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.

Surface wind fields (on Earth)

This document sets out to clarify the role of fronts and other atmospheric features on the form of surface wind fields. This is intended as a basic meteorological review of the typical features we will encounter in wind fields. Thus there is a strong emphasis on description at a fairly rudimentary level. The document should prove useful as we think about different models we could adopt for wind fields.

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.

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.

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.

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.

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.

Typical kernel size and number of sparse random matrices over Galois fields: a statistical physics approach

Using methods of statistical physics, we study the average number and kernel size of general sparse random matrices over GF(q), with a given connectivity profile, in the thermodynamical limit of large matrices. We introduce a mapping of GF(q) matrices onto spin systems using the representation of the cyclic group of order q as the q-th complex roots of unity. This representation facilitates the derivation of the average kernel size of random matrices using the replica approach, under the replica symmetric ansatz, resulting in saddle point equations for general connectivity distributions. Numerical solutions are then obtained for particular cases by population dynamics. Similar techniques also allow us to obtain an expression for the exact and average number of random matrices for any general connectivity profile. We present numerical results for particular distributions.

Properties of sparse random matrices over finite fields

Typical properties of sparse random matrices over finite (Galois) fields are studied, in the limit of large matrices, using techniques from the physics of disordered systems. For the case of a finite field GF(q) with prime order q, we present results for the average kernel dimension, average dimension of the eigenvector spaces and the distribution of the eigenvalues. The number of matrices for a given distribution of entries is also calculated for the general case. The significance of these results to error-correcting codes and random graphs is also discussed.

The measurements of neutron and gamma dose rates in mixed radiation fields, using a liquid scintillation counter

Measurements of neutron and gamma dose rates in mixed radiation fields, and gamma dose rates from calibrated gamma sources, were performed using a liquid scintillation counter NE213 with a pulse shape discrimination technique based on the charge comparison method. A computer program was used to analyse the experimental data. The radiation field was obtained from a 241Am-9Be source. There was general agreement between measured and calculated neutron and gamma dose rates in the mixed radiation field, but some disagreement in the measurements of gamma dose rates for gamma sources, due to the dark current of the photomultiplier and the effect of the perturbation of the radiation field by the detector. An optical fibre bundle was used to couple an NE213 scintillator to a photomultiplier, in an attempt to minimise these effects. This produced an improvement in the results for gamma sources. However, the optically coupled detector system could not be used for neutron and gamma dose rate measurements in mixed radiation fields. The pulse shape discrimination system became ineffective as a consequence of the slower time response of the detector system.

Assessing visual fields for driving in patients with paracentral scotomata

Background: The binocular Esterman visual field test (EVFT) is the current visual field test for driving in the UK. Merging of monocular field tests (Integrated Visual Field, IVF) has been proposed as an alternative for glaucoma patients. Aims: To examine the level of agreement between the EVFT and IVF for patients with binocular paracentral scotomata, caused by either ophthalmological or neurological conditions, and to compare outcomes with useful field of view (UFOV) performance, a test of visual attention thought to be important in driving. Methods: 60 patients with binocular paracentral scotomata but normal visual acuity (VA) were recruited prospectively. Subjects completed and were classified as “pass” or “fail” for the EVFT, IVF and UFOV. Results: Good agreement occurred between the EVFT and IVF in classifying subjects as “pass” or “fail” (kappa?=?0.84). Classifications disagreed for four subjects with paracentral scotomata of neurological origin (three “passed” IVF yet “failed” EVFT). Mean UFOV scores did not differ between those who “passed” and those who “failed” both visual field tests (p?=?0.11). Agreement between the visual field tests and UFOV was limited (EVFT kappa?=?0.22, IVF kappa 0.32). Conclusions: Although the IVF and EVFT agree well in classifying visual fields with regard to legal fitness to drive in the UK, the IVF “passes” some individuals currently classed as unfit to drive due to paracentral scotomata of non-glaucomatous origin. The suitability of the UFOV for assessing crash risk in those with visual field loss is questionable.

Visual evoked magnetic fields to flash and pattern in 100 normal subjects

The practicality of recording visual evoked magnetic fields in 100 subjects 15-87 yr of age using a single channel d.c. SQUID second order gradiometer in an unshielded environment was investigated. The pattern reversal response showed a major positive component between 90 and 120 msec (P100M) while the response to flash produced a major positive component between 90 and 140 msec (P2M). Latency norms of the P100M were more variable than the corresponding P100 and P2 visual evoked potentials. The latency of the P100M may show a steep increase with age in most subjects after about 55 yr whereas only a small trend of latency with age was detected for the flash P2M.

A brief review of magnetic fields from the human visual system

Both the eye and brain generate magnetic fields when stimulated with a variety of visual cues. These magnetic fields can be measured with a magnetometer; a device which uses superconducting technology. The application of this technique to measuring the magnetooculogram, magnetoretinogram and visually evoked fields from the brain is described. So far the main use of this technique has been in pure research. Its potential for diagnosing ocular and neurological diseases is discussed.

The use of flash and pattern evoked fields in the diagnosis of Alzheimer's disease

Subjects with Alzheimer's disease (AD) exhibit normal visually evoked potentials (VEP) to pattern reversal stimuli but a delayed P2 flash response. The pattern response may originate in the primary visual cortex via the geniculo-calcarine pathway while the flash P2 may originate in the association areas via the cholinergic-tectal pathway. We now show: a) that the pathology of AD is more prominent in the visual association areas B18/19 than in B17 and b) that the magnetic signal to flash and pattern may originate from B18/19 and B17 respectively.