Tailoring magnetic field gradient design to magnet cryostat geometry

Eddy currents induced within a magnetic resonance imaging (MRI) cryostat bore during pulsing of gradient coils can be applied constructively together with the gradient currents that generate them, to obtain good quality gradient uniformities within a specified imaging volume over time. This can be achieved by simultaneously optimizing the spatial distribution and temporal pre-emphasis of the gradient coil current, to account for the spatial and temporal variation of the secondary magnetic fields due to the induced eddy currents. This method allows the tailored design of gradient coil/magnet configurations and consequent engineering trade-offs. To compute the transient eddy currents within a realistic cryostat vessel, a low-frequency finite-difference time-domain (FDTD) method using total-field scattered-field (TFSF) scheme has been performed and validated

Dynamics of on-line gradient descent learning for multilayer neural networks

We consider the problem of on-line gradient descent learning for general two-layer neural networks. An analytic solution is presented and used to investigate the role of the learning rate in controlling the evolution and convergence of the learning process.

Transients and asymptotics of natural gradient learning

We analyse natural gradient learning in a two-layer feed-forward neural network using a statistical mechanics framework which is appropriate for large input dimension. We find significant improvement over standard gradient descent in both the transient and asymptotic phases of learning.

Natural gradient matrix momentum

Natural gradient learning is an efficient and principled method for improving on-line learning. In practical applications there will be an increased cost required in estimating and inverting the Fisher information matrix. We propose to use the matrix momentum algorithm in order to carry out efficient inversion and study the efficacy of a single step estimation of the Fisher information matrix. We analyse the proposed algorithm in a two-layer network, using a statistical mechanics framework which allows us to describe analytically the learning dynamics, and compare performance with true natural gradient learning and standard gradient descent.

Blurred edges look faint, and faint edges look sharp:The effect of a gradient threshold in a multi-scale edge coding model

A multi-scale model of edge coding based on normalized Gaussian derivative filters successfully predicts perceived scale (blur) for a wide variety of edge profiles [Georgeson, M. A., May, K. A., Freeman, T. C. A., & Hesse, G. S. (in press). From filters to features: Scale-space analysis of edge and blur coding in human vision. Journal of Vision]. Our model spatially differentiates the luminance profile, half-wave rectifies the 1st derivative, and then differentiates twice more, to give the 3rd derivative of all regions with a positive gradient. This process is implemented by a set of Gaussian derivative filters with a range of scales. Peaks in the inverted normalized 3rd derivative across space and scale indicate the positions and scales of the edges. The edge contrast can be estimated from the height of the peak. The model provides a veridical estimate of the scale and contrast of edges that have a Gaussian integral profile. Therefore, since scale and contrast are independent stimulus parameters, the model predicts that the perceived value of either of these parameters should be unaffected by changes in the other. This prediction was found to be incorrect: reducing the contrast of an edge made it look sharper, and increasing its scale led to a decrease in the perceived contrast. Our model can account for these effects when the simple half-wave rectifier after the 1st derivative is replaced by a smoothed threshold function described by two parameters. For each subject, one pair of parameters provided a satisfactory fit to the data from all the experiments presented here and in the accompanying paper [May, K. A. & Georgeson, M. A. (2007). Added luminance ramp alters perceived edge blur and contrast: A critical test for derivative-based models of edge coding. Vision Research, 47, 1721-1731]. Thus, when we allow for the visual system's insensitivity to very shallow luminance gradients, our multi-scale model can be extended to edge coding over a wide range of contrasts and blurs. © 2007 Elsevier Ltd. All rights reserved.

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.

Continuous chromatographic biochemical reaction-separation

Combined bioreaction separation studies have been carried out for the first time on a moving port semi-continuous counter-current chromatographic reactor-separator (SCCR-S1) consisting of twelve 5.4cm id x 75cm long columns packed with calcium charged cross-linked polystyrene resin (KORELA V07C). The inversion of sucrose to glucose and fructose in the presence of the enzyme invertase and the biochemIcal synthesis of dextran and fructose from sucrose in the presence of the enzyme dextransucrase were investigated. A dilute stream of the appropriate enzyme in deionised water was used as the eluent stream. The effect of switch time, feed concentration, enzyme activity, eluent rate and enzyme to feed concentration ratio on the combined bioreaction-separation were investigated. For the invertase reaction, at 20.77% w/v sucrose feed concentrations complete conversions were achieved. The enzyme usage was 34% of the theoretical enzyme amount needed to convert an equivalent amount of sucrose over the same time period when using a conventional fermenter. The fructose rich (FRP) and glucose rich (GRP) product purities obtained were over 90%. By operating at 35% w/v sucrose feed concentration and employing the product splitting and recycling techniques, the total concentration and purity of the GRP increased from 32% w/v to 4.6% and from 92.3% to 95% respectively. The FRP concentration also increased from 1.82% w/v to 2.88% w/v. A mathematical model was developed for the combined reaction-separation and used to simulate the continuous inversion of sucrose and product separation using the SCCR-S1. In the biosynthesis of dextran studies, 52% conversion of a 2% w/v sucrose concentration feed was achieved. An average dextran molecular weight of 4 millIon was obtained in the dextran rich (DRP) product stream. The enzyme dextransucrase was purifed successfully using centrifugation and ultrafiltration techniques.