basis function approximation based algorithm converges to the original algorithm and has beneficial characteristics when estimating (hyper-)parameters. We validate our new approach on a nonlinear double well potential dynamical system.

Evaluation of RF power degradation in microwave photonic systems employing uniform period fibre Bragg gratings

The frequency dependent RF power degradation in direct modulated microwave photonic systems employing uniform period fibre Bragg gratingsFBG.as reflective elements is investigated. The results have implications in terms of the available RF bandwidth and the stability requirements for the fibre Bragg gratings.

Transmission of non-uniform OTDM channels in nonlinearly-guided dispersion-managed fibre system

The effects of channel inequality on nonlinear signal switching in a nonlinear optical fiber loop mirror (NOLM) were investigated. It was found that the channel-to-channel amplitude differences in optical time division multiplexing (OTDM) have strong impact on swiching behavior of individual channels in a 2R regenerator. The optical pulses in different channels face either suppression of the amplitude noise or increase in noise, depending on the inter-channel amplitude difference. It was stated that appropriate control of the channel uniformity in the OTDM transmitters is required to support stable long-haul transmission in 2R regenerated systems.

Computer interpretation of engineering drawings as solid models

Much of the geometrical data relating to engineering components and assemblies is stored in the form of orthographic views, either on paper or computer files. For various engineering applications, however, it is necessary to describe objects in formal geometric modelling terms. The work reported in this thesis is concerned with the development and implementation of concepts and algorithms for the automatic interpretation of orthographic views as solid models. The various rules and conventions associated with engineering drawings are reviewed and several geometric modelling representations are briefly examined. A review of existing techniques for the automatic, and semi-automatic, interpretation of engineering drawings as solid models is given. A new theoretical approach is then presented and discussed. The author shows how the implementation of such an approach for uniform thickness objects may be extended to more general objects by introducing the concept of `approximation models'. Means by which the quality of the transformations is monitored, are also described. Detailed descriptions of the interpretation algorithms and the software package that were developed for this project are given. The process is then illustrated by a number of practical examples. Finally, the thesis concludes that, using the techniques developed, a substantial percentage of drawings of engineering components could be converted into geometric models with a specific degree of accuracy. This degree is indicative of the suitability of the model for a particular application. Further work on important details is required before a commercially acceptable package is produced.

Approximation of photonic crystal fibres with large air holes by the step index fibre model

An equivalent step index fibre with a silica core and air cladding is used to model photonic crystal fibres with large air holes. We model this fibre for linear polarisation (we focus on the lowest few transverse modes of the electromagnetic field). The equivalent step index radius is obtained by equating the lowest two eigenvalues of the model to those calculated numerically for the photonic crystal fibres. The step index parameters thus obtained can then be used to calculate nonlinear parameters like the nonlinear effective area of a photonic crystal fibre or to model nonlinear few-mode interactions using an existing model.

Sparse signal representation by adaptive non-uniform B-spline dictionaries on a compact interval

Non-uniform B-spline dictionaries on a compact interval are discussed in the context of sparse signal representation. For each given partition, dictionaries of B-spline functions for the corresponding spline space are built up by dividing the partition into subpartitions and joining together the bases for the concomitant subspaces. The resulting slightly redundant dictionaries are composed of B-spline functions of broader support than those corresponding to the B-spline basis for the identical space. Such dictionaries are meant to assist in the construction of adaptive sparse signal representation through a combination of stepwise optimal greedy techniques.

Numerical approximation of the one-dimensional inverse Cauchy–Stefan problem using a method of fundamental solutions

We investigate an application of the method of fundamental solutions (MFS) to the one-dimensional parabolic inverse Cauchy–Stefan problem, where boundary data and the initial condition are to be determined from the Cauchy data prescribed on a given moving interface. In [B.T. Johansson, D. Lesnic, and T. Reeve, A method of fundamental solutions for the one-dimensional inverse Stefan Problem, Appl. Math Model. 35 (2011), pp. 4367–4378], the inverse Stefan problem was considered, where only the boundary data is to be reconstructed on the fixed boundary. We extend the MFS proposed in Johansson et al. (2011) and show that the initial condition can also be simultaneously recovered, i.e. the MFS is appropriate for the inverse Cauchy-Stefan problem. Theoretical properties of the method, as well as numerical investigations, are included, showing that accurate results can be efficiently obtained with small computational cost.

Generalized mean field approximation for parallel dynamics of the Ising model

The dynamics of the non-equilibrium Ising model with parallel updates is investigated using a generalized mean field approximation that incorporates multiple two-site correlations at any two time steps, which can be obtained recursively. The proposed method shows significant improvement in predicting local system properties compared to other mean field approximation techniques, particularly in systems with symmetric interactions. Results are also evaluated against those obtained from Monte Carlo simulations. The method is also employed to obtain parameter values for the kinetic inverse Ising modeling problem, where couplings and local field values of a fully connected spin system are inferred from data. © 2014 IOP Publishing Ltd and SISSA Medialab srl.

A survey of methods of numerical approximation to functions

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Single uniform FBG for simultaneous measurement of liquid level and temperature

In this paper, we propose and demonstrate a novel scheme for simultaneous measurement of liquid level and temperature based on a simple uniform fiber Bragg grating (FBG) by monitoring both the short-wavelength-loss peaks and its Bragg resonance. The liquid level can be measured from the amplitude changes of the short-wavelength-loss peaks, while temperature can be measured from the wavelength shift of the Bragg resonance. Both theoretical simulation results and experimental results are presented. Such a scheme has some advantages including robustness, simplicity, flexibility in choosing sensitivity and simultaneous temperature measurement capability.

Hierarchized block wise image approximation by greedy pursuit strategies

An approach for effective implementation of greedy selection methodologies, to approximate an image partitioned into blocks, is proposed. The method is specially designed for approximating partitions on a transformed image. It evolves by selecting, at each iteration step, i) the elements for approximating each of the blocks partitioning the image and ii) the hierarchized sequence in which the blocks are approximated to reach the required global condition on sparsity. © 2013 IEEE.

Hierarchized block wise image approximation by greedy pursuit strategies

An approach for effective implementation of greedy selection methodologies, to approximate an image partitioned into blocks, is proposed. The method is specially designed for approximating partitions on a transformed image. It evolves by selecting, at each iteration step, i) the elements for approximating each of the blocks partitioning the image and ii) the hierarchized sequence in which the blocks are approximated to reach the required global condition on sparsity. © 2013 IEEE.