The braneology of 3D dualities

In this paper, we study the reduction of four-dimensional Seiberg duality to three dimensions from a brane perspective. We reproduce the nonperturbative dynamics of three-dimensional field theory via a T–duality at a finite radius and the action of Euclidean D–strings. In this way, we also overcome certain issues regarding the brane description of Aharony duality. Moreover, we apply our strategy to more general dualities, such as toric duality for M2–branes and dualities with adjoint matter fields.

Surgical correction of astigmatism during cataract surgery

High levels of corneal astigmatism are prevalent in a significant proportion of the population. During cataract surgery pre-existing astigmatism can be corrected using single or paired incisions on the steep axis of the cornea, using relaxing incisions or with the use of a toric intraocular lens. This review provides an overview of the conventional methods of astigmatic correction during cataract surgery and in particular, discusses the various types of toric lenses presently available and the techniques used in determining the correct axis for the placement of such lenses. Furthermore, the potential causes of rotation in toric lenses are identified, along with techniques for assessing and quantifying the amount of rotation and subsequent management options for addressing post-operative rotation.

Requirement for and optimisation of premium intraocular lenses

Premium intraocular lenses (IOLs) aim to surgically correct astigmatism and presbyopia following cataract extraction, optimising vision and eliminating the need for cataract surgery in later years. It is usual to fully correct astigmatism and to provide visual correction for distance and near when prescribing spectacles and contact lenses, however for correction with the lens implanted during cataract surgery, patients are required to purchase the premium IOLs and pay surgery fees outside the National Health Service in the UK. The benefit of using toric IOLs was thus demonstrated, both in standard visual tests and real-world situations. Orientation of toric IOLs during implantation is critical and the benefit of using conjunctival blood vessels for alignment was shown. The issue of centration of IOLs relative to the pupil was also investigated, showing changes with the amount of dilation and repeat dilation evaluation, which must be considered during surgery to optimize the visual performance of premium IOLs. Presbyopia is a global issue, of growing importance as life expectancy increases, with no real long-term cure. Despite enhanced lifestyles, changes in diet and improved medical care, presbyopia still presents in modern life as a significant visual impairment. The onset of presbyopia was found to vary with risk factors including alcohol consumption, smoking, UV exposure and even weight as well as age. A new technique to make measurement of accommodation more objective and robust was explored, although needs for further design modifications were identified. Due to dysphotopsia and lack of intermediate vision through most multifocal IOL designs, the development of a trifocal IOL was shown to minimize these aspects. The current thesis, therefore, emphasises the challenges of premium IOL surgery and need for refinement for optimum visual outcome in addition to outlining how premium IOLs may provide long-term and successful correction of astigmatism and presbyopia.

Evaluation of modern intraocular lenses

Accommodating Intraocular Lenses (IOLs), multifocal IOLs (MIOLs) and toric IOLs are designed to provide a greater level of spectacle independency post cataract surgery. All of these IOLs are reliant on the accurate calculation of intraocular lens power determined through reliable ocular biometry. A standardised defocus area metric and reading performance index metric were devised for the evaluation of the range of focus and the reading ability of subjects implanted with presbyopic correcting IOLs. The range of clear vision after implantation of an MIOL is extended by a second focal point; however, this results in the prevalence of dysphotopsia. A bespoke halometer was designed and validated to assess this photopic phenomenon. There is a lack of standardisation in the methods used for determining IOL orientation and thus rotation. A repeatable, objective method was developed to allow the accurate assessment of IOL rotation, which was used to determine the rotational and positional stability of a closed loop haptic IOL. A new commercially available biometry device was validated for use with subjects prior to cataract surgery. The optical low coherence reflectometry instrument proved to be a valid method for assessing ocular biometry and covered a wider range of ocular parameters in comparison with previous instruments. The advantages of MIOLs were shown to include an extended range of clear vision translating into greater reading ability. However, an increased prevalence of dysphotopsia was shown with a bespoke halometer, which was dependent on the MIOL optic design. Implantation of a single optic accommodating IOL did not improve reading ability but achieved high subjective ratings of near vision. The closed-loop haptic IOL displayed excellent rotational stability in the late period but relatively poor rotational stability in the early period post implantation. The orientation error was compounded by the high frequency of positional misalignment leading to an extensive overall misalignment of the IOL. This thesis demonstrates the functionality of new IOL lens designs and the importance of standardised testing methods, thus providing a greater understanding of the consequences of implanting these IOLs. Consequently, the findings of the thesis will influence future designs of IOLs and testing methods.

Specialist contact lens fitting

What is meant by the term ‘specialist contact lens fitting’? Or put another way, what would be considered non-specialist contact lens fitting? Is there such a thing as routine contact lens fitting? Soft or silicone hydrogel fitting for daily wear would probably be considered as routine contact lens fitting, but would extended or flexible wear remain in the same category or would they be considered a specialist fit? Different eras will classify different products as being ‘specialist’. Certainly twenty years ago soft toric contact lenses were considered as being speciality lenses but today would be thought of as routine lenses. Conversely, gas permeable lenses were thought of as mainstream twenty years ago but now are considered as speciality lenses. Although this would not be the same globally, as in some countries (such as Netherlands, France and Japan) gas permeable lens fitting remains popular and is not on the decline as in other countries (Canada, Australia and Sweden) [1]. Bandage soft lenses applied after surface laser refractive procedures would be considered as therapeutic lenses but in reality they are just plano thin hydrogel lenses worn constantly for 3–4 days to allow the underlying epithelium to convalesce and are then removed [2]. Some patients find that wearing hydrogel lenses during periods when they suffer from seasonal allergies actually improves their ocular comfort as the contact lens acts as a barrier to the allergen [3] and [4]. Scleral lenses have long been considered speciality lenses, apart from a time when they were the only lenses available but at that time all contact lens work would have been considered speciality practice! Nowadays we see the advent of mini-scleral designs and we see large diameter gas permeable lenses too. It is possible that these lenses increase the popularity of gas permeable lenses again and they become more main stream. So it would seem that the lines between routine and speciality contact lens fitting are not clear. Whether a lens is classed a specialist fit or not would depend on the lens type, why it was fitted, where in the world the fitting was being done and even the era in which it was fitted. This begs the question as to what would be considered entry level knowledge in contact lens fitting. This may not be an issue for most BCLA members or CLAE readers but certainly would be for bodies such as the College of Optometrists (UK) or the Association of British Dispensing Opticians when they are planning the final registration examinations for budding practitioners or when planning the level of higher level qualifications such as College Certificates or Diplomas. Similarly for training institutions when they are planning their course content. This becomes even trickier when trying to devise a qualification that spans across many countries, like the European Diploma in Optometry and Optics. How do we know if the training and examination level is correct? One way would be to analyse things when they go wrong and if patterns of malpractice are seen then maybe that could be used as an indicator to more training being needed. There were 162 Fitness to Practice Hearing at the General Optical Council between 2001 and 2010. Forty-seven of these were clinically related case, 39 fraud related, and 76 others. Of the clinical ones only 3 were contact lens related. So it would appear that as whole, in the profession, contact lens clinical skills are not being questioned too often (although it seems a few of us can’t keep our hands out the cookie jar!).

Astigmatism and vision:should all astigmatism always be corrected?

As technology and medical devices improve, there is much interest in when and how astigmatism should be corrected with refractive surgery. Astigmatism can be corrected by most forms of refractive surgery, such as using excimer lasers algorithms to ablate the cornea to compensate for the magnitude of refractive error in different meridians. Correction of astigmatism at the time of cataract surgery is well developed and can be achieved through incision placement, relaxing incisions and toric intraocular lens (IOL) implantation. This was less of an issue in the past when there was a lower expectation to be spectacle independent after cataract surgery, in which case the residual refractive error, including astigmatism, could be compensated for with spectacle lenses. The issue of whether presurgical astigmatism should be corrected can be considered separately depending on whether a patient has residual accommodation, and the type of refractive surgery under consideration. We have previously reported on the visual impact of full correction of astigmatism, rather than just correcting the mean spherical equivalent. Correction of astigmatism as low as 1.00 dioptres significantly improves objective and subjective measures of functional vision in prepresbyopes at distance and near.

Refracting the pseudophakic patient

Pseudophakic patients are frequently encountered in optometric practice, often the result of cataract extraction but also presbyopia correction. Given advances in technology and surgery, the demand for intraocular lenses for correcting a variety of refractive requirements has increased owing to an ageing population. Based on the patient’s needs, either fixed focus, toric, accommodating or multifocal intraocular lenses (IOLs) may be implanted. During optometric examination, attention should be drawn to a history of IOLs and the potential complications they may cause in order to manage them effectively, particularly where sight is threatened. Although objective and subjective refraction does not differ greatly between phakic and pseudophakic patients, care should be taken to set the patient up correctly and the reflex during retinoscopy observed for posterior sub-capsular opacification. Additional tests such as reading speed, and glare and contrast sensitivity are necessary to determine the outcome of IOL surgery and detect potential problems associated with multifocal and accommodating IOLs. Based upon the results of these tests, refraction, and type of IOL, contact lens or spectacle correction may be required to meet the visual demands of the patient.

Optical quality and visual performance with customised soft contact lenses for keratoconus

Purpose: This study investigated how aberration-controlling, customised soft contact lenses corrected higher-order ocular aberrations and visual performance in keratoconic patients compared to other forms of refractive correction (spectacles and rigid gas-permeable lenses). Methods: Twenty-two patients (16 rigid gas-permeable contact lens wearers and six spectacle wearers) were fitted with standard toric soft lenses and customised lenses (designed to correct 3rd-order coma aberrations). In the rigid gas-permeable lens-wearing patients, ocular aberrations were measured without lenses, with the patient's habitual lenses and with the study lenses (Hartmann-Shack aberrometry). In the spectacle-wearing patients, ocular aberrations were measured both with and without the study lenses. LogMAR visual acuity (high-contrast and low-contrast) was evaluated with the patient wearing their habitual correction (of either spectacles or rigid gas-permeable contact lenses) and with the study lenses. Results: In the contact lens wearers, the habitual rigid gas-permeable lenses and customised lenses provided significant reductions in 3rd-order coma root-mean-square (RMS) error, 3rd-order RMS and higher-order RMS error (p ≤ 0.004). In the spectacle wearers, the standard toric lenses and customised lenses significantly reduced 3rd-order RMS and higher-order RMS errors (p ≤ 0.005). The spectacle wearers showed no significant differences in visual performance measured between their habitual spectacles and the study lenses. However, in the contact lens wearers, the habitual rigid gas-permeable lenses and standard toric lenses provided significantly better high-contrast acuities compared to the customised lenses (p ≤ 0.006). Conclusions: The customised lenses provided substantial reductions in ocular aberrations in these keratoconic patients; however, the poor visual performances achieved with these lenses are most likely to be due to small, on-eye lens decentrations. © 2014 The College of Optometrists.

Visual performance and optical quality with soft lenses in keratoconus patients

Purpose: To assess visual performance and ocular aberrations in keratoconic patients using toric soft contact lenses (SCL), rigid-gas-permeable (RGP) contact lenses and spectacle lens correction. Methods: Twenty-two keratoconus patients (16 RGP lens wearers and six spectacle wearers) were fitted with toric SCL. Ocular aberrations were measured with and without the patient's habitual RGP lenses and with the SCL in place. In the spectacle wearers, aberrations were measured with and without the SCL. Visual performance (high- and low-contrast visual acuity) was evaluated with the patient's habitual correction and with the SCL. Results: In the RGP lens wearers both the habitual lenses and the toric SCL significantly reduced coma, trefoil, 3rd-order, 4th-order cylinder and higher-order root-mean-square (RMS) aberrations (p≤0.015). In the spectacle wearers the toric SCL significantly reduced coma, 3rd-order and higher-order RMS aberrations (p≤0.01). The patients' habitual RGP lenses gave better low-contrast acuity (p≤0.006) compared to the toric SCL; however, no significant difference was found between lens types for high-contrast acuity (p=0.10). In the spectacle wearers no significant differences in visual performance measurements were found between the patients' spectacles and the toric SCL (p≥0.06). Conclusion: The results show that RGP lenses provided superior visual performances and greater reduction of 3rd-order aberrations compared to toric SCL in this group of keratoconic patients. In the spectacle-wearing group, visual performance with the toric SCL was found to be comparable to that measured with spectacles. Nevertheless, with the exception of spherical aberration, the toric SCL were successful in significantly reducing uncorrected higher-order aberrations. Ophthalmic & Physiological Optics © 2012 The College of Optometrists.

Do educators need educating?

Actual text: I was recently at the Spanish College of Optometry biennial conference and attended a meeting of contact lens lecturers from around Spain and Portugal. We discussed various ideas, mainly about how to share good practice and improve standards. What came to my mind was ‘is there a blueprint for training trainers?’ Well probably not but there are many things that we need to acknowledge such as the way students learn for example. Many educators themselves were taught by lecturers who would write on a blackboard or use acetate on an overhead projector, then came the 35 mm slide era followed by the Powerpoint era. More recently there is a move towards a much more integrated approach of various teaching methods. At my university our contact lens and anterior eye lectures generally follow a format where a narrated Powerpoint lecture is uploaded onto our internal virtual learning environment. This narrated version of the slides is designed to give the didactic element of the topic. The students listen to that before attending an interactive seminar on that topic. The seminar is also recorded so that students can listen to that afterwards. The seminar is designed to give additional information, such as case reports, or to clarify key points or for live demonstrations. It is a good way of doubling the contact time with the students without imposing further on an already packed formal timetable as the students can work in their own time. One problem that we noticed with this approach was that attendance can vary. If the students feel that they will gain something from the interactive seminar then they are more likely to attend – exam tips usually win them over! At the Spanish meeting the educators decided that they wanted to have regular meetings. The industry colleagues in attendance said that they were happy to help but could not necessarily give money, but they could offer meeting rooms, pay for lunch and evening meals. They even said that that they were happy to host meetings and invite other companies too (except to manufacturing plants). In the UK the British Committee of Contact Lens Educators (BUCCLE) meets for one day on three occasions in the year. The American Optometric Contact Lens Educators (AOCLE) meets annually at a three day event. Both these organisations get some help from industry. BUCCLE usually has one of its meetings at a university, one at a company training centre/manufacturing plant/national headquarters and one meeting the day before the BCLA annual conference. BUCCLE usually has its pre-BCLA meeting in conjunction with the International Association of Contact Lens Educators (IACLE). So when educators meet what would they discuss; well probably the focus should be on education rather than actual contact lens knowledge. For example sharing ideas on how to teach toric lens fitting would be better than discussing the actual topic of toric lenses itself. Most universities will have an education department with an expert who could share ideas on how to use the internet in teaching or how to structure lectures or assessments etc. In the past I have helped with similar training programmes in other countries and sharing good practice in pedagogy is always a popular topic. Anyone who is involved in education in the field of contact lenses should look at the IACLE web page and look out for the IACLE World Congress in 2015 in the days preceding the BCLA. Finally, IACLE, AOCLE and BUCCLE all exist as a result of generous educational grants from contact lens companies and anyone interested in finding out more about should refer to their respective web pages.

A Smooth Four-Dimensional G-Hilbert Scheme

2000 Mathematics Subject Classification: 14C05, 14L30, 14E15, 14J35.

Evaluating techniques to improve visual performance with and assessment of premium intraocular lenses

Premium Intraocular Lenses (IOLs) such as toric IOLs, multifocal IOLs (MIOLs) and accommodating IOLs (AIOLs) can provide better refractive and visual outcomes compared to standard monofocal designs, leading to greater levels of post-operative spectacle independence. The principal theme of this thesis relates to the development of new assessment techniques that can help to improve future premium IOL design. IOLs designed to correct astigmatism form the focus of the first part of the thesis. A novel toric IOL design was devised to decrease the effect of toric rotation on patient visual acuity, but found to have neither a beneficial or detrimental impact on visual acuity retention. IOL tilt, like rotation, may curtail visual performance; however current IOL tilt measurement techniques require the use of specialist equipment not readily available in most ophthalmological clinics. Thus a new idea that applied Pythagoras’s theory to digital images of IOL optic symmetricality in order to calculate tilt was proposed, and shown to be both accurate and highly repeatable. A literature review revealed little information on the relationship between IOL tilt, decentration and rotation and so this was examined. A poor correlation between these factors was found, indicating they occur independently of each other. Next, presbyopia correcting IOLs were investigated. The light distribution of different MIOLs and an AIOL was assessed using perimetry, to establish whether this could be used to inform optimal IOL design. Anticipated differences in threshold sensitivity between IOLs were not however found, thus perimetry was concluded to be ineffective in mapping retinal projection of blur. The observed difference between subjective and objective measures of accommodation, arising from the influence of pseudoaccommodative factors, was explored next to establish how much additional objective power would be required to restore the eye’s focus with AIOLs. Blur tolerance was found to be the key contributor to the ocular depth of focus, with an approximate dioptric influence of 0.60D. Our understanding of MIOLs may be limited by the need for subjective defocus curves, which are lengthy and do not permit important additional measures to be undertaken. The use of aberrometry to provide faster objective defocus curves was examined. Although subjective and objective measures related well, the peaks of the MIOL defocus curve profile were not evident with objective prediction of acuity, indicating a need for further refinement of visual quality metrics based on ocular aberrations. The experiments detailed in the thesis evaluate methods to improve visual performance with toric IOLs. They also investigate new techniques to allow more rapid post-operative assessment of premium IOLs, which could allow greater insights to be obtained into several aspects of visual quality, in order to optimise future IOL design and ultimately enhance patient satisfaction.

Error tolerance of topological codes with independent bit-flip and measurement errors

Topological quantum error correction codes are currently among the most promising candidates for efficiently dealing with the decoherence effects inherently present in quantum devices. Numerically, their theoretical error threshold can be calculated by mapping the underlying quantum problem to a related classical statistical-mechanical spin system with quenched disorder. Here, we present results for the general fault-tolerant regime, where we consider both qubit and measurement errors. However, unlike in previous studies, here we vary the strength of the different error sources independently. Our results highlight peculiar differences between toric and color codes. This study complements previous results published in New J. Phys. 13, 083006 (2011).

Moduli Space of (0,2) Conformal Field Theories

In this thesis we study aspects of (0,2) superconformal field theories (SCFTs), which are suitable for compactification of the heterotic string. In the first part, we study a class of (2,2) SCFTs obtained by fibering a Landau-Ginzburg (LG) orbifold CFT over a compact K\"ahler base manifold. While such models are naturally obtained as phases in a gauged linear sigma model (GLSM), our construction is independent of such an embedding. We discuss the general properties of such theories and present a technique to study the massless spectrum of the associated heterotic compactification. We test the validity of our method by applying it to hybrid phases of GLSMs and comparing spectra among the phases. In the second part, we turn to the study of the role of accidental symmetries in two-dimensional (0,2) SCFTs obtained by RG flow from (0,2) LG theories. These accidental symmetries are ubiquitous, and, unlike in the case of (2,2) theories, their identification is key to correctly identifying the IR fixed point and its properties. We develop a number of tools that help to identify such accidental symmetries in the context of (0,2) LG models and provide a conjecture for a toric structure of the SCFT moduli space in a large class of models. In the final part, we study the stability of heterotic compactifications described by (0,2) GLSMs with respect to worldsheet instanton corrections to the space-time superpotential following the work of Beasley and Witten. We show that generic models elude the vanishing theorem proved there, and may not determine supersymmetric heterotic vacua. We then construct a subclass of GLSMs for which a vanishing theorem holds.

Generalized cluster states based on finite groups

We define generalized cluster states based on finite group algebras in analogy to the generalization of the toric code to the Kitaev quantum double models. We do this by showing a general correspondence between systems with CSS structure and finite group algebras, and applying this to the cluster states to derive their generalization. We then investigate properties of these states including their projected entangled pair state representations, global symmetries, and relationship to the Kitaev quantum double models. We also discuss possible applications of these states.