Measurements of generalisation based on information geometry

Neural networks are statistical models and learning rules are estimators. In this paper a theory for measuring generalisation is developed by combining Bayesian decision theory with information geometry. The performance of an estimator is measured by the information divergence between the true distribution and the estimate, averaged over the Bayesian posterior. This unifies the majority of error measures currently in use. The optimal estimators also reveal some intricate interrelationships among information geometry, Banach spaces and sufficient statistics.

Dynamics of learning with restricted training sets

The dynamics of supervised learning in layered neural networks were studied in the regime where the size of the training set is proportional to the number of inputs. The evolution of macroscopic observables, including the two relevant performance measures can be predicted by using the dynamical replica theory. Three approximation schemes aimed at eliminating the need to solve a functional saddle-point equation at each time step have been derived.

Noise, regularizers, and unrealizable scenarios in online learning from restricted training sets

We study the dynamics of on-line learning in multilayer neural networks where training examples are sampled with repetition and where the number of examples scales with the number of network weights. The analysis is carried out using the dynamical replica method aimed at obtaining a closed set of coupled equations for a set of macroscopic variables from which both training and generalization errors can be calculated. We focus on scenarios whereby training examples are corrupted by additive Gaussian output noise and regularizers are introduced to improve the network performance. The dependence of the dynamics on the noise level, with and without regularizers, is examined, as well as that of the asymptotic values obtained for both training and generalization errors. We also demonstrate the ability of the method to approximate the learning dynamics in structurally unrealizable scenarios. The theoretical results show good agreement with those obtained by computer simulations.

A theoretical and experimental analysis of the no-load air gap magnetic field in squirrel cage induction machines

In induction machines the tooth frequency losses due to permeance variation constitute a signif'icant, portion of the total loss. In order to predict and estimate these losses it, is essential to obtain a clear understanding of the no-load distribution of the air gap magnetic field and the magnitude of flux pulsation in both stator and rotor teeth. The existing theories and methods by which the air gap permeance variation in a doubly slotted structure is calculated are either empirical or restricted. The main objective of this thesis is to obtain a detailed analysis of the no-load air gap magnetic field distribution and the effect of air gap geometry on the magnitude and waveform of the tooth flux pulsation. In this thesis a detaiiled theoretical and experimental analysis of flux distribution not only leads to a better understanding of the distribution of no-load losses but also provides theoretical analysis for calculating the losses with greater accuracy

Automatic refinement of constructive solid geometry models

Geometric information relating to most engineering products is available in the form of orthographic drawings or 2D data files. For many recent computer based applications, such as Computer Integrated Manufacturing (CIM), these data are required in the form of a sophisticated model based on Constructive Solid Geometry (CSG) concepts. A recent novel technique in this area transfers 2D engineering drawings directly into a 3D solid model called `the first approximation'. In many cases, however, this does not represent the real object. In this thesis, a new method is proposed and developed to enhance this model. This method uses the notion of expanding an object in terms of other solid objects, which are either primitive or first approximation models. To achieve this goal, in addition to the prepared subroutine to calculate the first approximation model of input data, two other wireframe models are found for extraction of sub-objects. One is the wireframe representation on input, and the other is the wireframe of the first approximation model. A new fast method is developed for the latter special case wireframe, which is named the `first approximation wireframe model'. This method avoids the use of a solid modeller. Detailed descriptions of algorithms and implementation procedures are given. In these techniques utilisation of dashed line information is also considered in improving the model. Different practical examples are given to illustrate the functioning of the program. Finally, a recursive method is employed to automatically modify the output model towards the real object. Some suggestions for further work are made to increase the domain of objects covered, and provide a commercially usable package. It is concluded that the current method promises the production of accurate models for a large class of objects.

Applications of differential geometry to high spin field theories

The main aim of this thesis is to investigate the application of methods of differential geometry to the constraint analysis of relativistic high spin field theories. As a starting point the coordinate dependent descriptions of the Lagrangian and Dirac-Bergmann constraint algorithms are reviewed for general second order systems. These two algorithms are then respectively employed to analyse the constraint structure of the massive spin-1 Proca field from the Lagrangian and Hamiltonian viewpoints. As an example of a coupled field theoretic system the constraint analysis of the massive Rarita-Schwinger spin-3/2 field coupled to an external electromagnetic field is then reviewed in terms of the coordinate dependent Dirac-Bergmann algorithm for first order systems. The standard Velo-Zwanziger and Johnson-Sudarshan inconsistencies that this coupled system seemingly suffers from are then discussed in light of this full constraint analysis and it is found that both these pathologies degenerate to a field-induced loss of degrees of freedom. A description of the geometrical version of the Dirac-Bergmann algorithm developed by Gotay, Nester and Hinds begins the geometrical examination of high spin field theories. This geometric constraint algorithm is then applied to the free Proca field and to two Proca field couplings; the first of which is the minimal coupling to an external electromagnetic field whilst the second is the coupling to an external symmetric tensor field. The onset of acausality in this latter coupled case is then considered in relation to the geometric constraint algorithm.

The influence of tool geometry on the performance of drilling tools

The main objective of the work presented in this thesis is to investigate the two sides of the flute, the face and the heel of a twist drill. The flute face was designed to yield straight diametral lips which could be extended to eliminate the chisel edge, and consequently a single cutting edge will be obtained. Since drill rigidity and space for chip conveyance have to be a compromise a theoretical expression is deduced which enables optimum chip disposal capacity to be described in terms of drill parameters. This expression is used to describe the flute heel side. Another main objective is to study the effect on drill performance of changing the conventional drill flute. Drills were manufactured according to the new flute design. Tests were run in order to compare the performance of a conventional flute drill and non conventional design put forward. The results showed that 50% reduction in thrust force and approximately 18% reduction in torque were attained for the new design. The flank wear was measured at the outer corner and found to be less for the new design drill than for the conventional one in the majority of cases. Hole quality, roundness, size and roughness were also considered as a further aspect of drill performance. Improvement in hole quality is shown to arise under certain cutting conditions. Accordingly it might be possible to use a hole which is produced in one pass of the new drill which previously would have required a drilled and reamed hole. A subsidiary objective is to design the form milling cutter that should be employed for milling the foregoing special flute from drill blank allowing for the interference effect. A mathematical analysis in conjunction with computing technique and computers is used. To control the grinding parameter, a prototype drill grinder was designed and built upon the framework of an existing cincinnati cutter grinder. The design and build of the new grinder is based on a computer aided drill point geometry analysis. In addition to the conical grinding concept, the new grinder is also used to produce spherical point utilizing a computer aided drill point geometry analysis.

The influence of cutting tool geometry upon aspects of chip flow and tool wear:a theoretical, three dimensional examination of the cutting geometry and the shape of the twist drill

This work is undertaken in the attempt to understand the processes at work at the cutting edge of the twist drill. Extensive drill life testing performed by the University has reinforced a survey of previously published information. This work demonstrated that there are two specific aspects of drilling which have not previously been explained comprehensively. The first concerns the interrelating of process data between differing drilling situations, There is no method currently available which allows the cutting geometry of drilling to be defined numerically so that such comparisons, where made, are purely subjective. Section one examines this problem by taking as an example a 4.5mm drill suitable for use with aluminium. This drill is examined using a prototype solid modelling program to explore how the required numerical information may be generated. The second aspect is the analysis of drill stiffness. What aspects of drill stiffness provide the very great difference in performance between short flute length, medium flute length and long flute length drills? These differences exist between drills of identical point geometry and the practical superiority of short drills has been known to shop floor drilling operatives since drilling was first introduced. This problem has been dismissed repeatedly as over complicated but section two provides a first approximation and shows that at least for smaller drills of 4. 5mm the effects are highly significant. Once the cutting action of the twist drill is defined geometrically there is a huge body of machinability data that becomes applicable to the drilling process. Work remains to interpret the very high inclination angles of the drill cutting process in terms of cutting forces and tool wear but aspects of drill design may already be looked at in new ways with the prospect of a more analytical approach rather than the present mix of experience and trial and error. Other problems are specific to the twist drill, such as the behaviour of the chips in the flute. It is now possible to predict the initial direction of chip flow leaving the drill cutting edge. For the future the parameters of further chip behaviour may also be explored within this geometric model.

Overcoming shadows in 3-source photometric stereo

Light occlusions are one of the most significant difficulties of photometric stereo methods. When three or more images are available without occlusion, the local surface orientation is overdetermined so that shape can be computed and the shadowed pixels can be discarded. In this paper, we look at the challenging case when only two images are available without occlusion, leading to a one degree of freedom ambiguity per pixel in the local orientation. We show that, in the presence of noise, integrability alone cannot resolve this ambiguity and reconstruct the geometry in the shadowed regions. As the problem is ill-posed in the presence of noise, we describe two regularization schemes that improve the numerical performance of the algorithm while preserving the data. Finally, the paper describes how this theory applies in the framework of color photometric stereo where one is restricted to only three images and light occlusions are common. Experiments on synthetic and real image sequences are presented.

Oxidized phospholipid inhibition of toll-like receptor (TLR) signaling is restricted to TLR2 and TLR4 roles for cd14, lps-binding protein, and md2 as targets for specificity of inhibition

The generation of reactive oxygen species is a central feature of inflammation that results in the oxidation of host phospholipids. Oxidized phospholipids, such as 1-palmitoyl-2-arachidonyl-sn-glycero-3-phosphorylcholine (OxPAPC), have been shown to inhibit signaling induced by bacterial lipopeptide or lipopolysac-charide (LPS), yet the mechanisms responsible for the inhibition of Toll-like receptor (TLR) signaling by OxPAPC remain incompletely understood. Here, we examined the mechanisms by which OxPAPC inhibits TLR signaling induced by diverse ligands in macrophages, smooth muscle cells, and epithelial cells. OxPAPC inhibited tumor necrosis factor- production, IB degradation, p38 MAPK phosphorylation, and NF-B-dependent reporter activation induced by stimulants of TLR2 and TLR4 (Pam3CSK4 and LPS) but not by stimulants of other TLRs (poly(I·C), flagellin, loxoribine, single-stranded RNA, or CpG DNA) in macrophages and HEK-293 cells transfected with respective TLRs and significantly reduced inflammatory responses in mice injected subcutaneously or intraperitoneally with Pam3CSK4. Serum proteins, including CD14 and LPS-binding protein, were identified as key targets for the specificity of TLR inhibition as supplementation with excess serum or recombinant CD14 or LBP reversed TLR2 inhibition by OxPAPC, whereas serum accessory proteins or expression of membrane CD14 potentiated signaling via TLR2 and TLR4 but not other TLRs. Binding experiments and functional assays identified MD2 as a novel additional target of OxPAPC inhibition of LPS signaling. Synthetic phospholipid oxidation products 1-palmitoyl-2-(5-oxovaleryl)-sn-glycero-3-phosphocholine and 1-palmitoyl-2-glutaryl-sn-glycero-3-phosphocholine inhibited TLR2 signaling from 30 µM. Taken together, these results suggest that oxidized phospholipid-mediated inhibition of TLR signaling occurs mainly by competitive interaction with accessory proteins that interact directly with bacterial lipids to promote signaling via TLR2 or TLR4.

The role of lipid geometry in designing liposomes for the solubilisation of poorly water soluble drugs

Liposomes are well recognised for their ability to improve the delivery of a range of drugs. More commonly they are applied for the delivery of water-soluble drugs, but given their structural attributes they can also be employed as solubilising agents for low solubility drugs as well as drug targeting agents. To further explore the potential of liposomes as solubilising agents, we have investigated the role of bilayer packaging in promoting drug solubilisation in liposome bilayers. The effect of alkyl chain length and symmetry was investigated to consider if using 'mis-matched' phospholipids could be used to create 'voids' within the bilayers, and enhance bilayer loading capacity. Lipid packing was investigated using Langmuir studies, which demonstrated that increasing the alkyl chain length enhanced lipid packing, with condensed monolayer forming, whilst asymmetric lipids formed less condensed monolayers. However this more open packing did not translate into improved drug loading, with the longer chain, condensed bilayers formed from long-chain, saturated lipids offering higher drug loading capacity. These studies demonstrate that liposomes formulated from longer chain, saturated lipids offer enhanced solubilisation capacity. However the molecular size, rather than lipophilicity, of the drug to be incorporated was also a key factor dominating bilayer incorporation efficiency.

Specific lipidome signatures in central nervous system from methionine-restricted mice

Membrane lipid composition is an important correlate of the rate of aging of animals. Dietary methionine restriction (MetR) increases lifespan in rodents. The underlying mechanisms have not been elucidated but could include changes in tissue lipidomes. In this work, we demonstrate that 80% MetR in mice induces marked changes in the brain, spinal cord, and liver lipidomes. Further, at least 50% of the lipids changed are common in the brain and spinal cord but not in the liver, suggesting a nervous system-specific lipidomic profile of MetR. The differentially expressed lipids includes (a) specific phospholipid species, which could reflect adaptive membrane responses, (b) sphingolipids, which could lead to changes in ceramide signaling pathways, and (c) the physiologically redox-relevant ubiquinone 9, indicating adaptations in phase II antioxidant response metabolism. In addition, specific oxidation products derived from cholesterol, phosphatidylcholine, and phosphatidylethanolamine were significantly decreased in the brain, spinal cord, and liver from MetR mice. These results demonstrate the importance of adaptive responses of membrane lipids leading to increased stress resistance as a major mechanistic contributor to the lowered rate of aging in MetR mice. © 2013 American Chemical Society.

Gratings in novel fibre geometry for applications in shape sensing

A long period grating (LPG) fabricated in progressive three-layered (PTL) fibre is described. The grating with a period of 391µm, had dual attenuation bands associated with a particular cladding mode. The dual attenuation bands have been experimentally characterised for their spectral sensitivity to bending, which resulted in the highest sensitivity to bending seen for this particular fibre and temperature. The spectral characteristics of the fibre have been modelled giving good agreement to the experimental data as well as showing that the attenuation bands are both associated with the second order HE/EH2,n cladding mode.

Experimental and theoretical studies on molecular geometry and polymorphism in crystalline drug substances

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