Distribution of the angle of rotation plane random walks

We study the probability distribution of the angle by which the tangent to the trajectory rotates in the course of a plane random walk. It is shown that the determination of this distribution function can be reduced to an integral equation, which can be rigorously transformed into a differential equation of Hill's type. We derive the asymptotic distribution for very long walks.

Contact sheet of portraits of George Victor Wolff Portraits; Men

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Molecular genetics of primary open angle glaucoma and exfoliation syndrome

Glaucoma is the second leading cause of blindness worldwide. It is a group of optic neuropathies, characterized by progressive optic nerve degeneration, excavation of the optic disc due to apoptosis of retinal ganglion cells and corresponding visual field defects. Open angle glaucoma (OAG) is a subtype of glaucoma, classified according to the age of onset into juvenile and adult- forms with a cut-off point of 40 years of age. The prevalence of OAG is 1-2% of the population over 40 years and increases with age. During the last decade several candidate loci and three candidate genes, myocilin (MYOC), optineurin (OPTN) and WD40-repeat 36 (WDR36), for OAG have been identified. Exfoliation syndrome (XFS), age, elevated intraocular pressure and genetic predisposition are known risk factors for OAG. XFS is characterized by accumulation of grayish scales of fibrillogranular extracellular material in the anterior segment of the eye. XFS is overall the most common identifiable cause of glaucoma (exfoliation glaucoma, XFG). In the past year, three single nucleotide polymorphisms (SNPs) on the lysyl oxidase like 1 (LOXL1) gene have been associated with XFS and XFG in several populations. This thesis describes the first molecular genetic studies of OAG and XFS/XFG in the Finnish population. The role of the MYOC and OPTN genes and fourteen candidate loci was investigated in eight Finnish glaucoma families. Both candidate genes and loci were excluded in families, further confirming the heterogeneous nature of OAG. To investigate the genetic basis of glaucoma in a large Finnish family with juvenile and adult onset OAG, we analysed the MYOC gene in family members. Glaucoma associated mutation (Thr377Met) was identified in the MYOC gene segregating with the disease in the family. This finding has great significance for the family and encourages investigating the MYOC gene also in other Finnish OAG families. In order to identify the genetic susceptibility loci for XFS, we carried out a genome-wide scan in the extended Finnish XFS family. This scan produced promising candidate locus on chromosomal region 18q12.1-21.33 and several additional putative susceptibility loci for XFS. This locus on chromosome 18 provides a solid starting point for the fine-scale mapping studies, which are needed to identify variants conferring susceptibility to XFS in the region. A case-control and family-based association study and family-based linkage study was performed to evaluate whether SNPs in the LOXL1 gene contain a risk for XFS, XFG or POAG in the Finnish patients. A significant association between the LOXL1 gene SNPs and XFS and XFG was confirmed in the Finnish population. However, no association was detected with POAG. Probably also other genetic and environmental factors are involved in the pathogenesis of XFS and XFG.

QTL for nodal root angle in sorghum (Sorghum bicolor L. Moench) co-locate with QTL for traits associated with drought adaptation.

Nodal root angle in sorghum influences vertical and horizontal root distribution in the soil profile and is thus relevant to drought adaptation. In this study, we report for the first time on the mapping of four QTL for nodal root angle (qRA) in sorghum, in addition to three QTL for root dry weight, two for shoot dry weight, and three for plant leaf area. Phenotyping was done at the six leaf stage for a mapping population (n = 141) developed by crossing two inbred sorghum lines with contrasting root angle. Nodal root angle QTL explained 58.2% of the phenotypic variance and were validated across a range of diverse inbred lines. Three of the four nodal root angle QTL showed homology to previously identified root angle QTL in rice and maize, whereas all four QTL co-located with previously identified QTL for stay-green in sorghum. A putative association between nodal root angle QTL and grain yield was identified through single marker analysis on field testing data from a subset of the mapping population grown in hybrid combination with three different tester lines. Furthermore, a putative association between nodal root angle QTL and stay-green was identified using data sets from selected sorghum nested association mapping populations segregating for root angle. The identification of nodal root angle QTL presents new opportunities for improving drought adaptation mechanisms via molecular breeding to manipulate a trait for which selection has previously been very difficult.

Three-dimensional corner reflector of arbitrary apex angle

A method of analysing a 3-dimensional corner reflector antenna of arbitrary apex angle is given. Expressions have been obtained for the far field of the 3-dimensional corner reflector fed by a dipole. The radiation resistance and the directive gain of the antenna have been calculated. The method described is applicable even when the feed dipole is arbitrarily oriented. It is found that the radiation along a prescribed direction can be circularly polarised (right or left) by suitably orienting the feed dipole.

International contact lens prescribing in 2014

Since the late 1990s, the International Contact Lens Prescribing Survey Consortium has prospectively gathered information about 285,000 contact lens fits from more than 50 countries. This article presents our 14th annual summary of current trends published in Contact Lens Spectrum. With only minor differences in the distribution of our surveys among markets, we have continued to adopt the same approach throughout the past 18 years. Through national coordinators, we approach contact lens prescribers in each country and ask them to record information about the first 10 patients whom they fit with contact lenses after receipt of our survey form. The information collected is generic, and respondents are weighted to reflect the volume of contact lens fits undertaken by each. For this 2014 report, we present information about 25,179 contact lens fits from 32 countries...

Contact lens citation metrics: The Spanish connection

To eye care practitioners, citation metrics may seem to be a somewhat esoteric and irrelevant concept, far removed from the realities or real world, day-to-day clinical practice. However, quantitative analysis of the published literature is becoming increasingly important, and a beautiful example of this is presented in this issue of the Journal of Optometry. My former PhD student, Genís Cardona, has teamed up with Joan Sanz to undertake a thorough and telling analysis of current worldwide publishing trends in the contact lens field. When held in the mirror, this work reflects the growing contributions from Spanish researchers to the field...

Trends in US contact lens prescribing 2002-2014

Purpose To document contact lens prescribing patterns in the United States between 2002 and 2014. Methods A survey of contact lens prescribing trends was conducted each year between 2002 and 2014, inclusive. Randomly selected contact lens practitioners were asked to provide information relating to 10 consecutive contact lens fits between January and March each year. Results Over the 13-year survey period, 1650 survey forms were received from US practitioners representing details of 7702 contact lens fits. The mean (±SD) age of lens wearers was 33.6 (±15.2) years, of whom 65.2% were female. Rigid lens new fits decreased from 13.0% in 2002 to 9.4% in 2014. Across this period, silicone hydrogels have replaced mid water contact lens hydrogels as the soft lens material of choice. Toric lenses represented about 25 to 30% of all soft lens fits. Multifocal soft lenses are generally preferred to monovision. Daily disposable lens fits have recently increased, and in 2014, they represented 27.1% of all soft lens fits. Most lenses are prescribed on 1 to 2 weekly or monthly lens replacement regimen. Extended wear remains a minority lens wearing modality. The vast majority of those wearing reusable lenses use multipurpose lens care solutions. Lenses are mostly worn 7 d/wk. Conclusions This survey has revealed prescribing trends and preferences in the United States over the past 13 years.

Contact lens prescribing trends 2015

Efron, Morgan and Woods share the findings of their latest annual survey of Australian contact lens prescribing habits.

International contact lens prescribing in 2015

We have been collecting data on worldwide contact lens prescribing habits for almost 20 years. Over this time period, we have amassed prospective information about 315,000 contact lens fits in 59 countries. This article marks our 15th report in Contact Lens Spectrum and features a breakdown of more than 23,000 contact lens fits in 34 markets. As in previous years, our international network of coordinators distributed survey forms to eyecare practitioners in their market who then recorded generic information about the first 10 patients fit with contact lenses after receipt. Information is gathered about patient age and gender; whether the contact lenses are prescribed as a new fit or a refit; contact lens material, design, and replacement frequency; number of intended days per week of use; wearing modality; and care system. Contact lens fits are weighted to reflect the number of fits undertaken by each eyecare practitioner. The study data were entered and processed at the University of Manchester and at the University of Waterloo.

Genetic control of nodal root angle in sorghum and its implications on water extraction

Genotypic variability in root system architecture has been associated with root angle of seedlings and water extraction patterns of mature plants in a range of crops. The potential inclusion of root angle as a selection criterion in a sorghum breeding program requires (1) availability of an efficient screening method, (2) presence of genotypic variation with high heritability, and (3) an association with water extraction pattern. The aim of this study was to determine the feasibility for inclusion of nodal root angle as a selection criterion in sorghum breeding programs. A high-throughput phenotypic screen for nodal root angle in young sorghum plants has recently been developed and has been used successfully to identify significant variation in nodal root angle across a diverse range of inbred lines and a mapping population. In both cases, heritabilities for nodal root angle were high. No association between nodal root angle and plant size was detected. This implies that parental inbred lines could potentially be used to asses nodal root angle of their hybrids, although such predictability is compromised by significant interactions. To study effects of nodal root angle on water extraction patterns of mature plants, four inbred lines with contrasting nodal root angle at seedling stage were grown until at least anthesis in large rhizotrons. A consistent trend was observed that nodal root angle may affect the spatial distribution of root mass of mature plants and hence their ability to extract soil water, although genotypic differences were not significant. The potential implications of this for specific adaptation to drought stress are discussed. Results suggest that nodal root angle of young plants can be a useful selection criterion for specific drought adaptation, and could potentially be used in molecular breeding programs if QTLs for root angle can be identified. (C) 2012 Elsevier B.V. All rights reserved.

QTL for root angle and number in a population developed from bread wheats (Triticum aestivum) with contrasting adaptation to water-limited environments

Root architecture traits in wheat are important in deep soil moisture acquisition and may be used to improve adaptation to water-limited environments. The genetic architecture of two root traits, seminal root angle and seminal root number, were investigated using a doubled haploid population derived from SeriM82 and Hartog. Multiple novel quantitative trait loci (QTL) were identified, each one having a modest effect. For seminal root angle, four QTL (-log10(P) >3) were identified on 2A, 3D, 6A and 6B, and two suggestive QTL (-log10(P) >2) on 5D and 6B. For root number, two QTL were identified on 4A and 6A with four suggestive QTL on 1B, 3A, 3B and 4A. QTL for root angle and root number did not co-locate. Transgressive segregation was found for both traits. Known major height and phenology loci appear to have little effect on root angle and number. Presence or absence of the T1BL.1RS translocation did not significantly influence root angle. Broad sense heritability (h 2) was estimated as 50 % for root angle and 31 % for root number. Root angle QTL were found to be segregating between wheat cultivars adapted to the target production region indicating potential to select for root angle in breeding programs. © 2013 Springer-Verlag Berlin Heidelberg.

Do small-aperture presbyopic corrections influence the visual field?

Purpose To explore the effect of small-aperture optics, designed to aid presbyopes by increasing ocular depth-of-focus, on measurements of the visual field. Methods Simple theoretical and ray-tracing models were used to predict the impact of different designs of small-aperture contact lenses or corneal inlays on the proportion of light passing through natural pupils of various diameters as a function of the direction in the visual field. The left eyes of five healthy volunteers were tested using three afocal, hand-painted opaque soft contact lenses (www.davidthomas.com). Two were opaque over a 10 mm diameter but had central clear circular apertures of 1.5 and 3.0 mm in diameter. The third had an annular opaque zone with inner and outer diameters of 1.5 and 4.0 mm, approximately simulating the geometry of the KAMRA inlay (www.acufocus.com). A fourth, clear lens was used for comparison purposes. Visual fields along the horizontal meridian were evaluated up to 50° eccentricity with static automated perimetry (Medmont M700, stimulus Goldmann-size III; www.medmont.com). Results According to ray-tracing, the two lenses with the circular apertures were expected to reduce the relative transmittance of the pupil to zero at specific field angles (around 60° for the conditions of the experimental measurements). In contrast, the annular stop had no effect on the absolute field but relative transmittance was reduced over the central area of the field, the exact effects depending upon the natural pupil diameter. Experimental results broadly agreed with these theoretical expectations. With the 1.5 and 3.0 mm pupils, only minor losses in sensitivity (around 2 dB) in comparison with the clear-lens case occurred across the central 10° radius of field. Beyond this angle, sensitivity losses increased, to reach about 7 dB at the edge of the measured field (50°). The field results with the annular stop showed at most only a slight loss in sensitivity (≤3 dB) across the measured field. Conclusion The present theoretical and experimental results support earlier clinical findings that KAMRA-type annular stops, unlike circular artificial pupils, have only minor effects on measurements of the visual field.

Finite element analysis of moving contact in mechanically fastened joints

The Finite Element Method (FEM) has made a number of otherwise intractable problems solvable. An important aspect for achieving an economical and accurate solution through FEM is matching the formulation and the computational organisation to the problem. This was realised forcefully in the present case of the solution of a class of moving contact boundary value problems of fastener joints. This paper deals with the problem of changing contact at the pin-hole interface of a fastener joint. Due to moving contact, the stresses and displacements are nonlinear with load. This would, in general, need an interactive-incremental approach for solution. However, by posing the problem in an inverse way, a solution is sought for obtaining loads to suit given contact configuration. Numerical results are given for typical isotropic and composite plates with rigid pins. Two cases of loading are considered: (i) load applied only at the edges of the plate and (ii) load applied at the pin and reacted at a part of the edge of the plate. Load-contact relationships, compliance and stress-patterns are investigated. This paper clearly demonstrates the simplification achieved by a suitable formulation of the problem. The results are of significance to the design and analysis of fastener joints.

Dynamics of dense sheared granular flows. Part II. The relative velocity distributions

The distribution of relative velocities between colliding particles in shear flows of inelastic spheres is analysed in the Volume fraction range 0.4-0.64. Particle interactions are considered to be due to instantaneous binary collisions, and the collision model has a normal coefficient of restitution e(n) (negative of the ratio of the post- and pre-collisional relative velocities of the particles along the line joining the centres) and a tangential coefficient of restitution e(t) (negative of the ratio of post- and pre-collisional velocities perpendicular to line joining the centres). The distribution or pre-collisional normal relative velocities (along the line Joining the centres of the particles) is Found to be an exponential distribution for particles with low normal coefficient of restitution in the range 0.6-0.7. This is in contrast to the Gaussian distribution for the normal relative velocity in all elastic fluid in the absence of shear. A composite distribution function, which consists of an exponential and a Gaussian component, is proposed to span the range of inelasticities considered here. In the case of roughd particles, the relative velocity tangential to the surfaces at contact is also evaluated, and it is found to be close to a Gaussian distribution even for highly inelastic particles.Empirical relations are formulated for the relative velocity distribution. These are used to calculate the collisional contributions to the pressure, shear stress and the energy dissipation rate in a shear flow. The results of the calculation were round to be in quantitative agreement with simulation results, even for low coefficients of restitution for which the predictions obtained using the Enskog approximation are in error by an order of magnitude. The results are also applied to the flow down an inclined plane, to predict the angle of repose and the variation of the volume fraction with angle of inclination. These results are also found to be in quantitative agreement with previous simulations.