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.

Objective analysis of toric intraocular lens rotation and centration

PURPOSE: To assess the repeatability of an objective image analysis technique to determine intraocular lens (IOL) rotation and centration. SETTING: Six ophthalmology clinics across Europe. METHODS: One-hundred seven patients implanted with Akreos AO aspheric IOLs with orientation marks were imaged. Image quality was rated by a masked observer. The axis of rotation was determined from a line bisecting the IOL orientation marks. This was normalized for rotation of the eye between visits using the axis bisecting 2 consistent conjunctival vessels or iris features. The center of ovals overlaid to circumscribe the IOL optic edge and the pupil or limbus were compared to determine IOL centration. Intrasession repeatability was assessed in 40 eyes and the variability of repeated analysis examined. RESULTS: Intrasession rotational stability of the IOL was ±0.79 degrees (SD) and centration was ±0.10 mm horizontally and ±0.10 mm vertically. Repeated analysis variability of the same image was ±0.70 degrees for rotation and ±0.20 mm horizontally and ±0.31 mm vertically for centration. Eye rotation (absolute) between visits was 2.23 ± 1.84 degrees (10%>5 degrees rotation) using one set of consistent conjunctival vessels or iris features and 2.03 ± 1.66 degrees (7%>5 degrees rotation) using the average of 2 sets (P =.13). Poorer image quality resulted in larger apparent absolute IOL rotation (r =-0.45,P<.001). CONCLUSIONS: Objective analysis of digital retroillumination images allows sensitive assessment of IOL rotation and centration stability. Eye rotation between images can lead to significant errors if not taken into account. Image quality is important to analysis 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.

Rotational and centration stability of an aspheric intraocular lens with a simulated toric design

Purpose: To assess the stability of the Akreos AO intraocular lens (IOL) platform with a simulated toric design using objective image analysis. Setting: Six hospital eye clinics across Europe. Methods: After implantation in 1 eye of patients, IOLs with orientation marks were imaged at 1 to 2 days, 7 to 14 days, 30 to 60 days, and 120 to 180 days. The axis of rotation and IOL centration were objectively assessed using validated image analysis. Results: The study enrolled 107 patients with a mean age of 69.9 years ± 7.7 (SD). The image quality was sufficient for IOL rotation analysis in 91% of eyes. The mean rotation between the first day postoperatively and 120 to 180 days was 1.93 ± 2.33 degrees, with 96% of IOLs rotating fewer than 5 degrees and 99% rotating fewer than 10 degrees. There was no significant rotation between visits and no clear bias in the direction of rotation. In 71% of eyes, the dilation and image quality was sufficient for image analysis of centration. The mean change in centration between 1 day and 120 to 180 days was 0.21 ± 0.11 mm, with all IOLs decentering less than 0.5 mm. There was no significant decentration between visits and no clear bias in the direction of the decentration. Conclusion: Objective analysis of digital retroillumination images taken at different postoperative periods shows the aspheric IOL platform was stable in the eye and is therefore suitable for the application of a toric surface to correct corneal astigmatism.

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.

Clinical outcomes after implantation of a new hydrophobic acrylic toric IOL during routine cataract surgery

PURPOSE: To assess the clinical outcomes after implantation of a new hydrophobic acrylic toric intraocular lens (IOL) to correct preexisting corneal astigmatism in patients having routine cataract surgery. SETTING: Four hospital eye clinics throughout Europe. DESIGN: Cohort study. METHODS: This study included eyes with at least 0.75 diopter (D) of preexisting corneal astigmatism having routine cataract surgery. Phacoemulsification was performed followed by insertion and alignment of a Tecnis toric IOL. Patients were examined 4 to 8 weeks postoperatively; uncorrected distance visual acuity (UDVA), corrected distance visual acuity, manifest refraction, and keratometry were measured. Individual patient satisfaction with uncorrected vision and the surgeon’s assessment of ease of handling and performance of the IOL were also documented. The cylinder axis of the toric IOL was determined by dilated slitlamp examination. RESULTS: The study enrolled 67 eyes of 60 patients. Four to 8 weeks postoperatively, the mean UDVA was 0.15 logMAR G 0.17 (SD) and the UDVA was 20/40 or better in 88% of eyes. The mean refractive cylinder decreased significantly postoperatively, from -1.91 +/- 1.07 D to -0.67 +/- 0.54 D. No significant change in keratometric cylinder was observed. The mean absolute IOL misalignment from the intended axis was 3.4 degrees (range 0 to 12 degrees). The good UDVA resulted in high levels of patient satisfaction. CONCLUSION: Implantation of the new toric IOL was an effective, safe, and predictable method to manage corneal astigmatism in patients having routine cataract surgery.

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.

Evaluating the effect of splitting cylindrical power on improving patient tolerance to toric lens misalignment

Purpose: Evaluating the impact of splitting toric power on patient tolerance to misorientation such as with intraocular lens rotation. Setting: University vision clinic. Methods: Healthy, non astigmats had +1.50D astigmatism induced with spectacle lenses at 90°, 135°, 180° and +3.00D at 90°. Two correcting cylindrical lenses of the opposite sign and half the power each were subsequently added to the trial frame misaligned by 0°, 5° or 10° in a random order and misorientated from the initial axis in a clockwise direction by up to 15° in 5° steps. A second group of adapted astigmats with between 1.00 and 3.00DC had their astigmatism corrected with two toric spectacle lenses of half the power separated by 0°, 5° or 10° and misorientated from the initial axis in both directions by up to 15° in 5° steps. Distance, high contrast visual acuity was measured using a computerised test chart at each lens misalignment and misorientation. Results: Misorientation of the split toric lenses caused a statistically significant drop in visual acuity (F= 70.341; p< 0.001). Comparatively better acuities were observed around 180°, as anticipated (F= 3.775; p= 0.035). Misaligning the split toric power produced no benefit in visual acuity retention with axis misorientation when subjects had astigmatism induced with a low (F= 2.190, p= 0.129) or high cylinder (F= 0.491, p= 0.617) or in the adapted astigmats (F= 0.120, p= 0.887). Conclusion: Misalignment of toric lens power split across the front and back lens surfaces had no beneficial effect on distance visual acuity, but also no negative effect. © 2013 British Contact Lens Association.

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

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Complexity and chirality indices for molecular informatics::differential geometry approach

Novel molecular complexity measures are designed based on the quantum molecular kinematics. The Hamiltonian matrix constructed in a quasi-topological approximation describes the temporal evolution of the modelled electronic system and determined the time derivatives for the dynamic quantities. This allows to define the average quantum kinematic characteristics closely related to the curvatures of the electron paths, particularly, the torsion reflecting the chirality of the dynamic system. A special attention has been given to the computational scheme for this chirality measure. The calculations on realistic molecular systems demonstrate reasonable behaviour of the proposed molecular complexity indices.

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 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 monolayers 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. © 2012 Elsevier B.V. All rights reserved.