Online approximations for wind-field models

We study online approximations to Gaussian process models for spatially distributed systems. We apply our method to the prediction of wind fields over the ocean surface from scatterometer data. Our approach combines a sequential update of a Gaussian approximation to the posterior with a sparse representation that allows to treat problems with a large number of observations.

Gaussian processes:iterative sparse approximations

In recent years there has been an increased interest in applying non-parametric methods to real-world problems. Significant research has been devoted to Gaussian processes (GPs) due to their increased flexibility when compared with parametric models. These methods use Bayesian learning, which generally leads to analytically intractable posteriors. This thesis proposes a two-step solution to construct a probabilistic approximation to the posterior. In the first step we adapt the Bayesian online learning to GPs: the final approximation to the posterior is the result of propagating the first and second moments of intermediate posteriors obtained by combining a new example with the previous approximation. The propagation of em functional forms is solved by showing the existence of a parametrisation to posterior moments that uses combinations of the kernel function at the training points, transforming the Bayesian online learning of functions into a parametric formulation. The drawback is the prohibitive quadratic scaling of the number of parameters with the size of the data, making the method inapplicable to large datasets. The second step solves the problem of the exploding parameter size and makes GPs applicable to arbitrarily large datasets. The approximation is based on a measure of distance between two GPs, the KL-divergence between GPs. This second approximation is with a constrained GP in which only a small subset of the whole training dataset is used to represent the GP. This subset is called the em Basis Vector, or BV set and the resulting GP is a sparse approximation to the true posterior. As this sparsity is based on the KL-minimisation, it is probabilistic and independent of the way the posterior approximation from the first step is obtained. We combine the sparse approximation with an extension to the Bayesian online algorithm that allows multiple iterations for each input and thus approximating a batch solution. The resulting sparse learning algorithm is a generic one: for different problems we only change the likelihood. The algorithm is applied to a variety of problems and we examine its performance both on more classical regression and classification tasks and to the data-assimilation and a simple density estimation problems.

Data visualization with simultaneous feature selection

Data visualization algorithms and feature selection techniques are both widely used in bioinformatics but as distinct analytical approaches. Until now there has been no method of measuring feature saliency while training a data visualization model. We derive a generative topographic mapping (GTM) based data visualization approach which estimates feature saliency simultaneously with the training of the visualization model. The approach not only provides a better projection by modeling irrelevant features with a separate noise model but also gives feature saliency values which help the user to assess the significance of each feature. We compare the quality of projection obtained using the new approach with the projections from traditional GTM and self-organizing maps (SOM) algorithms. The results obtained on a synthetic and a real-life chemoinformatics dataset demonstrate that the proposed approach successfully identifies feature significance and provides coherent (compact) projections. © 2006 IEEE.

Dynamic simulation of chemical plant

A CSSL- type modular FORTRAN package, called ACES, has been developed to assist in the simulation of the dynamic behaviour of chemical plant. ACES can be harnessed, for instance, to simulate the transients in startups or after a throughput change. ACES has benefited from two existing simulators. The structure was adapted from ICL SLAM and most plant models originate in DYFLO. The latter employs sequential modularisation which is not always applicable to chemical engineering problems. A novel device of twice- round execution enables ACES to achieve general simultaneous modularisation. During the FIRST ROUND, STATE-VARIABLES are retrieved from the integrator and local calculations performed. During the SECOND ROUND, fresh derivatives are estimated and stored for simultaneous integration. ACES further includes a version of DIFSUB, a variable-step integrator capable of handling stiff differential systems. ACES is highly formalised . It does not use pseudo steady- state approximations and excludes inconsistent and arbitrary features of DYFLO. Built- in debug traps make ACES robust. ACES shows generality, flexibility, versatility and portability, and is very convenient to use. It undertakes substantial housekeeping behind the scenes and thus minimises the detailed involvement of the user. ACES provides a working set of defaults for simulation to proceed as far as possible. Built- in interfaces allow for reactions and user supplied algorithms to be incorporated . New plant models can be easily appended. Boundary- value problems and optimisation may be tackled using the RERUN feature. ACES is file oriented; a STATE can be saved in a readable form and reactivated later. Thus piecewise simulation is possible. ACES has been illustrated and verified to a large extent using some literature-based examples. Actual plant tests are desirable however to complete the verification of the library. Interaction and graphics are recommended for future work.

Simultaneous chemical reaction and distillation of formaldehyde

The thesis is concerned with the development and testing of a mathematical model of a distillation process in which the components react chemically. The formaldehyde-methanol-water system was selected and only the reversible reactions between formaldehyde and water giving methylene glycol and between formaldehyde and methanol producing hemiformal were assumed to occur under the distillation conditions. Accordingly the system has been treated as a five component system. The vapour-liquid equilibrium calculations were performed by solving iteratively the thermodynamic relationships expressing the phase equilibria with the stoichiometric equations expressing the chemical equilibria. Using optimisation techniques, the Wilson single parameters and Henry's constants were calculated for binary systems containing formaldehyde which was assumed to be a supercritical component whilst Wilson binary parameters were calculated for the remaining binary systems. Thus the phase equilibria for the formaldehyde system could be calculated using these parameters and good accuracy was obtained when calculated values were compared with experimental values. The distillation process was modelled using the mass and energy balance equations together with the phase equilibria calculations. The plate efficiencies were obtained from a modified A.I.Ch.E. Bubble Tray method. The resulting equations were solved by an iterative plate to plate calculation based on the Newton Raphson method. Experiments were carried out in a 76mm I.D., eight sieve plate distillation column and the results were compared with the mathematical model calculations. Overall, good agreement was obtained but some discrepancies were observed in the concentration profiles and these may have been caused by the effect of limited physical property data and a limited understanding of the reactions mechanism. The model equations were solved in the form of modular computer programs. Although they were written to describe the steady state distillation with simultaneous chemical reaction of the formaldehyde system, the approach used may be of wider application.

Relating two simultaneous events in discourse: the role of on-goingness devices in L1 Tunisian Arabic, L1 French and L2 French by Tunisian learners

Our PhD study focuses on the role of aspectual marking in expressing simultaneity of events in Tunisian Arabic as a first language, French as a first language, as well as in French as a second language by Tunisian learners at different acquisitional stages. We examine how the explicit markers of on-goingness qa:’id and «en train de» in Tunisian Arabic and in French respectively are used to express this temporal relation, in competition with the simple forms, the prefixed verb form in Tunisian Arabic and the présent de l’indicatif in French. We use a complex verbal task of retelling simultaneous events sharing an interval on the time axis based on eight videos presenting two situations happening in parallel. Two types of simultaneity are exploited: perfect simultaneity (when the two situations are parallel to each other) and inclusion (one situation is framed by the second one). Our informants in French and in Tunisian Arabic have two profiles, highly educated and low educated speakers. We show that the participants’ response to the retelling task varies according to their profiles, and so does their use of the on-goingness devices in the expression of simultaneity. The differences observed between the two profile groups are explained by the degree to which the speakers have developed a habit of responding to tasks. This is a skill typically acquired during schooling. We notice overall that the use of qa:’id as well as of «en train de» is less frequent in the data than the use of the simple forms. However, qa:’id as well as «en train de» are employed to play discursive roles that go beyond the proposition level. We postulate that despite the shared features between Tunisian Arabic and French regarding marking the concept of on-goingness, namely the presence of explicit lexical, not fully grammaticalised markers competing with other non-marked forms, the way they are used in the discourse of simultaneous events shows clear differences. We explain that «en train de» plays a more contrastive role than qa:’id and its use in discourse obeys a stricter rule. In cases of the inclusion type of simultaneity, it is used to construe the ‘framing’ event that encloses the second event. In construing perfectly simultaneneous events, and when both «en train de» and présent de l’indicatif are used, the proposition with «en train de» generally precedes the proposition with présent de l’indicatif, and not the other way around. qa:id obeys, but to a less strict rule as it can be used interchangeably with the simple form regardless of the order of propositions. The contrastive analysis of French L1 and L2 reveals learners’ deviations from natives’ use of on-goingness devices. They generalise the use of «en train de» and apply different rules to the interaction of the different marked and unmarked forms in discourse. Learners do not master its role in discourse even at advanced stages of acquisition despite its possible emergence around the basic and intermediate varieties. We conclude that the native speakers’ use of «en train de» involves mastering its role at the macro-structure level. This feature, not explicitly available to learners in the input, might persistently present a challenge to L2 acquisition of the periphrasis.

Contrast discrimination with simultaneous monocular and dichoptic masks

In experiments reported elsewhere at this conference, we have revealed two striking results concerning binocular interactions in a masking paradigm. First, at low mask contrasts, a dichoptic masking grating produces a small facilitatory effect on the detection of a similar test grating. Second, the psychometric slope for dichoptic masking starts high (Weibull ß~4) at detection threshold, becomes low (ß~1.2) in the facilitatory region, and then unusually steep at high mask contrasts (ß~5.5). Neither of these results is consistent with Legge's (1984 Vision Research 24 385 - 394) model of binocular summation, but they are predicted by a two-stage gain control model in which interocular suppression precedes binocular summation. Here, we pose a further challenge for this model by using a 'twin-mask' paradigm (cf Foley, 1994 Journal of the Optical Society of America A 11 1710 - 1719). In 2AFC experiments, observers detected a patch of grating (1 cycle deg-1, 200 ms) presented to one eye in the presence of a pedestal in the same eye and a spatially identical mask in the other eye. The pedestal and mask contrasts varied independently, producing a two-dimensional masking space in which the orthogonal axes (10X10 contrasts) represent conventional dichoptic and monocular masking. The resulting surface (100 thresholds) confirmed and extended the observations above, and fixed the six parameters in the model, which fitted the data well. With no adjustment of parameters, the model described performance in a further experiment where mask and test were presented to both eyes. Moreover, in both model and data, binocular summation was greater than a factor of v2 at detection threshold. We conclude that this two-stage nonlinear model, with interocular suppression, gives a good account of early binocular processes in the perception of contrast. [Supported by EPSRC Grant Reference: GR/S74515/01]

Simultaneous dibit recovery of a DQPSK signal using a single Mach-Zehnder Interferometer

The dibit recovery of a DQPSK signal will be demonstrated using a single Mach Zehnder Interferometer, containing a 1-bit delay, and a single balanced receiver. The electrical output levels of the balanced receiver are dependent upon the relative phase delay between the arms of the Mach Zehnder Interferometer. This paper will investigate this characteristic when the input signal is DQPSK modulated. It will also be shown that with a certain amount of phase shift the DQPSK signal can be converted into four different equally spaced electrical signal levels. With each decoded level representing one of the four possible dibits.

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.

Grouping and the pitch of a mistuned fundamental component:effects of applying simultaneous multiple mistunings to the other harmonics

Mistuning a harmonic produces an exaggerated change in its pitch. This occurs because the component becomes inconsistent with the regular pattern that causes the other harmonics (constituting the spectral frame) to integrate perceptually. These pitch shifts were measured when the fundamental (F0) component of a complex tone (nominal F0 frequency = 200 Hz) was mistuned by +8% and -8%. The pitch-shift gradient was defined as the difference between these values and its magnitude was used as a measure of frame integration. An independent and random perturbation (spectral jitter) was applied simultaneously to most or all of the frame components. The gradient magnitude declined gradually as the degree of jitter increased from 0% to ±40% of F0. The component adjacent to the mistuned target made the largest contribution to the gradient, but more distant components also contributed. The stimuli were passed through an auditory model, and the exponential height of the F0-period peak in the averaged summary autocorrelation function correlated well with the gradient magnitude. The fit improved when the weighting on more distant channels was attenuated by a factor of three per octave. The results are consistent with a grouping mechanism that computes a weighted average of periodicity strength across several components. © 2006 Elsevier B.V. All rights reserved.

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.

Simultaneous demultiplexing, data regeneration, and clock recovery with a single semiconductor optical amplifier-based nonlinear-optical loop mirror

We demonstrate simultaneous demultiplexing, data regeneration and clock recovery at 10Gbits/s, using a single semiconductor optical amplifier–based nonlinear-optical loop mirror in a phase-locked loop configuration.

Simultaneous interrogation of fiber Bragg grating sensors using an acoustooptic tunable filter

We describe a novel technique to provide demultiplexing of fiber Bragg grating sensors, interrogated using interferometric wavelength shift detection. Amplitude modulation of multiple radio frequency driving signals allows an acoustooptic tunable filter to provide wavelength demultiplexing. We demonstrated a noise limited strain resolution of 150 nanostrain/v(Hz) and a crosstalk better than -50 dB.

Simultaneous refractive index and temperature measurement using cascaded long-period grating in double-cladding fibre

A compact scheme for simultaneous temperature and surrounding refractive index (SRI) measurement using two long-period gratings (LPGs) of different periods inscribed side-by-side in a single piece of a double-cladding fibre is presented. One of the LPGs is sensitive to both SRI and temperature, whilst the second is sensitive to temperature only.