Hierarchical GTM: constructing localized non-linear projection manifolds in a principled way

It has been argued that a single two-dimensional visualization plot may not be sufficient to capture all of the interesting aspects of complex data sets, and therefore a hierarchical visualization system is desirable. In this paper we extend an existing locally linear hierarchical visualization system PhiVis ¸iteBishop98a in several directions: bf(1) We allow for em non-linear projection manifolds. The basic building block is the Generative Topographic Mapping (GTM). bf(2) We introduce a general formulation of hierarchical probabilistic models consisting of local probabilistic models organized in a hierarchical tree. General training equations are derived, regardless of the position of the model in the tree. bf(3) Using tools from differential geometry we derive expressions for local directional curvatures of the projection manifold. Like PhiVis, our system is statistically principled and is built interactively in a top-down fashion using the EM algorithm. It enables the user to interactively highlight those data in the ancestor visualization plots which are captured by a child model. We also incorporate into our system a hierarchical, locally selective representation of magnification factors and directional curvatures of the projection manifolds. Such information is important for further refinement of the hierarchical visualization plot, as well as for controlling the amount of regularization imposed on the local models. We demonstrate the principle of the approach on a toy data set and apply our system to two more complex 12- and 18-dimensional data sets.

A principled approach to interactive hierarchical non-linear visualization of high-dimensional data

Hierarchical visualization systems are desirable because a single two-dimensional visualization plot may not be sufficient to capture all of the interesting aspects of complex high-dimensional data sets. We extend an existing locally linear hierarchical visualization system PhiVis [1] in several directions: bf(1) we allow for em non-linear projection manifolds (the basic building block is the Generative Topographic Mapping -- GTM), bf(2) we introduce a general formulation of hierarchical probabilistic models consisting of local probabilistic models organized in a hierarchical tree, bf(3) we describe folding patterns of low-dimensional projection manifold in high-dimensional data space by computing and visualizing the manifold's local directional curvatures. Quantities such as magnification factors [3] and directional curvatures are helpful for understanding the layout of the nonlinear projection manifold in the data space and for further refinement of the hierarchical visualization plot. Like PhiVis, our system is statistically principled and is built interactively in a top-down fashion using the EM algorithm. We demonstrate the visualization system principle of the approach on a complex 12-dimensional data set and mention possible applications in the pharmaceutical industry.

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.

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]

Transition in homogeneously heated inclined plane parallel shear flows

The transition of internally heated inclined plane parallel shear flows is examined numerically for the case of finite values of the Prandtl number Pr. We show that as the strength of the homogeneously distributed heat source is increased the basic flow loses stability to two-dimensional perturbations of the transverse roll type in a Hopf bifurcation for the vertical orientation of the fluid layer, whereas perturbations of the longitudinal roll type are most dangerous for a wide range of the value of the angle of inclination. In the case of the horizontal inclination transverse roll and longitudinal roll perturbations share the responsibility for the prime instability. Following the linear stability analysis for the general inclination of the fluid layer our attention is focused on a numerical study of the finite amplitude secondary travelling-wave solutions (TW) that develop from the perturbations of the transverse roll type for the vertical inclination of the fluid layer. The stability of the secondary TW against three-dimensional perturbations is also examined and our study shows that for Pr=0.71 the secondary instability sets in as a quasi-periodic mode, while for Pr=7 it is phase-locked to the secondary TW. The present study complements and extends the recent study by Nagata and Generalis (2002) in the case of vertical inclination for Pr=0.

Soliton switching using cascaded nonlinear-optical loop mirrors

We demonstrate multiple-peaked switching in a nonlinear-optical loop mirror and present an experimental investigation of device cascading in the soliton regime based on a sequence of two independent nonlinear-optical loop mirrors. Cascading leads to an enhanced switching response with sharper switching edges, flattened peaks, and increased interpeak extinction ratios. We observe that pulses emerging from the cascade retain the sech2 temporal profile of a soliton with minimal degradation in the spectral characteristics.

Experimental demonstration of SOA based non-inverting optical memory

We have experimentally investigated two non-inverting optical memory configurations: a TOAD based device & an integrated hybrid Mach-Zehnder interferometer. Experimental results for both devices and a comparison of the two techniques is presented.

Three-dimensional magnetic resonance imaging of the phakic crystalline lens during accommodation

To quantify changes in crystalline lens curvature, thickness, equatorial diameter, surface area, and volume during accommodation using a novel two-dimensional magnetic resonance imaging (MRI) paradigm to generate a complete three-dimensional crystalline lens surface model.

Some studies relating to the design of shallow, fluidized bed boilers

The concept of shallow fluidized bed boilers is defined and a preliminary working design for a gas-fired package boiler has been produced. Those areas of the design requiring further study have been specified. Experimental investigations concerning these areas have been carried out. A two-dimensional, conducting paper analog has been developed for the specific purpose of evaluating sheet fins. The analog has been generalised and is presented as a simple means of simulating the general, two-dimensional Helmholtz equation. By recording the transient response of spherical, calorimetric probes when plunged into heated air-fluidized beds, heat transfer coefficients have been measured at bed temperatures up to 1 100°C. A correlation fitting all the data to within ±10% has been obtained. A model of heat transfer to surfaces immersed in high temperature beds has been proposed. The model solutions are, however, only in qualitative agreement with the experimental data. A simple experimental investigation has revealed that the effective, radial, thermal conductivities of shallow fluidized beds are an order of magnitude lower than the axial conductivities. These must, consequently, be taken into account when considering heat transfer to surfaces immersed within fluidized beds. Preliminary work on pre-mixed gas combustion and some further qualitative experiments have been used as the basis for discussing the feasibility of combusting heavy fuel oils within shallow beds. The use of binary beds, within which the fuel could be both gasified and subsequently burnt, is proposed. Finally, the consequences of the experimental studies on the initial design are considered, and suggestions for further work are made.

Transition in convective flows heated internally

The stability of internally heated convective flows in a vertical channel under the influence of a pressure gradient and in the limit of small Prandtl number is examined numerically. In each of the cases studied the basic flow, which can have two inflection points, loses stability at the critical point identified by the corresponding linear analysis to two-dimensional states in a Hopf bifurcation. These marginal points determine the linear stability curve that identifies the minimum Grashof number (based on the strength of the homogeneous heat source), at which the two-dimensional periodic flow can bifurcate. The range of stability of the finite amplitude secondary flow is determined by its (linear) stability against three-dimensional infinitesimal disturbances. By first examining the behavior of the eigenvalues as functions of the Floquet parameters in the streamwise and spanwise directions we show that the secondary flow loses stability also in a Hopf bifurcation as the Grashof number increases, indicating that the tertiary flow is quasi-periodic. Secondly the Eckhaus marginal stability curve, that bounds the domain of stable transverse vortices towards smaller and larger wavenumbers, but does not cause a transition as the Grashof number increases, is also given for the cases studied in this work.

Novel hardwired distributive tactile sensing system for medical applications

This thesis described the research carried out on the development of a novel hardwired tactile sensing system tailored for the application of a next generation of surgical robotic and clinical devices, namely a steerable endoscope with tactile feedback, and a surface plate for patient posture and balance. Two case studies are examined. The first is a one-dimensional sensor for the steerable endoscope retrieving shape and ‘touch’ information. The second is a two-dimensional surface which interprets the three-dimensional motion of a contacting moving load. This research can be used to retrieve information from a distributive tactile sensing surface of a different configuration, and can interpret dynamic and static disturbances. This novel approach to sensing has the potential to discriminate contact and palpation in minimal invasive surgery (MIS) tools, and posture and balance in patients. The hardwired technology uses an embedded system based on Field Programmable Gate Arrays (FPGA) as the platform to perform the sensory signal processing part in real time. High speed robust operation is an advantage from this system leading to versatile application involving dynamic real time interpretation as described in this research. In this research the sensory signal processing uses neural networks to derive information from input pattern from the contacting surface. Three neural network architectures namely single, multiple and cascaded were introduced in an attempt to find the optimum solution for discrimination of the contacting outputs. These architectures were modelled and implemented into the FPGA. With the recent introduction of modern digital design flows and synthesis tools that essentially take a high-level sensory processing behaviour specification for a design, fast prototyping of the neural network function can be achieved easily. This thesis outlines the challenge of the implementations and verifications of the performances.

Settlement of fill with particular reference to opencast coal mining sites

A study of information available on the settlement characteristics of backfill in restored opencast coal mining sites and other similar earthworks projects has been undertaken. In addition, the methods of opencast mining, compaction controls, monitoring and test methods have been reviewed. To consider and develop the methods of predicting the settlement of fill, three sites in the West Midlands have been examined; at each, the backfill had been placed in a controlled manner. In addition, use has been made of a finite element computer program to compare a simple two-dimensional linear elastic analysis with field observations of surface settlements in the vicinity of buried highwalls. On controlled backfill sites, settlement predictions have been accurately made, based on a linear relationship between settlement (expressed as a percentage of fill height) against logarithm of time. This `creep' settlement was found to be effectively complete within 18 months of restoration. A decrease of this percentage settlement was observed with increasing fill thickness; this is believed to be related to the speed with which the backfill is placed. A rising water table within the backfill is indicated to cause additional gradual settlement. A prediction method, based on settlement monitoring, has been developed and used to determine the pattern of settlement across highwalls and buried highwalls. The zone of appreciable differential settlement was found to be mainly limited to the highwall area, the magnitude was dictated by the highwall inclination. With a backfill cover of about 15 metres over a buried highwall the magnitude of differential settlement was negligible. Use has been made of the proposed settlement prediction method and monitoring to control the re-development of restored opencase sites. The specifications, tests and monitoring techniques developed in recent years have been used to aid this. Such techniques have been valuable in restoring land previously derelict due to past underground mining.

Reactive processing of polymers: structural characterization of products by 1H and 13C NMR spectroscopy for glycidyl methacrylate grafting onto EPR in the absence and presence of a reactive comonomer

Grafted GMA on EPR samples were prepared in a Thermo-Haake internal mixer by free radical melt grafting reactions in the absence (conventional system; EPR-g-GMA(CONV)) and presence of the reactive comonomer divinyl benzene, DVB (EPR-g-GMA(DVB)). The GMA-homopolymer (poly-GMA), a major side reaction product in the conventional system, was almost completely absent in the DVB-containing system, the latter also resulted in a much higher level of GMA grafting. A comprehensive microstructure analysis of the formed poly-GMA was performed based on one-dimensional H-1 and C-13 NMR spectroscopy and the complete spectral assignments were supported by two-dimensional NMR techniques based on long range two and three bond order carbon-proton couplings from HMBC (Heteronuclear Multiple Bond Coherence) and that of one bond carbon-proton couplings from HSQC (Heteronuclear Single Quantum Coherence), as well as the use of Distortionless Enhancement by Polarization Transfer (DEPT) NMR spectroscopy. The unambiguous analysis of the stereochemical configuration of poly-GMA was further used to help understand the microstructures of the GMA-grafts obtained in the two different free radical melt grafting reactions, the conventional and comonomer-containing systems. In the grafted GMA, in the conventional system (EPR-g-GMA(CONV)), the methylene protons of the GMA were found to be sensitive to tetrad configurational sequences and the results showed that 56% of the GMA sequence in the graft is in atactic configuration and 42% is in syndiotactic configuration whereas the poly-GMA was predominantly syndiotactic. The differences in the microstructures of the graft in the conventional EPR-g-GMA(CONV) and the DVB-containing (EPR-g-GMA(DVB)) systems is also reported (C) 2009 Elsevier Ltd. All rights reserved.

How accurate are photographic surrogate markers used to detect macular edema in the English national screening programme?

DESIGN. Retrospective analysis PURPOSE. Macular oedema is not directly visible on two dimensional digital photographs such that surrogate markers need to be used. In the English National Screening Programme these are exudate within one optic disc diameter (DD) of the fovea, group of exudates within two DD of the fovea and haemorrhages or microaneurysms (HMA) within one DD of the fovea with best corrected visual acuity (VA) worse than 6/9. All patients who present with any of these surrogate markers at screening are referred to an ophthalmology clinic for slit lamp examination. The purpose of this audit was to determine how many patients with positive maculopathy diagnosis on photography were truly identified by optical coherence tomography (OCT) with macular oedema. METHODS. Data was collected from patients attending digital diabetic retinopathy screening. Patients who presented with surrogate markers for macular oedema also had an OCT scan. The fast macula scan on the Stratus OCT was used and an ophthalmologist reviewed the scans to determine whether macular oedema was present. RESULTS. Maculopathy by exudates: Of 155 patients 45 (29%) showed thickening on the OCT of these 12 required laser. Those who also had pre-proliferative retinopathy (n=20) were more likely to have macular oedema (75%) than those with background diabetic retinopathy. Maculopathy by HMA and VA worse than 6/9: Of 66 patients 11 (16.7%) showed thickening on the OCT. 5 (7.6%) of these had macular oedema, 5 (7.6%) epi-retinal membrane, and 1 (1.5%) age related macular degeneration. None of these patients required laser. CONCLUSIONS. The likelihood of the presence of macular oedema and requiring laser treatment is greater with macular exudation than HMA within one DD and reduced VA. Overall the surrogate markers used show low specificity for macular oedema, however combining OCT with photography does identify those with macular oedema who require a true referral for an ophthalmological slit lamp examination.

CFD and bubble column reactors:simulation and experiment

The simulation of two-phase flow in bubble columns using commercially available software fromFluent Incorporated is presented here. Data from a bubble column with a ratio of height to thecolumn diameter of 5 : 1 are compared with simulations and experimental results for time-averaged velocity and Reynolds stress proles are used to validate transient, two-dimensional simulations.The models are based on multiphase biological reactors with applications in the food industry. An example case of the mass transfer of oxygen through the liquid phase is also presented.