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.

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.

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.

Automated assessment of visual fields and their inter-relation to evoked potentials in visual disorders

The Octopus Automated Perimeter was validated in a comparative study and found to offer many advantages in the assessment of the visual field. The visual evoked potential was investigated in an extensive study using a variety of stimulus parameters to simulate hemianopia and central visual field defects. The scalp topography was recorded topographically and a technique to compute the source derivation of the scalp potential was developed. This enabled clarification of the expected scalp distribution to half field stimulation using different electrode montages. The visual evoked potential following full field stimulation was found to be asymmetrical around the midline with a bias over the left occiput particularly when the foveal polar projections of the occipital cortex were preferentially stimulated. The half field response reflected the distribution asymmetry. Masking of the central 3° resulted in a response which was approximately symmetrical around the midline but there was no evidence of the PNP-complex. A method for visual field quantification was developed based on the neural representation of visual space (Drasdo and Peaston 1982) in an attempt to relate visual field depravation with the resultant visual evoked potentials. There was no form of simple, diffuse summation between the scalp potential and the cortical generators. It was, however, possible to quantify the degree of scalp potential attenuation for M-scaled full field stimuli. The results obtained from patients exhibiting pre-chiasmal lesions suggested that the PNP-complex is not scotomatous in nature but confirmed that it is most likely to be related to specific diseases (Harding and Crews 1982). There was a strong correlation between the percentage information loss of the visual field and the diagnostic value of the visual evoked potential in patients exhibiting chiasmal lesions.

Relaxation procedures for an iterative MFS algorithm for the stable reconstruction of elastic fields from Cauchy data in two-dimensional isotropic linear elasticity

We investigate two numerical procedures for the Cauchy problem in linear elasticity, involving the relaxation of either the given boundary displacements (Dirichlet data) or the prescribed boundary tractions (Neumann data) on the over-specified boundary, in the alternating iterative algorithm of Kozlov et al. (1991). The two mixed direct (well-posed) problems associated with each iteration are solved using the method of fundamental solutions (MFS), in conjunction with the Tikhonov regularization method, while the optimal value of the regularization parameter is chosen via the generalized cross-validation (GCV) criterion. An efficient regularizing stopping criterion which ceases the iterative procedure at the point where the accumulation of noise becomes dominant and the errors in predicting the exact solutions increase, is also presented. The MFS-based iterative algorithms with relaxation are tested for Cauchy problems for isotropic linear elastic materials in various geometries to confirm the numerical convergence, stability, accuracy and computational efficiency of the proposed method.

Fiber optic sensing of magnetic fields utilizing femtosecond laser sculpted microslots and long period gratings coated with Terfenol-D

Fiber optic sensors are fabricated for detecting static magnetic fields. The sensors consist of a UV inscribed long period grating with two 50 micron long microslots. The microslots are fabricated using the femtosecond laser based inscribe and etch technique. The microslots and the fiber surface are coated with a magnetostrictive material Terfenol-D. A spectral sensitivity of 1.15 pm/mT was measured in transmission with a working resolution of ±0.2 mT for a static magnetic field strength below 10 mT. These devices also present a different response when the spatial orientation of the fiber was adjusted relative to the magnetic field lines.

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.

Characterisation and performance of a Terfenol-D coated femtosecond laser inscribed optical fibre Bragg sensor with a laser ablated microslot for the detection of static magnetic fields

We present a novel device for the characterisation of static magnetic fields through monitoring wavelength shifts of femtosecond inscribed fibre Bragg grating and micromachined slot, coated with Terfenol-D. The device was sensitive to static magnetic fields and can be used as a vectoral sensor for the detection of magnetic fields as low as 0.046 mT with a resolution of ± 0.3mT in transmission and ± 0.7mT in reflection. The use of a femtosecond laser to both inscribe the FBGs and micromachine the slot in a single stage prior to coating the device significantly simplifies the fabrication.

Femtosecond laser inscribed Bragg sensor in Terfenol-D coated optical fibre with ablated microslot for the detection of static magnetic fields

A novel device for the detection and characterisation of static magnetic fields is presented. It consists of a femtosecond laser inscribed fibre Bragg grating (FBG) that is incorporated into an optical fibre with a femtosecond laser micromachined slot. The symmetry of the fibre is broken by the micro-slot, producing non-uniform strain across the fibre cross section. The sensing region is coated with Terfenol-D making the device sensitive to static magnetic fields, whereas the symmetry breaking results in a vectorial sensor for the detection of magnetic fields as low as 0.046 mT with a resolution of ±0.3mT in transmission and ±0.7mT in reflection. The sensor output is directly wavelength encoded from the FBG filtering, leading to simple demodulation through the monitoring of wavelength shifts that result as the fibre structure changes shape in response to the external magnetic field. The use of a femtosecond laser to both inscribe the FBG and micro-machine the slot in a single stage, prior to coating the device, significantly simplifies the sensor fabrication.

Femtosecond laser inscribed Bragg sensor in Terfenol-D coated optical fibre with ablated microslot for the detection of static magnetic fields

A novel device for the detection and characterisation of static magnetic fields is presented. It consists of a femtosecond laser inscribed fibre Bragg grating (FBG) that is incorporated into an optical fibre with a femtosecond laser micromachined slot. The symmetry of the fibre is broken by the micro-slot, producing non-uniform strain across the fibre cross section. The sensing region is coated with Terfenol-D making the device sensitive to static magnetic fields, whereas the symmetry breaking results in a vectorial sensor for the detection of magnetic fields as low as 0.046 mT with a resolution of ±0.3mT in transmission and ±0.7mT in reflection. The sensor output is directly wavelength encoded from the FBG filtering, leading to simple demodulation through the monitoring of wavelength shifts that result as the fibre structure changes shape in response to the external magnetic field. The use of a femtosecond laser to both inscribe the FBG and micro-machine the slot in a single stage, prior to coating the device, significantly simplifies the sensor fabrication.

Towards an integrative theory of religion and politics

In the social sciences, debate on the relationship between religion and politics is mainly the subject of analysis in the sociology of religion and the theory of international relations. While each of these fields promotes different approaches to study their interdependency. The individual's perception of religion and politics is neglected by current research. The faithful, who participates in religious ceremonies, listening and behaving according to specific religious teachings, actively engaging in the liturgical life of the institutional form of his religion, has a specific way of understanding the relationship between religion and politics. I argue that this aspect is under-researched and misrepresented in the literature of sociology and international relations. However, a more complex analysis is offered by the study of nationalism, and especially by its ethnosymbolic approach, which includes at the micro and macro societal level the presence of myths and symbols as part of the individual's and the nation's life. An integrative theory analysing the connection between religion and politics takes into account the role of myths and symbols from the perspectives of both individuals and ethnic communities.

Measuring the spatial arrangement patterns of pathological lesions in histological sections of brain tissue

The development of abnormal protein aggregates in the form of extracellular plaques and intracellular inclusions is a characteristic feature of many neurodegenerative diseases such as Alzheimer's disease (AD), Creutzfeldt-Jakob disease (CJD) and the fronto-temporal dementias (FTD). An important aspect of a pathological protein aggregate is its spatial topography in the tissue. Lesions may not be randomly distributed within a histological section but exhibit spatial pattern, a departure from randomness either towards regularity or clustering. Information on the spatial pattern of a lesion may be useful in elucidating its pathogenesis and in studying the relationships between different lesions. This article reviews the methods that have been used to study the spatial topography of lesions. These include simple tests of whether the distribution of a lesion departs significantly from random using randomized points or sample fields, and more complex methods that employ grids or transects of contiguous fields and which can detect the intensity of aggregation and the sizes, distribution and spacing of the clusters. The usefulness of these methods in elucidating the pathogenesis of protein aggregates in neurodegenerative disease is discussed.

Methods of studying the planar distribution of objects in histological sections of brain tissue

This article reviews the statistical methods that have been used to study the planar distribution, and especially clustering, of objects in histological sections of brain tissue. The objective of these studies is usually quantitative description, comparison between patients or correlation between histological features. Objects of interest such as neurones, glial cells, blood vessels or pathological features such as protein deposits appear as sectional profiles in a two-dimensional section. These objects may not be randomly distributed within the section but exhibit a spatial pattern, a departure from randomness either towards regularity or clustering. The methods described include simple tests of whether the planar distribution of a histological feature departs significantly from randomness using randomized points, lines or sample fields and more complex methods that employ grids or transects of contiguous fields, and which can detect the intensity of aggregation and the sizes, distribution and spacing of clusters. The usefulness of these methods in understanding the pathogenesis of neurodegenerative diseases such as Alzheimer's disease and Creutzfeldt-Jakob disease is discussed. © 2006 The Royal Microscopical Society.

Emulation of random output simulators

Computer models, or simulators, are widely used in a range of scientific fields to aid understanding of the processes involved and make predictions. Such simulators are often computationally demanding and are thus not amenable to statistical analysis. Emulators provide a statistical approximation, or surrogate, for the simulators accounting for the additional approximation uncertainty. This thesis develops a novel sequential screening method to reduce the set of simulator variables considered during emulation. This screening method is shown to require fewer simulator evaluations than existing approaches. Utilising the lower dimensional active variable set simplifies subsequent emulation analysis. For random output, or stochastic, simulators the output dispersion, and thus variance, is typically a function of the inputs. This work extends the emulator framework to account for such heteroscedasticity by constructing two new heteroscedastic Gaussian process representations and proposes an experimental design technique to optimally learn the model parameters. The design criterion is an extension of Fisher information to heteroscedastic variance models. Replicated observations are efficiently handled in both the design and model inference stages. Through a series of simulation experiments on both synthetic and real world simulators, the emulators inferred on optimal designs with replicated observations are shown to outperform equivalent models inferred on space-filling replicate-free designs in terms of both model parameter uncertainty and predictive variance.