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.

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.

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.

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.

Non-zero mean Gaussian process prior wind field models

This report outlines the derivation and application of a non-zero mean, polynomial-exponential covariance function based Gaussian process which forms the prior wind field model used in 'autonomous' disambiguation. It is principally used since the non-zero mean permits the computation of realistic local wind vector prior probabilities which are required when applying the scaled-likelihood trick, as the marginals of the full wind field prior. As the full prior is multi-variate normal, these marginals are very simple to compute.

Adding constrained discontinuities to Gaussian process models of wind fields

Gaussian Processes provide good prior models for spatial data, but can be too smooth. In many physical situations there are discontinuities along bounding surfaces, for example fronts in near-surface wind fields. We describe a modelling method for such a constrained discontinuity and demonstrate how to infer the model parameters in wind fields with MCMC sampling.

Statistical mechanics of low-density parity check error-correcting codes over Galois fields

A variation of low-density parity check (LDPC) error-correcting codes defined over Galois fields (GF(q)) is investigated using statistical physics. A code of this type is characterised by a sparse random parity check matrix composed of C non-zero elements per column. We examine the dependence of the code performance on the value of q, for finite and infinite C values, both in terms of the thermodynamical transition point and the practical decoding phase characterised by the existence of a unique (ferromagnetic) solution. We find different q-dependence in the cases of C = 2 and C ≥ 3; the analytical solutions are in agreement with simulation results, providing a quantitative measure to the improvement in performance obtained using non-binary alphabets.

Modeling equity market integration using smooth transition analysis:a study of Eastern European stock markets

This paper assesses the extent to which the equity markets of Hungary, Poland the Czech Republic and Russia have become less segmented. Using a variety of tests it is shown there has been a consistent increase in the co-movement of some Eastern European markets and developed markets. Using the variance decompositions from a vector autoregressive representation of returns it is shown that for Poland and Hungary global factors are having an increasing influence on equity returns, suggestive of increased equity market integration. In this paper we model a system of bivariate equity market correlations as a smooth transition logistic trend model in order to establish how rapidly the countries of Eastern Europe are moving away from market segmentation. We find that Hungary is the country which is becoming integrated the most quickly. © 2005 ELsevier Ltd. All rights reserved.

Model specification and forecasting foreign exchange rates with vector autoregressions

This study examines the forecasting accuracy of alternative vector autoregressive models each in a seven-variable system that comprises in turn of daily, weekly and monthly foreign exchange (FX) spot rates. The vector autoregressions (VARs) are in non-stationary, stationary and error-correction forms and are estimated using OLS. The imposition of Bayesian priors in the OLS estimations also allowed us to obtain another set of results. We find that there is some tendency for the Bayesian estimation method to generate superior forecast measures relatively to the OLS method. This result holds whether or not the data sets contain outliers. Also, the best forecasts under the non-stationary specification outperformed those of the stationary and error-correction specifications, particularly at long forecast horizons, while the best forecasts under the stationary and error-correction specifications are generally similar. The findings for the OLS forecasts are consistent with recent simulation results. The predictive ability of the VARs is very weak.

Seeing edge blur: receptive fields as multiscale neural templates

Edge blur is an important perceptual cue, but how does the visual system encode the degree of blur at edges? Blur could be measured by the width of the luminance gradient profile, peak ^ trough separation in the 2nd derivative profile, or the ratio of 1st-to-3rd derivative magnitudes. In template models, the system would store a set of templates of different sizes and find which one best fits the `signature' of the edge. The signature could be the luminance profile itself, or one of its spatial derivatives. I tested these possibilities in blur-matching experiments. In a 2AFC staircase procedure, observers adjusted the blur of Gaussian edges (30% contrast) to match the perceived blur of various non-Gaussian test edges. In experiment 1, test stimuli were mixtures of 2 Gaussian edges (eg 10 and 30 min of arc blur) at the same location, while in experiment 2, test stimuli were formed from a blurred edge sharpened to different extents by a compressive transformation. Predictions of the various models were tested against the blur-matching data, but only one model was strongly supported. This was the template model, in which the input signature is the 2nd derivative of the luminance profile, and the templates are applied to this signature at the zero-crossings. The templates are Gaussian derivative receptive fields that covary in width and length to form a self-similar set (ie same shape, different sizes). This naturally predicts that shorter edges should look sharper. As edge length gets shorter, responses of longer templates drop more than shorter ones, and so the response distribution shifts towards shorter (smaller) templates, signalling a sharper edge. The data confirmed this, including the scale-invariance implied by self-similarity, and a good fit was obtained from templates with a length-to-width ratio of about 1. The simultaneous analysis of edge blur and edge location may offer a new solution to the multiscale problem in edge detection.

Effect of β-adrenoceptor antagonists on autonomic control of ciliary smooth muscle

Purpose: Pharmacological intervention with peripheral sympathetic transmission at ciliary smooth muscle neuro-receptor junctions has been used against a background of controlled parasympathetic activity to investigate the characteristics of autonomic control of ocular accommodation. Methods: A continuously recording infrared optometer was used to measure accommodation on a group of five visually normal emmetropic subjects under open- and closed-loop conditions. A double-blind protocol between saline, timolol and betaxolol was used to differentiate between the localised action on ciliary smooth muscle and effects induced by changes in stimulus conditions. Data were collected before and 45 min following the instillation of saline, timolol or betaxolol. Open-loop post-task decay was investigated following 3 min sustained near fixation of a stimulus placed 3 D above the subject's pre-task tonic accommodation level. Closed-loop dynamic responses were recorded for each treatment condition while subjects viewed sinusoidally (0.05-0.6 Hz) or stepwise vergence-modulated targets over a 2 D range (2-4 D). Results: Open-loop data demonstrate a rapid post-task regression to pre-task tonic accommodation levels for saline and betaxolol control conditions. A slow positive post-task shift was induced by timolol indicating that sympathetic inhibition contributes to accommodative adaptation during sustained near vision. Closed-loop accommodation responses to temporally modulated sinusoidal stimuli showed characteristic features for both saline and betaxolol control conditions. Timolol induced a reduced gain for low- and mid-temporal frequencies (< 0.3 Hz) but did not affect the response at higher temporal frequencies. Response times to stepwise stimuli increased following the instillation of timolol for the near-to-far fixation condition compared with the controls and was related to the period of sustained prior fixation. Conclusions: Modulation of accommodation under open- and closed-loop conditions by a non-selective β-blocker is consistent with the temporal and inhibitory features of sympathetic innervation to ciliary smooth muscle. Although parasympathetic innervation predominates there is evidence to support a role for sympathetic innervation in the control of ocular accommodation. © 2002 The College of Optometrists.

Adding constrained discontinuities to Gaussian process models of wind fields

Gaussian Processes provide good prior models for spatial data, but can be too smooth. In many physical situations there are discontinuities along bounding surfaces, for example fronts in near-surface wind fields. We describe a modelling method for such a constrained discontinuity and demonstrate how to infer the model parameters in wind fields with MCMC sampling.

Non-metallic cold-cathode electron emission from composite metal-insulator microstructures

A detailed investigation has been undertaken into a field-induced electron emission (FIEE) mechanism that occurs at microscopically localised `sites' on uncoated, dielectric-coated and composite-coated metallic cathodes. An optical imaging technique has been used to observe and characterize the spatial and temporal behaviour of the populations of emission sites on these cathodes under various experimental conditions, e.g. pulsed-fields, gas environment etc. This study has shown that, for applied fields of 20MVm^-1, thin dielectric (750AA) and composite metal-insulator (MI) overlayers result in a dramatic increase in the total number of emission sites (typically 30cm^-2), and hence emission current. The emission process has been further investigated by a complementary electron spectroscopy technique which has revealed that the localised emission sites on these cathodes display field-dependent spectral shifts and half-widths, i.e. indicative of a `non-metallic' emission mechanism. Details are also given of a comprehensive investigation into the effects of the residual gas environment on the FIEE process from uncoated Cu-cathodes. This latter study has revealed that the well-known Gas Conditioning process can be performed with a wide range of gas species (e.g. O_2, N_2 etc), and furthermore, the degree of conditioning is influenced by both a `Voltage' and `Temperature' effect. These experimental findings have been shown to be particularly important to the technology of high-voltage vacuum-insulation and cold-cathode electron sources. The FIEE mechanism has been interpreted in terms of a hot-electron process that is associated with `electroformed' conducting channels in MI, MIM and MIMI surface microstructures.

Non-curliation of Escherichia coli O78:K80 isolates associated with IS1 insertion in csgB and reduced persistence in poultry infection

The elaboration of curli fimbriae by Escherichia coli is associated with the development of a lacy colony morphology when grown on colonisation factor antigen agar at 25 degrees C. Avian colisepticaemia E. coli isolates screened for curliation by this culture technique showed lacy and smooth colonial morphologies and the genetic basis of the non-curliated smooth colonial phenotype was analysed. Two smooth E. coli O78:K80 isolates possessed about 40 copies of the IS1 element within their respective genomes of which one copy insertionally inactivated the csgB gene, the nucleator gene for curli fibril formation. One of these two isolates also possessed a defective rpoS gene which is a known regulator of curli expression. In the day-old chick model, both smooth isolates were as invasive as a known virulent O78:K80 isolate as determined by extent of liver and spleen colonisation post oral inoculation but were less persistent in terms of caecal colonisation.