Thermalized polarization dynamics of a discrete optical-waveguide system with four-wave mixing

Statistical mechanics of two coupled vector fields is studied in the tight-binding model that describes propagation of polarized light in discrete waveguides in the presence of the four-wave mixing. The energy and power conservation laws enable the formulation of the equilibrium properties of the polarization state in terms of the Gibbs measure with positive temperature. The transition line T=∞ is established beyond which the discrete vector solitons are created. Also in the limit of the large nonlinearity an analytical expression for the distribution of Stokes parameters is obtained, which is found to be dependent only on the statistical properties of the initial polarization state and not on the strength of nonlinearity. The evolution of the system to the final equilibrium state is shown to pass through the intermediate stage when the energy exchange between the waveguides is still negligible. The distribution of the Stokes parameters in this regime has a complex multimodal structure strongly dependent on the nonlinear coupling coefficients and the initial conditions.

Bayesian retrieval of scatterometer wind fields

The retrieval of wind fields from scatterometer observations has traditionally been separated into two phases; local wind vector retrieval and ambiguity removal. Operationally, a forward model relating wind vector to backscatter is inverted, typically using look up tables, to retrieve up to four local wind vector solutions. A heuristic procedure, using numerical weather prediction forecast wind vectors and, often, some neighbourhood comparison is then used to select the correct solution. In this paper we develop a Bayesian method for wind field retrieval, and show how a direct local inverse model, relating backscatter to wind vector, improves the wind vector retrieval accuracy. We compare these results with the operational U.K. Meteorological Office retrievals, our own CMOD4 retrievals and a neural network based local forward model retrieval. We suggest that the neural network based inverse model, which is extremely fast to use, improves upon current forward models when used in a variational data assimilation scheme.

Splines and vector splines

The thrust of this report concerns spline theory and some of the background to spline theory and follows the development in (Wahba, 1991). We also review methods for determining hyper-parameters, such as the smoothing parameter, by Generalised Cross Validation. Splines have an advantage over Gaussian Process based procedures in that we can readily impose atmospherically sensible smoothness constraints and maintain computational efficiency. Vector splines enable us to penalise gradients of vorticity and divergence in wind fields. Two similar techniques are summarised and improvements based on robust error functions and restricted numbers of basis functions given. A final, brief discussion of the application of vector splines to the problem of scatterometer data assimilation highlights the problems of ambiguous solutions.

Modelling frontal discontinuities in wind fields

A Bayesian procedure for the retrieval of wind vectors over the ocean using satellite borne scatterometers requires realistic prior near-surface wind field models over the oceans. We have implemented carefully chosen vector Gaussian Process models; however in some cases these models are too smooth to reproduce real atmospheric features, such as fronts. At the scale of the scatterometer observations, fronts appear as discontinuities in wind direction. Due to the nature of the retrieval problem a simple discontinuity model is not feasible, and hence we have developed a constrained discontinuity vector Gaussian Process model which ensures realistic fronts. We describe the generative model and show how to compute the data likelihood given the model. We show the results of inference using the model with Markov Chain Monte Carlo methods on both synthetic and real data.

Enzymatic production of oligosaccharides in centrifugal fields

The aims of this work have been to identify an enzymatic reaction system suitable to investigate and develop the high-speed centrifuge as a novel reaction system for performing such reactions. The production of galacto-oligosaccharides by the trans-galactosyl activity of the enzyme β-galactosidase on lactose monohydrate was identified as a model enzymatic system to elucidate the principles of this type of process. Galacto-oligosaccharides have attracted considerable commercial interest as food additives which have been shown to be beneficial to the health of the human gastrointestinal tract. The development of a single unit operation capable of controlling the biosynthesis of galacto-oligosaccharides whilst simultaneously separating the enzyme from the reaction products would reduce downstream processing costs. This thesis shows for the first time that by using a combination of (a) immobilised or insolubilised β-galactosidase , (b) a rate-zonal centrifugation technique, and (c) various applied centrifugal fields, that a high-speed centrifuge could be used to control the formation of galacto-oligosaccharides whilst removing the enzyme from the reaction products. By layering a suspension of insolubilised β-galactosidase on top of a lactose monohydrate density gradient and centrifuging, the applied centrifugal fields generated produced sedimentation of the enzyme particles through the substrate. The higher sedimentation rate of the enzyme compared to those of the reaction products allowed for separation to take place. Complete sedimentation, or pelleting of the enzyme permits the possible recovery and re-use. Insolubilisation of the enzyme allowed it to be sedimented through the substrate gradient using much lower applied centrifugal fields than that required to sediment free soluble enzyme and this allowed for less expensive centrifugation equipment to be used. Using free soluble and insolubilised β-galactosidase stirred-batch reactions were performed to investigate the kinetics of lactose monohydrate hydrolysis and galacto-oligosaccharide formation. Based on these results a preliminary mathematical model based on Michaelis-Menten kinetics was produced. It was found that the enzyme insolubilisation process using a chemical cross-linking agent did not affect the process of galacto-oligosaccharide formation. Centrifugation experiments were performed and it was found that by varying the applied centrifugal fields that the yield of galacto-oligosaccharides could be controlled. The higher the applied centrifugal fields the lower the yield of galacto-oligosaccharides. By increasing the applied centrifugal fields the 'contact time' between the sedimenting enzyme and the substrate was reduced, which produced lower yields. A novel technique involving pulsing the insolubilised enzyme through the substrate gradient was developed and this was found to produce higher yields of galacto-oligosaccharide compared to using a single enzyme loading equivalent to the total combined activity of the pulses. Comparison of the galacto-oligosaccharide yields between stirred-batch and centrifugation reactions showed that the applied centrifugal fields did not adversely affect the transgalactosyl activity of the insolubilised enzyme.

Combined bioreaction and separation in centrifugal fields

The aim of this work has been to investigate the principle of combined centrifugal bioreaction-separation. The production of dextran and fructose by the action of the enzyme dextransucrase on sucrose was employed to elucidate some of the principles of this type of process. Dextran is a valuable pharmaceutical product used mainly as a blood volume expander and blood flow improver whilst fructose is an important dietary product. The development of a single step process capable of the simultaneous biosynthesis of dextran and the separation of the fructose by-product should improve dextran yields whilst reducing capital and processing costs. This thesis shows for the first time that it is possible to conduct successful bioreaction-separations using a rate-zonal centrifugation technique. By layering thin zones of dextrasucrase enzyme onto sucrose gradients and centrifuging, very high molecular weight (MW) dextran-enzyme complexes were formed that rapidly sedimented through the sucrose substrate gradients under the influence of the applied centrifugal field. The low MW fructose by-product sedimented at reduced rates and was thus separated from the enzyme and dextran during the reaction. The MW distribution of dextran recovered from the centrifugal bioreactor was compared with that from a conventional batch bioreactor. The results indicated that the centrifugal bioreactor produced up to 100% more clinical dextran with MWs of between 12 000 and 98 000 at 20% w/w sucrose concentrations than conventional bioreactors. This was due to the removal of acceptor fructose molecules from the sedimenting reaction zone by the action of the centrifugal field. Higher proportions of unwanted lower MW dextran were found in the conventional bioreactor than in the centrifugal bioreactor-separator. The process was studied on a number of alternative centrifugal systems. A zonal rotor fitted with a reorienting gradient core proved most successful for the evaluation of bioreactor performance. Results indicated that viscosity build-up in the reactor must be minimised in order to increase the yields of dextran per unit time and improve product separation. A preliminary attempt at modelling the process has also been made.

A novel framework of training hidden Markov support vector machines from lightly-annotated data

Natural language understanding (NLU) aims to map sentences to their semantic mean representations. Statistical approaches to NLU normally require fully-annotated training data where each sentence is paired with its word-level semantic annotations. In this paper, we propose a novel learning framework which trains the Hidden Markov Support Vector Machines (HM-SVMs) without the use of expensive fully-annotated data. In particular, our learning approach takes as input a training set of sentences labeled with abstract semantic annotations encoding underlying embedded structural relations and automatically induces derivation rules that map sentences to their semantic meaning representations. The proposed approach has been tested on the DARPA Communicator Data and achieved 93.18% in F-measure, which outperforms the previously proposed approaches of training the hidden vector state model or conditional random fields from unaligned data, with a relative error reduction rate of 43.3% and 10.6% being achieved.

Spiral attractor created by vector solitons

Mode-locked lasers emitting a train of femtosecond pulses called dissipative solitons are an enabling technology for metrology, high-resolution spectroscopy, fibre optic communications, nano-optics and many other fields of science and applications. Recently, the vector nature of dissipative solitons has been exploited to demonstrate mode locked lasing with both locked and rapidly evolving states of polarisation. Here, for an erbium-doped fibre laser mode locked with carbon nanotubes, we demonstrate the first experimental and theoretical evidence of a new class of slowly evolving vector solitons characterized by a double-scroll chaotic polarisation attractor substantially different from Lorenz, Rössler and Ikeda strange attractors. The underlying physics comprises a long time scale coherent coupling of two polarisation modes. The observed phenomena, apart from the fundamental interest, provide a base for advances in secure communications, trapping and manipulation of atoms and nanoparticles, control of magnetisation in data storage devices and many other areas. © 2014 CIOMP. All rights reserved.

Rotation invariant iris feature extraction using Gaussian Markov random fields with non-separable wavelet

Rotation invariance is important for an iris recognition system since changes of head orientation and binocular vergence may cause eye rotation. The conventional methods of iris recognition cannot achieve true rotation invariance. They only achieve approximate rotation invariance by rotating the feature vector before matching or unwrapping the iris ring at different initial angles. In these methods, the complexity of the method is increased, and when the rotation scale is beyond the certain scope, the error rates of these methods may substantially increase. In order to solve this problem, a new rotation invariant approach for iris feature extraction based on the non-separable wavelet is proposed in this paper. Firstly, a bank of non-separable orthogonal wavelet filters is used to capture characteristics of the iris. Secondly, a method of Markov random fields is used to capture rotation invariant iris feature. Finally, two-class kernel Fisher classifiers are adopted for classification. Experimental results on public iris databases show that the proposed approach has a low error rate and achieves true rotation invariance. © 2010.